A See 1. 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 into * tersections of one line with another are also points.” III. 6 If two lines are such that they cannot coincide in any two points, ś without coinciding altogether, each of them is called a straight line.” “ Cor. Hence two straight lines cannot enelose a space. Neither can two straight lines have a common segment; that is, they cannot " coincide in part, without coinciding altogether.” IV. “Cor. The extremities of a superficies are lines; and the intet. sections of one superficies with another are also lines." V. A plane superficies is that in which any two points being taken, the straight line between them lie's 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. * The definitions marked with inverted commas are different from those of Euclid. с 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 vers tex of the angle, that is, at the point in which the straight lines that 6 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 (he 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 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. straight line makes the adjacent angles VIII. 1 İx. X. word area denotes the quantity of space contained in a figure, without any reference to the nature of the line or lines which bound it. 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 cer. tain point within the figure to the circumference, are equal to one another. XII. XIII. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumfereace. XIV. A semicircle is the figure contained by a diameter and the part of the circuinference cut off by the diameter. XV. Rectilineal figures are those which are contained by straight lines. XVI, XVII. XVIII. Multilateral figures, or polygons, by more than four straight lines. XIX. or three sided figures, an equilateral triangle is that which has three equal sides. XX. AAN XXI XXII. XXIII. XXIV. 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 wbich 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. O 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. XXX. being produced eper so far both ways, do not meet, POSTULATES. I. Let it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III, And that a circle may be described from any centre, at any distance from that centre. AXIOMS. I. Things which are equal to the same thing are equal to one another, 1. If equals be added to equals, the wholes are equal. III. IV. V. VI. VII. Things which are balves of the same thing, are equal to one another. VIII. Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another. IX: The whole is greater than its part. All right angles are equal to one another. XI. $6 Two straight lines which intersect one another, cappot be both parallel to the same straight line.”. |