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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 768, page id 1815201908:0825
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768
236 hyperb.
B Colligieu
discur
hriu.
DV CTES PLAN
DROBOSTTIO ZCLI
AETFHUM ADC LECCFFECTA GNAHISLED Non per centrum acra, duecis.
que per A e B orchogonis AC, B H describantur oppolice lecriones
AIE B, C L. Hhabences cenerum M commune cum cenero circuli.
Dico E L ducrum in TK ad F L duccum II IC, cam habere rarionem
quam L. LL seclangulum haber act ectangulum PIC.
Demonstratio.
EctangIUm a Z TK est ad rectanGN-
lum LTK, ve ATB rectangulum ad
rectanigulum AIB, id est ve F IC rectan-
oum ad rectangulum F IC. Ergo omnia
rectaHguIa L. IK Cunc ad omnia F LC, ve
vrum LIK ad vnum FFC. unde cum
AB alcicudosc communis, crie b L I pla-
num ductum in planum IK ad FI ductum
in TO VEL TK rectangulum ad rectangu-
lum FTC. Ouod Fuit demonstrandum.
cunque orthogond LL, qua etum paralieta ad L P. hancque CI lincis
Demonstratio.
Veatur diamerex FB N cransiens pet
coractum B, ostensum cslib. de TIyperb.
cpncta BHHI eNC ad Hyperbolam: vnde
LHIT rectadgulum est ad rectangulum
L. HLL vE N EI quadracum ad quadrarum
NHL, id elt B quadrarum ad quadearum
TB, lcd ve IB quadracum ad quadracum IB:
sc eriam M IO rectangulum est ad rectanou.
lum MTO id es IM L. rectansulum ad re.
ctangulum IML.; igituE P III rectangula
proporcionalia lune rectangulis TML. ergo
omnia rectangula IIII sunc ad omnia re-
ctangula TML vernum rectangulum THL.
ad ruum rectangulum TM L. vnde cum EB
R 
Seo circulo AB C quadratum circum leripeum DE, actisque per C
scenerum lineis GM I qua circulu iccene in M, 2gantur per MI quot-
POSITIO XCV.
aquales HE LII, constat puncta LIHL, eNc ad hyperbolam.
Dico te planum ductum in plaHuI LIL, ad IM, ductum in ML, ese
ve IHI L. rectangulum ad rectangulum INI L.
202. By
bob.
135. hyperb
16. tains
dum.
Collisicur alcicudo sic communis, cFTT ductum in FTF, ad TMI ductum in MF, eam obcinet
n discursa rarionem quam L. HIL rectangulum ad rectangulum ZM L. Quod suic demonstran-