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# Piece: https://leibnizlegible.com/api/records/42680/text
# Catalogue record: 42680 — [Math. Aufz.]
# Incipit: Radii paralleli DF ab arcu circuli EF centro A descripti forment linea
# Date: 1680
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=42680&katnr=39567
# Work: https://leibnizlegible.com/work/00068195
# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folios: Bl. 19 (from the shelfmark LH 35, 12, 2 Bl. 19): 2 pages, canvases 37–38, page ids 00068195:0037 to 00068195:0038
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=37
# Lines: 65 recognised on 2 of 2 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.
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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 19r — 00068195:0037
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000037.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 64 lines, status machine
corpo Globus A, tendens linea 1A2A,  2A, mcrit in globum B
quiescentem B, quaeritur locu3A et locus 3B, qua perve ubi post
ictum erunt AB, tempore aequali eodem quo ante ictum A venit
ab 1A ad 2A,
sit centrum gravitatis commune D
id post ictum id initio sit in , C, momento ictus sit in y2C,
tandem post ictum eodem tempore perveniat in 3C, utique
1C, 2C, 3C, sunt in directum, et cadent in eandem rectam, et
1C2C = 2C3C. Aursus corpus B quiescens ibit in recta 2C12B
l
cujus daretur quantitas, etiam Eaetera darentur. Assumatur
 queatr prona. Haec ita assumi debet
quoniam Nam jungatur 3B3C, et continuetur erit 3A in
recta 3B3C, praeterea 3A, erit ad 3B 3B3C, ut B ad A,
seu 1AIC ad 12BAC. itaque habebitur ipsum punctum 3A,
sed oportet esse qu (12B3B) + qu (A3A) = qu. 1A2A
Hinc determinabitur recta 11B2B
si globi forent aequales caderet 2C in punctum
contactus, nunc cadit citra
Radii paralleli DF ab arcu circuliquee
centro A descripti forment lineam
Causticam C. (C).
Ex C ad axem AE normalis sit C B,
et AB, X, BC, y quaeritur aequatio
exprimens naturam curvae C 1C)
Ex puncto F in AE sit normalis FG. AG sit Z
et FG sit V et AF a. Aequales sunt anguli DFA, et CFA
seu FAE et CF(. Ergo BF = BA producatur
FC  eA ut ipsi AE occurrat in H. Erunt aequals
ob Triangulum _HFA angulos in F et A habens
aliu
sed nos quaramus rationem HG ad FG. estante
23+ v0 a a
quaentur HG: GF, Est ant G, V
ergo quaeritur HG. HG = FB HP FG2 seu HC - v2
quaeantur ae HF = R H. ducatur ad AF nermalis HK
ob Triangula H AK H et AGF similia erit
AK HH; AH:.  a F
KH AK  (Za): AH : AG (Z): AF (a)
fit Ergo RH = CC_ ad : 2Z et HG = 227 - aa;
et HG: FG = 2ZZ- a4,: z0.
jam faciamus
ut etiam x et y calculum ingrediatur nempe AB est
Ergo HB est X = aa : 2Z jam HB: Beseuus ut HG: GF
ergo fit 247 au V = 2ZX = aa, B: 62y = 27Z- aa: (2V
seu fit 2ZXV - aav = 223X - aa y
Et praeterea
est gy+ vv aa ex his aequationibus, potest solvi
Accedente utriusque differentia
X et y considerantur ut determanata
poblenta; Acceden
indifferentiabiles. Ex 1 fit differentrando, 2X ylo + 2xvdZue-aadv =
ubi
unde tollendo dii
et ex 2 fit Adque + vdv =0
 ae ponatur Z et puo, que ponatur V
tione
fiet  = 2XZZ + 2X WV + aa Z = 4XZ y. etsit v = 2Xaa tZua  
Ex 1fl v = 222X
X -aa
4 XZ1Z
ex gela fiet ag. nova sisae.
Exad 
ope horm hiam ipsius  valorum facile tollitur 2

## Folio 19v — 00068195:0038
# Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000038.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
ounorai crone