| Mathematics - 1885 - 150 pages
...The simplest figures, bounded by lines alone, are on a plane superficics, and this is defined as " **that in which, any two points being taken, the straight...line between them lies wholly in that superficies."** But it is of importance to observe that a line is "length without breadth," that a superficics is "... | |
| W. J. C. Miller - Mathematics - 1885 - 154 pages
...figure. The simplest figures, bounded by lines alone, are on a plane superficies, and this is denned as " **that in which, any two points being taken, the straight...line between them lies wholly in that superficies."** But it is of importance to observe that a line is "length without breadth," that a superficies is "that... | |
| Nathaniel Bowditch - Nautical astronomy - 1888 - 704 pages
...straight or rig/it line is the shortest distance between two points on a plane surface. A flaue surface **is that in which any two points being taken, the straight line between them lies wholly in that** surface. Parallel lines are. such as are in the same plane, and if extended infinitely never meet.... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Superficies is that which has only length and breadth. 6. The Extremities of a Superficies are lines. 7. **A Plane Superficies is that in which any two points...line between them lies wholly in that superficies.** 8. A Plane Angle is the inclination of two lines to one another in a plane, which meet together, but... | |
| Isaac Hammond Morris - Geometry, Plane - 1890 - 440 pages
...— upon a plane surface. A plane surface is perfectly level, and is defined by Euclid as ' a surface **in which, any two points being taken, the straight line between them lies wholly in that** surface.' Henrici calls it 'the path of a moving line.' These representations are effected by means... | |
| John Fry Heather - Geometry, Modern - 1890 - 252 pages
...line drawn close along such an edge will also be straight.* 11. A piano or flat surface is that on **which any two points being taken, the straight line between them lies wholly in** the surface. Hence to test the flatness of a surface, a straight edge is to be laid upon it, aitd if... | |
| 1890 - 580 pages
...straight line, on the whole being turned about the two centres of the spheres, will describe a surface **in which any two points being taken, the straight line between them,** with its prolongation either way, may be demonstrated to lie wholly in that surface. A surface of this... | |
| Euclid - Geometry - 1892 - 460 pages
...length and breadth, but no thickness. The boundaries of a surface are lines. 5. A plane surface is one **in which any two points being taken, the straight line between them lies wholly in that** surface. A plane surface is frequently referred to simply as a plane. NOTE. Euclid regards a point... | |
| Augustus De Morgan - Mathematics - 1898 - 316 pages
...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, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...and breadth, but no thickness. G. The boundaries of a surface are lines. 7. A plane surface is one **in which any two points being taken, the straight line between them lies wholly in that** surface. A plane surface is frequently referred to simply as a plane. NOTE. Euclid regards a point... | |
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