Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth BooksJ. Rivington, 1765 - 464 sider |
Fra bogen
Resultater 6-10 af 25
Side 387
... cone , is greater than the cone whose base is the circle ABCD : but it is lefs too , because it is contained in it , which is impoffible : Therefore the cylinder is not greater than thrice the cone . I lay moreover , that the cylinder ...
... cone , is greater than the cone whose base is the circle ABCD : but it is lefs too , because it is contained in it , which is impoffible : Therefore the cylinder is not greater than thrice the cone . I lay moreover , that the cylinder ...
Side 388
... cone , for this is contained in that . Therefore the pyramid whose bafe is the fquare A B CD , and vertex the fame as that of the cone , is greater than one half the cone . Bi- fect the parts A B , BC , C D , DA of the circumference in ...
... cone , for this is contained in that . Therefore the pyramid whose bafe is the fquare A B CD , and vertex the fame as that of the cone , is greater than one half the cone . Bi- fect the parts A B , BC , C D , DA of the circumference in ...
Side 389
... cone , thus taken for a pyra- mid , will also be one third of a cylinder , of the fame altitude , thus taken for a prifm . " PROP . XI . THEOR . Cones and cylinders having the fame altitude , are to one another as their bases . Let the ...
... cone , thus taken for a pyra- mid , will also be one third of a cylinder , of the fame altitude , thus taken for a prifm . " PROP . XI . THEOR . Cones and cylinders having the fame altitude , are to one another as their bases . Let the ...
Side 390
... cone is less than the circumfcribed pyramid : Therefore the pyramid whose base is the square E FG , and vertex the fame as that of the cone , is greater than one half the cone . Bifect the parts EF , FG , GH , HE of the circumference in ...
... cone is less than the circumfcribed pyramid : Therefore the pyramid whose base is the square E FG , and vertex the fame as that of the cone , is greater than one half the cone . Bifect the parts EF , FG , GH , HE of the circumference in ...
Side 391
... cone EN . But the cone AL is greater than the pyramid which is in it : Therefore the folid x is greater than the pyramid which is in the cone EN : But it is lefs too ; which is abfurd . Therefore it is not as the circle ABCD to the ...
... cone EN . But the cone AL is greater than the pyramid which is in it : Therefore the folid x is greater than the pyramid which is in the cone EN : But it is lefs too ; which is abfurd . Therefore it is not as the circle ABCD to the ...
Andre udgaver - Se alle
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning - 2023 |
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books Euclid,David Gregory Ingen forhåndsvisning - 2016 |
Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 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...
Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 110 - If any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle.
Side 130 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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...