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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 81r, page id 00068198:0161
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Nec di aeg. Pydy +xyd -bbar initib resolo uda licet facere y: a = dy: dco
vel simile atquad assumento deo proelemento curvae cc, quod repraesentatur per
radicum circu secantis, nam cum id detur adx, si Ergosi dy. y da retur ad de,
e AE CG = p ABEY LB F. X, ., 4  ut Y:  B 19: p:: F ax: ax: dc
daretur etiam  ad X.
X+ Y,de pdus, sit vadis ubi r est unica, cete ut et de sed xy
sunt geminae et fiet XC Xdc + sed X et  sunt geminae, una quaelibet
autem ex ipsis dx, vel dy, vel de constans vel aliteue assumi potest
emneme
si ergo in generalitate maneamus sit xerdx gn
sit XEY, de = pd firtue Xddc + rdde + tour- e dc dx = pddp
viq de P similiter vade + qdde + dcdv = p ddx
jam ddc = _dx ddx + duoda: 
C
ergo hit x + X dyddus (x+Y) drldret xer dx dit + dyca
Ex eodemodo
poe
pax
XEr dx ddx + xer dxddv dedcdx = p de ddv
Et fier vtqu avado + v+q ax ddx + dededo = pdc ddX
per priorem fit ddv = XFY dx ddax  dededx, :, pdc - xer du = pavdxta dd
 pdvar-pdad)
 Pavtex de
pox do ga, vel ddque P Bei non
utudosideratione, alterutra
potest Verum si jam anedat Et habemus breviter aequationem hauc generalem
utrobius ergo prodit idem, seu ex generat
seu p= de : duddx- dxddo. In recta
est deddx -dx dav =0, atque ideo tunc p, fieret infinita, unde non habet circulum
de sit constans summari semper posse de: p. cur
ndxdd pdo ddx - p dx ddv = de
si e fdc  = de te fiat de sdc:p = drdedece Avax + ( dede,: dede
Si jam hoc Sed nunc accedamus ad curvae cc naturam specialem. sit verb. gratia
De caetero hinc patetC
seu xdo  = vdx =0, et vidv-2dvdx - vax Ce=0 et fiet
lautem
ddx = vadx + 2d vdx, : D. sed ex aeq. D est  ddx = pavadx - de,: pax quos duo
ose
valores aerquando, fit ap V dxcdx + 2p dxdx du = vp duadx - vde. Adeoque
XV = aa
Hujus ope tollendo ddx ex
aeq. 6) fiet tandem prodibit tandem aequatio in qua do representaritur per e radium
in Hyperbola siet cdx = 2p dxdx dv + v dc,: p du- x
de dy. ubi v et do tolli possunt ope
et similiter dx tolli potest = a adX: XX et de = Sdadx + dodo, seu
quanquam ipsam de etiam repraescutet
in qua es extabunt dx, X, dx,  v, du
radius, quod compendio construdionis inservire potest, quem admodum nec B dx
X, quia aa : X = v
valore ipsius du per datas oportet tantu seu inventa
XX
x TaaTNE. X dx Sa +X
recta quae sit ad radium C) in figura paginae primae, ut du est ad deo: seu
de =
is
collere necesse est. 
65,, pro de substituendo ND, pro de
substituendo radium ei, pro dus substicuendo cV, nonnalem ad cp, habebitur
invento igitur
 et per 2p ducatur ipsi cp parallela occurrens
quod idem est ubique pro du substituendo
circulo in N et junctarum N collineatio ert curva QR, erirque tota linea et
ex aequatione altina valor ipsius
aequalis G ipsi y quaesitae
sev
sent
locuiut