| United States. Congress. Senate - United States - 1880
...point on the curve. I the tangents at A, B in D, E ; prove that AB is a mean proportional betwi 12. **Similar triangles are to one another in the duplicate ratio of their** sides. TRIGONOMETRY. Examiner,— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
| Sir Norman Lockyer - Electronic journals - 1886
...book. To mention one only- the proof which he judiciously gives of the fundamental proposition that " **similar triangles are to one another in the duplicate ratio of their homologous sides** " depends directly on the ist Proposition only of the Sixth Book, instead of the chain being carried... | |
| Dalhousie University - 1887
...YEAR. APRIL 18.— 10 AM TO 1 PM 1. Explain " duplicate ratio " and prove that, " similar tranples **are to one another in the duplicate ratio of their homologous sides."** 2. If four straight lines be proportionals, the similar rectilineal figures descriled on them shall... | |
| Canada. Department of the Interior - 1888
...rectangles under the sides containing the equal angles. 15. From tho last deduce tho proposition " **similar triangles are to one another in the duplicate ratio of their homologous sides.''** No. of Mark-. 13 10 13 13 li 13 13 13 PLANE TRIGONOMETRY. Time, 3 hours. 1. Find the number of degrees... | |
| E. J. Brooksmith - Mathematics - 1889
...will touch the circle circumscribing ABC in the point A. 8. Describe a circle about a given square. 9. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 10. In a right-angled triangle if a line be drawn from the right angle perpendicular to the base it... | |
| New Brunswick. Board of Education - Education - 1889
...another, are proportionals ; and those which are opposite to the equal angles, are homologous sides. fi. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** T. ALGEBRA. Time, 1 hour SO mitt. Ei-Jiibit the work. 1. Find the value of x in each of the following... | |
| William Ernest Johnson - Plane trigonometry - 1889 - 504 pages
...product of two lengths. This is equivalent to Euclid's statement that " Similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides."** 24. The area of any rectilineal figure may be found by dividing it into triangles : and applying the... | |
| Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 pages
...one another, and shall have those angles equal about which the sides are proportionals. 6. Prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** If ABC be an obtuse-angled triangle, having the obtuse angle BAC; and if AD, AE, be drawn to meet BC... | |
| |