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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... "
An Elementary Treatise on Algebra: Theoretical and Practical - Page 501
by James Ryan - 1824 - 516 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...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...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...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...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - Astronomy - 1822 - 508 pages
...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,...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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 , ,...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...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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