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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 27, page id 834940469:0035
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=834940469&page=35
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.87
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monus
X
componendi
alcior potectare vila ipsius a in vlcimo producto rerininn
ba 2 F b 2a, quoniam illos cum aequalibus quantitari biS a
dendo substrahendo; scc, Tempermaner in factis cedem po-
reltares, _ illos in se eodem modo mulciplicando lemper
masiseleuacur alcior potestas in termino a3 F a 2 b quam.
eleuarur deprectior porestas in termino ba2F b =a, e ex illis
caldemradices extrahendo, voi a Fuerus clenarior in pores
tate erit etiam elevariorinradice. de quoniam cadem repe-
ritur alcissima potestas ipsius a in termino ab 2 F b3 GuXe re-
peritur inrermino 2b2a, demonstratur ve ante alcissimam
potectatem iplius a in vlcimo producto ex termino ab 2 F b3
eandem esse cum alcissima porectare ipsius a invleimo pro-
ducto extermino 2b2a: in vleimo igitur produeto cermine
a3 F a2 b reperitur alcior porestas iplius a quam in vlcimo
productoterminiba 2 F b 2a, X in vlcimo producto termi-
ni ab 2 + b3 altissima poreltas iplius a eadem est cum al-
cillima pocectare ipsiusa in rltimo producto termini 2b2a; X
isitur vlcima producta ex terminis a 3 F ab, ab 2 F b33 c0-
demmodoincer se addica, subducta, mulciplicata, diuila,
ecc. semper efficient quantitarem; in qua repericur alcior po-
rectas ipsius a quam vila quae reperiri porest in quancitateFu
eta exeadem prortus addicione. Subductione, mulciplica-
tione, divisione, _c, productoru a terminis ba 2 F b = a, 2b2 a;
quoniam altior porestas eum alcera porestare semper altiore
Facit porestarem quam depressior porestas cum eadem altera
POrcRatC; de 1Bitur istx duae quancitares non porsunt ese in-
definice aequales, cum reperiatur alcior poteltas ipliusia in
vna quam in altera: aequehine cuidens est quod sectorcir
Culi ellipleos relhyperbole ABIPnon possic componi ana-
Iyrice arriangulo ABP e crapeZIO ABFP, quod deWoM
Arandum erac.
Veaucem evidentius hatpropolicum, aliam demonstra-
rionem breviorem. Faciliorem ee ex aliomedio pecicam hIC
Tubiunso: quanciras non pores componi analyriCE CxFeemI
HISa 3 F a : b, ab 2 F b3, ecdem modo quo componicur Cd-
ACHi QuAMEICAS ExTeEIIS ba 2 F b2a, 2b =a; quOWIAn
dendon
C
si
estr
tu