## The Elements of Plane Geometry |

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### Common terms and phrases

ABCD adjacent base bisector bisects called centre chord circle circumference circumscribed common Conclusion construct Consult Prop contained describe diagonals diameter difference distance divided draw equal equilateral triangle equivalent exterior angle extremities feet figure Find the area four given circle given line given point given straight line greater half hexagon homologous hypotenuse Hypothesis inches included inscribed interior intersect isosceles triangle legs limit line drawn measured median meet middle point opposite sides parallel parallel lines parallelogram passes perimeter perpendicular perpendicular drawn point of contact point of intersection Problem produced Proof Proposition prove quadrilateral quantities radii radius ratio rectangle regular polygon respectively right angle right triangle SCHOLIUM segments similar square straight line student tangent Theorem third touch transversal trapezoid triangle ABC vertex vertical angle

### Popular passages

Page 46 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 54 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 180 - If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. Given two triangles ABC and A'B'C', having the angle A equal to the angle A'.

Page 6 - 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.

Page 200 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.

Page 34 - 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 179 - 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.

Page 79 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.

Page 21 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.