Page:Cyclopaedia, Chambers - Volume 1.djvu/837
Fractions <"« Sfecies, or Algebraic Quantities.
i b 7*o reduce Fractions *» Species to their leaft Terms: The Numerators and Denominators are to be divided by the greatefl common Divifor as in Numbers. a a c .
Thus the Fraction ■ , is reduc d to a more fimple one
—. .- by dividing both a a c, and b c by c ; and ., is re-
duc'd to a more fimple one — by dividing both 203 and
,203 aac . 7 «»
«« 7 by 29 ; and - ^ c is reduc d to — j by dividing by
, 6a'— (1 ace zaa—$cc
20 c. And to — ; becomes — by divid-
y 6aa-\-*ac za+c
ing by 3 a. And , becomes
- ' - a a — a a
by dividing by a— b.
2 P To reduce Fractions in Species to a common ^Denomi- nator.
The Terms of each are to be multiplied by the Deno- minator of the other.
Thus, having -j- and-r, multiply the Terms of one -j- by d, and alfo the Terms of the other-jby £, and they will become t -y and j-y, whereof the common Denomina-
' b d
a ,ab a c
r — and — become —
tor is b d. And thus a and-
, a b and — . c
But where the Denominators have a common Divifor, it is fufficient to multiply them alternately by the Quotients.
a i .a* a* d
Thus the Fraction j— and-r-j are reduc d to thefe-r-^
andi — -i, by multiplying alternately by the Quotients cand
d, ariiing by the Divifion of the Denominators by the com- mon Divifor b.
Addition and SubJiraBion o/Fractions in Species.
The Proceft is in all refpects the fame in Species, as in Numbers. E. gr. Suppofe it required to add the FraBions
-=- and — r • Thefe, when redue'd to the fame Denomina- a
and -j—j . Confequently their Sum is
tion, wi. a d 4- b c
So, if the FraBion-r- were to be fubtrafled 6om-j ;
Having redue'd them, they will be-^-j and ~y,T> as ° e "
b c — ad fore. Their Difference, therefore, is — ^ — .
Multiplication and 2>iviJton c/Fractions in Species.
Here too, the Procefs is perfectly the fame as in Vulgar Arithmetic. Thus, E. gr. Suppofe the Faflors, or Fra- Bions to be multiplied, —r- and —r ■ The Product will be, a c
a c Or,fuppofe the Fractions required to be divided, ~TT and
a , _ . .„ , a c b abc c
-rx the Quotient will be -7—7 ■ — rr— ~J~-
it ' ^- b d a abd d
a c . -
Hence, as a = — ■ : The Product of a mto-T, that is, of
, i c a ac an integral Quantity into a Fraction, -, = -j- • Whence
it appears, that the Numerator of the Fraction is to be multiplied by the Integer.
Hence alfo, the Quotient of y by a, that is, of the Excels
This Fraction inftead of three Quarters of one Pound may be confider'd as a fourth Part of three Pounds ; that is, by taking as many of the Integers, as the Numerator expreffes (viz. 3.) and dividing them by 4, the Denominator ; for then the Quotient of the fame Value will arife for 4 ) 60s. 15 s. This fhews the Reafon of that manner of Expref-
fion us'd by Geamaters and Algebraifts, who read 4- , thus,
a divided by b.
Logarithm of a Fraction, fee Logarithm.
Summing of infinite Fractions, fee Summatory Cal- culus.
FRACTURE, in Medicine, and Chirurgery, a Breach, or Rupture of a Bone : Or, a Solution of Continuity in a Bone, when it is crufh'd or broken, by foroe external Caufe. See Bone.
In Fractures, the Bone is either broken breadth-wife, that is, tranfverfely ; or length-wife, which laft is properly call'd a FiJ/iire. See Fissure.
Tranfverfe Fractures are more eafy to difcover, but more difficult to cure than longitudinal ones. A Fracture in the Middle of a Bone is lefs dangerous than towards the Arti- culation. When the Fracture is attended with a Wound, Contufion, &c. or when the Bone is fhatter'd into feveral Pieces, 'tis highly dangerous. A Fracture of the Femur in Adults is very rarely, if ever cur'd -but there Hill remains a Lamenefs. Fractures of the leffer Bones are ufually cur'd in feven or fourteen Days ; thofe of the greater, in 20 or 40 Days.
In the Cure of Fractures, the Chirurgeon has two Things to attend to : Firit to reftore the fractufd Bone into its na- tural Situation ; and to keep it tight with Ferulce, or Splin- ters, and Bandages : In which cafe Nature takes on her felf the Office of healing and conglutinating it, by forming a Callus thereon. See Callus.
If there be an Inflammation, it muft be cur'd before any thing be attempted about the Fracture. If the Bone hap- pen to be broke again, it never breaks in the Callus, but at a diftance from it. After fetting or replacing thefractur'd Bone, Bleeding is requir'd, to prevent any Lodgment of Blood on the Part aggriev'd, by the Violence upon the Fibres.
A Fracture of the Cranium is certain Death, without Trepanning. See Trepanning.
FRJ5NUM, Bridle, in Anatomy, a Name given to di- vers Ligaments, from their Office in retaining, and curbing the Motions of the Parts they are fitted to.
The Fmsnum Lingua, or 'Bridle of the Tongue, is a mem- branous Ligament, which ties the Tongue to the Os Hyoi- des, Larynx, Fauces, and lower Part of the Month. See Tongue.
In fome Subjects, the Frienum runs the whole Length of the Tongue, to the very Tip : In which Cafes, if it were not cut, it would takeaway all Poffibility of Speech.
The Fr<enum of the 'Penis is a flender Ligament, where- by the Prsepuce is tied to the lower Part of the Glans. See Penis.
Natute varies in the Make of this Part ; it being fb fliort in fome, that unlefs divided, it would not admit of perfect Erection. See Erection.
There is alfo a kind of little Franum, faften'd to the lower Part of the Clitoris. See Clitoris.
FRAIGHT, Freight, or Fret, in Navigation and Commerce, the Hire of a Ship, or of a Part of it; for the Conveyance and Carriage of Goods, from one Part, or Place to another : Or the Sum agreed on between the Matter and the Merchant, for the Hire and Ufe of a Veffel.
The Fraight of a Veffel is ufually agreed on at the Rate of fo much for the Voyage ; by the Month, or per Tun.
Fraighting, or letting out of Veffels on Fraight, or Hire, is one of the principal Articles in the Ttade of the Hollanders : They are the Carriers of all the Nations of Europe, and their Purveyors; notwithflanding that their Country produces nothing at all, and that they are fore'd to to have every thing neceffary for the Building of a Veffel from other Countries.
The principal Laws and Rules relating to fraighting, are: That if a whole Veffel be hired, and the Merchant, or Perfon who hires it, don't give it its full Load, or Bur- then; the Mafler of the Veffel cannot without his Confent take in any other Goods, without accounting to him for Fraight.
That, tho' the Merchant don't load the full Quantity of Good, agreed on in the Charter Party ; yet he fhall pay the whole Freight ; and if he load more, he fhall pay for the »
broken Quantity, divided by the whole one,-j —=-^j.
Befide the common Notion of a Fraction, there is an- other neceffary to be underftood. Thus,
Suppofe i or so s. or a Pound Sterling, were the Fraction:
That, the Mafter may fet a-fhore fuch Goods as he finds in his Veffel, which were not notify'd to him ; or take 'em at a higher Rate, than was agreed on for the reft.
That, if a Ship be ftopp'd or detain'd in its Courfe, either thro' the Matter's, or the Merchant's Default 5 the Delin- quent fhaH be accountable to the other.