| George Washington Hull - Geometry - 1807 - 408 pages
...a right triangle, I. The triangles formed are similar to the whole triangle, and to each other. II. **The perpendicular is a mean proportional between the segments of the hypotenuse.** III. Either leg is a mean proportional between the whole hypotenuse and the adjacent segment. AJ) "... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...that either side is a mean proportional between the hypotenuse and segment adjacent to il, and that **the perpendicular is a mean proportional between the segments of the hypotenuse.** Again, I. 38. in which it is demonstrated that, in every triangle, if a perpendicular be drawn from... | |
| Mathematics - 1835 - 684 pages
...square of either side is equal to the rectangle xmder the hypotenuse and the segment adjoining to it; ie **the perpendicular is a mean proportional between the segments of the hypotenuse,** and either side is a mean proportional between the hypotenuse and the segment adjoining to it . cor.... | |
| Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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,... | |
| Charles Davies - Geometry - 1854 - 436 pages
...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,... | |
| Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...(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. 2d. Either... | |
| Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...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,... | |
| Horatio Nelson Robinson - Geometry - 1860 - 470 pages
...triangles have the sides about "the equal angles proportional, (Def. 16), we have BD : AD :: AD : CJ); or, **the perpendicular is a mean proportional between the segments of the hypotenuse.** 3. Again, BC :_BA :: BA : BD hence, BA2 = BC.BD (1) also, BC_i CA : : CA : CD hence, C!T - BC.CD (2)... | |
| 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 to... | |
| Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...vertices of the triangle ; the» AN x HI, x CM = AM x CL x BN. 14.' In a right angled triangle, if л **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. 2d. Either... | |
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