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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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L LL
V
Sectionum oppositarum ac coniuratarum affectiones consulerat.
PRO POSITIO XXXII.
EctiOnES OpPOLIEX COMMIULES HaBEHEaCyMPEOTOS.
Demonstratio.
Inc ABC hyperbolX asyMPEOTI DL, DF:
policoque axe DB, ducancur concingenri
per B, duaae, aequidictances GI, AR: prO-
ductis deinde lineis F. D, FD, BD, AaNEDL, DV.
DT aqualesipsiS DB, DI, DK; ponancurque
PeF L, V, T linCA ML, NP, OS parallele li-
neis EB, IO, TIK; quoniam igicur aqualeslime
linex DE, DB, _ anguli D L M, :DB F. ad hxem
recti; criangula D L. M, DBP. adcoque e lacera
TM, BF xqualia Cunc: Similicer octenduneur la-
cera VN, T9 aequalia laceribus at TIK: igicuE
Ehanc L. M quadracox qualia rectangula NOP.
DRS; puncta L, O. RD ad lxperbolam Cunc.
CUIUS 2CyMPEOTI DMI, DP: dE NOP, ORS
rectangulaaqualia lunc rectangulis a GB, II AX
quia F B, LM quadraca xquancur; xqualia au-
cem lunc quadraca NV, OT quadracis an AIKi
reliqua igicur quadrata OV, RT xqualia lune
celiquiscir, AR; sunc aucem per constructionem
distantia D L, DV, D Y aequales dictanciis DB,
DBDK, CoppolicE igitur sectiones lunE L. OR,
BC A; que communibus faudene alymproris. Ouod crat demonstrandum.
PROPOSITIO XXZIII.
rEctiones oppolx lacera recta habent aqualia, quae communi infer.
muncdiametro.
Demonstratio.
i Adem allumatur fgura; Scque BZ lacus rectum hyperbole AB C, e per Z _
D Centrum, recta AUCAEUE, OCCUTEeNS P MI linex in Z: PaceE L X xequari ZB
(cum DB, D E linEx xqualeS SInC, _ anguli DLM, DB F xgualeS, Ob L M, BF
parallelas.) dico aurem L. X lacus recrum esse hyperbole ROT: recta Z Z pro.
ducta, OcCurrAE NV, ar lineis in Z e c: quoniam igirur Z B lacus rectum est, e
ExH hu. C Y ordinarim posica ad diamerrum D B, proporrionales (ine d linex BL, (7 1, las est
durem BI aequalis L V, per hypochelim, e ex demonstracione pexcedenci, rectae
C, 1co aequales VO; VY: recte quoque LV, VO, V Y proxortionales lunt: quare
La lalutc Tecum clthyperbolE I. OR. Ccctiones igicur oppolitc, et c. Ouod erat
demonstrandum.
lina
positarum
b11. buius.
bid.
P R O
nee e  o oa