 | Euclides - 1816 - 588 pàgines
...may be described upon a 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 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 Mason Good - 1819 - 800 pàgines
...line to describe a rectilineal figure similar, and similarly situated to a given rectilineal figure. 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, having... | |
 | John Playfair - 1819 - 354 pàgines
...may be described upon a given 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,... | |
 | John Playfair - 1819 - 350 pàgines
...may he described upon a given straight line similar to one given, and so^ou. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homOlogousjides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let... | |
 | Anthony Nesbit - 1824 - 476 pàgines
...both ; then the 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 - 1046 pàgines
...be described upon a given straight line similar to one given, and so on. Which was to be done. PHOP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homo¡ogout sides. Let ABC, DEF be similar triangles, having the angle В equal to the angle E, and... | |
 | Euclid - 1826 - 234 pàgines
...described similar and similarly situated to the given rectilineal figure CE. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. EF, and let BC be the side homologous to EF ; then the triangle ABC has a duplicate ratio to the triangle... | |
 | Euclides - 1826 - 226 pàgines
...the angle ABG equal to that at CDF; hence the remaining angle. AG в is QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. EF, and let вс be the side homologous to EF ; then the triangle ABC has a duplicate ratio to the... | |
 | George Lees - 1826 - 276 pàgines
...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 - 546 pàgines
...similar to one given, and so on. Which was 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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
