 N. equiangular to one another, each to each, that is, of which the folid angles are equal, each to each ; have to one another the ratio which is the fame with the ratio compounded of the ratios of their fides.  Books 10-13 and appendix - Page 345by Euclid - 1908Full view - About this book
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...are to one PAGE another as their bases 73 FIVE COROLLARIES 74 THEOREM 1i. Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides . . 76 S1x COROLLARIES 76 THEOREM 13. In any circle angles at the centre have to one another the ratio... | |
 | Alexander Charles Ewald - Civil service - 1870 - 292 pages
...of the parts may be equal to the square of the other part. 3. Prove that equiangular parallelograms have to one another the ratio compounded of the ratios of their sides. What form does this theorem take in trigonometry ? 4. Solve the following equations : — (2) |C 2... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...antecedents to the rectangle contained by the consequents. THEOR. 14. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio... | |
 | James Maurice Wilson - 1878 - 450 pages
...antecedents to the rectangle contained by the consequents. THEOREM 14. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. Let ABC, DEF be two triangles, having the altitudes AG, DH respectively;... | |
 | J. G - 1878 - 408 pages
...including sides of the first to the including sides of the second. " 23." Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. We may observe that Prop. 7, which in ordinary editions of Euclid is... | |
 | Mathematical association - 1883 - 86 pages
...antecedents to the rectangle contained by the consequents. THEOR. 14. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio... | |
 | Electronic journals - 1917 - 330 pages
...or of any two ratios equal to these. Thus in VI, 23, Euclid proves that: Equiangular parallelograms have to one another the ratio compounded of the ratios of their sides. There is a close relationship between the notion of the ratio of two incommensurables implied in Definition... | |
 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...and DC, the triangle ADE will be equal to the triangle BDC. THEOR. 15. Triangles and parallelograms have to one another the ratio compounded of the ratios of their bases and of their altitudes. Let ABC, HKL be two triangles, AD, HM their altitudes : A then shall... | |
 | Henry Sinclair Hall, Frederick Haller Stevens - Geometry - 1892 - 286 pages
...the ratio compounded of BC to FG and BM to FQ, for these parms. are equiangular. .'. parms. BD, FH have to one another the ratio compounded of the ratios of their bases and of their altitudes. But A ABC = half par™. BD and AEFG =half parm. FH- Hence the same is... | |
 | Archimedes - Geometry - 1897 - 524 pages
...of their bases and of their heights*. The same method of proof will show that any segments of cones have to one another the ratio compounded of the ratios of their bases and of their heights. The proposition that any 'frustum ' of a cylinder is triple of the conical... | |
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