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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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Plane and Solid Geometry

Arthur Schultze, Frank Louis Sevenoak - Geometry - 1902 - 370 pages
...and the lines joining their homologous vertices meet in a point. PROPOSITION XXVI. THEOREM 303. Two similar polygons may be divided into the same number of similar triangles similar each to each and similarly placed. >zi A* ^^ E E' Hyp. Polygon ABCDE ~ polygon A'B'C'D'E'....
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The Possibility of a Science of Education

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...
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Manual

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...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

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...
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Annual Report of the Commissioners ..., Volume 71

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...
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Syllabus of Plane Geometry: (corresponding to Euclid, Book I-VI) ; Prepared ...

Cora Lenore Williams - Geometry - 1905 - 42 pages
...corresponding sides proportional. ing angles equal and their corresponding sides proportional. Prop. 115. Similar polygons may be divided into the same number of similar triangles. Prop. 116. Polygons similar to the same polygon are similar to each other. Prop. 117. If in a right-angled...
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Science Examination Papers

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....
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Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Plane - 1910 - 263 pages
...KF BC+CD + DE + EA _ AB FG + GH+ HJ + JK+ KF FG ' § 363 §335 PROPOSITION XXVI. THEOREM. 376. Two similar polygons may be divided into the same number of similar triangles, similarly placed. Given two similar polygons, ABCDE and FGHKL. To prove As ABC, ACD, etc., similar,...
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Elements of Solid Geometry

William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 110 pages
...homologous altitudes of two similar triangles have the same ratio as any two homologous sides. 376. Two similar polygons may be divided into the same number of similar triangles, similarly placed. 391. The square of the x hypotenuse of a right triangle is equal to the sum of the...
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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 ABCDE ~ polygon A'B'C'D'E'. To prove A ABC...
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