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 . D 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 . D 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 © 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 © 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 , CH ...
... 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 , CH ...
Page 65
... centre of the circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point of the subtended are , are points of the radius perpendicular to the chord . But two points determine the position of a straight ...
... centre of the circle . Scholium . The centre C , the middle point D of the chord AB , and the middle point of the subtended are , are points of the radius perpendicular to the chord . But two points determine the position of a straight ...
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Common terms and phrases
AB² ABCD adjacent angles altitude angle ACB apothem Applying logarithms base and altitude centre chord circle circumference circumscribed cone consequently convex surface cosec Cosine Cosine D Cotang cylinder demonstrated in Book denote diameter distance divided draw edges Equation feet find the area following RULE Formula frustum given angle greater hence homologous hypothenuse included angle inscribed intersection less Let ABC log cot log sin lower base mantissa measured by half number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle principle demonstrated prism PROPOSITION proved pyramid quadrant radii radius rectangle regular polygon right angles right-angled triangle Scholium segment similar slant height solution sphere spherical polygon spherical triangle square straight line Tang tangent THEOREM triangle ABC triangular prism triedral angle upper base vertex volume whence write the following