## Elements of Geometry: With Notes |

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### Common terms and phrases

ABCD adjacent angles altitude angle ABC angle ACB angle BAC antecedent base bisected centre chord circle circum circumference circumscribed polygon consequently construction Converse of Prop corollary demonstration described diagonals diameter divided draw equal angles equal Prop equiangular equimultiples equivalent Euclid exterior angle Geometry greater half hence hypothenuse hypothesis included angle inscribed angle inscribed polygon intersect isosceles triangle join less line drawn lines be drawn magnitudes multiple number of sides obtuse opposite angles parallel perimeter perpendicular PROBLEM proportion PROPOSITION PROPOSITION XII quadrilateral radii radius rectangle rectangle contained regular polygon respectively equal rhomboid right angled triangle right angles Prop Scholium scribed side BC similar polygons similar triangles square submultiple subtended surface tangent THEOREM third three angles trapezium triangle ABC vertex whence

### Popular passages

Page 177 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Page 31 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Page 185 - If a straight line meets two straight lines, so as to make "the two interior angles on the same side of it taken " together less than two right angles...

Page 196 - BAG is a right angle (Def. 30.), the two straight lines AC, AG upon the opposite sides of AB, make with it at the point A the adjacent angles equal to two right angles; therefore CA is in the same straight line (i.

Page 38 - Any side of a triangle is less than the sum of the other two sides...

Page 157 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.