 | Euclid - Euclid's Elements - 1833 - 216 pages
...to FIL as AC to KC, or in <B8>5Def. 10the duplicate ratio of AC to FL (8). PROP. XX. THEOR. Fig. 25. Similar polygons may be divided into similar triangles,...duplicate ratio of their homologous sides. Part 1. For the angles G and E are equal, and the (i) Hypoth. sides about them proportional (1), therefore... | |
 | Ireland commissioners of nat. educ - 1834 - 370 pages
...triangles being to each other as the squares of their homologous sides, (19. VI.) we Cor. As similar polygons are to each other in the duplicate ratio of their homologous sides, (20. VI.) it follows that the square of the side of any polygon, multiplied by the area of a similar... | |
 | Mathematics - 1836 - 366 pages
...into equal triangles by lines drawn from a point within it to its four corners. 34. Similar triangles are to each other in the duplicate ratio of their homologous sides. 35. In a given rectangle inscribe another, whose sides shall bear to each other a given ratio. 36.... | |
 | Euclides - 1840 - 82 pages
...Similar polygons may be divided into the same number of similar triangles, each similar pair of which are proportional to the polygons; and the polygons are...in the duplicate ratio of their homologous sides. COR. 1.—It is obvious that what is here demonstrated of similar polygons may be in like manner proved... | |
 | Euclides - 1840 - 192 pages
...(ABCDE, FGHKL) may be divided into the same number of similar triangles, each similar pair of which are proportional to the polygons; and the polygons are...in the duplicate ratio of their homologous sides. Draw the lines AC, AD and FH, FK, resolving the polygons into triangles : and because the polygons... | |
 | Joseph Denison - 1846 - 106 pages
...approach towards similarity, and therefore when they coincide in A, they become altogether similar, and are to each other in the duplicate ratio of their homologous sides. But the question recurs, what useful inference can be drawn from this lemma, which amounts to no more... | |
 | Cambridge univ, exam. papers - 1847 - 40 pages
...the tangent planes. FRIDAY, January 8, 1847. Nine o'clock to half-past Eleven. 1. Similar triangles are to each other in the duplicate ratio of their homologous sides. a. Draw a straight line perpendicular to a plane from a j>iven point above it. 3. Find the positive... | |
 | London univ - 1852 - 358 pages
...are equal, the circumferences on which the angles stand will be equal likewise. 6. Similar triangles are to each other in the duplicate ratio of their homologous sides. What is the ratio of two similar triangles, the homologous sides of which are 3, 12, respectively ?... | |
 | War office - 1861 - 714 pages
...R— 4 2. Define duplicate ratio ; express the duplicate ratio of 3 : 5. Prove that similar triangles are to each other in the duplicate ratio of their homologous sides. 3. Prove that the second term of the expansion of (!+#)" is nx. Write down the 7th term of 4. Given... | |
 | Euclides - 1865 - 402 pages
...proportional, are equal • I C. Relating to Similar Polygons and Rectilineal Figures in ge?ieral. 1. Similar polygons may be divided into similar triangles...other in the duplicate ratio of their homologous sides . VI. 20. 2. Kectilineal figures which are similar to the same figure are similar also to each other... | |
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... polygons are to each other in the duplicate ratio of their homologous sides. 
