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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 148, page id 826603459:0194
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De Divisione.
C
cationem e Dirisionem rocesillae primari a _ maximc propria
lua signiticarione innuane. Ec quo sen lu numeri Fracti PrO NU-
meris habentur eodem ec pro F’actoribus in Mulciplicatione, d
in Dirisione pro Dirilore vel Ouoriente haberi possune. Icagi
_ hoc senlu, quilibee numerus (sive inceger Ere etiam Cractus)
numerum quemlibee diridere poceric.
Adcogi, ue rem paucis comprehendam, cum lensu srictio-
xi lumancue, Multiplicario quaerit numeri dati multiplum; divisio a
liguoram parrem: cum Centu vero laxiori usurpantur, dicenda
Potius eA Mulriplicatio, gnantitasi aliam in darararione exhibere; Cive
quantitatem, quae ad datam datam habeatrarionem, investicare: Divisio
vero, datis duabus quantitatibus homogeneis earum ad invicem rationem
investicare. Neq; incerim aliquem cerreat, quod hoc laxiori sen-
Iu cadem operatio utroris ad libicum nomine appellari postuc,
nam il lud ommino concedendum est, cum perinde sic omnino
Mulciplicare per 33 2, Z, _c. acq; dividere per Z, 2,3, ec. ut
luo deinceps loco clarius patebit. Ouod eo minus mirandum
eA, cum _ idem in aliis oppolicis operationibus contingar; uto
Doce in additione se Subductione, cum perinde omnino cA sire
addauS 23 i 33 4, _c. live Cubdacaas i 233, L 4, _C.
uc ex lupra dictis pacet.
evisio non Incerim monendum ese, quod, ue mulciplicatione (laxiori
sempe nu lensu Cumpca) non Cemper ausecur quanticas mulciplicaca, sed
rum minuir. aliquando vel eadem manec rel eciam minuieur: sc dirisione
Claxioriicem Censu CumpEa) non Temper minvitur quancicas
dirila, Ccd vel eadem manet rel eriam ausetur. Nempe, quo
eies Dirilor ectunitace major, Ouoriens eric numero dividendo
minor; quocies aurem Dirilor est unitare minor, Ouocions erte
numero diridendo major, si deniqs Dirilor sic unitas, Ouori
ens numero dividendo aequalis eric. Racio manifecta est. C um
enim numerus Diridendus ostendac quories iple contincar uni-
cacem; Ouociens autem, quories idem diridendus contineae
dirilorem: Si dirisor Rcunicare major, pura 2; manifectum est
quorientem numero diridendo minorem esse, cum eodem nu-
mero diridendo pauciores concinentur binarii (Nuasts) quam
unicares: Cin diricor sE unicace minor, puca Z; manifectum
icem est quociencem numero diridendo Futurum majoré, cum
numerus diridendus plures contineae lemisses quam inceeras
unicaces:  deniq; DiriCor sic unicas, quociens erit numero divie
dendo