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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 Proportionibus Dialoeum.
extiyporhieh: Ereo, per Axioma cicacum, Duplum C, 
quacur duplo i cripli A. ACTuplum 2V C, (vel tatences
exedo, Meibomio,) est Sexcuplum ro A: ergo _. Duplum
eripliA, est sexcuplum rs A. Si aurem nec dum sic latis per-
Spicuum; id ielum sic quario aggrediamur. Duplum, conmuni
sententia, omnes homines. judicant, quod bis habet simplum; triplum, quod
iria simpla aequat; centuptum, quod cemum; Cet, ni Fallor, lexru
plum, quod Cex:) asserence Meibomio D. 170. l. 13. ErBO Cum
C. Ec, exhypocheli criplum A; erit C aequale md A cer posico.
hoc cA, C = 3 A =- A + A + A. Icem, cum F sic, exhyDocheM
duplum 7u C, eric F aequale nad C bis pohito, adeoque de
3 A bis potico, hoc est, iptis A + A + A bis politis, hoc eA.
A + A F A plus A + A F A, hoc eA A + A F A + A + AF A
hoc est, rd A (exies polico, hoc cA, sexcuplo ru A. Onod crat
demonstrandum. Verum icag; est quod aftirmac ThcOn, cax
retondSeor VO SNaS, rC)) r EEaNdor, Sitri-
plum alicujus duplaverimus, fiet ip sius scaemplum. Bp ES e SciEa.
Verum quidem cAt, nec nos inticias imus, quod longe alio
senlu dicatur, rationis iriplae ratio duplicata (Sronaoicor) est non-
cupla; quia nempe Z. x Z = 2: ob concinuam mulciplicatio-
nem. Acincerim non minus verum cA, _ tripli duplum esse sexru-
plum; quia nempe ZX 2 = 2: quod astirmat Theon, e cum
illo, excepto Mcibomio, alii omnes.
Acque cademratione, tripli semissem, sire Pemistis criplum,
dicimus selquialcerum, (quod asfirmat Theon p. 28, 1. 18.)
quia 2X 2 = Z x 3 = Z - - LZ. Sic Cemissis, Cre SubdupIi, du-
plum, dicimus inceorum, quia ZX 2 = Z = T. quanquam re-
rum eciam sic, rationis subdupla racionem (non duplam se-
andocor, Ced) duplicatam, simaosora, esle subquadruplam,
quia a = =X Z.
Oua omnia cum ica clara sine ue nihil magis, non eAt cur
qut explodat ea Meibomius, auc, A explodac vel maxime, nos
illud morear. Ec quidem, si C quod aic Meibomius P. 99. L. 26.)
Elementa quoque Fuclidis, ad quae fuse haec tradidit Clavius, hanc explica-
tionem ferre sint coacta: non est tamen, cur id, vel nos, vel ipsum
Duclidem, malehabeat; quipre cui Fuclides nulpiam retra-
Ouod aurem Archimedes (ut D. XOT, l. 5. D rationem 23 dix-
BaCuE.
erit niuoxsor sesgnialteram (incellisc, triplicatae subduplicatam) ra
11OBH