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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383371EPISTOL AE.
ALIA DEMONSTRATIO NONÆ, ET DECIMÆ
ſecundi Euclidis.
Petro Catenæ.
QVamvis nona ac decima ſecundi Euclid. aliter à Comandino & Mau-
rolico demonſtratæ fuerint, nihilominus mihi etiam viſum eſt non nihil
meo moræ in eas tibi ſcribere, vt ſenſibiliter quoque cognoſcas il-
las veras eſſe.
Eſto linca.a.b. pro nona propoſitione, diuiſa per æqualia in .c. per inæqualia verò
ſit .c.f. & quadratum .c.d. ſit .c.K. clarum enim erit .K.h. æqualem exiſtere ipſi .a.c.
ſeccetur igitur .e.h. in .g. ita vt .h.g. ęqualis exiſtat ipſi .K.h. vnde .g.e. æqualls erit
c.d. perficiatur etiam quadratum .h.n. vnde in totali quadrato .a.h. habe bis duplum
quadrati partis .c.d. nempe .c.K. et .f.g. & quadratum .a.u. cum gnomone .u.g.h.k.
In decima autem propoſitione, quadratum totalis lineæ .a.d. ſit .d.e. & lineæ .b.d. ſit .b.i. et
c.d. ſit .d.n. et .a.c. ſit .c.f. et .f.e. ſit .e.u. vnde .n.u. æquale erit quadrato .b.i. vnde in qua
drato totali .a.h. videbis duo quadrata æqualia .f.c. et .g.k. partis .a.c. & quadratum .c.
K.