POINT is that which has position, but not magni- See Notes. tude 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. "If two lines are such that they cannot coincide in any "two points, without coinciding altogether, each of "them is called a straight line." "COR. Hence two straight lines cannot inclose a space. "Neither can two straight lines have a common segment; for they cannot coincide in part, without coinciding altogether." 66 66 IV. A superficies is that which has only length and breadth. "COR. The extremities of a superficies are lines; and "the intersections of one superficies with another are "also lines." * The definitions marked with inverted commas are different from those of EUCLID. BT V. Book F. 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 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 contained by BD, CB is call❝ed 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 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." The space contained within a figure is called the Area of the Figure." 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. This point is called the centre of the circle. XIII. 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. XV. Book I. Rectilineal figures are those which are contained by straight lines. XVI. Trilateral figures, or triangles, by three straight lines. XVII. Quadrilateral, by four straight lines. XVIII. Multilateral figures, or polygons, by more than four straight lines. XIX. Of three-sided figures, an equilateral triangle is that which has three equal sides. XX. An isosceles triangle is that which has only two sides equal. XXI. A scalene triangle, is that which has three unequal sides. XXII. A right angled triangle, is that which has a right angle. XXIII. An obtuse angled triangle, is that which has an obtuse angle. XXIV. An acute angled triangle, is that which has three acute Book I. angles. XXV. Of four sided figures, a square is that which has all its sides equal, and all its angles right angles. XXVI. An oblong, is that which has all its angles right angles, but has not all its sides equal. XXVII. A rhombus, is that which has all its sides equal, but its angles are not right angles. ᄆᄆ XXVIII. A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles. XXIX. All other four sided figures besides these, are called |