SỬ DỤNG BĐT CỔ ĐIỂN ĐỂ CHỨNG MINH BĐT LƯỢNG GIÁC


Trong chuyên đề này, ta sẽ tìm hiểu về 4 bất đẳng thức cổ điển và ứng dụng của chúng trong giải bất đẳng thức lượng giác. Các bất đẳng thức bao gồm:
1. Bất đẳng thức Cauchy (AM – GM)
2. Bất đẳng thức Bunhiacốpxki
3. Bất đẳng thức Jensen
4. Bất đẳng thức Chebyshev

1. Bất đẳng thức Cauchy (AM – GM):
Với mọi số thực không âm ${a_1},{a_2},....,{a_n}$ ta luôn có:
              $\frac{{{a_1} + {a_2} + ... + {a_n}}}{n} \geqslant \sqrt[n]{{{a_1}{a_2}...{a_n}}}$

Ví dụ 1:
Cho A,B,C là 3 đỉnh của 1 tam giác nhọn. CMR:
            $\tan A + \tan B + \tan C \geqslant 3\sqrt 3 $
Lời giải:
Vì $\tan \left( {A + B} \right) =  - \tan C \Leftrightarrow \frac{{\tan A + \tan B}}{{1 - \tan A.\tan B}} =  - \tan C$
$ \Rightarrow \tan A + \tan B + \tan C = \tan A.\tan B.\tan C$
Tam giác ABC nhọn nên tanA, tanB, tanC dương.
Theo Cauchy ta có:
            $\tan A + \tan B + \tan C \geqslant 3\sqrt[3]{{\tan A.\tan B.\tan C}} = 3\sqrt[3]{{\tan A + \tan B + \tan C}}$
            $ \Rightarrow {\left( {\tan A + \tan B + \tan C} \right)^2} \geqslant 27\left( {\tan A + \tan B + \tan C} \right)$
    $ \Rightarrow \tan A + \tan B + \tan C \geqslant 3\sqrt 3 $
Đẳng thức xảy ra$ \Leftrightarrow A = B = C \Leftrightarrow \Delta ABC$đều.

Ví dụ 2 :
Cho $\Delta ABC$ nhọn. CMR: $\cot A + \cot B + \cot C \geqslant \sqrt 3 $
Lời giải:
Ta luôn có:
         $\begin{array}
  \cot \left( {A + B} \right) =  - \cot C  \\
   \Leftrightarrow \frac{{\cot A.\cot B - 1}}{{\cot A + \cot B}} =  - \cot C  \\
   \Leftrightarrow \cot A.\cot B + \cot B.\cot C + \cot C.\cot A = 1  \\
\end{array} $
Khi đó:
         ${\left( {\cot A - \cot B} \right)^2} + {\left( {\cot B - \cot C} \right)^2} + {\left( {\cot C - \cot A} \right)^2} \geqslant 0$
    $ \Leftrightarrow {\left( {\cot A + \cot B + \cot C} \right)^2} \geqslant 3\left( {\cot A\cot B + \cot B\cot C + \cot C\cot A} \right) = 3$
    $ \Rightarrow \cot A + \cot B + \cot C \geqslant \sqrt 3 $
Dấu bằng xảy ra khi và chỉ khi $\Delta ABC$đều.

Ví dụ 3:
Chứng minh rằng với mọi $\Delta ABC$ nhọn ta  có:
$\sqrt {\frac{{\cos A\cos B}}{{\cos \frac{A}{2}\cos \frac{B}{2}}}}  + \sqrt {\frac{{\cos B\cos C}}{{\cos \frac{B}{2}\cos \frac{C}{2}}}}  + \sqrt {\frac{{\cos C\cos A}}{{\cos \frac{C}{2}\cos \frac{A}{2}}}} \\
                           \leqslant \frac{2}{{\sqrt 3 }}\left( {\sin \frac{A}{2}\sin \frac{B}{2} + \sin \frac{B}{2}\sin \frac{C}{2} + \sin \frac{C}{2}\sin \frac{A}{2}} \right) + \frac{{\sqrt 3 }}{2}$
Lời giải:
Ta có:  $\frac{{\cos A}}{{2\cos \frac{A}{2}}} = \sin \frac{A}{2}\cot \frac{A}{2}$
$ \Rightarrow \frac{{\frac{3}{4}\cos A\cos B}}{{4\cos \frac{A}{2}\cos \frac{B}{2}}} = \left( {\sin \frac{A}{2}\sin \frac{B}{2}} \right)\left( {\frac{3}{4}\cot A\cot B} \right)$
Theo Cauchy:
$\frac{{\frac{3}{4}\cos A\cos B}}{{4\cos \frac{A}{2}\cos \frac{B}{2}}} \leqslant {\left( {\frac{{\sin \frac{A}{2}\sin \frac{B}{2} + \frac{3}{4}\cot A\cot B}}{2}} \right)^2}$
$ \Rightarrow \sqrt {\frac{{\cos A\cos B}}{{\cos \frac{A}{2}\cos \frac{B}{2}}}}  \leqslant \frac{2}{{\sqrt 3 }}\left( {\sin \frac{A}{2}\sin \frac{B}{2} + \frac{3}{4}\cot A\cot B} \right)$
Tương tự ta có:
$\sqrt {\frac{{\cos B\cos C}}{{\cos \frac{B}{2}\cos \frac{C}{2}}}}  \leqslant \frac{2}{{\sqrt 3 }}\left( {\sin \frac{B}{2}\sin \frac{C}{2} + \frac{3}{4}\cot B\cot C} \right)$
$S = pr \Rightarrow \frac{8}{3}{\left( {\frac{S}{{2r}}} \right)^2} = \frac{{{{(a + b + c)}^2}}}{6}$
Cộng theo vế ta được:
$\sqrt {\frac{{\cos A\cos B}}{{\cos \frac{A}{2}\cos \frac{B}{2}}}}  + \sqrt {\frac{{\cos B\cos C}}{{\cos \frac{B}{2}\cos \frac{C}{2}}}}  + \sqrt {\frac{{\cos C\cos A}}{{\cos \frac{C}{2}\cos \frac{A}{2}}}} $
$ \leqslant \frac{2}{{\sqrt 3 }}\left( {\sin \frac{A}{2}\sin \frac{B}{2} + \sin \frac{B}{2}\sin \frac{C}{2} \\                          + \sin \frac{C}{2}\sin \frac{A}{2}} \right) + \frac{{\sqrt 3 }}{2}\left( {\cot A\cot B + \cot B\cot C + \cot C\cot A} \right)$
$ = \frac{2}{{\sqrt 3 }}\left( {\sin \frac{A}{2}\sin \frac{B}{2} + \sin \frac{B}{2}\sin \frac{C}{2} + \sin \frac{C}{2}\sin \frac{A}{2}} \right) + \frac{{\sqrt 3 }}{2}$    $ \Rightarrow $ Đpcm.

2. Bất đẳng thức Bunhiacốpxki:
Với 2 bộ số ${a_1},{a_2},...,{a_n}$ và ${b_1},{b_2},...,{b_n}$ ta luôn có:
             ${\left( {{a_1}{b_1} + {a_2}{b_2} + ... + {a_n}{b_n}} \right)^2} \leqslant \left( {{a_1}^2 + {a_2}^2 + ... + {a_n}^2} \right)\left( {{b_1}^2 + {b_2}^2 + ... + {b_n}^2} \right)$
Nhận xét:
-Nếu như với bất đẳng thức Cauchy, ta luôn phải nhớ điều kiện của các biến là phải không âm thì đối với bất đẳng thức Bunhiacốpxki, ta có thể áp dụng cho các biến là số thực.
-Bất đẳng thức Cauchy và Bunhiacốpxki là 2 bất đẳng thức tỏ ra rất hiệu quả khi dùng để chứng minh các bất đẳng thức lượng giác. Ta sẽ xét các ví dụ sau:

Ví dụ 1:
CMR với mọi $a,b,\alpha $ ta có:
$\left( {\sin \alpha  + a\cos \alpha } \right)\left( {\sin \alpha  + b\cos \alpha } \right) \leqslant 1 + {\left( {\frac{{a + b}}{2}} \right)^2}$  
Lời giải:
Ta có: $\left( {\sin \alpha  + a\cos \alpha } \right)\left( {\sin \alpha  + b\cos \alpha } \right) = {\sin ^2}\alpha  + \left( {a + b} \right)\sin \alpha \cos \alpha  + ab{\cos ^2}\alpha $
            $ = \frac{{1 - \cos 2\alpha }}{2} + \frac{{\left( {a + b} \right)}}{2}\sin 2\alpha  + ab\frac{{1 + \cos 2\alpha }}{2}$
            $ = \frac{1}{2}\left( {1 + ab + \left( {a + b} \right)\sin 2\alpha  + \left( {ab - 1} \right)\cos 2\alpha } \right)$    (1)
Theo Bunhiacốpxki ta có:
        $A\sin x + B\cos x \leqslant \sqrt {{A^2} + {B^2}} $       (2)
Áp dụng (2) ta có:
        $\left( {a + b} \right)\sin 2\alpha  + \left( {ab - 1} \right)\cos 2\alpha  \leqslant \sqrt {{{\left( {a + b} \right)}^2} + {{\left( {ab - 1} \right)}^2}}  = \sqrt {\left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)} $       (3)
Thay (3) vào (1) ta được:
        $\left( {\sin \alpha  + a\cos \alpha } \right)\left( {\sin \alpha  + b\cos \alpha } \right) \leqslant \frac{1}{2}\left( {1 + ab + \sqrt {\left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)} } \right)$     (4)
Ta chứng minh bất đẳng thức sau đây đúng với mọi a,b:
        $\frac{1}{2}\left( {1 + ab + \sqrt {\left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)} } \right) \leqslant 1 + {\left( {\frac{{a + b}}{2}} \right)^2}$     (5)
Thật vậy:
         (5)$ \Leftrightarrow \frac{1}{2} + \frac{{ab}}{2} + \frac{1}{2}\sqrt {\left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)}  \leqslant 1 + \frac{{{a^2} + {b^2}}}{4} + \frac{{ab}}{2}$
              $ \Leftrightarrow \sqrt {\left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)}  \leqslant \frac{{{a^2} + {b^2} + 2}}{2}$
              $ \Leftrightarrow \sqrt {\left( {{a^2} + 1} \right)\left( {{b^2} + 1} \right)}  \leqslant \frac{{\left( {{a^2} + 1} \right) + \left( {{b^2} + 1} \right)}}{2}$       (6)
Theo Cauchy thì (6) hiển nhiên đúng$ \Rightarrow $ (5) đúng với mọi a,b.
Từ (1) và (5) : với mọi $a,b,\alpha $ ta có: $\left( {\sin \alpha  + a\cos \alpha } \right)\left( {\sin \alpha  + b\cos \alpha } \right) \leqslant 1 + {\left( {\frac{{a + b}}{2}} \right)^2}$
Đẳng thức xảy ra khi ở (1) và (6) dấu bằng đồng thời xảy ra
$ \Leftrightarrow \left\{ \begin{array}
  {a^2} = {b^2}  \\
  \frac{{a + b}}{{\sin 2\alpha }} = \frac{{ab - 1}}{{\cos 2\alpha }}  \\
\end{array}  \right. \Leftrightarrow \left\{ \begin{array}
  \left| a \right| = \left| b \right|  \\
  \tan \alpha  = \frac{{a + b}}{{ab - 1}}  \\
\end{array}  \right. \Leftrightarrow \left\{ \begin{array}
  \left| a \right| = \left| b \right|  \\
  \alpha  = \frac{1}{2}\arctan \frac{{a + b}}{{ab - 1}} + k\frac{\pi }{2}  \\
\end{array}  \right.$ 

Ví dụ 2:
CMR với mọi $\Delta ABC$ ta có:
   $\sqrt x  + \sqrt y  + \sqrt z  \leqslant \sqrt {\frac{{{a^2} + {b^2} + {c^2}}}{{2R}}} $   
với x,y,z là khoảng cách từ điểm M bất kì nằm bên trong $\Delta ABC$ tới 3 cạnh AB, BC, CA của tam giác.
Lời giải:
Ta có:
         $\begin{array}
  {S_{ABC}} = {S_{MAB}} + {S_{MBC}} + {S_{MCA}}  \\
   \Leftrightarrow \frac{{{S_{MAB}}}}{{{S_{ABC}}}} + \frac{{{S_{MBC}}}}{{{S_{ABC}}}} + \frac{{{S_{MCA}}}}{{{S_{ABC}}}} = 1  \\
   \Leftrightarrow \frac{z}{{{h_c}}} + \frac{y}{{{h_b}}} + \frac{x}{{{h_a}}} = 1  \\
\end{array} $
$ \Rightarrow {h_a} + {h_b} + {h_c} = \left( {{h_a} + {h_b} + {h_c}} \right)\left( {\frac{z}{{{h_c}}} + \frac{y}{{{h_b}}} + \frac{x}{{{h_a}}}} \right)$
Theo Bunhiacốpxki thì:
$\sqrt x  + \sqrt y  + \sqrt z  = \sqrt {{h_a}} \frac{{\sqrt x }}{{\sqrt {{h_a}} }} + \sqrt {{h_b}} \frac{{\sqrt y }}{{\sqrt {{h_b}} }} + \sqrt {{h_c}} \frac{{\sqrt z }}{{\sqrt {{h_c}} }} \\
                               \leqslant \sqrt {\left( {{h_a} + {h_b} + {h_c}} \right)\left( {\frac{{\sqrt x }}{{\sqrt {{h_a}} }} + \frac{{\sqrt y }}{{\sqrt {{h_b}} }} + \frac{{\sqrt z }}{{\sqrt {{h_c}} }}} \right)}  = \sqrt {{h_a} + {h_b} + {h_c}} $
mà $S = \frac{1}{2}a{h_a} = \frac{1}{2}ab\sin C \Rightarrow {h_a} = b\sin C$, ${h_b} = c\sin A$, ${h_c} = a\sin B$
$ \Rightarrow \sqrt {{h_a} + {h_b} + {h_c}}  = \sqrt {\left( {a\sin B + b\sin C + c\sin A} \right)}  = \sqrt {\frac{{ab}}{{2R}} + \frac{{bc}}{{2R}} + \frac{{ca}}{{2R}}} $
$ \Rightarrow \sqrt x  + \sqrt y  + \sqrt z  \leqslant \sqrt {\frac{{ab}}{{2R}} + \frac{{bc}}{{2R}} + \frac{{ca}}{{2R}}}  \leqslant \sqrt {\frac{{{a^2} + {b^2} + {c^2}}}{{2R}}}  \Rightarrow $ Đpcm.
Đẳng thức xảy ra khi và chỉ khi $\left\{ \begin{array}
  a = b = c  \\
  x = y = z  \\
\end{array}  \right. \Leftrightarrow \Delta ABC$đều và M là tâm đường tròn nội tiếp$\Delta ABC$.

3. Bất đẳng thức Jensen:
Cho $f:{R^ + } \to R$ thỏa mãn $f(x) + f(y) \geqslant 2f\left( {\frac{{x + y}}{2}} \right)$  $\forall x,y \in {R^ + }$. Khi đó với mọi  ${x_1},{x_2},....,{x_n} \in {R^ + }$ ta có bất đẳng thức sau:
                          $f({x_1}) + f({x_2}) + ...... + f({x_n}) \geqslant nf\left( {\frac{{{x_1} + {x_2} + ... + {x_n}}}{n}} \right)$

-Bất đẳng thức Jensen thật sự là một công cụ chuyên dùng cho chứng minh các bất đẳng thức lượng giác. Tuy không phải là một bất đẳng thức chặt nhưng nếu thấy có những dấu hiệu của BĐT Jensen, chúng ta nên dùng ngay.
 
Ví dụ 1:
Chứng minh rằng với mọi$\Delta ABC$ ta có
                      $\sin A + \sin B + \sin C \leqslant \frac{{3\sqrt 3 }}{2}$
Lời giải:
Xét $f(x) = \sin x$ với $x \in \left( {0,\pi } \right)$ $ \Rightarrow f(x)$ là hàm lồi. Theo Jensen ta có:
$f(A) + f(B) + f(C) \leqslant 3f\left( {\frac{{A + B + C}}{3}} \right) = 3\sin \frac{\pi }{3} = \frac{{3\sqrt 3 }}{2} \Rightarrow $Đpcm.
Đẳng thức xảy ra khi và chỉ khi $\Delta ABC$đều.

Ví dụ 2:
Chứng minh rằng với mọi $\Delta ABC$đều ta có:
           $\tan \frac{A}{2} + \tan \frac{B}{2} + \tan \frac{C}{2} \geqslant \sqrt 3 $
Lời giải:
Xét $f(x) = \tan x$ với$x \in \left( {0,\frac{\pi }{2}} \right)$
$\begin{array}
(1) \Leftrightarrow {a^2}({a^2} - bc) + {b^2}({b^2} - ca) + {c^2}({c^2} - ab) \geqslant 0  \\
\Leftrightarrow \left[ {{a^2} + {{(b + c)}^2}} \right]{(b - c)^2} + \left[ {{b^2} + {{(c + a)}^2}} \right]{(c - a)^2} + \left[ {{c^2} + {{(a + b)}^2}} \right]{(a - b)^2} \geqslant 0  \\
\end{array} $ là hàm lồi. Theo Jensen ta có:
$f\left( {\frac{A}{2}} \right) + f\left( {\frac{B}{2}} \right) + f\left( {\frac{C}{2}} \right) \geqslant 3f\left( {\frac{{\frac{A}{2} + \frac{B}{2} + \frac{C}{2}}}{3}} \right) = 3\sin \frac{\pi }{6} = \sqrt 3  \Rightarrow $Đpcm.
Đẳng thức xảy ra khi và chỉ khi $\Delta ABC$đều.

Ví dụ 3:
Chứng minh rằng với mọi $\Delta ABC$ta có:
$\sin \frac{A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2} + \tan \frac{A}{2} + \tan \frac{B}{2} + \tan \frac{C}{2} \geqslant \frac{3}{2} + \sqrt 3 $
Lời giải:
Xét $f(x) = \sin x + \tan x$ với $ \Rightarrow $là hàm lồi. Theo Jensen ta có:

$f\left( {\frac{A}{2}} \right) + f\left( {\frac{B}{2}} \right) + f\left( {\frac{C}{2}} \right) \geqslant 3f\left( {\frac{{\frac{A}{2} + \frac{B}{2} + \frac{C}{2}}}{3}} \right)$$ = 3\left( {\tan \frac{\pi }{6} + \sin \frac{\pi }{6}} \right) = \frac{3}{2} + \sqrt 3  \Rightarrow $Đpcm.
Đẳng thức xảy ra khi và chỉ khi $\Delta ABC$đều.

4. Bất đẳng thức Chebyshev:
Với 2 dãy số thực đơn điệu cùng chiều ${a_1},{a_2},...,{a_n}$ và ${b_1},{b_2},...,{b_n}$  ta có:
             ${a_1}{b_1} + {a_2}{b_2} + ... + {a_n}{b_n} \geqslant \frac{1}{n}\left( {{a_1} + {a_2} + ... + {a_n}} \right)\left( {{b_1} + {b_2} + ... + {b_n}} \right)$

Ví dụ 1:
Chứng minh rằng với mọi $\Delta ABC$ ta có
               $\frac{{aA + bB + cC}}{{a + b + c}} \geqslant \frac{\pi }{3}$
Lời giải:
Không mất tổng quát giả sử $a \leqslant b \leqslant c \Leftrightarrow A \leqslant B \leqslant C$

Theo Chebyshev thì
$\left( {\frac{{a + b + c}}{3}} \right)\left( {\frac{{A + B + C}}{3}} \right) \leqslant \frac{{aA + bB + cC}}{3}$
$ \Rightarrow \frac{{aA + bB + cC}}{3} \geqslant \frac{{A + B + C}}{3} = \frac{\pi }{3}$
Đẳng thức xảy ra khi $\Delta ABC$đều.

Ví dụ 2:
Chứng minh rằng với mọi $\Delta ABC$ ta có
              $\frac{\sin A + \sin B + \sin C}{\cos A + \cos B + \cos C} \leqslant \frac{\tan A\tan B\tan C}{3}$
Lời giải:
Không mất tổng quát giả sử$A \geqslant B \geqslant C$
               $ \Rightarrow \left\{ \begin{array}
  \tan A \geqslant \tan B \geqslant \tan C  \\
  \cos A \leqslant \cos B \leqslant \cos C  \\
\end{array}  \right.$
Theo Chebyshev ta có:
$ \Leftrightarrow \frac{{\sin A + \sin B + \sin C}}{{\cos A + \cos B + \cos C}} \leqslant \frac{{\tan A + \tan B + \tan C}}{3}$
Mà $\tan A + \tan B + \tan C = \tan A\tan B\tan C$$ \Rightarrow $Đpcm.
Đẳng thức xảy ra khi và chỉ khi $\Delta ABC$đều.

Ví dụ 3:
Chứng minh rằng với mọi $\Delta ABC$ ta có
$2\left( {\sin A + \sin B + \sin C} \right) \geqslant \frac{3}{2}\frac{{\sin 2A + \sin 2B + \sin 2C}}{{\cos A + \cos B + \cos C}}$
Lời giải:
Không mất tổng quát giả sử $a \leqslant b \leqslant c$
                    $ \Rightarrow \left\{ \begin{array}
  \sin A \leqslant \sin B \leqslant \sin C  \\
  \cos A \geqslant \cos B \geqslant \cos C  \\
\end{array}  \right.$
Theo Chebyshev ta có:
$\left( {\frac{{\sin A + \sin B + \sin C}}{3}} \right)\left( {\frac{{\cos A + \cos B + \cos C}}{3}} \right) \geqslant \frac{{\sin A\cos A + \sin B\cos B + \sin C\cos C}}{3}$
$ \Leftrightarrow 2\left( {\sin A + \sin B + \sin C} \right) \geqslant \frac{3}{2}\frac{{\sin 2A + \sin 2B + \sin 2C}}{{\cos A + \cos B + \cos C}} \Rightarrow $ Đpcm.
Đẳng thức xảy ra khi và chỉ khi $\Delta ABC$đều.

BÀI TẬP:
Bài 1.

CMR với mọi tam giác ABC ta có:
$\left( {\sin \frac{A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2}} \right)\left( {\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}} \right) \geqslant \frac{{9\sqrt 3 }}{2}$
Lời giải:
Theo BĐT Cô-si  ta có:
$\frac{{\sin \frac{A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2}}}{3} \geqslant \sqrt[3]{{\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}}}$
Mặt khác:
$\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2} = \cot \frac{A}{2}\cot \frac{B}{2}\cot \frac{C}{2} = \frac{{c{\text{os}}\frac{A}{2}c{\text{os}}\frac{B}{2}c{\text{os}}\frac{C}{2}}}{{\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}}}$
$ = \frac{{\frac{1}{4}(\sin A + \sin B + \sin C)}}{{\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}}} = \frac{{\sin \frac{A}{2}c{\text{os}}\frac{A}{2} + \sin \frac{B}{2}c{\text{os}}\frac{B}{2} + \sin \frac{C}{2}c{\text{os}}\frac{C}{2}}}{{2\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}}}$
                 $ \geqslant \frac{3}{2}.\frac{{\sqrt[3]{{\sin \frac{A}{2}c{\text{os}}\frac{A}{2}\sin \frac{B}{2}c{\text{os}}\frac{B}{2}\sin \frac{C}{2}c{\text{os}}\frac{C}{2}}}}}{{\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}}}$
Suy ra:
$\left( {\sin \frac{A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2}} \right)\left( {\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}} \right)$
$ \geqslant \frac{9}{2}.\frac{{\sqrt[3]{{\sin \frac{A}{2}\sin \frac{A}{2}\sin \frac{C}{2}\sin \frac{A}{2}c{\text{os}}\frac{A}{2}\sin \frac{B}{2}c{\text{os}}\frac{B}{2}\sin \frac{C}{2}c{\text{os}}\frac{C}{2}}}}}{{\sin \frac{A}{2}\sin \frac{B}{2}\sin \frac{C}{2}}}$
$ = \frac{9}{2}.\sqrt[3]{{\cot \frac{A}{2}\cot \frac{B}{2}\cot \frac{C}{2}}}$  (1)
Mà ta cũng có:
$\cot \frac{A}{2}\cot \frac{B}{2}\cot \frac{C}{2} \geqslant 3\sqrt 3 $
$ \Rightarrow \frac{9}{2}.\sqrt[3]{{\cot \frac{A}{2}\cot \frac{B}{2}\cot \frac{C}{2}}} \geqslant \frac{9}{2}.\sqrt[3]{{3\sqrt 3 }} = \frac{{9\sqrt 3 }}{2}(2)$
Từ (1),(2) :
$\left( {\sin \frac{A}{2} + \sin \frac{B}{2} + \sin \frac{C}{2}} \right)\left( {\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}} \right) \geqslant \frac{{9\sqrt 3 }}{2}$
$ \Rightarrow $ đpcm.

Bài 2.
Cho $\Delta ABC$ nhọn .CMR:
              $\left( {\cos A + \cos B + \cos C} \right)\left( {\operatorname{t} a{\text{nA}} + \tan B + \tan C} \right) \geqslant \frac{{9\sqrt 3 }}{2}$
Lời giải:
 Vì $\Delta ABC$ nhọn nên $\cos A,\cos B,\cos C,\operatorname{t} {\text{anA}},\tan B,\tan C$ đều dương.
Theo AM-GM ta có:
$\begin{array}
  \frac{{\cos A + \cos B + \cos C}}{3} \geqslant \sqrt[3]{{\cos A\cos B\cos C}}  \\
  \operatorname{t} a{\text{nA}} + \tan B + \tan C = \operatorname{t} a{\text{nA}}\tan B\tan C = \frac{{\sin A\sin B\sin C}}{{\cos A\cos B\cos C}}  \\
\end{array} $
$ = \frac{{\frac{1}{4}(\sin 2A + \sin 2B + \sin 2C)}}{{\cos A\cos B\cos C}} = \frac{{\sin A\cos A + \sin B\cos b + \sin C\cos C}}{{2\cos A\cos B\cos C}}$
$ \geqslant \frac{3}{2}.\frac{{\sqrt[3]{{\sin A\cos A\sin B\cos B\sin C\cos C}}}}{{2\cos A\cos B\cos C}}$
Suy ra:
$\begin{array}
  (\cos A + \cos B + \cos C)(\operatorname{t} a{\text{nA}}\tan B\tan C)  \\
   \geqslant \frac{9}{2}.\frac{{\sqrt[3]{{\cos A\cos B\cos C\sin A\cos A\sin B\cos B\sin C\cos C}}}}{{\cos A\cos B\cos C}}  \\
   = \frac{9}{2}.\sqrt[3]{{\operatorname{t} a{\text{nA}}\tan B\tan C}}(1)  \\
\end{array} $
Mặt khác:
$\begin{array}
  \tan {\text{A}}\tan B\tan C \geqslant 3\sqrt 3   \\
   \Rightarrow \frac{9}{2}.\sqrt[3]{{\operatorname{t} a{\text{nA}}\tan B\tan C}} \geqslant \frac{9}{2}.\sqrt[3]{{3\sqrt 3 }} = \frac{{9\sqrt 3 }}{2}(2)  \\
\end{array} $
Từ (1),(2) suy ra:
$(\cos A + \cos B + \cos C)(\tan {\text{A}}\tan B\tan C) \geqslant \frac{{9\sqrt 3 }}{2}$  $ \Rightarrow $ đpcm.

Bài 4.
Cho tam giác ABC bất kì .CMR:
$\frac{{{a^3} + {b^3} + {c^3}}}{{abc}} \geqslant 4 - \frac{{2r}}{R}$
Lời giải:
Ta có S=$\frac{{abc}}{{4R}} = pr = \sqrt {p(p - a)(p - b)(p - c)} $
$\begin{array}
   \Rightarrow \frac{{2r}}{R} = \frac{{8{S^2}}}{{pabc}} = \frac{{{a^2}b + a{b^2} + {b^2}c + b{c^2} + {c^2}a + c{a^2} - {a^3} - {b^3} - {c^3} - 2abc}}{{abc}}  \\
   \Rightarrow 4 - \frac{{2r}}{R} = \frac{{{a^3} + {b^3} + {c^3}}}{{abc}} + 6 - (\frac{a}{b} + \frac{b}{a} + \frac{b}{c} + \frac{c}{b} + \frac{c}{a} + \frac{a}{c}) \leqslant \frac{{{a^3} + {b^3} + {c^3}}}{{abc}}  \\
\end{array} $
Suy ra đpcm

Bài 5.
Cho tam tam giác ABC.CMR
$(\frac{a}{{\cos A}} + \frac{b}{{\cos B}} - c)(\frac{b}{{\cos b}} + \frac{c}{{\cos C}} - a)(\frac{c}{{\cos C}} + \frac{a}{{\cos A}} - b) \geqslant 27abc$
Lời giải:
Bất đẳng thức cần chứng minh tương đương với: $\begin{array}
  (\frac{{\sin C}}{{\cos A\cos B}} - \sin C)(\frac{{\sin A}}{{\cos B\cos C}} - \sin A)(\frac{{\sin B}}{{\cos C\cos A}} - \sin B) \geqslant 27\sin A\sin B\sin C  \\
   \Leftrightarrow \frac{{1 - \cos A\cos B}}{{\cos A\cos B}}.\frac{{1 - \cos B\cos C}}{{\cos B\cos C}}.\frac{{1 - \cos C\cos A}}{{\cos C\cos A}} \geqslant 27  \\
\end{array} $
Đặt x = tanA/2,y = tanB/2,z = tanC/2, khi đó ta có
$\cos A = \frac{{1 - {x^2}}}{{1 + {x^2}}},\cos B = \frac{{1 - {y^2}}}{{1 + {y^2}}},\cos C = \frac{{1 - {z^2}}}{{1 + {z^2}}}$
Và $\tan A = \frac{{2x}}{{1 - {x^2}}},\tan B = \frac{{2y}}{{1 - {y^2}}},\tan C = \frac{{2z}}{{1 - {z^2}}}$
Khi đó :$\frac{{1 - \cos A\cos B}}{{\cos A\cos B}} = \frac{{2({x^2} + {y^2})}}{{(1 - {x^2})(1 - {y^2})}}$ mặt khác :${x^2} + {y^2} \geqslant 2xy$ nên:
$\frac{{1 - \cos A\cos B}}{{\cos A\cos B}} \geqslant \frac{{2x}}{{1 - {x^2}}}.\frac{{2y}}{{1 - {y^2}}} = \tan A\tan B$    (1)
Tương tự ta có:
$\begin{array}
  \frac{{1 - \cos B\cos C}}{{\cos B\cos C}} \geqslant \tan B\tan C  \\
  \frac{{1 - \cos C\cos A}}{{\cos C\cos A}} \geqslant \tan C\tan A  \\
\end{array} $
Nhân vế theo vế (1) (2) và (3) ta được đpcm

hay quá!! ^_^ –  Linh Dracula 09-04-16 01:03 PM
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  • Mạcc Anhh: The development of genetically modified (GM) pants and animals had led to a huge minimal. Opponents that GM-Frankenfoods threat to our well-being, and proponents say that the risks are is say are a shirt these days here is one aspect of the war over GM that is often overlooked. Anyone who wears a cotton crop Cotton is the only major non-food GM crop at present. but others are coming If GM GM cotton plants that is not food has not stomed the most passionate GM ts from objecting. sing a GM on is in field next to fields of non-GM conon, they argue, then how to keep genes from being trans grown a health hazards in food. so rom ield to ticiu. his danger, however, is not as connemne to the public as possible ere is fury GM eotton pesticides. Planting of GM cotton no great over the need for GM Fumers GM cotton seeds produce higher yields, and they do without hairin China, is now has increased fivefold since 1997: three quarter of cotton in America, and over like it because it increases their profits. colors or scents, tougher other options for non-food GM include new vancty of nowers with different another grasses for lawns, and plants designed to soak up pollutants from the soil. The paper industry provides is and a example of potential for GM to help produce better and cheaper products. Paper is made from pulp, and pulp generally made from trees. Researchers in New Zealand and Chile have been working on insect-resistant pines, Japanese firm has combined carrot genes with tree genes to make them better in poor soil. grow Another interesting case is that of tobacco. It is not food crop, but it is consumed, and GM tobacco plants with both more and less nicotine have been ereated. The tobacco plant, however, is an ideal target for GM, since its genetics are very well understood and it produces a lot of leaves. The of the drugs that could be produced by value GM tobacco is so high, many farmers could from growing tobacco for cigarettes to growing it for medicine- Since medical cost is rising. consumers would also be happy to use drugs produced in bulk by GM tobacco. 9/27/2016 12:18:51 AM
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  • Mạcc Anhh: The development of genetically modified (GM) pants and animals had led to a huge minimal. Opponents that GM-Frankenfoods threat to our well-being, and proponents say that the risks are is say are a shirt these days here is one aspect of the war over GM that is often overlooked. Anyone who wears a cotton crop Cotton is the only major non-food GM crop at present. but others are coming If GM GM cotton plants that is not food has not stomed the most passionate GM ts from objecting. sing a GM on is in field next to fields of non-GM conon, they argue, then how to keep genes from being trans grown a health hazards in food. so rom ield to ticiu. his danger, however, is not as connemne to the public as possible ere is fury GM eotton pesticides. Planting of GM cotton no great over the need for GM Fumers GM cotton seeds produce higher yields, and they do without hairin China, is now has increased fivefold since 1997: three quarter of cotton in America, and over like it because it increases their profits. colors or scents, tougher other options for non-food GM include new vancty of nowers with different another grasses for lawns, and plants designed to soak up pollutants from the soil. The paper industry provides is and a example of potential for GM to help produce better and cheaper products. Paper is made from pulp, and pulp generally made from trees. Researchers in New Zealand and Chile have been working on insect-resistant pines, Japanese firm has combined carrot genes with tree genes to make them better in poor soil. grow Another interesting case is that of tobacco. It is not food crop, but it is consumed, and GM tobacco plants with both more and less nicotine have been ereated. The tobacco plant, however, is an ideal target for GM, since its genetics are very well understood and it produces a lot of leaves. The of the drugs that could be produced by value GM tobacco is so high, many farmers could from growing tobacco for cigarettes to growing it for medicine- Since medical cost is rising. consumers would also be happy to use drugs produced in bulk by GM tobacco. 9/27/2016 12:19:00 AM
  • Mạcc Anhh: The development of genetically modified (GM) pants and animals had led to a huge minimal. Opponents that GM-Frankenfoods threat to our well-being, and proponents say that the risks are is say are a shirt these days here is one aspect of the war over GM that is often overlooked. Anyone who wears a cotton crop Cotton is the only major non-food GM crop at present. but others are coming If GM GM cotton plants that is not food has not stomed the most passionate GM ts from objecting. sing a GM on is in field next to fields of non-GM conon, they argue, then how to keep genes from being trans grown a health hazards in food. so rom ield to ticiu. his danger, however, is not as connemne to the public as possible ere is fury GM eotton pesticides. Planting of GM cotton no great over the need for GM Fumers GM cotton seeds produce higher yields, and they do without hairin China, is now has increased fivefold since 1997: three quarter of cotton in America, and over like it because it increases their profits. colors or scents, tougher other options for non-food GM include new vancty of nowers with different another grasses for lawns, and plants designed to soak up pollutants from the soil. The paper industry provides is and a example of potential for GM to help produce better and cheaper products. Paper is made from pulp, and pulp generally made from trees. Researchers in New Zealand and Chile have been working on insect-resistant pines, Japanese firm has combined carrot genes with tree genes to make them better in poor soil. grow Another interesting case is that of tobacco. It is not food crop, but it is consumed, and GM tobacco plants with both more and less nicotine have been ereated. The tobacco plant, however, is an ideal target for GM, since its genetics are very well understood and it produces a lot of leaves. The of the drugs that could be produced by value GM tobacco is so high, many farmers could from growing tobacco for cigarettes to growing it for medicine- Since medical cost is rising. consumers would also be happy to use drugs produced in bulk by GM tobacco. 9/27/2016 12:19:01 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:06 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:08 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:09 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:11 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:13 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:15 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:18 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:20 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:22 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:24 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:25 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:28 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:30 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:32 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:34 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:35 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:20:38 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:02 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:03 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:06 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:08 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:10 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:12 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:14 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:16 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:19 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:21 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:23 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:25 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:27 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:28 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:30 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:32 AM
  • Mạcc Anhh: The lack of printing regulations and the unenforceability of British copyright law in the American colonies made it possible for colonial printers occasionally to act as publishers. Although they rarely undertook major publishing project because it was difficult to sell books as cheaply as they could be imported from Europe, printers in Philadelphia did publish work that required only small amounts of capital, paper, and type. Broadsides could be published with minimal financial risk. Consisting of only one sheet of paper and requiring small amounts of type, broadsides involved lower investments of capital than longer works. Furthermore, the broadside format lent itself to subjects of high, if temporary, interest, enabling them to meet with ready sale. If the broadside printer miscalculated, however, and produced a sheet that did not sell, it was not likely to be a major loss, and the printer would know this immediately, There would be no agonizing wait with large amounts of capital tied up, books gathering dust on the shelves, and creditors impatient for payment. In addition to broadsides, books and pamphlets, consisting mainly of political tracts, catechisms, primers, and chapbooks were relatively inexpensive to print and to buy. Chapbook were pamphlet-sized books, usually containing popular tales, ballads, poems, short plays, and jokes, small, both in formal and number of pages, they were generally bound simply, in boards (a form of cardboard) or merely stitched in paper wrappers (a sewn antecedent of modern-day paperbacks). Pamphlets and chapbooks did not require fine paper or a great deal of type to produce they could thus be printed in large, cost-effective editions and sold cheaply. By far, the most appealing publishing investments were to be found in small books that had proven to be steady sellers, providing a reasonably reliable source of income for the publisher. They would not, by nature, be highly topical or political, as such publications would prove of fleeting interest. Almanacs, annual publications that contained information on astronomy and weather patterns arranged according to the days, week, and months of a given year, provided the perfect steady seller because their information pertained to the locale in which they would be used “nội dung được trích dẫn từ 123doc.vn - cộng đồng mua bán chia sẻ tài liệu hàng đầu Việt Nam” 9/27/2016 12:21:35 AM
  • Mạcc Anhh: Galaxies are not evenly distributed throughout the universe. A few are found alone, but almost all are grouped in formations termed galactic clusters. These formations should not be confused with stellar clusters, globular clusters of stars that exist within a galaxy. The size of galactic clusters varies enormously, with some clusters containing only a dozen or so members and others containing as many as 10,000. Moreover, galactic clusters themselves are part of larger clusters of clusters, termed superclusters. It is surmised that even clusters of superclusters are possible. Our galaxy, the Milky Way, is part of a galactic cluster called the Local Group, which has twenty members and is typical in terms of the types of galaxies it contains. There are three large spiral galaxies: Andromeda, the largest galaxy in the group; the Milky Way, the second-largest galaxy; and the Trianglum Spiral, the third largest. There are also four medium-sized spiral galaxies, including the Large Cloud of Magellan and the Small Cloud of Magellan. There are four regular elliptical galaxies; the remainders are dwarf ellipticals. Other than our own galaxy, only Andromeda and the Clouds of Magellan can be seen with the naked eye, and the Clouds are visible only from the Southern Hemisphere. In the vicinity of the Local Group are several clusters, each containing around twelve members. The nearest cluster rich in members is the Virgo Cluster, which contains thousands of galaxies of all types. Like most large clusters, it emits X-rays. The Local Group, the small neighboring clusters, and the Virgo Cluster form part of a much larger cluster of clusters – the Local Supercluster. The existence of galactic clusters presented a riddle to scientists for many years – the “missing mass” problem. Clusters are presumably held together by the gravity generated by their members. However, measurements showed that the galaxies did not have enough mass to explain their apparent stability. Why didn’t these clusters disintegrate? It is now thought that galaxies contain great amounts of “dark matter”, which cannot be directly observed but which generates gravitational pull. This matter includes gas, dust, burnt-out stars, and even black holes. 9/27/2016 12:16:52 AM Mạcc Anhh: The development of genetically modified (GM) pants and animals had led to a huge minimal. Opponents that GM-Frankenfoods threat to our well-being, and proponents say that the risks are is say are a shirt these days here is one aspect of the war over GM that is often overlooked. Anyone who wears a cotton crop Cotton is the only major non-food GM crop at present. but others are coming If GM GM cotton plants that is not food has not stomed the most passionate GM ts from objecting. sing a GM on is in field next to fields of non-GM conon, they argue, then how to keep genes from being trans grown a health hazards in food. so rom ield to ticiu. his danger, however, is not as connemne to the public as possible ere is fury GM eotton pesticides. Planting of GM cotton no great over the need for GM Fumers GM cotton seeds produce higher yields, and they do without hairin China, is now has increased fivefold since 1997: three quarter of cotton in America, and over like it because it increases their profits. colors or scents, tougher other options for non-food GM include new vancty of nowers with different another grasses for lawns, and plants designed to soak up pollutants from the soil. The paper industry provides is and a example of potential for GM to help produce better and cheaper products. Paper is made from pulp, and pulp generally made from trees. Researchers in New Zealand and Chile have been working on insect-resistant pines, Japanese firm has combined carrot genes with tree genes to make them
  • Mạcc Anhh: Bé's Ngốc'ss: â 9/26/2016 11:54:45 PM Bé's Ngốc'ss: a 9/26/2016 11:54:45 PM Bé's Ngốc'ss: a 9/26/2016 11:54:45 PM Bé's Ngốc'ss: a 9/26/2016 11:54:45 PM Bé's Ngốc'ss: a 9/26/2016 11:54:46 PM Bé's Ngốc'ss: a 9/26/2016 11:54:46 PM Bé's Ngốc'ss: a 9/26/2016 11:54:46 PM Bé's Ngốc'ss: a 9/26/2016 11:54:46 PM Bé's Ngốc'ss: a 9/26/2016 11:54:46 PM Bé's Ngốc'ss: a 9/26/2016 11:54:46 PM Bé's Ngốc'ss: a 9/26/2016 11:54:47 PM Bé's Ngốc'ss: a 9/26/2016 11:54:47 PM Bé's Ngốc'ss: a 9/26/2016 11:54:47 PM Bé's Ngốc'ss: a 9/26/2016 11:54:47 PM Bé's Ngốc'ss: a 9/26/2016 11:54:48 PM Bé's Ngốc'ss: a 9/26/2016 11:54:48 PM Bé's Ngốc'ss: a 9/26/2016 11:54:48 PM Bé's Ngốc'ss: a 9/26/2016 11:54:48 PM Bé's Ngốc'ss: a 9/26/2016 11:54:48 PM Bé's Ngốc'ss: a 9/26/2016 11:54:49 PM Bé's Ngốc'ss: a 9/26/2016 11:54:49 PM Bé's Ngốc'ss: a 9/26/2016 11:54:49 PM Bé's Ngốc'ss: a 9/26/2016 11:54:49 PM Bé's Ngốc'ss: a 9/26/2016 11:54:50 PM Bé's Ngốc'ss: a 9/26/2016 11:54:50 PM Bé's Ngốc'ss: a 9/26/2016 11:54:50 PM Bé's Ngốc'ss: a 9/26/2016 11:54:50 PM Bé's Ngốc'ss: a 9/26/2016 11:54:50 PM Bé's Ngốc'ss: a 9/26/2016 11:54:51 PM Bé's Ngốc'ss: a 9/26/2016 11:54:51 PM Bé's Ngốc'ss: a 9/26/2016 11:54:51 PM Bé's Ngốc'ss: â 9/26/2016 11:54:51 PM Bé's Ngốc'ss: a 9/26/2016 11:54:51 PM Bé's Ngốc'ss: â 9/26/2016 11:54:52 PM Bé's Ngốc'ss: a 9/26/2016 11:54:52 PM Bé's Ngốc'ss: a 9/26/2016 11:54:52 PM Bé's Ngốc'ss: a 9/26/2016 11:54:53 PM Bé's Ngốc'ss: a 9/26/2016 11:54:53 PM Bé's Ngốc'ss: â 9/26/2016 11:54:53 PM Bé's Ngốc'ss: â 9/26/2016 11:54:54 PM Bé's Ngốc'ss: a 9/26/2016 11:54:54 PM Bé's Ngốc'ss: a 9/26/2016 11:54:54 PM Bé's Ngốc'ss: a 9/26/2016 11:54:54 PM Bé's Ngốc'ss: a 9/26/2016 11:54:54 PM Bé's Ngốc'ss: a 9/26/2016 11:54:55 PM Bé's Ngốc'ss: a 9/26/2016 11:54:55 PM Bé's Ngốc'ss: a 9/26/2016 11:54:55 PM Bé's Ngốc'ss: a 9/26/2016 11:54:55 PM Bé's Ngốc'ss: a 9/26/2016 11:54:56 PM Bé's Ngốc'ss: a 9/26/2016 11:54:56 PM Bé's Ngốc'ss: a 9/26/2016 11:54:56 PM Bé's Ngốc'ss: a 9/26/2016 11:54:56 PM Bé's Ngốc'ss: a 9/26/2016 11:54:57 PM ๖ۣۜღBossღ๖ۣۜ๖ۣۜ: wave 9/26/2016 11:55:43 PM Bé's Ngốc'ss: mà 9/26/2016 11:56:19 PM Bé's Ngốc'ss: ông lấy lại đk nik òi à 9/26/2016 11:56:26 PM .: laughing 9/26/2016 11:58:18 PM Mạcc Anhh: good morning, everybody big_grin : )) 9/27/2016 12:13:10 AM Mạcc Anhh: Galaxies are not evenly distributed throughout the universe. A few are found alone, but almost all are grouped in formations termed galactic clusters. These formations should not be confused with stellar clusters, globular clusters of stars that exist within a galaxy. The size of galactic clusters varies enormously, with some clusters containing only a dozen or so members and others containing as many as 10,000. Moreover, galactic clusters themselves are part of larger clusters of clusters, termed superclusters. It is surmised that even clusters of superclusters are possible. Our galaxy, the Milky Way, is part of a galactic cluster called the Local Group, which has twenty members and is typic
  • zzz02042001: yawn 9/27/2016 8:20:52 AM
  • zzz02042001: yawnyawnyawn 9/27/2016 8:20:54 AM
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  • Giải đáp toán lý hóa 24/7: big_grin 9/27/2016 11:12:21 AM
  • Giải đáp toán lý hóa 24/7: em Hồng Lam có đây k nhỉ 9/27/2016 11:14:30 AM
  • Giải đáp toán lý hóa 24/7: big_grin 9/27/2016 11:14:33 AM
  • Hương_shine: toán 9/27/2016 11:52:41 AM
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