 | I. N. Herstein, Irving Kaplansky - Mathematics - 1978 - 256 pages
...has no magnitude. 2. A line is length without breadth. 3. The extremities of a line are points. 4. A straight line is that which lies evenly between its extreme points. Styles of mathematical exposition have changed. These are highly descriptive phrases, somewhat in the... | |
 | David Park - Science - 1990 - 488 pages
...begins his Elements with a group of definitions, such as "a point is that which has no parts," and "a straight line is that which lies evenly between its extreme points." Let us not worry about whether these words uniqurly define what they are supposed to define; we know... | |
 | Ivor Grattan-Guinness, Gerard Bornet - Mathematics - 1997 - 310 pages
...defined and needing directly or indirectly a supplementary addition. Of this kind is the definition A straight line is that which lies evenly between its extreme points.* The idea conveyed is that of similarity and uniformity not only of the different parts of the line... | |
 | C.C. Gaither, Alma E Cavazos-Gaither - Mathematics - 1998 - 506 pages
...treatises on that subject. A point is defined to be that "which has no parts and which has no magnitude"; a straight line is that which "lies evenly between its extreme points." ... In this case the explanation is a great deal harder than the term to be explained, which must always... | |
 | John R. Silvester - Mathematics - 2001 - 332 pages
...has gone before. Thus he starts: l. A poim is that which has no parts, or which has no magnitude. Il. A line is length without breadth. III. The extremities of a line are poims, IV. A straight line is that which lies evenly between its extreme poims, The tendency nowadays,... | |
 | Julian Seymour Schwinger - Science - 2002 - 274 pages
...points, straight lines, circles, ellipses, and triangles. From Book l of the Elements: Definition 4, 1. A straight line is that which lies evenly between its extreme points. lt is quoted, not for its clarity, but its spirit. We would say that a straight line is the shortest... | |
 | Laura J. Snyder - Science - 2010 - 386 pages
...(within Euclidean geometry) only because of how Euclidean geometry defines "straight line" (that is, "A straight line is that which lies evenly between its extreme points"). The axiom would not even be true, let alone necessary, if our geometry defined "straight line" as one... | |
 | Physics - 1874 - 1094 pages
...a definition is to be attempted at all, it would be hard to produce a better than the old one — " A straight line is that which lies evenly between its extreme points ;" but, of course, the word evenly as much requires definition as the word straight. Mr. Wilson adds... | |
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A straight line is that which lies evenly between its extreme points. 
