 | Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...triangle is a mean proportional between the hypotenuse and the adjacent segment of the hypotenuse; and the perpendicular is a mean proportional between the segments of the hypotenuse. Ex. 13. Name the sides of the three triangles which are homologous to one another. Ex. 14. The segments... | |
 | James Wallace MacDonald - Geometry - 1894 - 76 pages
...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
...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... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...: (1) The two triangles on each side of it are similar to the whole triangle and to each other. (2) The perpendicular is a mean proportional between the segments of the hypotenuse. (3) Each side about the right angle is a mean proportional between the hypotenuse and the adjacent... | |
 | Euclid - Geometry - 1890 - 442 pages
...hypotenuse — (a) the triangles on each side of it are similar to the whole and to each other : (j3) the perpendicular is a mean proportional between the segments of the hypotenuse : (y) each of the sides is a mean proportional between the hypotenuse and its segment adjacent to that... | |
 | William Chauvenet - 1893 - 336 pages
...figures) whence (12) AB __ BC _ CD _ A'B' B'C' C'jy '°'''"' 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... | |
 | Henry Martyn Taylor - 1893 - 486 pages
...In a right-angled triangle, if a perpendicular be drawn from, the opposite vertex to the hypotenuse, the perpendicular is a mean proportional between the segments of the hypotenuse, and each of the sides of the triangle is a mean proportional between the hypotenuse and the segment... | |
 | Great Britain. Education Department. Department of Science and Art - 1894 - 892 pages
...right-angled triangle a perpendicular is let fall from the right angle to the hypotenuse. Show that the perpendicular is a mean proportional between the segments of the hypotenuse, and also that each of the sides is a mean proportional between the hypotenuse and the segment adjacent... | |
 | Charles Ambrose Van Velzer, George Clinton Shutts - Geometry - 1894 - 522 pages
...right triangle: I. The triangles thus formed are similar to each other and to the whole triangle. II. The perpendicular is a mean proportional between the segments of the hypotenuse. III. Each side is a mean proportional between the hypotenuse and the segment adjacent to that side.... | |
 | John Macnie - Geometry - 1895 - 386 pages
...right triangle, if a perpendicular be drawn from the vertex of the right angle to the hypotenuse, 1°- The perpendicular is a mean proportional between the segments of the hypotenuse. 2°. Each arm is a mean proportional between the hypotenuse and the adjacent segment. Given : In a... | |
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If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. 
