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# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 154, page id 1677894601:0334
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fig. 60.
154
Si radices illae Tunt signi contrarii habetUE C On-
choidalis cum Parabola ad alteras partes ACYmptoti.
Duae species est quinquasetima sexta.
(Siquando in primo aequationum casu terminus
verbolismi tsyper Uterq; a X _ b X X deest, figura erit FIrperbolismus
sectionis alicujus Conicae. IIyperbolilinum Agurae
voco cujus Ordinata prodit applicando contentum (ub
Ordinata Rrura illius e recta data ad ABCcictam com-
munem. ITac ratione linea recta vertitur in hyper.
bolam Conicam, ex sectio omnis Conica vertitur in
aliquam tisurarum quas hic Fyperbolilmos sectio-
num Conicarum voco. Nam aequatio ad Aguras
de quibus asimus, nempe Xy y ] Cy = Cx F d, seu
=
et V cc + 4dX Y 4 CXX generatur appli-
cando contentum sub Ordinata sectionis Conicae
CtV ec F 4 dX F + CX X _ recta data m ad currarum
Abscissam communem X. Unde liquet quod figura
genita LEyperbolismus erit Iperbola, Fllipleos vet
Parabolae perinde ut terminus c Z aftirmatirus est
vel nesatirus vel nullus.
Typerbolimus Hlyperbolae tres habet alumptotos
quarum una est Ordinata prima ex principalis Ad,
alterae duae sunt parallelae ABICillae AB _ ab eadem
hinc inde aequaliter distant. In Ordinata principali
Ad cape Ad, A5 hinc inde aequales quantitati VC
et per puncta d ac s’agc d8, 8y Alymptotos AB.
Ccistae A B parallelas.
Ubi terminus ey non deest tigura nullam ha-
bet diametrum. In hoc casu E aequationis hujus
CXX ] dX ] CC =0 radices duae AP, Ap sunt reales
XX
Ouatuor TYy
bola