 | David Munn - 1873 - 160 pàgines
...shew that the areas of their inscribed circles are as 4 : 3. 53. If /., p w p, denote the lengths of the lines drawn from the angles of a triangle to the middle of the opposite sides, prove that side 54. In a given circle is inscribed an equilateral triangle,... | |
 | Isaac Todhunter - 1874 - 378 pàgines
...Articles of this Chapter by applying them to demonstrate some properties of a triangle. The straight lines drawn from the angles of a triangle to the middle points of the opposite sides meet at a point. Let ABC be a triangle, D, E, F the middle points of the sides ; take A for the origin,... | |
 | Euclides - 1874 - 120 pàgines
...rectangle contained by the segments of the base. [See Ex. 63, and Prop. 5 Book ii.] 75. If lines be drawn from the angles of a triangle to the middle points of the opposite sides four times the sum of the squares on these lines will be equal to three times the sum of the squares... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pàgines
...construction; these will depend on the ingenuity of the analyst. 1. THEOREM.— If straight lines be drawn from the angles of a triangle to the middle points of the opposite sides, they will cut one another in a point of triscction. Let D, F, and H, the middle points of the sides... | |
 | David Munn - 1874 - 374 pàgines
...shew that the areas of their inscribed circles are as 4 : 3. S3- If A> A' Pc denote the lengths of the lines drawn from the angles of a triangle to the middle of the opposite sides, prove that side 54. In a given circle is inscribed an equilateral triangle,... | |
 | Edward Atkins - 1875 - 410 pàgines
...drawn perpendicular to AC, and EF perpendicular to BC, then С = Ъ sin-1 u?. Ok 10. The lines joining the angles of a triangle to the middle points of the opposite sides, meet in a point. 11. Show that (i.) log sec 2 6 = 2 | tan2 0 + } tan" a + } tan10 6 + &cl. (ii.) 2... | |
 | James White - 1878 - 160 pàgines
...it through the given point is the required straight line. III. Prove that the three straight lines from the angles of a triangle to the middle points of the sides meet in a point, which cuts one-third of each above the sides. If two bisectors of the sides... | |
 | Isaac Sharpless - 1879 - 282 pàgines
...similar to (Prop. 9). From the last theorem the following propositions may be proved: 1. The three lines drawn from the angles of a triangle to the middle...of the opposite sides intersect in the same point. 2. The three lines drawn bisecting the angles of a triangle intersect in the same point. 3. The three... | |
 | Charles Mansford - 1879 - 112 pàgines
...rectangle contained by the segments of the base. [See Ex. 63, and Prop. 5 Book ii.] 75. If lines be drawn from the angles of a triangle to the middle points of the opposite sides four times the sum of the squares on these lines will be equal to three times the sum of the squares... | |
 | De Volson Wood - 1882 - 360 pàgines
...a = p, and z cos /9 + y sin/3 =p, and cutting at right angles the line z cosy + у sin у =р". 15. The lines drawn from the angles of a triangle to the middle of the opposite sides meet iu one point. (For a solution by Quaternions, see Articles 335-7.) 16. Show... | |
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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. 
