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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 140, page id 834940469:0224
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240
Per speculi vel Teneis TOKH extremitacems Ex CenErO A AaC
SpheraIONKIliirem per punctum D ex eodem centro AAE
Sphera ERDSC, cuius supersicici porcio a coni AIOKN su-
pertcie comprehen(a3 AFRF. SD. Cuoniam sol ex omni parre
aequalicerradior, Facile ese deducere ex 6 dehnitione s ele-
mentoru omnes radiossclares esse ad radios in specului vel
lentem TorW incidentes, uc inceera superficies spherica ad
eius portionem TOKH: Se d ex archime de de sphera e cylin-
deo, inccora luperticies sphaerica cl ad eius portionem 10
RN vequadracum diamerri ad quodrarum chordae Pemissis
arcus IK; e proinde omnes radii lolares sune ed radios in
sxeculum rel lencem LOkNincidences, hoc escradios in cir.
culum MPL Q congresatos, uc quadrarum dismetri ad qua
dracum chordae lemissis arcus jK. Bodem modoprobatur
omnesradios solaresese ad radios in circulum DRES inci
dences, ut quodrerum dimerri ad quodracum chordae le-
misis arcuS D F. SCd quonism arcUS IR, DE, lunc similes
quedrarum diameeri circuli IKII condem habent ratione ad
quadracum chorda Cemisis arcus Hl. quam habet quadracum
diamerri circuli ED C ad quadracum chordae semilis arcus
F:D; _ ideo omnes radii solares eandem haber racionem ad
radios congregaros in circulo L PM G. quam habenciidem
omnesradii solares ad radios congregatos in circulo RESD;
unc igicur radii congregaci in circulo LPM Qaequales radiis
congregaris in circuloDSER. Deinde ex construaione Rl
eAt ad LM UFK A ad D A; _ ob similicudinem crianoulorum
EAB DAE; HA eA ad DA VE RI adDF; _ ideOLM, DE, funE
aequales; e igitur circuliLPMC, DSER, sunc aequales: acque
xquales radiiin aequalibus spaciis eundem producune ette-
ctum; e proinde combultio in circulo DR ES aequalis elt
combuctioni in circulo L. PMO quod demonstrandum erat.