| University of Durham - 1879 - 158 páginas
...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... | |
| Great Britain. Parliament. House of Commons - 1861 - 588 páginas
...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... | |
| 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... | |
| University of Cambridge - 1830 - 508 páginas
...intensity. SATURDAY MoRNING .... 9 to 11. First, Second, TJiird and Fourth Classes. 1. SIMILAR triangles **are to one another in the duplicate ratio of their homologous sides.** t 2. If two straight lines meeting one another, be parallel to two straight lines which meet one another,... | |
| Wales univ, univ. coll. of Wales - 1878 - 188 páginas
...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 - 1844 - 550 páginas
...from (E), and u the distance of E' from E. FRIDAY, January 5, 18-14. 9. ..Hi. 1. SIMILAR triangles **are to one another in the duplicate ratio of their homologous sides.** 2. Every solid angle is contained by plane angles which are together less than four right angles. 3.... | |
| University of St. Andrews - 1891 - 440 páginas
...at the centres of equal circles from the ratio of the arcs on which they stand. 6. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** To construct a triangle similar to a given triangle and equal to half of it. 7. If two straight lines... | |
| Education Department - 1879
...which between two given straight lines shall be divided in a given proportion. 5. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Show that they are also in the duplicate ratio of the radii of their circumscribing circles. 6. When... | |
| University of Cambridge - 1828 - 454 páginas
...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... | |
| Euclid - 452 páginas
...10 corresponding sides. And it was also proved in the case of triangles ; therefore also, generally, **similar rectilineal figures are to one another in the duplicate ratio of** the corresponding sides. QED i. in the same ratio as the wholes. The same word ip.iX0701 is used which... | |
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