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<p>152</p> | |||
<head>Rule.</head> | |||
<p>In multiplying, observe<lb/> | |||
to add to the<lb/> | |||
right hand place of<lb/> | |||
the product, so many<lb/> | |||
units as there are tens<lb/> | |||
in the product of the<lb/> | |||
left hand place of the<lb/> | |||
repetend; and the product<lb/> | |||
shall contain a<lb/> | |||
repetend, whose places<lb/> | |||
are equal to those in<lb/> | |||
the multiplicand; &<lb/> | |||
if there are more<lb/> | |||
places of figures in<lb/> | |||
the multiplier than<lb/> | |||
one, make all the<lb/> | |||
several products conterminous<lb/> | |||
towards<lb/> | |||
the right hand.</p> | |||
<head>Case VII.</head> | |||
<p>If the multiplier be a<lb/> | |||
compound repetend,</p> | |||
<head>Rule.</head> | |||
<p>Multiply each figure<lb/> | |||
of the repetend, and<lb/> | |||
add the several products<lb/> | |||
together; then<lb/> | |||
add the result in this<lb/> | |||
manner; set the left<lb/> | |||
hand figure so many<lb/> | |||
places forward<lb/> | |||
as exceeds the number<<lb/>b/> | |||
of places in the | |||
repetend by one, and<lb/> | |||
the rest of the figures<lb/> | |||
in order after it; &<lb/> | |||
thus proceed, till the<lb/> | |||
result last added be<lb/> | |||
carried beyond the<lb/> | |||
first; lastly, add the<lb/> | |||
several results together,<lb/> | |||
beginning under<lb/> | |||
the right hand<lb/> | |||
place of the first; &<lb/> | |||
from thence dash as<lb/> | |||
many figures for a<lb/> | |||
repetend, as the repetend<lb/> | |||
of the multiplier<lb/> | |||
consists of.<lb/> | |||
If the multiplier<lb/> | |||
hath any terminate<lb/> | |||
places joined with<lb/> | |||
the repetend, and if<lb/> | |||
the repetend be small,<lb/> | |||
and these many, multiply<lb/> | |||
and add the products<lb/> | |||
of the repetend<lb/> | |||
first; then multiply<lb/> | |||
by the terminate figures,<lb/> | |||
and add their<lb/> | |||
products to the sum<lb/> | |||
of the products of<lb/> | |||
<add>the</add></p><pb/> | |||
<p>the repetend; and to<lb/> | |||
this last result, add<lb/> | |||
the said sum of the<lb/> | |||
repetend products.<lb/> | |||
But if the terminate<lb/> | |||
figures are few, and<lb/> | |||
the places of the repetend<lb/> | |||
many, subtract<lb/> | |||
the terminate figures<lb/> | |||
from those of the repetend,<lb/> | |||
and multiply<lb/> | |||
by the remainder as<lb/> | |||
a repetend.</p> | |||
<head>Case VIII.</head> | |||
<p>If both factors have<lb/> | |||
compound repetends,</p> | |||
<head>Rule.</head> | |||
<p>Proceed as in the two<lb/> | |||
last cases.</p> | |||
<head>Division of Decimals.</head> | |||
<head>Case. I.</head> | |||
<p>When the divisor and<lb/> | |||
dividend are both<lb/> | |||
finite decimals,</p> | |||
<head>Rule.</head> | |||
<p>Divide as in whole<lb/> | |||
numbers, and from<lb/> | |||
the right hand of the<lb/> | |||
quotient point off for<lb/> | |||
decimals so many<lb/> | |||
places as the decimal<lb/> | |||
places in the dividend<lb/> | |||
exceed those in the divisor;<lb/> | |||
and those to the<lb/> | |||
left, if any, are integers,<lb/> | |||
but if the places of the<lb/> | |||
quotient are not so<lb/> | |||
many as this rule<lb/> | |||
requires, supply the<lb/> | |||
defect by prefixing cyphers<lb/> | |||
to the quotient;<lb/> | |||
but if the decimal<lb/> | |||
places in the divisor<lb/> | |||
be more than those<lb/> | |||
in the dividend, annex<lb/> | |||
cyphers to the<lb/> | |||
dividend to make<lb/> | |||
them equal, and the<lb/> | |||
quotient<lb/> | |||
will be integers<lb/> | |||
<sic>untill</sic> all those<lb/> | |||
cyphers are used</p> | |||
<head>Case II.</head> | |||
<p>To contract the work<lb/> | |||
of division, when the<lb/> | |||
divisor consists of many<lb/> | |||
decimal places.</p> | |||
<head>Rule.</head> | |||
<p>Having determined<lb/> | |||
the value of the quotient<lb/> | |||
figures, let each<lb/> | |||
remainder be a new<lb/> | |||
<add>dividend</add></p><pb/> | |||
152
Rule.
In multiplying, observe
to add to the
right hand place of
the product, so many
units as there are tens
in the product of the
left hand place of the
repetend; and the product
shall contain a
repetend, whose places
are equal to those in
the multiplicand; &
if there are more
places of figures in
the multiplier than
one, make all the
several products conterminous
towards
the right hand.
Case VII.
If the multiplier be a
compound repetend,
Rule.
Multiply each figure
of the repetend, and
add the several products
together; then
add the result in this
manner; set the left
hand figure so many
places forward
as exceeds the number<
b/>
of places in the
repetend by one, and
the rest of the figures
in order after it; &
thus proceed, till the
result last added be
carried beyond the
first; lastly, add the
several results together,
beginning under
the right hand
place of the first; &
from thence dash as
many figures for a
repetend, as the repetend
of the multiplier
consists of.
If the multiplier
hath any terminate
places joined with
the repetend, and if
the repetend be small,
and these many, multiply
and add the products
of the repetend
first; then multiply
by the terminate figures,
and add their
products to the sum
of the products of
the
---page break---
the repetend; and to
this last result, add
the said sum of the
repetend products.
But if the terminate
figures are few, and
the places of the repetend
many, subtract
the terminate figures
from those of the repetend,
and multiply
by the remainder as
a repetend.
Case VIII.
If both factors have
compound repetends,
Rule.
Proceed as in the two
last cases.
Division of Decimals.
Case. I.
When the divisor and
dividend are both
finite decimals,
Rule.
Divide as in whole
numbers, and from
the right hand of the
quotient point off for
decimals so many
places as the decimal
places in the dividend
exceed those in the divisor;
and those to the
left, if any, are integers,
but if the places of the
quotient are not so
many as this rule
requires, supply the
defect by prefixing cyphers
to the quotient;
but if the decimal
places in the divisor
be more than those
in the dividend, annex
cyphers to the
dividend to make
them equal, and the
quotient
will be integers
untill all those
cyphers are used
Case II.
To contract the work
of division, when the
divisor consists of many
decimal places.
Rule.
Having determined
the value of the quotient
figures, let each
remainder be a new
dividend
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Identifier: | JB/135/088/003"JB/" can not be assigned to a declared number type with value 135. |
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135 |
posology |
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088 |
collectanea |
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003 |
reduction of decimals / addition of decimals / subtraction of decimals / division of decimals |
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|
collectanea |
4 |
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recto |
[[page_numbering::f153 / / f152 [sic] /]] |
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