Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 59
... 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 60
... circumference touches all of the sides of the polygon . OOD хо о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... circumference touches all of the sides of the polygon . OOD хо о POSTULATE . A circumference can be described from any point as a centre , and with any radius . PROPOSITION I. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
Page 61
... radius CD . In the tri- angle ACD , we have AD less than ( B. I. , P. equal to A the sum of AC and CD VII . ) . But this sum is AB ( D. 3 ) : hence , AB is greater than AD ; which was to be proved . i PROPOSITION III . THEOREM . A ...
... radius CD . In the tri- angle ACD , we have AD less than ( B. I. , P. equal to A the sum of AC and CD VII . ) . But this sum is AB ( D. 3 ) : hence , AB is greater than AD ; which was to be proved . i PROPOSITION III . THEOREM . A ...
Page 64
... radius which is perpendicular to the chord AB : then will this radius bisect the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB ...
... radius which is perpendicular to the chord AB : then will this radius bisect the chord AB , and also the arc AGB . For , draw the radii CA and CB . Then , the right - angled triangles CDA and CDB will have the hypothenuse CA equal to CB ...
Page 65
... 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 , will pass through the third , and be perpendicular to the ...
... 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 , will pass through the third , and be perpendicular to the ...
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Common terms and phrases
ABē ABCD altitude apothem Applying logarithms centre chord circle circumference cone consequently convex surface cosec Cosine Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area Find the logarithmic following RULE frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC linear units log cot log sin lower base lune mantissa multiplied number of sides opposite parallel parallelogram parallelopipedon perpendicular plane MN polar triangle polyedral angle polyedron principle demonstrated prism proportional PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar six right slant height solution sphere spherical angle spherical excess spherical polygon spherical triangle square straight line subtracting Tang tangent THEOREM triangle ABC triangular prism upper base vertex volume whence write the following