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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/> | ||
< | <del>wor</del> it can be <del>shewn</del> <del>to <gap/> <gap/></del> to bear<lb/> | ||
on any other occasion.</p> | on any other occasion.</p> | ||
<p> | <p> | ||
The two sides of the one triangle, says<lb/> | <del>The</del> two sides of the one triangle, says<lb/> | ||
Euclid, I suppose to be equal to two sides<lb/> | Euclid, I suppose to be equal to two sides<lb/> | ||
of the other triangle each to each. The <del><gap/></del><add>real</add><lb/> | of the other triangle each to each. The <del><gap/></del><add>real</add><lb/> | ||
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he has for the purpose given the <del>parts</del> sides<lb/> | he has for the purpose given the <del>parts</del> sides<lb/> | ||
of [the <add>each triangle</add> two triangles] among themselves: given<lb/> | of [the <add>each triangle</add> two triangles] among themselves: given<lb/> | ||
I say in his own kind, tho' not announced<lb/> | I say in his own <unclear>kind</unclear>, tho' not announced<lb/> | ||
< | <unclear>which</unclear> he should have done to have made<lb/> | ||
his meaning clear.</p> | his meaning clear.</p> | ||
—<lb/> | —<lb/> | ||
<p>Correspondent one to what? <add>the answer is</add> in situation:<lb/> | <p>Correspondent one to what? <add>the answer is</add> in situation:<lb/> | ||
for there is no other particular in which<lb/> | for there is no other particular in which<lb/> | ||
the two sides of the same triangle | the two sides of the same triangle are<lb/> | ||
have any such arbitrary difference assigned<lb/> | have any such arbitrary difference assigned<lb/> | ||
them as can serve to characterize them.< | them as can serve to characterize them.<lb/> | ||
To ascertain by a general description <add>in a</add><del>beyond</del><lb/> | To ascertain by a general description <add>in a</add><del>beyond</del><lb/> | ||
<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/> | ||
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<p>should be supposed, we must give the two<lb/> | <p>should be supposed, we must give the two<lb/> | ||
figures | figures an arbitrary situation</p> | ||
—<lb/> | —<lb/> | ||
<p>correspondant to it that is on some < | <p>correspondant to it that is on some <unclear>assignable</unclear><lb/> | ||
particular of resemblance; tho' | particular of resemblance; tho' none 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/> | 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>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/> | <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/> | is any difference in length the longest <add>side</add> <del>have</del><lb/> | ||
in one Triangle, equal to the longest | in one Triangle, equal to the longest in the<lb/> | ||
other: the shortest to the shortest. If there is<lb/> | other: the shortest to the shortest. If there is<lb/> | ||
no difference in length between those of <lb/> | no difference in length between those of <lb/> | ||
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one triangle is equal to one in the other<lb/> | one triangle is equal to one in the other<lb/> | ||
be that one which it may, all four <add>sides</add> are<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> | equal <add>according to</add><del>by</del> the . . . .<add>an</add> axiom.</p><pb/> | ||
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
wor it can be shewn to to bear
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
which he should have done 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 are
have any such arbitrary difference assigned
them as can serve to characterize them.
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 an arbitrary situation
—
correspondant to it that is on some assignable
particular of resemblance; tho' none 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 in 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.
---page break---
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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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