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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 224, page id 826603459:0270
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uantitarum invicem comparatio
CAP. 25
cetsus sire differentia. IEa B CX L2 auFexAntUF 1O, rettant 2; du
abus itagiunicacibus, hoc ille major est, hic illo minor numerus.
Si ex cripondio bipondium auteratur, excelsus reperitur esse II.
miuspondo. Nempe, h Peracta subductione nihil vel luversit vel
deticiac, Equales sune illae quanritates: sin secus, inaequa less
quipre Major illa, ubi aliquid redundar; Minor, cui aliquid de-
est quo minus alceri sic xqualis.
Polterioris Colurio Diridendo inveltisacur. Diritionisnem.
De quotiens ostendic rationem Diridui ad Dirilorem. Sic I 12
Ratio inve. per 6 diridaneur, prodibic ouociens 2; cui cognominis ratio
stieatur Di. Dupla, illa est quam habet numerus 12 2d6. Icem quadru-
dstbebee
Dondium est bipondii duplumi quia h 4 pondo per 2 pondo di-
vidancur, prodibic quotiens 2: quippe tories hoc illo pondus
concinetur. Ecpropterca, Dbi quorientes invicem equantur, ibi
e quantitates in eadem ratione constitmra incelliBanEuT. OuipDe Ra-
rio ex Quoro rectimaturs adeoq; de exhorum aequalicace aequali
eas carum.
Verum incerim nocandum et; de illa rantum Diritione jam
Sed ea tan- agi, quaquonticas per aliem quancicacem sbi homorencam
ium quae est diriditur: ( quippehomogenearum cancum quancicacum e
guantitarum ad inricem racio.) Oua ouociens Cemper henumerus, vel
homocenea- Quid numero homogeneum, quod quaeltioni Duot vel Duories
rumo
relpondeac. Sic rario q A ad A (sire linc illae dux lincae, vel
duae luverticies, vel duo pondera, rel dux alixe quaecunque
quanticares homogenca,) cA quadrupla, quia A) 4A C4; nem.
Dequancitas +A, quanciratem A, concinet quater. Sic racio zA
ad 2A est Celquialtera, ca nempe quae est 3 ad 3, quia 2A) 3A (33
nempe major minorem conrinet Z ricibus, sive Cemel cum
Lemisse, Cire roties quories 3 concinent 2. Sic ratio rectanguli
VBad AB eA Z, quia AB) VBC X; nempe rectangulum
VB cocies continet rectangulum AB, quocies recta V continee
rectam A. Sic ratio 6 ad 2 cA eripla, quia 2) 6 (3. Racio 6
a l4 eAt Celquialrera; live ca quae 3 ad 2, quia 4) 6 (2 = 12.
Sic 3)2(3. A) V CX. Exin aliis Cimilicee,
Acqi hinc eA, quod rario alterna non ubiqs obcinoc; sed lo-
lum in quacuor proxorcionalibus homogeneis. (Ouod nOtanE
incerpreces ad 16c5.) Puca, lipondus A ad pondusB, uc li-
neaae ad lineam B: non camen dici potelt, pondus A ad line
ama, uc pondus B ad lineam B. Ob caulam jam astignacans
Idc045
224