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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 304, page id 1815201908:0361
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ELLIPSIS.
productis occurrens in E _ F. deinde ex cenero B ducarur BG, ipSIF F
Dicopunctum C eAc in Peripheria ellipleos, cuius diamecri coniusa-
Demonstratio.
IXcencro ad concactum dueacur BD, ex quia C B ex
Chypochesi est parallela cangenei LD, eric OB ordi-
nacim polica ad BD, _ quidem ad centrum. vnde BD,
OB sunc diameeri coniugacx. iunsantur deinde AHIC
et DE, ex C duCatUE CK paFalIela ipH AB, Oc.
CurrenS BD procracta in K: qua sectionem in C
concinsit, crirquore AHI ad TIC, ita BHI ad TTK:
sedre AII ad FIC, ita est AB FI criangulum aderian
sulum HBC, _ ve BHI ad FTK, ica est criangulum
HIB C, adcriangulum HC R: ergo vecriangulum ABII
ad ipsum FTB C ica est criangulum FTB C ad criangu.
lum FICK: erro componendo, ac permurandocrian-
sulum AB C; ad criangulum BC R cst. ve. criangulum
BFT C ad triangulum FIC K, id est re iam oltentum, ve
criangulum AB FT ad criangulum FIBC, id est velinea
b Pares ex Sulum AB C. ad criangulum BD F, VE AFI ad FIC. Vicerius quoniam DF, GB
olemensis. Lune parallela, eric criangulum b G DB, ad DB F criangulum; ve GB, ad DF:
sed, quoniam ex hypochesi FD, GB, DF sune concinux, ratio GB ad D F,
crog. hy. eH dimidiacarationis F. D ad D F. Frsoracio crianguli C D B ad criangulum DBF,
dimidiara estrationis F. D ad D F. Aequicracio AEI ad IIC, hoc est reostensum
supra, ratio crianguli ABC ad criangulum DB F, dimidiaca quoque est rationis
FD ad DF. crootriangulum GDB est aderiangulu D B F, vecriangulu AB C ad
idem criangulum DB F. aquantur igicur criangula CDB, AB C. ergo e parallelo-
erammum concentum semidiamerris, re supra ostendi, coniugacis, CB, B D in angu-
aeacaex lo OBD aequacur parallelosrammo concento sub semidiamerris coniugatis AB.
2 huimo. B C. Ergo spunctum C eAt ad ellipuim. Quod eras demonctrandum.
eROPOSITIO CXVIII.
Inc rursum binae diameeri coniugare B A, BC. FF sumpeo inperime.
Vero ellipsis puncto D inter A, ac C, tangac elliplim F F in D, Oc.
currens diameeris in P. de F. Deinde ex centro B ducatur ad perime.
erum BC parallela tangenti.
DicoFD, CB, D F eseinconcinua analogia.
304
aquidistans, (EGue G D IHCdIA INECE F LD, DF.
Ex AB, BC, _ TangCIIS LV.
2 30. huius.
Demonstratio.
FHOI HC AIIGA L B MHIOT VeI MaIOI quam CB media inFeF F. D, DF. FreO
ver praecedentem punecum L estad elliplim. quodtieri non potenteum ex
Docheli punctum C ad ellipsim existar. Nullaisicur praerer CB media estincer BD,
DF. erSOF D, CB, D F sunc continux proporcionales. Duod erar demonstrandum.
e e e  e  e i. 1 st e  e  e t  et  e   t te ste   1  e t t  te 1e  p p e  e      t s t s e   e s  s e e tt e t e u et  e uss 1  1