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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 274, page id 1815201908:0331
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L IPS
Constructio es demonstratio.
Tuisis AB C D bitariam in F. _ F, ASAHEUE CX
G CCnErO Per F e F diamerri CII, Cl; cum
eL dividacur in R, Sicur FY Ci diuisa cA in F, POna
curque per R ordinacim L. M, PaFeE per 53. huius
LIMI, AHIB segmenca esse aequalia; est aucem L. M
paralIela dace C D, igirur daco in cllipu sermento,
dec. Duoderar taciendum.
LABPOSTTIO LVITF
Demonstratio.
Voniam R L, ELL sunc parallelX rect_ AB, qua
es dIaCEEF CBNIUGAFA ip (I DC, CTUNE RL, FILOr.
dinatim posira ad BC. ergo ve rectangulum D GC,d
rectangulum DF. C, ica quadracum R C, ad quadrarum
HF. adeoque cum rectangula sine aequalia, cciam qua-
dracacruneaquaa, unde de rectae RC. FTF aequales
Cunc. Suncrero d CF, P I aequales, e anguli R OF.
lLL (quod HIBKC sinc parallela) aequales lunti igi.
cuF RC. F. criangulum aequale eAt criansulo PP. L, angu
lusque IF P Equalis angulo G FK, _ quia G F F. lines
recta cAt, anguli IF ES R F C ad verricem consticuri
sunc aquales: vnde R F. I, puncta sunc in directum, adc09;
(ectores RF D, CFL luncad vercicem constiraci: quia
aurem ostendi eriangulum K F C, aequari eriansuloIF F,
de simili discicsa ostendi possir criansulum quoq; DK C
Aequi e sectores D F R, IF C ad verricem posici. sune aquales. Pgitur reliqua etiam
segmenta DK, JC inter se aequalia crunc. code modo octenduntur D L, IL C legmen-
caxquasta. lcerum cum duo lacera RC, C FHnc duobis laceribus DC, C+ L. Xqua-
lia, de angulilareribus equalibus concenci ad verrice aequalesierune eriangula O7K F,
DOF Me aqualia, _ angulus CRF equalis angulo alcero CTL. D: ad eoquo
b st. Muus. K F L D F linexe parallelX. quare D D R, L L segmenea lunc inter se ae qualia: eA vero
iam ostenlum (cgehea quoque CI DR xequalia eNe, aequancurisicureria legmen.
Ea DR, LI, CT. vicerius quia DC, P. I jungutir equales d parallelas GL, FP I.
ipla eciam eruneparallelae unde rurtiim c Cegmenta CI, D Po aqualia liimrei ae quan-
cur lzicur quatuor sezmenea DL, C BFT, Id K. Rurlum quia K HI, L L. iUnSUnEKL,
HEaquales _ parallelas, suncipse eriam parallela: orune ergo nae qualia, criam se-
Ementa KHI, L. I. aequancur isicur quinque segmonca III, L ISR D, DF, CI. ACqui
etiam ostentum est requalia esse segmenca HIC, DI; aequaneur igitur omnia sexle.
omenca. Duod Fuerac demonstrandum. 
Vocetur aurem figura D K FTCIL, ellips inseripta, polrsonum regulare.
EenE ABC ellipum coningaex duae diamerri A B, C D. diuilaque
D illarum alcera quadritariam in P G, aGRNEUE peF F _ C rectae
II, IE L aequidistances diameero AB, iunganturq puncta D, K, L, C
dico L. D, DR, KH, HC, CI, IL. lincas legmenca auterre aqualia
aequari eriangulo TCF, cricrriangulum cocum D K F, xequale rori criangulo IC F.
111
47. huin
2bid.
d ibid
deL e
esto et
bit
i  s ts  pu  t s a tet at s    t et. p eti te te t e tt u le s ta  e  te ps et  e  e  et e e sa e e e  ute u e u u  e e    i aiut