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# Catalogue record: 55430 — [Overbeck]: Calculus Analyticus pro Aeqvatione a²y²...
# Incipit: Conditiones sunt x/a = ⊙/☿
# Date: 1716-04
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=55430&katnr=36921
# Work: https://leibnizlegible.com/work/DE-611-HS-861255
# Title: LBr. 705 · Overbeck
# Folios: Bl. 112 (from the shelfmark LBr 705 Bl. 112): 2 pages, canvases 223–224, page ids DE-611-HS-861255:0223 to DE-611-HS-861255:0224
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=223
# Lines: 161 recognised on 2 of 2 pages, mean confidence 0.75
# 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.
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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 112r — DE-611-HS-861255:0223
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000223.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 157 lines, status machine
2(1)
Calculus Analyticus pro Aequatione ag = bX + aCX + a) X + a9
Conditiones sunt
Fiat X = aO: 8
X = a C: 82
X3 = a 03. 73
X = 0
e = aD: Q
y = a52.
ay = a+ D2: X2
Expositio Planetarum
Sif 6 = 10a + 11Z + 1ZD
42
D= 20a + 21Z +22V
2=30a +31Z+ 32p
ur
Inde ad: 2 - b a: 8 + ca0: X + fa0:
Fit
Multiplicando totum per
a 7D2 (2)
604cF0 +f
1 = 15. 10. a + 2) 10. 1. aZ + 2) 10. 12. aV + 11. 11. Z L 2) 11. 12. ZD + 12. 12B
5= 30 a + 31Z + 32V
(8 = 10. 10. 30 a + 2) 10. 11. 30 aZ +2) 10. 12. 30 a V + 11. 11. 302a +2) 11. 12. 30 aZn + 12. 12. 30 Va
+ 10. 10. 31 a7
+2)10. 11. 31. Z a + 2) 10. 12. 31. aZV
+10. 10. 32aV.
25)
+g4
+11. 11. 31. Z + 2 11. 12. 31. FB + 12. 12. 31. ZV
+2) 10. 1. 32 aZV +2) 10. 12. 32Va
11. 11. 32Z2y +2)1. 12. 32. ZV 412. 12.32V
Ex his habebis O notulas Sinistras 3. in 1. ubique mutando Item 83. notulas sinistras 1. in 3. vertendo
Iaque
utrumque horum simul faciendo accipies
520
Bdenique notulas sinistras 1. in 2. mutando aderit D
973 = 30. 30. 30ag. + 330. 30. 31a Eg +3) 30.30. 32 9a B. + 3) 30. 31 31. a2 g +6) 30. 31. 32 u ZB. +3)30. 32. 32gaV 131 3131 Z t 3) 31 31. X2 Xy + 3 31. 323 2V 132. 32. 32. 9V
2) 30. 32. 2
3 2) 31. 32. 11,9t 2) 31. 32. 12
2)30.31. 11. 2 2)31. 32. 10.
+30. 30. 1. fa L + + 30. 30. 12. fa B + + 31. 31. 10. fa Z L 1) 30.32. 11. fa ZV F +3232. 10. faB + 31. 31. 11. fZ + + 31. 31. 12. fIX + 132. 32. 11. fZV + 32. 32.12fB
+f0( = 30. 30.10. fa3 + 2)30. 31. 1023, 2) 30. 32. 10 c2
D10. 11.30.
2)30. 31. 12.
L +2)10. 12. 30 2)
210. 11. 31. 42 2) 1. 12.30.
C40 = 10. 10. 30. ca + +10. 10. 31. Ca2 410. 10. 32 CaB + f11. 11. 30 caL + 910. 12. 31. CaZB + 2)10. 12. 32
2) 10. 11. 32
13, 3) 11. 12. 31.
I. 1.3 +E. 1232. 1
+bC = 10. 10. 10. b a + 3)10. 10. 11. ba Z + 3) 10. 10. 12 ba 2B + 3)10. 11. 11. ba Z + 6)10. 11. 12. b a ZV +3) 10. 12. 12. b aV 4 1. 1. 1. bZ 3 + 3) 11. 11. 12 b0Z + 3) 1. 12. B2bZV L 12. 1 2. 12. bV
3 -2) 20. 21. 30
29 -2)20. 22.30, 2 -2) 20. 21. 31. 42 - 2) 21.22. 30
a8D = - 20. 2030ad - 20. 20. 314a 2 - 20. 20. 32 a AD - 21. 21. 304, 48- 820. 22. 31. A a~
=2) 20. 21.32
2)20. 223
3 - 2)21. 24.3112 - 2)21. 223242
-2222. 30. a, a1 - 21. 21. 21. a5 -21. 21. 32C - 22. 22. 3, aXV - 22. 22. 32 aB
Scopus calculi est ut in hac Aequatione valor D non ascendat ultra unam Dimensionem
f.1. Ergo tollitur primo D Facit 32. 32. 32g +32. 32. 12f + 32. 12.12~ +12. 12. 12b = 22. 22. 32a Ut Aequatio sit infra Catum
faciendum est 12 =0. Ergo 32. 32. 32, = 22. 22. 32 a. Id est 22. 22. = 32. 32. g. Sumendo a. pro Unitate Facit Z2 = 32Vg
5.2. Tollitur secundo ZV Facit somissis per 12 =0 affectis) 3) 31. 32. 329 132. 32. 11 (= 2) 21. 22. 324 + 22. 22. 31 a Jam ex 8. 1. restituantur
22. = 32Y9, et 22. 22. = 32. 32.9. Farit 3) 31. 32. 3E9 +32.32. 11. f = 2)21. 3219. 32 +32. 32.9. 31. Sumto a pro Unitate
Dividendo totum per 32. 32. fit 3) 31g + 11f = 2) 2IVg +314. Id est 2) 319 +1f = 2) 21Yg. Ergo 11. = 2) EIrg. f -231g: f quis si totam
dS
adauc 311
e1
8.3. Tollitur tertio aB Facit (omissis per 12 =0 affectis) 3) 30. 32. 32+ 10. 32. 32 f = 2) 20. 22. 32 a +22. 22.30. a. Frat Restitutio ex .
sicut B. 2. fecimus Fiet 3)30. 32. 329. 410. 3232 f 32o. 3219. 32, +32. 329. 30. sumto a. pro Unitate
Dividendo per 32. 32. fit 3) 309. +10f D2org +309. Facit 2) 309 +10f =2) 20r9. Ergo 10 = 2) 2org: F, -2) 309: f
Ex his emergit Aequatio Refermata ponendo 10 = (2): f, (20rg - 30g _ 11 = B. f, (21rg, - 319)
88 = 30. 30. 30ga + 3) 30. 30. 31 a Zg + 3) 30. 30. 32 a vg + 3) 30. 31. 31. a Zg +6) 3a. 31. 32ga Zv + 31. 31. 3192 + 31. 31. 32. 902
+f0P = 2) 30. 30 eorg- 309) a + 4) 30. 31. (20r g - 309)
+4) 30. 32 (2o g- 309) ap + 4) 30. 31 fuIrg - 319), G2 g) 31 32 (2org. 309)
(20. 20g.  + 3) 30. 30 (21Y9-319) a2
+CDD - 4 30, ffr. 2 20. 20193 3 + 4) 30 (20. 21. 9
(2. 30g aC f
=31. 2058
130. 319
430(20. 204
120.30. y3
+30.3C21. YaS
2). 20.30.315
 30. 30. 31. 999
Gv. d. 30. X
(20209
 +2) 31.31. (2org- 309f114) 20. 32 eurg- 319   i3 E1 4. 319) (4 4)3132 2 19. 31 9)VZ
,2=2) 20. 90193=p + 831 seo 21. g
3+ 30. 30. 92 L
a20.DVa
20. 30. 31Y2
d
a F. 130309e) Cl
-2) 20630Y
a
2- 2) 20. 32Yg. 30
-20. 20. 31. a =C - 20. 20. 02. Al1.
. 31. 30)
f
J: 31- 208
+ 4) 36
130. 31 92
f2I.EI.4
22) 21.3V
F (+ 3L. 31q2
(1t. 21. 20 Va
lizue
(20. 21. 9
X +8) 32 -71. 307
Ac
G2
c
=31. 20)
43031. 92 L GC.) la31 319
e
a
+ga ex Aequa
tione prima
21. 21.9
1
6) 32 (2I. E19
7
bitsuse
Dui
X X X C1 11 cc
de est
(2 +2) V. 31. 209
L21. 21. 303d
f31. 31. 20.7545
3 23)
a
4
2t
21. 21.
= 3) 21. 21. 5
+3) 20. 30. 30r
. 30. 30. 3093
deest
deeit
+2) 21. 21.30) d
vitido
-2.) 21. 329. 38. 52
=2) 20. 3219. 31 a(D - 21. 21. 2
eygrona. br
G.
X = +
L3I. 31. 30.99
3 9 sioro 20rg
+bb=
3)2020304
Af (+ 3) 2030.3619
30.30. 3093
2d = = l. 30.300
=27 20. 21.31.
)21. [9)231
D siad

## Folio 112v — DE-611-HS-861255:0224
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000224.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 4 lines, status machine
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LBr. 705, (2
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