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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 275, page id 1815201908:0332
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E L L IPS+8
eR OPOSIFIOLIR
Adem manence Egura propolicum sic ellipsi heragonum regulare
inlcribere.
Constructio e demonstracto.
Vmancur dux quaeuis dinmetri coniueata AB, CD, duitaque ED quadrita-
riam in F e G7, AGAHEUF Per F _ C lincae FTF, RL aquidistances AB: du-
CaNEUTGUC DR, RFI, ETC, CI, IL, LD: Pacec per praecedencem: rectas illas se
smenca auterre aqualia, adeoque figuram hexagonam DR, ITC, TT. D, eAcregu.
larem; igicur ellipsi hexasonum inscriplimusregulare. Ouodcrac taciendum.
PR OP OSITIO LX.
ECenE AB C ellipum duxe quanis linee A C, D E auFerentes (esMen-
ea equalia, dueaneurque adillarum extremirates Pemidiameeri P A,
iC, FD, FF
DicOlectOTES AFC, DFF, este equales, et Si Pectores fyerinE e qua
les, dico legmenta esse aequalia.
Demonstratio
Tuitis A C, D F bitariam in C _ FY aGanEuF PeF
G e II, diamerri FB, F P iungancurquo AB, BC.
DP, ET. quoniam (CDMONES AC, D F ex Bypoches
sunexqualia, ergo rectae, qux puncta C _ F; A _ D
iungerene, Forencaparallelae. ergo bcriangulasesmen-
eis AC, D P inCoripeorum maxima, sunc aqualia, sed
ABC, DTF, csunt inscripeorum maxima erunc igi-
cur rriangula ABC, D TF, aequalia: quia aurem F B,
EI diamerri in G et FT, lunc propoecionalicer ddiui-
Ex:isicur ve ABC triangulum est ad criangulu AF C.
Ac DFF. criangulum est ad crianoulum DEF, dE Per
murando ve AB C criangulum est ad criansulu D IF
sIC AF C criangulum est ad criangulum D F F. Cum
isicurtriangula ABC, D TF xqualia Cine, criam erian-
sula AFC, DF P aqualia cxunc. Ouare addieis equa-
libussesmentis AC s D F; erune (CCtOTESF AC, FDF
aequales.
Sinc iam lectoFes A F C, D F F aequales, iunsatiturque AC, D F. Dico AB C.
DIF segmenca quoque eNC aqualia; sin vero: SC alcerverum (puca) DTF minus
alceros duenturquec ex D linea D R. segmentm auferens xequale segmenco ABC:
e iunsantur ti, H Ononiam igiturscomentut D IK equale CA PeginenEO A I C
TCCtOT DFR aegualis est sectori AFC, id est sectori DH F. quod hcrinon pacest.
(cxtchea cleo AC, L F non plaequalla sunt. le daequalia. Duo d exac demonstran dut
Corollarium.
52. hutus.
Bubes
quales, corumque subceme er de Il une btariam. Quod diamecriper du
HI ductxe, ijldem pirtes proporcionalicer dividaneurs
SCcoMO eccoreS O HFC. DF F terine aquales, lubcendancurque iplorum
ansulirectis AC, D F: quoderiansula AFC; D F F. sncequalia.
Fercio hinc cale problema Colurur: daco AF B sECtOTE quOCUnQUE, OpOEtCE Cx F.
MI 2
duas
EX hac _ Cx sz. huius se quicL PEILIO, A A F C, D F L Leclaes gutuis tuerine a-