GUNTER’S LINE. 
But generally in this, ant i in moft other works, make ufe 
ef the {mall divifions in the middle of the line; that you 
may the better eftimate the fraétions of the numbers you 
make ufe of ; for how. much you mifs in icp ng the com- 
paffes to the firft and fecond term, fo much the mere you 
will err in the fourth; therefere the alae part will 
moft ufeful. For or-example, as to 11, fo is 12 to 16.5, if 
you imagine one integer to be divided into a parts, as 
they are on the line ona two-feet rule. See Sripine- 
2. One number being given to be multiplied by Sickie. to ssi 
the res —-Extend the compafles from 1 to the multiplica- 
tor; and the fame extent, apphea the fame way from the mul- 
Siplicand, will make the moveable point fall on the produ& : 
thus, if 6 be given to be multiplied by 5, extending the 
compaffes from 1 to 5, the fame extent will reach from 6 to 
go, the produd& fought. 
3 in number being given to be divided by another, to find 
quotient. Extend the compaffes from the divifor, e. g. 2 Sy 
to I, and os fame extent will reach from _ re bi 
50, to the quotient 30; or extend the compaffes from 
ae to the dividend, the fame extent will reach the mn 
way from 1 to tlie _— ient. 
reduce a vulgar best into a decimal.—In this cafe, 
the Setiunintnas ef the given fradtion is to the numerator as 
1 is to the decimal eaiiead: let the fraction be 2, extend 
the compaffes from 8 to 7, and this extent wes the fame way 
from 1 will reach to .875, the tequived decim 
a 
is the circumfer- * 
ence of 
proportion. 
6. Three numbers being given, to 
Serinesnotiene th 
oe fuppofe 60, to the icone of the fame denom 
nation, viz. 30; if nye diftance be applied from the thied 
back will reach to the fourth number 
ste fourth in 
inverfe pro. 
being given, da fourth in duplicate 
proportion —If the hing sfoem 20 a dee rit and feeond 
terms be lines, extend the —— from the firft term to 
een of the nation; this done, that ex- 
tent being applied twice the fame way ‘fom the third term, 
the moveable point will fall on the Fourth te term required, 
E. gr. area of a circle, who: being 
078539, what. wil! the con : fe diame 
er is 28? Apply the Sr este 1 to 28, the fame way 
ve 
4 inch shee cme weight of 
othe is 6 i hes: the 
wich to 
e, ri aes « Ll 
oe, np dint of 
bifection. will fall on che mean faethe 
the quotient of the two crt dnd by oe another, 
scons bain head g the mide pies ete 
| eee To mean proportionals bteocen too given 
ced eae c between the two given extremes the two 
will give the two means required ; thus, for fome 
whole disdweies is - 28, seh Archimedes’s 
plac 
firft of the ee 
Fat wil fll on 616, the and the 
fines.— and horizon, 
if 8 and 27 
be found 12 and 1 
11. To fiud the far root of any number under paises 
The {quare root 0 umber is always a mean 
between 1, and the number whofe root is 
with this general caution, 
we even, that is 2 » 4, 6, 8, 
middle r will be moft convenient to be counted unity, 
po root and fquare will be found from thence forward to- 
8 10. On this principle the > age root of 9 will be 
poe to be 3; the {quare root of 64,.to be 8, 
12. To find the cube root of any number under 1 000000060. 
1¢ cube root is a the firit of two mean proportion- 
als between 1 an e given number, and therefore to be 
found by trifecting ae aoe between them. Thus the cube 
root of 1728 will be found 12; ; the root of 17280, a 
26; Che root of rane almo ott 6. 
hand falls on the lait fi 
muft be placed at 1 in 
the a and the Aes will all fall forward to be end of 
middle and end ef the 
found 2; and Neat of oa 
that of 216, 6, & 
We may 25 ane in general, with regard to thefe two om 
problems, that the line of numbers is only a line of k 
rithins, and any logarithm divided by 2, quotes the lo 
of the fquare root of its natural n mber ; if divided as 3 
it gives the logarithm of the cube a and if by 6, it aa 
33 ; that of 64, 43 that of 125, 53 
y heme By notae 
gures) will give th the: rene bes 
into 49 &c. heh} half 
—— and laid off ar m unit 
or value of . a. fi 
be ~~ two given extremes, the two meang wil : 
