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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 24v, page id 00068022:0048
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 25r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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porro ut RG  2X ad teax 1, ZF RF ad QF idesst sutar rax
ad 2X. ita RF 
DV, ad BFpBR+ BN, BG)
N
s ad RF H TF ⊓ DV seu le a +x ad quartam
ERgo _  DH xra
et DV, ax + 2X
SAX +2aX
EX
2 +X et
DV
Quae Unde ax 1 xt
Ixtecax
a ex , 4Xy + 2aY, et X ray
Unde a xt + 4 a X + 4X Y
4XY + 2aY
.. Unde
  DV.
et quia dividi potest, fiet per 2X + a, fiet: X
DDZ9V7
quae est aequatio ad Hyperbolam Unde palei quadratum ipsius RF
esse velut diagonalem, et B quadrasi semiquadrati, RBF)
jam si a + ax + X, anferatur: Xa + X restabit:
a + ax, sive a + 2aX, et Sa t raX  L. LV, BT
4
Jam LV, vocundo y. fiet 4y  a + 2aX, et eric
4 Y - a
2a
X.  Quem valorem ipsius X inserendo in DV
Xa + 2X fiet
47 - a, c 4 + 16y - 84y + a
29
Aar
1
24
sive V, DV i +y a ( a) + 15y - 3 a y (F a)
ny Ro a  quae facile
es Au
mal tro transmatum sivet DV p it a7.-a
et y t -a vocundo
Habem, ergo Naturam
aq curvae nostrae, quantum licet aequatione expressam
nam abscissa LV, posita y, erit ordinata DC
Y Piy -a
 Ceuto +, sed examinandum in verositu) DB
s
IB autem scum aequetur curvae H parabolicae DF explicari
a
analytice non potest nisi per seriem, numerorum.
Tantum addam AL aequari 1Bd ( a) d Ergo circulum
per centro Li radio Ld descriptu transire pe (A) locum. pesius A
verum ergo zari venio.
Ulnum jam superest niomendum nempe BT aequari sive
LV, aequari BG. et ptroinde quod optabam D9
absussam parabolae, aequari AH, abscissae Trochocidis respident,
ac proinde, descripta teriparabola DFH, transtata in
AH
 merpe D in A, et H F in W vuctaque WVDB
cuvam rectari DB fore curvae A.N aequalem Rect
Utibus ergo pro I. incognitam junemus abscistam sumemus
aequaler abscissae parabolica
AV