# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/60673/text
# Catalogue record: 60673 — [Aufz. zu Kurven]
# Incipit: AB, x CB, y EF, z CF, v AG, g GE, e vel AH : AΠ : HΠ :: m : n : h
# Date: 1696
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60673&katnr=57660
# Work: https://leibnizlegible.com/work/00068197
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folios: Bl. 102–103 (from the shelfmark LH 35, 13, 2a Bl. 102-103): 4 pages, canvases 203–206, page ids 00068197:0203 to 00068197:0206
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=203
# Lines: 77 recognised on 2 of 4 pages, mean confidence 0.86
# 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.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# 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 102r — 00068197:0203
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 103v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000203.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 59 lines, status machine
AB, X Cb, y.
EF, Z CF, V
AG, g GE C
AH, in A n H E, h AHoA D : H ,I:: m: n: h
vel AHim A Ht
Quaeruntur valores ipsarum Z et v, ex ipsis X, y, v, g. , 2, 4
(1mO) B = CK = KF, (2d0) CK = yh: M (o) KF =
HK. n. h HH (4t0) HK A An - AK et 6to)
AX = L -XB et (6to) KB = yn. M. Ergu juventa suat quae
Quaeruntur, et fit AResimo) AK = x gnim et HK = m - X + gn:m et
(9no) KF = muh: xnch t ynnitm et () ex , per 2 et 9. fiet
Iomo) vC gh. m iin. h 4 Xn. h ynritum seu v =  th. Mr. timi) Gy A-mi 
seu (12mo)  v= my (m X) e sch Sed si
(3tio) K F = HK n: h et (ta HK = AH - AK (6t) AH = g + GH.
EX5per 6
EH (6to) GH = em: n sit AH= g. (7mo) AH = g + em:n (8VO) AK =
X = KB et (9no) KB = yn: M et ()  ex 8 per 9 fit (1omo) MX-
um
X -gn: m. Et ex 4 per 7 et 10 fit HK = g + em: n - X + yn: m. Et
(2) ex 3 per 11, fit (12 m0) KF = gn: h + em: h = Xn: h + ynn :tm, et
B3tio ex 1 per 2 et 12 fit V = yh: m = gn: h - em: h + Xnih - ynnitm
seu (7to) v = (X- 9) n: h + ystit - nn: hm) - em: h. sed f tm tan = tih
sed (15+0) ex hypothesi nm + nn = hh. Ergo ht m 16to fit
(16to) hh-nn: hm = mm: hM = m: h., Ergo ex 14 per 16 fiet
10
17 no) D = (X - gn + (y = e) m :h seu fit CF = GnGB + M) β: h
u CF. adhibitis punctis S,B,  (3 rectis GB, VB, et
qvia ergo determinabime
ratione trianguli H A 7. Ut oportet eodem modo determinari
C adhibitis rectis VB et ratione trianguli LAh, quod est simile
gno
ipsi HA ,I Ergo fiet  Z seu EF seu C= mGB + ng. h
posito G: GE: HE  m. n
similitr ergo invertendo figuram Hinc data relatione inter Z et
 substitutis valoribus, et explicando GB et VB habetur relatio inter X et y.
 non Ronamus jam porro immoto manente plano BBE ABB moperi
in eo curvam CC, q  angu 9 reco XFEF; poterunt successive
reterminari loca curvae et cuinclibet in ea puncti. Hinc si duus valores
ipsius Z, itemque ipsius B, investigemus, fiet m M:n vocemque Y, et  mot
h = rmmtn  h.  = hih m hh etum = mm t u: Est  nm = 1+ 1: 1
mm:th = mm:, nm + um = 1:, 1+ (1: rY)  et M: h = r: Ser+I
nn: hh = nn: mntin = 1:, er+ 1 et n: h = 1: srrti. Et fit
proinde Z= rGB+1)B: fitrr et v= . GB+ rVB,: Sit Ir.
itaque si curva Cc moveatur, et diverse ecudem in ea puncti situs
conferantur, fiet FGB + 1VB,: siter = (Y) (GB) + 1 B): Si + r)
et a 1GB+ rVB: sitrr = 1 (GB) + (Y) (B): Si+Y). Ergo
FGB+ 1VB, Sia r)
C Bs+ 1). sirn
est cnstans. et GB+ rV3, 1+ () est constans
GB + (V B3) FIt rr 7
Ergo t unum multiplicando per alterum inversum, fiet
1GBF YG6. + 173, 1(GB) + () (2.β,
constans seu fiet deniu
quatuor ret (Y) et,
(r+ V B: 50 8, 1+ B). GB)1)  subi to occurrunt: est B. 58, et
1t AA CB)
1 + 8Y3: 50Y (Y 1 P]: (60)
M
 et _1(). 13B)

## Folio 102v — 00068197:0204
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 103r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000204.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 18 lines, status machine
sit  aequatio 1X y = dy: dx. fiatsa fint dy: dx = e Ergo fiet
(Itao
B3tio) e = E. 2 quae est aequatio ad curvas infinitas, ordinatim datas, variantes
secundum e parametrum mutabilem. Mutemus sed ponamus jam aeg. 1.
simplicissine
fuisse factam ex transformatae datae habentis  et co, pro e ponendo
 et co explicando arbitrarie per X et y, quod fieri poterit, si sit
A si fiat D = 10X + 21y, :, 10X + 20y et c0 = 31X + 41, :, 30x + 40y
Hhoc modo jam efficiamus secundum aquationem paginae praecedentis, ut
C
fiat curvae diversae sint congruae, seu diversa vestigia ejusdem.
Eadem res inverso modo tentari poterit in curva
data ubi relatio inter Z et V secundum paginam
praecedentem subsistuanturque valores ipsarum Z et v, secundum
paginam praecedentem, et quidem bis;  videndum
an possibile sit effici, ut aequatio sic sriens inter X et y, pro uno situ
sita ab ea quo eritur similis plane sit ei quae oritur pro alio situ
mico tantum numero differente. quod

## Folio 103r — 00068197:0205
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 102v); this page is its right half.
# No recognised text on this page (recognized).

## Folio 103v — 00068197:0206
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 102r); this page is its left half.
# No recognised text on this page (recognized).