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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 16, page id 834940469:0024
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etlis mehodus invenientus omnium scrierior
onuers ectum terminationes.
PROP. VI. THIEOREMATA.
Dico differentiam intertrianeulum ABP ex trapeZium ABKF
a
maiorem esse duplo differentiae interiravexium
ABIP esx polyeonum ABDLP.
lerriangusum ABP A, craperium ABFP, B; Trapexium
ABIP, C, ee POIyGONUM ABDLP, D: quoniam A
eA ad C vEC ad B, 1gicur vr differencia iurer A et C. ac
Aita differencia incer C et B dd C; e permutando, vedisse-
rencia incer A ee C. ad d.Nerenciam incer C de Bira A ad C:
e componendo, reditterentin inter A ee C de differentia in-
ter C de B Cimu), hoc est difterencia incer A et B, ad differen.
Eia incer C _ B, i. a A  C ad C sled ve A F. C ad C 11d2C
adD. de ideo differencia incex A ec B est ad difterenciam in-
ter C e Bve Z C ad D. quoniam A C CAt ad C. VE ZC, adD,
erir permurando ve A C ad2C ica C ad D; et dividendo,
vedisterencia inter A et C 2d2 C ird differencia inter C eD
ad D; d permucando, differencia inter A e C est ad disseren-
tis inter C _ D vr 2C ad D; led demonstrarum est disteren-
eiam inter A X B esse ad differencia incer C et B ve 2C ad D;
et proinde dissereria inter A eC B CR ad dIAereMEI L InteTC et
B, ve difserecia inter Re C 2d dIFerer eiam inter C Se D; sed
differentia incer A ec B est maior dlseremia inter C eB, de
ideo disterentia inter A X C est maior difterentia inter C de
D: de praedictam analogiam permutando, disterentia inter A
_ B elt ad differentiam incer A e C, ve disserecia incer C _ B
ad disterenria incet C et Diac disterencia incer A d BeA mai-
or difterencia incer A e C. _ ideo diftereneia inter C e B CR
maior disterencia inter C ee D;acqué disterencia inter A ee B
aequalis est differencijs, inter A ee C, inter C e B; cumque
earum veravis sie Maior diAerenei a inter C ee D, manitestum
est difterentium inter A de Bmaiorem esse duplo differentix
IntEK