# THE SOLUTIONS OF GEOMETRICAL PROBLEMS (Google eBook)

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### Contents

 Section 1 1 Section 2 9 Section 3 10 Section 4 32 Section 5 42 Section 6 54 Section 7 61 Section 8 64
 Section 18 159 Section 19 161 Section 20 166 Section 21 179 Section 22 182 Section 23 185 Section 24 186 Section 25 192

 Section 9 104 Section 10 106 Section 11 126 Section 12 131 Section 13 134 Section 14 145 Section 15 147 Section 16 148 Section 17 151
 Section 26 193 Section 27 207 Section 28 219 Section 29 225 Section 30 228 Section 31 257 Section 32 259 Section 33 265

### 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.