Elements of Geometry and Trigonometry: From the Works of A. M. Legendre |
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Page 59
... centre . The bounding line is called the cir- cumference . # :) 2. A 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 ...
... centre . The bounding line is called the cir- cumference . # :) 2. A 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 ...
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
... centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circumference , into two equal parts ; which was to be proved . PROPOSITION II . THEOREM . A diameter is greater than any other chord . Let AD be a ...
... centre ; which is impossible ( D. 1 ) : hence , AB divides the circle , and also its circumference , into two equal parts ; which was to be proved . PROPOSITION II . THEOREM . A diameter is greater than any other chord . Let AD be a ...
Page 63
... centre C , and the point E upon A ; then , because the arc EGP is greater than AMD , the point P will fall at some point H , beyond D , and the chord EP will take the position AH . Draw the radii CA , CD , and CH . Now , the sides AC ...
... centre C , and the point E upon A ; then , because the arc EGP is greater than AMD , the point P will fall at some point H , beyond D , and the chord EP will take the position AH . Draw the radii CA , CD , and CH . Now , the sides AC ...
Page 65
... centre of the circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a ...
... centre of the circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point G of the subtended arc , are points of the radius perpendicular to the chord . But two points determine the position of a ...
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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