ee 
Bologna avoid the contagious aes 
demic which Bed at the “fet mentioned place. 
maintained a literary correfpondence with mott of an reat 
: age, efpecially ie cardinal Bembo, 
e friend, and to 
= 
ftudy of aftrology and cofmography, and oe of apoplexy 
on the 6th of Auguit, 1553, at the age o1 ears. 
All the works of Fracaftorius have ey etn under 
era omnia Philofophica et Medica,” 
wor 
/ 
Libri tres,’’ firft ‘p 
an and French langage 
is, Liber i 
‘bell a 
ry 
ms 
°o 
r on 
; 1538; with the following, 3. § 
4. De 
dierum | criticorum :”” s Lanes et Antipathia, 
ib 
er: 5. & De Co eee et Contagio ofis eg : 
rum ae Libri ‘ Naugerius, 
Bodtica a logus :”’  Purrius, five de TatelleCione 
ad 8. &s baa ae de Anima Dialogus :” 
“ Jofe chi Libri duo: ? 
ai. % Car sae Liber unus 3”? 12, Alcon, five de cura 
canum ee 
The town of Marcha, hae had’ or cata ere€ted ho- 
eachumertt to llus and of 
lafs Trade 
ita which the glafs veffels already foaned are ed when 
the tower over the wor. furnace, and by means of 
which they are drawn out through the ah that they 
ol by degrees. . 
may be-taken gradually from the fire, and co 
*RACTION, in Arithmetic oe Algebra, a part or di- 
te number which ftands to 
whole. 
he word literally imports a b 
ene are ufually divided aie decimal, " fevagefimal, 
ndv 
° For: nae and Sexagefi imal fra€tions, fee Deeimax and 
St — MAL. 
Fr ons, Vulgar, called alfo fimply fraétons, are 
a ae by two num oe TS, the one placed over the 
other-with a line between t 
The lower, called the paneer of the fraGtion, — 
the unit, or whole, that is divided isto parts; and the upper, 
called the numerator of the fraGtion, expreffes the parts 
given in the prefent cafe. 
Fhus,-two third parts of a dine, or ~~ thing, are writ- 
ten %: where the denominator 3 fhews that the whole 
Again, twenty-nine fixtieths is written $33 W where the 
mnmerator 29 expreffes 29 parts of an integer Givided into 
. FRA 
603 and the denominator 60 gives the denomination to 
thefe parts, which are called fixtieths. 
The real defign of adding the denominator, is to thew 
what aliquot part the broken number has in commpn with 
unity. 
a all fraGtions, | as the numerator is to the denominator, 
fo is the poner itfelf t to the whole cia it is a fraction. 
fuppofing 4 of a pound oe 
243215: 20. - Whence 
may be infinite fractions of fe ae 
other ; iuafmuch as there may be anne numbers Gund 
which fhall have the ratio of 3: 
deine ace either Proper or inpre per. 
Fraction, Proper, is that 
than the Aes | and, c 
than the whole, or integer, a 
FRACTION, Tc A adh 1S ae the numerator is ae 
equal to, or bigger than the denominator, and of co 
the fraction a. 2 or greater than the miele, or oe 
as 23 or $3; or 2 
PrsGions, again, are either /imple or compound. 
Fracrio a le, a S fuch as ean ioe ae one nus 
merator, and o ominator 3 as 
Fra arene Conpounh ale a Ifo yieties of Sandie 
are fuch as rae of abe al numerators and den 
nators; as # of {4 of 3 of 4 
Of pares, ‘hoe’ are oa to each other whofe nu- 
merators hav ame ratio to their denominators. 
Thofe are ee i ofe numerators haves a greater ratio ; 
and hole lefs Hee have lefs: thus =2i= 1, 
But ,3, is greater than 2; and 4 les tha in Hence if both 
the nitmerator and denominator of a fra&tio 
mber 2; ce roduéts i 
the quotients in the latter 4, will 
conftitute trations ail to the firft fraGtion given. 
e arithmetic of fraétions confifts in the redudion, ad= 
diti ae fibration, and multiplication ef them 
‘udlion of. I. To reduce 
where the numerator i is lef 
confequently, the ee lefs 
iven whole 
— hus we fhall fin 3=+4 and 
— es 
he ste Sieger a th a Sth denominator, the produét 
i d 
= i9,and 7= 
hi Neneeninate, he given, the number is reduced to 
fraGtion, by writing 1 underneath it, as a denominator. 
Thus 3, 4,23. 
2. Tt 0 reduce a given fradtion to a oe equal to it, that 
i have a given denomin aOR ly the numerator 
by the given as nator, an e the produ& by the 
form nator, and the quotient _ over the given 
denominator is ie fraGtion required. e propofed 
a 
7 
[aM 
a) 
3 
° 
t be 
to reduce 3 to an ar ‘fraction with ae denominator 
38 X 3-4= 
3. To reduce ven re to its lowef? terms, i.e. te 
nd a 
ag 
&tion ee to a given fraction (42), but 
efs num ivi 
er, as 
ae 
And if the aivifion be performed _ the geack num- 
er that will i de them both, the fration 1s reduced te 
its loweft terms. See Co Meafare 
If it ha epee that unity. is the only common meafure of 
‘the nuinerator and denominator ; then is the fraéti 
capable of being reduced any low 
Srigae common meafure is unit, are faid to be prime. to 
‘eac er. 
4. To 
