## Elements of Geometry, Volume 1 |

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### Common terms and phrases

ABCD altitude apply base bisecting bisector called centre chord circle circumference circumscribed coincide common construct contains conversely describe diagonals diameter difference distance divided Draw drawn equal equally distant equilateral triangle equivalent Exercise extremities fall figure Find Find the area four GEOMETRY given given circle given point given straight line given triangle GIVEN—the greater half Hence hexagon hypotenuse inscribed intercepted intersection isosceles length less limit locus measured meet method middle points opposite sides parallel parallelogram passes perpendicular plane polygon position PROBLEMS proof PROPOSITION PROVE quadrilateral quantity radii radius ratio rectangle regular regular polygon right angles right triangle ruler segment similar square straight line Substituting Suppose symmetry tangent THEOREM triangle ABC triangles are equal turned unequal unit variable vertex vertices

### Popular passages

Page 10 - 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 46 - ... 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 248 - The area of a regular hexagon inscribed in a circle is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 5 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.

Page 215 - 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 67 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 145 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.

Page 71 - The perpendiculars from the vertices of a triangle to the opposite sides meet in a point.

Page 180 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.

Page 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.