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# Piece: https://leibnizlegible.com/api/records/60460/text
# Catalogue record: 60460 — [Aufz. zur Approximation von Kurvensegmenten]
# Incipit: Si a trilineo ABCA curvae AC circumscripto abscindatur triangulum maxi
# Date: 1713-11-11
# Akademie-Ausgabe: AA VII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60460&katnr=57388
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 71 (from the shelfmark LH 35, 13, 1 Bl. 71): 2 pages, canvases 141–142, page ids 00068196:0141 to 00068196:0142
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=141
# Lines: 57 recognised on 2 of 2 pages, mean confidence 0.83
# 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 71r — 00068196:0141
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000141.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
quantitates
ordinariae
D inte tres indeterminata relatio potest exprami per aequation
Si sint
determinentur:
quarum ex una caeterae habeantur, inveniri potest aequata rationat inter
etet
eas pelatio expressa per aequationem rationalem; ita ut ex una datis duabus
tertia rationaliter haberi possit. Nam sunto quantilates X, y, Z
Et ponatur Y haberi ex X aequatione quacunque istenqu, Z et X aequatione quacunque
satet ope duarum harum aequationum tolli posse omnes potentias ipsius X, ita
ut habeatur X rationaliter per y et Z. Sed hoc initelligentum derequo
ou quantilatibus relationem inter se ordinariam habentibus
Licebit ne si possemus finitam aliquam licet transcendentem
invenire aequationem;  qua generaliter duarum quantitatu nata relatio
srvicem exprim posset, ut hoc possumus serie infinita y_= 1oX + 11X + 12x 
haberemus rem maximi momenti. Possemus quidem facere x
a
dy = d 10. X
X
ger
y = 10. X
1. 4. 
e
+ 10 X d (1X logX)
nx
log y = log1o +  bgX. I1X
la= log  X = vlogx = logy fit Y  + logxar = du
seu x + logx do = d. fit dy = X, de vlog X)
ux 12.X Ex + 10 FX  d(X) = X d (vlog+)
Ud
C t lugX d (I1X
inililer ha explicabutur a (UX,) ut ante d (10 X C.. 7
sed haec relatio et ipsa est infinita
a An saltem finita generalis delatio haberi potest inter tres, verbig y= X
Naevis quantilas consi derari potest ut alterius potentia, seu potest consideram
C =  b sed si c et b hoc si c et b sint determinatae, n  si vero
per eas aoordinatae alicujus curvae incertae intelligantur, alia quaestro est
2 licet sed tunc nova quaestro est quid sit e,
bu
 An liceat facere y = X
nom non potest esse constans. An poterit esse y = Xex posita X
constante non putem Quomodo enim ingredcerentur calculum aliae quantitates
numero findtae
generaliter diei potest y =  vel. X seu g= X
sed talis expressio non inservit canculo
si detur g: a = X X. Z
v
et adhuc semel detur
y: a= ∞.Z vatur dabitur Y: a - X:
dabitur item  y: a  X, a per X: a, se 3: a = X: a
x
eo A unsa circum scripto abscindatur tianintum maximum Bd)
recta abscindens DF curvam tunget in E (nam si tungeta poterit paralleta
isi duci intra ipsam et curvam, quae hiangulum majus abscindet. Huoc et trilinea
AdEA, et EFCL, e simul eintit minimum. Etiam AdFC eut minimum

## Folio 71v — 00068196:0142
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000142.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
aeniscire roorsauuc