| Robert Potts - 1864
...described upon a given straight line similar to one given, and so on. QE r. 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... | |
| Alexander Kennedy Isbister - 1865
...describe a rectilineal figure similar, and similarly situated, to a given rectilineal figure. Prop. **19. Similar triangles are to one another in the duplicate ratio of their homologous sides.** Cor. If three straight lines be proportionals as the first is to the third, so is any triangle upon... | |
| 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 (Civil Engineer) - 1865 - Liczba stron: 232
...then, the triangle ABC is to the triangle AED as the square of AB is to I lie. square of AE : that is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous,... | |
| 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... | |
| James Robert Christie - 1866 - Liczba stron: 404
...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 - 1867 - Liczba stron: 400
...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 - Liczba stron: 410
...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... | |
| How - 1868
...English, Latin, and Greek tongues, and understood (what few lads of my age then understood) , that ' **similar triangles are to one another in the duplicate ratio of their homologous sides."** In a word, then, I was something of a scholar, and I may well be forgiven if I were a little proud... | |
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