 | Thomas Perronet Thompson - 1833 - 168 σελίδες
...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... | |
 | Euclides - 1834 - 518 σελίδες
...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... | |
 | Euclid - 1835 - 540 σελίδες
...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.... | |
 | Robert Simson - 1835 - 544 σελίδες
...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... | |
 | 1836 - 352 σελίδες
...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... | |
 | 1836 - 530 σελίδες
...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... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...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... | |
 | Euclides - 1838 - 264 σελίδες
...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.... | |
 | Euclides - 1841 - 378 σελίδες
...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... | |
 | Euclides - 1842 - 316 σελίδες
...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,... | |
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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 two lines to one another in a plane, which meet together, but are not in the same... 
