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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121
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DE PERSPECT.
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cundum figuram quadrilateram
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. </
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<
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xml:space
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">Communis autem ſectio ſuperficiei
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cum dicto plano, ſit
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quæ
<
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perpendicularis erit
<
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>
ſuperficiei orizontali ex
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19. lib. 11. quia
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eſt etiam orizonti perpendicularis ex .18. eiuſdem, cum
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ei-
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dem perpendicularis exiſtat. </
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<
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xml:space
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<
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>.i.x.</
var
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erit altitudo trianguli
<
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>.i.q.d.</
var
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& æqualis ipſi
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<
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o.p.</
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ex
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. </
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<
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xml:space
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<
reg
norm
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communis
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type
="
context
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ſectio ſuperficiei triangularis
<
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>.o.a.u.</
var
>
<
reg
norm
="
cum
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type
="
context
">cũ</
reg
>
<
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ſuperficie
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>.p.t.</
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quæ
<
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>.o.l.</
var
>
ſecando lineam
<
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>.e.r.</
var
>
in puncto
<
var
>.Z.</
var
>
nobis oſtendet quantum di-
<
lb
/>
ſtare ſeu eminens eſſe debeat latus
<
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>.e.r.</
var
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in plano ab
<
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>.q.d.</
var
>
medio ipſius
<
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>.z.x</
var
>
. </
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>
<
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xml:id
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xml:space
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">Et quia
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præſuppoſuimus
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>
in eodem medio, inter
<
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>.u.s.</
var
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et
<
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>.a.n.</
var
>
ideo
<
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>.x.q.</
var
>
ęqualis erit
<
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>.x.d.</
var
>
<
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/>
& ex .4. lib. primi
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>.i.q.</
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ipſi
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>.i.d.</
var
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et
<
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>.e.r.</
var
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parallela ipſi
<
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>.q.d.</
var
>
ex .6. lib. 11. cum ipſa quoque
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ſit perpendicularis ſuperficiei
<
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>.p.t.</
var
>
ex
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id
="
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">.19. eiuſdem</
ref
>
. </
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<
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xml:space
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">Hucuſque igitur in figura cor-
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porea
<
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>.A.</
var
>
prodeunt in lucem omnes cauſæ effectuum figuræ ſuperficialis
<
var
>.A.</
var
>
ideſt vn
<
lb
/>
de fiat, vt in ipſa figura ſuperficiali, triangulum
<
var
>.o.p.l.</
var
>
tale conſurgat, & quid ſignifi-
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cet
<
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>.o.</
var
>
et
<
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>.o.p.</
var
>
et
<
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>.p.l.</
var
>
et
<
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>.o.l.</
var
>
& quam ob cauſam tale quoque formetur triangulum
<
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>.i.
<
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/>
q.d.</
var
>
atque in tantam altitudinem, quantam obtinet
<
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>.o.p.</
var
>
& quid ſint latera
<
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>.i.q.</
var
>
et
<
var
>.i.
<
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/>
d.</
var
>
& quare erigatur
<
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>.x.i.</
var
>
parallela ipſi
<
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>.p.o.</
var
>
ab eadem
<
var
>.p.o.</
var
>
tanto ſpatio diſtans, & qua
<
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/>
ratione producatur à puncto
<
var
>.Z.</
var
>
ipſa
<
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>.Z.r.e.</
var
>
parallela ipſi
<
var
>.q.d</
var
>
.</
s
>
</
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<
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xml:space
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">Nunc obſeruandum eſt, quòd ſi planum ipſius
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var
>
in figura corporea aliquan-
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tulum inclinatum eſſet orizontem verſus, anguli
<
var
>.i.q.d.</
var
>
et
<
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>.i.d.q.</
var
>
maiores exiſterent,
<
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/>
quàm cum idem eſt ipſi orizonti perpendiculare, quemadmodum clarè demonſtra-
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tum fuit in .39. primi Vitelionis.</
s
>
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<
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<
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xml:space
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">Non igitur rectè fit ſi in figura ſuperficiali ducatur à puncto
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>.B.</
var
>
parallela ipſi
<
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>.q.d.</
var
>
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abſque maiori apertura angulorum
<
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var
>
et
<
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var
>
.</
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xlink:href
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">CVM verò duæ præcedentes figuræ intellectæ erunt, facilè quoque erit intel-
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ligere duas ſubſequentes
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in corporea quarum
<
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var
>
extra lineas
<
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>.u.s.</
var
>
et
<
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>.a.n.</
var
>
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reperitur, vbi enim aduertendum erit oportere ſumere ſemper
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>.p.x.</
var
>
figuræ ſuperfi-
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cialis æqualem ei, quæ eſt corporeæ, & eidem ſuperficiali, adiungere
<
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>.x.d.</
var
>
æqualem
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ei, quæ eſt corporeæ, & compoſito
<
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>.p.d.</
var
>
ex dictis duabus lineis, in figura ſuperficiali,
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addere
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>.d.q.</
var
>
æqualem ei, quæ eſt figuræ corporeæ, deinde accipere punctum
<
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>.l.</
var
>
in fu-
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perficiali </
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