 | George Roberts Perkins - 1860 - Liczba stron: 472
...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 - 1862 - Liczba stron: 252
...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 - Liczba stron: 376
...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 - 1867 - Liczba stron: 276
...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 - 1867 - Liczba stron: 298
...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 - 1868 - Liczba stron: 150
...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 - 1868 - Liczba stron: 286
...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 - 1870 - Liczba stron: 304
...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 - 1873 - Liczba stron: 352
...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 - 1873 - Liczba stron: 120
...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. 
