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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 95
by John Mason Good - 1813
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Schultze and Sevenoak's Plane Geometry

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...
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The Dublin University Calendar, Volume 1

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...
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English Mechanic and World of Science: With which are ..., Volume 28

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...
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Schultze and Sevenoak's Plane and Solid Geometry

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...
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The Dublin University Calendar, Volume 1

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...
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Schultze and Sevenoak's Plane and Solid Geometry

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...
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Education in Scotland

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...
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Report of the Minister of Education

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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The Durham University Journal, Volume 1

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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