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" Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet. "
A Treatise on Surveying, Containing the Theory and Practice: To which is ... - Page 26
by John Gummere - 1814 - 346 pages
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...the center, and terminated both ways by the circle. 56. An Arc is a part of a circle. 57. Parallel Lines are such as are in the same plane, and which,...being produced ever so far both ways, do not meet. The point is called the Vertex, and the lines are called the Arms, of the angle. A line drawn from...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1886 - 366 pages
...the center, and terminated both ways by the circle. 56. An Arc is a part of a circle. 57. Parallel Lines are such as are in the same plane, and which,...being produced ever so far both ways, do not meet. CJ) The point is called the Vertex, and the lines are called the Arms, of the angle. A line drawn from...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 pages
...be drawn through the mid-point of the join of two fixed points, it is equidistant from them. DEF.— Parallel straight lines are such as are in the same...being produced ever so far both ways, do not meet. The symbol for ' parallel ' is ||. PROPOSITION 27. THEOREM. If a straight line falling on two other...
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The Teaching and History of Mathematics in the United States

Florian Cajori - Mathematics - 1890 - 400 pages
...used in this country. I. — NEW DEFINITIONS. Euclid's definition of parallel lines is as follows: "Parallel straight lines are such as are in the same...being produced ever so far both ways do not meet? This definition has been retained by the larger number of American writers,1 and seems indeed the most...
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The Teaching and History of Mathematics in the United States, Volumes 890-893

Florian Cajori - Mathematics - 1890 - 400 pages
...used in this country. I. — NEW DEFINITIONS. Euclid's definition of parallel lines is as follows: "Parallel straight lines are such as are in the same...which being produced ever so far both ways do not meet.19 This definition has been retained by the larger number of American writers,1 and seems indeed...
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The Teaching and History of Mathematics in the United States, Volumes 890-893

Florian Cajori - Mathematics - 1890 - 400 pages
...used in this country. I. — NEW DEFINITIONS. Euclid's definition of parallel lines is as follows: "Parallel straight lines are such as are in the same plane, and whioh being produced ever so far both ways do not meet." This definition has been retained by the larger...
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A history of elementary mathematics

Florian Cajori - Mathematics - 1896 - 304 pages
...proving the parallelpostulate from the nature of the straight line and plane angle. Euclid's definition, parallel straight lines are such as are in the same...being produced ever so far both ways do not meet, still holds its place as the best definition for use in elementary geometry. The first known writer...
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A History of Elementary Mathematics: With Hints on Methods of Teaching

Florian Cajori - Mathematics - 1896 - 304 pages
...nature of the straight line and plane angle. Euclid's definition, parallel straight lines are st1ch as are in the same plane, and which being produced ever so far both ways do not meet, still holds its place as the best definition for use in elementary geometry. The first known writer...
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A Manual of Logic, Volume 1

James Welton - Logic - 1896
...There is a breach of this rule in Euclid's definition of parallel straight lines as ' those which lie in the same plane, and which, being produced ever so far both ways, never meet.' Another example of the came fault is when Euclid defines a point as ' that which has no...
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Euclid, His Life and System

Thomas Smith (D.D.) - Euclid's Elements - 1902 - 227 pages
...the truth of the story. It ought to be true ! But the definition of parallel straight lines as being "such as are in the same plane, and which, being produced ever so far both ways, do not meet," is the field on which the trumpet has blared and the clang of deadly weapons has rung for generations,...
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