| University of Sydney - 1901
...forty seconds to one minute. 7. Triangles of the same altitude are to one another as their bases. 8. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 0. Find the diameter of a cylindrical pipe, two feet long, containing a volume of 000 cubic inches.... | |
| 1903
...the special case when AB is one side of an equilateral triangle inscribed in the circle. 8. Show that **similar triangles are to one another in the duplicate ratio of their homologous sides.** ABC is a triangle. Two circles are drawn, one to touch Alt at A and to pass through C, the other to... | |
| Samuel Bower Sinclair - Education - 1903 - 126 pages
...method of teaching the preposition is superior to the former method is as true as the statement that **"similar triangles are to one another in the duplicate ratio of their homologous sides."** And yet notwithstanding all this there are many good teachers who are vigorously opposed to all study... | |
| Euclid - Euclid's Elements - 1904 - 456 pages
...FE jular to the A FD. FE.' ewn that DE. CF, ED. DFE, vI. 4. V. 14. VI. 4. PROPOSITION 19. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** A Let ABC, DEF be similar triangles, having the L ABC equal to the L DEF, and let BC and EF be homologous... | |
| 1905
...Describe an isosceles triangle having each of the angles at the base double of the vertical angle. 4. **Similar triangles are to one another in the duplicate ratio of their homologous** titles. 5. If any similar rectilineal figure be similarly described on the three sides of a right-angled... | |
| Great Britain. Education Department. Department of Science and Art - 1908
...correspond, show that the remaining angles are either equal or supplementary. (30) 44. Show that the areas of **similar triangles are to one another in the duplicate ratio of their homologous sides.** Show that similar triangles are to each other in the same ratio as the areas of their inscribed circles.... | |
| Industrial arts - 1879
...beautifully demonstrated in Euclid's Sixth Book, Propositions 19 and 20, that " similar rectilinear figures **are to one another in the duplicate ratio of their homologous sides"** — that is, that these figures — meaning the areas of them— are to one another as the squares... | |
| Trinity College (Dublin, Ireland) - 1919
...Prove that a right-angled triangle may be divided into two triangles each similar to the whole. 7. **Similar triangles are to one another in the duplicate ratio of their** corresponding sides. Practical. 8. Construct a square containing 6 square inches without extracting... | |
| 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... | |
| Education - 1852
...circle. 8. It is required to describe a square that shall be equal to a given rectilineal figure. 9. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 12. — EXAMINATION PAPER in Mensuration and the Rudiments of Mechanics. April mh, 1852. TIME : ONE... | |
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