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]

#### Table of figures

< >
[Figure 61]
[Figure 62]
[Figure 63]
[Figure 64]
[Figure 65]
[Figure 66]
[Figure 67]
[Figure 68]
[Figure 69]
[Figure 70]
[Figure 71]
[Figure 72]
[Figure 73]
[Figure 74]
[Figure 75]
[Figure 76]
[Figure 77]
[Figure 78]
[Figure 79]
[Figure 80]
[Figure 81]
[Figure 82]
[Figure 83]
[Figure 84]
[Figure 85]
[Figure 86]
[Figure 87]
[Figure 88]
[Figure 89]
[Figure 90]
< >
page |< < (45) of 445 > >|
5745THEOREM. ARIT. componendo ſic ſe habebit .k.y. ad .m.y. ſicut .e.a. ad .o.a. & permutando .k.y. ad .e.
a.
ſicut .m.y. ad .o.a. & ex .19. quinti ita .k.m. ad .e.o. ſicut .k.y. ad .e.a. & permutando .
k.m.
Nunc producatur .f.t. donec .t.i. æqualis ſit .k.y. produ-
ctaque;
.m.t. done c.t.s. æqualis ſit vnitati .x. termineturque; rectangulum .s.i. ex quo da-
ex .24. ſexti, aut quinta octaui, ſed ita etiam proportio .q.b. ad .a.e. componitur ex
eiſdem proportionibus, nempe ex .q.b. ad .o.e. æquali .m.t. ad .t.s. & ex proportione .
o.e.
ipſius .k.y. ęqualis eſt proportioni numeri .q.b. ad .a.e. nempe .k.g. ad .k.u. hoc eſt .k.p. ad
x.y. ex quo ſequitur .k.p. conſtare numero ęquali .f.m. proueniens igitur ex diuiſione
numeri .k.z. per .f.m. æquale eſt numero ipſius .a.e.
77[Figure 77]
THEOREMA LXX.
HAEC porrò concluſio alia etiam via demonſtrari poteſt.
Significetur numerus diuidendus atque multiplicandus linea .b.a. Deinde
diuidentes & multiplicantes ſint .k.m. et .m.y. prouenientia ex diuiſione ſint .a.o. et .o.
e.
atque .a.o. ex .m.y: o.e. verò ex .k.m. proueniat, quorum ſumma ſit .a.e: productum
autem .b.a. in .k.m. ſit .b.p. et .p.s. productum .b.a. in .m.y. ad hæc rectangulum .k.y. ſit
productum .k.m. in .m.y: quo to-
tum productum .a.s. diuidatur, pro
ueniensque; ſit .a.c. cui, a.c: productum .
a.s.
eandem proportionem ſeruabit, quam