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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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Demonstratio.
SILtsura AD C hyperbOLA Cx qua FOrmaTuI
est conoides, ec axis sED R: quo producto in-
veniatur lirperbolae ADC cenerum F. sectio
nedenique tacta DBF peraxem, e astumpeo
quonis puncto C in perimetro AD C, demit-
cacur ex eo normalis ad axem D F. qux (C C+ R3
exK aUTeM C R FI, normalis icem ad axem, ex
aoacur hyperbota DF A in orbem, aonec per-
venerie ad sectionem D FTB. quoniam igicurtry-
perbola CD A gencrat ex hrpotheli iplum co-
noides, paccclincam R C (ol0 Reu differre à li-
nea REI; eltvero e F A aequalis B F, cum am-
bxe sinc semidiam eeri. ErGO VE quadFAFI F. A ad
quadratum R C. Sic quadracum B F. ad quadca-
tum HIK. Scd, quia AD C ex hrpochehi est hy-
perbola, ve quadracum F. A ad quadraEuM K C, Sc a rectangulum F F. D ad rectan- ar. hyperb.
sulum FKD. ergovE quadrarum B F. ad quadracum IIK, SIC rectangulum F F, D
ad rectangulum LKD. Ergo D FTB hyperbola est eadem cum AD C, quae Forma-
vic conoides. Ouoderac demonstrandum.
PROPOSITIO CLXVI
ulnis sectio in conoide hyperbolico bali aquidistans circulum For-
MaE.
Demonstralio.
PFEconoides AB CD, d sectiONESPEFAxM AD C et DFB; lecllo aurem paral-
tela bas sic OTTI: ex dictis propol. 165. Pacer K C aqualem elle R HL, ec eodem
modo ostendam reliquaS OmMEs guX ex K ad perimecrum CK ducuntur, ae quales
essc. ergo OFII circulus eAt. Ouoderat demonstrandum.
PROPOSITIO CLXVII
Ionoides hyperbolicum sc-
scecur plano inclinaro ad
aXem.
Dico per axem conoideos
posse duci planum quod reccum
Cir ad plarum dacum.
CON OTDES HYDERBOLTCFH.
nobtosot abbe.
97
normaliter GFT ex C ad planum DB. F, crunt CHI _ C B, in eodem plano quod
per 18. undecimirectum exie plano D E. F. F. X quo Patet propolicum.
IEconoideos ABC planum D E F, Ce cans obliquE Arem B L in G: crect a deinde
 e  . 1 u .   t    i 1  . 1 . i i   .  e . 1        .    t       u.      . 1.   e    e  e1