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A line is said to be curved, if when a straight line is made
to join the its 2 axtreams, these 2 lines do not coincide.
Or if any assumed points are supposed to be the extreams, and
dealt accordingly otherwise a circumference Circle could not be proved a Curve
line having no axtreams, although any part of it could.

If a straight line touches joins the extremity of a Curved line so as if produced to
make a tangent to it these 2 lines namely the straight
and the adjoining Curve may be considered as one and called
a mixed line.

If the straight line joins the Curved one so as if produced not to make
a Tangent to it it is said to make an angle with it
called a Mixed angle.

Equal Measure of
without superposition
Equal angles are those which who the boundaries of which are
equally distantted angles for the distant. This distance
may be measured by the length of line drawn square from
a point of equally distant from one of the lines entering an each angle.

A right Line is a Being which Mathematicians consider as
extended in Length, and at the same time abstract from it, the
Idea of Breadth, (which is inseparably connected with a
Physical Line) because they make no use of that appendage
of a Line in all the Variety of purposes to which they apply
it; they moreover say that a Right Line lies equally between
its extremes, or it is the Shortest distance possible between them, to
as the Specific difference between the Right-Line and every
other Species of Lines, by which it may in all Cases be
distinguished from them.

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Species of
The Propositions generally used by Mathematicians are
the following 1st: Definitions — 2o. Axioms, or Self-evident :
Speculative Truths. 3o. Postulates, or Self evident practical Truths.
4o: Theorems, or demonstrable speculative Proof Truths of a speculative
nature. 5o. Problems, or demonstrable practical truths of a practical
Principles Genus
Postulates} Species
Nature. 6o Lemma, or p demonstrations of some premisses
to facilitate the demonstration of any of the former. 7o.
Corollaries or obvious Conclusions drawn from a
preceding demonstration. 8o. Scholia-Containing
Remarks, Elucidations &c &, — or<add>a</add> are analogous to the
Annotations of Classical Authors.

Oblique Triangles are such as have no right angle
the species of them are Acute and Obtuse Triangles.

Square. Def of. A Square is a Figure bounded by four Equal right Lines,
jointed joined together by right Angles. an equilateral
rectangle or right angl'd Parallelogram.

Each to one When one parcel of magnitude is compared to another equinumeral
parcel of Magnitude one at a ime in one parcel
[++] When it is determined
which 2 are to be
compared to gether
each of them is said
to be correspondent
to the other
to one at a line in the other they are said to be
be compared each to one, by saying each to one you
to determine which in one parcel shall be compared
to any assumed one in the other. When afterwards
you have occasion to speak of that one in one parcel
Correspondent together with that with which it was compared in the other
you call one the correspondent to the other .[++]

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Identifier: | JB/135/014/002
"JB/" can not be assigned to a declared number type with value 135.


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copy/fair copy sheet

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jeremy bentham; samuel bentham; uk14


[[watermarks::[gr with crown] [britannia with lion motif]]]


sir samuel bentham

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