# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/779785487:0485
# Permalink to this reading: https://leibnizlegible.com/page/779785487:0485?run=74
# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 427, page id 779785487:0485
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=779785487&page=485
# Source image: https://digitale-sammlungen.gwlb.de/content/779785487/jpgs/default/00000485.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 90 lines, status machine
# Lines: 90 recognised, mean confidence 0.90
# 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.

F18. 4
in
L. 1B. II. DE ALTERATIOHE.
PEOP. ZCLI.
Ia diuidi posest radius, et lumi-
na proeressionem arihimericam se-
guantur: Sic enimm radius NT; di-
nidatur in S, ita; re quadrarum
SN, sic ad quadearum PNI, VE 1.
ad 2. cum in R, ita ve quadrarum
RN, sic ad quadracum TH, vcL.
2d 3. cum in l. ita requadracum
PN, sic ad quadracum TN, vEr.
ad 4. tum in O, ica ve quadiatu
ON, sic ad quadracum INI, VE 1.
2d5. Xc. ceree lumen in T clt 1.
in S, 2. In R, 3. In P, 4. in O, 5.
vides progressionem arichmeriea
Smplicem.
PROP. ZC III.
In nostra hypothesi quancumlibet
dividatur radius, in iisdem punctis,
idem lumen est, secus in proeressio-
ne ceometrica dupla; Sic enim V. 8.
18. 3. radius AB, dinilus bitariam in 6.
in C lumen eAt rx 4. curmr diuida-
tur in quatuor parres aequales, hoc
est quodliber seomentum bitariam,
aequalicer, in HI, e in I, in C
luinen adhuc ek ve 4. in II, vE 16.
in l, vt 1. =. deinde dividatur ad-
huc quodliber legmentum bifariam
aequalicer, in N, M, L, R; lumen
in C, est semper ve 4. In FL, YE16.
in I, veI =. vides, Cemper eamdem
elle progressionem luminis, idem-
que lumen in lingulis punctis,
quancumliber radius dimidatur: aE
vero in progressione geomerrica
dupla, secus accidic, siE enim ra-
dius CD, divilus in octo legmen-
ea aequalia. sirque progressio lumi-
nis in Ccgmentorum lerie, 1. 2. 4.
8. 16. eEc. certe a dinidas vlcerias
(CGIENFADV, VT, FS, RLC. HOn
Ceruarur amplius praedicta prosret.
sio, v. 8. accipe seementum DV.
a dinide bitariam in Z; Cerré (
in Z, lumen est ve 2. in V erit vt
4. ve seruetur peatara progrestio;
sed iam in V Cupponitur cslc vE 2.
S vero lumen in V SIC CeIMPeF VE 2.
IDieUE IN Z nON CPIE VE 2. neC VET.
ioicur in his punctis D, Z. V lumen
non dittunditur iuxta progressio-
nem geomerricam duplam.
PROP. Z CIV.
Si assumatur conus luminis; cum
bast rectilinea, insimeulis basis pun-
ctis, lnmen aque intensum non est:
Sit enim conus luminis ABF, cum Fi8. 5.
balirectilinca, cuius diamerer (IE
recta BF; dico in punctis D, C, B,
lumen aeque incentum non esté,
quia B longius distat a Centro
SphaerX A, quam C; X C, quam
D, re pacee; igirur in D, plus
est luminis, quam in C; e in C,
quam in B, ve paret ex dictis: hinc
in cenero baHS, plus est luminis;
nempe proxime omnium, ad cen-
rrum accedit; minus vero in ipla
Peripheria balis; hinc in lingulis
punctis praetara peripheria, lumen
aeque incensum est; quia lingula
aeque distant a CCMErO A; icem si in
eadem bali alii minores circuli de-
Feribantur. eodem duMFAZAE CeMLIO
D. in lingulis peripheriae punctis,
lumen aeque incensum exit; FLinC
in lingulis punctis Cemidiamerri
Bats DB, diverla est luminis in-
rensio; quia diuerta est à CCMEIO
A diltantia.
PROP. AC
Definiri possunt raliones iba
num in sinculis punctis: V. 8. (InE
puncta DB; dico lumina esse in
duplicaca DA. B A. permucando; AIF
TIIh 2 enim