. 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. b 2. 3. each of the circles, the straight line BD falls within each** ofcCor. them : and their centres are«= in the straight line GH which bi-sects BD at right angles; therefore GH passes through the pointd 11. 3. of contact J ; but it does not pass through it, because the pointsli, D are without the
. 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. b 2. 3. each of the circles, the straight line BD falls within each** ofcCor. them : and their centres are«= in the straight line GH which bi-sects BD at right angles; therefore GH passes through the pointd 11. 3. of contact J ; but it does not pass through it, because the pointsli, D are without the straight line GH, which is absurd: there-fore one circle cannot touch another on the inside in more pointsthan one. OF EUCLID. 79 Nor can two circles touch one another on the outside in Book than one point: for, if it be possible, let the circle ACK <^-ymJtouch the circle ABC in the points A, C, and join AC: there-fore, because the two points A, C are inthe circumference of the circle ACK, thestraight line AC which joins them shallfall within*» the circle ACK: and the cir-cle ACK is without the circle ABC ; andtherefore the straight line AC is withoutthis last circle ; but, because the points A,C are in the circumference of the circleABC, the straight line AC must be wi
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
