Elements of Geometry and Trigonometry |
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Page 47
... centre ; and of two unequal 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 ...
... centre ; and of two unequal 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 ...
Page 48
... centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the circle , and be a secant . * PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be three cases ...
... centre upon this tangent would be shorter than CA ; hence this supposed tangent would enter the circle , and be a secant . * PROPOSITION X. THEOREM . Two parallels intercept equal arcs on the circumference . There may be three cases ...
Page 49
... centres C and D ( Prop . VI . Sch . ) . But no more than one straight line can be drawn through two points ; hence the straight line , which passes through the centres , will bisect the chord at right angles . PROPOSITION XII . THEOREM ...
... centres C and D ( Prop . VI . Sch . ) . But no more than one straight line can be drawn through two points ; hence the straight line , which passes through the centres , will bisect the chord at right angles . PROPOSITION XII . THEOREM ...
Page 50
... centres of two circles is equal to the sum of their radii , the two circles will touch each other exter- nally . Let C and D be the centres at a distance from each other equal to CA + AD . The circles will evidently have the point A ...
... centres of two circles is equal to the sum of their radii , the two circles will touch each other exter- nally . Let C and D be the centres at a distance from each other equal to CA + AD . The circles will evidently have the point A ...
Page 51
... centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles contained by the radii will also be equal . Let C and C be the centres of equal circles , and the angle ACB = DCE ...
... centre , intercept equal arcs on the circumference : and conversely , if the arcs intercepted are equal , the angles contained by the radii will also be equal . Let C and C be the centres of equal circles , and the angle ACB = DCE ...
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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