## Page View

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

Based on date of publication, this material is presumed to be in the public domain.| For information on re-use, see: http://digital.library.wisc.edu/1711.dl/Copyright