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# Title: Qua Continentur, Oratio Inauguralis. Mathesis Universalis; sive, Arithmeticum opus Integrum, tum Numerosam Arithmeticam tum Speciosam complectens. Adversus Meibomii, de Proportionibus Dialogum, Tractatus Elencticus (shelfmarks Leibn. Marg. 84:1, Stück 1; Leibn. Marg. 84:1)
# Folio 35, page id 826603459:0481
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DEDTEATIO:
rarias) caidem verobique. F.A enim r Hoc cA, OD, id eH
(hoccaTu) AD. NempC
Cuprema = Cursum + 3 d V3  deorlum = 3 d V 3.
AD L media = AA = Curtum 0  deorlum 0.
Cintima = Tursum = 3d V3 = deortum t 3 d N3.
Adeoque (cum sE PD, hoc eR g Curlum Fr + 3d, d q de-
Orlum =r  3d,) erie
luprema = Turtum = 3dv 3F 3d = dcortu - 3d Y3- 38
DDL media L DA = Tursum 0 F 3 d i deorlum 0 r. 3 d.
Linsima = Cursum = 2d V3 F 3d = deorlum F 3dV 3 L 3d.
Vides itaque jam probe convenire omnia. Nempe cum
DA = 3d quod suxponic cua prima demonstracio; tum AD F
DD deorium  AD deorlum = 3d~ 3 = 3d, pl: F 3d = 3 d V3.
quod habee demonstracio cna secunda; tum rectam AD non
esse bilectam in p, (non quidem quia 3d a 3 F 3d  3d V 3 = 3d.
nei primum videbacur, sed) quia 3d = 3dV3  3d. Ec prop.
cerea neque rectam a n esse diametrum.
Verum adhuc ingnico, nova hic emersie difticulcao, (quali
non cam Proccus sic quam Hlydra quieum MINC aBACUE.
Cum enim D punctum, sc, per constructionem, diametri
punctum illud cui ordinacim applicatur recta OD in curra
a a cerminaca: qui omnino fieri possic, uc ejulmodi ullum re-
periatur punctum Cupra verricem A quod tamen infinuae
haec aequacio: cujus liquidem Calcem una radix, Curtum Cy-
menda, Cuxea verricem excurrie, (nam PD = 3 d V 3 F 3dTur-
sum, major cA quam PA = 3 d, adeoque rerricem luperatre-
Ao AD = 3 d V 3.)
Dicendum itaque (quod quidem ha c erincic instancia) cur-
vam Paraboloidis Cubicalis a A, supponendam esse ulera ver-
licem A non deorlum Recti ad B, Ccd surtum porius ad 2:
Adeoque ipsius genuinum sicum ese (quod parum Forcan pu-
cavecis