. 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. there are two , lines ABC, ABD in the same plane that have a commonsegment AB, which is impossible. Therefore, one part, S^ E. D. 1. PROP. II. THEOR. TWO Straight lines which cut one another are in see plane, and three straight lines which meet oneanother are in one plane
. 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. there are two , lines ABC, ABD in the same plane that have a commonsegment AB, which is impossible. Therefore, one part, S^ E. D. 1. PROP. II. THEOR. TWO Straight lines which cut one another are in see plane, and three straight lines which meet oneanother are in one plane. Let two straight lines AB, CD cut one another in E ; AB,CD are one plane : and three straight lines EC, CB, BE whichmeet one another, are in one plane. Let any plane pass through the straightline EB, and let the plane be turned aboutEB, produced, if necessary, until it passthrough the point C : then because thepoints E, C are in this plane, the straight line EC is in it^ : for the same reason, the / \ ,l. straight line BC is in the same ; and, bythe hypothesis, EB is in it: therefore thethree straight lines EC, CB, BE are in oneplane : but in the plane in which EC, EBare, in the same are ^ CD, AB : therefore, AB, CD are in one plane. Wherefore, two straight lines. E.
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Keywords: ., bookauthoreuclid, bookcentury1800, booksubje, booksubjectgeometry
