 | Benjamin Greenleaf - Geometry - 1868 - 340 pages
...AB2 : : BC : B D. In like manner, we have, BC2 : AC2 : : BC : C D. 240. Cor. 3. If a perpendicular be drawn from the vertex of the right angle to the hypothenuse, the squares of the sides about the right angle will be to each other as the adjacent segments of the hypothenuse.... | |
 | Benjamin Greenleaf - 1869 - 516 pages
...DE would also be divided into equal parts at the points I, K, L. PROPOSITION XXVII. — THEOREM. . the triangle will be divided into two triangles similar...and to each other. In the right-angled triangle ABC, from the vertex of the right angle BAC, let AD be drawn perpendicular to the hypothenuse BC ; then... | |
 | 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 to the... | |
 | 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 and to... | |
 | André Darré - 1872 - 226 pages
...proportion, S : s + s, : : A2 : «2 + b2. But A8 = a2 + b2 (90), consequently, S = s + «i. THEOREM. 120. In a right-angled triangle if a perpendicular is drawn...vertex of the right angle to the hypothenuse, the square or any other figure on the hypothenuse is to the square or other similar figure on either of... | |
 | Charles Davies, William Guy Peck - Mathematics - 1872 - 602 pages
...be drawn to the 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 hypothcnuse,' 1st. The triangles formed are similar to each other and to the whole triangle. 2cl. Either... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...in the ratio of similitude of the polygons (40). 10 APPLICATIONS. PROPOSIT1ON XIII.— THEOKEM. 44. 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... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...sides are homologous. Thus, DE is homologous with AB, DF with AC, and EF with BC. THEOREM XVII. 210i In a right-angled triangle, if a perpendicular is...and to each other. In the right-angled triangle ABC, from the vertex of the right angle BAC, let AD be drawn perpendicular to the hypothenuse BC ; then... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...triangles AC :AB = AB:AD And since ABC and BCD are similar AC: CB=CB:CD that is, if in a right triangle a perpendicular is drawn from, the vertex of the right angle to the hypothenuse, either side about the right angle is a mean proportional between the whole hypothenuse and the adjacent... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...triangles AC :AB — AB :AD And since ABC and BCD are similar AC : CB=CB:CD that is, if in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypothenuse, either side about the right angle is a mean proportional between the whole hypothenuse and the adjacent... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
