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Transcribe Bentham: A Collaborative Initiative

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Lines Geometrical

Could the maximum of exactness whi with which a line could be
drawn be determined. Geometry then It would be useless
for Geometry to want you to suppose one more perfect.
but this is not the case the maximum can by means
be determined. To prevent therefore mechanics from
producing lines too narrow and too regular for Geometrical
propositions to hold good of them. Geometers have
done made use of the perfect lines to exemplify this
Prop. They have made it necessary to suppose no
irregularities at all to exist. had they not done
that but wished set about to adhere closely to the
Phisical existances to such lines as people must with
in practice it then would be necessary to demonstrate
their truth propositions taking every individual figure
alternately. new by divesting themselves of the trouble
of considering the imperfection of theoretical operations
they demonstrate their propositions with respect to
perfect lines and leave it to the practical mechanic
to discover how near the lines he can make will
approach to what is demonstrated of perfect ones.
A practical mechanic will not be able to make a
smaller circle touch one a little larger on the inside
in so small a part as on the out- in other words he
cannot make a convex surface touch a concave in so far
points as he can make it touch another convex one
yet he cannot determine what the difference will be.

Identifier: | JB/135/063/001
"JB/" can not be assigned to a declared number type with value 135.


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Folio number


Info in main headings field

lines geometrical





copy/fair copy sheet

Number of Pages




Page Numbering

f2 / f3


sir samuel bentham


[[watermarks::[britannia emblem]]]


Paper Producer


Paper Produced in Year

Notes public

ID Number


Box Contents

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