 | Duncan Farquharson Gregory - Calculus - 1841 - 566 pages
...bination of (l) with (3) will rise only to the degree n (n — 1), which therefore represents the greatest number of tangents which can be drawn from a given point to a curve of и dimensions. Waring had fixed the limit at и2, as it at first sight appears to be ; the preceding... | |
 | George Salmon - Conic sections - 1852 - 338 pages
...multiple point of the order k would (Art. 66) be a multiple point of the order * According to M. Poncelet, Waring was the first who investigated the problem...can be drawn from a given point to a curve of the n"t degree. (Miscellanea Analytics, p. 100.) This number he fixed as at most n2. M. Poncelet showed... | |
 | George Salmon - Conic sections - 1852 - 329 pages
...multiple point of the order k would (Art. 66) be a multiple point of the order * According to M. Poncelet, Waring was the first who investigated the problem of the number of tangents which can^be drawn from a given point to a curve of the n th degree. (Miscellanea Analytica, p. 100.) This... | |
 | Bartholomew Price - Calculus - 1857 - 672 pages
...curve, none. If n = 3, n (n — 1 ) = 6 ; and therefore six is the greatest number of tangents that can be drawn from a given point to a curve of the third degree; and if the point from which the tangents are drawn is on the curve, only four tangents... | |
 | Percival Frost - 1863 - 526 pages
...= 0 and (X + /*/) D = 0 have their roots equal, or the equation of the envelope is or 391. To find the number of tangents which can be drawn from a given point, to meet a surface in three consecutive points. Let P' be the given point, then, if three positions of... | |
 | 1885 - 522 pages
...or other of the equi-conjugate diameters of the ellipse. 8. Prove that n(n — 1) tangents at most can be drawn from a given point to a curve of the w'* degree. Prove that two tangents and no more can be drawn from the point (b, b) to the curve xs... | |
 | Joseph Edwards - Differential calculus - 1886 - 540 pages
...of the normal is -^ -u = U'cos (6 - a) - Usin (0 - a). 184. Class of a Curve of the wth degree. DBF. The number of tangents which can be drawn from a given point to a rational algebraic curve is catted its class. Let the equation of the curve be f(x, 2/) = 0. The equation... | |
 | 1890 - 608 pages
...PAPER. Professor Nanson. 1. Find the general equation of the tangent at any point of a curve, and find the number of tang-ents which can be drawn from a given point to a curve of the n'" deg-ree. Express in the form x cos a + y sin a '=.if(a) the equation of the tangent at any point... | |
 | Joseph Edwards - Mathematics - 1892 - 550 pages
...three normals which pass through a given point (x, y). 208. Class of a Curve of the n01 degree. DBF. The number of tangents which can be drawn from a given point to a rational algebraic curve is called its class. Let the equation of the curve \tef(x, J/) = 0. The equation... | |
 | Joseph Edwards - Differential calculus - 1896 - 288 pages
...therefore there are n (n — 1) points of contact corresponding to n (n — 1) tangents, real or imaginary, which can be drawn from a given point to a curve of the иш degree. Thus for a conic, a cubic, a quartic, the maximum number of tangents which can be drawn... | |
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Waring was the first who investigated the problem of the number of tangents which can be drawn from a given point to a curve of the n"t degree. 
