 | André Darré - 1872 - 226 pages
...+ 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 figure... | |
 | William Frothingham Bradbury - Geometry - 1873 - 132 pages
...and A BD are similar 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... | |
 | William Frothingham Bradbury - Geometry - 1873 - 288 pages
...ABD are similar 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... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...is homologous with AB, DF with AC, and EF with BC. THEOREM XVII. 210i 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 and to each... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...homologous with AB, DF with AC, and EF with £ C. THEOREM XVII. 210. 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 and to each... | |
 | Harvard University - 1876 - 554 pages
...has for its measure half the concave arc intercepted between its sides, minus half the convex arc. 2. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypothenuse, what relations exist between the three triangles thus formed * Prove. How is this proposition... | |
 | Robert Fowler Leighton - 1877 - 372 pages
...has for its measure half the concave arc intercepted between its sides, minus half the convex arc. 2. If, in a right triangle, a perpendicular is drawn from the vertex of the right angle to the hypothenuse, what relations exist between the three triangles thus formed ? Prove. How is this proposition... | |
 | George Anthony Hill - Geometry - 1880 - 332 pages
...'54£\ABC~ABCD; therefore AB : BC = BC: BD. AA CD ~ ABCD ; therefore AD : CD. = CD : BD. Theorems. — If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : — I. Either leg is a mean proportional beewecn the hypotenuse and the adjacent segment. II. The... | |
 | William Frothingham Bradbury - Geometry - 1880 - 260 pages
...Since ABC and ABD are similar triangles 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 hypotenuse... | |
 | Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...then DE is 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,... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
