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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254
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IO. BABPT. BENED.
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266
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file
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0266
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xlink:href
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cundam verò ex .37. et .38. eiuſdem, </
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<
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xml:space
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diametro ipſius hyperbolis & defectionis, In .38. autem mediante minori diametro
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ordinatè ad maiorem.</
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<
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xml:space
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">Tertia autem paſſio, non niſi circulo conuenit; </
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<
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<
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xml:space
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>
cuius diameter ſit
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>.q.b.</
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>
contingentes vero ab extre
<
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/>
mitate diametri ſint
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>.d.b.</
var
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et
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per punctum autem
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>.o.</
var
>
quoduis, ipſius
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type
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,
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tranſeant
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et
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>.q.o.d</
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>
. </
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<
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xml:id
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xml:space
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in
<
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>.q.d.</
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vel
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in
<
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>
ęquale eſ-
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ſe quadrato
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quod ita probo.</
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<
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xml:space
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">Nam angulus
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ſeu
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>
rectus eſt ex .17. tertij Eucli. et
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>.b.o.q.</
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>
ſimiliter re-
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ctus ex .30. ipſius lib. angulus verò
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>
ſeu
<
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var
>
communis eſt. </
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>
<
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xml:id
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xml:space
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">quare
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>
media
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proportionalis erit inter dictas lineas
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var
>
et
<
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>.q.o.</
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>
& inter
<
var
>.b.g.</
var
>
et
<
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>.b.o</
var
>
. </
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<
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xml:space
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">Vnde ſequetur
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propoſitum ex .16.6. Eucli.</
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<
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xml:space
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">Sed ſi circa diametrum
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>
mente fingamus aliquam elipſim, quætangat ipſum
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circulum duobus punctis me-
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diantibus
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>.q.</
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et
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>
(nam pluribus
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eſſet impoſſibile, ex .27. quarti
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Pergei) clarè patebit, quod
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ctus
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>.o.</
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>
erit extra
<
reg
norm
="
circunferentiam
"
type
="
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">circunferentiã</
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>
<
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ipſius defectionis, </
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>
<
s
xml:id
="
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xml:space
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">quare ipſa cir
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cunferentia ſecabit
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>.b.g.</
var
>
vel
<
var
>.q.
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/>
d.</
var
>
in alio puncto, vnde ipſi non
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occurret id quod probauimus
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de circulo.</
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</
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<
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<
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xml:space
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">Admiratus etiam ſum, ipſum
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Cardanum dicere hyperbolem
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ita vocari, eo quod angulus con
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/>
tentus ab axe ipſius figuræ, & à
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/>
latere trigoni in hyperbole ma-
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/>
ior ſit quam in parabole, quod
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/>
eriam confirmat paulo inferius,
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/>
nam hoc verum non eſt, imo fal
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ſiſſimum. </
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>
<
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xml:space
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">Talis enim ſectio ita
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nominata fuit, hoc eſt hyperbo
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/>
les, ſimili ratione, qua elipſis ſeu
<
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/>
defectio etiam vocata fuit, nam
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/>
ſicut in ipſa defectione quadra-
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tum ordinatę
<
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>.l.m.</
var
>
minor eſt pro
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ducto lineæ
<
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>.e.m.</
var
>
in
<
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>.e.t.</
var
>
per figu
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/>
ram ſimilcm producto
<
var
>.d.e.</
var
>
in
<
var
>.e.
<
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/>
t.</
var
>
quæ eandem obtineat
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dinẽ</
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ipſius
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>.e.m.</
var
>
vt ipſe Pergeus
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monſtrat in .13. primi lib. ita in
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hyperbole
<
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quadratum ex
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cedit quantitatem illius figuræ,
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per ſimilem dictæ vt in .12.
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Pergei facilè videre eſt. </
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prae ter
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ter</
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illas paſſiones, quas notat </
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