Elements of Geometry and Trigonometry |
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Page 118
... become equal , they will exactly coin- cide , and have a common perimeter . But as the sides of the circumscribed polygon cannot fall within the circle , nor the sides of the inscribed polygon without it , it follows that the perimeters ...
... become equal , they will exactly coin- cide , and have a common perimeter . But as the sides of the circumscribed polygon cannot fall within the circle , nor the sides of the inscribed polygon without it , it follows that the perimeters ...
Page 121
... become equal to the circumfe- rence of the circle , the perpendicular OF will become equal to OA , and the area of the polygon to the area of the circle ( Prop . VIII . Cor . 1. & 3. ) . But the expression for the area will then become ...
... become equal to the circumfe- rence of the circle , the perpendicular OF will become equal to OA , and the area of the polygon to the area of the circle ( Prop . VIII . Cor . 1. & 3. ) . But the expression for the area will then become ...
Page 182
... become the semicircle , OI will become equal to OA , and the solid described by the semi - polygon will become the sphere : hence the solidity of the sphere is equal to OA2 × EA , or by substituting 20A for EA , it becomes 4.OAX OA ...
... become the semicircle , OI will become equal to OA , and the solid described by the semi - polygon will become the sphere : hence the solidity of the sphere is equal to OA2 × EA , or by substituting 20A for EA , it becomes 4.OAX OA ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
14 other sections not shown
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex