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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 103, page id 1815201908:0160
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GF O M E HBR IO A. 51
Ad argumentum porro respondendum est; dum dicitur: Priusquam Achilles ex A
verueniae ad B punctum, indtd CA cestudo ex B in F:
sensum huius propositionis coincidere cum hoc quo dicerur, prius debet Actoles apae p
ctum B, quam notet phuctum F. quod repuenat cursui secundum rationem motus; nam omnis
assienatio in hac materia contingurationem sub sistentia v Mathemarici serriunt, salcem fet
cundum incellectum acpreinde alicuius quietiso quae morui repuenat. erum hec in et atu
Philo sephorum dicta sufficiant. XD cuuxilSI L5 . A EL ILS ~ SIID Et tB ET A
Moina2 c3 mbfi RO P,
ighi edu
XFI. F
XX
AEd A B, CuiuS cercIA ParS AIE GB, RAE VE EOEA A B, Id C B eerciam
Tui parcem, ita C B ad C D, _ C D ad DF, e DF 3d LF, aC
que ita LeimpeT.
1F 12 040 5
Dico K cerminum huius prooressionis, bitariam dividere propolicam
magnicudinem AB.
Demonstratio.
CiRicenim ex hypocheti AB cum B K, aequalis coci seriei properrionis etiplX. aE-
Lequicoca series rations eriplae, a sesquralcera est magnicudinis primae, ergo AB a 86. huinso
cum BR, selquistera est prima magnieudinis ABs ergo BK, est eiudem dimidia.
quoderacdem onstrandum. :c st sih 2501100 il canibi
crgdusi credtii fis
p
37934. 7
S5
 BGCHII 23AOIDEL
tatur daturom Edant itcinup aidaoins
A ieu eril, eelae rirchreilonait OKFFIB, es l eoseq pluneg
2
1p S. SCI, EDBC FEIIBAO:
Etur quanticas AB, cuius quarta pars (ic B C; (I AaE vetOta AB ad
quarram lui parcem BC iet BC adOD, _ CD ad DF, E DF
ad F. F; acque ita semper concinuando, punctum Hhujusprogressionis
Terminus emersaC: C)  et se: olenih esi IA. L essiul. 10 230 31BI1F : b 3, 1A 
Dico B Hellc certiam parrem propoliex quanticatis AB. , 3: il BC A
Ba. S YA 10121CIET 3V 53I. YLN.
vissir
3C. acEI c Demonstratio:  1Ct. () Y. Isi uI tci
B1I
est 2i5.
Y 1
15. 1111
TAmexhypoches AB cum B K, est cora series proporcionis quadrupIx. Acquico-
caseries rarionis quadruplae est b auprimam magnicu dinem, re quacuor ad cria, b87. huius.
ErgO BK cum AB, est ad AB, ve quaruor ad cria. et dividendo K B ad AB, VE
urum aderia, hoc eA, KBcerria parS est ip suS AB. Quod erac demonAtrandum
et BC
P R G P OS, Lt. F. L. 8 mc HE.
AE1C ELCIEZ CCHEYISI BGCLCHLO S B, 3HAOSCI ssIOCIBEIN
15.
103
Acam magnicudinem A R, im in duobus punctis B, C, dividere, bE
AB ad B C, habeat TactMCaca CaCLL. L.POPLCIILB
ad BC. Concimuacae prooresio cerminerur in l.
C02