 | Robert Simson - 1806 - 546 σελίδες
...also be proportionals when taken joindy, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to...second, as the third and fourth together to the fourth. Let AE, EB, CF, FD be proportionals ; that is, as AE to EB, so is CF to FD ; they shall also be pioportionals... | |
 | John Playfair - 1806 - 320 σελίδες
...that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth. If A : B : : C : D, by composition, A+B : B : : C+I> : D. Take wz.A+B and wB any multiples whatever... | |
 | John Mason Good - 1813 - 714 σελίδες
...is, if the first be to the second, as the third to the fourth, the first and second together shall he to the second, as the third and fourth together to the fourth. Prop. XIX. Theor. If a whole magnitude be to a whole, as a magnitude taken from the first, is to a... | |
 | Euclides - 1816 - 588 σελίδες
...also be proportionals when taken jointly, that is, if the first be to the second, a§ thethirdhto the fourth, the first and second together shall be to...second, as the third and fourth together to the fourth. Let AE, EB, CF, FD be proportionals ; that is, as AE to EB, so is CF to FD ; they shall .also he proportionals... | |
 | John Mason Good - 1819 - 800 σελίδες
...be proportionals, when taken jointly, that is, if the first lie to the second, as the third to the fourth, the first and second together shall be to...second, as the third and fourth together to the fourth. Prop. XIX. Theor. If a whole magnitude be to и n-hole, as a magnitude taken from the first, is to... | |
 | John Playfair - 1819 - 354 σελίδες
...that is, if the first be to the second as the third to the fourth, the first and second together will be to the second, as the third and fourth together to the fourth. If A : B : : C : D, then, by composition, A+B : B : :\C+D : D. Take m(A+B), and nB any multiples whatever... | |
 | Rev. John Allen - 1822 - 508 σελίδες
...Compounding; when it is inferred, if four magnitudes be proportional, that the first and second together is to the second, as the third and fourth together to the fourth. Prop. 18th of Iliis book. 19. Dividing ; when it is inferred, if four magnitudes be pro portional,... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...these -two ratios are equal, therefore we have ^+1=^+1, consequently AC B=D' A : B : : C : D. QED PROP XVIII. THEOR. If magnitudes taken separately 'be proportionals,...Since the ratio of A to B is the same with that of Cto D. /• f AC therefore |j-=jp to each side of this equation add unity, and we have A , , C , ,... | |
 | Robert Simson - 1827 - 546 σελίδες
...proportionals when taken jointly : that is, if the fast be to the second, as the third to the fourth, the Jirst and second together shall be to the second, as the third and fourth together to the fourth. Let AE, EB, CF, FD be proportionals; that is, as •2.5. t Hyp. • 5 Def. 5. t4Ax. 1. t 5 Ax. 1. t... | |
 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...that is, if the first be to the second as the third to the fourth, the first and second together are to the second as the third and fourth together to the fourth. Let AE, EB, CF, FD be proportionals ; that is, if AE • EB = CF : FD: then also AB : BE = CD : DF.... | |
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IF magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly, that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together... 
