 Next, let there be four magnitudes A, B, C, D, and other four E, F, G, H, which, taken two and two in a cross order, have the same ratio, viz.: A...  Euclid, book v. proved algebraically, so far as it relates to commensurable ... - Página 30por Charles Lutwidge Dodgson - 1874Vista completa - Acerca de este libro
 | John Playfair - 1836 - 488 páginas
...D, H, G, Book V. Next, let there be four magnitudes, A, B, C, and D, and other four, E, F, G, and H, which, taken two and two, in a cross order, have the same A, B, C, D, E, F, G, H, ratio, viz. A:B::G:H; B:C:: F : G, and C : D : : E : F, then A:D:: E : H. For,... | |
 | Euclid, James Thomson - 1837 - 410 páginas
...and C:D::E:F: then A : D : : E : H. Because A, B, C, are three magnitudes, and F, G, H other three, which, taken two and two in a cross order, have the same ratio ; by the first case, A : C : : F : H. But C : D : : E : F ; wherefore again, by the first case, A :... | |
 | Andrew Bell - 1837 - 290 páginas
...B:C::F:G, andC:D::E:F,thenA:D::E:H. For, since A, B, C, are three magnitudes, and F, G, H, other three, which, taken two and two in a cross order, have the same ratio, by the first case A : C : : F : H. But C : D : : E : F ; therefore again, by the first case, A : D... | |
 | Robert Simson - 1838 - 434 páginas
...be any number, &c. QED PROP. XXIII. THEOR. IF there be any number of magnitudes, and as many others, which, taken two and two, in a cross order, have the same ratio; the first shall have to the last of the first magnitudes the same ratio which the first of the others has to... | |
 | Euclides - 1840 - 192 páginas
...B:C::F:G, andC:D::E:F, thenA:D:: E:H. For, since A, B, C are three magnitudes, and F, G, H other three, which, taken two and two, in a cross order, have the same ratio, by the first case, A : C : : F : H. But C : D : : E : F, therefore again, by the first case, A : D... | |
 | Oliver Byrne - 1841 - 140 páginas
...<?> :; (¿) : /\ For, because Гу, i^=J, |з) are three magnitudes, and @, ПП, /N. other three, which, taken two and two in a cross order, have the same ratio, therefore, by the first case, [^ 0 :: 0 : /^> therefore again, by the first case, ГП : o) :; and... | |
 | Euclides - 1841 - 378 páginas
...F: then A shall be to D, as E to H. Because A, B, C, are three magnitudes, and F, G, H other three, which, taken two and two in a cross order, have the same ratio; therefore, by the first case, A is to C, as F to H: but C is to D, as E is to F; therefore again, by... | |
 | Oliver Byrne - 1841 - 144 páginas
...(5 def. v.). Next, let there be four magnitudes, and other four, (V), 0, r¡~|, /7\» \vhich, when taken two and two in a cross order, have the same ratio ; namely, then shall ^) : Q : ; (¿) : /\ For, because \*~), (*J, Qj are three magnitudes, and Q, ПП,... | |
 | John Playfair - 1842 - 332 páginas
...F (def. 5. 5.). Next, Let there be four magnitudes, A, B, C, and D, and other four, E, F, G, and H, which, taken two and two in a cross order, have the same ratio, viz. A : B : : G : H ; B : C : : F : G, and C : D : : E : F, then, A : D : : E : H. For.since A, B,... | |
 | Euclides - 1842 - 316 páginas
...last.* First, let there be three magnitudes A, в, c, and other PROPOR. OF GEOMETRY. three D, E, F, which, taken two and two in a cross order have the same ratio, viz. A : в : : E : F, and в : c : : D : E : then A : c :: D : F. Let P measure both в and c, and... | |
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