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.

CAP. VII.

ALiarn tamen inueni viam breuiorem vt in figura .H.H. in qua ſit punctus .
b. perfecti, & .k. degradati plani. Nunc ducantur .b.c.s. ab rectos cum .
p.m. indefinitè, quæ quidem abſcindatur in punctoque .s. ita quòd .c.s. æqualis ſit alti
tudini perfectæ, deinde coniungatur rectà. s. cum .i. Tunc ſi ab .k. vſque ab protractam
i.s. lineaque fuerit .k.R. parallela li-
figure: 194
[Figure 194]
neę .c.s. hæc .R.k. ergo altitudo
quæſita ſeu degradata.
quem ita probo. Iam nulli du
bium eſt quin .f.V. ſit æqualis alti-
tudini quęſitæ ſeu degradatę, quo
tieſcunq; erit probauerimus .k.R.
æqualem eſſe lineæ .f.V. habebi-
mus propoſitum. Quare certum
nobis ergo eandem proportionem
eſſe lineæ .c.s. ab .k.R. quae .c.i. ab
k.i. et .c.i. ab .k.i. vt .x.i. ab .f.i. et .x.
i. ab .f.i. vt .m.o. ab .f.o. et .m.o. ab .
f.o. vt .m.T. ab .f.V. eg ſimilitudine
triangulorum. erit .m.T. ab .f.V.
ergo vt .c.s. ab .k.R. eg .11. quinti,
ſed .c.s. ſumpta fuit æqualis .m.T.
quare .c.s. ab .f.V. ergo, vt .m.T. ab
eandem .f.V. eg .7. quinti, & eg .11. eiuſ-
dem .c.s. ab .f.V. ergo vt .c.s. ab .k.R.
quapropter eg .9. eiuſdem .k.R. æqualis ergo .f.V.

CAP. VIII.

MOdus ab antiquis philoſophis obſeruatus, eſt etiam vtilis, compendioſaq́; via
progreditur, cuius ſpeculationem, in ſubſcripta figura, quadam eg parte ſecũ-
dum morem antiquum, quadam etiam eg parte ſecundum ingenij mei vires cõſtru-
cta, cognoſcemus. In qua ego diuiſi .x.i. in punctoque .s. ab .x. ita eleuato, quanta eſt
figure: 195
[Figure 195]

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