. 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. d from a point D witiiin it draw a the straight IjneDE at right angles to the plane ABC; in DE take DE, DPequal to one another, upon the opposite sides of the plane,and let G be any point in EF ; join DA, DB, DC; EAEB, EC; FA, FB, FC; GA, GB, GC: because the straightline EDF is at right angles to the plan
. 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. d from a point D witiiin it draw a the straight IjneDE at right angles to the plane ABC; in DE take DE, DPequal to one another, upon the opposite sides of the plane,and let G be any point in EF ; join DA, DB, DC; EAEB, EC; FA, FB, FC; GA, GB, GC: because the straightline EDF is at right angles to the plane ABC, it makes iightangles Avith DA, DB, DC which it meets in that plane ; andin the triangles EDB, FDB, ED and DB are equal to FD andDB, each to each, and they contain right angles ; therefore b 4. 1. ? the base EB is equal bto the base FB; in thesame manner EA is e-qual to FA, and EC toFC: and in the trianglesEBA, FBA, EB, BAaic equal to FB, BA,and the base EA is e-qual to the base FA;wherefore the angle c 8. 1. EBA is equalc to the ^ anele FBA, and the tri- „ .^--^ I ? . ~ C angle EBA equal b tothe triangle FBA, andthe other angles equal tor 4. 6. the other angles; there- p d< fore these triangles are^ ^- similar d; in the same manner the triangle EBC is similar to. NOTES. 343 the triangle FBC, and the triangle EAC to FAC ; therefore Book are two solid figures, each of which is contained by six v.^v->»/triangles, one of them by three tri^^ngles, the common vertexof which is the pomt G, and their bases the straight lines AB,BC, CA, and by three other triangles the common vertexof which is the point E, and their bases the same lines AB,BC, C A; the otner solid is contained by the same three tri-angles the common vertex of which is G, and their bases AB,BC, CA ; and by three other triangles of which the commonvertex is the point F, and their bases the same straight linesAB, BC, CA: now the three triangles GAB, GBC, GCAare common to both solids, and the
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
