 Hence all prisms are to one another in the ratio compounded of the ratios of their bases, and of their altitudes. For every prism is equal to a parallelopiped of the same altitude with it, and of an equal base (2.  The Works of Archimedes - Page 121by Archimedes - 1897 - 326 pagesFull view - About this book
 | Arhimēdēs - 2004 - 522 pages
...respectively. The height of the cone PQQ' is then PK, where PK is perpendicular to Now the cones are in the ratio compounded of the ratios of their bases and of their heights, ie the ratio compounded of (1) the ratio of the circle about BB' to the ellipse about QQ', and (2)... | |
 | 562 pages
...equiangular to one another, each to each, that if, of which the solid angles are equal, each to each, have to one another the ratio compounded of the ratios of their sides. The proof follows the method of the proposition xi. 33, and we can use the same figure. In order... | |
 | Walter Roy Laird, Sophie Roux - Science - 2008 - 320 pages
...not-previously-defined operation found in Book VI, proposition 23, which states: Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides.8 What is meant here by "compounded of"? What Euclid does to compound two proportions is to take... | |
 | Peter M. Engelfriet - Mathematics - 1998 - 516 pages
...indicated as an alternative to supplying the lemma (II, pp. 242-6). 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... | |
 | Euclid - 452 pages
...vi. 23 which shows how to compound two ratios between straight lines. PROPOSITION 5. Plane numbers have to one another the ratio compounded of the ratios of their sides. Let A, B be plane numbers, and let the numbers C, D be the sides of A, and E, F of B ; 5 I say... | |
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