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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 675, page id 1815201908:0732
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Dett.
labe
exmi
CtOs,
relb,
HIB
uam
dia.
E
ecta
aH.
dia.
HI,
ant
C
une
1F.
ad
elea
158
S DIR A L. 15.
PR OPOSITIO VIIL.
Archimedis 25. parabola applicatur.
Tinhelicem in secunda renolurione Fa-
LDCtaI ReCtX (AO, AR) ceciderin à
principio helicis, eandem rationem hu-
iulmodi recta ad invicem, quam dicti ar-
CUS(BXKE, BX L) cum eora circuli (BK L)
circumterencia limul alumprahabebunc.
HIoc est AOeriEadt AR, VE arcUSBXH
cu cora peripheria BXH L, ad arcuB X L
vna cum circumferentia cora BXHL.
Ex quo lequitur, (I CeHETO APeF P X R
ducancur circuli OM, RN, rectam ANI
Fucuram ad AN, vearcuS BXK cum cota
peripheria ad arcum BX L. cum cora peripheria.
APPLTCATVR PARABOLA.
Parerisicur ex 4. primis propol. huius, segmenta
Parabolica AaB, BR F. F reterre spiralia ordine
spacia. AL B quidereterre primumi BR F. F. vero
secundu: Rectam quoque DB exhibere periphe.
riam primi circuli. Producatur modoD Bin t.
Ouoniam AEI bilecta est in D, etiam AF bise-
cracst in F. Duare cum per 5. Archim. de spit. DB
(icad BF, vE AF ad F F, etiam D F bilccta est in
B, ee aequales sunc BF, BD. Cum igitur DB re-
Ferac peripheriam primi circuli, reterer eriamm BF.
Ducantur deinde reCFx AG, AR SCCANECS D2-
rabolam in O _ R, rectam vero DBF in K, de L; ex quoniam tam BF
quam BD, ve ance ostendi, retert primi circuli peripheriam, eius partes
BK, BL reterenEDrima pCciphCrIK ParTeSB XKE, B X L. IEAGUE FOTZDH
retere roram peripheriam cum arcu BZ R, _ rora DL. toram peripheriam
cum arcu B Z L. Denigue per 3, d R ducantur parallelX TM, V N, qua
extribebune peripherias MIO, N R. RCCEX AUTCM AMI, A N CINEA, T, AV,
repraelentabunt in spirali reCtaS AMI, A N.
Dico AM este ad AN, sive AT, ad AV, veD KE ad D L.
Demonstratio.
A RN, AC DF ad F I. Sed per 5. Archim. de parabola, ve T9 ad OM, AC
AM ad HI F, DeGUC VX Ae AH, HC AH adt NY F: GHIARC DE AMI ad MR, SCDR
ad RF; et AN ad N E, vE D L. ad L F. Parer isicur ex elementis AM esfe ad
AN
Aca Ec parabola AB F. cuius diameter (IC
EHI, cansens AH, qua bisectâ in D, ex L
Tac DB parallelam ad HF, iungancurqi AB, AF.
Vin paralelae (InE, YNI, D FS Crit Y O ad OM, DE DK ad RF; vEquC V R
ot  e pere sti et e i t ete   e te  e te e t      et e tet e te a et  e e  t   t st  et  e    ti     et e  te   e