## Elements of Geometry with Notes |

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ABCD altitude antecedent appears base bisected centre chord circle circumference circumscribed coincide common consequently construction contained continually converse definition demonstration described diagonals diameter difference distance divided double draw equal equivalent Euclid expressed extremities figure follows formed former four geometry given greater half hence hypothesis included inscribed intersect isosceles join latter less line drawn longer magnitudes manner mean measure meet method middle multiple opposite parallel perimeter perpendicular polygon portion PROBLEM produced Prop proportion proposed PROPOSITION quadrilateral radii radius reasoning rectangle regular remain respectively equal rhomboid right angled triangle right angles Scholium shown sides similar space square straight line subtended suppose surface taken tangent THEOREM third triangle ABC twice vertex VIII whence whole

### 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 184 - If a straight line meet 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 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 89 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...

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

Page 24 - The difference of the angles at the base of any triangle, is double the angle contained by a line drawn from the vertex perpendicular to the base, and another bisecting the angle at the vertex.

Page 16 - 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 213 - We have already said that by the term convex line we understand a line, polygonal, or curve, or partly curve and . partly polygonal, such that a straight line cannot cut it in more than two points.

Page 196 - Now the parallelogram BL is double of the triangle ABD, because they are upon the same base BD, and between the same parallels...

Page 37 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.