 | George Darley - Euclid's Elements - 1836 - 172 pages
...which arc not bounded by right lines, as a circle, &c. R. Simson gives another definition, viz. '* A plane superficies is that in which any two points...line between them lies wholly in that superficies." To which it may be objected, that, in the first place, this is not a definition, but a theorem (if... | |
 | Mathematics - 1836 - 530 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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...a superficies are lines ; and the intersections of one superficies with another are also lines. 8. A plane superficies is that in which any two points...line between them lies wholly in that superficies. 9. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...superficies are lines ; and the intersections of " one superficies with another are also lines." 5. A plane superficies is that in which any two points...line between them lies wholly in that superficies. 6. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together,... | |
 | 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 have... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies is that in which any two points...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,... | |
 | Euclides - 1838 - 264 pages
...breadth. V. Therefore the boundaries of a surface are lines. VI. A plane surface, or simply a plane, is that in which any two points being taken, the straight line between them lies wholly in that surface. The meaning of this is that a plane surface is such that whatever two points in it be taken... | |
 | Euclides - Geometry - 1841 - 378 pages
...superficies is that which hath only length and breadth. VI. The extremities of a superficies are lines. VII. A plane superficies is that in which any two points...line between them lies wholly in that superficies. VIII. " A j,1,.tn' angle is the inclination of two lines to one " another in a plane, which meet together,... | |
 | Thomas Grainger Hall - Geometry, Descriptive - 1841 - 214 pages
...and thickness. (3) That which bounds a solid is a superficies. (4) A plane superficies, or a plane, is that in which any two points being taken, the straight...line between them lies wholly in that superficies. (5) A straight line is said to be perpendicular, or at right angles to a plane, when it is perpendicular... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...superficies are lines ; and the intersections of " one superficies with another are also lines." 5. A plane superficies is that in which any two points...line between them lies wholly in that superficies. 6. A plane rectilineal angle is the inclination of two straight lines to one another, which meet together,... | |
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A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line. 
