 | Joseph Denison - 1840 - 84 sider
...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... | |
 | London City Mission - 1840
...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,... | |
 | Euclides - 1840
...rectilineal figure similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles, each similar... | |
 | Euclides - 1840
...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 - 1841 - 184 sider
...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... | |
 | Joseph Denison - 1841 - 184 sider
...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 - 1841 - 351 sider
...sides, and it has already been proved* in triangles: therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous * 11. 6. sides, a third* proportional M be taken, AB... | |
 | Euclides - 1842
...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... | |
 | John Playfair - 1842 - 317 sider
...the same has already been proved of triangles : therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. , COR. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def.... | |
 | William Pease - 1843 - 68 sider
...similar polygon, equal to the sum of the given polygons. For, " universally, similar'rectilineal figures are to one another in the duplicate ratio of their homologous sides." Duplicate ratio is the ratio of the square of one quantity to the square of another. EXAMPLES. 1. Make... | |
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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
