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# Catalogue record: 379 — Data relatione inter Arcum et chordam seu radium, vel aliam ex coordinatis, datur solutio per quadraturas
# Incipit: Detur (in exemplum) relatio inter AC et EC, seu inter emissam et
# Date: 1692
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=379&katnr=57955
# Work: https://leibnizlegible.com/work/00068199
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folios: Bl. 105r (from the shelfmark LH 35, 13, 2c Bl. 105r°): 1 page, canvas 209, page ids 00068199:0209 to 00068199:0209
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068199&page=209
# Lines: 42 recognised on 1 of 1 pages, mean confidence 0.93
# 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 105r — 00068199:0209
# Source image: https://digitale-sammlungen.gwlb.de/content/00068199/jpgs/default/00000209.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
seu radium
 ata relatione inter. Arcum et chordam, vel aliam ex
coordinatis, vatur solutio per quadraturas
Detur i rela (in exemplum) relatio inter AB AC et EC, seu
seu inter radium et arcume emissam et arcum sit emissa e
areus etC sit c, et detur relatio inter C et C per aequationem
quaeritur curva. _Circulo centro A, radio quocunque AB describatur
arcol circuli arcus RMN, et per puncta C ) Mmissae exA,
occurrant arcui circulari in M, siatque duae sibi vicinae AC
Ex C in A(C) agatur normalis Cd erit CD ad M(M) ut AC ad AIs
RM vocetur m fi et AR a fint CD = ∞ dm. C: a et
C(C) seu de  de jam C (Gqu. = CDqu. + D(C) qu. Ergo
Data sit aeq. L)
fit de de = dmamee: aa  dede.
Unde differentiandos Dabitur
ex hibens relationem in ter c et e
3) valor ipsius dc: de per e nam differentiando Tolli potest C. Et pro de substi
ordinaria,
tuendo in aeq. 3. valorem ex aeg. 1. habebitur aeq. (8) in qua dabitur dui per
id est problema reductum est ad quadra
furas. Sed duplices. Nam inventa summa ipsius a dm, rursus decude
ex m du: de per e.
opus est dimensione arcus circuli, vel saltem descriptione lineae
sinuum aut similis ad ducendam hinc hinc punctum m, nam
absoluta quadratura habetur relatio inter AC et RM.
s aeg. L esset transcendens primi gradus seu differentialis
at 4+
ad sollendam C opus esset ire ad differentio differentiales. inde
∞y.
haberetur aeq. 4, in qua ami, dam, e, de dde, quod polest reduci
dedde = de
quod aequivalet
ad ordinariam problema, fangentium posito ad
inde enim colleudo e,  superest am, dam, de, dde,
inter curvam d emissam
ordinario laagentiam judersorum problematu.
seu radium vel chordam, locum etiam habet pro relatione inte
 relatione
aterum quod diximus
Ecurvam, et alteram coordinatarum vel aliam sunctionem
absolutam.
Nam secu est defanctionibus