 | 1836 - Liczba stron: 488
...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... | |
 | John Playfair - 1836 - Liczba stron: 148
...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 sides a third proportional M be taken, AB has (15. Def.... | |
 | Andrew Bell - 1837 - Liczba stron: 290
...proportionals, they are similar to one another ; and in the same manner, a rectilineal figure of six or more sides may 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... | |
 | Euclid, James Thomson - 1837 - Liczba stron: 410
...already been proved (VI. 19.) in respect to triangles. Therefore, universally, similar rectilineal 6gures are to one another in the duplicate ratio of their homologous sides. Cor. 2. If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V. def.... | |
 | Robert Simson - 1838 - Liczba stron: 434
...proportionals, they are similar to one another ; and in the same •manner a rectilineal figure of six or more sides may be described upon a given straight line...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 BD, as DE to EF, so... | |
 | Euclides - 1838 - Liczba stron: 264
...angles proportionals, they are similar to one another. In a similar manner a rectilineal figure of six sides may be described upon a given straight line...PROP. XIX. THEOR. Similar triangles are to one another as the squares of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal... | |
 | Euclides - 1840 - Liczba stron: 82
...line to describe a 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... | |
 | Joseph Denison - 1840 - Liczba stron: 96
...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 - Liczba stron: 620
...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 - Liczba stron: 192
...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... | |
| |
SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
