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That may be found
better without than
with a diagram From the same point are drawn different right two lines one to
one point, another to another
a right line is the shortest that can be drawn
between any two points
If any othera right lines are once more use drawn from
the first point point in question to the 2 others, they must
be either the same with the two others
or different
If they are the same they dont come under
the point of the proposition which is predicated
of such as are different
They are eithermust state
taken together they must either be greater
than the first or less or equal
If taken together they are greater than one
at least if not both, must be greater & so
[+] to the corresponding
one of the other. each is not equal:[+] if taken together they
are less, than one at least if not both
must be less, & so in this case to, each
is not equal.
If taken together they are equal with the two
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L I Prop. 8 corresponding onestaken together, they must coincide
with them.
CLASSIFICATION
This proposition may serve as an example to
shew prove that the order of demonstration is not the
same with the order of invention.
It seems as if the Author had gotten some
inexplicit notion of the truth of it in the
ways I have been mentioning: but that which he
has used happen'd to be the first method that
occurred to him of proving it against
a gainsayer.
[+] to the several parts that are to be considered
names are given according to the
Ordinary method of Notation, it is included
in 3 boundaries to one of these boundaries is given
the name of A to another B to the remaining one
C. to the whole triangle thus included the
complex name ABC,
---page break---
Having then The Appellatives Upon precisely this footing that is the footing of Proper names stand those Appellatives which in the ordinary method of notation in use in Geometry are applied to denote any figure or part of a figure upon which is drawn the demo???? is exemplified. The Proposition we sill say conceives Triangles [Triangles we will say are the subject of the Proposition] a Triangle is drawn [+] this Triangle the moment it is drawn is of a particular sort of Triangles it is either an equilateral triangle an Isosceles or a scalene not only so it isi that an INdividual one triangle which is drawn it is that Individual triangle which is drawn. Of what isi t then that these letters are expressive? preparatively the Individual lines which are its boundaries together Of the Individual space included between the lines either the of those lines be situated as they are so as to bound that whole individual triangle or as we may say the whole area of that triangle or else the Area itself that is so banded
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Identifier: | JB/135/029/002"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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029 |
euclid |
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002 |
classification |
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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] [britannia motif]]] |
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46147 |
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