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1832 Jany 15
Posology
Observations on Euclid
Definitions.
Problem
1
By parallel lines understand lines in any number more than one which are parallel
to each other.
By lines parallel to each other understand lines
which are at the same distance from each other in every part
of the length to which they, both of them, extend.
For the mode of describing parallel lines see Book
— Proposition. The principle on or say manner in, which this description is effected is
analogous to that on which the description of a circle is effected.
Of two parallel lines call one the inferior, or say the bas line the other
the superior, line.
Call
Problem How to describe two parallel lines
Solution. 1. You have one line already drawn: call this the
inferior line.
2 2 From this line you know how to draw another which shall
be perpendicular to it: that is to say a line which shall have
the two angles one of which is on one side of that same inferior
line, the other on the other side of it.
3 Call this other line the moving line
4. Conceive the moving line placed at either end of the inferior
line: say for example, the left end.
5. From the left end of the inferior line move slide the moving
line on to the right end thereof; keeping it all along as above at tight
angles with the inferior line, and in contact with the same.
6. Having thus done, you have described above the inferior
line a superior line which is equal and parallel to it
7 Whatsoever angles one on one side, the other on the other
side of it the moving line makes with the inferior line, you
may describe a superior line which shall be parallel to the inferior;
provided the moving line continues making the same
angles with it the whole of the way: but, if you proceed
in this manner, one part of each line will have a corresponding
part of the other, without unaccompanied by a parallel to it.
Identifier:  JB/135/169/001 "JB/" can not be assigned to a declared number type with value 135.



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