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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 42, page id 834940469:0050
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PROP. RAVII. THEOREMA.
TIdem postis: ducatur A Trectam F P bifariam diuidens
 in Iechyperbolam incerlecans in puncto (7, Aarque era
perium sectori circum scriprum AFCL, quod dico ese mediii
Geometricum inter parallelIOBranIMA FDMK, PLMD. Cx
demonstraris Gregorii a S. Vincerio cuidens est craperium
AFOL aequalC CNCrectilinCO DFCL M. X quoniam AOI rC-
eta secar rectam FL bitariam in I, ex eiuldem GFregorii a S.
Vincerio Lib. dehyperbola, manifectum eAt rectas L. M, GII,
F.D, esse continue proporrionales in cadem rarione cum eri-
Duscontinue proportionalibus AD, AFI, AM. alyM PEOTO A
Oper punctum C ducatur parallella recta RCS rectis FD
MK, Occurens in punctis R, S. quoniam rectX FD, OHI, L. M.
Tunt continue provortionales, erie dinidendo ee Dermutan-
AOFR ad SL veCIFLAdLMI: _ quONIAMFCCLE MA, HA, DA.
tunc concinue proporrionales, cric eriam dividendo ee per-
ucandOMFTadEID hOCCASCTadGRVEHA ad DA vel ve
OFT ad LMI; d proinde FR est ad SI VESCadGR, curaque
anguliFRC, GSL, Sncaequales ob parallellas FR, SL, crunE
eriangula FRC, GL S, equalias X proinde Darallellogram-
MUIM RDMS aequale CArectilinEO DFCLM sCu EraPCZIO A
FCL; sed parallellogrammum RDMS est medium geomo-
cricum inter paraIIelIAGPAMIMA PDML, FDMK, quoniam
eandem habeneia alcicudinem eorum bales nempe L MI, SN,
KM, Cunc continue provorcionalesid ideo craperium AFCI.
estmedium geomerricum inrer paraHleltaBTAMMA PDML,
FDMK, quod demonstrare oporruit.
eROD.
XR
Leaicelic
TIdem poliris ducaneur rectae FF, L. P, HY perBOLAM LANSCM-
tes in punctis I, L, ve compleacur traperium AFE. L, Guod
dico esse medium harmonicum inter parallellosramma PD
ML, FDDMK. criangulum ALL, crapexium AFCL, de medii
Rat.