| 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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