| Nathaniel Bowditch - Nautical astronomy - 1931 - 866 pages
...or right line is the shortest distance between two points on a plane surface. A plane surface is one **in which, any two points being taken, the straight line between them lies wholly** within that surface. Parallel lines are such as are in the same plane and if extended indefinitely... | |
| David E. Smith - Mathematics - 1958 - 756 pages
...on these statements until the i8th century, when Robert Simson (1758) suggested the definition that **"a plane superficies is that in which any two points...the straight line between them lies wholly in that** superficies,"4 a statement which Gauss (c. 1800) characterized as redundant. Fourier (c. 1810) gave... | |
| R. H. Warn, John G. Horner - Crafts & Hobbies - 2002 - 292 pages
...straight line is that which lies evenly between extreme points. 4. A plane superficies, or surface, **is that in which any two points, being taken, the...line between them lies wholly in that superficies.** 5. The extremities of a superficies are lines. 6. A plane rectilineal angle is the inclination of two... | |
| Euclid - Euclid's Elements - 1920 - 304 pages
...sight. Simson substituted in his Euclid a different definition to the effect that 'A plane surface **is that in which, any two points being taken, the straight line** joining them lies wholly in the surface,' a definition which is equivalent to others found in Heron... | |
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