...parts, or which hath no mag- Book I. nitude. v^y^/ See Notes. II. A line is length without breadth. III. The extremities of a line are points. IV. A straight...which lies evenly between its extreme points. V. A super/ides is that which hath only length and breadth. VI. The extremities of a superficies are lines....

...straight line is that which lies evenly between its extreme points. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plain superficies is that in which any two points being See N. taken, the straight line between them...

...placed upon that surface, we conclude that the surface is plane. Hence the definition of a plane surface is that in which, any two points being taken, the straight line joining these points lies wholly upon the surface. Two straight lines have a relation to one another...

...cannot be mistaken for one moment, unless it be by means of the attempt to explain them by saying that a straight line is ' that which lies evenly between its extreme points.' The line and surface are distinct species of magnitude, as much so as the yard and the acre. The first...

...THE ELEMENTS OF EUCLID. BOOK I. DEFINITIONS. I. A POINT is that which hath no parts, or which hath no magnitude. n. A line is length without breadth....its extreme points. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies...

...extremities of a line are points; and the intersection of one line with another is also a point. IB. A straight line is that which lies evenly between its extreme points. The idea of a geometrical straight line may be gained from that of a physical stretched line or thread....

...magnitude. II. A line is length without breadth. III. The extremities of a line are points. IV. A straigU line is that which lies evenly between its extreme points. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies...

...which has no parts, or which has no magnitude. IL A line is that which has length without breadth. III. The extremities of a line are points. IV. A straight...VI. The extremities of a superficies are lines. VII. VIII. " A plane angle is the inclination of two lines to one another " in a plane : the lines meeting,...

...attainment, is a clear comprehension of the theoretical and practical import of the above definitions. III. The extremities of a line are points. IV. A Straight...that which lies evenly between its extreme points. Lines are either Straight, Curved, or Mixed. 1. A Curved Line continually changes its direction between...

...is that which hath no parts, or which hath no magnitude. II. A line is length without breadth. III. The extremities of a line are points. IV. A straight...its extreme points. V. A superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies...