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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 980, page id 1815201908:1037
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980
YN GV LM CXLIA DALCIA.
PR OPOSITIO XXX.
Erenta Agura propolicionis 28. LIFIRWOIUCTUM IL R NIR NOO SC.
L Bomencirngularis IBL. NO, ducanturque rectae BL, BI.
Dico dacum legmenti ungularis involuerum x quari duabus prrami-
dibus, quae generancur ex ductibus criangulorum BPK, et B L. M in
Ccipla.
Demonstrabicur eodem discurtu quo pracedetto, ex 40. abul de alletu plani in
Planum ee Scholio25. huius.
11
F. Denique huiclemicirculo ncibacus parabola AABC, CuuSasISBL.
Dicorngulam cylindricam cuius alcicudo est diameter C A, basIS VerO
semicirculus ABC, ad luum involuetum eam habere racionem quam
parabola AH BC ad planum mixcilinCUM HIK, LIR.
Demonstratt.
PROCDSITIO XXXI.
IF Temicirculus AB C PutaeSaOCctanSUIO ADE C IMICH-
DPeus,  BF normalis ad AC. cumorrum, diuidac eam bitariam in
128. auct. Y Emontrarum e Moo dc ductu plani in planum a Pemicirculum AB C ductum
Schol. 19. L inseiplum, hoc eltorngulam cuiusbasis est semicirculus AB C, alcicudo AC
mmius.
equari exlindro parabolico, cuius balis parabola AGBK C, alcicudo BF. Demon-
CSchol27. Etracum quoque est in eodem libro planum F G, II C ductum in planum compoli-
ius.
jus balis el pranum tL alciendo eadem BF, vebalisad Ba, Hoe en de patabota
do AC, cud uuminuoluerum ve parabola AR B R C. ad planum mXEIClI
cum ex HI CFIC, ex toro circulo cuius diamerer A C, hoc est c involuerum vneulg.
d136. duct. xquari solido d quod haber balim FTK, TTK, alcicudinem vero BF. Aequi crlin-
drus pataoocus cums baus en pacavera LLlCBR C alcicudo B F, est ad Colidum cu-
AR BK C acP LLH. CGd taga Cuius basis est Temicircutus ABC, alcicu
ob
HIK. Ouod erac demonstrandum.