Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Page 314
... cylinder are the circles described by two of the oppofite fides of the parallelogram generating the cylinder . 24. Similar cones , and cylinders are those whose axes and the diameters of their bafes are proportional . e This definition ...
... cylinder are the circles described by two of the oppofite fides of the parallelogram generating the cylinder . 24. Similar cones , and cylinders are those whose axes and the diameters of their bafes are proportional . e This definition ...
Page 386
... cylinder which has the fame bafe and an equal altitude . B E H For let a cone have the fame bafe as a cylinder , viz . the circle A B C D , and an equal altitude : I fay the cone is a third part of the cylinder ; that is , the cylinder ...
... cylinder which has the fame bafe and an equal altitude . B E H For let a cone have the fame bafe as a cylinder , viz . the circle A B C D , and an equal altitude : I fay the cone is a third part of the cylinder ; that is , the cylinder ...
Page 387
... cylinder are erected ; each of thefe erected parallelepipedons will be double the prifms which are in the triangles A E B , BF C , CGD , DHA ; and the fegments of the cylinder are lefs than the erected folid parallelepipedons ...
... cylinder are erected ; each of thefe erected parallelepipedons will be double the prifms which are in the triangles A E B , BF C , CGD , DHA ; and the fegments of the cylinder are lefs than the erected folid parallelepipedons ...
Page 388
... cylinder . Let there be fuch left , which let be thofe upon A E , E B , BF , FC , CG , GD , DH , HA . Then the ... cylinder : Therefore the prifm whose base is the polygon A E B FCGDH , and altitude the fame as that of the cylinder , is ...
... cylinder . Let there be fuch left , which let be thofe upon A E , E B , BF , FC , CG , GD , DH , HA . Then the ... cylinder : Therefore the prifm whose base is the polygon A E B FCGDH , and altitude the fame as that of the cylinder , is ...
Page 389
... cylinder having the fame bafe as it , and an equal altitude . Which was to be demonstrated . d Some demonftrate this theorem thus : Every cone may be confidered as a pyramid with a polygonous base , of an infinite number of exceeding ...
... cylinder having the fame bafe as it , and an equal altitude . Which was to be demonstrated . d Some demonftrate this theorem thus : Every cone may be confidered as a pyramid with a polygonous base , of an infinite number of exceeding ...
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...