 | Bewick Bridge - 1814 - 630 sider
...and Pf, /jg of tkif figure correspond to PA" and Arjg in Figure, page 54, .'. 4PMx. tQ=Pt*. (b) For when three quantities are in continued proportion, the first is to the third in the duplicate ratio of the Jirst to ike second, or of the second to the third ; :. 4p : tQ :: Pt*... | |
 | Jeremiah Day - 1820 - 352 sider
...first quantity, to the fourth power of the second. Hence, 397, If three quantities are proportional, the first is to the third, as the square of the first, to the square of the second ; or as the square of the second, to the square of the third. In other words, the first has to the... | |
 | William Nicholson - 1821 - 376 sider
...— a : ar1 — ar :: or' — ar : ar3 — ar', Sec. " In any geometrical progression, the first term is to the third, as the square of the first to the square of the second." Let a, ar, ar', &c. be the progression ; then a : ar' :: a* : ai ri. Hence it appears, that the duplicate... | |
 | Adrien Marie Legendre - 1822 - 394 sider
...: : A : B, we shall have A2 : B2 : : BA : BC ; or(Cor. 2. Theor. 11.) A2 : B2 : : A : C. Hence in a continued proportion, the first is to the third as the square of the first is to the square of the second. The ratio which A bears to C is sometimes called the duplicate of that... | |
 | James Wood - 1825 - 322 sider
...: ar'! — ar :: ar — ar : ar3 — ar', &c. (218.) In any geometrical progression, the first term is to the third, as the square of the first to the square of the second. Let a, ar, ar-, &c. be the progression; then a : ar2 :: a~ : a2г2. Hence it appears, that the duplicate... | |
 | George Lees - 1826 - 276 sider
...equivalent to the triangle DEFe. Again, e 10- 4because BC : EF : : EF : BG, and that, if three quantities be in continued proportion, the first is to the third...the square of the first to the square of the second? ; therefore, BC : BG : : t 121. Alg. BC2 : EF2 ; but, BC : BG : : triangle ABC : triangle ABGs, 8 l-... | |
 | Jeremiah Day - 1827 - 352 sider
...first quantity, to the fourth power of the second. Hence, 397. If three quantities are proportional, the first is to the third, as the square of the first, to the square of the second ; or as the square of the second, to the square of the third. In other words, the first has to the... | |
 | Jeremiah Day - 1831 - 358 sider
...first quantity, to the fourth power of the second. Hence, 397. If three quantities are proportional, the first is to the third, as the square of the first, ta the square of the second; or as the square of the second, to the square of the third. In other words,... | |
 | Jeremiah Day - 1835 - 356 sider
...first quantity, to the fourth power of the second. Hence, 397. If three quantities are proportional, the first is to the third, as the square of the first, to the sqv/are of the second; or as the square of the second, to the square of the third. In other words,... | |
 | Andrew Bell - 1837 - 290 sider
...suggested a considerable improvement in the form of astronomical angular instruments. 6. If three lines be in continued proportion, the first is to the third, as the square of the difference between the first and second, to the square of the difference between the second and third.... | |
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If three quantities are proportional, the first is to the third, as the square of the first to the square of the second ; or as the square of the second, to the square of the third. 
