## An Elementary Treatise on Pure Geometry with Numerous Examples |

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### Common terms and phrases

ABCD asymptotes axes axis bisects called centre circle circular points circumscribed coaxal coincide collinear common common chord common points concurrent conjugate conjugate diameters constant construct conversely corresponding points cut the conic determined divide double points draw drawn ellipse envelope equal figure five fixed line fixed point focus four points given conic given line given point harmonic Hence homographic ranges homologue imaginary infinity inscribed intersection involution lies line at infinity locus meet orthogonal pair pairs of points parabola parallel passes pencil perpendicular perspective plane points of contact polar pole position projection Prove quadrangle quadrilateral ranges rays reciprocal rectangular hyperbola relation respectively right angle segment sides Similarly straight line subtend taken tangents theorem touch transversal triangle variable vertex vertices

### Popular passages

Page 333 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.

Page 354 - The nine-point circle of any triangle touches the inscribed and escribed circles. Let ABC be a triangle, / the inscribed circle touching BC in Q, and E the escribed circle opposite to A touching £C in Q'. Bisect BC, CA in M and M...

Page 166 - Two vertices of a triangle self-conjugate for a given conic move on fixed lines ; show that the locus of the third vertex is a conic passing through the intersections of the given lines with the given conic and through the poles of the given lines for the given conic. Ex. 6. A A' are a pair of opposite vertices of a quadrilateral whose sides touch a conic at L, M, N, R.

Page 305 - To find the locus of the centre of a circle which passes through a given point and touches a given straight line.