 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...be described upon a given straight line similar to one given ; and so on. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF, he similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Euclides - 1838 - 264 pages
...Therefore the triangles ABC, OEF are to each other as the squares on the homologous sides BC, EF. p.. ED PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles, which are to each other as the polygons themselves ; and the polygons are to one another as the squares... | |
 | Euclides - 1840 - 82 pages
...rectilineal figure similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate...divided into the same number of similar triangles, each similar pair of which are proportional to the polygons; and the polygons are to each other in... | |
 | London city mission - Christian socialism - 1840 - 620 pages
...argument nor testimony would suit the determination of such a case. If I want to determine whether similar triangles are to one another in the duplicate ratio of their homologous sides; the proper evidence will be to examine, by the powers of the mind, into the proofs which are alleged,... | |
 | Joseph Denison - Euclid's Elements - 1840 - 96 pages
...square of b$ is to the homologous side de ; or as the square of ac is to the homologous side ae. Because similar triangles are to one another in the duplicate ratio of their homologous sides (6 Euclid, 19), the triangle ate is to the triangle abe in the duplicate ratio of the side ab to the... | |
 | Euclides - 1840 - 192 pages
...but ABC : CAG : : AB : AG (vi. Prop. i) ; and therefore ABC : DEF : : AB : AG, that is to say, the triangles are to one another in the duplicate ratio of their homologous sides AB, DE (v. Def. ii). COR. — Hence it is manifest that if three straight lines be proportional, as... | |
 | Joseph Denison - Mechanics - 1841 - 210 pages
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the simi-lar triangles are to one another as the squares of their homologous... | |
 | Euclides - Geometry - 1841 - 378 pages
...a given rectilineal figure of six, or any number of sides. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Joseph Denison - Mechanics - 1841 - 210 pages
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their homologous... | |
 | Euclides - 1842 - 316 pages
...may be described upon a given straight line similar to one given, and so on. QEF PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. ABC has to the triangle DEF the duplicate ratio of that which вc has to EF. Take BG a third proportional... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
