. Gli elementi di Euclid : cioè i primi sei libri, insieme con l'undicesimo e il dodicesimo : gli errori, con cui il theon, o altri, hanno già da tempo vistato questi libri, sono corretti, e alcune delle dimostrazioni di Euclid sono ripristinate : Inoltre, il libro dei dati di Euclid, in modo simile corretto. A del planeCAD al planeCAE. In BF takeBM pari ad AK, edal punto M trafila, nei piani FBG, FBH, le linee rettilinee MG, MN ortogonali a BF; quindi l'angolo GMNè l'inclinazione a del piano FBG rispetto al piano FBH: JoLD, NG; E perché nei triangoli KAD, MBG, theangles KAD, MB

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. 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. a of the planeCAD to the planeCAE. In BF takeBM equal to AK, andfrom the point M draw, in the planes FBG, FBH, the straightlines MG, MN at right angles to BF; therefore the angle GMNis the inclination a of the plane FBG to the plane FBH: joinLD, NG; and because in the triangles KAD, MBG, theangles KAD, MBG are equal, as also the right angles AKD, BMG, and that the sides AK, BM, adjacent to the equalangles, are equal to one another; therefore KD is equal ^ to b 26. 1MG, and AD to BG: for the same reason, in the trianglesKAL, MBN, KL is equal to MN, and AL to BN: and in thetriangles LAD, NBG, LA, AD are equal to NB, BG, and theycontam equal angles; therefore the base LD is equal <= to the c 4.1base NG. Lastly, in the triangles KLD, MNG, the sides DK, KL are equal to GM, MN, and the base LD to the base NG;therefore the angle DKL is equal d to the angle GMN : but the d 8.1.angle DKL is the inclination of the plane CAD to the planeCAE, and the angle GMN is the inclination of the plane FBG. 222 THE ELEMENTS Book XI. to the plane FBH, which planes have therefore the same incli-*—V—^ nation » to one another: and in the same manner it may be de-a 7. monstrated, that the other planes in which the equal angles are dof. 11. Yiave the same inclination to one another. Therefore, if two so-lid angles, See. Q. E. D. PROP. B. THEOR. See N, IF two solid angles be contained, each by threeplane angles which are equal to one another, each toeach, and alike situated; these solid angles are equalto one another. Let there be two solid angles at A and B, of which the solidangle at A is contained by the three plane angles CAD, CAE, EAD; and that at B by the three plane angles FBG, FBH, HBG ; of whic

Parole chiave associate all'immagine

• bookauthoreuclid
• bookcentury1800
• booksubje
• booksubjectgeometry