Longer & Shorter
and as relative
In comparing lines with one the longer the other
the shorter [use the words longer and shorter as relative
or by Figures. COMMONPLACE
Have a little Book printed or written containing only the
Definitions Axioms, Postulates and Propositions without
their Demonstrations, on thin paper in a very small
pocket form. All the propositions under concerning each
figure be ranged together, or and any more convenient
order adopted as the demonstrations would not be there
to their order. NB The several steps of the Figures
might be in this so as to answer the purpose of deleting the
Demonstrations and of making them exemplifying them
in the larger work. The Copper & would be smaller.
Some would the perhaps understand demonstration by figures
better than by words.
The Bounds of
what is Usefull & what
Settle the Boundaries between what is usefull in pure Mathematics
and what is simply curious. The Doctrine that is usefull is
the doctrine of those Mathematical existances that have their
Architypes in nature.
What parts have
Of Quantity every conceivable modification may have its
Architype in Nature.
Of Figure many have already 2 been 1 proved to have had
this Architypes in Nature, many not yet. If if any
it was certain that it has not have its Architype,
it would then appear certain that the doctrine of
modification would be Useless.of Figure
Of Modification of Figure some stand exemplified in the
Boundaries of material substances. Others in the tract describes
potents of material substances in motion moving through a space
Def of Straight
If 2 lines whose extremities coincide, being when applied
to each other in all directions these lines must
be straight lines. To shew of a line be straight if
from the extreme points any line can be drawn so as to
coincide with it in one side and then still to coincide with it
if placed on the other that line must be straight.
There cannot be two straight lines drawn from & to the same points, their nature will admit
will admit of no variation.
>In Geometry the Breadth of a line is never considered
neither is are the dimensions of a Point. so that
but the line must have Breadth to be conceived
and the Point dimensions. Therefore if instead
of saying a circle touches a straight line
only therefore to know how much of a circle touches another
or a line instead of saying at a Point should
mean that it touched in a span equal to that
of the Breadth of the line of which it was composed
wherefore though there are no Geometrical points
yet a circle without another has as much common to another line when
it cuts another line it as it does has when it touches
it or joins it meets it of the line or of equal
thickness and this space which is common to
both should have some name and that may
as well be a point as any other.the Dimensions
This is just as much common as the breadth of a line
therefore if you say a line is made by the motion of a point same the dimensions of that point common.
Identifier: | JB/135/024/002
"JB/" can not be assigned to a declared number type with value 135.
sir samuel bentham
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