paring for that University. It contains all that is required for the examination at Responsions. If the student does not intend to pursue the subject further, he may omit the Deductions. The additional matter by the present Editor has been included in brackets, that the student may be able to distinguish what is absolutely required of him, from what is only intended to help him in acquiring that knowledge. It is very desirable that every student entering at Oxford should have read over these books at least once. 5. Lower Crescent, Clifton, May, 1852. DIRECTIONS TO THE LEARNER. First. Procure a case of instruments. Secondly. Draw each figure correctly as the construction in the Proposition directs. Thirdly. In subsequent cases of having to draw the same figure, use the shorter method (if any) pointed out in the Note which follows the Proposition. Fourthly. If possible, go over the first five Propositions of the First Book, vivâ voce, with a teacher. Fifthly. Read the First Book twice before proceeding to the Second. THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. I. A POINT is that which hath no parts, or which hath no BOOK I. magnitude. A II. A line is length without breadth. A B C D E III. The extremities of a line are points. IV. A straight line is that which lies evenly between its extreme points. [A, B, C, above, are straight lines; D, E are not straight. lines, but curves.] B A superficies is that which hath only length and breadth. The extremities of a superficies are lines. [The superficies, fig. 1., is bounded by four straight lines; that in fig. 2. by one straight line and two lines which are not straight lines, but curves.] VII. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. "A plane angle is the inclination of [Fig. 1., plane rectilineal angle; B Fig. 1. Fig. 2. |