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# Title: De Locis Solidis Secunda Divinatio Geometrica (shelfmark Leibn. Marg. 151)
# Folio 90, page id 898203430:0282
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=898203430&page=282
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VINCEHTH VIVIANI DE LOCB SCLHIS
90
Aciplam D F esse mediam Harmonicam incer caldem datas A B.
BC, sic demonstrabitur.
TUNSANEUT AD, CD, quibus ex F. sinc ParaIICla FC, FH.
Ouum sic enim D F aequalis verique R A, B C, etit quoquC LL aedalis
verilque EH, EC. Ec quum in similibus criangulis DE. B, B L. L sicDL
ad E B ve BE ad FF, erit _ C F ad F B ve BF: ad F FI, de ve disserentias
CB ad disserentiam BH. EE quoniam CF, vet iAF ad, F. B cA vE BF.
ad FH, vel ad F. C, exie componendo, ee permutgndo, AB ad BC, vt
BE ad F. C,, vel ad F HI, vel ve
CB ad BHI, _ IICTUM pErMULAM.
ao AB ad BC vE C B ad BFI;
Sed C B est disserentia inter pri-
MaI AB, _ A C, vel InteT AB,
e secundam DF; BHL vero est dit
ferencia inter CFI, vel inter le
Cundam DF, _ Tertiam C B, at-
que est prima diferentia C B ad L
secundam B FT DE primus TerminuS
AB ad certium BC: ergo DF es tandem media Harmonica inter datas
A B, B C. Sunt isitur inter datas AB, B C inventae ires medixe F D
Arichmetica,. D B Geometrica, ee D. F FTarmonica. Ouod erat _c.
Optime ioitur quidam Antiguorum asseruie ( licet id non ostenderie,
Ted tanquam verum tantum indicauerie) in Cemicirculo eres huiulinodi
Medietaces simpliciter exponi posse; adeo ve ille, immerito forlan, a Pap.
Po Alexandrino ad secundum Problema Libri certii suarum Collectionum.
reprehendatur. Visum est enim huic eres AB, BD, BC constitere MC-
diecatem Arichmeticam, EreS verO A B, B D, BC Geometricam, e
tres denique A B, DF, B C Etarmonicam Mediecacem; ac simpliciter
omnes inter ealdem A B, B C: simplicius enim extriberi nequeune in
semicirculo ipsae eres Medietates quain opc carundem rrium ED, DB,
DE: SCCUS Per ea, guxe aliter PApPUS CONArUZCTAE, aC demonstraVerat.
1
R O
L. L
Terum apparet eres ipsas medias inter duas caldem maenicudines esse
inter se in eadem conrinua ratione Ceometrica, quoniam F. D ad DB
est ve DB ad D F, ob similicudinem criangulorum EDB, BDF.
Ex hac proprietare, facile soluendum se praebet ad praxum leguens
PROML.