### Contents

 SYLLABUS OF GEOMETRICAL CONSTRUCTIONS 1 Definitions 7 Section 15 Equality of Areas 21 The Circle 26
 7 28 Section 4 32 Of Ratio and Proportion 38 Proportion 50 Section 2 56

### Popular passages

Page 14 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 17 - Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles...
Page 14 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Page 13 - Any two sides of a triangle are together greater than the third side.
Page 23 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Page 13 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 34 - If the distance between the centres of two circles is equal to the difference of their radii, the two circles will touch each other internally.
Page 56 - If three straight lines be proportionals, the rectangle contained by the extremes is equal to the square on the mean ; and conversely, if the rectangle contained by the extremes be equal to the square on the mean, the three straight lines are proportionals.
Page 28 - In the same circle, or in equal circles, equal arcs are subtended by equal chords : and conversely, equal chords subtend equal arcs.
Page 4 - The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is B, and the conclusion, that C is D.