| Euclides, James Hamblin Smith - 1879
...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 - 400 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 - 335 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
...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 - 1881
...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
...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
...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... | |
| 1882
...than a right angle. 4. Inscribe a regular equilateral and equiangular pentagon in a given circle. 5. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 6. Two circles whose centres are A and B, intersect in C and D, shew that AB bisects CD at right angles.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...proportionals ; therefore they are similar to one another. [VI. Definition 1, 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 BC... | |
| Mathematical association - 1883
...to one another the 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... | |
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