# The Elements of Plane Geometry

### Contents

 SYLLABUS OF GEOMETRICAL CONSTRUCTIONS 7 Angles at a point 14 Triangles 21 Parallels and Parallelograms 46 Problems 66 Loci 81 Definitions Axioms Postulates 91 Equality of Areas 97
 Tangents 49 Two Circles 64 Inscribed and Circumscribed Figures 72 The Circle in Connection with Areas 87 Fundamental Propositions of Proportion 105 Section II 117 Of Ratio and Proportion 127 Definitions 135

 Problems 122 The Circle 9 Angles at the Centre and Sectors 16 Angles in Segments 37
 Fundamental Geometrical Propositions 144 Proportion 151 Areas 169 Loci and Problems 184

### Popular passages

Page 41 - 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 182 - 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 67 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 167 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 32 - Any two sides of a triangle are together greater than the third side.
Page 34 - 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 23 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
Page 63 - If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
Page 39 - 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 106 - 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.