The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Seite 189
A prism is said to be inscribed in a cylinder when its bases are inscribed in the bases of the cylinder ; and , a cylinder is said to be described about a prism , when its bases are described about the bases of the prism . IV .
A prism is said to be inscribed in a cylinder when its bases are inscribed in the bases of the cylinder ; and , a cylinder is said to be described about a prism , when its bases are described about the bases of the prism . IV .
Seite 194
equal to the prism GFCH KL ; and the pyramid A EG H is equal to the pyramid HKL D. Therefore the two prisms EBFGH K and GFCHKL are greater than the two pyramids AEG H and H KLD . Wherefore the whole pyramid A BCD is divided into two ...
equal to the prism GFCH KL ; and the pyramid A EG H is equal to the pyramid HKL D. Therefore the two prisms EBFGH K and GFCHKL are greater than the two pyramids AEG H and H KLD . Wherefore the whole pyramid A BCD is divided into two ...
Seite 195
H is to the prism RVFSTY . But it has been proved that the prism LXCOMN is to the prism RV FSTY , as the base ABC is to the base DEF . Therefore , the base ABC is to the base DEF , as the two prisms in the pyramid ABCG is to the two ...
H is to the prism RVFSTY . But it has been proved that the prism LXCOMN is to the prism RV FSTY , as the base ABC is to the base DEF . Therefore , the base ABC is to the base DEF , as the two prisms in the pyramid ABCG is to the two ...
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A B C ABCD altitude applied base bisected Book Cassell's centre circle circumference cloth coincide common cone Const contained Corollary cylinder definition demonstration described diagonal diameter divided double draw Edition equal equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half Illustrated inscribed interior join less magnitudes manner meet multiple parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proportionals proposition proved pyramid ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle sphere square straight lines A B taken THEOREM third touch triangle triangle ABC twice vertex Vols Wherefore whole