| 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... | |
| John Playfair - Geometry - 1836 - 114 pages
...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 - Euclid's Elements - 1837 - 240 pages
...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 - Geometry - 1837 - 390 pages
...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.... | |
| Euclid, Robert Simson - Geometry - 1838 - 416 pages
...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
...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
...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 - Euclid's Elements - 1840 - 84 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... | |
| London City Mission - Christian socialism - 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
...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... | |
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