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<p><head>Prop IV. Theor</head>If the first of four, has the s<lb/>to the second which the third<lb/>fourth: then any equimultip<lb/>of the first and third shall have<lb/>ratio to any equimultiples of<lb/>and fourth, viz the equimultip<lb/>first, shall have the same ratio<lb/>the second which the equimultipl<lb/>third has to that of the fourth.</p>-----<p><head>Prop D Theo</head>If the first be to the second<lb/>third to the fourth and<lb/>be a multiple or part of<lb/>the third is the same one<lb/>part of the fourth.</p>-----<p><head>Prop XII The</head>If any number of magni<lb/>proportionals, as <gap/> of<lb/>cedents is to its consequ<lb/>shall all the Antecedents<lb/>all the Consequents.</p>-----<p><head>Prop XVIII The</head>If magnitudes taken separate<lb/>tionals, they shall also be prop<lb/>when taken jointly, that is, if<lb/>to the second as the third to<lb/>the first and second together<lb/>the second as the third and<lb/>ther to the fourth. —</p>-----<p><head>Prop XXIII Theor</head>If there be any number of mag<lb/>as many others, which taken tw<lb/>a cross order, have the same<lb/>first shall have to the last<lb/>first magnitudes the same<lb/>the first of the others has to the<lb/>NB This is usually cited by<lb/>exaequali in proportione<lb/>or ex acquo perturbato.</p> | |||
Prop IV. TheorIf the first of four, has the s
to the second which the third
fourth: then any equimultip
of the first and third shall have
ratio to any equimultiples of
and fourth, viz the equimultip
first, shall have the same ratio
the second which the equimultipl
third has to that of the fourth.
-----
Prop D TheoIf the first be to the second
third to the fourth and
be a multiple or part of
the third is the same one
part of the fourth.
-----
Prop XII TheIf any number of magni
proportionals, as of
cedents is to its consequ
shall all the Antecedents
all the Consequents.
-----
Prop XVIII TheIf magnitudes taken separate
tionals, they shall also be prop
when taken jointly, that is, if
to the second as the third to
the first and second together
the second as the third and
ther to the fourth. —
-----
Prop XXIII TheorIf there be any number of mag
as many others, which taken tw
a cross order, have the same
first shall have to the last
first magnitudes the same
the first of the others has to the
NB This is usually cited by
exaequali in proportione
or ex acquo perturbato.
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Identifier: | JB/135/072/004"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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004 |
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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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