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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 169, page id 1815201908:0226
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P
3A
e
CIRCV LV
Femicirculo A F B, crune similia triangula e
aequalia ABF, E B C: vnde _ AP, F C Xqu2 - 3
les lune lincx.
Ouarto. Contingar recta C D, circulum dia-
merri AB in A, adeog d punctum F, idem sic
cum puncto A. cum igicur D C sc ContinsenS,
erune B AD, B A C anguli recti: lune aurem
aequales anguli ADB, ACB, aequalium sc-
mencorum; igicur criangula ADB, ABC, A-
milia Cunt e xequalia. uod fuit demonstrandum.
PROPOSITIO III
luilo circulo in sex parces aequales, punctis A, B, C, D, C, F. ductis.
Que BF, C F, PONANEuE BD, F D, Occurrentes C L. in C de HI.
Dico C. F. lineam in C 8 HI eritariam esse divilam.
Demonstratio.
Vm enim arCUS BD, DF, F B pONAnEuEX-
quales, eric BDF criangulum aequilacerum.
inde cum CF, aequidistee BF, crit _ GDHI
aequilacerum: CA aueC GD aequalis b C C+ eCFID
aequalis FTF; igicur C G, GTF, FTE linex, lunE
incer lexquales, ex CF in C e II critariam di-
vila. Quod erat demonctrandum.
PROPOSITIO IV.
Ecent seinuicem equales duo circuli ABC, DEF- per mutua cen
DEra C, F, tranleuntes: linex vero BD, per veriulque contrum actx,
parallelaponacur quaenis HIC, occurrens perimetro in F; de per F li-
nea C F A.
Dico GF, F A, aquales este.
Demonstratio.
VCaCUE F FI; quoniam FTG quidisAE BC CFIE AM-
suluS FHIP aequalis angulo HIF B. e quia arcus
HB, FF ob circulorum equalicarem xequales quoque
Cune, erit angulus FC F. xequalis angulo HIFB, adcoque
ansulo FHIF; unde parallelogrammum vel Rhombus eA
CHI: de HIF lincx aequalis C F, id elt CF; estaurem
rectansulo CF A, Cqualec HIF C rectangulum; ixieur
AF, C F linex dquoque inter le equantur. Juod tuie de-
monstrandum
Corollarium.
Inclequitur HF, BF lineas quoqueincer le requari
CUm HIF linca aquetuE ip(I F C: _ quia IIC cA
quaecumque aquidistans diametro BC, sequirur paral.
lelasomnesrecta. BF. caua circuli ABC, e conuexa
PFD peripheria incercepras, esse inter se aequales, cum
singula xquencur ipli BF.
B Deducien
1x105
lit
C35. 21r1i
sexsi