 | Francis Joseph Grund - 1830 - 274 páginas
...82) ; and we shall therefore have the proportion BD : AD = AD : DC ;* that is, the perpendicular AD, is a mean proportional^ between the two parts into which it divides the hypothenuse. 2dly, From the two similar triangles, ABC, ABD, we shall have the proportion BD:AB = AB:BC;... | |
 | Francis Joseph Grund - 1834 - 212 páginas
...page 70) ; and we shall therefore have the proportion BD: AD=AD:DC;* that is, the perpendicular AD is a mean proportional between the two parts into which it divides the hypothenuse. (Theory of proportion, page 66.) Idly. From the two similar triangles, ABC, ABD, we shall... | |
 | Eugenius Nulty - 1836 - 242 páginas
...establish their importance. THEOREM XIV. 54. In a right angle triangle, a perpendicular drawn from the right angle to the hypotenuse, is a mean proportional between the segments of this side; either of the sides containing the right angle is a mean proportional between... | |
 | Nicholas Tillinghast - 1844 - 110 páginas
...equiangular with ABC, and hence similar. 72 PERPENDICULAR ON HYPOTENUSE. [BOOK V. PROP. XVIII. THEOREM. The perpendicular from the vertex of the right angle to the hypotenuse of a right-angled triangle, divides it into two triangles similar to each other, and similar to the... | |
 | Benjamin Greenleaf - 1862 - 518 páginas
...to that side. 271. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles ABD, ADC are similar, by comparing their homologous sides we... | |
 | Benjamin Greenleaf - 1862 - 532 páginas
...to that side. 271. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles ABD, ADC are similar, by comparing their homologous sides we... | |
 | Benjamin Greenleaf - 1866 - 328 páginas
...to that side. 271. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse, For, since the triangles ABD, ADC are similar, by comparing their homologous sides we... | |
 | Benjamin Greenleaf - 1873 - 202 páginas
...to that side. 212. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles ABD, ADC are similar, by comparing their homologous sides we... | |
 | Benjamin Greenleaf - 1874 - 206 páginas
...to that side. 212. Cor. 2. The perpendicular from the vertex of the right angle to the hypothenuse is a mean proportional between the two parts into which it divides the hypothenuse. For, since the triangles AB D, ADC are similar, by comparing their homologous sides we... | |
 | Aaron Schuyler - 1876 - 384 páginas
...AHB be a triangle right angled at H; a, h, b, the sides respectively opposite the angles, A, H, B; p, the perpendicular from the vertex of the right angle to the hypotenuse ; m and n, segments of the hypotenuse respectively adjacent to a and b. 1. The triangle BDH is similar... | |
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In any right triangle the perpendicular from the vertex of the right angle on the hypotenuse divides the triangle into two triangles each similar to the given triangle. 
