. 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. 72 THE ELEMENTS Booklll. For, if it be possible, let E be their centre: join EC, and ^?^v*^ draw any straight line EFG meet-ing them in F and G ; and because CE is the centre of the circle ABC,CE is equal to EF: again, be-cause E is the centre of the circleCDG, CE is equal to EG: but ^CE was shown to be e
. 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. 72 THE ELEMENTS Booklll. For, if it be possible, let E be their centre: join EC, and ^?^v*^ draw any straight line EFG meet-ing them in F and G ; and because CE is the centre of the circle ABC,CE is equal to EF: again, be-cause E is the centre of the circleCDG, CE is equal to EG: but ^CE was shown to be equal to EF;therefore EF is equal to EG, theless to the greater, which is impos-sible : therefore E is not the centreof the circles ABC, CDG. Where-fore, if two circles, &c. Q. E. PROP. VI. THEOR. IF two circles touch one another internally, theyshall not have the same centre. Let the two circles ABC, CDE touch one another internally inin the point C; they have not the same centre. For, if they can, let it be F; join FC, and draw any straightline FEB meeting them in E and B; C and because F is the centre of thecircle ABC, CF is equal to FB;also, because F is the centre of thecircle CDE, CF is equal to FE: andCF was shown equal to FB; there-fore FE is equal to FB, the less to Athe greater, which is impossible:wherefore F is not the centre ofthe circles ABC, CDE. Therefore,if two circles, Stc. Q. E. D.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
