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# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 148, page id 1677894601:0328
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1677894601&page=328
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(.148
AGmptoton cum FIyperbola ansuinea circa ACymp
toton tertiam. Quae lpeciescnona.
Fit hi sunt omnes radicum casus possibiles. Nam
li duae radices sunt aequales inter le, e aliae duae lunt
etiam inter se equales, Figura cradet Sectio Conica
cum linea recta.
Si HIyperbola redundans habet unicam tantum
decim redundan- Siametrum sit ejus Diameter AbIcica AB, X aequa-
rescumunicaran CiOnis hujus a X3 ] bXX ) CX  d = O quaerE ETCS Ed-
dices Ceu valores X.
Si radices illa lunt omnes reales e ejusdem heni,
Figura constabit ex Ovali intra triangulum Dd s ja-
cente ex tribus Iyperbolis adt angulos ejus, nempe
circum seripta ad angulum D X inseriptis duabus act
ansulos d X o. Et haec est species decima.
Si radices duae majores lunt aequales a tertia ejur-
dem signi, crura IIyperbolae jacentis rerlus D sele
decultabunt in Forma NVodi propter contactum Ova-
lis. Duae Species est undecima.
Si tres radices lunt aequales, TIyperbola ilta sit
cuspidata sine Ovali. Ouae Species est duodecima.
Si radices duxe minores Cunt aequales e tertia ejus-
dem tgni, Oralis in punctum eranuit. Ouae species
est decima tertia. In speciebus quatuor novissimis
Ayperbola quae jacet verlus D Alymptotos in sinu
uo amplectitur, reliqua duae in linu AIYmPtOLOM
Jacent.
Si duae exradicibus sunt impolsibileshabebunturtres
EErperbola purae linc Orali decustatione vel cuspide.
fit hujus casus species Tunt quatuor, nempe decima
quarta si Fyperbola circumleripta jacet vertus D a
decima
yperbolae duo-
tum Diametro.
Fic. 20.
ut