| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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.... | |
| 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,... | |
| 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... | |
| 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,... | |
| 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... | |
| 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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