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# Title: Opticks: Or, A Treatise Of The Reflexions, Refractions, Inflexions and Colours Of Light (shelfmark Leibn. Marg. 193)
# Folio 144, page id 1677894601:0324
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1677894601&page=324
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144.
BC e ABIcissam AB detinitur, Temmper induet hanc
FOTIAM XY = aX-) DXZ F CX-F d.
Ouod si crura illa opposita Parabolici sint generis
recta C. B C ad Curram utrinque, E Heri potest, ter-
minata in plagam crurum ducatur a bilecetur in B,
et locus puncti B erit linea recta. Sit ista AB, ter
minata ad datum quodris punctum A, e sequatio
qua relatio inter Ordinatam BC. X AbIcisam AB
detinitur, semper induet hanc Formam, Yy = aX
FDXX + CX ] d.
At vero E recta ilta C. B C in unico tantum puncto
occurrat C urrae, ideoq; ad Curram utrinq; terminari
non postit: sit punctum illud C, X incidat recta illa
ad punctum B in rectam quamris aliam positione
datam X ad datum quodris punctum A terminatam
AB: X aequatio qua relatio inter Ordinatam BC. 8
ABICilam AC detinitur semper induet hanc Forma,
Y = 4X3. ] bZX- ] CX Y d.
Finumerando curras horum casuum, IIyperbolam
vocabimus inscriptam quae tota jacet in Alimptoton
angulo ad instar Arperbolae conicae, circumscriptam
quae Alymptotos secat X partes abscictas in Cinu (uo
amplectitur, ambieenam quae uno crure infinito in-
scribitur ex altero circumscribitur, convereentem
cujus crura concaritate lua seinvicem respiciunt de
in plasam eandem diriguntur, divergentem cujus crura
convexitate sua seinvicem recipiunt a in plagas con-
trarias dirisuntur, cruribus contrariis praeditam cujus
crura in partes contrarias convexa unt _ in plasas
contrarias infinita, Conchoidalem quae rertice concaro
_ cruribus divergentibus ad alymptoton applicatur,
ansuineam quae Aexibus contrariis alymproton secat
e
Casus terciu.
Casus quartus.
Nominaformu
pum.