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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 333, page id 1815201908:0390
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1
DE.
CenII
esta
F L L IPSIS.
REVC HII ad F I AC L MI ad OM: IBICUEDE KN ad PH, AC LM CM d OM. d
permurando ve K N adt LM, hoc es EN ad IMI, sic PN ad OM. in directum
igitur TunE I, O, P. GNArOCUM RNI, LM ad AC, sine perpendiculares, ac proin-
de incer le parallelaes criere II ad P. R, Ac IO ad OP. Guoderac demonstrandu.
PR OP OSITIO CLXX.
Virculum ABC secent diamerri dux AB, C D ad rectos sele angulos
decultances, actxe que per C e D linee que circulum contingane inC
d D, concinganccriam ellipsim A F. B cuius aliqua sic diamerer A B. dein
quaeuis ducatur C HI parallela C F; occurrens circulo in G dc l, ellip(i
vero in I e FI, e C D linee in HI.
Dicolineas GI, HIK essexquales.
Demonstratio.
EX concactu ponacur ad centrum
FN, quae aproducta incider in
punctum concactus L’ad hanc dia-
mecrum, vepacet ex alibi hoc in libro
demonstracis, eruncordinacim poli-
Ex K HI, AB, inde rectangulu P L. F.
eA ad rectangulu F. NV, ve qua
deacum L. II ad quadracum NB, Scd
rectangulum P L F est ad rectangu.
Ium FNF, ve rectangutum CMD
ad rectangulum CNYD, (cum enim
CF, DF b dC K HT exhypoches sInC
parallelae, rectangulorum illoxum
rariones ex ijldem rarionibus Com-
Ponuneur,) et rectangulum CM D, est ad rectansulum C ND; DE quadratuIM ML
ad quadrarum NB, quadeacumigicur M I est ad quadracum NB, ve quadeacum
E II ad quadratum NB; x quantur ergo quadrata MI, L. IT, adeoque _ rectX NI I
LH carumque dupla C, L, K HL x quales lunc. Ouod erat demonstrandum.
PROPOSITIO CLXXI.
VEmicirculum AB C cuius diameter A B ee concrum F; contingat
recta CD, aequidistans AB, et per A de B, puncta elliplis describa-
cur que diametrum habeat AB, e rectam C. D concinsat in puncto
quonis D: ex D vero ponatur D F occurrens circuli peripherix in F, 192-
curq per P parallela CH, secans elliplim in H ex I, circulum vero in 
de F
Dico lineam CHL in 1 et F, critariam c e divilam.
Demonstratio.
3
ona el per praecedene e aqua
lis efablata Co LF, aset FHI,
aequalis CI; sed iph FII aequatur IF (quia
FEI ordinacim posica est ad diaetrum DP)
aequancurigirur GB, IF; FR linea. Quoe
Cracdemonstrandum.
B13. bol 11