The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in Plane Co-ordinate Geometry, Proposed at St. John's College, Cambridge, from Dec. 1830 to Dec. 1846. 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
J. & J. J. Deighton, 1847 - 263 σελίδες
Άλλες εκδόσεις - Προβολή όλων
a₁ a²² axes axis b₁ base becomes bisected Book C₁ centre chord chord of contact circle co-ordinates coincide College common conic section constant cos² curve described determined diagonals diameter direction draw drawn Edition ellipse equal equation Euclid extremities fixed point focus four given points hence hyperbola inclined inscribed line joining locus m₁ meet middle point negative origin parabola parallel pass perpendicular plane points of contact points of intersection position Problems produced prove quadrilateral figure radius represented respectively right angles shew sides similar Similarly sin² straight line t₁ t₂ taken tangents third touch triangle values vertex
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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*.
Σελίδα 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.
Σελίδα 10 - ... not in the same plane with the first two ; the first two and the other two shall contain equal angles.