Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

DR TAYLOR, THE GEOMETRY OF KEPLER AND NEWTON. 199
vnus D eft intra feEtionem, alter vel extra vel intra fetionem in
axe fingendus eft infinito interuallo à priore remotus, adeô vt
eduaa HG vel IG ex illo caeco foco in quodcunque punurum
fetionis G. fit axi DK parallelos. In Hyperbola focus externus 35
f PAGE 94.
// dl
b
F interno E tantô eft propior, quanto eft Hyperbole obtufior.
Et qui externus eft alteri feétionum oppofitarum, is alteri eft internus & contra.
Sequitur ergo per analogiam, vt in reaa linea vterque focus
(ita loquimur de reCca, fine vfu, tantum ad analogiam complen- 5
dam) coincidat in ipfam reEtam: fitque vnus vt in circulo. In
circulo igitur focus in ipfo centro eft, longiffimè recedens à circumferentia proxima, in Ellipfi iam minus recedit, & in parabole multo minus, tandem in re5ta focus minimum ab ipfa recedit, hoc eft, in ipfam incidit. Sic itaque in terminis, Circulo & re- Io
é5a, coëunt.foci, illic longiffimè diftat, hic plan incidit focus in
lineam. In media Parabole infinito interuallo diftant, in Ellipfi
& Hyperbole lateralib. bini aau foci, fpatio dimenfo distant; in
Ellipfi alter etiam intra eft, in Hyperbole alter extra. Vndique PAGE 95.
funt rationes oppofitæ.
Linea MN quæe focum in axe metatur, perpendiculariter in
axem infiihens, dicatur nobis chorda, & quæe altitudinem oftendit foci à proxima parte feétionis à vertice, pars nempe axis BR. 5