| Robert Potts - 1879
...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... | |
| Robert Potts - 1879
...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... | |
| James Russell Soley - 1880 - 335 pagina’s
...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... | |
| Isaac Todhunter - 1880 - 400 pagina’s
...In like manner it may be shewn that similar four-sided figures, or figures of any number of sides, **are to one another in the duplicate ratio of their homologous sides** ; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures... | |
| Euclides - 1881
...drnwn from the point D to its different nngles. The proof In thus also more easlly established. PROP. **XIX. THEOREM. Similar triangles are to one another...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 to BC,... | |
| 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.) - 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.... | |
| 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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