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" From this it readily follows that all the three lines drawn from the angles of a triangle to the middle of the opposite sides, pass through one and the same point. "
Mensuration of lines, surfaces, and volumes - Page 97
by David Munn - 1873
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Recreations in Mathematics and Natural Philosophy ...

Jacques Ozanam - Mathematics - 1803 - 548 pages
...them both within it, dr touches the one without and the other within ? PROB. xxxin. Given the three lines, drawn from the angles of a triangle to the middle of each of the opposite sides ; to determine the triangle. PROB. xxxu. The base of a triangle, the sum...
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The Principles of Analytical Geometry: Designed for the Use of Students

Henry Parr Hamilton - Geometry, Analytic - 1826 - 354 pages
...being identical, it follows, that the 'three perpendiculars intersect in the same point. 62. PROP. 3. The lines drawn from the angles of a triangle to the middle points of the opposite sides, intersect in the same point. Let AM, BN, CP, (fig. 34.) be drawn to the...
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A Million of Facts: Connected with the Studies, Pursuits, and Interests of ...

Sir Richard Phillips - Encyclopedias and dictionaries - 1832 - 450 pages
...= 135. l 55"/ X I93X.84 = Ki-.l MATHEMATICS AND PHYSICS. 70 The intersection of three linee, drawn from the angles of a triangle, to the middle of the opposite sides, is its centre of gravity and percussion. If the lines bisect the angles, it is the centre of the inscribed...
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A million of facts

sir Richard Phillips - 1835 - 608 pages
...l-4th of the height. In the human body it is in the pelvis, between the hips. The intersection of three lines, drawn from the angles of a triangle, to the middle of the opposite sides, is its centre of gravity and percussion. If the lines bisect the angles, it is the centre of the inscribed...
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Recreations in mathematics and natural philosophy, recomposed by m. Montucla ...

Jacques Ozanam - 1840 - 850 pages
...to the middle of the hase, being given ; to determine the triangle. PROR, xxxin.— Given the three lines, drawn from the angles of a triangle to the middle of each of the opposite sides; to determine the triangle. PROR, xxxiv. — Given the hase of в triangle,...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...line drawn I'rom the vertex to the middle of the base, to determine the triangle. 12. Given the three lines drawn from the angles of a triangle to the middle of each of the opposite sides, to determine the triangle. 13. Given the base of a triangle, and the sum...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...[9] gives this THEOREM. Sixteen times thf sum of the products, taken two at a time, of the squares of the lines drawn from the angles of a triangle to the middle points of the opposite sides, is equal to nine times the sum of the products, taken two at a time,...
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The Treasury of Knowledge and Library of Reference: A million of facts [The ...

1850 - 766 pages
...5.36 12.06 21.44 = 33.64 = 48.25 65.08 85.69 108.56 134.01 162.12 193. 0 The intersection of three lines, drawn from the angles of a triangle, to the "middle of the opposite sides, is its centre of gravity and percussion. If the lines bistct the angles, it is the centre of the inscribed...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...[9] gives this THEOREM. Sixteen times the sum of the products, taken two at a time, of the squares of the lines drawn from the angles of a triangle to the middle points of the opposite sides, is equal to nine times the sum of the products, taken two at a time,...
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Young Scientist: A Practical Journal for Amateurs, Volume 1

1851 - 716 pages
...lying towards the bisected side is half of the other. From this it readily follows that all the three lines drawn from the angles of a triangle to the middle of the opposite sides, pass through one and the same point. If we bisect the angle a of the triangle abc (pi. 3, fig. 37),...
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