OF GEOMETRY, CONTAINING THE FIRST SIX BOOKS OF EUCLID, WITH A SUPPLEMENT ON THE QUADRATURE OF THE CIRCLE AND THE GEOMETRY OF SOLIDS. BY JOHN PLAYFAIR, F. R. S. EDIN, PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF EDINBURGH. PHILADELPHIA, PRINTED FOR F. NICHOLS, 1-27-37 33559 A POINT is that which has position, but not magnitude." See Notes. II. A line is length without breadth. “ COROLLARY. The extremities of a line are points'; and “ the intersections of one line with another are also points." III. “ Lines which cannot coincide in two points, without coin ciding altogether, are called straight lines. « Cor. Hence two straight lines cannot inclose a space. Nei “ther can two straight lines have a common segment; “ that is, they cannot coincide in part, without coinciding altogether.” IV. A superficies is that which hath only length and breadth. “ Cor. The extremities of a superficies are lines; and the “ intersections of one superficies with another are also lines.” А Book I. V. ken, the straight line between them lies wholly in that su- VI. lines to one another, which meet together, but are not in N. B. "When several angles are at one point B, any one of them is expressed by three letters, of which the letter that is at the vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these * two is somewhere upon one of those straight lines, and the other upon the other line : thus the angle which is contained by the straight lines AB, CB, is named the angle “ABC, or CBA; that which is contained by AB, BD, is ' named the angle ABD, or DBA; and that which is con‘tained by BD, CB, is called the angle DBC, or CBD; but, ' if there be only one angle at a point, it may be expressed by a letter placed at that point ; as the angle at E.' VII. other straight line makes the adja- Book I. VIII, IX. X. XI. called the circumference, and is such that all straight lines XII. XIJI. centre, and terminated both ways by the circumference. XIV. part of the circumference cut off by the diameter. |