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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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568
PR OPOKLIONALTTATES
quae rationum limuao apvellatur. ex quo Caris apparee; Geometriam
hucvique, quemadmodum circa varias macerias, ita quoque ineaquxe
proportiones considerar, mucilam remantisse; tanquam si rarionum dif-
limilium proporrio, ad Geometram non spectaret. Conabimur itaque
hoc libro dissimillimas etiam rarionum proportiones ad Geometriam
revocare: quirlus maxime ad Colidx magnicudinis considerariones con-
ducir; vrinam Ccomerrix studioli rasticarem Oceani Geomerrici perspe-
Ctam haberene, non haererent in elementis sulque deque inuerrendis, e,
vediciloles, decharra in papyrum eransterendis.
dt t 
Rationum denominatores Vocd, quantitates qua mutua habitudine
sua exponunt qualis ibsat a terrationes proporrio intercedat.
l
LLEATLO
 line raciones Aad B, C adD, e lincrocidem
ea, E, e F, quarum ratio exprimat proporcio
nem rationis AB, ad rarioneM C D; hoc CH, SiEquem-
admodum linea F. ad lineam F icaracio AB ad rario-
nem C D: haslineas, F nimirum _ F, datarum ratio.
num denominacores appellabimus.
Porro concemplationem cam omnem q; circa ratio-
num proportiones denominatorelq; verlatur, ad veram perrinere Gco-
meriam, de qua demonstraciones illa luas non lecus ac de simplicibus
quanciratibus, Formare poltic, exera controverliam esse debet: quae res ve
clarius inrelligatur sciendum est, non Polum lincas, Cuperkicies, d corpora,
ad Geomerriam spectare; sed orme id eni convenit eadem ratiO PFOPTeF
quam vel linex, vel superficies, vel corpora a Geomerra cractari postinc:
linea enim, Superficies, e Colida, non minus ad phylicam concemplario.
nem, imo Mecaphylicam perrinene, sccundum considerariones singulis
proprias, quam ad Geomerriam, gux in lincis, superhciebus de Colidisni-
hil aliud contemplacur, quam diductionem quancitacis, secundum quàs
linex incer se comparantur, aur superticies, aut Colida, quatenus vna ma-
ior velminor alcera, aut alceri est a qualis, aur vna per alteram mulciplica-
ri, vel inuicem vna alceti addi, auc ab alia demiporest. quae omnia circax-
qualicatem aur inx qualitarem verlaneur. vnde Omnes reS PHVLICX, pTOUE
huic considerationi sune subiecte, ad Geomerriam non minus spectane,
quam eres primaria species quanciraris: nam cemporis durario, motus
affectiones, ponderum momenta, ee sexcenta alia, secundum caldem
considerationes, Geomerricis Theorematibus subiecta sunt. Ouarecum
rationes quantitarum inter se parrim sint aequales, parrim inxquales, ac
proinderia alceri aqualis, alia vero maior, aut minor alcera, cumq. rario
minor amaiore colli queat, e rario per rarionem mulciplicari, de ratiora-
cioniadiunsi, etc. necessario concludicur etiam cationum noriciam, ad
Geome.
L F.
Pt
per