Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Adapted to the Course of Mathematical Instruction in the United States |
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Page 61
... RADIUS is a straight line drawn from the centre to any point of the circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters ...
... RADIUS is a straight line drawn from the centre to any point of the circumference . 3. A DIAMETER is a straight line drawn through the centre and terminating in the circumference . All radii of the same circle are equal . All diameters ...
Page 62
... its circumference touches each of the sides of the polygon . ооо о POSTULATE . A circumference can be described from any point as a rentre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
... its circumference touches each of the sides of the polygon . ооо о POSTULATE . A circumference can be described from any point as a rentre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 62 GEOMETRY .
Page 63
... radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ; which was to be proved . D B PROPOSITION III . THEOREM . A ...
... radius CD . In the tri- angle ACD , we have AD less than the sum of AC and CD ( B. I. , P. VII . ) . But this sum is equal to AB ( D. 3 ) : hence , AB is greater than AD ; which was to be proved . D B PROPOSITION III . THEOREM . A ...
Page 66
... radius which is perpendicular to the chord AB : then this radius bisects the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right - angled triangles CDA and CDB have the hypothenuse CA equal to CB , and ...
... radius which is perpendicular to the chord AB : then this radius bisects the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right - angled triangles CDA and CDB have the hypothenuse CA equal to CB , and ...
Page 67
... radius perpendicular to the chord . But two points determine the position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , passes through the third , and is per- pendicular to the chord ...
... radius perpendicular to the chord . But two points determine the position of a straight line ( A. 11 ) : hence , any straight line which passes through two of these points , passes through the third , and is per- pendicular to the chord ...
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Common terms and phrases
AB² ABCD AC² adjacent angles altitude angles is equal apothem base and altitude bisects centre chord circle circumference circumscribed cone consequently convex surface corresponding Cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant equilateral feet find the area formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC logarithm lower base mantissa mean proportional measured by half number of sides parallel parallelogram parallelopipedon perimeter perpendicular plane angles plane MN polyedral angle polyedron prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solution sphere spherical angle spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence