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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 AP. 25
Guoad Differemiam, e quoad Rationem.
325
Ideoq; quocielcunq: de proportione alcerna, Icu permucata
agitur, (aliare quae hanc involvacs ) haec semper lubincelligen-
da caurio, etiamli non delerris rerbis adiuncta fuerit. Oua de
re plura deinceps dicencur ubi propolicionem illam Fuclidis
26C8 tractabimus.
Eavero Diriliolire Applicacio, qua, verbi graria, rectanen.
Jum AB applicari dicitur ad lacus vel alticudinem A uE PrO
veniac ba(is B, vel COnEra; nempe A) AB (B, vel B) AB (A
vel eciam qua Colidum ABC axplicacur ad planum BC uc prg.
veniac lacus A, vel ad rectam A uc proveniac planum BC;nem- Micatione
DE BC) ABC (A, vel A) ABC (BC; aliaq; hujusmodi; non quid sentien-
nili narazensincos Diritiones rocantur: nec praelenci negorio cum
Tunc accommodae. Ouod enim prodie, Duoriens proprienon
eA, nec quaectioni quor aur quories respondet. Ouippe quae de nu-
mero quaerit (aue quod numero est homogeneum) non de
magnicudine, aliare quancitace numero hecerogenea. Nec qui.
dem Applicaciones illa, ad Dirilionem, alio nomine viden-
cur reterendae, quam prove quancirares illae lingulae ad instar
numerorum conliderantur. Non enim quaritur, quoties linea
A in Cuperticic rectangula A B concinetur; aur quocies vel A
dinea, vel BC planum, continetur in Colido ABC: Cquippe hoc
omnino eset incongruum.) Scd, quocies numerus pura quadea-
eorum in area paralleloerummi AB, contineac numerum longitu-
dinum in latere A, uc proveniac numerus lonsitudinum in lace-
re reliquo B. Icem, quocies numerus cuborum in Tolido ABC
contineac, vel numerum lonsirudinum in recta A, uE HaBCACMEnu-
merus quadracorum in basi BC; vel numerum quadracorum im:
Bali B C, uc habeacur numerus lonsicudinum in recta A.
Sed e ubi magnicudo alioua numero dividicur, PuCa
2) A
2
== A, non eam diriliO eAt CEaIEEM GUA PTRSenEI
negocio conveniat) quam mulciplicario; (nempe quancicas
A non cam dividicur per 2, quam mulciplicatur per Z;) quio-
renon quaericur, quories numerus 2. coneineacur in magnitudine A.
quod ablurdum esec) Sed dacae quancicaci A, alia in data ra-
tione quaericur; quod Mulriplicationis e, porius quam Divi-
sionis; quippe qua in Mulciplicarione Racio dacur, in Diritione.
quaericur.
Acq; hinC PATCE, Rationes omnes, quarumcunque ad invicem quanti-
BaSHB
Dequartita
tum ad hete-
rogeneas ap