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]

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], 1585

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IO. BAPT. BENED.

q. radicem eſſe quadratam producti .l.e. in .e.p. quem 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, vocenturq́; .l.x. et .x.p. quo
facto, cogitemus corpus .a.g. tamquam productum cubum .l.b. in quadratum .e.p. Vn-
de eg decimaoctaua, aut decimanona ſeptimi, eadem ergo proportio .a.g. ab .c.g.
quæ eſt .l.b. ab .l.x. corporeum, ſed eg .25. vndecimi & prima ſexti, ita ſe habet .a.K.
ab .K.c. vnitatem linearé ſicut .a.g. ab .c.g. & eg eiſdem ita ſe habebit .b.e. ab .e.x. vnita-
tem linearem, ſicut .l.b. ab quadratum .l.x. corporeum. Itaque ſic ſe habebit .b.e. ab
vnitatem linearem .e.x. videlicet .K.c. ſicut .a.K. ab ipſam .K.c. Vnde eg nona quinti .
a.K. æqualis ergo .e.b. & conſequenter æqualis .m.e. Iam verò ſit .u.g. productum .l.b.
cubum, in cubum .o.p. vt ſupra dictum eſt, Hinc patebit eg quauis duarum propoſitio-
num, decimaoctaua, aut decimanona ſeptimi, eandem futuram proportionem .u.g.
ab .a.g. quæ eſt .o.p. ab .x.p. quadratum corporeum. Quare eg poſtremis, dictis ratio-
nibus, eadem ergo proportio .u.K. ab .a.K. quæ eſt .o.e. ab vnitatem linearem .e.x. at
eg dictis decimaoctaua & decimanona ſeptimi, ita ſe habet numerus .m.q. ab numerum
ſuperficialem .m.e. qui producitur à lineari .m.e. in vnitaté linearem ipſius .e.q. ſicut nume
rus .q.e. ab ſuam vnitaté, ſed cum numerus .a.K. æqualis ſit numero .m.e. vt probatum eſt
ergo erit eg vndecima & nona quinti, numerus .u.K. æqualis numero .m.q. At .f.g.
pariter æqualis eſt numero .m.q. eg præcedenti theoremate, vnde .K.u. pariter æqua
lis ergo .f.g. Itaque ſequitur .u.g. cubum eſſe, & f.g. radicem ipſius, æqualem numero .
m.q. quem quærebatur.

figure: 27

[Figure 27]

figure: 28

[Figure 28]

VT autem in uniuerſum ſciri poſſit totum infinitum dignitatum, hoc eſt radicem
producti duarum dignitatum ſimilium, productum eſſe duarum radicum ea-
rundem dignitatum.

Ponamus, exempli gratia, duas radices quadratas .q.p. et .g.K. incognitas, quas
qui velit adinuicem multiplicare, cogatur earum quadrata cognita .e. cum .i. multi-
plicare, quorum productum ſit quadratum .m. radix cuius ſit .b.d. quae dico æqualé

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