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" And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to... "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 117
by Euclides - 1860
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The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855 - 230 pages
...to D ; or, the ratio of A to D is said to be compounded of the ratios of A to B, B to C, and C to D. In like manner, the same things being supposed, if...then, for shortness sake, M is said to have to N, the ratio compounded of the ratios of E to F, G to H, and K to L. Arithmetically ratios arc compounded...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...briefly expressed by saying, A has to D the ratio compounded of the ratios of E to f, G to H, and K to L. In like manner, the same things being supposed, if...; then, for shortness' sake, M is said to have to K the ratio compounded of the ratios of B to F, G to H, and K to JL. This definition marked A, is usually...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1856 - 318 pages
...same with the ratios of E to F, G to H. and K to L. \ In like manner, the same things being suppose^ if M has to N the same ratio which A has to D, then,...compounded of the ratios of E to F, G to H, and K to I,. 11. If three magnitudes are continual proportionals, the ratio of the first to the third is said...
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The Elements of Euclid with Many Additional Propositions and Explanatory Notes

Eucleides - 1860 - 396 pages
...briefly expressed, by saying A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...then, for shortness sake, M is said to have to N, the ratio compounded of the ratios of E to F, G to H, and K to L. Arithmetically ratios are compounded...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...briefly expressed by saying, A has to D the ratio compounded of the ratios of E t&F, G to H, and Kto L. In like manner, the same things being supposed, if M has to N the same ratio which A has to il ; then, for shortness' sake, M is said to have to N the ratio compounded oi the ratios of E to F,...
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 pages
...if 3 : 4 = 6 : 8 ; 4 : 5 = 8 : 10 ; and Л : 7 = 10 : 14 ; then, Д = 6 of JL of .10 = б : 14. l о In like manner, the same things being supposed, if...the same ratio which A has to D; then, for shortness fake, M is said to have to N the ratio compounded of the ratios of И to F, G to II, and К to L. Thus...
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The Propositions of the Fifth Book of Euclid Proved Algebraically: with an ...

George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...expressed by saying, A has to "D the ratio compounded of the ratios of E to F, G to H, and К to L. In like manner, the same things being supposed, if M has to 2V the same ratio which A has to D ; then, for shortness' sake, M is said to have to N the ratio compounded...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...briefly expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...; then for shortness' sake, M is said to have to N the ratio compounded of the ratios of to F, G to H, and K to L. xn. In proportionals, the antecedent...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...briefly expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if...ratio which A has to D ; then, for shortness' sake, 11 is said to have to N the ratio compounded of the ratios of E to F, G to H, and KtoL. XII. In proportionals,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...briefly expressed by saying, A has to D the ratio compounded of the ratios of E to F, G to H, and K to L. In like manner, the same things being supposed, if M has to N the same ratio that A has to D ; then, for the sake of shortness, M is said to have to N the ratio compounded of the...
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