# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068207:0082
# Permalink to this reading: https://leibnizlegible.com/page/00068207:0082?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 42v, page id 00068207:0082
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 41r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=82
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000082.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.75
# 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.

as +bkK aeq. biquadrato sit f= 120βB + 11 B3A + HO B, + 100X et R eadem solu pro 1
fiat aff= a 120
a lo2 M
1091
1012∞
+2. 4. 120. 111 βX + 24., 12a1or BpH + 2. a. 120. 110β3 2a. 120. 101BPA Y7 a. 10 ( 2a. 10
a 102. I11 BX3 + a 11I II
eidem modos bkK summu teinde aff 1b) CK
ex extilabitur ex
102. 101 A
equemo  biquadrato quod
300β + 3015) +300
110 105 CNV 10I XEY 1I
MI. IIO BCAY
111. 101 BMY
vereor ne eo ipso tam aff+ bKK debet
ut eotandem defungamur aequi biquadrato, redeati ad ipsum quod
Hlabet autem justitiae consideratio plurimum esus in calculo tum ad p. par sitiones, tum etiam ad diminuendam ejus
nitio fuit a quastione
prolinitatem, nam cum literae diversae pari jare utuntur, unius valore seripto, alterique vales pine calculo scribi potest. prod est atia
ad calculi examen. sed place hunc calculam reup praesentem reapse aggredi ontvides com sit plitera constans seu
sib r pro unitate compendii cava sit (4t) aCf + bhk = C et 6t0) aec + btq = D _ ) res ibls, n
e(5() 2acF + aec 4 2bgK + bhh = Y e (7mo) aB +bKK = S et (Qvo acc + bgg= Q et sq) fict
ex 1 fiet, 390 = 284. Ex 2 fint (10mo )3DD = 288. Ex3 fiet (12mo)   (D = 450. valores ex
9 et 10 substituendo in a4. 12. fit e ASC
sit
eat)
e
63
c
8:9= 165548 sen 1340) = 6 100 unde exet 10p 13
si 1653 e (15+0) D4 = 16∞93. Tergo valoris D, D,  habentur per
per 6 et Q seu per f,. X, C, 9. jam quaeram porhas etiam e et h. Ex 4 et 5 fit
(1to) e=  = bhK,: af  = (17mo) D = bhgg: aC, quos valons aequando sit
DC =bchk  = Df bfhg. ser (18H0)h= Sc = Df,: bcK = bfg. et pari
jare (19no) e = C) q = DK,: af9- a CK. Hi valores h et e, substituantur in 1yh
fint (20 m0)  C99 + C - 204K (+ (C) cct PN- 20D es
+(3a cf +2bgX  (0sR99 + CC KK = EfCGK) = et fgGH= 2fCgK
compendii causa foL CK sit (2) nd) = r9 et (ad d0) ac f+ FbgK = rrB. nima
sumta Yer
incente pro
4aCC X
4ba9
a
10
e unitate. et a in aeq. 26 haec substituendo, ut et vafore
13t1g
14 15, funcer _g. 29c siet _
Yord. 9r95Q+ 2Yy) 2r ab 844 = Itab. 6
seB. ex 13,
+ +aB
es aCC + bg9) 5 idem quod 60 et lass +b KK)  idem qua quoque
 CQiKK
quoa dE. Exrom X9. E5 omnia hoc reducuntur, faciumus ergo Z= er WW
Sed exZ et 
itta ex aq 2Z. si divilione facta per 2. fiet E. )  grr W3- 4 rron
+ab 899  ab 5abgqW. ob atic. 24 7, 8 tit ass ibi.k e rbgC
(96t0)  i qu’ an eroo per aeg9. 21, 22, 26 quaeramus sipsas, k, f, etc. Nempe
ex 21 est (27 0) R =  59.rq): C et ex 22, f 28VOIK= Yrefib
quos vaton aqndo fik bfgg- ibgg = rrc8- accF seu 90) fiet
rrc Arbgg: accbgg unde parijure fet B0mo
rrgq ragC, i bggotacC. NempC pro a, C, aponendo respe
aive lu cive b,9, =q, et vice versa. Ratio autem cur pro
C=
o
aponatur a est. Qvia in aeg. Funeda mentali 21, set X sic difserunt
ut f, c,4se Lhabeant respective, utik, 9,-g. Sed hoc obiter. Fun
damentalis autem esse respecm ininq jam valoribus fet K (inventi, per 2930) substio
tutis in aeq. 26. per 8, siet Ar Gci  rrabb 4499(+ 2r3 ab99 c∞) +r685
 erraabquae ( 2Y a49CaO = (21 mo) r OOWH
et destendo destruendo, dividendoque per rr, ordinandoque, B
rr58 + ab94, GC = r489 wu ergo vel fiet 9 =
flet (33ti0) rrga +abga- Laviv, seuqque no resteat
ed uras est gu (3a10) = 4rru?- ArrGWW,, 3ab- ab 8 quoe duas
aores aquando fit 
S1-+W- FuW+ (3 = 4W- 4gW
WW + 388W - 3 = 0, id est (6to) W =O = C
Seu W = _; A unde per 33, ut fit qr 127mo) g= s (nisi scil. ut dictumqus
35t0) 13
u
caciamus a seu acc + bgg =0) hinc per 37 et 21. fiet B5) f: K = c:9, qu
Etet ex agg. 29,30, posta vam q= 0 Hinc et si in aeg. 29 et 20 posito
0 imdrituantur valores ipsarum et X tiunt 0gq. identicae. idemque est
 100Y
44. 26 pro, W, , K substituas valoris per 26, 22, et 38. Pata
tiam per 18, 19 hince foce
snu remrieta
expliceno
d)
phicemus C et D in 244. 18. 14
 (39) OC-D5=0 ut 40) 39-DL =0 quod et
quod si jam distimulandor seu f9 - Cx esse B
 imihiingreditinontita
ima    rc, CV0 Sir e irb. ex   ile 1 B
et quia ex 3dfitiaomo d.
ao
+
eb