. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. re greater than the angleE ; wherefore the double of A, B together is greater thanthe three angles A, B, E together, which three are conse-quently less than four right angles ; and every two of thesame angles A, B, E are greater tliun the third ; therefore,by prop. 23, 1), a solid angle may be made contai
. The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected. re greater than the angleE ; wherefore the double of A, B together is greater thanthe three angles A, B, E together, which three are conse-quently less than four right angles ; and every two of thesame angles A, B, E are greater tliun the third ; therefore,by prop. 23, 1), a solid angle may be made contained by threeplane angles equal to the angles A, B, E, each to each. Letthis be the angle F contained by the three plane angles GFH,HFK, GFK wiiicn are equal to the angles A, B, E, each toeach : and because the angles C, D together are not greaterthan the angles A, B together, therefore the angles C, D, Eare not greater than the angles A, B, E: but these last three areless than four right angles, as has been demonstrated : where-fore also the angles C, D, E are together less than four rightangles, and every two of them are greater than the third; there-fore a solid angle may be made which shall be contained by threea 23. 11. plane angles equal to the angles C, D, E, each to each a: and. by prop. 26, 11, at the point F in the straight line FG a solidangle may be made equal to that which is contained by thethree plane angles that are equal to the angles C, D, E : letthis be made, and let the angle GFK, which is equal to E, beone of the three; and let KFL, GFL be the other two whichare equal to the angles, C, D, each to each. Thus there is asolid angle constituted at the point F contained by the four planeangles GFH, HFK, KFL, GFL v/hich are equal to the anglesA, B, C, D, each to each. Again, Find another angle M such, that every two of thethree angles A, B, M l)e greater than the third, and alsoevery tv/o of the three C, D, M be greater than the third:
Size: 2586px × 966px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
