| Euclides - 1816 - 528 sider
...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... | |
| John Playfair - 1819 - 333 sider
...the same has already been proved of triangles : therefore, universally similar rectilineal figuree **are to one another in the duplicate ratio of their...sides. COR. 2. And if to AB, FG, two of the homologous** sidei, a third proportional M be taken, AB has (def. 11. 5.) to M the duplicate ratio of that which... | |
| John Playfair - 1819 - 317 sider
...straight line similar Co 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.** D Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC,... | |
| Euclides - 1821
...proportionality of the sides about 'the «£^.s composing them. 52 PROP. XIX. THEOR. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Assume on the greater base from either extremity a third proportional to that base and the homologous... | |
| Anthony Nesbit - 1824 - 434 sider
...triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles **are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19. Simp. IV. 24. Em. II. BC THEOREM XIV. In any triangle ABC, double the square of a line... | |
| Peter Nicholson - 1825 - 372 sider
...Coa. 1. In like manner, it may Le proved, that p-milar four sided figures, or of any number of suies, **are one to another in the duplicate ratio of their...2. And if to AB, FG, two of the homologous sides, a** third proportional M be taken, AB has ( 10. de', i.) to II the duplicate ratio ofthat which AB has... | |
| Euclid - 1826 - 180 sider
...duplicate ratio of their homologous sides ; and it has been already proved in triangles. Wherefore **universally similar rectilineal figures are to one...in the duplicate ratio of their homologous sides.** QB p. 2. And if to AB, FG, we take a third proportional x ; AB has to xa duplicate ratio of that which... | |
| Euclides - 1826
...second. duplicate ratio of their homologous sides; and it has been already proved in triangles. Wherefore **universally similar rectilineal figures are to one...in the duplicate ratio of their homologous sides.** QEF Deduction. Any regular polygon inscribed in a circle, is a mean proportional between the inscribed... | |
| George Lees - 1826
...triangles, &c. QED Cor. The same may be demonstrated of parallelograms. PROP. XI. THEOREM. Simi'ar 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 : BC : : DE... | |
| Robert Simson - 1827 - 513 sider
...to be done. • 12 Def. •11.6. * 16. 5. t Co1utr. • 11. 5. 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... | |
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