| 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... | |
| George Salmon - Conic sections - 1852 - 338 pages
...prove that three points are in one right line. Thus the equations a + /3 = 0, /3-y = 0, y + a = 0, **interpreted one way, express that two external bisectors...use of these equations of the first degree. Ex. 1.** Tfie bisectors of the sides of a triangle meet in a point; viz., in the point a + /3 + y = 0. of the... | |
| 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 - 730 pages
...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... | |
| 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 - 286 pages
...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... | |
| Mathematics - 1865 - 132 pages
...B + ft cos3 B + y cos C sin2 B) (aa + bft + cy). 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... | |
| 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... | |
| James McDowell - Mechanics - 1867 - 120 pages
...same point and cut each other in a point of trisection. (EXERCISES, p. 3, No. 5.) Also the straight **line joining the middle points of two sides of a triangle is parallel to the third side,** and equal to half of it. (1) Let AB CD be a rhombus. In the triangles ABC, ADC, the sides AB, AC are... | |
| Richard Wormell - Geometry, Plane - 1870 - 300 pages
...Therefore DQ=D R. Consequently PR, which is equal to P D+DR, is equal to P D+D Q. Therefore EC=P D+D Q. 2. **The line joining the middle points of two sides of a triangle is** equal to half the third side, and is parallel to it. Let ABC be the triangle, D and E the middle points... | |
| |