| Great Britain. Scottish Education Dept - 1896
...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.** Describe a polygon which shall be similar to a given polygon, but shall have half its area. 8. Draw... | |
| University of Durham - 1879
...angle at the base. 6. Define similar triangles, duplicate ratio : — Prove that similar triangles **are to one another in the duplicate ratio of their homologous sides.** 8. Define a conic section, the tangent to a conic section : — If S be the focus, P any point on the... | |
| 1870
...triangles, having ! h.- same ratio to one another that the polygons Jan. 1870. have7. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 8. If from any point without a circle lines be drawn touching it, the angle contained by the tangents... | |
| University of Bombay - 1903
...T, so that DX and DY may be equal. 9. Give the definition of duplicate ratio. 10 Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Deduce that the duplicate ratios of equal ratios are equal, and also that similar triangles are to... | |
| Manchester univ - 1877
...that equal magnitudes have the same ratio to the same magnitude and conversely. 10. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Bisect a triangle by a line perpendicular to one of the sides. 11. Enunciate and prove the general... | |
| 1904
...liberty which each of these excellent works takes with Euclid's Prop. 19, Bk. vi. — " similar triangles **are to one another in the duplicate ratio of their homologous sides** " — mysterious but high-sounding to countless generations of schoolboys. Here it is, in identical... | |
| Samuel Greatheed, Daniel Parken, Theophilus Williams, Josiah Conder, Thomas Price, Jonathan Edwards Ryland, Edwin Paxton Hood - 1814
...have met it before. The demonstration of the 19th Prop, of Euclid's Oth book, ie " Similar triangles **are to one another in the duplicate ratio of their homologous sides,"** requires the previous or the syn hro nous establishment of Props, vi. 11, v. 10, v. 11, vi. 15., and\i.... | |
| Wales univ, univ. coll. of Wales - 1878
...and their difference is equal to the difference of their squares. 12. Prove that similar triangles **are to one another in the duplicate ratio of their homologous sides.** 13. If two chords of a circle intersect, the rectangles contained by the segments are equal. 14. ABC... | |
| University of Cambridge - 1828
...SATURDAY MORNING. ... 9 o'clock to 11. Pint, Second, Third and Fourth Classes. • 1. SIMILAR triangles **are to one another in the duplicate ratio of their homologous sides.** 2. If a straight line be at right angles to a plane, every plane passing through that straight line... | |
| Cowley Oxon, dioc. school - 1860
...circumference upon the same base, that is upon the same part of the circumference. 5. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 6. If two triangles have two sides of the one equal to two sides of the other, and have likewise their... | |
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