Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books |
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Seite 314
A cylinder is a solid figure made by the entire revolution of a right angled parallelogram about one of its sides , which remains at rest during the revolution of the parallelogram 8 . 22. The axis of the cylinder is that side of the ...
A cylinder is a solid figure made by the entire revolution of a right angled parallelogram about one of its sides , which remains at rest during the revolution of the parallelogram 8 . 22. The axis of the cylinder is that side of the ...
Seite 386
Every cone is a third part of a cylinder which has the same base and an equal altituded . For let a cone have the same base aś à cylinder , viz . the circle ABC D , and an equal altitude : I say the cone is a third part of the cylinder ...
Every cone is a third part of a cylinder which has the same base and an equal altituded . For let a cone have the same base aś à cylinder , viz . the circle ABC D , and an equal altitude : I say the cone is a third part of the cylinder ...
Seite 387
be completed , upon which folid parallelepipedons of the fame altitude as the cylinder are erected ; each of these erected parallelepipeduns will be double the prisms which are in the triangles À E B , BFC , CGD , DHA ; and the segments ...
be completed , upon which folid parallelepipedons of the fame altitude as the cylinder are erected ; each of these erected parallelepipeduns will be double the prisms which are in the triangles À E B , BFC , CGD , DHA ; and the segments ...
Seite 388
be left some portions of the cone that will be less than the excess of the cone abové one third part of the cylinder . Let there be such left , which let be those upon A E , E B , BF , FC , CG , GD , DH , HA .
be left some portions of the cone that will be less than the excess of the cone abové one third part of the cylinder . Let there be such left , which let be those upon A E , E B , BF , FC , CG , GD , DH , HA .
Seite 389
Therefore every cone is one third part of the cylinder having the same base as it , and an equal altitude . Which was to be demonstrated . d Some demonstrate this theorem thus : Every cone may be considered as a pyramid with a ...
Therefore every cone is one third part of the cylinder having the same base as it , and an equal altitude . Which was to be demonstrated . d Some demonstrate this theorem thus : Every cone may be considered as a pyramid with a ...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
A B C ABCD added alſo altitude baſe becauſe centre circle circumference common cone continue cylinder definition demonſtrated deſcribed diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid exceeds fall fame fides figure firſt folid fore four fourth given right line greater half inſcribed join leſs magnitudes manner meet multiple oppoſite parallel parallelogram perpendicular plane polygon priſms PROP proportional propoſition proved pyramid ratio rectangle remaining angle right angles right line A B right lined figure ſame ſay ſecond ſegment ſhall ſides ſimilar ſince ſolid ſome ſphere ſquare ſtand ſum taken THEOR theſe third thoſe thro touch triangle triangle ABC twice vertex Wherefore whole whoſe baſe
Beliebte Passagen
Seite 245 - 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.
Seite 28 - 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...
Seite 246 - 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.
Seite 16 - 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.
Seite 30 - 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.
Seite 54 - 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.
Seite 389 - 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...
Seite 108 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Seite 128 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 181 - 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...