| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...of its sides. 9. To bisect a parallelogram by a line drawn from a point in one of its sides. 10. A **line joining the middle points of two sides of a triangle, is parallel to the** base, and equal to the half of it. 11. The quadrilateral formed by joining the successiYe middle points... | |
| 1847
...middle points of the edges AC, AB, BD, BC, DA, DC respectively. Then, since the line drawn to bisect **two sides of a triangle is parallel to the third side, and equal to** half of it, we have BC = 2KN = 2HG, DC = 2MG = 2LK, AC = 2HL = 2MN, DA = 2KH = 2GN, AB = 2LG = 2KM,... | |
| George Salmon - Curves, Algebraic - 1852 - 316 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that **the line joining the middle points of two sides of a triangle is parallel to the third side.** 5. We give now some examples of the use of these equations of the first degree. Ex. 1. The bisectors... | |
| George Salmon - Conic sections - 1852 - 316 pages
...triangle meet on the internal bisector of the third angle : interpreted the other way, express that **the line joining the middle points of two sides of a triangle is parallel to the third side.** 5. We give now some examples of the use of these equations of the first degree. Ex. 1. Tfie bisectors... | |
| Euclides - 1853 - 146 pages
...to four right angles. 10. To describe a square equal to the difference of two given squares. II. A **line joining the middle points of two sides of a triangle is parallel to the** "base, and equal to half of it. 12. To bisect a given parallelogram by a line drawn from a point in... | |
| Education - 1856
...is an easy deduction, from any one of this series, that a straight line cutting off' equimultiples **of two sides of a triangle is parallel to the third side ; and,** conversely, a parallel to one side cuts off equimultiples of the other two sides. We need now to have... | |
| Euclides - 1858
...The square of a line is equal to four times the square of its half. 11. The st. line which bisects **two sides of a triangle, is parallel to the third side, and equal to one-half of it.** 12. If two sides of a triangle be given, its area will be greatest when they contain a rt. angle. 13.... | |
| Euclides - 1860 - 142 pages
...therefore equidistant from P, and the line BC joining them is parallel to AE. EXERCISE XLIX. — THEOREM. **The line joining the middle points of two sides of a triangle is parallel to the** base, and equal to the half of it. Let ABC be a triangle, the line DE, that joins the middle points... | |
| Euclides - 1860
...given point, and such, that the line joining them shall be parallel to the other given line. 49. A **line joining the middle points of two sides of a triangle, is parallel to the** base, and equal to the half of it. • I 50. The quadrilateral formed by joining the successive middle... | |
| 1865 - 128 pages
...B + ft cos3 B + 7 cos C sin2 B) (aa + i0 + C7). 3. To find the equation to the circle described on **the line joining the middle points of two sides of a triangle.** Let D, F (Fig. 3) be the middle points of BC, BA; join DF and draw the perpendiculars DH, FK. Then... | |
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