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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 1
# Folio 40r, page id 00068073:0079
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Brevitatis  causa arcum Eiß appechemus a, et
11,β sinum complementi ejus appellemus R et
2 Sinum ejus appellemus  BB
fer
et quadrantis arcum 9. fret: 101) ordinata spralis
aequ.
Xa
similia est
Ob eadem hiangula
(10 aequ C ( a seu (16 aequ. Ba
eut sit Radius Y, erit Aio aequ
Y- Ba. Jum
datis Aiv. et 1viV dabitur et A, V. nam
AIV est aequ. VA10 ( +  iv1Y (2.
ergo A1V aequ.  K a + r9 - 2YBa unde patet
p
posito A.V aequ. 0. vel a aequ. 0. firi evanescere g. seu
fieri aequationem identicam. Quod praevideram
Sed et jam video nisi esae. curvae determnatio
ab initio tatem aequationem ferat, qualem
posturamus omnem inquisitionem in an curva videri
inutilem quod ita ostendo: ponantur verbi gratiae
ex punctis curvae V verbigratia ex 5) demetti pergien
diculares in aliaquam langentem curvae 1)a. et
investrgari valorem perpendicuraris generalem, eumque
cenique poni in ipso puncto 1s nihilo aequarem, quid
C
aline inde prodibit quam quod initio posuccamus nempe
cura aequastio ad curvam vel quae ex illa pendet ad ejus
tangentem seu aequatio curvae mutata in differentialem;
alitus nihil inde novi habebitur qoq locabimur
quicquam Cum ergo versimile sit carvas
Co Trodoidum quadlatricum aliasque
pocralium
tractatas sionbu nihil tale vid
suae aequationis. praebere alioqui statum in hiumod
ad genus jam
tissent qui has curvas tractavere.
ideo superest sut videamus  fabricare liceat
curvas et adeas aequationes quae instituto nostro
satisfaciant.
in specimen aequationis
denerallis supra positam
samanies brevem