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

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### Common terms and phrases

AC AC adjacent angles altitude angles of parallel apothem base and altitude bisector bisects centre chord circumference circumscribed circle coincide construct a square decagon Def.-The diagonals diameter distance divided draw drawn equally distant equilateral triangle Exercise.-If exterior angle external tangents figure Find the area given circle given line given point given square given straight line GIVEN TO PROVE given triangle Hence homologous sides hypotenuse included angle intersection isosceles triangle locus mean proportional middle points number of sides opposite sides parallel to BC parallelogram perpendicular Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rect rectangle regular inscribed regular polygon respectively equal right angles right triangle secant segments similar polygons similar triangles square equivalent straight line joining tangent THEOREM third side triangle ABC triangle is equal triangle whose sides vertex vertices

### Popular passages

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

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 63 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.

Page 49 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.

Page 148 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.

Page 47 - ... the third side of the first is greater than the third side of the second.

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

Page 47 - If two triangles have two sides of one equal respectively to two sides of the other...

Page 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.

Page 140 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.