A first course in projective geometry . be ob-tained and the conic constructedby Ex. 1. (a) To construct a conicu-iven four points and the tangentat one of them. Fig. 1266. 8 4. The particular cases of Pascals and Brianchons theorems are of service in solving such problems as the following: (6) To construct a conic givenfour tangents and the point ofcontact of one of them. It should be noted that to be given a tangent and its pointof contact is to be given two ultimately coincident points ortangents. So that the conditions given are equivalent tofive points or five tangents. The det
A first course in projective geometry . be ob-tained and the conic constructedby Ex. 1. (a) To construct a conicu-iven four points and the tangentat one of them. Fig. 1266. 8 4. The particular cases of Pascals and Brianchons theorems are of service in solving such problems as the following: (6) To construct a conic givenfour tangents and the point ofcontact of one of them. It should be noted that to be given a tangent and its pointof contact is to be given two ultimately coincident points ortangents. So that the conditions given are equivalent tofive points or five tangents. The details of the construction are exactly as in § 5, Chap. XV., and are left to the student. Ex. 2. id) Construct a conic {h) Construct a conic given 3 given 3 points and the tangents at tangents and the points of contacttwo of them. of two of them. THE CONSTRUCTION OF A CONIC 251 jij 5. Any line parallel to an asymptote meets the conic inone point at infinity. So to be given the direction of anasymptote is equivalent to being given a point on the curveat infinity, viz. the point at infinit
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
