| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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