# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068049:0063
# Permalink to this reading: https://leibnizlegible.com/page/00068049:0063?run=73
# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 32r, page id 00068049:0063
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 33v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068049&page=63
# Source image: https://digitale-sammlungen.gwlb.de/content/00068049/jpgs/default/00000063.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 75 lines, status machine
# Lines: 75 recognised, mean confidence 0.80
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

Dimensionis Curvae Ponicae reductio ex eo pendet, ut formula facta
extubus X+a, xtb, etc, aequetur quadrato infinite. Quod cum hactenus non potueriur
commode praestare, et vel non succedentibus calculis, vel nimis prolixe procurrentibus, ut absolvere
non vacaret, venit in mentem, ut res redueretur ad partes irrutionales, quamnum
quidem non conrideret nisi factum ex duaibus radicibus, et si omnes partes simul res tales
continerlt. Rem sic nuper commodissima datione aggressus videor.
debet v + ab aequani quadrato. sit v + aeb: a = C et  Gnxt p Apu + K M rX ipr
+9
fitque 90 = B9XX + 99PX +9BP F agK X + egk p L XX+ qX + qu, :, X + 2q2 +9q
4
KK. + KKp. +KKpY
sit v =  Pax+aq + B daxtar,: laxtaque. Et fiet
itabs dD = WVEX ) _X +W9q HABY X + asVB HGL ExFGX +gr, :, XXt 24C +9q
pa
BB..
+BD2Y. +DDrY
678.. +6784 +6789Y
ei
ab. trabus. abqu
Fu) compendio
Qu  So  4 D 
+
ve t  = + vy 3D+67838+ 478217838; 
ac
BbEQ
Quoniam autem coincidere debent valores 3 et 5 ipsius 30 debent identificari per
aquationes comparatitias. Et pro is Et pro iis scribatur compendio
302 2xx + 13X + 14 + 22X + 231xxY qX + qu3 : HXt2qX +99
Ergo per XX, comparando, tiet gy+KK = 12 et per X f..., fiet 29K= 22 Er fiet
gg. + KK + 2gK = 12+22 seu g+K = S1+22. Et similiter per 3et E firt gy+XX - 2GK = 12 -22
seu g -R = S12 - 22, et addendo o etio fiet g = s12 + 22 + = F12- 22, et à 9 auferendo 10, fiet:
K = L Sit22 = = Si2 - 22. Et per 1 quadrando fiet 49g = 12 + 22 +12 - 22 4 2 112. 12 - 22. 22
seu g9 L12 + L Yr. 12 - 22. 22 similiterque XK = L 1 - + S1212 - 2222. Et quia 
(4)
12= VV + BB + 6VC + ab et 22 = 478 V+B Hinc patet g et K, haberi ex solis V et D
(6)
porro 29K p = (23 =) 41) BV9+Dr.  comparanto scil.23X... .. in valoribus OO itaque per B, fiet
22p = 4YB 14 + Br seu p 411879 + 25BY quem valorem ipsiis p, si in dublicibus
valor ipsius B3X, itemque ipsius  14, substituamus, necmpe in 99p + 994+ KK PL KKY, itemque
priore
in ggpus +XKPY. habebimus aequationes duas pro q et r, ubi aberit pa Nempe per
3ffiet (9g + HK Hest) e p (ggFKX, id est per 3e t 7) 12. + SBV9 + 12. 4 s Bor + 99g + KKY 
= 27γ9 + 2dBY + 6769 +67OY + 2 ab9, vel compendio H09+ nor eq+ fr = 0. Simi
lter per 14Y, fiet 394  499V sIB 9 + 4XKB (yB rr + 4ggB B qr= . y V44  drrB
ope Aq. 17
4pNV 8. +ab ine 
seu compendio _ l99 + mrY + n gr = o unde per 19 et 31 tollendo simul 9 et Y, quia : 9.
rell
+ per 21 est N + HY  + 1 20 seu gt + H Y + UX 2 nn- um seu x= Jun-alm - n
Mq
nm anm
quos duos valores ipsius r: g ex N9q. 22 et 25, aequare debemus inter se, et quia nihil aliud sub
valoribus ipsarum l, m, n continetur quam g, X, V, B, et gatque K jam reductae sunt ad V et B ut
patet ex notis post aequ. 16. itaque aequando duos valores ipsius r:q nov debet determinati relatio inter
Vet B, et ita impos qua reperta impositus erit finis inquisitioni. Sed ut compentium qualicet
sestemnt videamas primum an non ex un aliqs (xexalicatione facta) reapse extrahi possit radi
Nempe per  aequ. 20 et 21,, n= (9gB + XKVC qSYB n 1 CVD ∞ 6,22h
fiet. seu per ag. 1b fit N= BBBFKK) - 5γB HB,: +D, seu fer  l 499yb. WVa Sab 2E: 2
seu  99γ - WY 1d: Y+D
n = AKKBsye 2 : 22 seu n = KKB - B6]+6,: 7 +D
127+ go ed CVDio, id Etf. 1B +KK,B 
Itper 28et 19 fit e= 12V +99 - 2)V - 67B - ab  B , , VB, er 5 = 1B +XK- 268- 6) B ) +B,:, 7+ B. videamus
Et per 18 et 1y fit 
quia autem duae supersunt indes  indetermionatae V et . Unaque tantum pro iis quaerenda superest aequatio, videam
1
an liceat on assume determinationem novam, aptam ad contrahendum calculum. sit 12.12 - 22 22 0. seu 12= + 22
fiet gg= KK = = 1E et V+B Y)Agy S +6VB.  A L4 sV. B. sB + BB = - ab. seu fiet
YY = IB = ab. Hinc n =  212 -61B (= 2 12) -WV _B,:, VB m = +12D - BB d:, HD et fiet
lm = 212. 124-F= n. ) 1B - = 12VBB p + B + VVob V1 B.)B. (( et 4lm = 12. 12Vb -2. 12738-212)71B-
= 2. 1271BB =2. 12VA3 +V 6B +)16L  VB,: MO jam VFd (HB = Y- ab Ergo +B = L- ab +2V)D
e V) + BB = -ab +) F + 4F - ab ) B C2)B. Ergo 12 = (ab) C 2VD + 4 f- ab JB +6)  ab) adeoque
fit 12 = (- ab + 2NVB, in +4YB = V+B in + 4VVB. Hinc in valoribus. e, F, l, in X divisio insti-
tur potest per V+D  fiet n = +2 . ab YB  - VB et l= + 2) sB- VY m = + 2D11B- 8B. celfiet t a
et Im = Y,BB (WVBN L 170B N (VIOS =17VOD L VoBLab - +WVBB = + 27B F. ab)B - Y)BB
Ansam = absas + 8 st abpe ess e0 f 37 8 s ab7 e t 4 17ob =  4eb i + 8)700