. 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. Q T C R Y Z i the same plane, they are parallel to one another: and MG,EK are parallels; therefore the plane MQ, ET, of which onepasses through MG, GQ, and the other through EK, KT, whichare parallel to MG, GQ, and not in the same plane with them> are parallel J to one another: for the sa
. 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. Q T C R Y Z i the same plane, they are parallel to one another: and MG,EK are parallels; therefore the plane MQ, ET, of which onepasses through MG, GQ, and the other through EK, KT, whichare parallel to MG, GQ, and not in the same plane with them> are parallel J to one another: for the same reason, the planesMV, GT are parallel to one another: therefore the solid QE isa parallelepiped : in like manner, it may be proved, that the SO-lid YF is a parallelepiped: but, from what has been domonstrat-ed, the solid EQ is equal to the solid FY, because they are uponequal bases MK, PS, and of the same altitude, and have theirinsisting straight lines at right angles lo the bases: and the so- OF EUCLID, 23-5 lid EQ is equal 1 to the solid AE; and the solid FY, to the solid Book : because they are upon the same bases and of the same alti- ^—v^^tude: therefore the solid AE is equal to the solid CF. Where-1 29. orfere, solid*t)arallelepipeds, &c. Q. E. D. PROP. XXXI
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
