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Books Books 41 - 50 of 51 on Solid parallelepipeds contained by parallelograms equiangular to one another, each....
" Solid parallelepipeds contained by parallelograms equiangular to one another, each to each, that is, of which the solid angles are equal, each to each, have to one another the ratio compounded of the ratios of their sides. The "
The Thirteen Books of Euclid's Elements - Page 347
by Euclid, Johan Ludvig Heiberg - 1908
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 143 pages
...ratio AB : AP is the ratio compounded of AB : AE and AD : AG. Art. 147. COROLLARIES. (1) Two rectangles have to one another the ratio compounded of the ratios of their sides. From (1) and the definition of duplicate ratio (Art. 129) it follows that 88 EUCLID, BOOKS V. AND VI....
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THE CONTENTS OF THE FIFTH AND SIXTH BOOKS OF EUCLID

M. J. M. HILL - 1900
...ratio AB : AP is the ratio compounded of AB-.AE and AD : AG. Art. 147. COROLLARIES. (1) Two rectangles have to one another the ratio compounded of the ratios of their sides. From (1) and the definition of duplicate ratio (Art. 129) it follows that Art. 148. EXAMPLE 69. The...
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Science in the Middle Ages

David C. Lindberg - Science - 1980 - 549 pages
...duplicate of ratio (A,B), and (A,D) its triplicate (V. defs. 9, 10), and that "equiangular parallelograms have to one another the ratio compounded of the ratios of their sides" (VI.23), he did not use or develop the concept further. 72 Mathematical astronomers found more use...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 488 pages
...alternative to supplying the lemma (II, pp. 242-6). 23l¿N¿th¿*fl¿ Heath Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides. (The ratio of two equiangular parallelograms: connect together the two ratios of each of the two sides of...
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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - Mathematics - 2000 - 419 pages
...following; "A ratio is that relation or habitude of homo18. This asserts, "Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides." Euclid does not actually define the term compound ratio, but from the context of the proof in Elements...
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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - Mathematics - 2000 - 419 pages
...following: "A ratio is that relation or habitude of homo18. This asserts, "Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides." Euclid does not actually define the term compound ratio, but from the context of the proof in Elements...
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The Works of Archimedes

Archimedes, Sir Thomas Little Heath - Mathematics - 2002 - 377 pages
...cylinder passes through P. Proposition 10. It was proved by the earlier geometers that any two cones have to one another the ratio compounded of the ratios of their bases and of their heights. The same method of proof will show that any segments of cones have to one...
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Descartes’s Mathematical Thought

C. Sasaki - History - 2003 - 496 pages
...23, which we have cited above (p. 2i0), had its arithmetical counterpart VIII, 5: “Plane numbers have to one another the ratio compounded [of the ratios] of their sides.” In his excellent monograph titled Philosophy of Mathematics and Deductive Structure in Euclid's Elements,...
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A Manual of Greek Mathematics

Sir Thomas Little Heath - Mathematics - 1931 - 552 pages
...to the similar figure similarly described on the second. Proposition 23 (equiangular parallelograms have to one another the ratio compounded of the ratios of their sides) is highly important in itself, and also because it introduces us to the method of compounding, ie multiplying,...
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The Art of Conjecturing, Together with Letter to a Friend on Sets in Court ...

Jacob Bernoulli, Edith Dudley Sylla - Mathematics - 2006 - 430 pages
...Compounding of ratios appears in Euclid, Elements, Book VI, Proposition 23, "Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides." See Edith Sylla, "Compounding Ratios: Bradwardine, Oresme, and the first edition of Newton's Principia,"...
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