| University of Durham - 1879
...eight times either 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... | |
| Edinburgh Mathematical Society - Electronic journals - 1900
...extremes be equal to the square on the mean, the three straight lines are proportional. EUCLID VI. 19. **Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC,** DEFbetwu similar triangles, having the angles at В, С equal to the angles at E, F respectively :... | |
| Anthony Nesbit - Measurement - 1859 - 450 pages
...both ; then the triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. "3 c VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XTV. In any triangle the double of the square... | |
| Manchester univ - 1877
...Explain this. Prove 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... | |
| 1870
...Di.i'AUTM i \r. 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... | |
| Great Britain. Parliament. House of Commons - Bills, Legislative - 1861
...describe a segment of a circle, which Khali contain an angle equal to a given rectilineal angle. 3. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 4. Investigate a rule for finding the greatest common measure of two algebraical expressions. 5. Reduce... | |
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