# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1040780814:0111
# Permalink to this reading: https://leibnizlegible.com/page/1040780814:0111?run=74
# Title: [Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa (shelfmark Leibn. Marg. 124)
# Folio 93, page id 1040780814:0111
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1040780814&page=111
# Source image: https://digitale-sammlungen.gwlb.de/content/1040780814/jpgs/default/00000111.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 77 lines, status machine
# Lines: 77 recognised, mean confidence 0.85
# 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: the recognised lines in reading order, one per line.

Cis
latIVa
rUTA.
ItUI
et it
ectusIu
n ex de
liS velo
ta IP
lel
ite
ib Bui
eriodica
Bhan
tatat
a aVeM
stuiat
intel
uIOrUI
per C1
OIMOBC
UIII
10 Orb
UIX
atio
ratio 
c
L. ID. 1.
SE CEROMETRLCA E, L EMEN PA.
LXXIT.) disterentia motuum angularium sunt ut translationes di
recte, e distantix a motus centro inverse: Ft isitur dicta differen-
tix motuum ansularium orbium concentricorum sunt reciprOCC
ut quadrata distantiarum à centro, e reciproce ut distantia à cen-
tro conjunetim; hoc cA, reciproce ut cubi distantiarum a centro.
Frgo, si ex omnibus punetis rectae 52 ex contro educta, ubi super-
ticies contisua orbium concentricorum illam secant, (nempC A, B,
C, D, CC.) erisantur ad S2 normales Aa, BB, cc, Dd, cubis iplarum
SA, SB, SC, SD, CC. reciproce proportionales; crunt ha ordinata
respectire ut praedicta difterentia motuum angularium respectiro.
rum orbium concentricorum, ex summa harum ordinatarum ut
summae dictarum differentiarum; hoc est, (cum orbis extimus seu
infinito disitus omnino non OvCatUL,) ut motus toti angulares.
Si jam crassitudo orbium minuatur in infinitum, (quomodo circum.
tulum medium catenus fir uniformiter Ruidum,) summa praedicta-
rum ordinatarum AenE atCX AZ a, BZB, CZC, DZ d, ec. Adeoque
IOtUS toti angulareS OrBIUM BFK, CCL, DMN, QEC. TUnE Ut aFeX
BZB, CZC, DZ d, _C. respectire. In Agura vero a2 a ordinata BB,
Cc, Dd _c. Sunt reciproce ut cubi rectarum SB, SC, 5D, dc. Vnde
(DET PFOP. LXXIIT.) areX BZB, CZC, DZ d, _c. Tunt inverse ut qua-
drata rectarum SB, SC, SD, ec. Ft ideo, motus angulares orbium
BFK, CGL, DMN, EC. sunt inverse ut quadcata suarum semidia-
MCETOrUIM SB, SC, SD, _C. Sed tempora periodica lunt motibus an
sularibus reciproce proportionalia: Frso tempora periodica orbi.
U BFK, CCL, DMN, SC. Sunt in ratione directa (quippe reciproca
inverlae) luarum distantiarum a Centros; nempe rectarum SB, SC,
SD, CcC. Adeoque patet provolicio, si medium sphaera circumtutum
constare intellisatur ex innumeris Tolidis orbibus tenuissimis con
centricis. Si vero dueta intellisantur infinita rectae quamplurima
continemtes cum axe ansulos aequalibus excessibus se mutuo super.
antes, ex his rectis circa axem rerolutis, e superticies conicas de-
feribentibus, concipiantur orbes in annulos innumeros lecti; annulus
unusguisque habebit annulos quatuor sibi contiguos, unum interio.
rem, alium exteriorem, e duos laterales, ex eodem orbe resectos.
Attritu interioris e exterioris nequit intermedius aliter moveri
quam prius ante sectos orbes: alioquin partes Auidi non persere-
rarent in motu suo uniformiter; sed medius ilte in motu luo acce
leraretur vel retardaretur, (ut prius de orbibus integris ostentum,
contra hypochelin. Pt proxterea annulorum series qualibet, à lo.
lida Sphaera centrali in infinitum recta persens, et inter duas Proxi
mas superticies conicas, comprehenta, movebitur codem prortus
modo quo ha ipsa morebantur anto diritionem orbium in annu.
105; niliquatenus quisque in hac serio annulus impeditur ab attritu
annulorum ad latera. FTic vero attritus nullus ell, quia annuli
omnes a media sphara Colida aequaliter distantes, (hoc eA, ex codem
orbe resecti,) eodem tempore revolruntur: Nam E hoc non fieret,
led qui versus polos citius ret cardius circuicus suos absolrerent,
quan