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.
Ponamus nunc quadratum lateris .a.u. eſſe .12. clarum ergo quodlibet quadratum
aliorum duorum laterum .a.q. et .u.q. futurum nouem, eg ijs quæ poſteriore loco dixi
mus, & quia quadratum ipſius .q.a. eſt tantò minus aliorum duorum quadratorum
ſumma, quantum eſt duplum producti ipſius .q.a. in .a.o. eg .13. ſecundi, ſed alia duo
quadrata ſimul collecta faciunt .21. à quo numero ſubtrahendo quadratum ipſius .a.
q. ideſt nouem, remanebit numerus .12. pro duplo producti ipſius .q.a. in .a.o. cuius
dupli me-
figure: 207
[Figure 207]
dia pars, id-
eſt ſimplex
productum
ipſius .q.a.
in a.o. ergo 6.
Sed quia qua
dratum ip-
ſius .q.a. eſt
nouem,
eius radix .
q.a. crit .3.
per quam di-
uidendo .6.
productum
ipſius .q.a.
in .a.o. pro
latere .a.o.
conſurgent
duo, cum er
go .a.o. ſint
duo tertia
ipſius .a.q.
certi erimus
a.o. eſſe latus dicti exagoni.

CAP. XV.

deſiderantes ſcire deinde .l.k. in figura .M. quar
figure: 208
[Figure 208]
ti cap. tertiæ partis perſpectiuę Danielis
Barbari, ſeu Zamberti, eſſe veram altitudinem cor-
poris octoaedri, primum ſcire debemus quod exiſtente .b.
h. vt etiam .b.l. tripla ab .b.k. vt eg ijs, quę ſuperius iam
diximus, facile percipi poteſt; eg penultima primi .
b.l. in potentia, ſeſquioctaua ergo ab .k.l. ipſa et .k.
l. dupla inpotentia ab .h.k. & ob id lineaque cum eſſet .h.
l. exiſteret in potentia tripla ab .h.k. & ſeſquialtera
ab .l.k. & ſeſquitertia ab .l.b. & ſic ab .h.b. vnde .l.h.
æqualis eſſet vni eg lateribus trianguli ęquilateri di-
cti corporis. eg rationibus igitur ſuperius hîc poſi-
tis .l.k. ergo altitudo dicta, id eſt diſtantia inter duas
facies inuicem oppoſitas, octoaedri.
Neq; volo te ignorare alium non paruum fuiſſe errorem
illius Zamberti: cum eodem capite affirmet angulos
octoacdri rectos eſſe cum ſint acuti, nam vnuſquiſq; minor eſt angulo cubum ſolido.

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