. 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. PROP. XIV. THEOR. PLANES to which the same straight line is per-pendicular, are parallel to one another. a 3. b c 8. Let the straight line AB be perpendicular to each of the planesCD, EF; these planes are parallel to one another. If not, they shall meet one another when produced ; le
. 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. PROP. XIV. THEOR. PLANES to which the same straight line is per-pendicular, are parallel to one another. a 3. b c 8. Let the straight line AB be perpendicular to each of the planesCD, EF; these planes are parallel to one another. If not, they shall meet one another when produced ; let themmeet; their common section shall be astraight line GH, in which take anypoint K, and join AK, BK : then, be-cause AB is perpendicular to the planeEF, it is perpendicular » to the straightline BK which is in that plane. There-fore ABK is a right angle. For thesame reason, BAK is a right angle ;wherefore the two angles ABK, BAKof the triangle ABK are equal to tworight angles, which is impossible *»:therefore the planes CD, EF, thoughproduced, do not meet one another;that is, they are parallel ^. Therefore,planes, &c. Q. E. OF EUCLIDu
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
