| John Playfair - Circle-squaring - 1819 - 333 pages
...ot Sis, or more, sides 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... | |
| John Mason Good - 1819
...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... | |
| Euclides - 1821
...*£-•& 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... | |
| 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
...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. Which was to be done.** PHOP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homo”ogout... | |
| 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 : EF, so that... | |
| Euclid - 1826 - 180 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
...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... | |
| Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...to one another: and in the same manner a reetilineal figure of six, or more, sides may be deseribed **upon a given straight line similar to one given, and so on.** Whieh was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplieate ratio... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...angles proportionals, they are similar to one another. In the same manner a rectilineal figure of six **sides may be described upon a given straight line...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... | |
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