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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 45r, page id DE-611-HS-3653099:0089
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concurrentibus AP, AD in fig. J. fit A(), qua delerminat )(D) Maxinun
vel minimum propire sic dicluti ad tangeatem parallelata axi; in fig. II. fit
A(p) determinans punclum reversionis (3): et ia fig. III. fit A) determrinans
punitum decussationis (D). Vides igitur quod s quadat curva propo
s
lita gaudeat punitis duorum vel omnium triuta cassuua, methodis Hud
e
deniana illa omnia una aquatione determinare debeat, idq, necescario
non ex acuidente: Atque hoc est propter quod varignonio scripieram
hanc methodum magno defectu laboraie, cum pereata non certisimus
quid invenermus, et facile puntum reversionis vel decassationis pro
punctomaxina vel minima dittantiae sumere possimut (quemadmodutm
reapre Rollio acidit, qui punctua demsationis in curva y = 2 +V(4+27
+ex sumit pro punito moximae distantia); calculo interim differet
fiali  singula haec punita distinilia et separatim exhibeate.
Quod vero taadem spertat ad tuam exceptionem a(( (Y- b) =
(2] (XX 2aX + a a - b6)- b, per quam putas te posse octendere ex
acideate tantum fuisce factut ut in culva priore duae rodices
(pratertertiah illam utilem) forte fortuna deteminarent puaita re
versionis; ed re fefellit quod hujus atterint Tua cuva veratu fi
quiam non conceperis, ean procul dubio prion simileta imaginando
loco quodtoto coelo ab ea differati adeoque quad sua
seus propunctis reversionit qua talia non sunt: Nom
debita ejus frigura est, ut haec altera quat hic deline
ata vides; ubi unicum eit punitum reversionis (D) et duo punita
A = X, PD = y, A(P) =a, ()
(DX= biZ (D) DD = b- Y
(8
=XA =b
minima dictantiae D, D et
quidem in cldeta illis locis
ea qlibus inprion curva
fuerant, perutata laatum
natura punlorum: non igitur
en auidentate, quod per me
thodum Huddeniatam eadem
quoque proveaiat aequatio
43
quae prus X - 3aXx+ 3aaX- a bbx + abb =0; nec duae radicet X - a +b et
a b, suat inubiles quemadmodum pubat, designant eaimm punita