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# Piece: https://leibnizlegible.com/api/records/60518/text
# Catalogue record: 60518 — [Bemerkungen zur Bestimmung spezieller Quadraturen mittels unendlicher Reihen]
# Incipit: Omnibus expensis ad Quadraturas speciales vel generales
# Date: 1686-04
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60518&katnr=57114
# Work: https://leibnizlegible.com/work/00068196
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folios: Bl. 216 (from the shelfmark LH 35, 13, 1 Bl. 216): 2 pages, canvases 427–428, page ids 00068196:0427 to 00068196:0428
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=427
# Lines: 39 recognised on 2 of 2 pages, mean confidence 0.97
# 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 216r — 00068196:0427
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000427.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 36 lines, status machine
Omnibus expensis ad
April. 1686.
Quadraturass speciales vel generales Algebraicas prout
possibile est inveniendas non puto rationem compendiosiorem, et, determinatiorem
trauscendente
dari, quam danc; ut data semel aequatione pro quantitate incognita
per seriem
investigemus prghessibte terminorum coefficientiam seu cognitarum terminos afficien
tium relationem inter se. Et deinde lacogni quancitatis Transcendentis quadralum
purum vel affectum quae rendo aut cubum,, quod rursus per seriem fit, iterum quaeratur
relatio terminorum ex se invicem, considereturque an ope hujus relationis effici
possit, ut quibusdam terminis deficientibus, alii omnes ultra quosdam limites
aequatio
positi deficiant in infinitum, atque ita quanlitas propsita fiat finita Eaque
methodus seriebus communis est, tum quae exprimunt ratramli
ordinatas indefinitas alicuius lineae, tum quae exprimunt quantitatem
determinatam. Et certe si possibile est dari quantitatem finitam
satisfacientem id utique debet posse demonstrari ex proposita serre-
omnis enim proprietas reciproca, qualis continetur, in aequatione
etiam
Et cum nelesse est sit.
per seriem, sufficit ad quamvis veritatem demonstrandam. Ego aequationem
oriri identicam si valor datus per seriem) secundum alicujus finitae aequationis
datu
egem atollatur; debet is identicismus ex natura serici demonstrari.
adeoque debet homogoneum comparationis tandem fieri quantitas finite
expressa. Quod ex terie ostendin si ex natura seriei ostenditur debet
ostendi posse optime ex eo quod terminorum seriri relationem inter se
e latione
exprimit, et hac enim necessario apparere debet, quinam termini possint
evanescere.
Hoc Methodus ideo placet quia  quadraturis
Servit etiam Melandi
algeoraicas
specialibus et generalibus communis est
tangentium inversae, si possibile est ad quodaturas revocandae

## Folio 216v — 00068196:0428
# Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000428.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 3 lines, status machine
DTTFRIED WILHELM LEIBNIZ BIBLIOTHEK
H35, 13, 1, (428] - 216V
NIEDERSACHSISLHE LANDESBIBLIOTHEK