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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)
# Folio 231, page id 826603459:0277
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1
CAP. 25.
De Proeressione Ariihmetica.
ille repericur. Vel (quod perinde eAt) daco cermino primo, &
ulcimo, cum excessu communi; invenire numerum termin-
rum.
4 Dacoterminoprimo, ee ulcimo, cum numero termino.
rum; communem excessum inrestigare.
5 Daconumero cerminorum, cum terminorum omnium
agoresaco, de excesu communi; primum cerminum invenire.
Per cerminum primum jam incelliso (quod e deinceps in-
cellisacur) cerminum minimum; _ per ulcimum, maximum.
Ouamris enim progrellio, sire crelcendo sive decrelcendo feri
Dollic; cgo tamen eanquam crescentem considero, acqu eo len-
Iu quae dicenda siune incellecta relim. Et proprerca, siguis ea
decrescenti seriei accommodare relic, id hec mutatis cantuni
his rocibus primo _ ulcimo: Nempe quae jam de primo crescen-
tis dicuntur, illic de cermino alcimo decrelcentis leriei inre
lisenda erunc; quae hic de ulcimo, illic de primo. Ouod semel
dictum esto, ne Caxius opus sic ucrumque calum Peortim pro-
Donere.
ExsemplI gratia. P. Siquisiter conficiens ambularerie per Solunntur.
modic 3 milliaria, secundo5, certio7, _ sic deinceps, divr-
num icer quocidie augendo binis milliaribus; Ouxritur quor
milliaria ambalarurus est dic Decimo
Ouoniam linguli dies post primum, addune incrementum
duorum milliarium; mulciplicecur numerus dierum post pri
mum, nempco, in communem excessum 2; e productum
18 = 9 n 2, addacur icineri primi diei, cricgue 21 = 18 +3
numerus quaelicus: cornempe milliaria confecturus est dic de-
cimo.
2 Si quaeratur insuper, ouor coro icinere ambulaverite
Addicis cermino primo e ulrimo (ica ur jam dictum eA in-
vento,) ducacur summa in numerum cerminorum: producti
dimidium est numerus quaesicuS. Puta 37 27 = 24; _ 24X
10 =- 290; hujus numeri lemittis, 120, cA numerus milliarium
1oco decem dierum icinere contectorum.
3 Si quaeratur, ouoro icineris die ambulaverie r5 milliariae
Ex numero assignaco 15, auteracur terminus primus 3; e re-
Eduum per communem excessum dividatur: quod prodic, indi-
cac quoc diebus polt primum ambularerie. Dempe 15 = 3-