. 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. equal to CD : therefore, the straight line AB co-<^^^fmmJ inciding with CD, the segment AEB must * coincide with the% 23. 3. segment CFD, and therefore is equal to it. Wherefore, similarsegments, &c. Q. E. D. PROP. XXV. PROB. See N. A SEGMENT of a circle being given, to describethe circle of which it i
. 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. equal to CD : therefore, the straight line AB co-<^^^fmmJ inciding with CD, the segment AEB must * coincide with the% 23. 3. segment CFD, and therefore is equal to it. Wherefore, similarsegments, &c. Q. E. D. PROP. XXV. PROB. See N. A SEGMENT of a circle being given, to describethe circle of which it is the segment. a 10. 11. Let ABC be the given segment of a circle; it is required todescribe the circle of which it is the segment. Bisect ^ AC in D, and from the point D draw ^ DB at rightangles to AC, and join AB: first, let the angles ABD, BADbe equal to one another; then the straight line BD is equal^to DA, and therefore to DC; and because the three straightlines DA, DB, DC are all equal, D is the centre of the cir-cle *!: from the centre D, at the distance of any of the threeDA, DB, DC describe a circle ; this shall pass through the otherpoints; and the circle of which ABC is a segment is described:and because the centre D is in AC, the segment ABC is a se-. micircle: but if the angles ABD, BAD are not equal to onee another, at the point A, in the straight line AB, make « the angleBAE equal to the angle ABD, and produce BD, if necessary, toE, and join EC: and because the angle ABE is equal to the an-gle BAE, the straight line BE is equal e to EA : and because ADis equal to DC, and DE common to the triangles ADE, CDE,the two sides AD, DE are equal to the two CD, DE, each toeach ; and the angle ADE is equal to the angle CDE, foreach of them is a right angle; therefore the base AE is equalf f to the base EC : but AE was shown to be equal to EB ; where-fore also BE is equal to EC: and the three straight lines AE; OF EUCLID. 89 EB, EC are therefore
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
