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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 90r, page id 00068197:0179
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 91v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=179
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 68 lines, status machine
# Lines: 68 recognised, mean confidence 0.77
# 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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# After the first blank line: the recognised lines in reading order, one per line.

40 = XX + ab, aD = XX + ac B = 10X +1 a, : 00.
Q = 20X +21a,: 00
68+ (10D = BZ saB + vNa D. fut  + HC3 + 2f6 Q 10D = 22a 0, vva D + Zv a O)
L et a7= 564 unde fiet
6694 + s0D = (F : mim) 58a0 + (mmo aa ) 4gag A
68 = 10. 10XX + 210. 11 aX + II. Haa, : 00. 00 9Q = 20. 20X X + 2. 20. 2 aX F 21. 21aa, : 00, 00
88G9 =  qu (10. DXX + 10. 21 ax + 11. 21a4) = 10no 3etox + 2. 10 702 a X + qoit nt anX 4 q on a axtua 3
Epet X datur ee 21
I1. 2C
Ex X et X A quaeranturfiet um
(est OD= Atod
Ex X et X, quaerantur 21: M, et 20. 10
et ultima aequatio est pro Xx
aaqu
4 1010, 21. 21
 11. 11, 20, 20
110. I1. 2
(.: nasB at F, 00. 10 X + 00. 2. 10 aX
H H2t
2. 11. 20.4
+ ff ab06  xx
+00.  aa Xx
F00 10 ab XX + 00. 2. 1a 1 abau
Mm gGaD) nm, 0d. 20X 4 05. 2. 1. 1a + 0d. i naxY
aa
12 A
sane XX  Nam tan =  fiet aam, amt an + 2a tum = XX et mm + aannB2a M A
=4aamn firi ata Zatitn) 
+00. 10ac Xx + 00. 2. 2. dacax totlacia
Exi Et Hic calculus esse ab solvendus inisi ex seqq. poter o rem bereius hateremus
ses
M
+harm
A = t acmtn) tasom et + = Sea Vmn + acmuni) = san + tan
videamus an ex a em 2a tem + a (ntn) possit extrahi radix, nempe fcat
radix 2Vmn + mAn possit extrahi radix sron 49 et fiet stmn  aagu  + rafigsima L 
2ann + a (mn) fiet fg= aa et  nn + aague = aemtr) seafmurq = a (n + n)
et et ob f- a g- aa: f fiet ssm + (a . ff)  (m + n) ubi pono f esse
+10aem + 1a, fet 11 = aa: f
constantem. sit n = iom + na, fiet ftmm + (a. 1) Aa m.
et m = 4 rC (1+ 10) a B, 10 fiet R = (1+10)18A +a: H, et fiet
Mn = qunoto ae: f et (1+10)B V. f +a:f = atqu f aarrons
e = anCatina)  + Ar a (10 + 10. 10 + 10, a)
Resumamus ( Jam + Van = t am + an + 2 Sam = Et fit Ht - a (men) = a qn
S
et H - =. Ergo + = (2 aVmn + a (mtn) = tam + tan. Videamus an Cx priore
latere hujus aequationis radix extrahi possit  brmn + ag = _ t et H= aagot ffmn + 2ag f smn
a  2a lmn 4+ abn +n) fit
a
9- a:f et aem = a (ntn) = a: st +smn, sit
sit n = 10m + ia: ∞ et fiet 00am + 114 =, a: ff +  10fmm + 11ff am
10 am
sit H1 : 00 = aa: H siet m = (00 + 10) a = 00: 10 ff et m = a: H et
fiet n = 10a:ff. + 00 c: H,: 00 et tan = ( f(a: 00f) 1(00. 10 + 00. 06)
et firt sam. Nan = faa: ) (L + (aa: 00f) (00 + 1(00 10 + 00- 00). ita altertetrum
non exr destmas absolutum in aequae fiet
Ln = =aH +am, :HM- a
Al extrahibile. Sod  si sit am- Exx tab, et an xxt ac
am = Xx + bX + ac et an = XX 1 sx taq, utique ex aequatione si siet
seu n = a ffm - a,: fm - aff,  seu n = (a: ff ffm - a; : ffm- a
 ita evanescente m, fit n. = a: f. Itaque aqu. 5 non prodest, ac
Videndum an possit esse quam ian=at tqte fit em  + 2a Ima ff + gema tafalum
sit Zam + ev an + 2Zvatmt. = aat + gymu +2afgtmu sit Z0 = fg et
22amF fgg un an = aafi +. ffmno 2 mn Rzvo: f), fiet. 0
HZZam + vuffan = anst, hqvomn: siet M = BZa am =aaG,:, Z Bm- avvis
Ego hoan tatineat nst cticem atsi cotesn a p as)
d
podate