Elements of Geometry and Trigonometry |
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Page 42
... tangent . The point M , where the tangent touches the circumference , is called the point of contact . M In like manner , two circumferences touch each other when they have but one point in common . 9. A polygon is circumscribed about a ...
... tangent . The point M , where the tangent touches the circumference , is called the point of contact . M In like manner , two circumferences touch each other when they have but one point in common . 9. A polygon is circumscribed about a ...
Page 47
... tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe - r rence . For , every oblique line CE , is longer than the perpendicular CA ( Book I. Prop . XV ...
... tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe - r rence . For , every oblique line CE , is longer than the perpendicular CA ( Book I. Prop . XV ...
Page 48
... 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 . First . If the two ...
... 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 . First . If the two ...
Page 50
... tangent to each other . For , they have only the point A common , and it through the point A , AE be drawn perpendicular to AD , the straight line AE will be a common tangent to all the circles . PROPOSITION XV . THEOREM . In the same ...
... tangent to each other . For , they have only the point A common , and it through the point A , AE be drawn perpendicular to AD , the straight line AE will be a common tangent to all the circles . PROPOSITION XV . THEOREM . In the same ...
Page 56
... tangent and a chord , is measured by half of the arc included between its sides . Let BE be the tangent , and AC the chord 56 GEOMETRY .
... tangent and a chord , is measured by half of the arc included between its sides . Let BE be the tangent , and AC the chord 56 GEOMETRY .
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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