THK ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. I. A POINT is that which hath no parts, or which hath no mag. See Notes. nitude. II. A line is length without breadth. III. The extremities of a line are points. IV. V. VI. VII. A plane superficies is that in which any two points being taken, See N. the straight line between them lies wholly in that superficies. VIII. " A plane angle is the inclination of two lines to one another See N. " in a plane, which meet together, but are not in the same direction. IX. to one another, which meet together, but are not in the same B 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 some where 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 o is contained by AB, DB is named the angle ABD, or DBA; 6 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 X. ther straight line makes the adjacent be XI. XII. XIII. XIV. XV. Book I. 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: XVI. XVII. XVIII. A semicircle is the figure contained by a diameter and the part of the circumference cut off by that 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. XXV. Book L ΔΔ Δ XXVI. XXVII. XXVIII. A XXIX. XXX. equal, and all its angles right angles. 1 XXXI. XXXII. are not right angles. XXXIII. another, but all its sides are not equal, nor its angles right Book I. XXXIV. XXXV. which being produced ever 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. III. tance from that centre. AXIOMS. 1. II. III. IV. V. VI. VII. VIII. The whole is greater than its part. |