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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 78r, page id 00068207:0155
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=155
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 93 lines, status machine
# Lines: 93 recognised, mean confidence 0.81
# 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.

mistabyam
ur Clarissime Amice
Honoratissime
aeris mihi tam profunde penetrasse
in aenigma df implicatissimum
ut vix aliam commodiorem solutionem peremu magis optandum, quam sperandur
Etesol enim optandum essett perinde ac in columna prima et secunda numeri compendio prodetent
prima et secunda humeri sine calculo pecilene opeso operoso
extrbentur; ita idem in caeteris praestari possit.
seq enim semper aeque compendia idmittit natura rerum
contenti simus igitur hoc tam praeclaro Catone.
Cui tantum theorematia quaedam addo
Gea esse (∞) - B,:t v
100
(5) - D (5,-5 (8I- E
p
(2)- 2, etc vocentur
undo si  ponatur 22 ab + 23 abc +24 abcd + 25 abede t etc vel
+ etc. vet
unde si 2 ponatur 55 abcde + 56 abedet + 57 abcdesqus + etc: 2 erit 22a + 22 ab 19 abc +24 abed + h abode
1 erit 55 abed +56 abcde + 5, abcdeft etc. iisdem manentibus
combination coeficientibus, sed depressis combinationibus. Reperietur
Aietur His positis reperietur
50 = 1 - 20 + = 0. ut
et ita porro. Atque adeo formulam qualis it dividi posse accurate
undo sen
per 0, 56 8, et per 1. 24, quod etiam re apse in formula
esse
succedet  Ex his conclusi esse 40D - ) -,  set 1 X - 2
jam
ele D6 - 3. + 2B et 80565 - O 3 43- 17
et 103874-O- = 5i + 2 7
Se = 1 - 20 et 5V + 23 = 1 - 40D et 5 + 2. 7 + 4 3 = 1 -806
Et ita porro quar
e
Et ita porri
 vet
hunmum ex duobus
et s + 23 + 4B + 8) = 1 - 16056E 16( 4) vel 20 - 1 X 4
Et simili ex iisdem duxi esse + - 1 - 252, per 1- D
 , -16C1 2) 1 = 15V + h Ca
potest etiam fieri C = 1 2D. 7 OD - 1 26. 3
Et ita porro, qua  ratione producta ex plurimis
vel 2X
reducuntur ad simplicia. patet etiam ex valorips valoribus
quantitatum s, 4, 3, etc. esse
28 5 Et 4 = 1- 22 6 et 1-
c
1 26
= ( 1-22. 0 e = = 1. 25
1- 22 8
1128 T
et quia quadr (1 - 267) = 1 et quadr. (1 - 2D) = 1, et ita in caeteris,
1-20
fiet 37 = O et 38 = D et 72 = s et i  = 8. ubi observandum
eota 5e, 2, B, T, 1) non esse notas dyadicas, quia possunt valere
aC
SX
non solum O et 1, sed etiam - 1 unde quadiatum hic non semper
demner
aequivalet lateri Sed quia 5 = 1 - 23, hinc (5. 5 = 1
am
intionaliter
unde sequitur esse 7 7 = C. unde  consequens est O
seu a- 2 ab + 4 abt habed etc. esse semper quadratam formulam, e qua educi possit radix, quae sit
qua educta radix sit 1a - 2 ab + 2 abc +0 abed - cabide + 8 abedet - Y abedesge F0, et = _ 7 = () - D, : p
cujus cuiust coefficientes sunt adem cum coet cilntibus  pns
25) +51, 1= 40
X = 1 - 20 multialicando atrobiue per 1 -2C
fiet a N = 205 = 1
H potest etiam fieri  = P2D, 7 et
Od = 1=20 3 0D6 = 1 - 28, 1
et 0D88 = 1 - 24, 1. ita producta
ex plurimis reducuntur ex producta ad
20s
S
4
421) - 1 8 =
2
5e+ 23
 4dd 
es 85
40 = 1 - 4
C44D2 - - 1+ 5V + 23
similiter ha
8.
5 + 27 + 4 3 et 16 81 = - 1+ X + L  + h1
et 3227 7) = -1 +5V+ 23 +43 147 + 16 11
Unde etiam 2D7 -O5e = 2 263-D1 = A
2E
7-53 = 1
271
q1 = 11