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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 42, page id 1815201908:0099
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put.  m puIyI
L EN E A R V M
nux proxortionales, erie BC F recrangulum, aquale quadrato C: igitur quadra-
BD A rectansclum, aqualc (ic quadrato C D.
cum A est ad receangulum BC F ve A quadracum, ad quadracum C; id cA peF
constructionem VE D ad F. Isitur recta B F quandam addidimus, etc. Duod crae
P R O P OSITTOLXVI.
Faciendum.
AEX linCX AB, inx qualicer in C diuila, quandam B D adiicere, vE
Conderuetio es demonsl acto.
tar AF aequalis C B. e AAE qua-
drato CB aequale rectangulum
CBD. Dico factum eNc quod peri
II Fuerie A ad B, ve C ad
BaLdat, ve  adFI.
 ico All rectangulum,
ad rectanoulum BC, cam
tur. Sunt enim per constructionem concinua DB, BC, CF, 8 quia AF xqua
25. Huius. lis est CB, CrUNEX BD, DC, D A a Concinux proporcionales; unde CD qua
draco a quale est rectangulum B D A. addidimus isicur rectam. Duod crac Facien-
F
STTTO LXVII.
auttt.
habererationem, quam habet C F rectansulum, ad rectan SulUI D F.
Demonstratio.
b23. Seuri. p Ario rectanguli AFI, ad B C rectangulum, ell ComPOHTA Ex rationC A ad b B,
_ ex FE ad C. Sed ecam ratio C F rectaHeII, du rectangulum DF, Compo-
SIca est ex FatiONe C ad D, Id eIE PCL COMICTACHIOHCII IL al D, d CK L AH F, id
est H ad C. isitur rectangulum A FI, ad rectangulum B C, cam habet rationem,
quam CF rectans, t ceast DP. Quod erat demonstrandum.
FInE
STTIO
Lin concinuaratione, line
L aurem e aliae qualuor Lt, C
FI in continua analogia;
Dico AII rectangulum, ad rectangulum D F, rationem habere eri-
plicaram eius, quam habetecai at, a ectan ulum C F.
demonsratio.
cIbid.
D Acio rectanguli AFF, ad rectangulum F. D, Ccomposita est ex ratiONC A ad D,
+20. Defn. L; d est sextriplicaca dracione B ad C, giia L, B, C Conla cumt proporcio-
duinti.
eZSei nales _ ex II ad B, id est ex criplicata Taloe e At F; led B C rectangulum,
de lectangulum C F, rarionem habet compoam ex cB ad C, _ Cx G ad fi: lgieUF
reccansuu A FL, acrecasc DC, rationem habec rriplicatam, eius quam
habec D F rectangulum, ad rectangulum C. F. Quod erac demonstrandum.
 ut t e e  i e es s . e t et  e i  p tle 1.     e p    p . 1    1.  1 t 1a   1 t qu  d Mrpn