# Appendix to Euclid's Elements

author, 1825 - Geometry - 93 pages

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### Contents

 Section 1 1 Section 2 10 Section 3 14 Section 4 22 Section 5 26 Section 6 35
 Section 7 44 Section 8 58 Section 9 72 Section 10 89 Section 11 92

### Popular passages

Page 36 - if the segments of the base produced, have the same ratio which the other sides of the triangle have, the straight line drawn from the vertex to the point of section divides the outward angle of the triangle into two equal angles. PROP. IV.
Page 53 - If from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than its half; and so on: There shall at length remain a magnitude less than the least of the proposed magnitudes.
Page 42 - the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle.
Page 31 - PROP. E. If four magnitudes be proportionals, they are also proportionals by conversion: that is, the first is to its excess above the second, as the third to its excess above the fourth. . PROP. XX.
Page 28 - of the second, or the same part of it, that the third is of the fourth; the first is to the second, aS the third is to the fourth. PROP. D.
Page 51 - .Solid parallelepipeds contained by parallelograms equiangular to one another, each to. each, that is, of which the solid angles are equal, each to each, have to one another the ratio which . is the same with the ratio compounded of > the - ratios of their sides. PROP. XXXIV.
Page 43 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.
Page 32 - PROP. XXIII. If there be any number of magnitudes and as many others, which, taken two and two, in cross order, have the same ratio;
Page 43 - If from any angle of a triangle a straight line be drawn perpendicular to the base; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. PROP. D. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.
Page 48 - If each of two solid angles be contained by three plane angles equal to one another, each to each; the planes in which the equal angles are, have the same inclination to one another.