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acute altitude axis base bisect called centre chord circle circumference coincide common cone Cons construct contained COROLLARY cylinder denote describe diagonals diameter difference dihedral angle direction distance divided Draw edges equal equal respectively equally distant equilateral equivalent extremities faces fall figure foot formed four frustum given given point greater Hence homologous sides included inscribed intersection isosceles joining lateral less Let A B limit line A B line drawn measured meet middle point oblique opposite parallel pass perimeter perpendicular plane polygon polyhedrons prism PROBLEM proportional PROPOSITION prove pyramid Q. E. D. PROPOSITION radii radius ratio regular polygon respectively right angles segment Show similar sphere square straight line surface symmetrical Take tangent THEOREM third triangle trihedral vertex vertices volume
Σελίδα 176 - 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.
Σελίδα 122 - 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.
Σελίδα 189 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 209 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 205 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Σελίδα xvi - Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.
Σελίδα 174 - 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.
Σελίδα 332 - A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases, of the frustum. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having the same altitude as the pyramid S-ABCDE, and a base A'B'C' equivalent to the base ABCDE, and in the same plane with it.