. 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. eal angle. Let ABC be the given triangle, and D the given rectilinealangle. It is required to describe a parallelogram that shall beequal to the given triangle ABC, and have one of its anglesequal to D. a Bisect a BC in E, join AE, and at the point E in the straight b line EC make ^ the angle
. 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. eal angle. Let ABC be the given triangle, and D the given rectilinealangle. It is required to describe a parallelogram that shall beequal to the given triangle ABC, and have one of its anglesequal to D. a Bisect a BC in E, join AE, and at the point E in the straight b line EC make ^ the angle CEF equal to D ; and through A draw c ^ AG parallel to EC, and throughC draw CG «= parallel to EF:therefore FECG is a parallelo-gram : and because BE is equalto EC, the triangle ABE is like- d 38. 1. wise equal ^ to the triangle AEC,since they are upon equal basesBE, EC, and between the sameparallels BC, AG : therefore thetriangle ABC is double of thetriangle AEC: and the paral- e4l. 1. lelogram FECG is likewise double e of the triangle AEC, be-cause it is upon the same base, and belv/een the same parallels :therefore the parallelogram FECG is equal to the triangleABC, and it has one of its angles CEF equal to the givenangle D. Wherefore there has been described a parallelogram.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
