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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 33, page id 834940469:0041
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e R OD. ZVII. YHT E OR F M A.
TIdem posiriss dicoexcessum A supra C maiorem ette
Aquadr uplo exCeNUSC SUPra F. ex praedictismanifeste
Tune sequencestres analogixe; prima, quoniam A, C, B, sUNE
continue proporrionalesi lecunda, quoniam C, D, B, CuncMar-
monice proportionales; _ terria, quoniam C, F, D, lunECO-
rinue proportionales; _ ideo excesus A supra C, hoc est,
Aun C, eltad excessum C lupra F hoc est C= Linratione ca-
Polita ex proportionibus A
ac C, A  C a d A _ P  C A - C: C no B:: A: C
ad C; _ ideo A- C cA ad C = B: C- D:: A si C: A
C F, VE ACHF. C AFF C D: C. F:: E C: C
C. C aa C C; dc BminOFCA qua
F, X idco AB, CCu CE minor es qua AF; _E IBITUr AF  CC
maior eA quam 2CC. aEque ACHFFC eAt ad 2 CC VEA
F ad 2C; sed A F maior est quam duo C, a ideo ACi
F.C maior elE qua 2CC; de proinde AC HL F. C iH RF.
. CC maior est quam 4 CC; de igirur A- C. IB 3IOI Clt
quadruplo ipsus C = F, quod demonstrare opOrruit.
PROP. ZVIIT. THEOREMA.
InE due quaneicates inaequaless A
+ D minor, Bmaior, C mediageome
erica, D media axichmerica. dico D
maiorem esse quam C. quonia B, C,
R. Tune continue prexorcionalesi erie
dividendo, permmutando. d componendo; veexcessus B su-
ora Aad excelsum C luprA A, ica A HF C ad A, aEquC ANC. C
MMaior est duplo ipsus A; ex proinde excelus B luvra A Mi-
or est duolo excelsus C lupra A; Led excessus B supra A du-
Dlus estexcenus D supra A, X _ ideo excessus D Iupra A
maior est excelsu C supra Riestisitur D maior qua C, quod
demonstare ODOrEUIE.
eROF