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# Piece: https://leibnizlegible.com/api/records/60698/text
# Catalogue record: 60698 — Calculus minuti secundi
# Incipit: Minutum secundum est pars peripheriae 129600_ma, reducenda est ad part
# Date: 1676-06-29
# Akademie-Ausgabe: AA VII,6 N. 033
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=60698&katnr=Cc2+1488%2Ftlw.
# AA VII,6: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-vii-6
# In the Akademie-Ausgabe: AA VII,6, p. 415 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/LAA-BdVII6.pdf#page=415
# Work: https://leibnizlegible.com/work/00068035
# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 17
# Folios: Bl. 6r (from the shelfmark LH 35, 5, 17 Bl. 6r°): 1 page, canvas 11, page ids 00068035:0011 to 00068035:0011
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068035&page=11
# Lines: 77 recognised on 1 of 1 pages, mean confidence 0.90
# 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 6r — 00068035:0011
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068035/jpgs/default/00000011.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 77 lines, status machine
ad eoque D (C) ad FC aequalis compositae ex CD ad AE, et Z ad 1. ergo
multu licutae per
multipticatia pent
DBC) ad FC
aequalis rati D Z ad AE,  C1. et quia D(C) est +d. FC est py AE est X.
CD est  aequal F() vel f. et Z est 2. 3. 4. 5 erit ratio
d ad y aequalis rationi 2f vel 3f vel 4f etc. ad X. cum supra
ostenderimus esse ajoem, quod est absurdum. absurdum ergo EC adcurvam tanga
pervenis
diver sam
Superest casus u reciprocarum  cum Z. V est - 1. seu cum
Alter est
V. major est quam Z:, sive cum ordinatae sunt in reciproca ratione c
potentiarum ab abscissis, e sset adeoque  Z - v a est - 1. et
F CZ est FC
C est autem F CL ida quod 
 Unde FC ad (F) (C) Z
est idem quod FC, ad (F) (C)
(+, quo sive idem
vel ac proinde  C idem quod  +, ad
 quantitatum
FC2: idem est quod N N B a idem est quod a 1) adeoque
omissa 1. in expuonente erput
FC ad (D (C)
L1
quod
idem ad id est reciproce
FC (F) (9)
ut (S) (C) ad FC ergo si sit Ergi erit cum differentia inter Z et v est 1. et D
sunt
est major quam 37C. t  F ad (F) (C) E Y ut positis FC. (F) (C) ordinata ex mrva C(1) in dire
sitque ex naturacuroa
dicectrice
et G F, G(F) abscisset ex ren in puncto fixo G incipientes; tunc
po si ex natura cuvae sint FC, ad (F) (C), 2n
idem erit ac si dicalu reciproce fore (F) (C) ad FC ut GFE ad G(F) Z
similiter
chicem GF (F) demissae
ut GF ad G(F) E
Hoc posito jam poo demonstrabo fore EF intervallum tangentis FC et
ordinatae EF in directrice sumtum ad GF abscissam, ut Z- v ad Z. id est
hoc loco ut - 1. ad Z. id est fore GF Zptam id est dus simptam, 2plam
tptam EF aequalem =1 GF. parem scilicet satem ipsi aequalem
aut partem ejus unicam, dupl dimidiam tertiam, etc sed ita tamen ut Cp
punctum E non sumatur vertus G, sed in eoutrariam purtem, ob signum negativum.
Hoc ergo si in reciprocis evicerimus, hoc quoque casu Theorema erit comprobatum.
 Minutum secundum est pars d peripheriae 129600ma reducenda e
ad partes decimales; posito radio.  vel 100000 Posit radio Eo casu peripheria
est 6628381. quanitur er 16628381
1296(00)  700000)
quaentur b
1117
628
leere
1296
fin G6 +162
1296
84 + 195
100,000
485 -
si fuciis 862 .
862 - 1 -
162
1296
Ergo minutum posito radio 100000 erit minutum secundum: 484862 - i - i
100000 etoba
484862 radi 215
8381 000 seu posito ratio 1. erit miuut. sec
60,000,C0,000 3 lachs radii ita
Utile est Tabulam ircuum Caliulari, secundum quam
expumatur eorio longitudo in relutione adradium
positum 100, 0vo; quod fanle potest hoc elementum tantu
moltipliando per numerum munitirum secandorum
72) 5
oeeu
S. enor non s minor quam
1294648