## Elements of Geometry, Part 1Harper & Brothers, 1896 - Geometry |

### Common terms and phrases

ABCD acute angle adjacent angles altitude angles are equal angles of parallel apothem arc BC bisects centre chord circumference circumscribed coincide Def.-The diagonal diameter distance divided Draw equal circles equilateral triangle Exercise.-The exterior angle external tangents figure given circle given line given point given straight line GIVEN TO PROVE given triangle Hence homologous sides hypotenuse included angle inscribed angle intercepted arc intersection isosceles triangle line parallel lines are parallel locus mean proportional measured by arc middle points number of sides opposite sides parallel axiom parallel to BC parallelogram PROPOSITION XI Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rect rectangle regular polygon right angles right triangle segment similar polygons similar triangles straight line joining symmetry tangent THEOREM third side third straight line triangle ABC triangles are equal unequal 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.