Elements of Geometry and Trigonometry |
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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
... its circumference touches all of the sides of the polygon . ооо хо POSTULATE . A circumference can be described from any point as a centre . and with any radius . PROPOSITION L. THEOREM . Any diameter divides the circle , 60 GEOMETRY .
... its circumference touches all of the sides of the polygon . ооо хо POSTULATE . A circumference can be described from any point as a centre . and with any radius . PROPOSITION L. 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 , 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 , 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
ABCD AC² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence