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< | <p>Prop IV Theor.</p> | ||
<p>If the first of four magnitudes has the same<lb/>ratio to the second which the third has to the<lb/>fourth then any equimultiples whatever<lb/>of the first and third shall have the same ratio<lb/>to any equimultiples of the second & fourth.<lb/>viz the equimultiple of the first shall have<lb/>the same ratio to that of the second which the<lb/>equimultiple of the third has to that of the<lb/>fourth.</p> | <p>If the first of four magnitudes has the same<lb/>ratio to the second which the third has to the<lb/>fourth then any equimultiples whatever<lb/>of the first and third shall have the same ratio<lb/>to any equimultiples of the second & fourth.<lb/>viz the equimultiple of the first shall have<lb/>the same ratio to that of the second which the<lb/>equimultiple of the third has to that of the<lb/>fourth.</p> | ||
< | <p>Prop V Theor.</p> | ||
<p>If one magnitude be the same multiple<lb/>of another, which a magnitude taken from<lb/>the first is of a magnitude taken from the<lb/>other: the remainder shall be the same<lb/>multiple of the remainder, that the<lb/>whole is of the whole.</p> | <p>If one magnitude be the same multiple<lb/>of another, which a magnitude taken from<lb/>the first is of a magnitude taken from the<lb/>other: the remainder shall be the same<lb/>multiple of the remainder, that the<lb/>whole is of the whole.</p> | ||
< | <p>Prop VI Theor.</p> | ||
<p>If two magnitudes be equimultiples of<lb/>two others, and if equimultiples of these be<lb/>taken from the first two, the remainders<lb/>are either equal to these others or<lb/>equimultiples of them. —</p> | <p>If two magnitudes be equimultiples of<lb/>two others, and if equimultiples of these be<lb/>taken from the first two, the remainders<lb/>are either equal to these others or<lb/>equimultiples of them.—</p> | ||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}}{{Completed}} | ||
Prop IV Theor.
If the first of four magnitudes has the same
ratio to the second which the third has to the
fourth then any equimultiples whatever
of the first and third shall have the same ratio
to any equimultiples of the second & fourth.
viz the equimultiple of the first shall have
the same ratio to that of the second which the
equimultiple of the third has to that of the
fourth.
Prop V Theor.
If one magnitude be the same multiple
of another, which a magnitude taken from
the first is of a magnitude taken from the
other: the remainder shall be the same
multiple of the remainder, that the
whole is of the whole.
Prop VI Theor.
If two magnitudes be equimultiples of
two others, and if equimultiples of these be
taken from the first two, the remainders
are either equal to these others or
equimultiples of them.—
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Identifier: | JB/135/072/001"JB/" can not be assigned to a declared number type with value 135. |
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135 |
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072 |
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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001 |
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private material |
3 |
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recto |
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sir samuel bentham |
[[watermarks::[tall thin motif with prince of wales feathers] icv]] |
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46190 |
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