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# Piece: https://leibnizlegible.com/api/records/28238/text
# Catalogue record: 28238 — Divisio instrumentorum per Transversales
# Incipit: Divisio instrumenti subtilis haberi potest
# Date: 1685
# Akademie-Ausgabe: AA VIII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=28238&katnr=41000
# Work: https://leibnizlegible.com/work/00067980
# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 18
# Folios: Bl. 16 (from the shelfmark LH 35, 1, 18 Bl. 16): 2 pages, canvases 31–32, page ids 00067980:0031 to 00067980:0032
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067980&page=31
# Lines: 96 recognised on 2 of 2 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.
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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 16r — 00067980:0031
# Source image: https://digitale-sammlungen.gwlb.de/content/00067980/jpgs/default/00000031.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 52 lines, status machine
Divisio instrumento rumm per transversale
divisio instrumentu subtilis haberi potest vel
quo
notas cochlensque mu videatur Hevelus
machina coelestis, vel per alam regulae affixem
regulae mobili sive cursori et paulo aliter quam
instrumentum divisam cujus divisiones tam encerta
latione divisionibus instrumenti coincidunt, (:quale
quid (lavius ded dedit, et quidam Burgundus
libro peculiari proceditus aeque in circuliac rectae
devisionibus: ) vel denique per linusversales, sed
ec ut vulgo asurpari solent in rectamin tantum
divisiore locum habent, epento 
applicantur. e cum tamen erpuididunti ratio sit
simplicissima nec quicquam Maeter simplex orgam planem
requirat cogitavi, an incommodo mederi liceret
a
et quidem transversalis non dividitur aequaliter
ut nec limbus licet arcus aequaliter
dividantur,
patet enim in
fig. 1. licet si
ab arcus ab.
bc, cd, de sint
aequales tamen
portiones rectae trans-
versalis e f nempe 54 9h.
le
hk He non esse posse aequale
Sed trescere quo magis accerunt
versus cireul enteriorum
imbi circulum exteriorem
Quoniam Tamen
transversale
tt
in fig. 2 patet
en longiorem esse quam arcum
ma ac proinde facilius dicudi
imo aeque facile acarcum
longe majorem pG. Hinc P
instrumentum parvum,
cujuscentran A radius
accurate dividi debeas
en circulus
M. aeque
divisor
ac rota
qua opifices a
 major thei peribe)  culius rabius
utuntur qua
 instrumentum
sit Ap. petet id fieri posse

## Folio 16v — 00067980:0032
# Source image: https://digitale-sammlungen.gwlb.de/content/00067980/jpgs/default/00000032.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 44 lines, status machine
dividendum cujus portio AM N rotae divisoriae
cuius portio ApG probe applicetur et per
rotae divi ducta linusversali ml per rotu
divisoriae divisiones, ut S. ducendo cursorem
seu regulam AR et notando ubi A
es
sect, regula A (R secet transversalem
espondentra m  in transver salibus
punctis s seu divisionibus angulorum in
nota divisoria majori respondentes
et habita semel a una tran sver sali
ul debite divisa ad ejus instar
si quis per puncta + centro A radio
 circulos totidem describere
velit eadem opera omnes transversales
2
m habebimus puncta divisiomu angulorum
ne
poterunt dividi aliae omnes, et
ut X7 eodem modo dividentur ut m
ed Cateum
obiter notari meretur, si quis velet
rectas dk, ch, b9 of aequaliter cruscere
seu proportionaliter arcabus ed ec eb, eo
necta tunc linea ekhGf non foret
recta sed sprralis Archimedis, quae continuata
tantum perveniret in centrum A.
Sed
posito ef esse realam radii Af, Ag, Ah, AK, AC
non Arithmetica, sed alia progressione quadam singulari
crescunt, quae haber quidem potest et a me alici
est determinata, sed operosior, quam ut huc transferi
cabculo 
hic poni, et ripiaxintransferrimereatur
cum prom
tior longe constructio sit adhibita rota divisoria majer
ut paulo ante explicui quod si illa careamus, adhiberi
poterit curjor alatus supradictus saetem ad effectum
dividendae semel transversalis. Denique si nihil  nullum
arsit onstrumentum exquitum, tunc fatect ad
calintum illum licet paulo operosiorem deveniendum
fore, quem tamem adhibitis sinuum Tabulis expeditus
lliquis intra duas horas peragere in falla
possi