| Nathaniel Bowditch - Nautical astronomy - 1826 - 732 pages
...shortest distance between the two points which limits its length, as A - ะก III. A PLANE SUPERFICES is that in which any two points being taken, the straight line between them lies wholly in that surface. IV. PARALLEL LINES are such as are in the same plane AB and which extended infinitely... | |
| Ferdinand Rudolph Hassler - Geometry - 1828 - 180 pages
...of the line however taken. 4. A surface, is that which has length and breadth without thickness. 5. A plane surface, is that in which any two points being...taken, the straight line between them lies wholly in that surface. 6. A rectilineal angle, is the inclination of two straight lines that cut each other.... | |
| Thomas Curtis - Aeronautics - 1829 - 814 pages
...lines, and the intersections of superficies with one another are also lines. 5. A PLANE SUPERFICIES is that in which any two points being taken, the straight line between them lies wholly in that superficies. 6. A PLANE RECTILINEAL ANGLE is the inclination of two straight lines to one another,which... | |
| Augustus De Morgan - 1831 - 108 pages
...it may be 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 - Euclid's Elements - 1833 - 216 pages
...B. L The learned Robert Simson gives a different definition of a plane surface. A plane superficies is that in which, any two points being taken, the straight line between them lies wholly in that superficies : this indeed is a well known property of a plane ; but as it can easily be deduced... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...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... | |
| George Darley - Euclid's Elements - 1836 - 172 pages
...bounded by right lines, as a circle, &c. R. Simson gives another definition, viz. '* A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies." To which it may be objected, that, in the first place, this is not a definition,... | |
| Mathematics - 1836 - 488 pages
...lines ; and the intersections of one superficies with another are also lines. 5. A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. 6. A plane rectilinial angle is the inclination of two straight lines to one another,... | |
| Mathematics - 1836 - 530 pages
...it may be 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 - Geometry - 1837 - 410 pages
...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... | |
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