| 1863
...how a rule of three sum may be solved geometrically. 9. Proposition 19. Theorem. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** J 0. If the superficial content of a triangle which has a base of 40 feet is 800 feet, what is the... | |
| Euclides - 1864 - 448 páginas
...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... | |
| McGill University - 1865
...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 - 172 páginas
...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... | |
| Thomas Baker (Civil engineer) - 1865 - 232 páginas
...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,... | |
| Robert Potts - 1865 - 528 páginas
...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... | |
| Euclides - 1865 - 402 páginas
...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... | |
| Euclid, Isaac Todhunter - 1867 - 424 páginas
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for **triangles ; therefore universally, similar rectilineal...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.... | |
| Euclid, Isaac Todhunter - 1867 - 426 páginas
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for **triangles ; therefore universally, similar rectilineal...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.... | |
| Robert Potts - 1868 - 410 páginas
...duplicate ratio of their homologous sides : and it has already been proved in triangles: (vi. 19.) **therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides.** AB has to Jf the duplicate ratio of that which AB has to FG: (v. def. 10.) but the four-sided figure... | |
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