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" If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle: 1st. "
Solid Geometry - Page 195
by Mabel Sykes, Clarence Elmer Comstock - 1922 - 218 pages
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Elements of Geometry and Trigonometry

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,...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

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....
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

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,...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Elements of Geometry: With Practical Applications to Mensuration

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...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1008 pages
...parallel chords in a circle, is a point in the diameter which is perpendicular to the chords. O. 4. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle, (1) the triangles thus formed are similar to each other and...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...in the ratio of similitude of the polygons (40). 10 APPLICATIONS. PROPOSITION XIII.— THEOREM. 44. If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a rigid triangle : 1st. The two triangles thus formed are similar to each other...
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First book of mathematics

Hugo Reid - Mathematics - 1872 - 146 pages
...Whence it appears that if from the right angle of a right-angled triangle a perpendicular be drawn to the hypotenuse, the perpendicular is a mean proportional between the segments of the hypotenuse. Farther, such perpendicular divides the triangle into two triangles similar to the large triangle and...
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...«2 + b2. But A8 = a2 + b2 (90), consequently, S = s + «i. THEOREM. 120. In a right-angled triangle if a perpendicular is drawn from the vertex of the right angle to the hypothenuse, the square or any other figure on the hypothenuse is to the square or other similar...
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