 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...•. AD •. •. JIE . AC, wbich is the case when the line DC is parallel to HE. THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides. Demonstration. Let the angle A = D (Jig. 122), and the an-Fie. 122. gle B — E, then, by the preceding... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...AB : AD : : AE : AC ; which would happen if. DC were parallel to BE. PROPOSITION XXV. THEOREM. Two similar triangles are to each other as the squares of their homologous sides. Let the angle A be equal to D, and the A. angle B=E. Then, first, by reason of the equal angles A and... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...or if AB : AD : : AE : AC, which is the case when the line DC is parallel to BE. THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides. Demonstration. Let the angle A = D (fig. 122), and the an- Fig. i«; gle B = E, then, by the preceding... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...x AE. AB : AD : : AE : AC, which is the case when the line DC is parallel to BE. THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides. Demonstration. Let the angle A = D (fig. 122), and the an- Fig. 12£ gle B — E, then, by the preceding... | |
 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...angles, which the student will not find much difficulty in demonstrating. PROPOSITION XVII. THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let the triangles ABC, DEF be similar, and let BC, EF be homologous sides ; that is, let the angles... | |
 | Francis Joseph Grund - Geometry, Plane - 1830 - 274 pages
...hypothenuse equals in area the two squares constructed upon the two sides, which include the right angle. 20. The areas of similar triangles are to each other, as the squares constructed upon the sides opposite to the equal angles, and also as the squares upon the heights of... | |
 | Francis Joseph Grund - Geometry, Plane - 1834 - 212 pages
...query, can you determine the proportion which the areas of similar triangles bear to each other ? A. The areas of similar triangles are to each other as the squares upon the corresponding sides. Q. How can you prove this, for instance, of the two similar triangles... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...art. 181, HP : PI= EF : FG, whence, on account of the common ratio HP : PI, — EF : FG. 266. Theorem. Similar triangles are to each other as the squares of their homologous sides. Demonstration. In the similar triangles ABC, A'B'C (fig. 109), we have, by art. 199, CE : CE' = AB... | |
 | Joseph Denison - Euclid's Elements - 1840 - 96 pages
...fc k But ab and ed are any two right lines ; wherefore, &c.— QED PROPOSITION XXXVI. — THEOREM. Similar triangles are to each other as the squares of their homologous sides. Let abe and ade be two similar triangles ; then will the triangle abe be to the triangle ade, as the... | |
 | Charles Davies - Geometrical drawing - 1840 - 264 pages
...opposite equal angles 1 Are these sides proportional 1 PLANE GEOMETRY. Properties of Polygons. 13. The areas of similar triangles are to each other as the squares described on their homologous sides. The similar triangles ABC, and DEF, are to each Other, as the... | |
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Similar triangles are to each other as the squares of their homologous sides. 
