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<head>Collectanea for <sic>Posology</sic></head> | |||
<p>A <sic>circulet</sic> is a compound repetend</p><pb/> | |||
<!-- Column heading in faint pencil: --> <head>Decimal fractions</head> | |||
<p>1<lb/> | |||
<!-- The remainder of this column is struck through in faint pencil --> | |||
In addition & subtraction, | |||
to place the<lb/> | |||
points of distinction<lb/> | |||
one under the other.</p> | |||
<p>2<lb/> | |||
In Multiplication,<lb/> | |||
to separate with a<lb/> | |||
point so many places<lb/> | |||
of the product to<lb/> | |||
the right hand, as<lb/> | |||
there are Decimal<lb/> | |||
Places both in the<lb/> | |||
Multiplicand and<lb/> | |||
Multiplier; and if<lb/> | |||
there are not so many<lb/> | |||
places in the<lb/> | |||
product, then to add<lb/> | |||
cyphers to the left<lb/> | |||
hand, 'till there are<lb/> | |||
so many places</p> | |||
<p>3<lb/> | |||
In Division, to separate<lb/> | |||
with a point<lb/> | |||
so many places of<lb/> | |||
the quotient to the<lb/> | |||
right as there are<lb/> | |||
decimal places in<lb/> | |||
the dividend more<lb/> | |||
than are in the divisor;<lb/> | |||
and if there<lb/> | |||
are not so many<lb/> | |||
places, then to add<lb/> | |||
cyphers to the left 'till<lb/> | |||
there are so many</p> | |||
<p>4<lb/> | |||
And by adding cyphers<lb/> | |||
to the right<lb/> | |||
hand of the dividend<lb/> | |||
any lesser number<lb/> | |||
given may be divided<lb/> | |||
by a greater.</p> | |||
<p>5<lb/> | |||
To reduce a vulgar<lb/> | |||
fraction to a Decimal<lb/> | |||
of the same<lb/> | |||
value — divide the<lb/> | |||
Numerator by the<lb/> | |||
Denominator and<lb/> | |||
the quotient will be<lb/> | |||
the Decimal Fraction<lb/> | |||
required</p> | |||
<p>6<lb/> | |||
And to reduce a Decimal<lb/> | |||
fraction to a<lb/> | |||
Vulgar — multiply the<lb/> | |||
decimal by the Denominator<lb/> | |||
of the Vulgar<lb/> | |||
and the product will<lb/> | |||
be the vulgar fraction<lb/> | |||
required</p><pb/> | |||
<head>Reduction of Vulgar<lb/> | |||
Fractions.</head> | |||
<head>Case. 1.</head> | |||
<p>To reduce a compound<lb/> | |||
fraction into a single<lb/> | |||
one.</p> | |||
<head>Rule.</head> | |||
<p>Multiply all the numerators<lb/> | |||
into one another<lb/> | |||
for a numerator,<lb/> | |||
and all the denominators<lb/> | |||
into one another<lb/> | |||
for the denominator</p> | |||
<head>Case 2.</head> | |||
<p>To reduce mixed numbers<lb/> | |||
& integers into<lb/> | |||
improper fractions.<lb/> | |||
I shall divide this case<lb/> | |||
into three parts.</p> | |||
<p>1. If the integer has<lb/> | |||
no assigned denominator.</p> | |||
<head>Rule</head> | |||
<p>An unit subscribed<lb/> | |||
most be the denominator.</p> | |||
<p>2. If the integer have<lb/> | |||
an assigned denominator.</p> | |||
<head>Rule.</head> | |||
<p>Multiply the integer<lb/> | |||
by the assigned denominator,<lb/> | |||
the product<lb/> | |||
is the numerator<lb/> | |||
to the assigned<lb/> | |||
denominator.</p> | |||
<p>3. If the integer have<lb/> | |||
a fraction annexed.</p> | |||
<head>Rule</head> | |||
<p>Multiply the integer<lb/> | |||
by the denominator,<lb/> | |||
and to the product<lb/> | |||
add the numerator;<lb/> | |||
the sum is the numerator<lb/> | |||
to the denominator<lb/> | |||
of the<lb/> | |||
annexed fraction.</p> | |||
<head>Case. 3.</head> | |||
<p>To reduce an improper<lb/> | |||
fraction into its<lb/> | |||
equivalent, whole, or<lb/> | |||
mixed numbers.</p> | |||
<head>Rule.</head> | |||
<p>Divide the numerator<lb/> | |||
by the denominator,<lb/> | |||
the quotient<lb/> | |||
gives the integer, &<lb/> | |||
under the remainder,<lb/> | |||
if any, subscribe<lb/> | |||
the denominator.</p> | |||
<head>Case 4.</head> | |||
<p>To abbreviate or reduce<lb/> | |||
fractions into their<lb/> | |||
lowest or least denomination.</p><pb/> | |||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}} | ||
Collectanea for Posology
A circulet is a compound repetend
---page break---
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
product, then to add
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
places, then to add
cyphers to the left 'till
there are so many
4
And by adding cyphers
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
---page break---
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
add the numerator;
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.
---page break---
|
Identifier: | JB/135/089/002"JB/" can not be assigned to a declared number type with value 135. |
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|---|---|---|---|
|
135 |
posology |
||
|
089 |
collectanea for posology |
||
|
002 |
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 |
||
