 | James Joseph Sylvester, James Whitbread Lee Glaisher - Mathematics - 1862 - 410 pages
...similitude of X and 2:" secondly, by observing that the triangle FGHm&j be constructed from 2 and Д (the triangle formed by joining the middle points of the sides of ABC) just as ÂED is constructed from X and ABC, whence it follows that these triangles are similar;... | |
 | McGill University - 1865 - 332 pages
...gravity of the perimeter of a triangle. o. Show that it is the centre of the circle inscribed in a new triangle formed by joining the middle points of the sides of the, original triangle. 4. Define a lever, and distinguish between the three kinds of levers. Find the condition of equilibrium... | |
 | Robert Henry Wright - Coordinates, Trilinear - 1865 - 174 pages
...ß coa B + 'y coaC - а coa A = 0, 7 cosC + а cos A - ß cos B = 0. 27. The equations to the three sides of the triangle formed by joining the middle points of the three sides of a triangle are respectively »j sin A + ß sin B - 7 sin С = 0, ß sin B + 7 sin С... | |
 | Isaac Todhunter - Mechanics - 1867 - 372 pages
...gravity of a wire bent into a triangular shape coincides with the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the original triangle. 7. If the centre of gravity of a triangle be equidistant from two angular points of the triangle, the... | |
 | Isaac Todhunter - Mechanics - 1867 - 368 pages
...gravity of a wire bent into a triangular shape coincides with the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the original triangle. 7. If the centre of gravity of a triangle be equidistant from two angular points of the triangle, the... | |
 | James McDowell - Mechanics - 1867 - 120 pages
...Shew that the centre of gravity of the perimeter coincides with the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the given triangle. Let ABC be the given triangle, D, E, F, the middle A points of its sides. The weights... | |
 | Joseph Wolstenholme - Mathematics - 1867 - 368 pages
...the sides of a triangle are the straight lines bisecting internally and externally the angles of a triangle formed by joining the middle points of the sides of the former triangle. 62. If two circles have four common tangents, the circles described on these common... | |
 | James Maurice Wilson - Geometry - 1868 - 150 pages
...middle points of the sides of a triangle is parallel to the base, and is equal to half the base. 6. The triangle formed by joining the middle points of the sides of a triangle is similar to the original triangle, and has one fourth of its area. 7. The lines that join... | |
 | Dublin city, univ - 1871 - 366 pages
...4. Prove that the centre of gravity of a triangular frame is the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the frame. $. Required, in Ibs., the force .F, which, acting freely for one minute upon the mass of i cwt.... | |
 | Dublin city, univ - 1875 - 386 pages
...radical centre of the three exscribed circles of a triangle is the centre of the circle inscribed in the triangle formed by joining the middle points of the sides of the original triangle. 2. A, S, C are given points on the circumference of a circle; find the envelope of a chord L, M, when... | |
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Show that the area of the triangle whose vertices are (4, 6), (2, —4), (—4, 2) is four times the area of the triangle formed by joining the middle points of the sides. 
