VIII. See N. а “ A plane angle is the inclination of two lines to one “ another in a plane, which meet together, but are IX. straight lines to one another, which meet together, C E 6 . < 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, DB is named the angle ABD, or, DBA; and that which is contained by · DB, CB, is called the angle DBC, or CBD; but, if there be only one angle at a point, it may be expressed X. straight line makes the adjacent angles XI. angle. XII. An acute angle is that which is less than a right angle. a XIII. “ A term or boundary is the extremity of any thing.” XIV. XV. called the circumference, and is such that all straight XVI. XVII. the centre, and terminated both ways by the circumference. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter. XIX. “ A segment of a circle is the figure contained by a “ straight line, and the circumference it cuts off.” XX. XXI. XXII. XXIII. Multilateral figures, or polygons, by more than four straight lines. XXIV. Of three-sided figures, an equilateral triangle is that which has three equal sides. XXV. equal. ΔΔΔ XXVI. XXVII. XXVIII. angle. XXIX. XXX. sides equal, and all its angles right angles. XXXI. XXXII. angles are not right angles. See N. XXXIII. to one another, but all its sides are not equal, nor XXXIV. XXXV. plane, and which being produced ever so far boch a Let it be granted that a straight line may be drawn from any one point to any other point. II. III. any distance from that centre. AXIOMS. I. II. III. IV. V. unequal. VI. Things which are double of the same, are equal to one another. VII. Things which are halves of the same, 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. X. XI. XII. “ If a straight line meet two straight lines, so as to 6 make the two interior angles on the same side of, 6 it taken together less than two right angles, these “ straight lines being continually produced, shall at length meet upon that side on which are the angles “ which are less than two right angles.” See the notes on Prop. 29. of Book 1. |