Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 391
... cylinder to cylinder ; for [ by 10. 12. ] the one is thrice the other ; and therefore as the circle ABCD is to the circle EFGH , fo are the cones and cylinders of the fame altitude ftanding upon them . Wherefore cones and cylinders of ...
... cylinder to cylinder ; for [ by 10. 12. ] the one is thrice the other ; and therefore as the circle ABCD is to the circle EFGH , fo are the cones and cylinders of the fame altitude ftanding upon them . Wherefore cones and cylinders of ...
Page 392
... cylinders are to one another in the triplicate ratio of the diameters of their bases . Let there be fimilar cones and cylinders , whofe bafes are the circles ABCD , EFGH , diameters of the bases BD , FH , and axes of the cones or ...
... cylinders are to one another in the triplicate ratio of the diameters of their bases . Let there be fimilar cones and cylinders , whofe bafes are the circles ABCD , EFGH , diameters of the bases BD , FH , and axes of the cones or ...
Page 395
... cylinder to the other ; for a cylinder having the same base and alti- tude as a cone , is thrice the cone , fince it is proved [ by 10. 12. ] that every cone is one third part of a cylinder of the fame base and altitude . Therefore one ...
... cylinder to the other ; for a cylinder having the same base and alti- tude as a cone , is thrice the cone , fince it is proved [ by 10. 12. ] that every cone is one third part of a cylinder of the fame base and altitude . Therefore one ...
Page 396
... cylinder be cut [ into two cylinders ] by a plane parallel to the oppofite planes ; it will be as one cylinder is to the other , fo is the axis of the one to the axis of the other . For let the cylinder AD be cut by the plane GH [ int two ...
... cylinder be cut [ into two cylinders ] by a plane parallel to the oppofite planes ; it will be as one cylinder is to the other , fo is the axis of the one to the axis of the other . For let the cylinder AD be cut by the plane GH [ int two ...
Page 397
... cylinder PG ; and equimultiples of the axis KF , and cylinder G D , viz . the axis KM and the cylinder G z . And it has been also demonftrated , that if the axis K L exceeds the axis KM , the cylinder PG will exceed the cylinder Gz ; if ...
... cylinder PG ; and equimultiples of the axis KF , and cylinder G D , viz . the axis KM and the cylinder G z . And it has been also demonftrated , that if the axis K L exceeds the axis KM , the cylinder PG will exceed the cylinder Gz ; if ...
Other editions - View all
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory No preview available - 2016 |
Common terms and phrases
A B C D alfo alſo angle ABC becauſe the angle bifected centre circle A B C circumference cone confequent cylinder defcribed demonftrated diameter equal angles equiangular equimultiples Euclid EUCLID's ELEMENTS fame altitude fame multiple fame ratio fame reafon fecond fegment femidiameter fhall fides A B fimilar fince firft firſt fixth folid angle folid parallelepipedon fome fphere ftand given circle given right line given triangle greater infcribed interfect join leffer lefs leſs parallel parallelogram perpendicular polygon prifm PROP propofition proportional pyramid rectangle contained regular polygon remaining angle right angles right line A B right lined figure right-lined SCHOLIUM ſquare thefe THEOR theſe thofe thoſe trapezium triangle ABC twice the fquare vertex the point Wherefore whofe bafe whoſe baſe
Popular passages
Page 247 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page 248 - But it was proved that the angle AGB is equal to the angle at F ; therefore the angle at F is greater than a right angle : But by the hypothesis, it is less than a right angle ; which is absurd.
Page 18 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Page 32 - Let the straight line EF, which falls upon the two straight lines AB, CD, make the alternate angles AEF, EFD equal to one another; AB is parallel to CD.
Page 56 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 391 - KL: but the cylinder CM is equal to the cylinder EB, and the axis LN to the axis GH; therefore as the cylinder EB to...
Page 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Page 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 183 - FK : in the same manner it may be demonstrated, that FL, FM, FG are each of them equal to FH, or FK : therefore the five straight lines FG, FH, FK, FL, FM are equal to one another : wherefore the circle described from the centre F, at the distance of...