# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1677894601:0342
# Permalink to this reading: https://leibnizlegible.com/page/1677894601:0342?run=74
# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 162, page id 1677894601:0342
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1677894601&page=342
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000342.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 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.

Construi etiam postunt aequationes per HIyperbo-
lilmum Parabolae cum diametro. Ut h construenda
sit haec aequatio dimentionum novem termino penul-
timO CaTENS, d F CXX Y dX3. ] ex  FX 5X-] hX
=M
) kXS F IX =0; allumatur aequatio ad Ayperbolil-
mum illum ZXY = 1 _ Scribendo y PrO =, aequatio
construenda vertetur inhanc ay F CVY F dX yy ) CY
FFxY Y mXXγ. - 8. ] hX -] kXX ] IX3 =O, qua CUT-
vam secundi generis delignat cujus delcriptione
Problema Tolretur. Ft quantitatum m ac s alter-
utra hic deesse potest, vel pro lubitu assumi.
Per Parabolam cubicam d Curras tertii generis
construuntur etiam aequationes omnes dimentionum
non plusguam duodecim, et per eandem Parabolam
e curras quarti generis construuntur omnes dimen-
tonum non plusquam quindecim, Ft BC deinceps in
intinitum. Ft curvae illa tertii quarti d luperiorum
generum describi semper postunt inveniendo eorum
puncta per Creometriam planam. UE si construenda
AE aequatio ~ X ) a X 10-= BX-] CX ] dX ] Cx6] FX5
8X2 ] hx3 f ixX F kX Y 1=0, e descripta
hrabeatur Parabola Cubica; sc aequatio ad Pa-
rabolam illam cubicam X = y, a scribendo y
PTO X aequatio construenda vertetur in hanc
74-7 aX 53 =) CXXYY F FXXY - IXX =O, quae e
=dx
BX +KX
aequatio ad Curram tertii generis cujus descriptione
Problema solvetur. Deleribi autem potest haec Curra
inreniendo ejus puncta per Creometriam planam, prop
terea quod indeterminata quantitas x non nili ad
duas dimentiones ascendit.