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# Title: [Vera Circuli Et Hyperbolae Quadratura] Vera Circvli Et Hyperbolæ Quadratura (shelfmark Leibn. Marg. 98)
# Folio 30, page id 834940469:0038
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PROP. XII. THTEOREMA.
Tccraperium ABIP, A; PoIrgonum
ABEIOP, C: polrgonum ABCC
IENP, D; _ polYGOnuM ABD L. P, B. di-
coD esse medium harmonicu incer C de B. Cx huiusq. A: C.:
C: B, d componendo A  C: C:: C  B: B, Sed ex huius5.
A C: C:: 2C: D; _e id eo C H B: B: : 2C: D, _E pErUTAB-
doB,  C: 2C:: B: D, X dividendo, disterentia incer B e C
estad2C, ve disterentia inter B e D ad D, e perimurando
differentia incer B  C eR ad disterentiam inter B SE D VE, 2C
ad D, hoc est, veC  B ad B, de diuidendo, difterentia inter
D_ C est ad disterenciam incer B e D ve C ad B; X proinde
Destmedium harmonicum inter. C de B, quod demonstrare
Oportuie.
Flac propositio eodem modo locum haber in omnibus
polssonis complicatis, repatet ex scholio s huius.
PROP. XIIL. THEOREMA.
Ncex duas quancicates A, B, Ci media a-
arichmerica C, media geometrica D e inc F
dia harmonica F. dico. C, D; F, eNC COn-
tinue proportionales. quoniam A, F, B,
sunemratione harmonicas erie differenria iner A e F 3d
difterentiam inter F _ B vr A ad B; d cemponendo erie dif
ferencia incer A de B ad differeDeia incer F de B, vi A  B ad
B. deinde permucando de componendo 2 A: A _ B: : F: B,
sed 2A est duplum ipbius A de A  B duplum 1p I:US C; et
ideo A: C:: F: B; de proinde CF = AB, _e AB = DD, iacOG;
C. F = DD: Scigitur C: D:: D. E, quou aCAAAIAre OPOE
TUIE.