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" If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. "
Elements of Geometry: Plane geometry - Page 140
by Andrew Wheeler Phillips, Irving Fisher - 1896
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...In a right angled triangle, if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of the perpendicular are...similar to the whole triangle, and to each other. Let ABC be a rt. angled ^\, having the rt. L BAC ; draw AD J_ BC; then ihe ^& ABD, ADC are similar...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...r na right angled triangle, if a perpendicular be drawn from the right angle to the opposite side, the triangles on each side of the perpendicular are...similar to the whole triangle, and to each other. Let ABC be a rt. angled ^, having the rt. Z. BAC ; draw AD_L BC; then die ^s ABD, ADC are similar to...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...a right-angled triangle, if a perpendicular is drawn from the right angle to the hypothenuse ; 1st. The triangles on each side of the perpendicular are similar to the whole triangle and to each other. 3d. Each of the sides is a mean proportional between the hypothenuse and its segment adjacent to that...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...divided also 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
...div'ded also 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
...be drawn to (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 - Geometry - 1857 - 444 pages
...divided also 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 Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...right-angled triangle, if a perpendicular is drawn from the right angle to the hypothenus.; , 1st. The triangles on each side of the perpendicular are similar to the whole triangle and to each other. 3d. The perpendicular is a mean proportional between the segments of the hypothenuse. 3d. Each of the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...divided into 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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