Elements of Geometry and Trigonometry |
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Page 30
... taken as many times less two , as the figure has sides . E Let ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain ...
... taken as many times less two , as the figure has sides . E Let ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain ...
Page 31
... taken as many times , less two , as the polygon has sides ( Prop . XXVI . ) ; that is , equal to twice as many right angles as the figure has sides , wanting four right angles . Hence , the interior angles plus four right angles , is ...
... taken as many times , less two , as the polygon has sides ( Prop . XXVI . ) ; that is , equal to twice as many right angles as the figure has sides , wanting four right angles . Hence , the interior angles plus four right angles , is ...
Page 35
... taken in order . 4. Three quantities are in proportion , when the first has the same ratio to the second , that the second has to the third ; and then the middle term is said to be a mean proportional between the other two . 5 ...
... taken in order . 4. Three quantities are in proportion , when the first has the same ratio to the second , that the second has to the third ; and then the middle term is said to be a mean proportional between the other two . 5 ...
Page 36
... taken alternately . Let M , N , P , Q , be the numerical representatives of four quanties in proportion ; so that M : N :: P : Q , then will M : P :: N : Q. Since M : N : P : Q , by supposition , MxQ = NxP ; there- fore , M and Q may be ...
... taken alternately . Let M , N , P , Q , be the numerical representatives of four quanties in proportion ; so that M : N :: P : Q , then will M : P :: N : Q. Since M : N : P : Q , by supposition , MxQ = NxP ; there- fore , M and Q may be ...
Page 37
... taken inversely . Let M : N :: P : Q ; then will N : M :: Q : P . For , from the first proportion we have MxQ = Nx P , or NxP = MxQ . But the products Nx P and MxQ are the products of the extremes and means of the four quantities N , M ...
... taken inversely . Let M : N :: P : Q ; then will N : M :: Q : P . For , from the first proportion we have MxQ = Nx P , or NxP = MxQ . But the products Nx P and MxQ are the products of the extremes and means of the four quantities N , M ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex