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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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CCAP. 41.
De Fractionibus sive Minuriis.
porcionem, assumpeum iri: (quippe parces simul omnes; tan-
eundem lune acque ipsum incegrum:) Sin Denominatore ma-
jor essee numerator, innueret illud iam plures iltius Inceori
Parces ejulmodi alsumendes, quam inibi ommino contineantur;
quod ellee impossibile: Superest itaque uE NumeraEOE, Cive
parcium assumendarum numerus, minor sc quam Denomina-
Cor, sire numerus parcium omnium in integro concentarum.
Si gpando ieaque conspiciatur (quod eamen ulu non raro Practiones
obrenice (olec) Numeracor vel Denominatori equalis, vel ip. impropria.
Lomajor; Hujulmodi Fractio Impropria dici lolet; uc quae quid
Ulnicaci aequale vel eriam ipsa majus indicet. Sunc enim ha-
umodiFractiones =3 237, _c. cancundem acque ipsa Vni-
tas r. Nempetum duo Cemisses, cum crescriences, cum quaru-
Or quadrantes, ac. iplum praecile Inreorum ablolvunc. AF Z3
233, ec. etiam duo incegra; quippe bis coc partes numerae
tractio, quoc denominacor indicar interro concineri. Item
2,233, _C. cancundem ralent acque 3, sive tria integra. PF
in religuis paricer. Similiter de 3, Z, _c. judicandum. Cum
enim 2, duo Temisseo, cantundem LinE aEque I; CrUnC Z, ErCB
Temisses, cancundem acque 1. Z. unitas cum Cemisse. Icem cum
 lexerientes, cantundem raleant acque 2; erunt Z, oe0
triences, cantundem acque 2 Z, duo cum duobuscrientibus. P B
similicer in aliis, ubi Numeracor DenominatOre MajOr, nec 12-
menhic illius aliguoca pars. Si enim Denominator At Nume-
ratorispars aliguota, Fractio haec impropria aequivalet nume-
roinccero: Sin minor, nec camen pars aliquocas reguiralce im-
propria Fractio numero incepro cum adjuneta parcicula (cu
Fractione propria.
Cum vero priorilla Fractionum exposicio, per nius Incea Firactionum
Bei in aequales aliguot parces diremprionem, uc ut tractionibus
propriis explicandis lacis accommoda, impropriis tamen haud
ulque adeo conveniae, (quippe Clnius Incegri plures altumi
partes non possunt, quam in ipso omnino conrinenturs quod
exigere videatur Impropriae Fractionis numeracor denomina.
coremajor:) Porerit secundo modo Fractionum nacura, com-
modius huic nezocio, explicari, per diremprionem, non unius
tancum, Ced plurium simul Inceororum (quoc nempe indicat
Numeracor) in partes aliquor aequales, (tot nempe quorDe-
nominacor postulac,) guarum unam aliquam allumendam Fra-
ai
explicatio
altera.