 | Thomas Simpson - 1760 - 296 sayfa
...icth and alfo enter) we are to prove, " That if there be " three 276 Notes geometrical and critical. " three magnitudes (A, B, C) and other three (D, *' E, F) which taken two and two have the fame ra« tio (A : B : : D : E, B : C : : E : F; if the firft(A) *' be greater than the third... | |
 | Robert Simson - 1762 - 488 sayfa
...ufually cited by the words " ex acquali in proportions perturbata, or, ex aequo per" turbate." Firft, Let there be three magnitudes A, B, C, and other three D, E, F, which taken two and two in a crofs order have the fame ratio, that is fuch that A is to B, as E to F ; and as B is to C, fo is D... | |
 | Euclid - 1765 - 492 sayfa
...equal to the fixtb : and if the firjl he lefs than the third, the fourth will he lefs than the fixth. Let there be three magnitudes A, B, c, and other three D, E, F which taken two and two are in the fame ratio, but in a crofs order ; viz. as A is to B, fo is E to F, and as B is to c, fo... | |
 | Robert Simson - 1775 - 534 sayfa
...aequali in proportione perturbata ;" or " ex aequo perturb ate" a 15- s. b Ii. 5. c 4. j. btl. i. Firft, let there be three magnitudes A, B, C, and other three D, E, F, which taken two and two in a crofs order have the fame ratio/that is, fuch that A is to B, as E to F ; and as B is to C, fo is D... | |
 | Euclid - 1781 - 552 sayfa
...in frofortiene ferturbata ;" or " ex atquo ferturbate." II. S. 4 II. CDEF Firft, Let there be thrre magnitudes A, B, C, and other three D, E, F, which, taken two and two, in a crofs order, have the fame ratio, that is, fuch that A is to B, as E to F j and as B is to C, fo is... | |
 | Euclid, John Playfair - 1795 - 462 sayfa
...laft of the firft magnitudes the fame ratio which the firft of the others has to the laft*, Firft, let there be three magnitudes, A, B, C, and other three, D, E, and F, which, taken two and two in a crofs order, have the fame ratio, viz. A : B : : E : F, and B... | |
 | Robert Simson - 1804 - 530 sayfa
...ufually cited by the words " ex aequali in proportions perturbata, " or, ex aeqvo perturbate" Firft, Let there be three magnitudes A, B, C, and other three D, E, F, which taken two and two in a' crofs order have the fame ratio, that is fuch that A is to B, as E to F; and as Bis to C, fo is D to... | |
 | John Playfair, Euclid - 1804 - 468 sayfa
...greater than the third, the fourth is greater than the fixth ; if equal, equal ; and if lefs, lefs. If there be three magnitudes, A, B, C, and other three, D, E, and F, fuch that A: B : : E : F, and B : C : : D : E ; 2fA>C, D>F; if A=C, D=:F, and if A<C,D<F. L... | |
 | John Playfair - 1806 - 320 sayfa
...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 will have to the last of...ratio which the first of the others has to the last*. First, let there be three magnitudes, A, B, C, and other three, D, E, F, which, taken two and two,... | |
 | Robert Simson - 1806 - 546 sayfa
...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 the last. NB This is usually cited by the words " ex aquali in proportione per*< turbata;" or, " ex aquo per... | |
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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 the last. 
