 | James Maurice Wilson - 1878 - 450 pages
...one another in the ratio compounded of the ratios of their bases and of their altitudes. THEOREM 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles having the angles at A, B, C respectively equal to the angles at... | |
 | Robert Potts - Algebra - 1879 - 672 pages
...triplícala ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. (Eue. VI. 19.) Let а, Ь, с ; a', I', c' represent the sides of two similar triangles ; Then, because... | |
 | Robert Potts - 1879 - 668 pages
...triplicate ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. (Eue. VI. 19.) Let а, Ь, с ; a', V, ¿ represent the sides of two similar triangles ; Then, because... | |
 | Euclides, James Hamblin Smith - 1879 - 376 pages
...or more sides may be described, on a given line, similar to a given fig. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their houwlogous sides. H Let ABC, DEF be similar A s, haying L s at A, B, C= L s at D, E, F respectively,... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...similarly situated to a given rectilineal figure of six sides ; and so on. y. KF PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BO... | |
 | James Russell Soley - Naval education - 1880 - 346 pages
...BC, AC meet the tangents at A, B in D, E; prove that AB is a mean proportional between AD, BE. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. TRIGONOMETRY. Examiner.— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 pages
...inscribe a triangle equiangular to a given triangle. Show how to inscribe a circle in a given rhombus. 9. Similar triangles are to one another in the duplicate ratio of their homologous sidos. The sides of a regular hexagon ABCDEF are produced both ways, forming with each other six points... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...point D to its different nngles. The proof In thus also more easlly established. PROP. XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, and let the angle ABC be equal to the angle DEF, and let AB be... | |
 | Education, Higher - 1884 - 538 pages
...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. . / 16. "From the same point in a given plane, there cannot be two straight lines at right angles to... | |
 | John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...to the square on the line which meets the circle, the line which meets the circle shall touch it. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. TnEEE-nouE PAPEE. 1. Quote the passages in Genesis which relate to a SAVIOUE, as nearly as you can... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
