. 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. ion, in a given angle HGC, for it is equal a 29. to the given angle ADC ; HGis given in position b ; but it is b 32. also in magnitude, because it is equal to c AD which is c 34. in magnitude ; therefore because G one of the extremi-ties of the straight line GH given in position 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. ion, in a given angle HGC, for it is equal a 29. to the given angle ADC ; HGis given in position b ; but it is b 32. also in magnitude, because it is equal to c AD which is c 34. in magnitude ; therefore because G one of the extremi-ties of the straight line GH given in position and magnitude isgiven, the other extremity H is given d; and the straight line d 30. , which is drawn through the given point H parallel to bCgiven in position, is therefore given e in position. e 31 dat. PROP. XXXVIII. IF a straight line be drawn from a given point totwo parallel straight lines given in position, the ratioof the segments between the given point and the pa-rallels shall be given. Let the straight line EFG be drawn from the given point Eto the parallels AB, CD, the ratio of EF to EG is given. From the point E draw EHK perpendicular to CD ; andbecause from a given point E the straight line EK is drawn toCD which is given in position, in a given angle EKC ; EK is .34-. given in position a ; and AB, CD are given in position; there»a 33. b the points H, K are given: and the point E is given ; b 28. c EH, EK are given in magnitude, and the ratio d ofc 29. is therefore given. But as EH to EK, so is EF to EG, ,j j j^^_because AB, CD are parallels ; therefore the ratio of EF to EGis given. PROP. XXXIX. 35,36. IF the ratio of the segments of a straight line be- See \veen a given point in it and two parallel sti-aightlines, be given, if one of the parallels be given in po-sition, the other is also given in position. 3 D 894 EUCLIDS From the given point A, let the straight line AED be drawnto the two parallel straight lines FG, BC, an
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
