 | 1835 - Liczba stron: 684
...the homologous sides of the figures, are to one another, each to each, in the same ratio. But similar triangles are to one another in the duplicate ratio of their homologous sides. Therefore the triangles into which the figure А В С DKF is divided, are to the similar triangles... | |
 | Euclid - 1835 - Liczba stron: 540
...the same has already been proved of triangles. Therefore, universally, «'milar 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, h lO.def. 5. a third proportional M be taken,... | |
 | John Playfair - 1836 - Liczba stron: 488
...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...having the angle B equal to the angle E, and let AB be to BC, as A DEtoEF,sothat the side BC is homologous to E Fa ; the triangle ABC has to the triangle... | |
 | 1836 - Liczba stron: 488
...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.... | |
 | 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.... | |
 | Andrew Bell - 1837 - Liczba stron: 290
...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. — If to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (V.... | |
 | Euclides - 1838 - Liczba stron: 264
...so on. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another as the squares of their homologous sides. Let ABC, DEF be similar...having the angle B equal to the angle E, and let AB be to BC, as DE to EF, «9Def 5 so t"1at tne S'cle BC may be* homologous to EF: the triangle ABC shall... | |
 | Euclides - 1840 - Liczba stron: 82
...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
...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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
