The Elements of Euclid |
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Page 275
... cylinder , because the cylinders are triple of the c 10.12 cone , each to each . Therefore , as the circle ABCD to the circle EFGH , so are the cylinders upon them of the same al- titude . Wherefore cones and cylinders of the same ...
... cylinder , because the cylinders are triple of the c 10.12 cone , each to each . Therefore , as the circle ABCD to the circle EFGH , so are the cylinders upon them of the same al- titude . Wherefore cones and cylinders of the same ...
Page 279
... cylinder to the cylinder ; b 15.5 . for every cone is the third part of the cylinder upon the same base , and of the same altitude : therefore also the cylinder has to the cylinder the triplicate ratio of that which AC has to EG ...
... cylinder to the cylinder ; b 15.5 . for every cone is the third part of the cylinder upon the same base , and of the same altitude : therefore also the cylinder has to the cylinder the triplicate ratio of that which AC has to EG ...
Page 280
... cylinder AD into the cylinders AH , GD ; for they are the same which would be described by the revolution of the parallelograms AK , GF , about the straight lines EK , KF : and it is to be shown , that the cylinder AH is to the cy ...
... cylinder AD into the cylinders AH , GD ; for they are the same which would be described by the revolution of the parallelograms AK , GF , about the straight lines EK , KF : and it is to be shown , that the cylinder AH is to the cy ...
Page 281
... cylinder BG to the cylinder GD . Wherefore , if a cylinder , & c . Q. E. D. PROP . XIV . THEOR . CONES and cylinders upon equal bases are to one another as their altitudes . Let the cylinders EB , FD be upon the equal bases AB , CD : as the ...
... cylinder BG to the cylinder GD . Wherefore , if a cylinder , & c . Q. E. D. PROP . XIV . THEOR . CONES and cylinders upon equal bases are to one another as their altitudes . Let the cylinders EB , FD be upon the equal bases AB , CD : as the ...
Page 282
... cylinder AX is equal to the cylinder EO , as AX is to the cylinder ES , so is the cylinder EO to the same ES . But as the cylinder AX to the cylinder ES , so a is the base ABCD to the base EFGH ; for the cylinders AX , ES are of the ...
... cylinder AX is equal to the cylinder EO , as AX is to the cylinder ES , so is the cylinder EO to the same ES . But as the cylinder AX to the cylinder ES , so a is the base ABCD to the base EFGH ; for the cylinders AX , ES are of the ...
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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