 | George Roberts Perkins - Geometry - 1860 - 472 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... | |
 | John Mulcahy - Geometry - 1862 - 252 pages
...also be proved by the converse of Lemma 2° of Art. 9. 7°. It is evident from Art. 9, Lemma 1 , that the lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. It is easily proved also that they insect each other. For, if AE and BD be the bisectors... | |
 | Isaac Todhunter - 1862 - 376 pages
...exemplify the articles of this chapter by applying them to prove some properties of a triangle. TJie lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. PROPERTIES OF A TRIANGLE. 'f oc, and a line through A perpendicular to AB for the... | |
 | W. P. Turnbull - Geometry, Analytic - 1867 - 276 pages
...to Euclid, I. 47, the lines FC, KB, AL meet in a point. 30. Prove by taking two sides for axes that the lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. 31. A point moves so that the sum of the squares of its distances from two points... | |
 | William Peveril Turnbull - Geometry, Analytic - 1867 - 298 pages
...to Euclid, I. 47, the lines FC, KB, AL meet in a point. 30. Prove by taking two sides for axes that the lines drawn from the angles of a triangle to the middle points of the opposite sides meet in a point. 31. A point moves so that the sum of the squares of its distances from two points... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...sides of a triangle drawn through their middle points meet in one point. 52. The three lines which join the angles of a triangle to the middle points of the opposite sides intersect in one point. 53. If two circles touch one another, the lines which join the extremities of parallel diameters... | |
 | Richard Wormell - Geometry, Modern - 1868 - 286 pages
...altitudes intersect in the same point. The straight lines which join the vertices of a triangle with the middle points of the opposite sides, intersect in the same point. 275. Let ABC be the triangle; A'B' the middle points of two sides. Draw B'D parallel to A A', then... | |
 | Richard Wormell - Geometry, Plane - 1870 - 304 pages
...altitudes intersect in the same point. The straight lines which join the vertices of a triangle with the middle points of the opposite sides, intersect in the same point. 275. Let ABC be the triangle; A',B' the middle points of two sides. Draw B'D parallel to A A', then... | |
 | Cincinnati (Ohio). Board of Education - Cincinnati (Ohio) - 1873 - 352 pages
...formed are isosceles, and every diagonal is divided in extreme and mean ratio. 8. Prove that the three lines drawn from the angles of a triangle to the middle points of the opposite sides, intersect in one point, cutting off one-third of each line. 9. To describe a circle tangent to a given circle at... | |
 | Braithwaite Arnett - Mathematics - 1873 - 120 pages
...angle OFC] therefore OF is at right angles to A C. Thus the proposition is true. PROP. IV. The straight lines drawn from the angles of a triangle to the middle points of the opposite sides meet •in a point. Let D, E, F be the middle points of the sides BC, CA, AB of the triangle ABC, and... | |
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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. 
