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" If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. "
A Text-book of Geometry - Page 156
by George Albert Wentworth - 1888 - 386 pages
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Elements of Geometry: Including Plane, Solid, and Spherical Geometry

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) "...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

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...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

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....
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Elements of Geometry and Trigonometry

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

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

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...
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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
...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 Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 472 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)...
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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 to...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...vertices of the triangle ; theĽ 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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