| Euclides - 1863
...and this has been proved of triangles (VI. 19); therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** Cor. 2.-—If to AB and FG, two of the homologous sides of the polygon, a third proportional M bo taken... | |
| 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... | |
| Thomas BAKER (Civil Engineer) - 1865 - 232 pagina’s
...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,... | |
| 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... | |
| James Robert Christie - 1866 - 404 pagina’s
...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 - 400 pagina’s
...qf 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 ABCDE,... | |
| Euclid, Isaac Todhunter - 1867 - 400 pagina’s
...; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
| 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... | |
| 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... | |
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