GUNTER’S SCALE. 
infert the divifions to every 5’, as far as 10°: 3 from 10° otherwife having a table of logarithmic verfed fines to 180%, 
to 30°, the fmall divifions are made is’ each; from 30° fubtraé& “ h logarithmic verfed fine from that of 180 pig 
° is m: r °° grees, and a the remainders fucefively taken from the 
only the whole degrees. On the improved fcale the fpace fale of equal parts on the ruler backwar d from the common 
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and from 20° down nward 8 are put in the degrees aes fixth fore o is put for the bexinsting, and the numbers thence 
ae fines is put ‘the uppermott ceeding through 10, 20, &c. towards the left, are pes 
of the three on te flider, and alfo the loweft on the up- fupplements of the verfed fines themfelves. 
per part of the fixed fcales, whereby the two feales of On the new ee the divifions ees aa fall too Soe 
i i © 60° every 
or the line of tangents, it is evident, fince the tangent fingle degree is teesMaoct 3 cdi 60° to pee every . 
of 45° is equal to the radius, or fine of go” » that 45° on and half degree ; from 10 t 
this fcale will terminate direétly oppofite to go” on the fines; of a degree 3 from 130° to 
and the feveral divifions of this feale of pe gs tangents 
e 
45; or towards the left hand. ‘The degrees above 4 45 are 
to be counted backwards on the {cale ; ‘thus, the divifion 
fhip’s ae ude at fea is kept ; each degree, in the new 
on the new Gunter, once on the flider ahd Bae on ee 
lowett fixed part. The ae of thefe lines of fines The feale of terial de 
aid tangents, above explained depends on the following ceding, and fhews the iy 
theorems in trigonometry ; 1, "The cofine is to the radius relative to the corref; on 
i "This Pale Sanne te in the improved Ciena pe od 
equal to the quotient of unit divided by the other ; but di- lengths of the ruler; the firft 
: 1 garith the ginning at 0° on the "ight, and proceeds thence towards the 
fubtraction of a logarithm is the fame as the addition of its i i 
arithmetical eo ment : Sean eee the logarithmic co- 50°, 
the fame degr 
fine and am ees are the arithmetical com- jnoit _tavigntors extend, except eee of the Gr ceil 
plements of one an nothe r: and, as she arithmetical comple-  fifherie 
f any nu ity i Gui TER'S Scale, ufe of. - The fe i Pie 
the next fuperior place, every natural fine and its arithmeti- right-angled triangle being given, a iles, an a 
0 radi ore, pe? 26 degrees, e Fo the length of the ipo 
; i nometrical canon or proportion is thus: as the fi 
In go’ at the other end, in a fcale of fines, the aiibsnetical the angle, 26 lerreek is to the b; bafe, 30 miles, fo # T te 
complement of any fine or its co-fecant, laid backwards pens 4 Mee = h of the hypothenufe. Set one foot of th 
from 90”, gives the divifion for that fine: and the cafe will erefore on the 26th de egree of the line of the 
be the fame in a fcale of logarithmic fines. And as the lo- fier ks oa d the other to 30 on the line of numbers 5 
garithmic tangents and co-tangents are the arithmetical com- I 
and the cialfee remaining thus opened, fet one foot on 
plements of one another, the divifions to the degrees both legr 
1 90 degrees, or the end of the line of fine nes, and ans 
angents, are or on the line of rouge this will give 684 
ou 
ferve, by are bafe of a Hib tog triangle being » 25 5 ais 
5. icular, 15, to find the ancle te to the perpen- 
For tle the eer fines: from the feale of “eqiuil parts take dicular.—As the ie eae is seh i cee ar, 1 5 
-the arithmetical complements ~ ae logarithmic cofi 
nes, or miles, fo is the radius to 
the fecants of the or thet 5» 10, 15, 20, 25, 30, Extend the com then, on the line of n 
cc, degrees, Sipe he indices and the double of thefe 1 5, the perpendicular given, to 0 255 the bafe 
betery ty will = the on the ete vated feale = fame ewes will reach 
ve 10, 20, 30, nts » the le fou 
continued and Eee Pee sh of the Hale Eemh fom 45 degrees to 31 degree the ang cise 
The bafe of a right-angled triangle being giv ee . 
