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" If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ...
by John Mason Good - 1813
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The principles and practice of arithmetic

John Hind - 1856
...Elements, that "Proportion is the Similitude of Ratios ; and the first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatever of the first and third being taken, and any equimultiples whatever of the second said fourth...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 318 pages
...therefore A=mnC /(, tj',;t<f'£ PROP. IV. THEOR. /, / 2. // //>5 If the first of four magnitudes has thr, same ratio to the second which the third has to the fourth, and if any equimultiples whatever be taken of the first and third, and any whatever of the second and...
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Practical Arithmetic: Uniting the Inductive with the Synthetic Mode of ...

James Bates Thomson - Arithmetic - 1858 - 384 pages
...answer is greater than the third term, arises from the fact, that theßrst türm of a proportion has the same ratio to the second, which the third has to the /он г £Л or answer ; consequently, if the answer is greater than the third term, the second term...
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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Euclides - 1859
...àiroiovovv ToXXaя-Xaíriaff/iov, rev áurоv i'Ctí Xóyov Xq^öivra raráXXqXa. If the first has the same ratio to the second which the third has to the fourth; any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...is to G, so is F to H. (v. def. 5.) Therefore, if the first, &c. QED Cos, Likewise, if the first has the same ratio to the second, which the third has to the fourth, then also any equimultiples whatever of the first and third shall have the same ratio to the second...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860
...first case in Euclid. G. (c) V. 2. PROPOSITION A. THEOREM. — If the first of four magnitudes have the same ratio to the second which the third has to the fourth, then, if the first be greater than the second, the third is also greater than the fourth ; and if equal,...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861
...the same ratio, as Ato I}; ie A : B = C : x. PROP. A, — THEOR. If the first of four magnitudes has the same ratio to the second which the third has to the fourth; then if the first be greater than the second the third is greater than the fourth ; and if equal, equal...
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The elements of algebra. [With] Answers

Robert Fowler - 1861
...those m = 16 j cases. PROPOKTION. 133. Def. — If there be four quantities, such that the first has the same ratio to the second which the third has to the fourth, then the four quantities are said to be proportionals. Thus if а, Ъ, с, d be the four quantities,...
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - Geometry, Algebraic - 1862 - 79 pages
...and therefore e ; / : ; g : A. Therefore, if the first, &c.— QED COR. Likewise, if the first has the same ratio to the second which the third has to the fourth, then also, any equimultiples whatever of the first and third have the same ratio to the second and...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...the less can be multiplied so as to exceed the other. V. The first of four magnitudes is said to have the same ratio to the second which the third has to...whatsoever of the first and third being taken, and auy equimultiples whatsoever of the second and fourth; if the multiple of the first b« IMS than that...
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