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 PHILADELPHIA, PRINTED FOR F. NICHOLS, BY THOMAS AND GEORGE PALMER, 116, HIGH STREET. I. 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. A Book I. V. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VI. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. 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 an"other, 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 con'tained 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 contained 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. When a straight line standing on an- VIII. An obtuse angle is that which is greater than a right angle. Book I. IX. An acute angle is that which is less than a right angle. X. A figure is that which is inclosed by one or more boundaries. XI. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another. XII. And this point is called the centre of the circle. XII. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. XIV. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. |