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<head>CLASSIFICATION (I)</head> | <head>CLASSIFICATION (I)</head> | ||
<note>Euclid’s Order<lb/> | |||
<p>1. If it <hi rend="underline">should</hi> be necessary to insert any new Propositions | preferred</note> | ||
<p>1. If it <hi rend="underline">should</hi> be necessary to insert any new Propositions.<lb/> | |||
Those of Euclid should still <add>retain</add> their former names, as they <lb/> | Those of Euclid should still <add>retain</add> their former names, as they <lb/> | ||
are refered to be those names | are <sic>refered</sic> to be those names from Books of Mechanics &c.</p> | ||
<note>Order how<lb/> | |||
Changeable<lb/> | Changeable<lb/> | ||
at pleasure<lb/> | at pleasure<lb/> | ||
Use of it</note><lb/> | Use of it</note> | ||
<p>2. By the assistance of the Cards described Method II.<lb/> | |||
The Order of Prop: and Cor: may be changed so as to<lb/> | |||
place all those together which relate to the several<lb/> | place all those together which relate to the several<lb/> | ||
genera & species, <del>and</del> By this means each parcel<lb/> | genera & species, <del>and</del> By this means each parcel<lb/> | ||
may be made equally perfect. For Ex: if after having<lb/> | may be made equally perfect. For Ex: if after having<lb/> | ||
divided Triangles and Parallelograms into 2 | divided Triangles and Parallelograms into 2 Parcels<lb/> | ||
you find that <del>for</del> Triangles as well as Parallelograms<lb/> | you find that <del>for</del> Triangles as well as Parallelograms<lb/> | ||
upon the same bases & between the same parallels<lb/> | upon the same bases & between the same parallels<lb/> | ||
are proved equal, But that Triangles only are <add>if on equal bases</add><lb/> | are proved equal, But that Triangles only are <add>if on equal bases</add><lb/> | ||
proved equal, then you perceive that Parallelograms<lb/> | proved equal, then you perceive that Parallelograms<lb/> | ||
should be proved equal under like circumstances</p> | should be proved equal under like circumstances.</p> | ||
<p>3. Consider the different orders <hi rend="underline">Geometerical | <note>Different Classification<lb/> | ||
of Different Authors</note> | |||
<p>3. Consider the different orders <hi rend="underline">Geometerical Truths</hi> have been<lb/> | |||
disposed in, by different Authors, and the different ends they<lb/> | disposed in, by different Authors, and the different ends they<lb/> | ||
had in view in [purposes they have sought to compass by] such<lb/> | had in view in [purposes they have sought to compass by] such<lb/> | ||
different Dispositions.</p> | different Dispositions.</p> | ||
<pb/> | |||
<p>CLASSIFICATION (I)</p> | |||
<p>The order necessary to be assumed for the purpose of <hi rend="underline">demonstrating</hi><lb/> | <p>The order necessary to be assumed for the purpose of <hi rend="underline">demonstrating</hi><lb/> | ||
the several Propositions is one thing.</p> | the several Propositions is one thing.</p> | ||
for the purpose of teaching<add>them</add> (were the business only<lb/> | <note>Species of Order</note> | ||
<p> The order which would be most <del>proper</del> convenient & methodical<lb/> | |||
for the purpose of teaching <add>them</add> (were the business only<lb/> | |||
to apprehend and retain them) would be another.</p> | to apprehend and retain them) would be another.</p> | ||
<p>The order in which they occurred to the Inventor, probably<lb/> | <p>The order in which they occurred to the Inventor, probably<lb/> | ||
was a third, certainly it was different from the first.</p> | was a third, certainly it was different from the first.</p> | ||
<note>Order of <lb/> | |||
1<hi rend="superscript">st</hi> Invention<lb/> | 1<hi rend="superscript">st</hi> Invention<lb/> | ||
Demonstration<lb/> | Demonstration<lb/> | ||
Systematical</note> We have therefore (unless the two latter coincide) three<lb/> | Systematical</note> | ||
<p>We have therefore (unless the two latter coincide) three<lb/> | |||
different <add>species of</add> Orders 1<hi rend="superscript">st</hi> the order of Demonstration.<lb/> | different <add>species of</add> Orders 1<hi rend="superscript">st</hi> the order of Demonstration.<lb/> | ||
2<hi rend="superscript">d</hi> the order of conception & retension 3<hi rend="superscript">dly</hi> the order of<lb/> | 2<hi rend="superscript">d</hi> the order of conception & retension 3<hi rend="superscript">dly</hi> the order of<lb/> | ||
Invention.</p> | Invention.</p> | ||
<p>The 1<hi rend="superscript">st</hi> and only state in which Geometry has been<lb/> | <p>The 1<hi rend="superscript">st</hi> and only state in which Geometry has been<lb/> | ||
transmitted to us by the <sic>Antients</sic> is a state | transmitted to us by the <sic>Antients</sic> is a state far advanced<lb/> | ||
towards perfection. I mean relatively according to the<lb/> | towards perfection. I mean relatively according to the<lb/> | ||
order of demonstration, we see it not in this Science<lb/> | order of demonstration, we see it not in this Science<lb/> | ||
in its first rude essays as we do those for example of<lb/> | in its first rude essays as we do those for example of<lb/> | ||
Natural History & Legislation</p> | Natural History & Legislation</p> | ||
<p>It will appear very plain that Euclid could never<lb/> | <p>It will appear very plain that Euclid could never<lb/> | ||
first thought of his Propositions in the order in<lb/> | have first thought of his Propositions in the order in<lb/> | ||
which he has placed them | which he has placed them, but it is to be supposed he<lb/> | ||
he placed them in their present order for the purpose <lb/> | he placed them in their present order for the purpose <lb/> | ||
of demonstration.</p> | of demonstration.</p> | ||
<note>Order of Instruction</note> | |||
<p> The order of Simple or Authoritative Illustration<add>[+]</add> is the<lb/> | |||
same with the Order of enquiry. It is in its Nature for Instruction<lb/> | |||
to be determined by the Order of Enquiry: for how should a man who had it<lb/> | to be determined by the Order of Enquiry: for how should a man who had it<lb/> | ||
in other respects in his choice think if answering questions, but in <lb/> | in other respects in his choice think if answering questions, but in <lb/> | ||
the order in which they were | the order in which they were asked.</p> | ||
<note><add>[+]</add> as it may be termed</note> | |||
<!-- DO NOT EDIT BELOW THIS LINE --> | <!-- DO NOT EDIT BELOW THIS LINE --> | ||
{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}}{{Completed}} | ||
CLASSIFICATION (I)
Euclid’s Order
preferred
1. If it should be necessary to insert any new Propositions.
Those of Euclid should still retain their former names, as they
are refered to be those names from Books of Mechanics &c.
Order how
Changeable
at pleasure
Use of it
2. By the assistance of the Cards described Method II.
The Order of Prop: and Cor: may be changed so as to
place all those together which relate to the several
genera & species, and By this means each parcel
may be made equally perfect. For Ex: if after having
divided Triangles and Parallelograms into 2 Parcels
you find that for Triangles as well as Parallelograms
upon the same bases & between the same parallels
are proved equal, But that Triangles only are if on equal bases
proved equal, then you perceive that Parallelograms
should be proved equal under like circumstances.
Different Classification
of Different Authors
3. Consider the different orders Geometerical Truths have been
disposed in, by different Authors, and the different ends they
had in view in [purposes they have sought to compass by] such
different Dispositions.
---page break---
CLASSIFICATION (I)
The order necessary to be assumed for the purpose of demonstrating
the several Propositions is one thing.
Species of Order
The order which would be most proper convenient & methodical
for the purpose of teaching them (were the business only
to apprehend and retain them) would be another.
The order in which they occurred to the Inventor, probably
was a third, certainly it was different from the first.
Order of
1st Invention
Demonstration
Systematical
We have therefore (unless the two latter coincide) three
different species of Orders 1st the order of Demonstration.
2d the order of conception & retension 3dly the order of
Invention.
The 1st and only state in which Geometry has been
transmitted to us by the Antients is a state far advanced
towards perfection. I mean relatively according to the
order of demonstration, we see it not in this Science
in its first rude essays as we do those for example of
Natural History & Legislation
It will appear very plain that Euclid could never
have first thought of his Propositions in the order in
which he has placed them, but it is to be supposed he
he placed them in their present order for the purpose
of demonstration.
Order of Instruction
The order of Simple or Authoritative Illustration[+] is the
same with the Order of enquiry. It is in its Nature for Instruction
to be determined by the Order of Enquiry: for how should a man who had it
in other respects in his choice think if answering questions, but in
the order in which they were asked.
[+] as it may be termed
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