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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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G AP. 33
De Proeressione Geometrica.
me MinOr R ) V; _ BC deinCEFS; V =a, P)
NV = 2, R. )V = s. 8c. Ouilibet enim cerminus per
rationem communem dirilus, dac cerminum prexime minorc.
Per det. proer. Ceom.
5. Ouilibecisicur cerminus aequalis cA, termino maximo
per racionis communis poteltarem distancia ab ulcimo cogno-
minem diviso. Nempe Rd) V. per Praeced.
6. Daro ersocermino Maximo, cum Ratione communis de
Distancia cermini quaesici a meximo; V, R, D; habecur cermi-
nus quaelicus. Pucalexcus a tine, sire ante ulcimum quincus,
S= R E) V. Perpraeced.
7. Vaco termino quoris, (ucf) cumratione communi, de
cujueris allienaci majoris dittancia a daco; F, la, D; inveni-
cur cerminus allienacus (puca i.) nempe, mulciplicandotermi-
num dacum in Racionis communis pocectarem dictantia c09-
nominem. Hoc eAt i =- fR d = sR.. Nam per det. vel prop.
2. prolingulis distanciae gradibus, pocectas racionis communis
unitace augerur; creo, pro omnibus gradibus, cocunicacibus
quoe lunc ipsi distanria pradus.
8 Dacocermino quovis, cum Racione communi, e cuju(-
vis altignaci minoris distantia a daco; (puta f, R, D:) invenitur
atIEnaCUS. (UE C.) Nempe diridendo dacum per Racionis po-
rettarem distantix coenominem. Puca Rd) f =- c, hoc cAt
2)s =c. VelRd)C =1 =R )E. Sequitur ex det. vel
DrOP. 4.
0. Data igitur duorum quorumvis cerminorum ab invicem
distancia, cum Racione communi: D, RE; datur eorundem ad
invicem racio. (Fuca i ad f; vel 5ad )nempe per 7 _ 8; majo.
ris ad minorem rario eA Rd, et hujusreciproca, cAminoris
ad majorem. Puca f =R d = fR; ee similiter C = R d
=R2; vel = = R d = R 23
20. Daca vero cerminorum quorumvis ad invicem Ratione,
cueorundem ab inricem distantia; (puca i ad f, D) datur com-
munis Racio. R. EA enim (per praeced.) dacorum cerminorum
ratio ad invicem, R d, rationis communis porettas distenciae
cognominis: exeracta isicur analosa radice, habetur commu-
nioratio. Nempe R = V dR d.