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" Ij the first be to the second as the third to the fourth, and if the first be a multiple, or a part of the second ; the third is the same multiple, or the same part of the fourth. "
The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ... - Page 54
by George Sturton Ward - 1862 - 79 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...demonstrated, A : C : : B : D ; therefore, inversely0, C : A, : : D : B. Therefore, &c. QED PROP. C. THEOR. IF the first be to the second as the third to the fourth, and if the first be a multiple or a part of the second, the third is the same multiple or the same...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...of the last two has to the other of these. Prob. XVIII. Theor. If magnitudes, taken separately, he proportionals, they shall also be proportionals, when...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...
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Easy Introduction to Mathematics, Volume 1

Charles Butler - Mathematics - 1814 - 540 pages
...clear, one or two more particulars will require an explanation. If four numbers are proportionals, that is, if the first be to the second as the third to the fourth, then will the first be to the third аз the second to the fourth; and this accounts for the usual...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...is to B, as C is to D: Therefore, if the first be the same multiple, A. &c. QED CD H PROP. D. THEOR. IF the first be to the second as the third to the s«- N. fourth, and if the first be a multiple or part of the second ; the third is the same multiple,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...&c. QED PROP. XVIII. THEOR. .. ; • v'i M IF magnitudes, taken separately, be proportional sj See N. they shall 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 the second, as the third and...
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An Elementary Treatise on Algebra

Bewick Bridge - Algebra - 1818 - 254 pages
...с : b : d, and b : d :; a.: c. cd cd, с а Тн. 5. "If there be six proportional quantities, and the " first be to the second as the third to the fourth ; and the third " to the fourth as the fifth to the sixth ; then will the first " be to the second...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...Therefore, &c. Q, ED PROP. XVIII. THEOR. If magnitudes, taken separately, be proportionals, they will also be proportionals -when taken jointly, that is,...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...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...the same ratio which the remaining one of the last two has to the other of these. Prop. XV11I. Theor. If magnitudes, taken separately, be proportionals,...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 the second,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...Therefore, &c. Q, ED PROP. XVIII. THEOR. If magnitudes, taken separately, be proportionals, they will also be proportionals when taken jointly, that is, if the first be to the seconrf at the third to the fourth, the first and second together will be to the second, as the third...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...Therefore (5. def. 5.), as AE is to tB, so is CF to FD. If then magnitudes, &c. QED PROP. XVIII. THEOR. > IF magnitudes, taken separately, be proportionals,...proportionals when taken jointly, that is, if the hrst be to the second, as the third to the fourth, the first and second together shall be to the second,...
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