...straight line, on the whole being turned about the two centres of the spheres,will describe a surf ace in which any two points being taken, the straight line between them, with its jirolongation either way, may be proved to lie tvholly in that surface. A surface of this...

...lies evenly between its extreme points. V. A superficies is that which hath only length and brendth. VI. The extremities of a superficies are lines. VII....plane superficies is that in which any two points be- Sw N. ing taken, the straight line between them lies wholly in that superficies. VIII. " A plane...

...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 line...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...

...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...

...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...

...one surface with another is also a line. 5. A plane surface, or, as it is generally called, a plane, is that in which any two points being taken, the straight line between them lies wholly in that surface..]Cor. Hence two plane surfaces cannot enclose a space. Neither can two plane surfaces have...

...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...

...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 line...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,...