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<p>The expression in Euclid is "<hi rend="underline">each to each</hi>".<lb/> | <p>The expression in Euclid is "<hi rend="underline">each to each</hi>". <note>Each to Each</note><lb/> | ||
This is inadequate: for the import he annexes<lb/> | This is inadequate: for the import he annexes<lb/> | ||
to it, is not conformable to any import the <lb/> | to it, is not conformable to any import the <lb/> | ||
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<del>a doubt</del><add>clear and indubitable manner between which of</add><lb/> | <del>a doubt</del><add>clear and indubitable manner between which of</add><lb/> | ||
the four objects he means the equality</p><pb/> | the four objects he means the equality</p><pb/> | ||
<p>should be supposed, we must give the two<lb/> | |||
figures and arbitrary situation</p> | |||
—<lb/> | |||
<p>correspondant to it that is on some <gap/>guable<lb/> | |||
particular of resemblance; tho' some has he<lb/> | |||
assigned <add>In</add> In <del>length</del> <add>magnitude</add> for example <add>that is, in length:</add> the only<lb/> | |||
<add>property</add> particular <del>those</del> except situation [in] which<lb/> | |||
<add>(they have)</add> they can either differ or again <add>[in]</add>. <add>That is</add> If there<lb/> | |||
is any difference in length the longest <add>side</add> <del>have</del><lb/> | |||
in one Triangle, equal to the longest on the<lb/> | |||
other: the shortest to the shortest. If there is<lb/> | |||
no difference in length between those of <lb/> | |||
the same triangle: then if any one <add>of the two</add> side in<lb/> | |||
one triangle is equal to one in the other<lb/> | |||
be that one which it may, all four <add>sides</add> are<lb/> | |||
equal <add>according to</add><del>by</del> the . . . .<add>an</add> axiom.</p> | |||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}} | ||
The expression in Euclid is "each to each". Each to Each
This is inadequate: for the import he annexes
to it, is not conformable to any import the
it can be shewn to to hear
on any other occasion.
The two sides of the one triangle, says
Euclid, I suppose to be equal to two sides
of the other triangle each to each. The real
eachmeaning is, each to it's correspondent one:
namely that one side of the one triangle
is equal to that side of the other triangle
that corresponds with it in some particular and the arrangement
he has for the purpose given the parts sides
of [the each triangle two triangles] among themselves: given
I say in his own kind, tho' not announced
he should have to have made
his meaning clear.
—
Correspondent one to what? the answer is in situation:
for there is no other particular in which
the two sides of the same triangle an
have any such arbitrary difference assigned
them as can serve to characterize them.
---page break---
To ascertain by a general description in abeyond
a doubtclear and indubitable manner between which of
the four objects he means the equality
---page break---
should be supposed, we must give the two
figures and arbitrary situation
—
correspondant to it that is on some guable
particular of resemblance; tho' some has he
assigned In In length magnitude for example that is, in length: the only
property particular those except situation [in] which
(they have) they can either differ or again [in]. That is If there
is any difference in length the longest side have
in one Triangle, equal to the longest on the
other: the shortest to the shortest. If there is
no difference in length between those of
the same triangle: then if any one of the two side in
one triangle is equal to one in the other
be that one which it may, all four sides are
equal according toby the . . . .an axiom.
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Identifier: | JB/135/027/002"JB/" can not be assigned to a declared number type with value 135. |
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not numbered |
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135 |
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027 |
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002 |
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copy/fair copy sheet |
2 |
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recto |
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sir samuel bentham |
[[watermarks::[gr with crown] [pro patria motif]]] |
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46145 |
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