| Euclides - 1864 - 448 Seiten
...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... | |
| McGill University - 1865 - 332 Seiten
...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... | |
| Thomas Baker (Civil engineer) - 1865 - 278 Seiten
...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... | |
| Euclides - 1865 - 402 Seiten
...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,... | |
| Robert Potts - 1865 - 528 Seiten
...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... | |
| James Robert Christie - 1866 - 426 Seiten
...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... | |
| How - 1868 - 296 Seiten
...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... | |
| Schools inquiry commission - 1868 - 532 Seiten
...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... | |
| Robert Potts - 1868 - 434 Seiten
...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... | |
| Sir Norman Lockyer - 1904 - 688 Seiten
...the liberty which each of these excellent works takes with Euclid's Prop, ig, Bk. vi.- — " similar **triangles are to one another in the duplicate ratio of their homologous** sides " — mysterious but high-sounding- to countless generations of schoolboys. Here it is, in identical... | |
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