The Elements of Euclid |
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Page 272
... cone . And it has been demonstrated that neither is it greater than the triple . Therefore the cylinder is triple of the cone , or the cone is the third part of the cylinder . Wherefore every cone , & c . Q. E. D. B F See Note . PROP ...
... cone . And it has been demonstrated that neither is it greater than the triple . Therefore the cylinder is triple of the cone , or the cone is the third part of the cylinder . Wherefore every cone , & c . Q. E. D. B F See Note . PROP ...
Page 273
Euclid Robert Simson. tex with the cone * , the pyramid inscribed in the cone is half Book Xft . of the pyramid circumscribed about it , because they are to one another as their bases : but the cone is less than the circum- a 6. 12 ...
Euclid Robert Simson. tex with the cone * , the pyramid inscribed in the cone is half Book Xft . of the pyramid circumscribed about it , because they are to one another as their bases : but the cone is less than the circum- a 6. 12 ...
Page 274
... cone , viz . the pyramid of which the base is the polygon EOFPGRHS , and its vertex the same with that of the cone , is greater than the solid X : in the circle ABCD describe the polygon ATBYCVDQ similar to the polygon EOFPGRHS , and ...
... cone , viz . the pyramid of which the base is the polygon EOFPGRHS , and its vertex the same with that of the cone , is greater than the solid X : in the circle ABCD describe the polygon ATBYCVDQ similar to the polygon EOFPGRHS , and ...
Page 275
... cone AL to any solid , which is less than the cone EN . In the same manner it may be demonstrated that the circle EFGH is not to the circle ABCD , as the cone EN to any solid less than the cone AL . Nor can the circle ABCD be to the ...
... cone AL to any solid , which is less than the cone EN . In the same manner it may be demonstrated that the circle EFGH is not to the circle ABCD , as the cone EN to any solid less than the cone AL . Nor can the circle ABCD be to the ...
Page 276
... cone ABCDL is similar to the cone EFGHN , AC is a to EG , as the axis KL to the axis MN ; and as AC to FG , sob is AK to EM ; therefore as AK to EM , so is KL to MN ; and , alternately , AK to KL , as EM to MN : and the right angles AKL ...
... cone ABCDL is similar to the cone EFGHN , AC is a to EG , as the axis KL to the axis MN ; and as AC to FG , sob is AK to EM ; therefore as AK to EM , so is KL to MN ; and , alternately , AK to KL , as EM to MN : and the right angles AKL ...
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Common terms and phrases
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