## The Elements of Plane Geometry |

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ABCD adjacent angles angle formed angle is equal apothem base angles bisector called central angle centre chord circumference circumscribed circumscribed circle Conclusion construct a circle construct a triangle Consult Prop decagon diagonals diameter draw drawn perpendicular equal circles equilateral triangle exterior angle Find the area find the length Find the locus find the number given circle given line given point given straight line given triangle homologous sides hypotenuse Hypothesis inches inscribed regular isosceles triangle legs line joining mean proportional median middle point number of degrees number of sides opposite sides parallel lines parallelogram perimeter perpendicular drawn point of contact point of intersection Problem produced Proof prove Q.E.D. Proposition quadrilateral radii radius ratio rectangle regular hexagon regular polygon rhombus right angle Scholium secant segments similar polygons subtended Theorem third side transversal trapezoid triangle is equal vertex vertical angle

### Popular passages

Page 48 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 47 - 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 56 - 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 182 - 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 206 - 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 35 - 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 181 - 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 81 - 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.