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" Two similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E. "
Elements of Geometry and Trigonometry Translated from the French of A.M ... - Page 87
by Charles Davies - 1849 - 359 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...Which was to be done. PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the angle B equal to the angle E ; and let AB be to BC, as DE to EF, so that the side BC is homologous to EFa;...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 pages
...corresponding terms of those proportions, omit C/ng the common term ABE ; we have ABC : ADE : : AB.AC : AD.AE. Cor. Hence the two triangles would be equivalent,...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...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 316 pages
...terms of those proper tions, omitting the common term ABE ; we have ABC : ADE : : AB.AC : AD.AE. 217. Cor. Hence the two triangles would be equivalent,...AC ; which would happen if DC were parallel to BE. 12 THEOREM. 218. Two similar triangles are to each other as the squares of their homologous sides....
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...angles. .• PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the angles at A and D equal; and let AC : AB : : DF : DE so that the side AB be homologous to DE (Proper....
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...DE.DF : : AC2 : DF. Consequently, " ABC : DEF : : AC2 : DF2. Therefore, two similar triangles ABC, DEF, are to each other as the squares described on their homologous sides AC, DF, or as die squares of any other two homologous sides. PROPOSITION XXVI. THEOREM. Two similar...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...corresponding terms of these proportion*, omitting the common term ABE ; we have ABC : ADE : AB .AC : AD.AE. Cor. Hence the two triangles would be equivalent,...having the angle A equal to D, and the angle B=E. Then, first, by reason of the equal an- Q gles A and D, according to the last proposition, we shall...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 372 pages
...corresponding terms of these proportions, omitting the common term ABE ; we have ABC : ADE : ABAC : AD.AE. Cor. Hence the two triangles would be equivalent,...if .the rectangle AB.AC were equal to the rectangle AD. AE, or if we had AB : AD : : AE : AC ; which would happen if DC were parallel to BE. PROPOSITION...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 252 pages
...lie opposite equal angles 1 Are thew sides proportional 1 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 squares G and H, described on the homologous...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...satisfactory manner possible, to show in tiie corollaries, that the areas of all similar rectilinear figures are to each other as the squares described on their homologous sides. These, in Euclid, Lcijendre, and other authors, are made the subjects of several propositions, but...
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Elements of Drawing and Mensuration Applied to the Mechanic Arts: A Book for ...

Charles Davies - Geometrical drawing - 1846 - 254 pages
...sum of the three to 120 x 3 = 360. 47. How are similar polygons to each other? Similar polygons are to each other as the squares described on their homologous sides. Thus, the two similar polygons ABCDE, FGHIK, are to each other as the squares described on the homologous...
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