 | John Ryley, John Gawthorp, John Whitley - Mathematics - 1818 - 308 pages
...Crowther, Garside, Johnson, and the proposer. (90) By Mr. J. BAINES, Mathematical School, Reading. Given the base, the vertical angle, and the distance from the centre of the circumscribing circle to the intersection of the perpendiculars from the angles upon the opposite... | |
 | Almanacs, English - 1807 - 910 pages
...about the given ellipsis. Required a demonstration. XII. QUEST. (1295), by Mr. John Whithy, Roilurham. Given the base, the vertical angle, and the distance...to the intersection of the perpendiculars from the angle» upon the opposite sides; to construct the plane triangle. XIII. QUEST. (1290), by Mr. (ieo.... | |
 | Charles Hutton - Mathematics - 1843 - 570 pages
...locus of the vertex. (2). Given the base and vertical angle of a triangle, to find the locus of (a) the intersection of the perpendiculars from the angles upon the opposite sides : (i) the centre of the inscribed circle : (c) the intersection of lines from the angular points to... | |
 | John Hind - Trigonometry - 1855 - 540 pages
...s—c = s tan ^ A tan ¿ В. 84. In a plane triangle, 0 is the centre of the circumscribed circle, P the intersection of the perpendiculars from the angles upon the opposite sides: then, OP divides into parts in the ratio of 2 : 1, any line joining an angle with the middle of its... | |
 | Education - 1858 - 428 pages
...69.—BY LD To construct a plane triangle, given the vertical angle, the base, and the distance of the centre of gravity to the intersection of the perpendiculars from the angles to the opposite sides. PROBLEM No. 70.—BY W. DOWNS. MATHEMATICAL WORKS. (Continued.) 51. Buxtons... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...equal. (Ex. 135.) 137. If O is the centre of the circle circumscribed aLout a triangle ABO, and P is the intersection of the perpendiculars from the angles upon the opposite sides ; the perpendicular from O upon the side BC is equal to onehalf the distance AP. (I. 132), (III. 25,... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...In any triangle, the centre of the circumscribed circle, the intersection of the medial lines, and the intersection of the perpendiculars from the angles upon the opposite sides, are in the same straight line ; and the distance of the first point from the second is one-half the... | |
 | 1873 - 126 pages
...directrices on the tangents from that point to a confocal ................ 38 3901. (S. Bills.) — Given the base, the vertical angle, and the distance from the centre of the circumscribed circle to the centroid of a plane triangle ; to construct the triangle ......................... | |
 | W. J. C. Miller - Mathematics - 1873 - 122 pages
...directrices on the tangents from that point to a confocal ................ 33 3901. (S. Bills.)— Given the base, the vertical angle, and the distance from the centre of the circumscribed circle to the centroid of a plane triangle ; to construct the triangle ......................... | |
 | Sir George Greenhill - Mathematics - 1876 - 318 pages
...a;2 cos2 a + (bx sina - c^!}, the equation of two conies. 6. If ABC is an acute-angled triangle and D the intersection of the perpendiculars from the angles upon the opposite sides, shew that the four conic sections which can be described touching the sides of the triangles DBC, DCA,... | |
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In any triangle, the centre of the circumscribed circle, the intersection of the medial lines, and the intersection of the perpendiculars from the angles upon the opposite sides, are in the... 
