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The Propositions of the Fifth and Sixth Books of Euclid as expressed by
Prop I Theor
If any number of magnitudes be
equimultiples of as many, each of each, what
multiple soever any one of them is of
its part, the same multiple shall all
the first magnitudes be of all the
other.
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Prop A Theor
If the first of the four magnitudes has
to the second the same ratio which
the third has to the fourth, then if
the first be greater than the second
the third is also greater than the fourth
and if equal, equal: if less, less.
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Prop IX Theor.
Magnitudes which have the
same ratio to the same magnitude
are equal to one another: and
those to which the same magnitude
has the same ratio are equal to one
another.
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Prop XV Theor. -
Magnitudes have the same ratio
to one another which their
equimultiples have.
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Prop XX Theor -
If there be three magnitudes and other
three, which taken two and two have
the same ratio, if the first be greater
than the third the fourth shall be
greater than the sixth: and if equal,
equal, and if less, less —
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Prop F Theor.
Ratios which are compounded of
the same Ratios are the same
with one another.
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Prop II Theor. -
If the first magnitude, be the same
multiple of the second that the third is of the
fourth, and the fifth the same multiple
of the second that the sixth is of the fourth:
then shall the first together with the
fifth, be the same multiple of the second
that the third together with the sixth is
of the fourth. —
-----
Prop B Theor.
If four magnitudes are
proportional, they are proportionals
also when taken inversely.
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the propositions of the fifth and sixth books of euclid as expressed by simson those written with red ink are added by himself |
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sir samuel bentham |
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