Elements of Geometry and Trigonometry |
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Page 118
... perimeter AB + BC , will become the arc AKBC . PROPOSITION IX . THEOREM . The area of a regular polygon is equal to its perimeter , multi- plied by half the radius of the inscribed circle . Let there be the regular polygon GHIK , and ON ...
... perimeter AB + BC , will become the arc AKBC . PROPOSITION IX . THEOREM . The area of a regular polygon is equal to its perimeter , multi- plied by half the radius of the inscribed circle . Let there be the regular polygon GHIK , and ON ...
Page 169
... perimeter of the polygon , multiplied by the altitude H ( Book VII . Prop . I. ) . Let now the arcs which subtend the sides of the polygon be continually bisected , and the number of sides of the polygon indefinitely increased : the ...
... perimeter of the polygon , multiplied by the altitude H ( Book VII . Prop . I. ) . Let now the arcs which subtend the sides of the polygon be continually bisected , and the number of sides of the polygon indefinitely increased : the ...
Page 177
... perimeter is equal to ( FH + HI + IP + PQ + QA ) × circ ON = AF × circ . ON Cor . The surface described by any ... perimeter will coincide with the circumfe- rence ABCDE , the perpendicular OF will become equal to OE , and the surface ...
... perimeter is equal to ( FH + HI + IP + PQ + QA ) × circ ON = AF × circ . ON Cor . The surface described by any ... perimeter will coincide with the circumfe- rence ABCDE , the perpendicular OF will become equal to OE , and the surface ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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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