## Elements of Geometry |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

A B C ABCD acute base bisect called centre chord circle circumference circumscribed coincide common Cons construct contained COROLLARY describe diagonals diameter difference direction divided Draw equal equal distances equal respectively equilateral equivalent erect extremities fall figure formed four given greater Hence homologous sides hypotenuse included increased inscribed intersecting isosceles joining less limit line drawn maximum mean measured meet middle point number of sides one-half parallel parallelogram perimeter perpendicular plane PROBLEM proportional PROPOSITION prove Q. E. D. PROPOSITION quantities radii radius equal ratio rect rectangles regular polygon required to construct right angles segment Show similar similar polygons square straight line Substitute subtend symmetrical Take tangent THEOREM third triangle variable vertex vertices

### Popular passages

Page 40 - 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 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...

Page 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.

Page 202 - In any proportion, the product of the means is equal to the product of the extremes.

Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.

Page 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.

Page 146 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.