# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1677894601:0323
# Permalink to this reading: https://leibnizlegible.com/page/1677894601:0323?run=74
# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 143, page id 1677894601:0323
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1677894601&page=323
# Source image: https://digitale-sammlungen.gwlb.de/content/1677894601/jpgs/default/00000323.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.92
# 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.

L
ctum contactus in intinitum abit. Nam haec rectu
in eandem plasam cum crure infinito dirisitur.
Lineae omnes Ordinis primi, tertui, quinti, sep.
cimi ex imparis cujusq; duo habent ad minimum varum omnoim
crura in intinitum vertus plasas oppolitas PrOSre seneris secundi ad
dientia. Et lineae omnes tertii Ordinis duo habent equationum casus
quatuor. Casus
ejulmodi crura in plasas oppoltas prosredientia in primus.
quas nulla alia earum crura insinita (Praeterguam
in Parabola Carteliana) tendunt. Si crura illa
sint Hyperbolici generis, st GAS eorum AIrmp-
totos e huic parallela agatur recta quaeris C. BC
ad Curvam utrinque (E tieri Potest) terminata
eademq; bilecetur in puncto Z, et locus puncti il. Fis. Lo
lius X erit FIrperbola Conica (puta X 8) cujus
una AIymptotOS eA AS. Sit ejus altera ACymp-
Eotos AB, X aequatio qua relatio inter Ordinatam
BC. e AbsCissam AB detinitur, S AB dicatuE Z 8
BC. y, Temper induet hanc formam XV yY L Cy = 2X
FbXX  CX. ] d. Ubi termini C, a, b, C, d, delig-
nant quantitates datas cum signis luis ) et afte-
ctas, quarum quaelibet deesse postunt modo ex carum
defectu figura in sectionem conicam non vertatur.
Potest autem FIyberbola illa Conica cum alrmpto-
tis suis coincidere, id est punctum X in recta AB
locari: e tunc terminus.  Cy decst.
Ath recta illa C. BC non potestutrinq; ad C urvam
terminari led Currae in unico tantum puncto occur-
rit: dee quamris positione datam rectam A B alrmp-
Eoto AS occurrentem in A, ut Xc aliam quamvis BC.
ymptoto illi parallelam Curraeque Occurrentem II
puncto C e aequatio qua relatio inter Ordinatam
BC
VIII.
Reductio Cur-
l.X.
Casus secunduia.