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Books Books 1 - 10 of 37 on C, which is compounded of the ratios of A to B, and B to C, is the same with the....
" C, which is compounded of the ratios of A to B, and B to C, is the same with the ratio of D to F, which is compounded of the ratios of D to E, and E to F. "
Elements of Trigonometry, and Trigonometrical Analysis, Preliminary to the ... - Page 61
by Augustus De Morgan - 1837 - 230 pages
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...been found. but if a fourth proportional to F, G, E cannot be found, then it can only be faid that the ratio of A to C is compounded of the ratios of A to B, and B to C, that is of the given ratios of D to E, and F to G. PROP. PRO P. X; , 9. F two or more magnitudes have...
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A compendious course of practical mathematics: Particularly adapted to the ...

Paul Hoste - Mathematics - 1769
...double tfce ratio of A to B ; and the ratio of A to D wilj be triple the ratro of A to B ; becaufe the ratio of A to C is compounded of the ratios of A to B, andofBtoC; and the 'ratio of A to D is compounded of the ratios of A to C, and of C to D, or of A to...
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The Elements of Euclid, viz: The errors, by which Theon, or others, have ...

Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...been found: But if a fourth proportional to F, G, E cannot be found, then it can only be faid that' the ratio of A to C is compounded of the ratios of A to B, and B to C, that is, of the given ratios of D to E, and F to G. a *. def. BCDEH FG PROP. PRO P. X 5. TF two or...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pages
...found : But if a fourth propor- j * tional to F, G, E cannot be found, then it can only be faid that the ratio of A to C is compounded of the ratios of A to B, and B to C, that is, of the given ratios of D to E, and F to G. PROP. PRO PX 9. IF twg or more magnitudes have...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - Euclid's Elements - 1795 - 400 pages
...proportionals, the t atio of A to C is duplicate of that of A to B, er of B to C : For by the laft definition, the ratio of A to C is compounded of the ratios of A to B, and of B to C ; but the ratio of A to B is equal to the ratio of B to C, becaufe A, B, C are continual...
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The elements of Euclid: viz. the first six books, with the eleventh and ...

Alexander Ingram, Robert Simson - Trigonometry - 1799 - 351 pages
...D to E ; \> 3. 5. therefore, by perturbate equality b, A is to C, as D to F ; that is, the ratio compounded of the ratios of A to B, and B to C, is the fame with the ratio compounded of the ratios of D to E, and E to F : and in like manner, the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1804 - 440 pages
...ratio of A to C is faid to be duplicate of the ratio of A to B. Hence, fince by the laft definition, the ratio of A to C is compounded of the ratios of A to B, and B to C, a ratio, which is compounded of two equal ratios, is. duplicate of either of thefe ratios." XII. OFGEOMETR...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804
...therefore, ex aequali, in proportion pertwbata b, A is to C, as D to F; that is, the ratio of A to C, which is compounded of the ratios of A to B, and B to C, is the fame with the ratio of D to F, which is compounded of the ratios of D to E, and E to F. and...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...been found : but if a fourth proportional to F, G, E cannot be found, then it can only be said that the ratio of A to C is compounded of the ratios of A to li, and B to C, that is, of the given ration of D to !•-, and F to G. PROP. X. 9. IF two or more...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Geometry - 1816 - 528 pages
...cequali in proportione perturbatab, A is to C, b23. 5. as D to F; that is, the ratio of A to C, which is compounded of the ratios of A to B, and B to C, is the same with the ratio of D to F, which is compounded of the ratios of D to E, ' and E to F : And...
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