Elements of Geometry and Trigonometry |
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Page 46
... three common points , there would be two circumferences passing through the same three points ; which has been shown by the proposition to be impossible . PROPOSITION VIII . THEOREM . Two equal chords are equally 46 GEOMETRY .
... three common points , there would be two circumferences passing through the same three points ; which has been shown by the proposition to be impossible . PROPOSITION VIII . THEOREM . Two equal chords are equally 46 GEOMETRY .
Page 47
... chords , the less is at the greater 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 ...
... chords , the less is at the greater 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 ...
Page 48
... chord MP . It will , at the same time be perpendicular to NQ ( Book J.Prop.XX.Cor.1 . ) ; therefore , the point H will be at once the middle of the arc MHP , and of the arc NHQ ( Prop . VI . ) ; therefore , we shall have the arc MH - HP ...
... chord MP . It will , at the same time be perpendicular to NQ ( Book J.Prop.XX.Cor.1 . ) ; therefore , the point H will be at once the middle of the arc MHP , and of the arc NHQ ( Prop . VI . ) ; therefore , we shall have the arc MH - HP ...
Page 49
... chord which joins the points of intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular be erected from the ...
... chord which joins the points of intersection , and will divide it into two equal parts . For , let the line AB join the points of intersection . It will be a common chord to the two circles . Now if a perpendicular be erected from the ...
Page 55
... chords , which intersect each other , is measured by half the sum of the arcs included between its sides . Let AB , CD , be two chords intersecting each BOOK III . 55.
... chords , which intersect each other , is measured by half the sum of the arcs included between its sides . Let AB , CD , be two chords intersecting each BOOK III . 55.
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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