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. IV. points. V. A superficies is that which hath only length and breadth. 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 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 6 lines AB, CB, is named the angle ABC, or CBA ; that which 6 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 be X. ther straight line makes the adjacent 6 XI. XII. ΧΙΙΙ. XIV. XV. Book I. the circumference, and is such that all straight lines drawn XVI. XVII. XVIII. XIX. XX. XXI. XXII. XXIII. XXIV. XXV. Book L A A A XXVI. XXVII. XXVIII. XXIX. XXX. equal, and all its angles right angleso, 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. I: II. III. tance from that centre. a AXIOMS. I. II. III. IV. v. VI. VII. VIII. The whole is greater than its part. |