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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 256, page id 826603459:0302
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CAF
De RationibH.
3)5(13 5)7 (13 6) TT (1 2
6)10(73 5)8 (13 7) 10(17
4)71∞ 539 (18 8) 15 (TE
10) 13(593 =2 10 = 24
200) 107(5307 = 1 100
200) 108 (1,08 =1 102
Ulbirero quantieatis majoris ad minorem ratio est Superpar-
tiens, superbiparciens, Cupereriparciens, _C; Pric minoris huius
ad illam majorem, racio subsuperparriens, subluperbiparciens,
sub supereriparciens, _c. Nempesatio 3 2d5, vel 6 ad 10, est
lubluperbipartiens certias; ec 4 ad 7. Lubsupereriparciens quar
CaS. Fc in aliis paritEF.
Notandum aurem est, in rationibus superpartientibus, deno-
minacorem partis aliguoex majorem este debere quam est Nu-
merus carundem aliquocarum partium altumpeari. Nonigitur
dicicur supertriparciens cercias, vel luperquadripartiens quartase
nam 3, rel Z, tantundem (UInCaC L. FF L Z, vel 1 Z, _C. idem
est acq; 2: ideoq; major minorem Capius quam lemel contine-
ret; (nempebis,) quod est concra detinitionem racionis lu-
perparcientis. Mulcominus dicendum erie, Superguadeipar-
tiens certias. vel quarras, ecc. (uc denominator aliguotarum
parcium minor sic quam carundem numerus;) ica enim major
Talcem bis suxponetur minorem concinere, et aliquid insuper.
Sed neq; rice dicitur, Ratio superbiparciens guartas, lexcas,
_C; vel lupercripartiens sextas, nonas, _c. vel luperquadri-
parciens octaras, decimas, duodecimas, _C; ec paricer in limili
bus: ue denominator aliquocarum parcium assumpearum, ee
carundem numerus, communem aliquem dirilorem habeane
quiurrumq exaere meriatur. Sunt enim 12 = 1Z, et 18 =
25, et 13 = 1 Z, CEF 3 =73, Ct15 -- +Z, 1 16 == 15,
ex 1, 2 = + 5 _c. Non igicur dicenda est ratio superbiparciens
quartas, aut suxertriparciens (extas, aur Cuperguadriparciens
Octaras; led ratio selquialtera. Negi item Superbipartiens lex
cas, aut supextriparciensnonas, auc luperquadripartiens duode.
cimas, sed racio selquicerria. Neque, Cuperquadriparciens de
cimas; sed suxerbiparciens quintas Pe similiter alibi.
Siquis urget; ver Racionis Cuperparcientis detinicionem, hujul-
modi loquendi Formulas non excludi: Dicendum crit, Ratio-
MI
Subsuperpar
tiens.