| Robert Potts - 1879
...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
...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... | |
| Isaac Todhunter - 1880 - 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.... | |
| Oxford univ, local exams - 1880
...middle point of the base to the opposite vertex. z. Euclid VI— XI, and Conic Sections. 10. Similar **figures are to one another in the duplicate ratio of their homologous sides.** Bisect a given triangle by a straight line drawn parallel to the base. 11. The rectangle contained... | |
| James Russell Soley - 1880 - 335 sider
...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
...Prove that АO . OD = BO . 0C (the corners А, C being opposite to one another). 11. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 1. Prove that am x a" = am + ', m and n being positive integers ; and assuming this formula to hold... | |
| 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... | |
| Euclides - 1881
...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... | |
| 1882
...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.... | |
| John Robertson (LL.D., of Upton Park sch.) - 1882
...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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