 | George Salmon - 1852 - 329 pages
...third side. 5. We give now some examples of the use of these equations of the first degree. Ex. 1. The bisectors of the sides of a triangle meet in a point; viz., in the point a + j3 + y = 0. of the line joining the middle point of AB to C, or by a + y = 0,... | |
 | Robert Henry Wright - 1865 - 174 pages
...since a has been taken negative, a. area BOC + ß.aie&AOC+ 7 . area A OB = 0, as was required. 222. The bisectors of the sides of a triangle meet in a point, TÎZ. a + ß + <y = 0, which is also the center of gravity; and since the point 0 is the center of... | |
 | Peter Guthrie Tait - 1867 - 364 pages
...may be easily verified by producing Aa to twice its length and joining the extremity with B. (I/.) The bisectors of the sides of a triangle meet in a...parallel, and equal, to the sides taken in order; the equation of Bb is (§ 28 (1)) p = That of Cc is, in the same way, P =At the point 0, where Sl and... | |
 | Philip Kelland - 1873 - 248 pages
...SUBTRACTION. 11 But line AB : AD = m, line BC : DE = n, .: AB : AD :: BО : DE. Ex. 4. The bisectors of tlw sides of a triangle meet in a point which trisects each of them. Let the sides of the triangle ABC be bisected in D, E, F ; and let AD, BE meet in G. Let vector BD... | |
 | 1884 - 538 pages
...that a rectangular hyperbola circumscribing a triangle passes through the orthocentre. 8. Prove that the bisectors of the sides of a triangle meet in a point, taking for axes two sides whose lengths are a and b. 9. Find the locus of P, if, when perpendiculars... | |
 | Hussein Tevfik (Pacha.) - 1882 - 98 pages
...or as А К = 1 , An А К A m -== An which is the length of the side of the demanded square. Ex. 3. The bisectors of the sides of a triangle meet in a point which trisects each of them. Let the sides of the triangle ADC be bisected in D, E, F and let в AE and С D meet in G ; it will... | |
 | Philip Kelland, Peter Guthrie Tait - 1882 - 296 pages
...(Art. 6). But line AB : AD = m, line BO : DE=n, .: AB : AD :: BG : DE. Ex. 4. The bisectors of tlie sides of a triangle meet in a point which trisects each of them. Let the sides of the triangle ABC be bisected in D, E, F ; and let AD, BE meet in G. Let vector BD... | |
 | 1891 - 644 pages
...straight line. 6. Show how to divide a given straight line into a given number of equal parts. Prove that the bisectors of the sides of a triangle meet in. a point of trisection of each. 7. Establish the formulse cos ( A — B) •=. cos A cos B + sin A sin B and... | |
 | George Albert Wentworth - 1899 - 496 pages
...is equidistant from AC and BC, and therefore in the bisector CF. (Why ?) Ex. 25. The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -l. bisectors EE' and DD' intersect at O.... | |
 | George Albert Wentworth - 1899 - 278 pages
...equidistant from AC and BC, and therefore in the bisector CF. (Why ?) -"^ " Ex. 25. The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the _L bisectors EE' and DD' intersect at 0.... | |
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The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -l. bisectors EE' and DD 
