 | Euclid, Isaac Todhunter - 1883 - 400 sider
...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.... | |
 | Mathematical association - 1883
...ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
 | John Harris - 1884 - 144 sider
...the square on A c, including the diagonal A e of the square on A b. Then because similar trianglcs are to one another in the duplicate ratio of their homologous sides (Euclid VI. 19) and the triangles A eb and Afc are similar, the " '' triangle A eb has the ratio to... | |
 | Dalhousie University - 1884
...and 2. GEOMETRY AND MENSURATION.— SECOND YEAR. APRIL 15iH.— 10 AM TO 1 p. M. I. Similar triangles are to one another in the duplicate ratio of their homologous sides. Prove this : and represent the ratio of the two triangles by means of two straight lines whereof one... | |
 | Euclides - 1884
...that these triangles have each to each the same ratio which the polygons have ; and that the polygons are to one another in the duplicate ratio of their homologous sides. Join BE, EC, GL, LH. Because the polygon ABCDE is similar to the polygon FGHKL, .-. LA = LF, and BA... | |
 | Sir Norman Lockyer - 1886
...only- the proof which he judiciously gives of the fundamental proposition that " similar triangles are to one another in the duplicate ratio of their homologous sides " depends directly on the ist Proposition only of the Sixth Book, instead of the chain being carried... | |
 | Association for the Improvement of Geometrical Teaching - 1888
...bisect the sides BC, AC in E and F. Compare the areas of the triangles AGB, FGE. THKOR. 12. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Let ABCD, HKLM be two similar figures, having the sides AB, HK homologous : then shall the figure ABCD... | |
 | Canada. Department of the Interior - 1888
...the sides containing the equal angles. 15. From tho last deduce tho proposition " similar triangles are to one another in the duplicate ratio of their homologous sides.'' No. of Mark-. 13 10 13 13 li 13 13 13 PLANE TRIGONOMETRY. Time, 3 hours. 1. Find the number of degrees... | |
 | William Ernest Johnson - 1889 - 504 sider
...have been proportional to the product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures are to one another in the duplicate ratio of their homologous sides." 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
