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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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laperants led acu lapecat aceropeacat quosim iaporum
ProressiOBC Z 3 2 3 2323 2.
loco (hoc eleprimo) ponarur: cujus dupta est Z; iriplas = 
continebit dua E, eis simplam Z. (recte qidem nam = = = X 2.)
Aiqui inquie, duple simplae addirae, efficiuni Z. Nullo modo: led
potius, mulciplicando compotica, non enim Z + 23 Ccd EX 3,
LunEZ. Sunc aucem = + Z = =, quam e progrestis extibet, &
lemma postulac. N. uera icaque demonstracio procedic. Pg
veco quam a0. Ilac ille veram rationis sesquiallerae procressionem
22 48 22 288 4C. vel 2. 3. 4. 28. _c. Non cA progressio
Arichmecica, quam lemma lupponit; led Geometrica; adeo-
22
2. 32
que nihil ad chombum. Acque de reliquis instanciis, par esto
Judicium.
Sed nec selicius luam ex ponic de Racionum Ratione doctri-
nam: quam (IC definIE, P. 17 4. l. 12. Ratio rarionum est duarum
rationum ejusdem seriei, a fundana ratione secundum naturales numeros
Prosredientis, secundum rationem certa quaedam inter ipsas relario. Cum
enim, inquie, rario aliqua alterius dupla, tripla, sesquialtera,
duplicara, eriplicaca eec ) dicitur; rario fundana e simpla
Choc es, radix.) secundum nacuralem numerorum seriem excrevisse,
hoc est, continua sui adposirione major facta, intellicitur; (hoc est
concinua mulciplicacione hune potectaces reliqua:) ita si
quaime Hnqu. rarionem sihi ipsi adzonam, fit ratio prioris, nempe sim-
plae  fundane, dupla, (duplicata; ) si hane cum fundana componam,
sit fundanae tripla esc. tripla aurem ad duplam C criplicata ad du.
Dlicatam) est ut 3 ad 2 Cur pocestas cercia ad secundam, (cu.
ee cubus ad quadeatum,) eEC. Porro possumus quamcunque ration
nem, fundane e simplae rationis, hoc est; unitatis (radicis leu po-
celtacii primX) lococollocare. Vade innumerae rationum proeression
nes exsureunt, quarum aliquos ensemplorum loco exposui.
Adversus MI Neibomii
nihilum. P. sCo. Ss CL. C aH. HaGu C, in hac rarionuM
dic pocius 2, 2,2, _c
non eric progrestio arichmerica;) rario 3 simpla sit,
us elita
alto
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Le0
TIMA
1
210c