The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 217
... cylinder are the circles described by the two revolving opposite sides of the parallelogram . XXIV . Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid ...
... cylinder are the circles described by the two revolving opposite sides of the parallelogram . XXIV . Similar cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid ...
Page 300
... 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 301
... cylinder , is greater than half of the cylinder . Bisect the circumferences AB , BC , CD , DA , in the points E , F , G , H ; and join AE , EB , BF , FC , CG , GD , DH , HA : then , each of the tri- angles AEB , BFC , CGD , DHA is ...
... cylinder , is greater than half of the cylinder . Bisect the circumferences AB , BC , CD , DA , in the points E , F , G , H ; and join AE , EB , BF , FC , CG , GD , DH , HA : then , each of the tri- angles AEB , BFC , CGD , DHA is ...
Page 302
... cylinder above the triple of the cone : let them be those upon the seg- ments of the circle AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the cylinder , that is , the prism of which the base is the poly- gon AEBFCGDH ...
... cylinder above the triple of the cone : let them be those upon the seg- ments of the circle AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the cylinder , that is , the prism of which the base is the poly- gon AEBFCGDH ...
Page 303
... 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 upon 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 upon the triangles erecting pyramids having their vertices the same with ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole