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# Piece: https://leibnizlegible.com/api/records/468/text
# Catalogue record: 468 — [Aufz. zur Zentripetalbewegung]
# Incipit: pro curva sumatur linea polygona, cujus duo latera, AB, BC. ponamus
# Date: 1702-05-05
# Akademie-Ausgabe: AA VIII (assigned, not yet published)
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=468&katnr=58045
# Work: https://leibnizlegible.com/work/00068124
# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folios: Bl. 25r (from the shelfmark LH 35, 8, 30 Bl. 25r°): 1 page, canvas 49, page ids 00068124:0049 to 00068124:0049
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068124&page=49
# Lines: 79 recognised on 1 of 1 pages, mean confidence 0.82
# 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 25r — 00068124:0049
# Source image: https://digitale-sammlungen.gwlb.de/content/00068124/jpgs/default/00000049.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 79 lines, status machine
Ergoisiet
pro curva sumatur pagga linea polygona, cujus
duo latera, AB BC. ponamus mobile percurrisse rectam AB
celeritate uniformi et directione AB, et si nihil impediat
eodem tempore percursuram esse lineam Bd ipsi AB, aequalem
et in directum jacentem sed attractione contrali ut BE tenden
versus punctum F, situm in recta B BF, ita ut BE sit
aequalis parallela et easdem partes ipsi de. Investigemius
magnitudinem ipsius BC, ex curvae natura determinata
pe datalue BC tek rationem  jungatur FA, et
imittatur perpendicularis CG ex C in FB et BH ex B in F
datur CG. GB per FB.
quaeritur EG; eo enim detruct
a BG, habetur BE. Triangulum EGC congruit triangulo BIA
ad hoc ergo transeamus FA in BH = AI in FR, Eru, est LpA FB
Erg si FA. BH. FB = IB AV AI Ergo IB= AB
A eu c Ct
d
V
V
2
 sed GC = A
BC FBG7d. 8
seu AB
BC
sed BE = BG
E diBGn (ABqu BCqu + BGqu.) d seu
+ BG. Ergo
EG. ex
m Begu. ABgu  equ = 2 BE. BG( + B Gqu) = B AB A B qu.= BCqu (+ BGqu)
et
dbu et
et trejecto BEgu.  et destructo BCqu. utrobius reectoque BEqu. ut
Begu): 2BG sit
BCdZ
u
caeteris incomparabili, fiet B BE=
et FB sit X ert BGdx et. it d(BCqu) = 2b ddZ  adeoque tandem
dz ddz: 2dx. tandemque B5
ad idaze
e
ut dZ seu BC ad dx seu p
exit Ba t 0 C rar tdu nu B. F  arver i
Hinc si Nipla FC, FB, FC metr Hac ausem intelligenda sunt
 ectorum ext
temporibus, id est arciprum elementis FBC  id est arecs niformit
1.
ciescentibos seu arearum elementis FBC semper positis aequalibus
Notabile autem est ipsas BG BE etiam esse Elementa ipsarum BF, veto
seu attractionum impressiones esse elementa velocitatum centrifugarum
paracentricarum seu BE esse dax. jam crescentibus
ut adeo dici possit esse dxdxdd (+d dZ ddZ seu + =dx ddx + Zd7 daz = 0
unde dxdx + d7dZ = dcodcolitaque summa quadratorum a BC et a BG est
constant seu arris etementarisd est rectangulis ex FB in CG proportionalis. Ex
nis quoque natet necessario  apcabus crescentibus, seu du positis affirmativis
etiam e et simul crestentibus arcuum elementis, decrescentibus vero X, crescere
ipses dx vel xe positis altirmativis et decrescentibus pocuum etementis
vel arcubus decrescentibus, simulus eam in crescendo esse habitudinem, gisorm
dx ddx d2, ad ne quo casutiat ax ddx = az ddque, alioqui enim
differentia ipsorum dudque et dxax, seu Gequ. foret constans quod fieri non potest
nisi cum. FB sconst seu X est constans ut in casu circuli, ubi dx est incompar
acomparable avec du, et ec  revient à BC oparablement au dessons de BC)
incomparabibiter minor ipsa aZ, et GC coincidit cum BC aequivalet ipsi BC seu abibim BC
25 Si ergo Curva ABC sit ipse circulus ejusque centrum F. latera e polygoni infictimnenli circulo
Circum seripti sunt insclipti sunt AB; BC ergo recta BF radius, bisecat angulum ABC, adeoque et chaedu
jam
e
atu AC in G angulis recto, ergo G incidit in punctum bisectioni
B in G angueo recto, cumque BG, DC sint parallela
eq occurvit ipsi
eo
cBE dupla
etit et C ipeilis B7
LBEBC BCuAt
FC- FB
seu
bec
2BCBCq
aet