 | 1824 - عدد الصفحات: 452
...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.... | |
 | Henry Parr Hamilton - 1826 - عدد الصفحات: 354
...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 middle points of the opposite... | |
 | Euclid, Dionysius Lardner - 1828 - عدد الصفحات: 542
...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,... | |
 | Henry Parr Hamilton - 1843 - عدد الصفحات: 318
...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 in the... | |
 | George Roberts Perkins - 1847 - عدد الصفحات: 326
...[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... | |
 | George Roberts Perkins - 1850 - عدد الصفحات: 332
...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... | |
 | Isaac Todhunter - 1855 - عدد الصفحات: 332
...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, AB for the... | |
 | George Roberts Perkins - 1856 - عدد الصفحات: 460
...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... | |
 | Charles Davies - 1856 - عدد الصفحات: 224
...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.... | |
 | Isaac Todhunter - 1858 - عدد الصفحات: 334
...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, AB for the... | |
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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. 
