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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 395, page id 1815201908:0452
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I.
10
B
15
0.
D AR AB O L A.
parabolam in B, _ F. C diamCETUM In F, OCCUF-
rens vero DC linex in F.
DicoAB, AC, A F lincas esC in continua ana-
lo8ia.
Demonstratio.
DOnancur ex B _ E. ordinarim linex B FL. F. J. Racio
AFL ad AD duplicaca eAtrarionis HB ad DC; id
eAt FIB ad IF: scd ve HTB ad TE, SiC ATI ost ad A L.
igicurracio AHI ad AD, duplicaca cA racionis AFF ad
AI: quare AHI, AI, AD lincx, id eA AB, A P, A F sune
proporcionales. Ouoderac demonstrandum.
PR OPOSITIO LXXII.
Sto A BC parabolX diameter A D: ductisque ex A lineis quibutuis
A sAB, AC, qua parabolx occurrant in B _ C, ponantur ordinatim li-
nEx C D, BF; e B E quidem A C linex occurrarin F; crect aq F C P2-
rallela diameero AD, ponacur per C ordinarim HC, occurrens diame-
eris IB, K C in l ec K. rectae aurem AB in L:
DicoHL, HO, HI, EIK lineas in concinua esse analogia.
Demonstratio.
Voniam HO, PB, D C, ordinacim POSCE TuHE.
L_ FC parallela diamecro AD, rect∞ FIC, ITI.
HK in concinua lune analogia. (od _ TIL, HIO
HI b proporcionales TunE. igitur HL; HG, HII
HI K in concinua lunc analosia. Quod erat demon-
Arandum.
PROPOSITIO L.XXIIL.
Sco ABC parabolae diamOteF AD, _C OF,
sdinacim ad illam polita C D. ducaturau-
rem ex A linea AF, sectioni occurrens in F:
actaque per F ordinarim FC, CrisatUF Ex C.
diameter C F, occurrens FC in F; iunganeurque A F, quae LD linex OE
curratin H, sectioni vero in Bpuncto ex quo diametet demrratur BH
secans FC lineani in L, & C D in H.
DicoHC ad C K duplicaram habe.
re rarionem eius quahhabecF F adF. L.
Demonstratio.
DOnatur ex B ordinatim linea BN. 900-
niam FC diamerer est _ HICD ordina.
tim polica ed diametrum AD, rectae AB;
A FC AFI proporrionales luncigitur et AN
AC, A D, icem BM, FC. dCDlincx, id cA
KD, CD; HID; in concinua lunc analogia.
Duare: cum veriusque Serici prima BNI, K D
equales sint, racio HD ad C D, terrix ad
t
   e t te   se s t  e  Al  
111
u