## Elements of Geometry |

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### Common terms and phrases

A B C acute adjacent altitude base bisect called centre chord circle circumference circumscribed coincide common Cons contained COROLLARY describe diagonals diameter difference direction divided Draw equal equal distances equal respectively equilateral equivalent erected extremities fall figure formed four given given line greater Hence homologous sides hypotenuse included inscribed intercept intersect isosceles joining less Let A B limit line drawn mean measured by arc meet middle point multiplied one-half opposite sides parallelogram perimeter perpendicular plane position PROBLEM proportional PROPOSITION prove quadrilateral quantities radii radius equal ratio rect rectangles regular polygon right angles segment Show similar similar polygons square straight line Substitute subtend surface symmetrical Take taken tangent THEOREM triangle variable vertex vertices

### Popular passages

Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 124 - To describe an isosceles triangle having each of the angles at the base double of the third angle.

Page 201 - In any proportion, the product of the means is equal to the product of the extremes.

Page 173 - Any two rectangles are to each other as the products of their bases by their altitudes.

Page 185 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other...

Page 73 - 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; as the figure ADB E.

Page 41 - The exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Page 140 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.

Page 113 - From A as a centre, with a radius equal to o, describe an arc ; and from B as a centre, with a radius equal to m, describe an arc intersecting the former arc at С.

Page 155 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.