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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 Proeressione Ariihmelica.
CAP. E
nE A ad B, eadem _ C ad D. Hujusmodi aurem A B. C. D i
nocabie caldem esse continne proporcionales. Progressio au-
cem Arichmetica, ubi opus est, sc poterie nocari A, B; C, D;
vel, Rcontinua Fuerit, A, B, C, D 
ACq; hactenus cum duplicem quancicacum invicem compa-
racionem lacis axeruisse rideamur; cum veriulq; progressionis,
Rrichmecieae scilicet _ Gcomerricae, nacuram, quas in lequenci
buscapicibus Fulius prolequar.
Procressionem autem sive proportionalitarem Farmonicam vel Mu-
sicam dictam, cum ad seopum nostrum minus videacur pertine.
re omietendam centui. P.a vero est (Equis quae hc Scire desiderat)
Flarmonicas quando in quaruor terminis est un primus ad quartum, sic differentia primt
e secundi ad differentiam terrii es quarti. Puta E A. D :: B = A.
D = C. Prunc illa quantitares A, B, C, D, harmonice pro
Porcionales. Sic numeri 5, 8, T2, 30. quia5. 30:: 8 - 5 = 3.
30  12 =- 18. Vel eciam, tres quantitares Flarmonice proportiona
les sunt, si ur prima ad terriam, sic differentia primae ex secundae, ad difa
ferentiam secundae e terriae. Duta A. C, 33B n A. C = B. eruNC,
hoc calu cres A, B, C, Harmonice proporcionales; vel, Ci li
bet, quaruor A, B, B, C. Sic numeri 3, 4, 6, vel 3, 4, 4, 6.
Nam 3. 6:: 4 m 3 - - 1. 6 = 4 = 2. Ouod imnuisse (uHI-
Ciat.
Proporrio
CAT. aV
Proeressio Arishmetica variorum problemalum familiarium
solurione explicatur.
E Arichmerica Progressione concinua, Colent hujulmod
proxoni Problemaca, aliaq; mulca his similia.
 Daco cermino primo, de communi terminorum excellus
terminum ulcimum, aliumre in progcessione quemlibet, inve-
Rigace.
nem Arib-
2 Dicoterminoprimo, communiitem excessu, et numerq
meticam spe. terminorum; Cummam cerminorum omnium inrenire.
3 Dacocerminoprimo, cum excestu communi, e alcerius
cujulris cermini valore; in renire quoro loco in Perie cerminus
Problemata
Proressio-
ctantia.