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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 326, page id 175905688X:0348
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=348
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 29 lines, status machine
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526
ER ANTCTSCF d SCHOOPEI
POEFO ANTUPEA D F D =Y S3 JUINSAEIE A F; DE Super AP
descripeo semicirculo AD F, collOcetur in COAC∞V9.
Centroque Pcirculus describatur, transiens per inven-
cum punctum C. Dui quidem Circulus IIyperbolam
Cocabit vel tanget in tot punctis, quot aequatio diversas
radices admieer, a guibus (i 2d lineam A C demittan.
tur perpendiculares HII, hi, _ hi: erunt ipsae radices
qualcX.
Ubinorandum, S A C major invenirecur; quam ut
Semicirculo super AF descripto inseribi poslec; aute.
tiam Circulus CFTh adco parvus eser, ut Hlyperbolam
ElEh in nullo prorsus puncto secaret vel tanseret, nul-
lam icidem cunc foreradicem in aequatione, quae non
esecimaginaria.
Demonstratio.
Fcenim linea TFI existente D Z, cum id, quod sub AD, DF.
vel sub AT, TFI CONTINCTUT, SIE D V S: eriE A Y SeuD H ∞ VS.
TInde CUIM DF _E DR a se invicem subductae relinGUAnEK F, de
DF(ic D =Yp. erit K F ∞. - (Cu - yp. 2deo que
DKFSemper ∞ S- = 1 . FA autem K FI ∞Z - : p seu
p - 2, ac proinde HKHI. seMPeF D Z Z - pZ -L iP P. FIinC
summa veriu sque simul, hoc est, D F H erit ∞
u
22= pZ  =PP. FIOCVETO CUI RGUeTUIEF o AFFpo AC, hoc
et, ∞ = PP: F - - 9: hec, ordinata aequalitate, Z + - pZ3 +
422 - r2 . ( s∞0. Oux eAt aequatio proposita. Unde liquet
IFI essC D Z.