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# Piece: https://leibnizlegible.com/api/records/15383/text
# Catalogue record: 15383 — Rudolf Christian von Bodenhausen für Leibniz: Aufgaben zur Analysis
# Incipit: Sit: aadx+bbdy+c...
# Date: 1695-11-27
# Sender: Bodenhausen, R.C. — Addressee: Leibniz
# Akademie-Ausgabe: AA III,6 N. 176
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=15383&katnr=35616
# AA III,6: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-6
# In the Akademie-Ausgabe: AA III,6, p. 129 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III6B.pdf#page=129
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 40 (from the shelfmark LH 35, 15, 5 Bl. 40): 2 pages, canvases 77–78, page ids 00068207:0077 to 00068207:0078
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=77
# Lines: 234 recognised on 2 of 2 pages, mean confidence 0.68
# 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 40r — 00068207:0077
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000077.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 87 lines, status machine
Snt. O
ut
FbKK
a
+ ab DD
X
(1)
14
C
(27
qu
ac t ex
2
a XX;
+2 et X Y 2Cf X + 2aceX + aaCC (5)
a
+2bhk
aa
tee
t2b9R
tbnh
a
+2bgh + abgque
9
qu
a
a
X-
K
aa
1∞ 1)
CX)
X 1amn
a
- m
2 2
L6mn
aa
2
X.
Jamnxm.
a
8
Ame per comparat: aaff + abKK = nt. aa et + abhK= 2mn. 2aalt tanee + 2abgk t abtih = bmn.
63
10)
aace t abgh 2mn. ) aacc + abgq e m.
sint brevitatis gr: aff + bkL =β; Baef + bhC - V: )2acf + ael + 2bgK + bhh = S; sacetbgh - 5; acc +bgg =b
Erunt:
(15
n: M
M: n = 25:7 = 37:5-8: 35 = 5: 20.) Unde 3)
CC16
nn: mM = V:E
= 255.)
(ex 13
=678. 3
250.
es (12)
=655.
3
s
1p14
4(36. (0d-
(20)
-9)5.
. et 1fit 3) =d et ex 16 fit 3E =d. Hinc
e
Eligantur aequationes 11, 16, 13. fiat 2β = V. quae est Hypothesis atse entitia. fiet 20=
(29)
per 19 et 20 fit V Z. Ergo per 17 et 18, sit β= B. Opus ergo est 4 aequationibus invicem independentibus; quales 21, 22, 3)+ 3E2d et 1+2B-s
qua quatua, 2 aeqqe. novissimae servant leges justitiae. jeam ae fta, c, e,F; ut b, g, n K.; et CdtC ut f, et gut 
1
L
Ex 2C habetur h, simpliciter il valor substituatur in ag24 prodit velor (26) ipsius e. sine h; unde vicissim ex lege justitiae habetur valor (27) ipsius h sine e.  valores
A
ox 26 et 27, substituantur in aeg. 23. fit aeq. (28) in qua supersunt solae P incognitus, C, F, gik. Sed eaedem solae reperiuntur in aeg. 22. Quarum
15)
C99. 22 et 28 ope ha haberi possunt Co B et b ner C 4 relatio ipsius F ad i   a, C; b, 9. Et (30) simulisrelatio is
ad b, g; a, C itam ope 22 eHs triendo k, habetur  29; et oper  22 et 28 tollendo f, habetur 30. Quod si aliqua
relatio sumi possit inter c a C; et b, G servans inter ipsa justitiam, et apta ad deprimendam actentiam ex aegus 29 et 30
intio Elegi 1g. 11, 16, C3, quia aeq. 13, est justitiaria perse. at agque.  11 et 16 si mul sumtae sunt justitiaria. Habent etiam hoc, quod hoc modo
reprimetur, altera simul + sed cavendum ne qua aliunde imcommodu decerminatia assumatur.
quam uinimum tassurgunt incommod incognilae, nemue s et e pon ultia quadratum; et e,F
es
d,k non ultra tubum denique ope ipsam
serventur commedissime ad depressionem maxunae per hypothesius unicam i

## Folio 40v — 00068207:0078
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000078.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 147 lines, status machine
11
s
H Reduita aequatione
3. fit: ee -q 1642C7
13
93 - cd3 FiC.f
(14.)
0. sit 9+ n = 20C
3
93rd - cd3d
(15
1
(16
et f
=q= n
(17)
et concessis p verba: ten monfund n pro artitrio aumint etv). erit e = 5 + (5s H. et s ponatur 
C22)
(23
93-
3244 - 15 = st
t 2
2
2
9+5
1X.1
t.
L+
4. 11 aq +as Lat, (2) rd- 495
2
199+
bb4, q + 5-
t
9t;
294- 55
4, 4 + 5
SuE: 322y 55: Cb2-1b = yY d.
IC
18)
=q = n (ex concus.) e=
ei
2
12
-
2
F
qu
2
1: a = 5HE:
de
et b c.C
c
C
a
16. 17.) R = C. 99 +95 =9t. (p 9. 16. 18.)
10
2
1
do
r- 445 F99t. (per 16. 20.)
qu
2
grpr us. vpiserend.  diferb Grazes
2.
F 44t
a
F49b - c. d
1X 259
2
s
u
d + + P =5 10
L6, 299 - 55 Fdt
2
C, (2299 - 55
445 +g4t  aad
2
C2 =d
e
F99t-
p-qq
el si faciamus 5= 5 (non =93 fit e = 5.2 et f=0
erint valores e, f, g, h, K, l, n, 9, sequentes h. ordino:
se 65
C
2
20
F
2249- 15 = st
1219q- 5 F st
2
∞(0) 9
ss
e5
-445 =99t: 219 A F3t. fip 17
i
2
2
l18
sitsxit. 5. F. E. By eurp tynnuo sgenn, best? D aesus. 71. utx no  aeres
nt
21. Mbono bggry. pero nerus uead pon 1 = sit ed pa 2 ∞ f orgrguo een erpceneer n n. f. d smch (+)) aepe anpgrs
a gens  sinen. bbv. 2 nH. fd2 +s
C+
dt- R i  foa + dd b  fb: it-
fr +308: Eb5fot-R b + fdg b2. + 3d b1 + d2: b=
dd
(YFdui-
E (h)Y _ hyti 2
e
egar Zuraumut. 1. etr n uviiaen d ruchs
O
. -- 2YF.
a
a
e
6 (2Y n ops a uncynur
es
+
1f 3d: e =
E (et, et 2
X. dy- Xt: 7g9 Xro = b n trpp xp. vars roviB
(L)
- dyf.dVf.. 2yf.. db
 2b L
(5) Xpherso. t sipxic +d. L siptd sd + Xp XVyD. + sipi + Xppy L
exd. 4. 2. atx vo n ckd + XI = a p 1Ky + XyL
(+ eonc anpures. Styvrens n ad +7. hiye=
ab. a r 0 = ps fper D N eont: a0. +7. be D f  b yprarbe ravit. a3+): ap 
s
V
(B 263 p. et 1. 6. d ∞ XYk  sipX. ucart aof)..
rccurs urt. dis y: elvo =rgu=
f.dCry ecycbc nonriu
C
E)
C2)
s
(C) E- ( = f.pter)
Cf + b
:Cp. seugnavte ant
getor fe exbo Zrenp. Xgre. 27o 3Cg Cv st. == Xpk d + hpX b + hpk e + Xp XC3 + tpgu. + xpov: rs 
ey
4i5=49
2
per 19. 20.21.
(per 8. 19. 20.21)