The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 173
... cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed . XXII . The axis of a cylinder is the fixed straight line about which the parallelogram revolves . XXIII ...
... cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides which remains fixed . XXII . The axis of a cylinder is the fixed straight line about which the parallelogram revolves . XXIII ...
Page 174
... cylinders are those which have their axes and the diameters of their bases propor- tionals . XXV . A cube is a solid figure contained by six equal squares . 1 XXVI . A tetrahedron is a solid figure contained by four equal and ...
... cylinders are those which have their axes and the diameters of their bases propor- tionals . XXV . A cube is a solid figure contained by six equal squares . 1 XXVI . A tetrahedron is a solid figure contained by four equal and ...
Page 238
... 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 shall be 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 shall be the third part of the cylinder ; that is , the cylinder ...
Page 239
... cylinder which are upon the segments of the 12 . circle cut off by AB , BC , CD , DA , are less than the solid parallelopipeds which contain them ; therefore the prisms upon the triangles AEB , BFC , CGD , DHA , are greater than half of ...
... cylinder which are upon the segments of the 12 . circle cut off by AB , BC , CD , DA , are less than the solid parallelopipeds which contain them ; therefore the prisms upon the triangles AEB , BFC , CGD , DHA , are greater than half of ...
Page 240
... cylinder : and thus dividing each of the circum- ferences into two equal parts , and joining the points of division and their extremities by straight lines , and up- on the triangles erecting pyramids having their vertices the same with ...
... cylinder : and thus dividing each of the circum- ferences into two equal parts , and joining the points of division and their extremities by straight lines , and up- on the triangles erecting pyramids having their vertices the same with ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore