| Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 304 pages
...base of a similar triangle is 6 in., lind the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two **similar polygons may be divided into the same number of similar triangles** similar each to each and similarly placed. Given polygon ABCDE ~ polygon A'B'C'D'£'. To prove A ABC... | |
| Trinity College (Dublin, Ireland) - 1914
...these equal angles are reciprocally proportional. 6. Prove that similar polygons can be divided up **into the same number of similar triangles, having...same ratio to one another that the polygons have.** 7. Parallelograms which are equiangular are to one another in the ratio which is compounded of the... | |
| 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... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 457 pages
...base of a similar triangle is 6 in., find the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two **similar polygons may be divided into the same number of similar triangles** similar each to each and similarly placed. Given polygon ABCDE ~ polygon A'B'C'D'£'. To prove A ABC... | |
| 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... | |
| Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 457 pages
...base of a similar triangle is 6 in., find the homologous altitude. PROPOSITION XXIV. THEOREM 313. Two **similar polygons may be divided into the same number of similar triangles** similar each to each and similarly placed. Given polygon ABCDF ~ polygon A'B'C'D'E'. To prove A ABC... | |
| 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... | |
| 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... | |
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