# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1677894601:0368
# Permalink to this reading: https://leibnizlegible.com/page/1677894601:0368?run=74
# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 176, page id 1677894601:0368
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1677894601&page=368
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000368.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 22 lines, status machine
# Lines: 22 recognised, mean confidence 0.76
# 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.

F
PROP. III. YHE OR. I.
Si prO abSCICa A B CE aFCa A F, PCU ABKF PFOA
milcue scribatur Z, ∞ (i pFO C -  frn + 872n -) - h23n.  XC.
seribatur R: EE autem aTCA CUEVa 2BR erit.
ordinatim applicata BC =
D
en + D
+ 0
C + an Ec. + 2anB + 3an hE. 3n + _C. IR Z. B. 2 R a. 1
Demonstratio.
Nam sI sIt 2BRN = V, erit Per PFOP. 1, D7ZRA
=AZRR~ =V. PrO Ra in primo aequationis ter-
mino e 2 in secundo seribe RR~1 _ 27 e fet
D2R  a2.R in 23 + R., =V. Frat autem R = c  - F2n
523n-] - H23n _c. _ inde per PFOD. T. fit R =
Fx7- 2n87722 ) entr223r  ) Xc. Quibus substitu
tis e scripta BF. seu L prO 2y Aet
et
( (2, 8c B t23n f RC. In 2D R ~1 = v = BC.
2. F. D.
PROP.