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ABCD altitude angles are equal apothem arc BC axis bisectors bisects chord circumference circumscribed Compute CONCLUSION construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equidistant equilateral triangle exterior angle feet Find the area Find the locus Find the radius frustum given circle given line given point homologous hypotenuse HYPOTHESIS inches inscribed intersecting isosceles triangle lateral area lateral edges lateral faces legs lune number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane MN polyedral angle polyedron prism Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular polygon rhombus right angles right triangle SCHOLIUM segments semicircle similar triangles slant height spherical angle spherical degrees spherical excess spherical polygon spherical triangle square equivalent straight line surface symmetrical tangent tetraedron THEOREM trapezoid triangle ABC triedral vertex vertices
Page 168 - 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.
Page 38 - ... 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 35 - Any side of a triangle is less than the sum of the other two sides...
Page 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Page 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 199 - 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.
Page 192 - The areas of two rectangles having equal altitudes are to each other as their bases.