# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068531:0224
# Permalink to this reading: https://leibnizlegible.com/page/00068531:0224?run=74
# Title: Leibniz-Handschriften zur Optik und Dioptrik LH 37, 2
# Folio 112v, page id 00068531:0224
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 111r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068531&page=224
# Source image: https://digitale-sammlungen.gwlb.de/content/00068531/jpgs/default/00000224.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 71 lines, status machine
# Lines: 71 recognised, mean confidence 0.84
# 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.

seu Ad BE
ponatur XF, y. fiet. CZ  C, ZV,, e+ h, e h
rit G et h, c-h
Sit ADe d BEB f
erit ECe c- Z.
DBHkZ D WC c.
et fiet: d +Z B AB H e.
et f2+ C + Z-2cZ BCph.
quae debet esse minima
fet t (d +G + c5C+Z nZomnium possibilium
minima: erit ponatur 
M
nn
N
n
sitque curva cujus ordinata B absust e M sit y. et absis
DB sit Z. Quaeritur ileut punctum M in quo minima
haec sit
est curvae lalitudo, seu ut sit BM omnium aliarum
minima. Patet tangensem in M. fore axi parallelum,
adeoque fore dus 10. est autem dus.
Est autem dus
2tZ, W0, (Z- tc
LLat XYf +C+ Z 202
fiet. Ve 5C+L= 2Z
d12
r seu
S52CF  - 21Z 10, Bc.7
id
 1o 7+ C- 2C3
P
Cl
f222
id est Bevs BC debet esse ad A BA, in composita ratione ex EC ad DB
et ex 2 ad T.
Producatur BC in F ut fiat BF aequ. BA. et per
F ducta FGparallela CE producatur BE dum ei occurrat in G.
erit FB seu AB: CB:: F G: EC. at spra
at paulo ante AB: CB:: BD in T: EC im -2
Ergo FG: EC:: Bd in T: EC in -2. et FG: Bd:: BZ
refractionis
erit ad
Rteuti
i
Bd Sinum anguli incidentiae in reciproca ratione densitatis mediorum, id est
incidens in medium rarius ideoque at radius incidens in medium densius
esin
incidens in medium rarius reflectitur perpendiculari, simu aucto.
Brevius sic concludemus: ex superioribus: AB: BF: : io compos. ex Bd: FG1t
et T. 2
est autem ratio  AB: BF aequalitatis, ex constructione, ergo composita
ratio ex BD: FG et T: u est ratio aequalitatis, Ergo ratio Bd: FG est
rationis T.  reciprioca, seu BD: FG2: 2.F sive sinus angulorum sunt in
ratione reciproca resistentiae mediorum.
e
Fper meam
methodum
tangentium
imo videq id non
licere sic enim
mroblema jam
heterminamue
ieque amplius datis
punctis ob. C
in potestate est
Quaerere B.
datur intersectione
circulorous ex centris
C et A
radis
CB. Ap descudsitom