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<head>Lines Geometrical</head> | <head>Lines Geometrical</head> | ||
Could the maximum of exactness <del>whi</del> with which a line could be<lb/> | <p>Could the maximum of exactness <del>whi</del> with which a line could be<lb/> | ||
drawn determined. <del>Geometry then</del> It would be useless<lb/> | drawn be determined. <del>Geometry then</del> It would be useless<lb/> | ||
for Geometry to want you to suppose one more perfect.<lb/> | for Geometry to want you to suppose one more perfect.<lb/> | ||
but this is not the case the maximum can by means<lb/> | but this is not the case the maximum can by means<lb/> | ||
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propositions to hold good of them. Geometers have<lb/> | propositions to hold good of them. Geometers have<lb/> | ||
<del>done</del> made use of the perfect lines to exemplify this<lb/> | <del>done</del> made use of the perfect lines to exemplify this<lb/> | ||
Prop. They have made <unclear>necessary</unclear> to suppose no<lb/> | Prop. They have made it <unclear>necessary</unclear> to suppose no<lb/> | ||
irregularities at all to exist. had they not done<lb/> | irregularities at all to exist. had they not done<lb/> | ||
that but <del>wished</del> set about to adhere closely to the<lb/> | that but <del>wished</del> set about to adhere closely to <del>the</del><lb/> | ||
<sic>Phisical</sic> <sic>existances</sic> to such lines as people must with<lb/> | <sic>Phisical</sic> <sic>existances</sic> to such lines as people must with<lb/> | ||
in practice it then would be necessary to demonstrate <lb/> | in practice it then would be necessary to demonstrate <lb/> | ||
their <del>truth</del> propositions taking every individual figure<lb/> | their <del>truth</del> propositions taking every individual figure<lb/> | ||
alternately. new by divesting themselves of the trouble<lb/> | <unclear>alternately</unclear>. new by divesting themselves of the trouble<lb/> | ||
of considering the imperfection of theoretical operations<lb/> | of considering the imperfection of theoretical operations<lb/> | ||
they demonstrate their propositions with respect to<lb/> | they demonstrate their propositions with respect to<lb/> | ||
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approach to what is demonstrated of perfect ones.<lb/> | approach to what is demonstrated of perfect ones.<lb/> | ||
A practical mechanic will not be able to make a<lb/> | A practical mechanic will not be able to make a<lb/> | ||
smaller circle | smaller circle touch one a little larger on the inside<lb/> | ||
in so small a part as on the out- in other words he<lb/> | in so small a part as on the out- in other words he<lb/> | ||
cannot make a convex surface touch a concave in so <unclear>far</unclear><lb/> | cannot make a convex surface touch a concave in so <unclear>far</unclear><lb/> | ||
points as he can make it touch another convex one<lb/> | points as he can make it touch another convex one<lb/> | ||
yet he cannot determine what the difference will be< | yet he cannot determine what the difference will be.</p> | ||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}} | ||
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.
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Identifier: | JB/135/063/001"JB/" can not be assigned to a declared number type with value 135. |
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135 |
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063 |
lines geometrical |
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001 |
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copy/fair copy sheet |
2 |
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recto |
f2 / f3 |
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sir samuel bentham |
[[watermarks::[britannia emblem]]] |
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46181 |
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