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ABCD acute angle altitude angle formed angles are equal bisector bisects called centre circumference circumscribed circumscribed circle coincide construct a square decagon diagonals diameter distance draw equal angles equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angle feet figure Find the area given angle given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersecting isosceles trapezoid isosceles triangle legs line drawn line joining mean proportional measured middle points number of sides obtuse opposite sides parallel parallelogram perimeter perpendicular plane Problem Proof Proposition prove quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle Scholium secant segments similar polygons square equivalent straight angle subtended tangent Theorem third side trapezoid triangle ABC triangle is equal vertex vertices
Side 46 - 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, the third side of the first is greater than the third side of the second...
Side 187 - Two triangles having 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.
Side 64 - 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 46 INTERCEPTS BY PARALLEL LINES.
Side 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Side 215 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 161 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Side 135 - 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.
Side 156 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.