 | William Nicholson - 1821 - 376 σελίδες
...— 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 σελίδες
...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 σελίδες
...: 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 σελίδες
...Again, e 10- 4because BC : EF : : EF : BG, and that, if three quantities be in continued proportion, the first is to the third as 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 σελίδες
...third, a duplicate ratio of the first to the second. And conversely, if the first of three quantities is to the third, as the square of the first to the square of the second, the three quantities are proportional. If a : b'.'.b : c, then a : c'. '.as : 63. Universally, 398.... | |
 | Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 σελίδες
...When three numbers are proportional, what relation has the first to the third ? The first is always to the third, as the square of the first to the square of the second ; thus in the above proportion, where 8 : 12 : : 12 : 18, 8 : 18 : : 64 : 144, where it is evident... | |
 | Euclides - 1838 - 264 σελίδες
...equal to the triangle DEF: and because BC • EF : : EF : BG ; and that if three straight lines be proportional, the first is to the third as the square of the first to that of the »16., ».i*,. second;* therefore BCistoBG as the square of BC . , , is to the square of... | |
 | Joseph Gwilt - 1842 - 1114 σελίδες
...the line В as the line С wanting the line D is to the line D. 950. PROP. LXXII. If three lines be proportional, the first is to the third as the square of the first is to the square of the second. If the line CD is to the line cd as the line cd is to a third line... | |
 | James Bates Thomson - 1844 - 266 σελίδες
...the ratio of the fourth power of the first quantity, to the fourth power of the second. Hence, 361. If three quantities are proportional, the first is...ratio of the first to the second. And conversely, if the first of the three QUEST.—When are quantities said to be in geometrical progression ? What is... | |
 | James Bates Thomson - 1844 - 272 σελίδες
...the ratio of the fourth power of the first quantity, to the fourth power of the second. Hence, 361. If three quantities are proportional, the first is to the third, as the square of the first tu the square of the second ; or as the square of the second, to the square of {he third. In other... | |
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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. 
