 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...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 - 612 pages
...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 pages
...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 - 464 pages
...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... | |
 | Architecture - 1863 - 300 pages
...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 - 122 pages
...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... | |
 | Education - 1863 - 406 pages
...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 pages
...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 - 278 pages
...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 - 174 pages
...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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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
