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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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Mensuration of lines, areas, surfaces, and volumes

Robert Rawson - 1856
...four-sided figures besides these, are called Trapeziums. XXXV. Parallel straight linos are such as arc in the same plane, and which being produced ever so far both ways, do not meet. POSTULATES. r Let it be granted, that a straight line may be drawn from any one point to any other...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...of the system. The definitions of parallel straight lines, and of a plane surface, are as follows : Parallel straight lines are such as are in the same plane, and being produced ever so far both ways do not meet. A plane surface is that in which any two points being...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 226 pages
...one which is less than a right angle. An obtuse angle is one which is greater than a right angle. 12. Parallel straight lines are such as are in the same plane, and which, being pi-oduced ever so far both ways, do not meet. 13. A plane figure is a plane terminated on all sides...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...one which is less than a right angle. An obtuse angle is one which is greater than a right angle. 12. Parallel straight lines are such as are in the same...being produced ever so far both ways, do not meet. 13. A. plane figure is a plane terminated on all sides b} lines either straight or curved. If the lines...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...produced, the ext. angle is greater than either of the interior opposite angles. Def. 35. Parallel st. lines are such as are in the same plane, and which being produced ever so far both ways do not meet. EXP. 3 D.35,Ax.l2 4 Pst. 1. 1 C. & Hyp. 2 P. 4. 3 Sub. 4 5 Ax. 3. P. 4. .6 Add. 7 8 9 Ax. 2. Const....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...angles right angles. XXXIV. AH other four-sided figures besides these, are called Trapeziums. XXXV. Parallel straight lines are such as are in the same...being produced ever so far both ways, do not meet. A. A parallelogram is a four-sided figure, of which the opposite side* are parallel : and the diameter,...
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ELEMENTS OF GEOMETRY AND CONIC SECTIONS

ELIAS LOOMIS, LL.D. - 1861
...which is less than a right angle. An obtuse angle is one which : s greater than a right angle. 12. Parallel straight lines are such as are in the same...being produced ever so far both ways, do not meet. 13. A. plane figure is a plane terminated on all sides lines either straight or curved. If the lines...
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Memoir of Theophilus Parsons: Chief Justice of the Supreme Judicial Court of ...

Theophilus Parsons - Judges - 1861 - 476 pages
...of two finite right lines, -which constitutes their parallelism. According to Euclid, parallel right lines are such as are in the same plane, and which,...being produced ever so far, both ways, do not meet. This is not a definition of the position of two finite right lines, which constitutes their parallelism,...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...angles right angles. XXXIV. All other four-sided figures besides these, are called Trapeziums. XXXV. Parallel straight lines, are such as are in the same...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...
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Euclid's plane geometry, practically applied; book i, with explanatory notes ...

Euclides - 1863
...^ • j. along opposite to each.Other), are such as t are in . .; the same plane, arid which i)eing produced ever so far both ways, do not meet; as AB, CD. - C • D The least objectionable definition'is that which, as Potts says (p. 50), " simply expresses...
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