| Euclides - 1865
...be described upon a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles, having... | |
| McGill University - 1865
...proportion, and show that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours each will... | |
| Thomas Baker (C.E.) - 1865
...greatest angle : theorem, 17 ; any two angles being Rven, the, becomes known : theorem, ' ; similar, **are to one another in the duplicate ratio of their homologous sides:** theorem, 17. Triangular prism, definition of, 52. Triangular fields, method of surveying with chain... | |
| John Playfair - Geometry - 1855 - 317 pages
...similarly described triangle upon the second. BC EF : EF AB BC : DE AB DE : BC BC EF : EF AB DE : EF **PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles,** ing the same ratio to one another that the polygons have ; and the polygon* have to one another the... | |
| James Robert Christie - Mathematics - 1866 - 404 pages
...together with the segmenta of the former will be equal to the square of the radius of the circle. i 3. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 4. If two straight lines be at right angles to the same plane, they shall be parallel to one another.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...Of similar triangles, having the same ratio to one another that the polygons have; and the polygons **are to one another in the duplicate ratio of their homologous sides.** Let ABCDE, FGHKL be similar polygons, and let AB be the side homologous to the side FG : the polygons... | |
| Robert Potts - 1868 - 410 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. **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... | |
| Schools inquiry commission - 1868
...inscribed in a circle is equal to the interior and opposite. 7. Describe a circle about a given square. 8. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** XIX. (Two hours.) Maximum. 1. Translate into French : — Two worthy peasants went together to find... | |
| Euclid - Geometry - 1872 - 261 pages
...AEDCB) may be divided inl» similar triangles, equal in number, and homologous to all. Ana the polygons **are to one another in the duplicate ratio of their homologous sides.** PART 1. — Because in the triangles FGI and AED, the angles G and E are ' equal, and the sides about... | |
| Manchester univ - 1872
...stand. cal angle and the segments into which the line bisecting it divides the base. 4. Similar polygons **are to one another in the duplicate ratio of their homologous sides.** 5. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the... | |
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