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Page 172
... circ . Kl = ( circ . OA + circ . CD ) ; therefore , the convex surface of a frustum of a cone is equal to its side multi- plied by the circumference of a section at equal distances from the two bases . Scholium . If a line AD , lying ...
... circ . Kl = ( circ . OA + circ . CD ) ; therefore , the convex surface of a frustum of a cone is equal to its side multi- plied by the circumference of a section at equal distances from the two bases . Scholium . If a line AD , lying ...
Page 177
... circ . ON . circ . NM ; hence EDx circ . NM = HI × circ . ON ; and since the same may be shown for each of the other sides , it is plain that the surface described by the entire perimeter is equal to ( FH + HI + IP + PQ + QA ) × circ ON = ...
... circ . ON . circ . NM ; hence EDx circ . NM = HI × circ . ON ; and since the same may be shown for each of the other sides , it is plain that the surface described by the entire perimeter is equal to ( FH + HI + IP + PQ + QA ) × circ ON = ...
Page 193
... circ . - BC , circ . - AC , circ.-AB. Thus the angle D , for example , is measured by the arc MI ; but MI + BC = MC + BI = circ .; hence the arc MI , the measure of D , is equal to circ .-- BC ; and so of all the rest . Scholium . It ...
... circ . - BC , circ . - AC , circ.-AB. Thus the angle D , for example , is measured by the arc MI ; but MI + BC = MC + BI = circ .; hence the arc MI , the measure of D , is equal to circ .-- BC ; and so of all the rest . Scholium . It ...
Contents
BOOK | 7 |
BOOK III | 41 |
Problems relating to the First and Third Books | 57 |
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Common terms and phrases
adjacent altitude angle ACB 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 equal angles 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 logarithm number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex