m ) o ( gg 
147 
exhiberi debere. Idem accidit in cæteris Curvis 
in fe redeuntibus, ubi centrum motus Radiorum 
Ve&orum intra easdem collocatur. Sic in circulo 
ADB (Tab. 1. Fig. 5), cujus femidiameter AC = a , 
fit diftantia EC—bJ & E centrum Veftorum ut FD, 
qui angulum facit =2; cum diametro AB\ ponatur 
a : b : : fin 2 : fin t>, erit v = CD E, &, dufla nor- 
mali CF ad ED , E F = b Cof2 , DF = Fd — a Cof 
adeoque ED — a Cof v + b Cof z, Ed = a Cofu -+• 
b Cof ( 2 4- 1 8o°) = a Cof v — b Cof 2. Jam vero 
a> £ j quare 2> v, Cof 2 < Cofu, & a fortiori 
a Cofu >6 Cof 2: erunt itaque ED , Ed ambo po- 
fitivi. Idem monet d’Alembertus (pag. 274. n. 9) 
asfumendo AE — a, EB — b , Dd — f, ED = x ; unde 
ab — X ./ — X, X = 4/ i: \/ %f 2 • — ab y ob AË . EB 
= DE .Ed <FD 2 
§• 3 - 
Defcriptio Curvarum per variationem Radiorum 
Veftorum in Hyperbola facile concipitur: fit AB — 
2a — axi transverfo (Tab. 1. Fig. 6), Excentricitas fi- 
ve Focorum F, E diftantia a Centro — CE — CF = f, 
& ponatur /^FF) = 2, erit FF) — ED — ia , (FD — 2 a ) 2 
= DE 2 — (ze — FD Cof2) 2 -f- FD 2 fin 2% unde 
e 2 ' — a 2 
FD = — „ In hac formula, fi pro 2 pona- 
e Cof 2 — a v * 
e 2 — a 2 
tur i8o° + 2, erit Fd = — — , quoniam FD 
-eCol2-fl 
— dF=2fl, convenienter cum hypothefi punfti D 
dat quantitatem five differentiam negativam -, e ft e- 
nim dE — Fd — ia quod fi asfumatur, ob (Ff + 20)* 
= dE 1 —{2e — Fd C0I2) 2 -F Fd 2 fin 2 a y habetur 
e 2 ' — a 2 
Fd — •. Idem itaque figni negativi ufus 
eCof2-fa T 2 in 
