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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 327, page id 1815201908:0384
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Oreo
itert
rectat
ELLIPSIS.
32
rectangulorum BC F. Ligitur ve quadracum LTC ad quadrarum FTC: Sic BG L
rectangulum elt adreetansulum BC L. quare puncta B, li, e omnia puncta LL, ad
eandem lune elliplim. Quod eracdemonstrandum.
PR O P OSITIO CLVII.
Sto ABC circali diameter AC _ ex C recta quaeuis alela C Boc.
curranic circuli perimeero in B, dein ex B demiltarecca B l que AC,
diametrum ad reccosangulos secet in IC. ducaneur quorcunque linex F. F
parallela rectae B l’occurrences AC. diamerro in C, de lince, BC in D:
hanEque E D F rectangula aequalia quadcaris (7FI.
DicoLLHC puncta eslead candem elliplim.
Demonstratio.
J Z ED Frectangulum adrectanigulum
P. DF, SiC BDC rectangulum est ad
rectangulum BD C, id est rectanoulum
KOC ad rectanoulum R C C: sed
(quemadmodum alternando patet ex hy-
Pocheh) veP. DF recrangulum ad reCEan-
sulum F DP, Sic ITG quadrarum est ad
quadeatum HIG: IBITUEVE RG C FCCTAN.
sulum est ad recrangulum KOC, SiC LTC
quadracum est ad quadracum FI 5. quaret
KHC puncca lunc ad ellipsim: Ouod Crat
demonctcundum.
eROPOSITIO CLVIII.
VECenE ABC circulum OrEOGO.
Dnalicer diametri AC, B F act 293
Per B tangente BD: ducacur per P. centrum recta Gua uIs L.D, Occur-
renstanseni BD in puncto quonis D. dein rectx ducancur FHTI, pa.
rallelae cangenei BD, OCCurrenteS E. B diamerro in LIFI, et P. D linex in
LI: RarGuC VEF HI ad F HE, SIC TK ad IK.
Dico AKD puncta esse ad eandem elliplim.
Demonstratio.
DE linea donee accx per Mcangencioccur.
FaC in N. Ouoniam BD, NM; FTI linex aequi
distane, eric ve reccanoulum BIrM ad reccall
sulum BHM, Sic D LN reccangulum ad FCCTAN-
sulum DIN; Sed cst ve BHIM recrangulum ad
rCCEangUIUM BITM, sic Fi FT quadeacum ad
quadratum FHI, id est quadrarum TK ad qua-
dracum TK. igicur ve DIN reccangulum ad re-
cransulum DIN, sic est quadrarum IK ad qua-
dracum IR. quarE AKD puncca sunc ad el
lixtin. Quoderac demonctrandum.
DROduCTA B F diamecto in MI. ProducaLIE dt