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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)
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De Mathematicis
dAP.
demonstratio a vera e proxima causa: Nam nih aequalicas
laccrum sic vera immediaea caula cur tigura constructa ett aequi
latera, quaenem ea vera caula sit non polsum eso vel conjoctur
ra assequi) sEqualicas aurem lacerum CA, AB, BC, demon.
Eracue, e0 quod CA, AB, sunt radii circuli B C, ideoque: aequales 3
item BA, BC radii circuli AC ideoque aequales: cum ixitur ram C A
quam C B aequatT recta A. B, sinEtres rectae C A, AB, BC, inter se a-
quales. EAq; haec demonstrario Fuclideao
Verum in hac demonstratione, inguit Smiglocius, e5 Nemo
Enon ridet, non allignari reram caulam essendi; non enim
c
criangulum idcirco est regnilarerum quia est inter duos circu-
cc0c construetum; nam cciam si non essor intor duos circulos
e
constructum adhuc esser requilarerum: Unde calis caula cA
decidencalis cali proprietaci
Cuiego mulca regero.
20. Dico, quod, ucut il lud verum esset quod aftirmatir, nempe de
monstraciones Machemacieas non per veram ec proximâ caulam
procedere; Cunt camen Pacis Scieneiticae, ti vel per caula remocio-
rem rel per effectu, vel per aliud aliquod medium ab alio arsu-
mentandi loco deductum procedani, modo certo concludane.
rem ita esse prour attirmarur, acq; alicer esse non posse. Sufticie
enim ad hoc, ur demonstracio sie scienciticas si procedat per medium
necessarium ex natura rei: uc _ ip(I quidem, qui hoc objiciune, non
negant, de Smiplesius eriam directe actirmac, Disp. 15 qu. 1. e alibi.
Ouarenoc iple, nec quos Ccio, aliis necabune, Disciptinas purs
Machemaricas Sciencias esse, ucue perteccissimum illis demon-
strandi mocum non concedane.
20
Nocandum ele, quod ipsi, qui neganthas demonstratio.
nes pertectas ette, in rarione demonstracionis (ue Loquuneur)
Potissimse; dubicane, an ulpiam alias occurrac in aliis scienciis
ejulmod