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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 9
# Folio 2v, page id 00068259:0004
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Nimirum si centrao A descriptus   arus circuli BDC,. Dataque sit subtenso arcus BDC
-1 + X +
-
i-
dentis ex circulo ortae, e (nempe Cycloeidis) quemadmodum orta ex Hyperbole, (Scilicet
et 10
Logarithigica) jam fece observaveram
eo sit X. posita ABA1. erit DLH X
Aaam
SN, R et QLB APerit,
arcus miter at ipsa EC NPB R5 est arcus C M DZM9
sumtis cogo ec R pro numeris, y, secundum
Posita ergo qR b QM it dixip X.
2C2 2DQ arcu H R
debet et
 RS  eMQ, positoque
5 toties contineri in RT, quotie
unitas in numero V. ergo F appellando cd.  et RS vocando Z. erit Z HL.
adtoque 3H G:. ram XA(+ I + b. + r, + sendo ergo
a
QL p V B X. B SN
eut aequatio explicans naturam cuvae cireiociis per ordinatas ad basin
2V5
Posita ordinata
22) +b + 12-1 +
8+L-sP-i
la alscissa RS,, Z. ordinata  sN H v. radio, 1
constatte quodam arculi eusque sasim   subtensa, b.
Si vero pro E0 sumamus non arcum, sed rectam quamlibuerit, vcognitam, vigs. 2. fiet
Ciuva non cycloeides, sed ei proportionalis, cujus omnia puncta quot libuerit Geometrice potere
inveniri, ersi non quod vis datum. Analytice tamen ope aequationis hujus transscendentis comnia
habebuntur: et si faciumus et b7. fiei denique aequatio  transscendentis figurae
Cycloeidi proportionalis eu figurae angulerm
2 
Quemadmodui aequatio
1I
alscissa
+ 2 posita matnatu RS
et ab ordinata A
b est aequatio Legarithmorum 
Et illud inprimis memorabile est Logarithmicam exegtipris ad refotvendas aequationes
erae
puras pertinere, Agutacegu
partes duas
Vicissimi ubi jam dantur cclculi circa bujusmodi figuras, quemadmodum dantur tangentes Cycloeidis
et Logaritmice, hinc vicissim lux aliqua circa tructanius aequationes transcendentes exergat
emicabit
nempe BC, et ponendo arcum BD esse ad arcum BDC ut Unitas ad quendam
numerum V. tunc posito radio 2. ebite et
BC  b. fe er BD X
fier
in
Hinc jam illut praeclaram ducemus, analyticam scilicet enuntiationem. curvae transcen-
1Z vocando 2, fei et multiplimd a ao, 
V)
aequatio  curvae
Angulorum, quemadmodum
Co (1) b aequaetio est curva
raltonum sive Logarithmicae
quas nsoledt da radicis sectione in partes opus esti
Angularem autem ad affectas prii gratus regerri, ubi resolutionis causa necesse est rancem secari in
Hinc illudiam praeclarum ducimus omnes aequasionum radices irrationales, etiam quibus interveniant
imaginariae, Geometrice explicari, per sectionem scilicet sive anguli sive rationis
illuo jam quaerendum est, quanam ratione hujusmodi aequationes calculo tractabiles reddi possint