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
| James Williamson - Mathematics - 1781
...equal. Which was to be demonftrated. '•.;':. . • . ' • " PROP. XXIII. Equiangular parallelograms **have to one another the ratio compounded of the ratios of their** fides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : I fay... | |
| John Playfair - 1819 - 317 pages
...that of the product LXMXN to the product / X m X n. COR. 3. Hence all prisms are to oĢe anpther in **the ratio compounded of the ratios of their bases, and of their** altitudes. For every prism is equal to a parallelepiped of the same altitude with it, and of ,an equal... | |
| John Martin Frederick Wright - Astronomy - 1831
...proposition usually cited Ex cequo. \.Euclid, Book 5, Prop. 22.] 10. Shew that the equiangular parallelograms **have to one another the ratio compounded of the ratios of their** sides. 1 1. Prove that two straight lines, which are each of them parallel to the same straight lines,... | |
| Mathematics - 1836 - 472 pages
...ratios of the areas of their bases, and of their altitudes. Cor. 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 parallelepiped of the same altititue with it, and of an equal... | |
| A. Bell - Conic sections - 1837 - 164 pages
...as AD to AX, so is the solid AF to the solid GO. COR. 2. — 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... | |
| John Playfair - Geometry - 1837 - 318 pages
...with that of the product LXMXN to the product IX m X n. COR. 3. 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 parallelepiped of the same altitude with it, and of an equal... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...with that of the product LXMXN to the product lx m X n. COR. 3. 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... | |
| John Playfair - Euclid's Elements - 1846 - 317 pages
...with that of the product LXMXN to the product lx m X n. COR. 3. 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... | |
| Samuel Hunter Christie - 1847
...bases, and altitudes equal to the altitudes of the prisms, (to which the prisms are respectively equal,) **have to one another the ratio compounded of the ratios of their bases and** altitudes (Prop. 58), that is, the ratio compounded of the ratios of the bases and altitudes of the... | |
| 1856
...proportionals, and those which are opposite to the equal angles are homologous. 2. Equiangular parallelograms **have to one another the ratio compounded of the ratios of their** sides. 3. If from any angle of a triangle a straight line be drawn perpendicular to the base, the rectangle... | |
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