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# Title: LBr. 57, 1 · Bernoulli, Joh.
# Folio 175v, page id DE-611-HS-958803:0352
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sed suun Mihi ingenium latis luperq perspectum est, atque ideo non dubitari
quin joco ad fucrit, quod allegaveris circulum:
diis
c.
a
B
Tubes me contiderare, an constructio mea qua in praecedentibus
meis feci s
2 4K
PL= a3,
ideoque PK = FL = a, id est annon hurva mea KIL sit cir
culus, cajus centrum P; et sio annon incidamus in eam curvans
quam Eecuso; sed pace sua ipse videris rem non satis conside
2PL
La3; neque pro hoc idem calculus prodit. Sed etiam nula ambiguitas nadicum hic
adest, quia non promiscue contideravi quadratum alterutrias segmenti seve m
joris sive minoris, sed sumsi contueto segmenti seu radicis majoris quadratum, quod
minus
multiplicavi per segmentum seu nadicem minorem. Hinc longe alia curva prodiret
2P I = a3, quae tamen nihilominus satisfaceret. Verum quid
si assumeretur Pk.
C
opus est verbis, si contrarium ejus quod putas res ipsa probat. Constructio mea
erat talis: assumta curva quacunque A F, cujus applicata D F vocetur, Y. fiat
alia AC, cujus applicata De seu qn sit = a6416)
a 3YV
dico, si sumatur PL= radici
majori et PK = radici minori hujus aequationis yy -9y + YY = 0, curvan KIL
fore quaesitam; de veritate hujus constructionis non dubitas, quia in precedentibus
viditti rationem, sed urges K9L esse circulum cujus centrum P; quid si autem osque
tendam PK et PL juxta constructionem meain esse variabiles: nunquid sen
tentiam mutabis? Radices dicta equationis sunt y = =g -V qqor et y-
29+ V urr; substitue valorem assignatum ipsius q et habetis 4 seu P X- Y4
a 3
et y seu PL =  quarum utraque variabilis eftnisi ponas v constantem id est A
Freclam et paradelam ipsi AD, quo solo casu KJL esset circulus cujus P cen-
12 P
R. FL seu
Y8 a3
s
FL
ab v4
= a constanti; non autem S
a3. Sublata ia dificultate, jam alia se proditi videlur
enim (cum PK, PL prodeant an quantitatibus rationalibus puncta L et K
non este in eadem curva, sed in duatus diversae nature; si hoc est erit
methodus Neutoniana fallax, et Tua quoque laborabit, quia eodem funda
mento nituntur. bale et am
Thoninga d. 15 Majibusque
Ampl.
3.
Obseroant scimum
ernoulle
1