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# JB/135/089/004

Completed

Collectanea for Posology.

A circulet is a compound repetend

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Decimal fractions

1
In addition & subtraction, to place the
points of distinction
one under the other.

2
In Multiplication,
to separate with a
point so many places
of the product to
the right hand, as
there are Decimal
Places both in the
Multiplicand and
Multiplier; and if
there are not so many
places in the
cyphers to the left
hand, 'till there are
so many places

3
In Division, to separate
with a point
so many places of
the quotient to the
right as there are
decimal places in
the dividend more
than are in the divisor;
and if there
are not so many
cyphers to the left 'till
there are so many

4
to the right
hand of the dividend
any lesser number
given may be divided
by a greater.

5
To reduce a vulgar
fraction to a Decimal
of the same
value — divide the
Numerator by the
Denominator and
the quotient will be
the Decimal Fraction
required

6
And to reduce a Decimal
fraction to a
Vulgar — multiply the
decimal by the Denominator
of the Vulgar
and the product will
be the vulgar fraction
required

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Reduction of Vulgar
Fractions.

Case. 1.

To reduce a compound
fraction into a single
one.

Rule.

Multiply all the numerators
into one another
for a numerator,
and all the denominators
into one another
for the denominator

Case 2.

To reduce mixed numbers
& integers into
improper fractions.
I shall divide this case
into three parts.

1. If the integer has
no assigned denominator.

Rule

An unit subscribed
most be the denominator.

2. If the integer have
an assigned denominator.

Rule.

Multiply the integer
by the assigned denominator,
the product
is the numerator
to the assigned
denominator.

3. If the integer have
a fraction annexed.

Rule

Multiply the integer
by the denominator,
and to the product
the sum is the numerator
to the denominator
of the
annexed fraction.

Case. 3.

To reduce an improper
fraction into its
equivalent, whole, or
mixed numbers.

Rule.

Divide the numerator
by the denominator,
the quotient
gives the integer, &
under the remainder,
if any, subscribe
the denominator.

Case 4.

To abbreviate or reduce
fractions into their
lowest or least denomination.

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If the numerator
and denominator
are even numbers,
take half the one,
and half the other,
as often as may be;
and when either of
them fall out to be
an odd number,
then divide them
by any number
that you can discover
will divide
both numerator
and denominator
without any remainder.

Or, by finding the
greatest common
measure by the
following —

Rule

Divide the greater
number by the lesser,
and that divisor
by the remainder
(if there be
any) and so on
continually untill
there be no remainder
left. Then
will the last divisor
be the greatest
common measure,
which if it happen
to be 1, then are
they prime numbers,
in their lowest
terms; but if otherwise,
divide the
numbers by the
last divisor, and
their quotients will
be their least terms
required.

Case 5.

To alter or change
different fractions
into one denomination,
retaining
the same value.

Rule.

Multiply all the
denominators into
each other for a
new & common
denominator, and
each numerator
into all the denominators
but its own
for 2 new numerators

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If there be two denominators
alike, you
need multiply
but by one of them,

2. When there are
only two fractions
to be reduced, if
one of the denominators
is a multiple
of the other,
divide; and by the
quote multiply the
numerator and
denominator of
that fraction which
hath the least denominator,
and
the fraction thus
found will be equivalent
to the given
ones.

3. Or if both of the
denominators have
a common multiple,
divide each
of the denominators
thereby, and
multiply the contrary
numerators
and denominators
by each contrary
quotient.

Case. 6.

To reduce a fraction
to an equivalent
one of any other
assigned denominator
viz: to find
a numerator, which,
with the assigned
denominator, will
make a fraction
equivalent to the
proposed one,
when possible.
Whenever the denominator
assigned
is divisible
(without a remainder)
by the denominator
of the given
fraction, the thing
is possible, otherwise
not.

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Case 7

To find whether one
fraction be greater or
less in value than
another.

Rule.

Multiply the numerator
into each other's
denominator, and if
the products are equal,
the fractions are so: otherwise
the numerator
of the greatest fraction
multiplied by
the denominator of
the other, will be the
greatest product.

Case 8.

To reduce coins, weights,
measures, &c into fractions

Rule

Reduce the coin, weight,
&c into the lowest name
mentioned for a numerator;
and put the
number of those parts
contained in a unit
of the integer, to which
the proposed fraction
is to be reduced for the
denominator; then
reduce the fraction
into its lowest terms

Case. 9.

To reduce a fraction of
an unit of a higher
denomination to an
equivalent fraction
of an unit of a lower
species of the same
kind with the higher.

Rule

Multiply the numerator
of the given fraction,
by the number of
units in the next inferior
species that
make an unit of the
denomination of your
fraction, and that product multiply by the
number of units in
the next inferior denomination
that
make

Identifier: | JB/135/089/004
"JB/" can not be assigned to a declared number type with value 135.

135

posology

089

collectanea for posology

004

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