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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 258, page id 826603459:0304
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SC
De Rarionibus.
Hujus Species lune, Dapla. Ec(-
quialcera, Dupla- selquicercia, Du-
Pla. Telquiquarta, _C. Tripla-
lelquialcera, Pripla. selquitertia,
_c. alixque ejulmodi in intini-
tum. Sic ratio 9 ad 4, est dupla-
Telquiquarca; 7 dd2, est cripla.
lelquialeera; 42 ad 20 est, quadrupla. Celquiquinta; rOr ad 10,
est decupla. selquidecima. LEparicer in aliis.
Dupliciitag; charactere opus elt ad hanc rationem expri
mendam; alcero, quo species mulciplicicaris indicetur, (dupla
cripla, Bec.) altero, quo delignetur aliguoca pars, puca, num
dimidia, cercia, _C.
Uibi aurem ratio quantitacis majoris ad minorem est mulei
Dlex- superparticularis; minoris huius ad illam majorem dicieur
Dubmulriplex. superparticularis. Hlujulque species speciebus illius
corrclpondene. F. Rigicur 4 ad 9, racio lubdupla. selquiquartas
2ad7. Cuberipla. Seiquialcera; 10 ad 42, Lubquadrupla. Celqui-
quinca; r0ad ror, subdecupls selquidecima. EF Rc in aliis.
Racio mulciplex- Superparciens, est racio quancitatis majoris
superparriens ad minorem, quando major minorem aliquoties concinet, et
Peo super
Parciens.
iplius inluper aliquot partes aliquocas. EIE8 ad 3. Nempen-
merus ille hunc concinetbis es duas insuper hujus parcescerti
aS Cre trientes.
Hlujus species lunc; Dapla- luperbiparciens. cerrias, Dupla-
Suxerquadripartiens quincas, Tripla. Cu.
perrriparciens. quartas, Oundrupla Cuper-
cripartiens, seprimes, aliaq; ejulmodi int.
nicx. Tales Tuncrationes 8 ad 3; 14 ad5;
I5 ad 4; 310d7. _C.
Triplici icagi charactere opus ese ad
hanc rarionem exprimendam: quo cum
numerus mulciplicicacis, cum numerus parctum aliquocarum
tum harum denominacio indicetur. ut pacet.
Ubi aurem quancitas major ad minorem est in ratione
Mulcipla suxerparcience; est minor haec ad illam majorem in
racione Submultiplici- superpartiente: et species hujus speciebus illiuo
correspondenc. Ica rario 3 ad8, est Cubdopla. Superbiparciens.
FerEiAS; 5 ad 14 lubdupla suxerquacriparciens. quincas; 4 ac
Submulie.
elex- super-
parricularis.
Mulriplex.
10) 42 (432 = 43
10) 102(10,F = 2015
Submulri