Euclidis Elementorum libri XV breviter demonstrati, opera Is. Barrow / [Euclid].

  • Euclid
Date:
1659
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Licence: Public Domain Mark

Credit: Euclidis Elementorum libri XV breviter demonstrati, opera Is. Barrow / [Euclid]. Source: Wellcome Collection.

    37/428 page 11
    Lm ||] ul (tls | «| /fy | | Liber I, X1 lem, fub equalibus ve&is lineis contentum, e» bafim uterque utvique , fub quibus equalia latera (ubten- duntur. $i pun&um D puncto A applicetur, & recta D Ere&tz A B fuperponatur ; cadet punctum E inB,;quia D F« — A B. Item recta D F cadet inA C, quia. ang. A « — D. Quinetiam pun- *?* &um F puncto C coineidet ; quia A C a — D F. Ergo retta E F, B C; cum eoídem habeant ter- minos; bcongruent, & proinde zquales funt. p , 4,5», Quare triangula BAC,EDE;&anguliB, E; itemque anguli C , F etiam congruunt , & «- quantur. Qaod erat Demonftrandum. pDpposeP. V. A | Ifofcelium triangulorum ABC qui ad baffm funt anguli A B C, A C B inter fe funt. equales. Et produttis equalibus ve&bis Uneis A B,A C qui fub bafe funt an- gui CBD, BCE inter fe e- quales erant. j * Acape A F—A D;&bjun- , js Et CD; acBF. : ) Quoniam in triangulis chyp. ACD,ABF; funt ABc — A C;& AF 4 — AD, deonfir. angulufq; A communis;e erit ang. ABF— ACD; c4. 1 & ang. AF Be—— AD C, &bas. BFe— DC; item F C f — D B. ergo in triangulis BF C , pas B D C gciitang.F CB, — DB C. Q.E.D. Item 2. ideo ang. F B C — D C B. atqui ang. ABE p — fh pr. A C D. ergo ang. ABC4— A CB. Q. E. D. ka.ex. | Corollarium. Hinc,Omne triangulum «quilaterum eft quo- que &quiangulum, PROP.
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