The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 173
... cone is called a right angled cone ; if it be less than the other side , an obtuse angled ; and if greater , an acute angled cone . XIX . . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The base ...
... cone is called a right angled cone ; if it be less than the other side , an obtuse angled ; and if greater , an acute angled cone . XIX . . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The base ...
Page 174
... cones 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 ...
... cones 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
... cone is the third part of a 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 ...
... cone is the third part of a 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 ...
Page 239
... cone : but this prism is triple of the pyramid 1 Cor . 7 . upon the same base , of which the vertex is the same 12 . with the vertex of the cone ; therefore the pyramid upon the base AEBFCGDH , having the same vertex with the cone , is ...
... cone : but this prism is triple of the pyramid 1 Cor . 7 . upon the same base , of which the vertex is the same 12 . with the vertex of the cone ; therefore the pyramid upon the base AEBFCGDH , having the same vertex with the cone , is ...
Page 240
... cone which it contains ; there- fore the pyramid upon the square ABCD , having the same vertex with the cone , is greater than the half of the cone . Bisect the circumferences AB , BC , CD , DA , in the points E , F , G , H , and join ...
... cone which it contains ; there- fore the pyramid upon the square ABCD , having the same vertex with the cone , is greater than the half of the cone . Bisect the circumferences AB , BC , CD , DA , in the points E , F , G , H , and join ...
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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