## THE SOLUTIONS OF GEOMETRICAL PROBLEMS |

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### Common terms and phrases

ABCD angular points asymptotes axis axis-major bisected chord of contact circle described circle whose centre coincide common tangent cone conic section conjugate hyperbola constant cos2 cosco curve diagonals directrix draw ellipse Euclid extremities find the equation find the locus fixed point foci focus given straight lines hence hexagon homogeneous function hyperbola inscribed joining the points latus rectum Let A fig meet middle point ordinates origin pair of tangents parabola parallel parallelogram pass through three perpendicular plane points of contact points of intersection polar equation polygon position Prop quadrilateral figure radius remaining sides respectively rhombus right angles shew sides may pass sides shall pass Similarly sin2 ST JOHN'S COLLEGE straight line passing tangents be drawn tangents drawn three fixed points three sides triangle ABC values vertex

### Popular passages

Page 54 - If two triangles which have two sides of the one proportional to two sides of the other, be joined at one angle, so as to have their homologous sides parallel to one another ; the remaining sides shall be in a straight line. Let ABC, DCE be two triangles which have the two sides BA, AC proportional to the two CD, DE, viz.

Page 117 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Page 272 - SOLUTIONS of the GEOMETRICAL PROBLEMS proposed at St. John's College, Cambridge, from 1830 to 1846, consisting chiefly of Examples in Plane Coordinate Geometry. With an Appendix, containing several general Properties of Curves of the Second Order, and the Determination of the Magnitude and Position of the Axes of the Conic Section, represented by the General Equation of the Second Degree.

Page 117 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.

Page 96 - The rectangle contained by the diagonals of a quadrilateral ,figure inscribed in a circle, is equal to both the rectangles contained by i'ts opposite sides.

Page 16 - MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another.

Page 28 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part*.

Page 28 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.

Page 10 - ... not in the same plane with the first two ; the first two and the other two shall contain equal angles.

Page 87 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.