...hath no magnitude. 2. A line is length without breadth. 3. the extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. 5. A superficies is that which hath only length and breadth. 6. The extremities of a superficies are...

...is the boundary of extension. 3. Extension has three dimensions; length, breadth, and thickness. 4. A line is length without breadth. The extremities of a line are called points. A point therefore has no extension. 5. A straight line, or right line, is the shortest...

...by any definition, a better notion of it than the mere mention of its name suggests. Euclid says, " A straight line is that which lies evenly between its extreme points*;" a definition which is both unsatisfactory and useless. Others, following Archimedes, define it as "the...

...Note*, magnitude. II. A line is length without breadth. III. The extremities of a line are points. IV. A 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...

...on that subject. A point is defined to be that " which has no parts, and which has no magnitude ;" a straight line is that which " lies evenly between its extreme points." Now, let any one ask himself whether he could have guessed what was meant, if, before he began geometry,...

...v^y^/ See Notes. II. A line is length without breadth. III. The extremities of a line are points. IV. A straight line is that 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...

...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...

...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....

...object the measure of extension. % Extension has three dimensions, length, breadth, and thickness. 2. A line is length without breadth. The extremities of a line are called points. A point, therefore, has no extension. 3. A straight or right line is the shortest way...

...IL A line is that which has length without breadth. III. The extremities of a line are points. IV. A straight line is that which lies evenly between its extreme points. V. A superficies is that which has only length and breadth. VI. The extremities of a superficies are...