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# Title: LBr. 396 · Hermann
# Folio 23v, page id DE-611-HS-973581:0046
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Ballierio ICto tradidi, qui beati nostri Profesiorii manibus parentabit.
Quatuor aut quinque jum sunt sextimanc ex quo Cl. noster Joh. Bornoulli
cum uxore et liberis incolumis huc appulit. Vacans Professio Mathematum a
Tari
Senatu nostro Academico perhonorifice fuit oblata, et ab Ampl. Mayistratu
aucto ipri Salario profehiorali confirmata, qui honor exceptir Buxtorfici nonnulle
ad alias Universitates quoque vocatis, nulli hactenus Profehorum notrorum contigit.
ante aliquot dies me eum invisentem roguoit ut Ampl. Tuue plurimam salute
suo nomine impertirem et in quoque epiitolum à el. Mogoruo Londino ad eum data
mihi perlegendam tradidit, quae multa continebat mathematica; et inter alia
Solutionem suam satis prolixam attulit Problematii a Cl. Joh. Bernoulli alim
in Actii propositi, de invenienda Curva tali, ut portio axis intercepta inton
tangentem aliquam sit ad iniam illam fangentem in data ratione madi.
Subiit chiniumaliam et moyoriana faciliorem quaera solutionem, et puto rem
ex voto mihi succesisse, verum Tuum et Vir Amplissne de ca judicure.
C
EC Sit itaque Cunva AGC ea quae quaritur, cajuraxis AB; ap.
plicata CB, tangens CR; jam pono CB. = X= yya Subtangs.
BB = 2Xy eritque tangens CD =  + yy et ex hynotheci
AD = mXX  mys abscessa vero AB = m L myu + 2Xy. tales
vero suppositionet ea imprimis consilie instituo, ut calculus
sigras radicaliblet non implicetur, quibus positis, erit
dx 2ydys
G6 0
enie
2, Xdx + glly + 2,y dx + Xdys
xdrs dn xdx dy ydx + Xds
X-77
Magus
2x7
y
5
2X - 77C
CB. AB
:: X -yy. 2Xy; hincus habebimus
vel transxonendo ydx +xdis
ixy et devidendo per xx+ gy, erit, ydx -xdy
Lax- Lay
x = 2
2X
ad altera partem, siet
pdr-xay (Xydx -Xyydy + y dx Xdy) m 2dx + ydy vel multiplicando ulique per
axy
n s
Xdx- Lde
X + y ergo
X 
6
 egy
idx tay.
2 y
24
m, xx+ ydus; verum
X+ yy
L2dy = m, xux + ydus
 + Y.
N+ yg
 = yy
Unde sequitum
2dg. L - y = = log. XF y = m, Log; X + gy  vel Log. X - y - Lg. XFy = Log.  F yy, ergo
+-y
X+7
100 3 C
yy aut ut l’ex homigeneorum servetur à
++y
x+gy
e
E.t.
Quantum ad methodum in eam attinet, qua curvam analyticam per quotlibet
data puncea duio, lubet eam hic pauci exponere omisto tam en calculo nimit