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# Piece: https://leibnizlegible.com/api/records/40838/text
# Catalogue record: 40838 — Umbilici seu foci
# Incipit: Sit Regula AR mobilis circa A et filum ARCF ex A exiens et regulam cir
# Date: 1678
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=40838&katnr=39672
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 148–149 (from the shelfmark LH 35, 12, 2 Bl. 148-149): 4 pages, canvases 295–298, page ids 00068195:0295 to 00068195:0298
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=295
# Lines: 94 recognised on 3 of 4 pages, mean confidence 0.92
# 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 148r — 00068195:0295
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 149v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000295.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 42 lines, status machine
umbilici seu foci
sit Regularig ARmobilis circa A. et filum ARCF
ex A exiens et regulam circumiens atq ind usque in C inde
reflexum in F paxillum. Mam tenentur ac vel stylo
alum regulae applicetur interea dum regula circumrotatur
linea filo desciplo A, lo descripta cD erit Hy perbola
si punctum  paxillus F manea immotus. Si vero idem
interea procedat, moveaturque in recta AF producta alia
quaecunque curva pro vario motu (ipsius F recto in comparatione
ad motum ipsius AR circularem, produici poterit. Semper autem
ai notaodum est uno moto, altenum ita Unde patest tres esse motus
unum paxilli  alterum rectum alterum regulae AR circularem
tertium Manus vel stili, quo id solum efficitur, ut filum semper maneat
tensum. ipsum scilidet ad regulam applecaudo quantum ud hoc satis
Porro utcunque id fiut semper recta PC. bisecans.
angulum FCR. erit perpendicularis ad curvam.
bonatur enim catera constare ex Membrillis indes utcunque parvis.
M promoveatu Ex his membrillis unum quod curvam attingit sive pro chorda
surpatur
ejus utcunque parva haberi potest. Huus unum punctum immobiliterfigatur altem
totum filum
circumagatur quantum satis est, ut procedentibus AR, et F
sattersum. motu (praescripto, filum sit tensum jam alterum
membrilli punctum, quod ipsi cum sequenti Membrillo commune est etram
sfigatur (liberato priore,) et circumagatur alterum nembrillum donec
procedentibus interim AR et F uti debent, filum iterum sit tensum.
sed hoc utfiat. Atque ita fiat iserum cum membrillo tertio et quarto
patet ipsa membrilea fore chordas cuqvae iutcunque parvas patet
perpendicularis sit ad curvam
etiam quod recta ad meubrillum
denique ea
peripendicularis. Porro salva tensione fili se
magnitudo membrillosum, ut semper contingat tentione
2
esse aequales Eigo
C
membrillum C(C) sit indefinite parvum, recta pe, vel
dC
vel P(C) nam coincidit; angulum FC A vel AC) A nam idem est
bifecabit. Unde patet tum caetera omnia sint determinata
necessario et membrillorum seu chordularum magnitudinem fuisse
e

## Folio 148v — 00068195:0296
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 149r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000296.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
determinandam. Hoc tamen ad huc examinandum accuratio
an scilicet alias alia proditura fuisset, curva, positis mem
bullis aequalibus vel alterius proportionis. Ita videtur
e
-
cer
Et tmen
 semper maneret differentia inter FC et AC constans, ve et
s
puncto F. A. loca sint data non ideo datum erit Triangulum A
in
nisi simul dentur forte adhua angulus C.  A tn
ane quando per totam curvam AF semper eadem est tunc
utique curva est locus omnium C ad eaudem F. sed si ipsa
distantia AF variatur, video nihil determinari huiberi nisi hoc
issum adjicias quomodo debeat esse anguus, sed aliud
suippiam
imo Video totam membrillorum considlrationem non recte
cotrocedere Nam non potest puncto A c(C) extendi
in rectam manente altentro puncto vel (C) immoto
sic meliqus: sit n triangulum A5F datum, sumtis
15 et 25  2 in f25 et 1 in ACF ut sint 15 et 25
aequales infinite pa vae, erit tiangulum 152 isa sceles
et perpendiculans ad 12 angulum 5 bisecabit.
jam per dotum punctum 2 trajiciatur F26 talis, ut
sit
A + F6 aequ. A5 + FF patet triamguerum A6F
esse datum obdatam basiu AF summatur laterns A6 + F6
et angulum 2F A vel bFA. sumatur similiter 26 aequ 26.
jungatur 22 et ita porro 34 inveniatur erunt 2. 27. 34.
phordae ipsius erva in finite parvae, ipsis (1. 2. 3. 4. sumlis pro
ego sinite parvo
distant ab ipsis 5. 6.7. augulum m bisecantes rectae
ecunt perpendiculares ad Mordas adeoque et ad curvam
dem est de differentris
Idem est c essi promediatur exempli
gralia F vel A, vel utrumque datis enim locis ipsorm A. F.
et ob punctum 2. datum dabitur semper angulus F adeaque est
triangulum. Examinandum tamen an non liceat ljo
modo puncta in venire: ut si chordam hucamus non 12. sed 18 angulum 215 bisccando

## Folio 149r — 00068195:0297
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 148v); this page is its right half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000297.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 12 lines, status machine
et per 8 Frajiciamus F8 producenda, utfieri possit
et cum et procedamus ut cum I. sed tunc videndum an non
chorda sequens in tantum iferum descendat in quantum alferrasta
ascendit quia siliret sine ratione aliquid stunsimius, seu an non
contragat, ut dude perpendiculares segetecent in distantia infinite parva
curvae
a curva , tunc enim duo pundta 1g. Vassum. possunt omisso puncto 8;
jumgantum
et juncta facient chordam. Videndium et si 5.6.
seu choroae suit 56. 67. 78. an verbi gratia perpendicntar
ad 56 bisecet angulum A2F
latus triangali

## Folio 149v — 00068195:0298
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 148r); this page is its left half.
# No recognised text on this page (recognized).