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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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SAP. 23. quoad Differentiam; e qudad Rarionem.
aueminus: Vel de Racione; puta quorupium vel quoncuxlum
Tichoc illius; num hoc illua contincat Cemel, bis, ter, _C. auE
Eemel cuns Eemisse, bis cum crience, _c. Elrroris modo compan
racorum, alcerum antecedens dici Coler, alcerum Consequens: quo-
rum quidem illud Relacum eAt, hoc Correlatum: Nempeilluc
cujus ad alcerum relatio exponitur; hoc, cui illud sic relaium
perhibecur. Puta E A ad B COMPATATUES A dicetUr Antece.
dens, B Consequens; dum Ecilicet A dicitur majus csse quam B,
vel minus, vel aequale; auceriam A iptius B duplum, criplum,
Temissis, _C.
Priori quaesico Catistc, si oRendatur res comparacas ae quales F arum com-
esse; vel, hinaequales, quanco haec illam excedic, vel hanc illa pararionum
Verbi gracia, Linea bipedalis est bixecali equalis; e numerus ab pro
binarius binario; ejusdem item rei (vel criom aegualium) lc discrmen
misses une inricem aequales; de paricer in aliis. COnera vero;
numerus octonarius lenarium, e hic icidem quarernarium, du-
abus unicatibus superat; linea eripedalis bipedtali cA. uno pece
Lonsior; quadripondium quam cripondium est uno pondo gra-
vius; acq; in alris paricer.
Secundo quaesito sacissie, abi ostenditur Ouomplum sie hoc
ad illud, sive quam rarionem (ut dici Toler) vel proportionem
habeant incer lc. Hoc modo dicimur, quadripondium bipon-
dii duplum esse; numerum senarium binariicriplum; lineam
tripedalem bipedali sclquialceram; unitatem binarii semissem
elle aut lubduplam, auc etiam dimidium; binarium icem bina-
sio equalem esse, vel in racione auc proxortione limpla; et pa-
ricer alibi.
In priori, abi de Differentia sive Excessa quaeritur, Rarion
nis sire Proportionis nulla ratio habetur: In posteriori, de Ra-
eione sire Proporcione quaeritur, Differencia incerim minime
considerata. Sic quacernarius cernarium, ee ternarius binarium,
eodem F xcessu Caperane; sed non in eadem Ratione: excestus e
nim verobiqs cA Ulnicas; at racio illic Selquirercia, hic Selgui-
alcera. C ontra vero, quacernarius binarium, et binarius unita-
tem, eadem Proportione Coperant; Ped non eodem Fxcessu: FA
enim proporcio sire ratio urrobio; Dupla; ac excessus iltic qui
dem Duarum unicarum, hic aucem Ulnius.
Diserenim
Prioris quaelii solucio, Subdoctione inrestieatur. Si Subdu subductione
CACUT enII MUETUS Ex numerO, Quod xcAaE CA EX. investieat
e
cectus