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<head>Collectanea for Posology</head> | |||
<p>157</p> | |||
<!-- The first column is split with JB/135/089/002 and is transcribed there. | |||
Second column: --> | |||
<p>make an unit of<lb/> | |||
the last denomination,<lb/> | |||
and thus<lb/> | |||
proceed till you<lb/> | |||
come to the lowest<lb/> | |||
you design; then<lb/> | |||
make the last product<lb/> | |||
a numerator<lb/> | |||
to the denominator<lb/> | |||
of the fraction<lb/> | |||
given.</p> | |||
<head>Case 10</head> | |||
<p>To reduce a fraction<lb/> | |||
of an unit of a lower<lb/> | |||
denomination<lb/> | |||
to an equivalent<lb/> | |||
fraction in the<lb/> | |||
denomination of<lb/> | |||
an higher:</p> | |||
<head>Rule.</head> | |||
<p>Multiply the denominator<lb/> | |||
by<lb/> | |||
the number of units<lb/> | |||
in the given fraction<lb/> | |||
that is equal<lb/> | |||
to an unit of the<lb/> | |||
next superior denomination,<lb/> | |||
and<lb/> | |||
the product by such<lb/> | |||
a number of units<lb/> | |||
of its denomination,<lb/> | |||
as is equal to an<lb/> | |||
unit of the next<lb/> | |||
above it; and thus<lb/> | |||
go on till you come<lb/> | |||
to the highest species<lb/> | |||
required, and<lb/> | |||
the last product is<lb/> | |||
a denominator to<lb/> | |||
the numerator of<lb/> | |||
the fraction given.</p> | |||
<head>Case 11.</head> | |||
<p>To find the value<lb/> | |||
of a fraction in<lb/> | |||
coin, weight, measure,<lb/> | |||
time, &c</p> | |||
<head>Rule.</head> | |||
<p>Multiply the numerator<lb/> | |||
of the given fraction by<lb/> | |||
the number of units<lb/> | |||
of the next<lb/> | |||
inferior species that<lb/> | |||
makes one of the<lb/> | |||
denomination of<lb/> | |||
<add>your</add></p><pb/> | |||
<p>your fraction, and<lb/> | |||
divide the product<lb/> | |||
by the denominator;<lb/> | |||
the quotient is so<lb/> | |||
many integers of<lb/> | |||
that lower species;<lb/> | |||
and if there is a<lb/> | |||
remainder, proceed<lb/> | |||
as before, still reducing<lb/> | |||
and dividing,<lb/> | |||
till you come to the<lb/> | |||
lowest species; and<lb/> | |||
the several quotients<lb/> | |||
with the remainder<lb/> | |||
(if any, which is always<lb/> | |||
the numerator<lb/> | |||
of a fraction of<lb/> | |||
the lowest species)<lb/> | |||
are the answer.</p> | |||
<p>If the fraction to<lb/> | |||
be valued be an improper<lb/> | |||
one, divide<lb/> | |||
the numerator by<lb/> | |||
the denominator,<lb/> | |||
and the quotient is<lb/> | |||
an integer of the<lb/> | |||
same species with<lb/> | |||
the fraction; then<lb/> | |||
reduce the remainder<lb/> | |||
as before.</p> | |||
<p>If the fraction to be<lb/> | |||
valued be an improper<lb/> | |||
one, divide the<lb/> | |||
numerator by the denominator,<lb/> | |||
and the<lb/> | |||
quotient is an integer<lb/> | |||
of the same species<lb/> | |||
with the fraction:<lb/> | |||
then reduce the remainder<lb/> | |||
as before.</p> | |||
<head>Addition of Fractions.</head> | |||
<p>In order to prepare<lb/> | |||
fractions for addition<lb/> | |||
or subtraction, all<lb/> | |||
compound fractions<lb/> | |||
must be reduced to<lb/> | |||
single ones; and if<lb/> | |||
they are of different<lb/> | |||
denominations they<lb/> | |||
must be brought into<lb/> | |||
the same denomination,<lb/> | |||
and reduced<lb/> | |||
so as all the fractions<lb/> | |||
shall have one common<lb/> | |||
denominator.</p><pb/> | |||
Collectanea for Posology
157
make an unit of
the last denomination,
and thus
proceed till you
come to the lowest
you design; then
make the last product
a numerator
to the denominator
of the fraction
given.
Case 10
To reduce a fraction
of an unit of a lower
denomination
to an equivalent
fraction in the
denomination of
an higher:
Rule.
Multiply the denominator
by
the number of units
in the given fraction
that is equal
to an unit of the
next superior denomination,
and
the product by such
a number of units
of its denomination,
as is equal to an
unit of the next
above it; and thus
go on till you come
to the highest species
required, and
the last product is
a denominator to
the numerator of
the fraction given.
Case 11.
To find the value
of a fraction in
coin, weight, measure,
time, &c
Rule.
Multiply the numerator
of the given fraction by
the number of units
of the next
inferior species that
makes one of the
denomination of
your
---page break---
your fraction, and
divide the product
by the denominator;
the quotient is so
many integers of
that lower species;
and if there is a
remainder, proceed
as before, still reducing
and dividing,
till you come to the
lowest species; and
the several quotients
with the remainder
(if any, which is always
the numerator
of a fraction of
the lowest species)
are the answer.
If the fraction to
be valued be an improper
one, divide
the numerator by
the denominator,
and the quotient is
an integer of the
same species with
the fraction; then
reduce the remainder
as before.
If the fraction to be
valued be an improper
one, divide the
numerator by the denominator,
and the
quotient is an integer
of the same species
with the fraction:
then reduce the remainder
as before.
Addition of Fractions.
In order to prepare
fractions for addition
or subtraction, all
compound fractions
must be reduced to
single ones; and if
they are of different
denominations they
must be brought into
the same denomination,
and reduced
so as all the fractions
shall have one common
denominator.
---page break---
|
Identifier: | JB/135/089/001"JB/" can not be assigned to a declared number type with value 135. |
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|---|---|---|---|
|
135 |
posology |
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|
089 |
collectanea for posology |
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|
001 |
decimal fractions / addition of fractions / subtraction of fractions / multiplication of fractions / division of fractions |
||
|
collectanea |
3 |
||
|
recto |
f154 / / f157 |
||
|
in two pieces (both stamped) |
46207 |
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