Elements of Geometry and Trigonometry: Translated from the French of A.M. Legendre by Daniel Brewster : Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 42
... tangent is a line which has but one point in common with the circumference . CD is a tangent . The point M , where the tangent touches the C circumference , is called the point of contact . M D In like manner , two circumferences touch ...
... tangent is a line which has but one point in common with the circumference . CD is a tangent . The point M , where the tangent touches the C circumference , is called the point of contact . M D In like manner , two circumferences touch ...
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- 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- 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 . la 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 . la the same ...
Page 56
... tangent and a chord , is measured by hulf of the arc included between its sides . 18 D C Let BE be the tangent , and 56 GEOMETRY .
... tangent and a chord , is measured by hulf of the arc included between its sides . 18 D C Let BE be the tangent , and 56 GEOMETRY .
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Common terms and phrases
adjacent altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equal angles equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater hence homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex