No T E s, CRITICAL AND GEOMETRICAL; CoNTAINING AN A CCOUNT OF THOSE TH INGS IN W H ICH THIS EID it ION E.M. Ehritus PROFESSOR OF MATHEMATICs in Tile UNIVERSITY OF GLASGOW. IT is necessary to consider a solid, that is, a magnitude Boo [. must either be a #. of the thick- H G M removed from the superficies ABCD, the line BC, which is the boundary of the superficies ABCD, remains the same as it was: Nor can the breadth that BC is supposed to have, be a part of the breadth of the superficies ABCD; because, if this be removed from the superficies KBCL, the line BC, which is the boundary of the superficies KBCL, does nevertheless remain: Therefore the line BC has no breadth: And because the line BC is in a superficies, and that a su perficies has nothickness, as was shown, therefore a line has The boundary of a line is called a point, or a point is the Thus, if B be the extremity of F. this extremity is called a point, D C L. part of the length of the line AB, A. K. neither breadth nor thickness, but only length. common boundary or extremity . of two lines that are contiguous: H G M - 21 E/TN/ the line AB, or the common ex- tremity of the two lines AB, KB, and has go length. For if it have *- Z any, this length must either be or of the line KB. It is not part of the length of KB; for if the line KB be removed from AB, the point B which is the extremity of the line AB remains the same as it was: Nor is it part of the length of the line AB; for, if AB be removed from the line KB, the point B, which is the extremity of the line KB, does nevertheless remain : Therefore the point B has no length: And because a point is in a line, and a line has neither breadth, nor thickness, therefore a point has no length, breadth, nor thickness. And in this, manner the definitions of a point, line, and superficies, are. to be understood. DEF. VII. B. I. INSTEAD of this definition as it is in the Greek copies, a more distinct one is given from a property of a plane superficies, which is manifestly supposed in the Elements, viz. that a straight line drawn from any point in a plane to any other in it, is wholly in that plane. DEF. VIII. B. "I. It seems that he who made this definition designed that it should comprehend not only a plane angle contained by two straight lines, but likewise the angle which some conceive to be made by a straight line and a curve, or by two curve lines which meet one another in a plane: But, though, |