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# Catalogue record: 59895 — [Aufz. zur Reduktion irrationaler Ausdrücke]
# Incipit: Videtur casus dari quo √[rrcc-2rf(r+f)x+ffxx]/[2rx-xx] deprimi possit
# Date: 1688-04
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=59895&katnr=57598
# Work: https://leibnizlegible.com/work/00068197
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folios: Bl. 19r (from the shelfmark LH 35, 13, 2a Bl. 19r°): 1 page, canvas 37, page ids 00068197:0037 to 00068197:0037
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=37
# Lines: 62 recognised on 1 of 1 pages, mean confidence 0.85
# 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.
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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 19r — 00068197:0037
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000037.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
Videtur casus dari, quo s rrcc - irs (rssu f5 XX
2YX = XX
deprimi possit
reddendo scilicet numeratorem divisibilem per nominatoris divisorem 2X-X
nempe multiplicetur 2Y - x per nec +s hex ner + rpX, prodibit
2nYd = nIrX = rPXX ~ rrcc - 2rf(r+f) X + ffXX
+ 2IrpX
X fit 2nP = rrce seu n = Cc: 2r Ob ex fit p = - ff: Y ob X fit 21f (21f) = ntr - 2rrp
sen 25(Y+ 5) = nr - 2rp, hoc est 25 (r+5) = =cc + 2ff  seu (Cc = qus +4- 4f.
sime
seu denique CC =2f, (S) V Adeoque ABaerit media proportionalis, inter f seu CD, et  a bis
est autem =a, ilem quod (C)d, posito C eadere inta circulum Ce
Et c seu AB eritu media proportionalis duplum mediae proportionalis inter radium
inter  OA radium, su seu Y; et inter OC, seu f
Itaque si inter C A si circa CA describatur Circulus; erg ejus chorda
angulo recto ad CA transiens per O, erit aequalis rectae AB, _ et centro A
radio qui sit aequalis dictae chordae, descriptus in cent plano 
plano, normaliter ad AC  eductam, in B vertice quaesito Coni scaleni
normali educam et angule,
cto
cujus superficies haberi potest. Itaque dato puncto C, dabitur conus scalemus
superficiei mensurabilis, ei respondens
prodibit ergo
art -Ert(risIX + ffXX.
2YX = XX
X - 2r dividat ffxx -erf (rts)X + 4Vs F ffX - Errf
X
2
+2rfsX
2rrs -
sed hoc fiustra, nam
chorda minor est quamfuns
diameter Circuli ergo minorqua
CA, ergo ex A noa poste potest
 pertingere dius
ad rectam exc normlaliter
edactu
videamus jam, qua quadhatura haberi possit dx Carrs. Bx, : X) - de
af dao: dx = f
Fingamus r+F =O, seu B imminer ipsi A die urr+ EX
2rX - XX
jam SSXX + CCrr = GX + er1-1, fx - eFY-1
Sx +c +GX-2Er, fiet c = + t 2f: 8- 1 - b
sed ita b constini non potest.
pr X assumamus Z7, et vi si esset r+f = + c, haberemus
etiam intentum, nam numerator esset extrahibilis
Y+ f = CA, sed se E = AB c = BA, itaque
sed BA et C A non possunt esse aequales, ergo nec r+f- +c
videamus, quid fial si r+f = -c, fiet rr+ ff + 2rf = Cc=
bb +rY + aar taa. Et sit. sed f- atr et fiat
YD+ (aa rar rn +2 rat im = bb + (41 n (+ 4art aa)
e
Ob
et fint b =0, quod est absurdum
nam lonicam, methado illa altiore, qua possumus  bx + xt ex +5) _rationalisandum reducere 
citoo b
hl_V + hfsu + fe ab vi  LabrvFabrr. = h∞ + ff + (∞ + 1 lb, hv+f-(ver) lab 
a, vv+ un ir
X Ab XDC, sit X=
ha ve+ alisu + ac vrae racw e urr
ves thv + (+)C, lv- 1f + (V er) Vac
ad est +gyrghus + rationalsandum. B