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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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C AV. 13.
De Divisioneo
numerus ille Cotus alcerum Diridere Cre Nsetiri apud B. 1ClI
dem dicendus erie, qui esipsius alignora pars, Ceu qui aliguories
policus Diridendum aequec; quocies aurem ponendum cst ut 2-
quec numerum dividendum, id diritione quaeritur. Verbi gra-
tia, E diridatur numerus 12 Per 3, sive quaeratur quoties po.
nendus numerUS Z UF aequeF numerum 22, Ouociens eric 4; quia
nempe numerus 3 Quater policus aequa bic nUMErUM 12. AC (I
proxonatur numerus r0 per 3 dividendus; id quidem tieri non
pocel cum hic illius non sc aliquota pars, nec aliquocies re-
pecicus iplum ae quabit; nam cex POsEUS (3X3 = 9) minOr
est, _ quater policus 3 X 4 = 12) major elt quam 10; acq;
inter 3 _ 4 non alius interce dic numerus, qui sic Onociens que
sIcus. Acq; idem concinset quorielcunq; provolicus Dirilor
non eltnumeri Diridendi aliquora pars.
Acq; hoc quidem incerest incer Rrichmeticas opcraciones
Synchecicas de Analycicas. Nempe, in Synchecicis, reris ne-
meris datis verus semper numerus emerger; ac non ica in Ana-
lyricis. Pata, in Addicione 5 = 4 = 9, 3 t 4 = - 7, _C. FF(I-
milicer continget quicunqe sine numeri dati addendi: AC in
subductione, quamquam illud aliquando conringic, ec 5 - 4-
2, _C; non tamen id Cemper, nam 3  4 a quabicur nulli vero
numero possibilis cu majus ex minori auterri non postic; Colemus
tamen ejulmodi suppoliciriam subductionem uccunq; innuere
ad hanc Forrram 3 = 4, vel eriam n 1. Sic, in mulcipli-
cacione, propolicis quibulcunq; reris numeris invicem mulci
Plicandis, verus Cemmper emersiEnmerUS, UE 4 + Z =8, 3+6
18, 5X 3 =- 15, _c. Ac in Divitione, licet illud aliquan-
doconeinsic, uc2) 4 (2; non raro camen secus accidie, ut A
3 Per 6, auF5 per 3, dividendi esene, ubi quoriences nullis ve-
ris numeris (incegris) altignari pollune; Colemus camen et hic
Suppolicicios illos quoros uccunq; innuere ad hanc Formam
6 rel =, _ E vel 1Z, _c. RC similicer in Pocectacibus compo-
nendis e relolrendis, concingic; daci enim cujulq; veri numeri
Ouadracum, Cubus, RC. veris numeris exhibebitur; ac non icem
dati cujusqs numeri Radix quadratica, cubica, _C. veris nu-
meris exhiberi poceric: ur luo loco patebie.
Verum ut mulciplicacio, laxiori senla lumpea, non ad illam Divisio lae
Tolummodo rekringicur ubi P’actus ett numeri provoliei MuL. iorisensu ac
ciplus; ita nec Dirilio ica restringi Colet ur Dirilor neceltario cepta.
sic Diridendi aliquoca pars; quam quam iliulmodi et MulcipI-
cationem