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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
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I11
id
9d
CAB. IL.
Analysis Infinitorum.
Parabola, ejulve trilinco, aut hyperbola, 8
existente applicata OD: y, INFCKCCDEA D. A: X
TUM ER = OF: b, 2XC AO: c, Fore ommia
OR seu b ad toridem seu omnia D sCu y,
UE p + g ad p. SIVeTO QUATATUE, Qudi AaBCANE
tationem omnia b ad quamlibet porestatem k
erectae, ad toridem y in eadem potestate consti-
tura, seu omnia be 2d omnia ye, sequenci
Modo inrestigari porect; 2C peimo, in F. X XNII.
seu paraboloidibus: PrODter aGMatIOLCM
pB = 4∞ 4 = yP, CA y 1= Y
a1
91
de P; Rat
JaM pE=rk 12, erit ralore hoc in locum
iplius rE repolito, ac divisione legitime per-
2Cd rD = 9N = ZP, quae Xquatio demIO CA a
parabolam; sIcCa GO, ubi manentE A: X;
ec O:6, HE OP: Z; dC OG: d; IaI VETO er
Coroll. I, uEp + g k ad p, ita omnia C O seu d 2d
Omn: POIcu Z hoc es ita omnia b l ad omnia p l.
cum enim mox fuecit suoposum y k= p R- 1 ∞)
eric eandem ob causaM b l Fi rk - 2d. Uade
constat ratiocinium.
Idem ( AaE in lpperboloide L AOFDL,
FIC. XXXITF. Cujus hic aequario, retentis Cym-
bolis yP x 4 =: bPC, AaFGHC y C = bL=. 2 IN-
venietur ratio omnium y e ad omnia b k, utp
2dp = gk. Posset ec, reducendo hyperbolitor-
em hanc xquationem ad parabolitormmem, idem
11121C. 2