 | Euclides - 1816 - 588 pages
...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 - Circle-squaring - 1819 - 350 pages
...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 - 354 pages
...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 - 294 pages
...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 - Surveying - 1824 - 476 pages
...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 - Mathematics - 1825 - 1046 pages
...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 - 234 pages
...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 - 226 pages
...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 - 276 pages
...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 - Trigonometry - 1827 - 546 pages
...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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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
