### Contents

 DEFINITIONS 1 ANGLES PERPENDICULARS 7 PARALLELS 18 TRIANGLES 24 QUADRILATERALS 38 MISCELLANEOUS THEOREMS 44 Loci 51 EXERCISES 57
 SIMILAR POLYGONS 99 REGULAR POLYGONS 111 EXERCISES 119 THE PYTHAGOREAN THEOREM 131 FORMULE OF COMPUTATION 142 MAXIMA AND MINIMA 162 SYMMETRY 171 BOOK V 185

### Popular passages

Page 60 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 219 - ... 4. Prove that, if from a point without a circle a secant and a tangent be drawn, the tangent is a mean proportional between the whole secant and the part without the circle.
Page 139 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 44 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 43 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 217 - Show that the areas of similar triangles are to each other as the squares of the homologous sides.
Page 89 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 107 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 218 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 218 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.