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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 598, page id 1815201908:0655
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AIY P F R BO L Ao
Constructioes demonstratio.
FTaE A C cerria proporrionalis, ad duas primas AB, AC. Dieo C. pundum esse
quod postulatur. Frisa ex s normalis ATI, delcribacurque hyperbola IRL,
cuius asympeori sInE A FI, A C: de AHI quidem xquidistances ponaneur ex punctis
7+. huins. B, C, D, Fn Fig Cr. Ve AB ad AC, a sCRC est ad IB; _ FD ad RC, vE AC
ad AD: Sedracio AB ad A C, auplicara est racionis A C ad AD; igicur _ Fa-
eio RC ad TB, duplicaca eA rariOMS ID ad RC. Similiter ratio MF. ad L D,
duplicaca est rationis NF ad HL, dec. Sed planum BK corles concinec planum
CLbquociesratio IB ad KC, mulciplicacrationem R C ad T. D. Duplum isi-
cur est planum BK, plani CP. limilicer CF planum duplum est DM, e hoc
c78. hu. duplum plani F. N, _c. Progleto isicur hlc est planorum in proporcione dupla.
Ouia vero AB, AC, AC lunc proporcionales, crunE C XO C, KC, IB con
cinux: ergo cumraris B L ae  duplicaca sicracionis BT, ad CK, planum 10
duplum est a plani BK, quod elac primum in Perio planorum proporcionis duplxs
 85. De Aequi cocaleriesmasemmum prepbrcionis duplxc dupla est prime magnicudi-
nis. Ergo planum TG aquacut cortleriei planorum BK, CL, D ME _C. hOC CATeF-
minus progressionis planorum est linea OC. Ouare et seriei linearum AB, AC,
AD, _C. in proportione ante posira continuaex que proeressionem planorum sem
per comitatur, cermihus est C. Exhibuimus isitur, ec. Quod erac taciendumn
PROPOSITIO CXXXIL
DOnatur icerum ratio BC ad BD, duplicata BD ad BF; _ racio
5.
Constructio eS demonstratio, ilqu
futac BL CerEia ProPOrtiOnalis de
BD, BC. Dico L cerminum
esequae sicum. Frecta ex B normali
ad B C, delcribatur txperbola
GFTT, cuius alympeocilinc AB; BC.
ec AB quidem aequidictances P0.
mancor Cer, DHI;LL, ER, LM. V
BC ad BD; EAC HTD est ad G C,
ae LL de AD, ee BD ad BF. lc
broprestior
B129. h1
Ius.
iasu
du
BD ad BF duplicaca rarionis BF ad BF, _C.
r31
Tacto BC ad BD. duplicaca clera
Oporreae terminum putus proerestionis extibere.
er cado. cionis BD adt BF, racio ixirur HID S ad C C duplicara quoque est racionis 1 1
l
  eC S a S C E B0 10 2022a Ea 25 3C et 120