 | Euclides - 1865 - 402 pagina’s
...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... | |
 | Robert Potts - 1865 - 528 pagina’s
...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 bo to BC, as... | |
 | Thomas Baker (Civil engineer) - 1865 - 278 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 - 332 pagina’s
...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 - 174 pagina’s
...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 - 428 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 - 426 pagina’s
...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... | |
 | How - 1868 - 296 pagina’s
...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... | |
 | Robert Potts - 1868 - 434 pagina’s
...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 - 532 pagina’s
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
