VIII. See N. “ A plane angle is the inclination of two lines to one 6 another in a plane, which meet together, but are IX. straight lines to one another, which meet together, 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 by a letter placed at that point: as the angle at E.' X. straight line makes the adjacent angles XI. angle. XII. An acute angle is that which is less than a right angle. 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. XXIV. which has three equal sides. XXV. equal. ΔΔΔ XXVI. XXVII. XXVIII. angle. 14 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. All other four-sided figures besides these, are called trapeziums. XXXV. Parallel straight lines are such as are in the same plane, and which being produced ever so far boch ways, do not meet. 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. circle be described from any centre at any distance from that centre. a AXIOMS. I. Things which are equal to the same thing, are equal to one another. II. III. IV. If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are 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 “ 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. |