| Robert Potts - 1860 - 361 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.** CoB. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vI. 11.) AB... | |
| EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 608 páginas
...The sides about the equal angles of equiangular triangles are proportionals. 12. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** LOGIC. I.—LOWER STANDARD. What ii the use of words ? Explain First and Second Intention. 2. Give... | |
| War office - 1861 - 714 páginas
...semicircle is greater than a right angle. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 2. Describe a rectilineal figure which shall be similar to one given rectilineal figure and equal to... | |
| Euclides - 1861 - 460 páginas
...Maps, and Geometrical Drawings of every kind. PROP. 19. — THEOR. (Very important.) Similar triangles **are to one another in the duplicate ratio of their homologous sides** ; ie, as the squares of their like sides. CON. 11, VI. DEM. Def. 12, V.— 16, V. If four Ms of of... | |
| 1863 - 298 páginas
...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 - 1863 - 118 páginas
...rectilineal figure of six sides; and so on. QEF PEop. XIX. (THEOHEM.)—Similar triangles (ABC, DEF) **are to one another in the duplicate ratio of their homologous sides.** Let the angle ABC be equal to the angle DEF, and let AB be to BC as DE to EF, so that the side BC is... | |
| 1863 - 404 páginas
...the triangle ABC. I should mention 2 to draw ox parallel to BG. Now we know that similar triangles **are to one another in the duplicate ratio of their homologous sides** . • . BGC : oxC::BGa : ox', or 47.04 : 42::11.2" : 112 the square root of which is 10.583+=ox, or... | |
| 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... | |
| Thomas Baker (Civil engineer) - 1865 - 276 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,... | |
| 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... | |
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