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# Piece: https://leibnizlegible.com/api/records/60619/text
# Catalogue record: 60619 — [Aufz. zu Gleichungen]
# Incipit: 0 = 120ωω + 102ψψ + 111ωψ + 110aω + 101aψ + 100aa
# Date: 1688-04
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60619&katnr=57607
# Work: https://leibnizlegible.com/work/00068197
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folios: Bl. 35r (from the shelfmark LH 35, 13, 2a Bl. 35r°): 1 page, canvas 69, page ids 00068197:0069 to 00068197:0069
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=69
# Lines: 100 recognised on 1 of 1 pages, mean confidence 0.84
# 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 35r — 00068197:0069
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000069.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 100 lines, status machine
o= 120WOC H02 WI + IncoI + 110 ( + 101 2 + 100na ea
0Z 240Co + 204  + 231 Co hp + 21312 + 222Coco  Y + 210C0C + 202p ( +21 7 240C0, 201a 2
oincul
quaeritur earum divisor communis (9310ld + 3012] + 300 a, multiplicandus per 510cd + 501H + 500a ut fiat eu
ut fiat et
nident unda
et multiplicandus per 630c0 +603 13 +621coco + 612co lpi +662oCcd, boa ian Pbionao orates loca
tieu
Ex 3 multiplicata sit = 310. ococo F 3501 i + 310. 50rCoep + 310. 500 ali + 301. 500 a  + 300. 500 aa
300.501 a 
301. 510..
5∞= 100 Hanc coincidenti a aequationi 1. fiet
3580. 510 acb
Ergo ex co l fiet 00. 111 = 310. 0. 102 : 301 +301. 0. 120: 310, sun (B0) M. 310. 301 = (10) 132. 310. 340. +60) 20. 301 201
510 = 00. 120:310 501 = 00. 102: 301 500 = ∞. 100: 300
Ex aco fiat 00. 110 = 310. 00. 100: 309, + 300. 00. 120. 31 seu 3r gea 10. 310. 300 = 100. 310. 310. = 120. 300, 300
Eodem modo ex ai fiet 101. 301. 300 = 100.301. 301 4 102. 300. 300 Ha tres aequationes novissimae
dant prima 310: 301
secunda 310: 300 tertia 301: 300 Ergo bis datur 310: 301
seu iatur aliqua relatio inter terminos aequationis datae
310   - 111 310 + X 111. 11I U1. 111 = -
4. 14. 101
 410L102
120
102
10L 301
Ergo 310. = CibC ( 111 + LCM. 111 = 4. 120. 102)
ot
301
Pari jure 310 =
300
Ergo itorum habetur
Et pari jure firt
02
110 + V(110. 110- 4. 120. 100)
310
301
s
3
2. 100
301
300
10 + Y (110. 110- 4. 120. 100)
101. + s (101. 101- 4. 102.100)
301 =
310
2. 110
:1I
111. 1H = 4. 120. 102
4. 102. 102
101 + Y (101. 101 - 4. 102. 100)
2
.t
11I + Y Cusi1 = 4. 120. 102) =
111 + YC 11I= 4. 120. 102)
2. 102
11  VCuI = 4. 120. 102)
2.110
ser  MI et ent  uae quatioidentiea
nam ila fitis
11I + Y(C1 c - 4. 120. 102)
Aliter ex 10g6 et 7 aq. 6 et 7 fist (+120. 102. 300. 300) + 100. 102. 310. 310 - 14 102. 310. 3002-
-120, 102. 300. 300)
= 100, 120. 301. 301 + 101. 120. 301. 300
Ergo
2. 102
et firt 300 = 100. 102. 310. 310 - 100.10. ∞ (301, :, 110. 102. 310 - 101. 120. 30)
Hutr ex oq. 6 et 7 fiet 10 120. 301. 301. 300. 300 = 301. 301. 10. 310. 300 (= 301. 301 100. 310. 31C
= 102. 310. 310. 300.300 + 310. 310, 101.301, 300 (310. 310, 100. 301.30
et fcet 200- 310.301, 110. 3+0, 50r. 301 = 101. 310.310304, : 120. 301. 301 = 102. 310. 310
110. 301 = 101. 310, 110. 102. 380 - 101, 120. 301
 pit = 100, qu (103. 310. 30 - 10. 201. 301) = 310. 301, 110 101 31 tot 120. 301
seu-100. 1 Hoc aequatio conjungenda est cum aequatione ita, ut tollatur 310, 301
Alia methodus in aequatione 1. substituatur valor ipsius a, ex aeq. 3. debet oriri aequatio identria
Multiplicetur aeq. 1. per 300. 300 fiat +120. 300. 300c + 111. 300 300 col. + 110300 20 aco + 100. 300. 300 aca
+192. 300. 300  V
-300a = 3loco +301 C et 300. 300 aa = 310. 310Cdcd + 2. 310 301005. et habebimus:
+120.30d Cdlo + 112. 305  + 111. 30023V.0. quae aequatio debet esse identica
201.301
odis
110. 300. 301c0
00. 2 10c0 V
101. 300. 300a
310.310 = 110 300. 310 + 110. 119 300 = 300,110
4100. 100
4. 100. 120
4. 100. 100
seu 310 = 300, 110.  + ( 110. 110 - 4. 100. 120)
10
110 -30l+ 1n. 300 - 2. 1,0. 11∞ 301. 300
ex co fit 31 210.200 = 110. 301 - 111. 300, : 2100. 301 - 101. 300 et 310, 3002 4. 100 301 + 101 2 300 - 4. 100.101. 101 30
4100. 316. 3lawsas 4, 301t3o1 Y H + 2. HD. 30301cs Y
.100
Et pari in 301 = 300, 101 + Y (101. 101 = 4. 100. 102
+ 120. 4. 100.301 + 120. 101. 30 22. 7. 108.10157
1td. 116. 301+ 10. 11I 200 = 2, 1. 110. 111. 301. 200.
et (100  E10. 310 - 110. 318 4 120 = - 11(. 1D. 3012 100, 301 = 110, 100. 301. 101. 300. 10. M 30012 1o 30
. 100
∞. 300
= 110 111. 300. 2. 100381- + 118. 111300. 101. 300