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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 Prefortionibus Dialoeum.
Prima inquie, proeressio est ration. s duplae; altera, triplae; tertias
guadruplae; guaria decuplae; quinta sesquiallerae. 8c. Pex ratiorem
Itaque fundanam, nozor  duerimer, Radicem incellisie, sive
Docectarem primam, uni menifestum cAt: cenrra quam iple
alibi p. 137. 1. 15. racionem aequalicacis = (nOn ANICM. UE
nunc, Radicem seu pocestacem primam,) appeIIaE ratiONUI
omnium Pundamentum es principium. Scd alicer adhuc D. 15. l. 23.
eodem fundanae rationis nomine, incellieie racionis in minimis
numeris designationem; Sic, inquit, ex Z. 4 5 32. qua omnes
sun inratione sesgniallera; suneus est, rduur, seu rduerines ncz
fundata (lesc fundana) ratio, 3. quae primis inter se numeris com
Prehenditur. Et sic de caereris. EE Cimilicer P. 165. l. 20. Adeo Ebi
inconstans est in luorum terminorum acceptatione. AC, inquam.
quicquid sic quod hac appellacione alibi relit, manifecum est
cum per rationem fundanam, hic incelligere, radicem sire pocectate
primam. Hinc aurem concinua alciplicaciene C live uc ille
loguimalie, concinua radicis fundanse adpolicione) cmeigie
Teries Geometrice proporcionalium 2b1 (cu Z inchoata; lioc
ekt, continua porectarum Ceriess Ouarum Radix, prima cA;
quadratum. seu racio duplicata, secunda; (reliquaque
juxca numerosnacurales deinccps denominondae; rario au-
tem aqualicacis =, PocestasnuIla. (Ft quidem E Cacis intcl CX-
aNet Meibomius, hoc nihil aliud esse quam quod univer Emm Ira-
di lolet, nempe 1. 2. 27. ∞. 2729. _C. ICVF. a. 14. a44.
aaaa. _ C. aNF 1. a. a2. a3. 2 _C. eHC GCOMCTKICE PFOFOTTI-
onalias corunque indices, sire exponences poccltacum
O. 1. 2. 3. 4. 5. _C. arichmetice proporcionales: NOn CACE
curille, perplexâ lua rei sacillimae cradicione hanc (bi de aliia
molesiaM CFCATET.) Pex rationum rationem icaque nihil aliud hic
incellisit Meibomius (ueve illud definicione lua lacis cbleure
tradiderit quam mucuum ad invicem sicum scu ordinem quem
incer se habene duo pluretre termini ejuldem progrectionis
Geometricae ab x inchionca. Adeoque rationem iriplem ad
duptam esse ut 3 ad 2, hec est, inratione sesguialiera; nil aliud (CnaE,
quam ejusdem racionis racionem criplicacam ad duplicatam,
esse ut ejuldem radicis potectas cercia ad secundam, cujus in-
dices sire exponentes 3, 2, lune in ratione selquialtera.
Sed et ulera nocandum ck, se in seriem Cuam nullos alioe
terminos admicrere, quam quitiune concinua appolcioneracio-