An introduction to geometry; containing the most useful propositions in Euclid, & other authors ...

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1768 edition. Excerpt: ...Defg paffing through the points A and B, to revolve, or turn about the line Ab as an axis, till it falls upon the point c, and there remains at reft. Now the points A, B, C are in the plain Defg.-above Therefore, the lines Ab, Bc, Ca are alfo in the plain Defg-------6 Confequentjy, the three fides of any plain triangle, are ia one plain.: 248. Corollary. Aplain niill pafs through any two /trait lines which meet each ether. 2 249. The Let the plains Ab, Cd cut one another in E and r, and join Ef; then the ftrait line Ef is their commoa iedion. For the points e and F being in the plain Ab, the itrait line E F will agree with the faid plain--6 By the fame reafon, the line Ef will agree with the plain Cd--------Th. the ftrait line Ef muft be their common fe&ion. Remark. If marry plains pa/s thro two points B and F, tit ftrait line if is the common Jeclion of them all.,,.4 t 1 f 153' 3 2JO. If a flrait line ftands at right dngfeito (wo Jirait lines cutting one another, at the point of feBient it will he perpendicular to the plain in which thoje lines are Jituate.-. F „ Let the line Ef (land at right angles to the lines Ab, co cutting each other in E; then Ef is perpendicular to the plain Acbd. For take Ea, Ec, Eb, Ed equal to one another, join Att, Cb, draw Geh at pleafure meeting Ad, Cb in p and H, and join Fa, Fg, Fd, Fb, Fh, Fc. Now Ea, Ed, Eb, Ec are equal--con. And the contained angles Aed, Bec are equal-70 Th. the angle Gae--Ebh, and Ad--Ec--62 But the angle Aeg = Beh----79' Therefore---AO = Bh, and Ge = Eh--77 2. The angles Fea,'fed, Feb, Fec are equal-54. Th. Fa, Fd, Fb, Fc are equal-62 Th. the angles Fad, Fbc are equal-'-66 3. The fides Fa, Ag are equal to Fb, Bh each to each above And the contained angles Fag, Fbh are...