Elements of Geometry and Trigonometry |
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Page 48
... radius CA ( Book I. Prop , XIV . Sch . ) ; hence in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ; hence this supposed ...
... radius CA ( Book I. Prop , XIV . Sch . ) ; hence in reference to this new tangent , the radius AC would be an oblique line , and the perpendicular let fall from the centre upon this tangent would be shorter than CA ; hence this supposed ...
Page 49
... 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 . For , to make an intersection possible , the triangle CAD must be possible . Hence , not ...
... 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 . For , to make an intersection possible , the triangle CAD must be possible . Hence , not ...
Page 50
... radius AD must be less than the sum of the radius AC and the distanceCD between the centres ( Prop . XII . ) ; which is contrary to the supposition . Cor . Hence , if two circles touch each other , either exter- nally or internally ...
... radius AD must be less than the sum of the radius AC and the distanceCD between the centres ( Prop . XII . ) ; which is contrary to the supposition . Cor . Hence , if two circles touch each other , either exter- nally or internally ...
Page 57
... radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from A and B. Find , in like manner , above or beneath the line AB , a second point E , equally distant from the points ...
... radius greater than the half of AB , describe two arcs cutting each other in D ; the point D will be equally distant from A and B. Find , in like manner , above or beneath the line AB , a second point E , equally distant from the points ...
Page 58
... radius greater than BA , describe two arcs intersecting each other in D ; draw AD : it will be the perpendicular required . For , the point D , being equally distant from B and C , must be in the perpendicular raised from the middle of ...
... radius greater than BA , describe two arcs intersecting each other in D ; draw AD : it will be the perpendicular required . For , the point D , being equally distant from B and C , must be in the perpendicular raised from the middle of ...
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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