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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2614IO. BAPT. BENED. q. radicem eſſe quadratam producti .l.e. in .e.p. quod productum ſit quadratuni
corporeum
.c.g. cogitemus pariter duo quadrata .l.e. et .e.p. eſſe pariter corpo-
rea
, tantę profunditatis, quantam, vnitas linearis radicum .m.e. et .e.q. requirit.
Hæc duo corpora producentur à ſuperficie in vnitatem, vocenturque; .l.x. et .x.p. quo
facto
, cogitemus corpus .a.g. tamquam productum cubi .l.b. in quadratum .e.p.
Vn-
de
ex decimaoctaua, aut decimanona ſeptimi, eadem erit proportio .a.g. ad .c.g.
quæ
eſt .l.b. ad .l.x. corporeum, ſed ex .25. vndecimi & prima ſexti, ita ſe habet .a.K.
ad
.K.c. vnitatem linearé ſicut .a.g. ad .c.g. & ex eiſdem ita ſe habebit .b.e. ad .e.x. vnita-
tem
linearem, ſicut .l.b. ad quadratum .l.x. corporeum.
Itaque ſic ſe habebit .b.e. ad
vnitatem
linearem .e.x. videlicet .K.c. ſicut .a.K. ad ipſam .K.c.
Vnde ex nona quinti .
a
.K.
æqualis erit .e.b. & conſequenter æqualis .m.e.
Iam verò ſit .u.g. productum .l.b.
cubi
, in cubum .o.p. vt ſupra dictum eſt, Hinc patebit ex quauis duarum propoſitio-
num
, decimaoctaua, aut decimanona ſeptimi, eandem futuram proportionem .u.g.
ad
.a.g. quæ eſt .o.p. ad .x.p. quadratum corporeum.
Quare ex poſtremis, dictis ratio-
nibus
, eadem erit proportio .u.K. ad .a.K. quæ eſt .o.e. ad vnitatem linearem .e.x. at
ex
dictis decimaoctaua & decimanona ſeptimi, ita ſe habet numerus .m.q. ad numerum
ſuperficialem .m.e. qui producitur à lineari .m.e. in vnitaté linearem ipſius .e.q. ſicut nume
rus
.q.e. ad ſuam vnitaté, ſed cum numerus .a.K. æqualis ſit numero .m.e. vt probatum eſt
erit
ergo ex vndecima & nona quinti, numerus .u.K. æqualis numero .m.q.
At .f.g.
pariter
æqualis eſt numero .m.q. ex præcedenti theoremate, vnde .K.u. pariter æqua
lis
erit .f.g.
Itaque ſequitur .u.g. cubum eſſe, & f.g. radicem ipſius, æqualem numero .
m
.q.
quod quærebatur.
29[Figure 29] 30[Figure 30]

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