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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 530, page id 1815201908:0587
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ARO PRIMILL
tosecono educit, primasque  fandamentales hyperbola passiones de-
Typerbolam; sectione sq oppositas, es coniuratas, denique  a sympto-
monstrat.
LLOPOSITIOMK
ullo aeil pla
16. PrO-
8. hu.
munemecet IL.
 io pel dacta tel
 TurBAC, cu
 aurem _ alECrO
plano, secante balim CM
lecundum rectam lincam
FD, ad BC balim cxianBu.
lectionem In luverHcie cOn
Faciar lincam DHF: sectio-
nis autem diameter LF pro-
ducta, cum A B lacerecrian-
suliperaxem, extraconiver-
ricem conveniae in puncto
L, deinde alTutapeo in FF
diametto puncto quonis I,
ponatur in plano criansuli
ABC, recta CKI, aequidi
Aans B C. e secundum G I,
platium ducatur OITI, Equil
distars plano bateos, exHi.
bens inplana LLi L, com.
Dico esc ve quadratum I FL ad quadrarum F D, SICI HF rectan
gulum ad rectarsulum. L. F F.
Demonstratio.
CMMelectiones parallelae, ec quia PD nornalis est adBC.
826. onac. recta quoque FTK ad TC Parallelam B C normalis est; rectarioulu ipitur CK L, a.
cimi.
quale est quadraro c HTK: rectangulu aucem B FC, Xquale est quadrato F D; qua-
ess.. deacumigicur IIK ad DF, quadracum, est ve C K Trecrangulum ad reccangulum
BFC: quia veroracio GKY rectanguli, ad rectangutum B F C. compolica est ex
ratione OH, ad BF, id CA LK ad LF, ee ex racione RL aH FC, id est FR
ad FF; Cic aurem ex ijidem quoque racio compolica rectanouli IK F ad LHB.
xectangulum: ve C KL reccangulum ad recrangulum BF C, id cAt quadcarum HR,
ad quacracum ED, sc P. K E recrangulum est ad recransulum PF F. Auod erat
demonstrandum.
Decieliscncthet eote goa eolsvop r. 213 Vocdtbi
li ABC normalem, quod
NVoniam planum OFIF, aequidistat plano balea BD C, circulus = eA C FF L, e
Su      ats t  ue pe te  t te e e te e t et  t  se te et t   t at Ae e te tote e set pt sse  t e e ute  e  e  e  t    te t ti e ut      e e t l 1