 | Sir John Leslie - Geometry, Analytic - 1809 - 542 pages
...B, from which the perpendicular BD is let fall upon the hypotenuse AC ; the triangles ABD and DBC, thus formed, are similar to each other and to the whole triangle ACB. For the triangles ABD and ACB, having the angle BAC common, and the right angle ADB equal to ABC,... | |
 | Sir John Leslie - Geometry - 1817 - 456 pages
...right-angled at B, from which the perpendicular BD falls upon the hypotenuse AC ; the triangles ABD and DBC, thus formed, are similar to each other, and to the whole triangle ACB. For the triangles ABD and ACB, having the angle BAC common, and the right angle ADB equal to ABC,... | |
 | Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...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 whole... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...also into equal parts at the points 7J K, L. PROPOSITION XXIII. THEOEEM. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse. \st. The triangles on each side of the perpendicular are similar to the whole triangle,... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...also into equal parts at the points I, K, L. PROPOSITION XXIII. THEOREM. In a right•angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse. 1st. The triangles on each side of the jxrpendicular are similar to the given triangle,... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...also into equal parts at the points I, K, L. PROPOSITION XXIII. THEOREM. In a right•angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse. 1st. The triangles on each side of the perpendicular are similat to the given triangle,... | |
 | Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...to (he vertices of the triangle ; then AN x BL X CM = AM X CL x BN. 14. In a right angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, 1st. The triangles formed are similar to each other and to the whole triangle. 2d. Either... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...equal parts at the points I, K, L. PROPOSITION XXVII. — THEOREM. 269. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the triangle will be divided into two triangles similar to the given triangle atul to... | |
 | Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...vertices of the triangle ; the» AN x HI, x CM = AM x CL x BN. 14.' In a right angled triangle, if л perpendicular is drawn from the vertex of the right angle to the hypothenuse 1st. The triangles formed are similar to each other and to the whole triangle. 2d. Either... | |
 | Benjamin Greenleaf - Geometry - 1866 - 328 pages
...equal parts at the points I, K, L. PROPOSITION XXVII. — THEOREM. 269. In a right-angled triangle, if a perpendicular is drawn from the vertex of the right angle to the hypothe«tt.se, the triangle will be divided into two triangles similar to the given triangle and to... | |
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If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st. 
