## A Treatise on the Analytic Geometry of Three Dimensions |

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### Common terms and phrases

angles axes axis becomes called centre circle co-ordinates coefficients common condition cone confocal conic conjugate consecutive consider constant contain corresponding cosß cosy cubic curvature curve denote determine developable diameters difference differential direction distance double point drawn edges eliminating envelope equal equation evidently expressed fixed focus follows four geodesic give given given line Hence hyperboloid infinity intersection last article length line joining line of curvature locus manner meets normal obtain origin parallel pass perpendicular plane curve point of contact pole principal projections properties proved quadric quantity radii radius of curvature ratio reciprocal regard relation represents respect result right angles right line roots seen sheet sides sphere squares substituting surface tangent plane theorem touch transformed triangle umbilic values vanish vertex written

### Popular passages

Page 174 - To find the locus of the foot of the perpendicular from the focus of a sphero-conic on the tangent.

Page 295 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.

Page 137 - If a quadrilateral be inscribed in a conic, its opposite sides and diagonals will intersect in three points such that each is the pole of the line joining the other two.

Page 154 - Hence we may immediately infer from the last article that the projection of the intersection of two confocal quadrics on a plane of circular section of one of them is a conic whose foci are the similar projections of the umbilics ; and, again, that given any curve...

Page 199 - From the expressions in this article we deduce at once, as in the theory of central conies, that the sum of the reciprocals of the radii of curvature of two normal sections at right angles to each other is constant ; and again, if normal sections be made through a pair of conjugate tangents (see Art.

Page 276 - ... is impossible. Cor. 3. The centre of a sphere, and the centre of any small circle of that sphere, are in a straight line perpendicular to the plane of the circle. Cor. 4. The square of the radius of any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1): hence, circles which are equally distant from the centre, are equal ; and of two circles which are unequally...