Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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162150IO. BAPT. BENED. lus u.A.C. æqualis ſit
angulo .K.B.T. & an-
gulus .C.A.F. æqua-
lis angulo .T.B.Z. nunc
comparatio eſt inter
angulum .D.B.F. & an
gulum .K.B.Z. miſtili-
neos, qui quidem duo
anguli, communem ha-
bent angulum miſtili
neum .K.B.F. quapro-
220[Figure 220] pter ſi angulus .K.B.Z.
miſtilineus maior eſt
angulo .D.B.F. miſti-
lineo per angulum .
K.B.Z.
contingentiæ,
circulorum ergo angu
lus miſtilineus com-
munis .K.B.F. æqualis
erit miſtilineo, angu-
lo .D.B.F. pars vide-
licet ſui toto.
Omnis
autem error in quem
Tartalea, Iordanusque;
lapſi fuerunt ab eo, quod
1010[Handwritten note 10] lineas inclinationum
pro parallelis viciſſim
ſumpſerunt, emana-
uit.
Septima propoſitio Tartaleæ, quæ eſt quinta quæſtio Iordani mihi videtur excipien-
da riſu, cum pondus ipſius .A. ponderi ipſius .B. exiſtens æquale, grauius ſit pondere
eiuſdem .B. ratione minoris aperturæ anguli contingentiæ in .A. quam in .B. in quo
idem error committitur, qui in præcedenti committebatur, cum ſcilicet ipſe putet
lineas .A.E. et .B.D. figuræ ab eo confictæ ſibi inuicem eſſe parallelas, quæ etiam ſi
æquidiſtantes eſſent (vnde angulus .E.A.G. minor eſſet angulo .D.B.F.) non eam ta
men ob cauſam huiuſmodiangulorum differentia cauſa eſſet differentiæ grauitatum
ipſorum .A. et .B. ob ea quæ cap .4. huius tractatus poſui.
Octaua autem propoſitio, quæ eſt .6. quæſtio Iordani Iongè melius demonſtratur
ab Archi. in .6. lib. primi de ponderibus, cum nec à Iordano, nec à Tartalæa probata
fuerit, cum ijdem non probauerint præcedentes, quas in dicta .8.
Tartalęa citat, qui
neque etiam probat nonam .10. 11. 12. et .13. cum ad pręcedentes probandas mini
mè acceſſerit.
Quartadecima verò, quæ eſt .10. quęſtio Iordani, duas ob cauſas eſt falſa, quarum
vna eſt, quod (ſupponendo .A.D.E.G.B. eſſe vnum brachium librę et .A. punctum centri
eiuſdem, et .D. pondus ęquale ponderi .E. & lineas inclinationum .D.K. et .E.M.) an
guli .K.D.E. et .M.E.G. ſibi inuicem non ſunt ęquales;
cum ille angulus ſit intrinſecus, hic
verò extrinſecus & oppoſitus dicto intrinſeco vnius trianguli terminati à. D.E. à .D.K.

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