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" The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. "
The Principles of Analytical Geometry ... - Page 66
by Henry Parr Hamilton - 1826 - 326 pages
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The Quarterly Journal, Volume 17

1824 - 452 pages
...continued. VOL. XVII. X Prop. 2. El. b. vi. as far a* it extends to commensurable lines. The three lines drawn from the angles of a triangle to the middle points of the opposite sides have a common point of intersection. Also, the three lines bisecting the angles of a triangle. Prop....
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...it would be greater by four times the square of the line E F. (303) If lines be drawn from the three angles of a triangle to the middle points of the opposite sides, three times the sum of the squares of the sides is equal to four times that of the bisectors. Let A,...
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An Analytical System of Conic Sections: Designed for the Use of Students

Henry Parr Hamilton - Conic sections - 1843 - 276 pages
...which joins the Origin and the Point in which two Lines MN', NM' meet ............... tb. The three Lines drawn from the Angles of a Triangle to the Middle Points of the opposite Sides meet in the same Point ................ ib. The Lines bisecting the three Angles of any Triangle meet...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 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, of the squares of the sides. Equation...
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...squares of the sides. Equation [10] gives this THEOREM. Sixteen times the sum of the fourth powers 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 fourth powers of the sides. stead of considering the triangle...
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A Treatise on Plane Co-ordinate Geometry: With Numerous Examples ...

Isaac Todhunter - Geometry - 1855 - 299 pages
...will exemplify the articles of this chapter by applying them to prove some properties of a triangle. The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. Let ABC be a triangle, D, E, F, the middle points of the sides ; take A for the origin,...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...squares of the sides. Equation (10) gives this THEOREM. Sixteen times the sum of the fourth powers 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 fourth powers of the sides. Equations (11), (12), and (13) would...
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Key to Davies' Bourdon: With Many Additional Examples, Illustrating the ...

Charles Davies - Algebra - 1856 - 224 pages
...twice РЕ, AО is equal to twice OE ; that is, If three lines be drawn from the vertices of the three angles of a triangle to the middle points of the opposite sides, the distance from either vertex to the point of intersection, will he two-thirds of the bisecting line....
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A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and ...

Isaac Todhunter - Conic sections - 1858 - 334 pages
...will exemplify the articles of this chapter by applying them to prove some properties of a triangle. The lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. Let ABC be a triangle, D, JE, F, the middle points of the sides ; take A for the origin,...
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 pages
...centre ; and those which are equally distant from the centre are equal to one another. 2. The straight lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. 3. Calculate by logarithms, 23-42 x -22652 , . 21 x (000256)* l ' 7000 X -006084 4....
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