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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 252, page id 1815201908:0309
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E. L L IPSIS
constructio es demonserculo.
deaco xquale rectangulum luper F B, B D; isitur _ quadraco A F. (nimirum GuartX
parri quadraci AC, cA enim AC bisecta in F) aqualC reCtanGUIUM SUPCF RP, F B,
quarca parsrectansuli FBD: quale, vein praecedenti ostendimus, ica criam hie
b23 sexri. ostendemus FT C quacato Guase eHe rectangulum TFTFTB. acqui RhombusBTHI
ad rectangulum TFTB, (rationes ent Llomei ad Rhomboidem de quadrari ad
rectangulum exiisdem rarionibus componuntur nempe ex TFT; 2d IFI ex THI ad
HIB, )etgocum quadracum THL deale sic rectangulo TFIB, etiam RhombusIFB
ordinacim applicacx LFFB. Qu(quod demonstratu cst Facile) à Rhomboide F BHI
in codemansulo, deticie khomboide limili ei qui in eodem ansulo sc à diametro
hntc. 7. DB d recta bP. BIMI FB est lacus, c redum. Quod perebarur.
Mnis recta (BF,) quae perterminum diamerri (BD) ducitur ordina-
Ecquae caris enri ducirur parallela, eA ordinarim ad diametru applicata.
Demonstratio.
otnins. PD VCatuEpEF E cenrum diameTEF A C (2) coniugata ips BD, haneque conci.
et ex
huins.
nux BD, AC, BF, ac B F quidem xquidistet diamCEO A C: ducacurque li-
nea F D, qua AC rectum secer in K, ducancurque ordinarim linex C FT, quX FD
linex occurrane in I: Ouoniam BD, A C, FB linex sune continux, erit A C qua-
in angulo IFIB est ad Rhomboidem THI B in eodem angulo, ve quadratum IHI
Rhomboidi TFTB aequalis crie; recta igitur PFT porest Rhomboidem in angulo
erOPOSITIO XIII.
tim applicatae (AC) r quidistans, elliplim contingit.
enim recta BF non concingar ellipum, secer illam
in C; diuisaque B C bitariam in FI, agacur per TI8
E, K Loccurrens vemque peripherix in L _ R. Quo
niam recta BC per Construccionem xquidistar AC
recamque aurem bisactam seccerecra IK d cric lR d12
meter e AC, BC lICa ordinacim ad illan poliex; leca
detem perconstructtonem recca A C ordinacim quoque
diameerum P D, igiettevna cademque reCTA A C ordi-
naC LCCat duaS diaMeCtOS BD, TR. Ouod Aerinon po-
cellidlias enim que ipli AC daceretur parallela, criam al
veraque tameero BD, K I ac proinde in duobus pun-
ccis bisecaretur; igirur patet FB lineam, sectionem
con-
 ue  u t ot a t t  . u     u  que  t   pt t te e t e e  u pu   et   e  t  t    p t     1   e      t i l 1