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" Let it be granted that a straight line may be drawn from any one point to any other point. "
Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ... - Page 220
by James Bates Thomson - 1844 - 237 pages
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Outlines of geometry; or, The motion of a point

Walter Marsham Adams - 1866 - 114 pages
...drawing straight lines or circles, and we can only assume the power. " Let it be granted," says Euclid, " that a straight line may be drawn from any one point to any other point," and " that a circle may be described," &c. As it is impossible to learn to swim without going into...
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A Dictionary of Science, Literature, & Art: Comprising the ..., Volume 3

William Thomas Brande, George William Cox - Encyclopedias and dictionaries - 1867 - 1090 pages
...something to be assumed, or taken for granted. Euclid lias constructed his Elements on the three following postulates: 1. That a straight line may be drawn from...to any other point. 2. That a terminated straight lino may be produced to any length in a straight line. 3. That a circle may be described from any centre...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...diagonal is the straight liue joining two of its opposite angles. POSTULATES. I. LET it be granted that a straight line may be drawn from any one point to any other point. IL That a terminated straight line may be produced to any length in a straight line. m. AXIOMS. I....
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The ratio between diameter and circumference in a circle demonstrated by ...

James Smith - 1870 - 634 pages
...(Prop. I, Book 1) should be based upon the simplest of the postulates, viz. : " Let it be granted, that a straight line may be drawn from any one point to any other point" Thus, Euclid begins by showing us how to construct an equilateral triangle. There can be no doubt that...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...construction of figures and the properties of geometrical mag--tudes. POSTULATES. Let it be granted I. That a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. That a circle...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...which is contained an exact number of times in each of them. BOOK V PROBLEMS Postulates. 1 A a'.raight line may be drawn from any one point to any other point. 2. A terminated straight line may be produced to any length in a straight line. 3. From the greater of...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...construction of figures and the prqperties pf geometrical magnitudes. POSTULATES. Let it be granted I. That a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. That a circle...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 580 pages
...plane, and which, being produced ever so far both ways, do not meet. POSTULATES. I. Let it be granted that a straight line may be drawn from any one point to any other point. II. That a terminated straight line may be produced to any length in a straight line. III. That a circle...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...points. A straight line is one which lies evenly between its extremities. It is taken for granted : That a straight line may be drawn from any one point to any other point; And also that a terminated straight line may be produced to any length in a straight line. A superficies...
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The Intuitions of the Mind Inductively Investigated

James McCosh - Intuition - 1874 - 484 pages
...definitions and in the propositions founded on them, such as the following, put in the form of maxims : "A straight line may be drawn from any one point to any other point ;" "A straight line may be produced to any length in a straight line ;" " There may be such a figure...
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