 Given the base of a triangle and the difference of the angles at the base, to determine the locus of the vertex. Taking the same axes as before, and putting a, a', for the tangents of the angles at the base...  The Elements of Analytical Geometry ... - Page 196by John Radford Young - 1835 - 288 pagesFull view - About this book
 | Thomas Leybourn - Mathematics - 1817 - 456 pages
...angle to the middle of the base, the line bisecting the vertical angle and terminated by the base, and the difference of the angles at the base ; to determine the triangle ? Answered by Mr. Mark Elstob. Construction. Make a right-angled A ABC, having its hypothenuse... | |
 | Mathematical recreations - 1827 - 296 pages
...WILLIAM GODWARD. — Given the distance of the centres of the inscribed and circumscribing circles, and the difference of the angles at the base, to determine the plane triangle by geometrical construction, whea the distance of the centre of the inscribed circle... | |
 | John Radford Young - Conic sections - 1830 - 342 pages
...the tangent of the angle a, which it makeswith the axis of ,r, the value tan. a — • PKOBLEM in. (144.) Given the base of a triangle and the difference...base, and t for the tangent of their difference, we have Y t- "~a' .-. x2+ — .ry — y2 — fc2 = 0. Consequently the locus is an hyperbola, and, because... | |
 | John Radford Young - Conic sections - 1830 - 360 pages
...PROBLEMS ON GEOMETRIC LOCI. PROBLEM I. (142.) Given the base of a triangle and the sum of the tangents of the angles at the base, to determine the locus of the vertex. Let AB be the given base, through M, the middle of which, draw the perpendicular, MY; then, taking... | |
 | John Radford Young - Conic sections - 1830 - 390 pages
...PROBLEMS ON GEOMETRIC LOCI. PROBLEM I. (142.) Given the base of a triangle and the sum of the tangents of the angles at the base, to determine the locus of the vertex. Let AB be the given base, through M, the middle of which, draw the perpendicular, MY; then, taking... | |
 | John Radford Young - Conic sections - 1833 - 310 pages
...extremities of the base, A, B. PROBLEM II. (143.) Given the base and the difference of the tangents of the angles at the base, to determine the locus of the vertex. Taking the same axes as before, we have = d, d being put tan. Z. B — tan. Z. A = ^ for the difference of the tangents. Hence the... | |
 | John Radford Young - Geometry, Analytic - 1838 - 296 pages
...base, to determine the locus of the vertex ... 55 178. Given the base and difference of the tangents of the angles at the base, to determine the locus of the vertex ... ... 56 179. Given the base and difference of the angles ut the base, tp determine the locus of... | |
 | John Radford Young - Geometry, Analytic - 1848 - 300 pages
...tangent of the angle a, which it makes with the axis of x, the value tan. a = — 1<I. PROBLEM III. (144.) Given the base of a triangle and the difference...base, and t for the tangent of their difference, we a — a' • have t = , or substituting for a, a', their re- ^ Consequently the locus is an hyperbola,... | |
 | Technology - 1849 - 656 pages
...questions and solutions. Ques. 11, gives "the line bisecting the base, the difference of the sides, and the difference of the angles at the base," to determine the triangle. The question had previously been proposed by Mr. Thomas Huhne, as No. 24 in the " MaIhemnlician,"... | |
 | Perry Fairfax Nursey - Industrial arts - 1849 - 650 pages
...questions and solutions. Ques. 11, gives " the line bisecting the base, the difference of the sides, and the difference of the angles at the base," to determine the triangle. The question had previously been proposed by Mr. Thomas Hu'.me, as No. 24 in the " Mathematician,"... | |
| |
