| Euclides - 1816 - 528 pages
...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 - 740 pages
...line to describe a rectilineal figure similar, and similarly situated to a given rectilineal figure. **Prop. XIX. Theor. Similar triangles are to one another...divided into the same number of similar triangles,** having the same ratio to one another that the polygons have ; and the polygons have to one another... | |
| John Playfair - 1819 - 317 pages
...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 - Euclid's Elements - 1819 - 333 pages
...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... | |
| Euclides - 1821 - 294 pages
...*£-•& follows ex aquo, from the 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... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 pages
...any triangle upon the first to a similar and similarly described triangle upon the second. PROP. T&. **THEOR. SIMILAR polygons may be divided into the same number of similar triangles,** having the same ratio to one another that the polygons have; and the polygons have to one another the... | |
| Anthony Nesbit - Measurement - 1824 - 434 pages
...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 - Mathematics - 1825 - 372 pages
...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 - 236 pages
...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 pages
...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... | |
| |