 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...divided into equal parts, at I, K, and L PROPOSITION XXIII. THEOREM. //, in a right-angled triangle, a perpendicular is drawn from the vertex of the right angle to the Injpothenuse : 1°. Tl1e triangles on each side of the perpendicular are similar to the given triangle,... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...B'C' + C'D' + etc. A'B' B'C' C'D'' That fc P AB _BC _ CD PROPOSITION XXVII. THEOREM. 286. In any right triangle, if a perpendicular is drawn from the vertex...the right angle to the hypotenuse : I. The triangles formed are similar to the whole triangle, and to each other. II. The perpendicular is a mean proportional... | |
 | William Chauvenet, William Elwood Byerly - Geometry - 1887 - 331 pages
...For we have (see preceding figures) whence (12) _ BC CD ^ B'C' C'D' '' PROPOSITION IX.—THEOREM. 25. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle: 1st. The two triangles thus formed are similar to each other and to the whole... | |
 | George Albert Wentworth - Geometry - 1888 - 264 pages
...consequent). NUMERICAL PROPERTIES OF FIGURES. ^ * PROPOSITION XV. THEOREM. y 334. // in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse: I. The perpendicular is a- mean proportional between the segments of the hypotenuse. II. Each leg of the right... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...Proposition XIV. A Problem. 224. To divide a line harmonically. Proposition XV. A Theorem. 225. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The right triangle is divided into two triangles similar to itself and to each other. II. The perpendicular... | |
 | James Wallace MacDonald - Geometry - 1889 - 80 pages
...Proposition XIV. A Problem. 224. To divide a line harmonically. Proposition XV. A Theorem. 225. In a right triangle, if a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The right triangle is divided into two triangles similar to itself and to each other. II. The perpendicular... | |
 | William Chauvenet - 1893 - 340 pages
...same number of triangles, similar each to each and similarly placed. PROPOSITION VIII. PROPOSITION IX. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st. The two triangles thus formed are similar to each othei and to the whole... | |
 | Webster Wells - Geometry - 1894 - 394 pages
...drawn from the vertex of the right angle to the hypotenuse of a right triangle, I. The triangles formed are similar to the whole triangle, and to each other. II. The perpend'uyular is a mean proportional between the segments of the hypotenuse. III. Either leg is a... | |
 | George Clinton Shutts - Geometry - 1894 - 412 pages
...AO equal to В A . Connect О and C. Prove that О С is perpendicular to В С. (Ex. 112.) Ex. 119. If a perpendicular is drawn from the vertex of the right angle of a right-angled triangle to the hypotenuse, prove that the two triangles formed are B* M c mutually... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...of two similar polygons have the same ratio as any two homologous sides. 334. If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The perpendicular is a mean proportional between the segments of the hypotenuse. II. Each leg of the right... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
