 | Francis Joseph Grund - 1830 - 274 σελίδες
...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 - 1834 - 212 σελίδες
...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... | |
 | Adrien Marie Legendre - 1836 - 394 σελίδες
...had 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 described on their homologous sides. Let ABC, DEF, be two similar trian- A. gles, having the angle A equal to D, and the angle B=E. Then,... | |
 | Nathan Scholfield - 1845 - 894 σελίδες
...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... | |
 | Charles Davies - 1846 - 254 σελίδες
...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... | |
 | Elias Loomis - 1849 - 252 σελίδες
...each other as the rectangles of the sides which contain the equal angles. PROPOSITION XXIV. THEOREM. Similar triangles are to each other as the squares described on their homologous sides. Let ABC, DBF be two simi- A lar triangles, having the angle A equal to D, the angle B equal to E, and... | |
 | Charles Davies - 1849 - 372 σελίδες
...had 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 described on their homologous sides. Let ABC, DEF, be two similar triangles, having the angle A equal to D, and The angle B=E. ABC : DBF... | |
 | Charles Davies - 1850 - 238 σελίδες
...the diameter and the adjacent segment. That is, 100 BOOK IV. Proportions of Triangles. THEOREM XIX. Similar triangles are to each other as the squares described on their homologous sides. Let ABC and DEF be two similar triangles, and AL and DN the squares described on the homologous sides... | |
 | Charles Davies - 1850 - 218 σελίδες
...diameter and the adjacent segment. That is, AD=BDxDC BOOK IV. Proportions of Triangles. THEOREM XIX. Similar triangles are to each other as the squares described on their homologous sides. Let ABC and DEF be two similar triangles, and AL and DN the squares described on the homologous sides... | |
 | 1850 - 488 σελίδες
...= the distance of the first' perpendicular measured from the acute angle of the triangle ; then as the areas of similar triangles are to each other as the squares of their like sides, we have . , .-. x = 1-732, and the distance of the other perpendicular is in like... | |
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Similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF be two similar triangles... 
