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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 272, page id 1815201908:0329
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S2. Mius.
143. vorodu .
E LLI.
d
Constructio ex demonstratio.
Vneancur B D, _ ex A ponacur A F 2. quidistans BD,
LiAnOAnEUEGAC E D. PACCE DCFPTRCCdeNEEI DE F LC-
mencum aquale esse legmenco ABC. IBITUT ex pun-
eto daco, al. Ouod cractaciendum.
PROPOSITIO LIII
ECenE ABC elliplm dux guaeuislince AB.
LdDE Segmenta auferences aequalia: divisis au-
tem AB, I E rectis bitariam in C et LI, du-
CanEUE ver C _ FI diamerri IG C, IIIF.
Dico illas in C d IL proportonalicer este divilas. FF si diametri sine
Demonstratio.
VDSANEUE AD, BE. AC, DF, OHT, CB, FP, CF. Ouo-
niam AC B, D F F segmenca ponunturaequalia, AD.
DET ad TTF, cum AB, DF linex in G _ FI divila
Sinebitariam, igitur ec C FI linea aquidistat AD, BF
Jam vero cuim AB lic ad diamerrum IC ordinacim po.
Sica, crunc seomenca AVC, BC C b xequalia, ad coque
resencum ACC amndium segmenci ACB. Cimili do
calla scemencum D I IIdimidium est Ccomenti DFF.
OuatC Cum TOCA LCGMENCA AC B, D F F. Ponaneur aqua.
lia. Ctunc etiam sCgmenEA AGC, DF TI, eorum dimidia
incer le xequalia. Deindec triangula AC B, D F F. maxi.
ma lunc corum quae seomentis inscribi postune, de quo.
+4. buius. niam A D, B P Osten(x lunc pataster, eriam dinter se aequalia crune; X quabuneur
C52. huins. BUS A G C, DF I. LemaCC A. GuaI2 A C, DC, ergo C F linca c xqui-
diltarrecle AD hoc est CLL. Guate veC G ad OI, siC FH ad HTI. Quod crac
demonterandum. Alinc tam vericas converla tcmanifesta.
proportionalicer diuile: dico legmenra este xqualia.
E B linca a parallelae lunc. CA auTeM VE AC ad G B, SC
e cccotobtti
a C Orol. 2
igicur ex corum dimidia rriangula ACC, DF II: quae si autoras a sesmentis x quali-
PROPOSITTO LIV
IIEin A B C elliph quaenis diameerorum coniuratio AC, BB, iun-
ctaque AB, ducaru Guacs  C Pacalicta LLB; aC L a , fecta
ponantur GHI, Fu canua au cacctos BD, AC.
Dico AC, B     L. PPOOCL C aIIaS.
Demonu
A te ee p i t  e  pe u    e   e  p et se et e       e   a t a ee et e te      e e e   at    ee te a e 1e   e e et s s et   1