. 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. a 17. 3. b Jo. 1. PROP. XXXIV. PROB. TO cut off a segment from a given circle whichshall contain an angle equal to a given rectilinealangle. Let ABC be the given circle, and D the given rectilineal angle ;it is required to cut off a segment from the circle ABC that shallcontain an angle equal to the given
. 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. a 17. 3. b Jo. 1. PROP. XXXIV. PROB. TO cut off a segment from a given circle whichshall contain an angle equal to a given rectilinealangle. Let ABC be the given circle, and D the given rectilineal angle ;it is required to cut off a segment from the circle ABC that shallcontain an angle equal to the given angle D. Draw » the straight line EF touching the circle ABC in thepoint B, and at the point B,in the straight line BF,make ^ the angle FBC equalto the angle D ; therefore,because the straight lineEF touches the circle ABC,and BC is drawn from thepoint of contact B, the angleFBC is equal = to the anglein the alternate segmentBAC of the circle : but the angle FBC is equal to the angle D ; therefore the angle in the seg-ment BAC is equal to the angle D : Avherefore the segment BACis cutoff from the gven circle ABC containing an angle equal tothe given angle D. Which was to be OF EUCLID.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
