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Chambers, Ephraim, 1680 (ca.)-1740 / Cyclopædia, or, An universal dictionary of arts and sciences : containing the definitions of the terms, and accounts of the things signify'd thereby, in the several arts, both liberal and mechanical, and the several sciences, human and divine : the figures, kinds, properties, productions, preparations, and uses, of things natural and artificial : the rise, progress, and state of things ecclesiastical, civil, military, and commercial : with the several systems, sects, opinions, &c : among philosophers, divines, mathematicians, physicians, antiquaries, criticks, &c : the whole intended as a course of antient and modern learning
(1728)

Forum - Friction,   pp. 81-100 PDF (19.6 MB)


Page 90


FRA
PRACTIONS in Species, or Algebraic 2jiantities.
1 Lao reduce Frac~ions in Species to their leaft Terms:
The Numerators and Denominators are to be divided by
the greateft common Divifor as in Numbers.
Thus the Fraftion b    is reduc'd to a more fimple one
h c~~~~~0
a by dividing both a a c, and b c by c; and---5 is re-
h                            ~~~~~~~~~~667
duc'd to a more fimple one17 by dividing both 203 and
23
o3 aac       ~     a
667 by 29 ; and 667 J is reduc'd to !--3 by dividing by
6a-6ac             aa -3 C
a9c   And fo 6a'  3ac becomes - a 4-c    by divid-
a3-aab-l-abb-b'           aa.b b
ing by 3a. And a-aa       b       becomes   a
by dividing by a-,b.
o9 71o reduce Fracions in Species to a common Denomi-
nator.
The Terms of each are to be multiplied by the Deno-
minator of the other.
Thus, having   and  - multiply the Terms of one
by d, and alfo the Terms of the other d by l, and they
ad  bc~~~~~
will become ba d and b d  whereof the common Denomina-
b   d     aba           b        a
tor is bd. And thus a and a  oa or - and - become c
x        c        C
ab
and
But where the Denominators have a common Divifor, it
is fufficient to multiply them alternately by the Quotients.
Thus the Frallion b  and--b-d are reduc'd to thefa' cd
and a cd by multiplying alternately by the Quotients c and
d, arifing by the Divifion of the Denominators by the com-
mon Divifor b.
Iddition and SubflraEfion ofFRACTIONS in Species.
The Procefs is in all refpecls the fame in Species, as in
Numbers. E. gr. Suppofe it required to add the Fratiions
a and d . Thefe, when reduc'd to the fame Denomina-
a d       b~c
tion, will be i-d and Td-. Confequently their Sum is
a d Jr b c
bd
So, if the Fra~fion  were to be fubtracted from d
ad      beC
Having reduc'd them, they will be b d and-d--d-, as be-
b c-a d
fore. Their Difference, therefore, is -b d
Multiplication and Divir/on of FRACTI ONS in Species.
Here too, the Procefs is perfecly the fame as in Vulgar
Arithmetic. Thus, E. gr. Suppofe the Factors, or Fra-
(lions to be multiplied, a and d: The Produat will be,
Or, fuppofe the Fractions required to be divided, a d and
a           a c   b   a b c   c~~~~~~b
b   the Quotient will be ac- a = ad-d
a                  *   c
Hence, as a --: The Produa of a into , that is, of
c a    ac
an integral Quantity into a Fraction, d-  d--. Whence
it appears, that the Numerator of the Fraction is to be
multiplied by the Integer.
Hence alfo, the Quotient of d by a, that is, of the
broken Quantity, divided by the whole one, d  I =
on , 7 a  ad '
Befide the common Notion of a Fraction, there is an-
ether neceffary to be underflood. Thus,
Suppofe xi or zo s. or a Pound Sterling, were the Fraction;
0 )
FR A
This Praction intleid of three Qtarters of one
be confider'd as a fourth Part of three Pounds;
taking as many of the Integers, as the Numerat
(Viz. .) and dividing thenm by 4, the Denominai
the Quotient of the fame Value will arife
IS S. This lhews tire Reafon of that manner
fion us'd by Geamaters and Algebraiils, who rei
a divided by b.
Logarithm of a FRACTION, fee LOGARITTI
Summing of infinite FRACTIONS, fee SUMM.
CUalus.
FRACTURE, in Medicine, and Chirurger"
or Rupture of a Bone: Or, a Solution of Con
Bone, when it is crufh'd or broken, by forne ext
See BONE.
In Fractures, the Bone is either broken breadi
is, tranfverfely; or length-wife, which laft is pro
a Fi/iure. See FISSURE.
Tranfverfe Fractures are more eafy to difcove
difficult to cure than longitudinal ones. A Frac
Middle of a Bone is leis dangerous than toward
culation. When the Fracture is attended with
Contufion, &c. or when the Bone is fhatter'd
Pieces, his highly dangerous. A Fracture of
in Adults is very rarely, if ever cur'd; but there
a Lamenefs. Fractures of the leffer Bones are
in feven or fourteen Days; thofe of the greater,
Days.
In the Cure of Fractures, the Chirurgeon has
to attend to: Firf to reflore the fractur'd Bon(
tural Situation; and to keep it tight with Ferul
ters, and Bandages: In which cafe Nature take
the Office of healing and conglutinating it, b'
Callus thereon. See CALLUS.
If there be an Inflammation, it mull be cur'
thing be attempted about the Fracture. If the
pen to be broke again, it never breaks in the C
a diflance from it. After fetting or replacing 1
Bone, Bleeding is requir'd, to prevent any I
Blood on the Part aggriev'd, by theViolence upo
A Fracture of the Cranium is certain De
Trepanning. See TREPANNING.
FRJNUM, BRIDLE, in Anatomy, a Name
vers Ligaments, from their Office in retaining,
the Motions ot the rarts they are fitted
The Frenum Lingue, or BRridle of t
branous Ligament, which ties the Tonj
des, Larynx, Fauces, and lower Part 4
TONGUE.
In fome Subjecls, the Frinumm runs
the Tongue, to the very Tip: In whic
not cut, it would take away all Poffibili
The Frenum of the 'Penis is a fiendi
by the Prxpuce is tied to the lower Par
PEN IS.
Nature varies in the Make of this Pa
in fome, that unlefs divided, it would r
Ereaion. See ERECTION.
There is alfo a kind of little Frenum,
Part of the Clitoris. See CLITORIS.
FRAIGHT, FREIGEIT, or FRET,
Commerce, the Hire of a Ship, or of
Conveyance and Carriage of Goods, fr&
to another: Or the Sum agreed on bet
the Merchant, for the Hire and Ulfe of
The Fraight of a Veffel is ufually ap
of fo much for the Voyage; by the Mc
FRAIGIITING, or letting out of Vc
Hire, is one of the principal Articles
Hollanders: They are the Carriers of
Europe, and their Purveyors; notwit
Country produces nothing at all, and ti
to have every thing necefary fbr the
from other Countries.
Slhe principal Laws and Rules re.
are: Thatif a whole Veflel be hired,
or Perfon who hires it, don't give it itk
then; the Maiter of the Veffel cannot
take in any other Goods, without ac
Fraight.
That, tho' the Merchant don't load
Good, agreed on in the Charter Party;
whole Freight; and if he load more, I
Excefs.
That, the Mafler may fet alhore fu
in his Veael, which were not notify'd t
at a higher Rate, than was agreed on
That, if a Ship be flopp'd or detain'c
thro' the Mailer's, or the Merchant's
quent IbaU be accountable to the othe


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