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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The first six books of the Elements of Euclid, with numerous exercises - Seite 4
von Euclides - 1853 - 147 Seiten
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The elements of plane geometry, Band 1

Mathematical association - 1884
...straight line parallel to a given straight line. POSTULATES OF CONSTRUCTION. Let it be granted that 1. A straight 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. A circle may be...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - 1884
...This Convention is embodied in the following POSTULATES OF CONSTRUCTION. Let it be granted that 1. A straight 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. A circle may be...
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An introduction to the Elements of Euclid, being a familiar explanation of ...

Stephen Thomas Hawtrey - 1884
...asks to be allowed to do (from postidare, to ask). He says, Let it be granted, Postulate 1.—That a straight line may be drawn from any one point to any other point: Postulate 2.—That a terminated straight line may be produced to any length in a straight line: Postulate...
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The text of Euclid's geometry, book 1, uniformly and systematically arranged ...

Euclides - 1884
...Postulate 3. A circle may be described from any centre, and at auy distance from that centre. Postulate 1. A straight line may be drawn from any one point to any other. Definition 15. A circle is a plane figure contained by one line, which is called the circumference,...
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Mathematical Questions and Solutions, from the "Educational Times ..., Band 42

W. J. C. Miller - 1885
...that it " lies evenly between its extreme points "; but in Postulate ii. he says, " Let it be granted, that a terminated straight line may be produced to any length in a straight line," and this gives us the idea of an infinite straight line. But do we require more than two infinite straight...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885
...less than, greater than, or equal to, the radius. POSTULATES. Let it be granted that — i. A right line may be drawn from any one point to any other point. "When we consider a straight line contained between two fixed points which are its ends, such a portion...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 Seiten
...less than, greater than, or equal to, the radius. POSTULATES. Let it be granted that — i. A right line may be drawn from any one point to any other point. When we consider a straight line contained between two fixed points which are its ends, such a portion...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...straight angles are equal to one another. IV. The Assumed Constructions. 100. Let it be granted that a line may be drawn from any one point to any other point. 101. Let it be granted that a sect or a terminated line may be produced indefinitely in a line. 102....
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 Seiten
...center and radius.) Join a point C, at which the circles cut one another, to the points Aandfi. (.100. A line may be drawn from any one point to any other point.) Then will ABC be an equilateral triangle. PROOF. Because A is the center of O BCD, .-. AB = AC, being...
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The Passenger from Scotland Yard

H. Freeman Wood - 1888 - 398 Seiten
...point A a straight line equal to BC. From the point A to B draw the straight line AB. Postulate 1 says that a straight line may be drawn from any one point to any other point ; so that I at once go on to describe upon it the equilateral triangle DAB., producing the straight...
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