Τ Η Ε Ε Ι Ε E M E E N T S OF E U CL L I I D. BOOK I. D E F IN I TI ON S. Pointi I. II. IU. 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 in a See N. plane, which meet together, but are not in the same direction.” IX. another, which meet together, but are not in the fame straight А LA BK C E * N.B. When several angles are at one point B, anyone of them is expressed by three letters, of which the letter that is at ihe ves. tex 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. XII. XIII. XIV. Book 1, XV. the circumference, and is such that all straight lines drawn from XVI. XVII. 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. XXV. Aa Book 1. AAA XXVI. XXVII. XXVII. A A A XXIX. XXX. equal, and all its angles right angles. XXXI. XXXII. are not right angles. See N. XXXIII. ther, but all its fides are not equal, nor its angles right angles. Book 1. XXXIV. XXXV. which being produced ever so far both ways, do not meet. POSTULAT E S. I. II. III. distance from that center. A X I 0 MS. T" I. II. III. IV. V. VI. VII. VIII. |