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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 82, page id 1815201908:0139
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 pmmm
DR OGR E SSION ES
Pariratione si ponacur vlcerius produci leries progressionis, ita ve A B, C B, VB,
F B, F B, XC. Ponantur continux proportionales, demonstrarr porerie quacuox re.
EtarIgUIA FBAC, EBCD, DBDF. e C BB F incer lelexqualia cMc.
55
i PnR. Cd P, O. S FrZI, L, O 9ZL. V. 10120
cest s
15t .s ei SSCN BC RSCC CEECI iCEsWNIMCS LNEM
aCte  enis D iuuib nar B aimobiu
CInE AB, CB, DB, FD in conurua analosia, dec.
2tuii B
Dico quinquerectansula incer se aequalia esses quorum primum, est
illud, quodlub AB, BC tanquam una linea, e sub D F, continctur; al-
terum, quod delcribitur a CB; e DB eanquam vna, ac recta C D;
certium, quod a DB et F. B tanquam vna, e recti AC conticitur:
quarcum, quod ab fC, e C B; denique illud quod ab AD, DB de-
Ccribitur.
243. FInIHS.
Demonstratie.
Ectangulum enim AB DL. aequale cs rectanoulo CBCD: _ rectatou
b1bin. CBDF aquale estrectansulob D B CD: duo isitur rectangula ABDL, ex
EBD B id estrectarisulum sub ABC B ranquam vua, ee D P. Xe qualia lunc duobus
CBCD _DBCD, id est concento sub C BD B cariquam vnd, de sub recta C D:
eodem modo octendam sub DB P B _ AC contentum, aequari prioribus; de reli
quis quoque idem simili discursus demonstrabitur. Constac ergo veritas propositionis.
eROeOSIIIO ALMI
VIncconcinux proporrionales AB, C B, IB, LB, _C.
D
Dico rectangula ABCF, C B AD, e duo simul sumpca ACB,
ACDB, deniquerrium aggregacum, Scilicor quadrari l. L, rectanguli
AC F, e rectansuli C F. B, esse inter se xequalia.
errlaius. 
Demonstratio.
Voniam est ve AC ad C D, ita CD ad DF, eric componendo _ altetMaMdO, M
AD ad CF, AC CD ad DF: CCd vE CD ad DR, ica cst AB c ad C Bi igieur
8r6. Scxri. VE AD ad C P, SiC CH AB ad C B, SE rect angulu d ABCF. Xequale crir rectangulo
CB A D. InSIpeF quia es vE AB ad C B, ICa A C ad C D, crie rectanguluM ABC. D.
aequale rectanrulo AC, CB. Ouia vero ex aequo criam cA vE AC ad DF, ita AB
ad DB, erit quoque rectangulum ACDB, aequale ipsi ABDF: sed rectangulum
L.ddunai AB DE, una cum AB CD, aequalia C sunc rectangulo AB CF: rectangulum ixi-
TUT AB CF, aequalceriam est duobus ACB eC AC DB. Deinde quia recta AB
pai. secta esin C _ B, erir F A B CF aequale rribus CF in C A. _ CF. in C F ducto
(hoc est quadrato C F) X eidem CP in E B ducto: aqualia LunEiBIEUT inEEF (o.
Duod tuerac demonstrandum.
tROFOSI
A la2
Ine in continua analogia minoris inae qualitaris, AB, AC, AD, AF,
dc. et Torider lta u  esulatato er eriei, CH,
222. 41, c11 cel.
Dico
 u e   t   ue an   usu u e s e a  . u . u  e   1 t     d  e  u 1      1t   .   s  t A p11