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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 22, page id 824573315:0042
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De Aneulo contactus.
vis mulciplicarus superare nequeac:) e, licet quoad alia homo.
geneus HIC, non censeri tamen ejusdem generis quod ad proporrionem
artinet Rerero quo pacto ea, qua quond alia lune homoge.
nea, sine quoad rarionem hecerogenca, cgc plane non video.
Euclides cercez d5, ubi Racionem detinie, Homogenea, non
dubicar esse, quoad rationem homosenca: EC enim, inquiE. no-
yO ratiO, NO MEEDEOY DUOZEVCOY n XHI ZMXIXOTT C3S aMnNa ma
geors, duarum magnicudinum, ejusdem generis, muiua quaedam quoad
quansicatem habiiude. Siquae igitur duxe guancitates hoWOSCNEE
line (prour Clarius non negachos cAc ongulos) earum murua
ad invicem quoad quancicatem habicudo Ratio dicieur.
Duod aurem accinee ad ejulinodi quanticares homogencas,
sire ejuldem generis, quarum alcera quancumris mulciplicata
retiquam nunguam luperabic: Fuclides nullas sgnoscie tates
ele; led pnnos alserie, 5d5, Ouanciraces omnes, quaruni una
ad alteram Rarionem hibere dicendae Tunc, (hoccA, per 3d5,
omnes guancicates homogeneas,) ica esse consticucas, uc mulripli-
catae se muruo superare possint, E propcerea, in 2 c 10, illud postu.
lacum assumie, quali per le nocum, quodqi cemonstracione non
indigeat. Quantirarem quam libet minorem tories mulriplicari pesse ut
tendem majorem quomlibet assienarem superet. Nam in ipta constru-
ctione lcu no. ondn ad iltam demonstraciorem, ctacim jubee
Magniiudinem minorem assienaram rories multiplicare, donec majorem a-
henatam superer; quasi quidem illud feri porse nemo dubicarerit.
Et similicer Aechimedes passim. ACneq: Euclides neq: Archi-
medes, illud heripose, in aliis lire ansulis live quancicacibus.
masis quam in ixlo ansulo concactus, alquam oltendic. V et
isicur universalirer rerum est, de postulandum, Cuamlibet
quanciencem minorem cories posse mulciplicari ut quantibce
majorem attienatam luperee; vel Calcem luclides aut Archite.
aes illud specialicer de gnibuldam quancicacibus demonstral-
lene, quibus illud conrenic, e non tanquam univerlalicer rc
rum _ per se cornicum pottulallent. Pocerat etiam Clavius
meminisse, se Puclidem reprehendisse, quod axiomare 1X (vel,
Cccundum alios, postulaco 5) alsumpleric, duas rectas ad invicem
in eodem plano inclinaras, si producantur, tandem concurrere; quoniam
hoc, quamvis rerum (c, non cmen sraris alsumendum erat led
demonstrandum, ideo nempe quia in lineis curris hoc non
conttat (de quibus nec Fuctides illud aRerit. ) Idcoq; C lavius
3