Elements of Geometry and Trigonometry |
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Page 46
... distances OA , OB , OC , are equal ; there- fore the circumference described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to ...
... distances OA , OB , OC , are equal ; there- fore the circumference described from the centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to ...
Page 47
... distance from the centre . First . Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D M A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and ...
... distance from the centre . First . Suppose the chord AB = DE . Bisect these chords by the per- pendiculars CF , CG , and draw the radii CA , CD . D M A In the right angled triangles CAF , DCG , the hypothenuses CA , CD , are equal ; and ...
Page 49
... distance between the centres of two circles is less than the sum of the radii , the greater radius being at the same time less than the sum of the smaller and the distance between the centres , the two circumferences will cut each other ...
... distance between the centres of two circles is less than the sum of the radii , the greater radius being at the same time less than the sum of the smaller and the distance between the centres , the two circumferences will cut each other ...
Page 50
... distance from each other equal to CA + AD . The circles will evidently have the point A common , and they will have no other ; because , if they had two points common , the distance between their centres must be less than the sum of ...
... distance from each other equal to CA + AD . The circles will evidently have the point A common , and they will have no other ; because , if they had two points common , the distance between their centres must be less than the sum of ...
Page 68
... distance between two opposite sides taken as bases , Thus , EF is the altitude of the parallelo- A gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its two parallel sides . Thus , EF is the altitude of the ...
... distance between two opposite sides taken as bases , Thus , EF is the altitude of the parallelo- A gram DB . 7. The altitude of a trapezoid is the per- pendicular drawn between its two parallel sides . Thus , EF is the altitude of the ...
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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