| John Playfair - Geometry - 1836 - 114 pages
...may be described upon a given straight line similar to one given, and so on. 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... | |
| Mathematics - 1836 - 472 pages
...by the extremes be equal to the square of the mean, the three straight lines are proportionals. XIX. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Сок. From this it is manifest, that if three straight lines be proportionals, as the first is to... | |
| Euclid - Geometry - 1837 - 410 pages
...more sides may be described on a given straight line, similar to one given : 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 angles B and E equal, and AB : BC : : DE : EF, so that... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 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... | |
| 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 - 194 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... | |
| Euclides - 1841 - 378 pages
...similarly situated, to 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 simi-lar triangles are to one another as the squares of their homologous... | |
| |