 Similar polygons may be divided into the same number 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.  Education in Scotland - Page 223by Great Britain. Scottish Education Dept - 1896Full view - About this book
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...and similarly described triangle upon the second. PROPOSITION XX. THEOREM. Similar polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homo-' logous sides have. Let ABCDE, FGHKL... | |
 | Eucleides - 1860 - 396 pages
...under the (. means. The lines are proportionals. The lines are proportionals. CONSEQUENCES. They may be divided into the same number of similar triangles,...same ratio to one another that the polygons have. The polygons have to one another the duplicate ratio of that which their homologous sides have. /Their... | |
 | 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... | |
 | John Playfair - Geometry - 1860 - 334 pages
...their homologous side* tng r polygons may be divided into the same number of similar triangles, havthe same ratio to one another that the polygons have; and the polygons have. Let ABCDE, FGHKL, be similar polygons, and let AB be the homologous side to FG: the polygons... | |
 | Euclides - 1861 - 464 pages
...are as the squares of the sides; and 2a : Ia = 4 : 1. PROP. 20. — THEOR. Similar Polygons may be divided into the same number of similar triangles,...one another that the polygons have, and the polygons have to one another the duplicate ratio of that which their homologous sides have. Similar polygons... | |
 | 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 - 1863 - 122 pages
...and this has been proved of triangles (VI. 19); therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2.-—If to AB and FG, two of the homologous sides of the polygon, a third proportional M bo taken... | |
 | 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... | |
 | 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 - 1864 - 448 pages
...and similarly described triangle upon the second. PROPOSITION XX. THEOREM. Similar polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have, Let ABCDE, FGHKL... | |
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