The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 198
... cylinder is the fixed straight line about which the parallelogram revolves . XXIII . The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram . XXIV . Similar cones and cylinders are ...
... cylinder is the fixed straight line about which the parallelogram revolves . XXIII . The bases of a cylinder are the circles described by the two revolving opposite sides of the parallelogram . XXIV . Similar cones and cylinders are ...
Página 269
... cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the cylinder ; that is , the cylinder ...
... cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the cylinder ; that is , the cylinder ...
Página 270
... cylinder is less than the prism upon the square described about the circle ABCD : therefore the prism upon the square ABCD of the same altitude with the cylinder , is greater than half of the cylinder . Bisect the cir- cumferences AB ...
... cylinder is less than the prism upon the square described about the circle ABCD : therefore the prism upon the square ABCD of the same altitude with the cylinder , is greater than half of the cylinder . Bisect the cir- cumferences AB ...
Página 271
... cylinder be less than the triple of the cone , Let it be less , if possible : therefore , inversely , the cone is greater than the third part of the cylinder . In the circle ABCD describe a square ; this square is greater than the half ...
... cylinder be less than the triple of the cone , Let it be less , if possible : therefore , inversely , the cone is greater than the third part of the cylinder . In the circle ABCD describe a square ; this square is greater than the half ...
Página 272
... cylinder . But this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the cylinder . Therefore this prism is greater than the cylin der of which the base is the circle ABCD . But it is ...
... cylinder . But this pyramid is the third part of the prism upon the same base AEBFCGDH , and of the same altitude with the cylinder . Therefore this prism is greater than the cylin der of which the base is the circle ABCD . But it is ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore