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# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 179, page id 1677894601:0371
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1677894601&page=371
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l179
nIEUI. POnC jaM e =F. F Fa = 5. 5  a = F _C. X
In aFCA ZRAX A--B,1-(-C 221 ]. D23n XC. Ecribe ip
Torum A, B, C, _C. valores inventos e prodibit
leries propohta. J. L. D.
tit notandum est quod Ordinata omnis duobus
modis in seriem resolvitur. Nam indexn vel afr-
matirus est potest vel negatirus. Proponatur Ordi-
3K lZ2
nata 22 st2 123) m24. laec vel sic scribi Potest
7. 2X ZL I~2XK 122  M23, vel SIC ZX - 1-  3H∞ 2
XI -12 -,K2 3 =2. In Casu priore eAt a = ZH. D = 0.
C - - - 1. C = - k. F = -0. 8 - -l. H = -M. a -
2 v-
1. C - - -. V =- 0. In
posteriore es a = - - l. b =- 0. C = 3k. C--m. F---1.
3- -0. h --1. 2 -- -  1 - - - 1. 8 - 1 - - 1. D - - 2. F - - 2
1
t =- -r. V =- -. Pentandus est calus uter
que. Fit si serierum alterutra ob terminos tandem
deticientes abrumpitur ac terminatur, habebitur area
Currae in terminis finitis. Sic in exempli hujus
priore casu scribendo in serie valores iplorum a, b,
Cus C, Fg8, hu a, B, F, 5, tu V, termini omnes post pri-
mum cranelcunt in intinitum e area C urrae procit
2
=12 Im3. FF haec area ob signum nesatirum
adiacet abscissae ultra ordinatam productae. Nam
area omnis aftirmatira adjacet tam abscissae quam
ordinatae, nesatira vero cadit ad contrarias par-
tes ordinatae ex adjacet abscistae productae, manente
Scilicet Piono Ordinatae. Hloc modo series alter-
utra e nonnunquam utraque semper terminaEUE
ex tinita evadit h Curra geometrice quadrari po-
test. AC si Curra talem quadraturam non admit-
cit, series utraqe continuabitur in intinitum, a ea-
A a a:
TUM