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" A straight line is that which lies evenly between its extreme points. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 1
af Euclides - 1816 - 528 sider
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Matters Mathematical

I. N. Herstein, Irving Kaplansky - 1978 - 256 sider
...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...
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The how and the why: An Essay on the Origins and Development of Physical Theory

David Park - 1990 - 488 sider
...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...
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George Boole: Selected Manuscripts on Logic and its Philosophy

Ivor Grattan-Guinness, Gerard Bornet - 1997 - 310 sider
...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...
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Mathematically Speaking: A Dictionary of Quotations

C.C. Gaither, Alma E Cavazos-Gaither - 1998 - 506 sider
...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...
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Geometry: Ancient and Modern

John R. Silvester - 2001 - 332 sider
...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,...
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Einstein's Legacy: The Unity of Space and Time

Julian Seymour Schwinger - 2002 - 274 sider
...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...
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Reforming Philosophy: A Victorian Debate on Science and Society

Laura J. Snyder - 2010 - 386 sider
...(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...
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The London, Edinburgh and Dublin Philosophical Magazine and Journal of Science

1874 - 1094 sider
...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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