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# Piece: https://leibnizlegible.com/api/records/28721/text
# Catalogue record: 28721 — [Mathem. Untersuchung] 2 Maji 1696
# Incipit: Dimensio curvae conicae reduci posset ...
# Date: 1696-05-12 (96-05-02)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=28721&katnr=55902
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 214–215 (from the shelfmark LH 35, 13, 1 Bl. 214-215): 4 pages, canvases 423–426, page ids 00068196:0423 to 00068196:0426
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=423
# Lines: 201 recognised on 3 of 4 pages, mean confidence 0.79
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 214r — 00068196:0423
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 215v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000423.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 82 lines, status machine
2 Maji 1696.
Addatur shediasma praecedens 1. Maje
dimensio Curva Conicae reduci posset ad
Quadraturam Rationalem, si posset extra
extrahibiliter deprimibilis reddi. hac fssml ex aula
formula bX +. X +. x +. X. Hoc ut tentemus, sit bXx + ccx+ d3 intte
Itaque re ut reddatur productum deprimibiliter ex trahibile puematur ipsius x
valor talis et rationalis, ut nominator sit quadratus e non assurgens atera ju,
Numerator vero talis,  pariter et nominator, ut rxte non assurgat 
non contineat in valore irrationali nisi  Ly+. y + y; et numeratir
Et 2do valor vero ipsius bxx + CCx + d3 sit exhahibilis Hae–
Haec ut assequamur fiat primum brevitalis eausa. X = lyy +m,:gu
ila , prior conditio obtinebitur nempe a+ =tE+ y ( C) Vyt: y
sed inu et posterior tentanda est fiet
i x = buy + 2blodyytom ∞ fpssy trofyy + an
Cc Ex = ccl. + ccm.
 = d:
ergo bff = bll + ccl + d seu f= Sbll+ ccl +d3. b
rursus 2bf = 2bl + cC sou f = 2bl + ec, : 2b 
Ergo bl F ccl + d3: b = 4bbu + 4blcc +C,: 4 bb. seu fiet
GbbU + 4bl cc + 4bd3 = (4 bbH + 4bl cd + ct. sed ita evanescunt quaesitae
et nihil est actum, nique adeo hac via obtineri ex trahibilitas depressica potes
ot
Faciamus ergo _ X = lyy+ m:,  gyt mytun, et ita  ert
exte erit Setoyu + Ency + enn:, ytn.
a yys tenye
super est ut sit
vel faciamus X = lyy + mmy+ n: gy fiet Sx+C = (t ejgyommy+n: y
b yt Xx = bUly + 2blmmis f ibn yy
+ bm.  + 2b mmay+br
cc X = cel.. + cemm .. + cen.
..
L
bpe  + 2479y3 + 26pV gy
+ b gt yy + 2699y + bp
Quae frmuila aequanda
quadcato a pyyty+n ducto
in B, lyy 
ly t mms jus 
+2l pi tumon  By + 2X py
+ lpp gs t mmpphs 
Ergo sit 49  Y6 = n6 et gu vel siplacet ro - n et qq = mm
et p = 2bl + cc,: 2b = bu + ccL + d3: B. Funde (4bbl1 + abl cett E =(bb l + 4blcd) + 4bd
ubo inciditur. in idem inconveniens quod ante: itaque faciamus,
 X = lgy + nmmus + 13: y+p, et ut interpretemur bxX + cc X + d, fint
ypt XX =  blly + Eblmm y3 + 2bl r yy
+ b n+. + 2bmm Ry + bn
CCyt X =s cel + cemm. + CCM.
+2cc lp +2cemmp.. + 2CCn p.
+ cc. Lpp. + cemmpp. + ccr pp
dg. +4dp +6dpp. +4dp. +d
 per compend.
aequ. quadrato a qu tryt
ducto in a
seu
(∞ agy +2a9ry + ragtys
art yt ra ly
aeus i  taggy + a hy + d a R ∞ agqust ragrus traq
13 = (+) 1 et rr = 15: 2+3 = (+) h: 2k3)
a72. t at y ab
un eex A+ +) 1g+CK +  9b -= 19b - = s’KS
s
Ebmmud + recrep= cemmept 4 D p3 SoulAd
= +ce + (+) 2eH e + (4) Sh: qeK illium temim t rcclp. +ad, Son t Cp
seu + (+) 4 ek g = 8 eeK F fh
2
+2
fit g = +e et 1r = f. 29 = 75: 2C 7 + BK = (X) etr vel 4(+) 5N = + eti
(+) ek AAa
seu 6. Ne autum calgulus Sit X- veo
tit (+) ppIo = F C
vet , adeK3: pp vocemus r
quasi a
tas perinde ac si l et l essent date. Iu f est y vel mon
alit
n
EtG Endem itatabe
inde derivatis aqualitaltina  siumpitur ex hongeniorum ipte p oc im. Hine rilile pulo fima raons ris pt
liter
quar
aqu
Ns ac et i t   eeS   tontrad m da  nbim

## Folio 214v — 00068196:0424
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 215r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000424.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
Itaque
4= ge
sit nd rpp,
fit sit Y =0
fiet f =0 et h5 = 0
+3 = (K g = 29+. Ergo g =  + (+). 2CK
fiet (+K = pp YbvV+ CCBYd:a et +e = sbllccl +d3: a
sed g =  blvpp 2bl Bb(tcC)P +6d  cel +6d pp + b m + 2cemmjo: a
ergo duos quabrs equando fit (2blV + CcV + cel +6d pp +bm + 2ce mmp =  cel H8, bB tecbr  p)
ubi prodit valor ipsius m L (2 pld l +  nm: p fit enim
bm: pp  +2CCmnip = 2 sb + ul +d, bvv + cev + d3 = 2blv - c B - ce l - 6d3
rursus ob f -0, fit -mm: p = 2ccl +4d3: 2bl +ec unde sipt 20 drul 
2cclbv + 433bV + celce + 2d3cC
et ob h 20 sit = mn: p = 2ccb + 9d3; , 260 + Cc. 2ccbbl + 4d il + cevcc + 2 d’ ec
unde fit v-l, 4d b+ c, = 0 sed non debet esse 40b + ct = 0 ergo
fit v - l = 0 vel v = l ergo n= Ipp et 1 el( 1) N = 
ergo n = lpP 9= soll+ ccl +d: a et  (seu (4) 13) = pp 9
et L. pp et - mm: p = 2cl + 4d3:, 2bl + cC et M ipp-
et exaeq. 8 sit b m ipp + 2cemm. p = F 2bll fi ccl ̸. d - 2 bll - 2 cel - 646d
ubi si X sit + fit bbm: pp +2cC Bmm: p = = 4d, seu bbm ipp 42 CC bmmip +  = c - 4bd
seu b mm: p = -cc + Sc - 4bd. Ergo demque fiet.
+cc: b - Sc - 4bd: l = 2ccl + 4d3: 2bl + cc = = mm: p = 2V
et fiet 2cel + 4d  = 2blW + cc W. seu l_ = cc WV - 4d3 :, 2cc - 2bW
et fiet
ce W-4d3
1y
X = _C c- 2bW.
y+p
= pWVV +  cc W- 4d3 pp
2 a v9
2
Si esset W = 0 fieret X =
2cc- 3bW
- 2d pp
y + p
2CC
se
centro (Cc = cd+ Sc- 4bd
et 
E) y +p
Sed hoc video non licere, quia sune fieret. cc+ c - 4b83 = 0 seu c = c - 4bd
Quod est absurdum manibit ergo Ait
ubi momum quid
Cc and
y.y
no
(2 yt p
=pWV Y + cciv -4d vp
2t c- 4bd
Ubi morum porito W = c et 4bd ab -ce - Sc - 4bd3 3: b
ubi mirum manere  indeterminatam
Sed opus erit calculum resamere pagina sequenti, ut magis secnti sinus,
y3+pP

## Folio 215r — 00068196:0425
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 214v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000425.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
depressive.
id agitur ut bXX+CX+ d, xte, reddatur spbiitr extrahibilis per explicatione
ipsius X, fiat ergo X = lyy + mnus + n,: ( y+p
fip a = bl s + 2blmmys + 2blnyy
+ b m.. + 2bmmny +
CCPX = Ca + CEmm. + CC n..
+ 2cc lp.. + 2cemmp.. + 2CCB p ..
+ celpp .. + cemmpp. + cer pp
= d. + 4d p.. +6d pp. + 4d p3.. + d pt
d
aqqus + 2a grry + 2agt yy
tart. trarrey + at
sit Y =0.  et sit n3 = ppY.
Et ex aeq 2)
Ex H Ilfil Exaeq. companato identificatrice i sit g = sbl + ccl + d: a p(t = pp rbWBCBa
Et ex aeq. 3, fit - mmip = 2ccl + 4d3:, 2bl + cC q unde (4bcc lD+ 8bd v + 2C2  cd) (ab celvusbdltumaud
Et ex aeq. 4 mmip = 2ccB + 4d3:, 2bv + cc) seu 4b 8bd L. v = 2c4 L- v = 0
seu firt bd - et l - B = 0. sed non licet facere 468 =c = 0. ergo fit l = v
superest aeg. 5. unde sit m: pp C + Eemm: p + 2bI +, cC l + 6d aequ + 2bll + rcl + 203
Ergo si F + ∞ + fiet bm: pp + rcemm: p + 4d =0 seu fiet
bb m : pp + 2CC b mm: p + C = c+ - 4 bd. seu b mm: p = e + cc B Sct - 4bd3 l
faccendo W0 =mmip et fit: Ecc l +4d3 :, 2bl + Cc. = c ccob - (ct -4bd: b -H
et fiet Eccl + 4d3 = 2blW + ccW fit l = ccW = 4d,: 2cc - 2bW ergo per valorem t
sit t= cc + 4d3 1y l = ceW - 4d:, 2sc - 4bd = v q- F: pp = Aurcl+ d: a
W seu - mm: p = cc: b - Sc- 4bd: b et
et fiet X
tam ceto -4d3=
et
2 Y1- 4bd3
sit
X=
cco- qd yy  - pV y +  ccl- +d
2 Set- 4b0
yyt 2py + pp
2YcF- 4683
pr
cSc abd - C + 4bccd NL pH e abd = sC
2b, c - 4bd3
(e Se abd - C + abccd) yy
C
1- 4bd
et pl 2b, ct- 4bd = - 2 ccp. + 2psC. 4ld
( - abd - Bcc) (1. 16d) py)
(C C - 1bd - c + 4bccd3) yy. + (C - 4b93 - CC) C - 4bd 2py + (C Set - 4b8 - C + 4bucd3) pp
2b, c - 4bd31 + p
vel compendio X = lyy = pa y + lpP, :, y + p, posito (= curv - 4d et W = cc - sc - 4bd
2 Sci a 4bd
ubi si esset =HyD 1, + Upp et IpW = ellp sin W = 2l, esset etiam x extrahbies, quod tamen hic
non licet licebi pou pro xte, ut fiat extrahibilis  poddibit +lgy - ploy + lpP: yp
+rep. + epp
ubi si fat -pco +rep,: lte = 2p sieiet rursus aliquid non est in potestate
quia evanescit p. Itaque hac methorto obtiaere non licet ut tres
formulae Cubicae radices una vice fiant extrahibiles obsine bitui tamen per
gradus  quod suficit
l = c -  c Sct - 4bd - 4bd Sc - 4bd - Cc -W
2b Set - 4bd
lyy +mmy+ n3
gy+ 2py + pp
= lppgus t mmppy n pp
+dp1) F2map. F 21 p.
Lly. Fmn. 7 13.
a gyyerrytt
Oyip
vis
s 2
e

## Folio 215v — 00068196:0426
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 214r); this page is its left half.
# No recognised text on this page (recognized).