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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Cuius rei hæc eſt ſpeculatio. Primus numerus minor, qui proponitur diuiſibilis
ſignificetur
linea .q.g. maior vero linea .x. tum cogitemus .q.g. diuiſam, cuius maior
pars
ſit .q.o. minor .o.g. differentia .q.p. ex quo .p.o. æqualis erit .o.g. ſit autem produ-
ctum
.b.o.
Oportet igitur, ut .b.o. ſimul cum differentia .q.p. æquale ſit numero .x. ſe-
cundò
propoſito, qui notus eſt,
quare etiam ſumma producti .b.o. cum differentia
q.p. cognita erit, ex qua detracto primo numero .q.g. reſiduum cognitum erit, nunc
igitur
quodnam erit hoc reſiduum?
attendamus qua ratione ex ſumma .b.o. et .q.p.
detrahenda
ſit .q.g.
In primis ſi ſubtraxerimus ex dicta ſumma .q.p. quę pars eſt .q.g.
ſupererit
detrahenda .p.g. ex .b.o. pars inquam ipſius .q.g. quod fiet quotieſcunque
cogitauerimus
.q.o. duabus vnitatibus diminutam, et per .o.g. multiplicatam, ſit au-
tem
productum .b.e. nam cum .o.g. toties .b.o. ingrediatur, quot ſunt in .q.o. vnitates
ex
prima ſexti aut .18. vel .19. ſeptimi, detrahendaque; ſit .p.g. ex .b.o. quæ .p.g. dupla
eſt
.o.g. patebit .o.c. æqualem eſſe .p.g. fu-
pererit
ita que .b.e. productum .q.e. in .e.
62[Figure 62] i. cognitum, erutis autem ex .q.g. ijſdem
duabus
vnitatibus, remanebit .q.i. nobis
nota
, ex quo .e.i. æqualis erit .e.c.
Cum
igitur
productum .q.e. in .e.i. cognoſcamus
ſimul
cum .q.i: Sivoluerimus partes .q.e.
et
.e.i. cognoſcere, vtemur .45. theorema-
te
huius libri, & propoſitum obtinebimus, nam cognoſcemus .e.i. & ex conſequen-
ti
.o.g. eius æqualem.

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