. 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. 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
. 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. 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.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
