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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 2r, page id 00068198:0003
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y = hX: 1
y. AC, C. F
C(C: H2H = AB: AL se Se) = ah. V:
C:x = SII+h: l. Ergo deA= xhdh: l S+hh, seu FC
jam CG: BB se dx =  X. h et CG = 1X. X. h
cu
G ex dx (2 X. HL = Habetur ergo CG
quadratum si detrahas quadralum et hadetur quadr. F G.
Ergo
jum cF habetur, si a quadrato C(C) detrahas quadr a7
et fiet cF2 = dh dh X: H = Xhi dhdh: U (H3 hh)
seu Ct (ah+h: () dtr X: H) U + hR = hh, (I+ sih.
seu CF2 =
fiet FG.-
Th X: (l + hu)
id detrahendo à C
dx (et (X. HC) = ati x. (1 hi
AC = AF
quia ax geremiranto habetur  vel
datim relatio inter X et ,
tio
ex, et
oltu, quae oia turbat
en angulus non datus sed alia one
quid si summcuus ex uno pun
afferentalis diversi grnus
per
couiderandum auliceat aptius fingere, an alius molus
(ono) seu DG: C0
Rem eo rec. rem resumamus sit  : a (compendio pro
dyidx et sit data aequalio langentiatis = Ha (2d0) y. l. a
commodius
ut calculum institummo
ido y X. t. a quod sig nnficat esse relationem rahovalem, uti sane
rationalis, 2d) t= X, y; a 1 assumatur 3iol ad cqvam AC
(tertio) + = X. y, h; a   et fiet (4to) X; y; a V = X. y;h; a 2
y X. h a 7.  posito y in aeq. 3 ad nullam potentiam
Unde fiat (5 tos
enseu
quod in arbitrio nostro esst
Hinc DE e _ dx Asec X) tia B3 et CG = dh d (sec. hd) X; h; a rY. 2
vel irationatem assurrex.
no
et L: a = dx  De sem dx)  3C + eG. Lx seu DG:, DE + 5G = X; y; h; a V
seu dx: dx d (SCc X) Xihi a; 13) dhd (sec h) X; h; a 2f. 3) = X; y; 6, _
Suo
unde tollendo y per aeg. 5. fiet (guo) dx
ax d sec p) pih, a 3) +Ah  ) X: h, a 
(imo F: a seu. DG; CD, = dy: dx _(2do) + = X; y; a 1. 1) Cstio) + =. y, Xi h; a . 2)
Meti distructius sic:
Sed qui y inveniri difficilius  aequ pure, video id non
esse necesse nam si aeg8. 4 differentietur secundum y, et X habebitur
De, utm si aequ. 4 ifferentietur
spendii causa
ut calculum instituamus commodius et universalius rem resumamus. Sit (imo (dy: ax = t: a
= DG: Cd. sit data curvae CG aequatio langentialis seu ratio Da DGad CD.
data per X, y, a, fietque  ((ado) 0- G b. X ya (nt rati
(2do t = X: y: a rat., posito t haberi rationaliter assumamus ergo
tertio srursus rationaliter t = X; y; Lja lu ut scilicet certo casu t sit d seu p
lamentis determinatio sit da determinata ex x, y, et constante a, in curva, et
constantissima a pro curvis AC omnibus, h variante a curva AC, ad curvam A(C.). His
positis per aeq. 2 et 3 fiet Xiyia rat. 1= X; y; h; a rat. 2 Hanc ceq. 4 differentiando
secundum y et X, fiet dytalis, = (sto) DE, et eandem  aeq. 4 defferentiam
cux
SE se
differentia inter duas
umm X( eempe A
y ejusdem cura bineae AC nempe cuter BC et BC, sed EC, discrimen tnber poti
e inter duas cursas eide at diversarum X nempe AB et AB, atque adeo diff. inter BC et BE
at EG diff. inter duas y ejusdem X seu AB, sed diversaua linearum AC et A(C)m
nteradque adeo diff. inter BE, et BG. unde et quia t: a = dx:, DE+ EG, seu
I L
hini pro t: a toltndo in xr. 7. valorem per aey. 2 bel n nam eodem redit, e. L
onend
pro DE, et EG ponendo valores utique rationales ex aeg. 45 et 6 prodibilae 9. 4) in qua
habetur dh: dx = X; y; h; a at. 3), ubi si cum  ope cqq. 74 ut 8 tollendo Y,
sunt tali potet  si vel x res reducta eset ad quadratura
n+tale
scilicet tan-
nentis curvae
(4 propuetat
existentes
in C
Xiffihi a (14)