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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EPISTOLAE.
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347
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file
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0347
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0347
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<
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<
s
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xml:space
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">Nam circa æqualitatem angulorum reflexionis & incidentiæ, iam tibi probaui
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illud non vniuerſaliter euenire à breuitate aggregati radiorum incidentiæ reflexio-
<
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nisque
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. </
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<
s
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xml:space
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">Sed hoc naſcitur potius ab eo, quod cum radius incidentiæ non poſſit ſuper
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ficiem corporis opaci penetrare, reflectit, vt citra ipſam
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cum
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type
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>
angulo æquali ei, quem
<
lb
/>
faceret cum eadem ſuperficie vltra ipſam ſi tranſiuiſſet.</
s
>
</
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<
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<
s
xml:id
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xml:space
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">Exempli gratia ſit
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>.a.</
var
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obiectum
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>.b.</
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autem
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oculus in figura
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>.A.</
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et
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>.c.e.</
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ſuperficies ipſius
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ſpeculi
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>.d.</
var
>
verò ſit punctum ipſius ſuperficiei, à quo ad oculum reflectitur imago ip-
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0347-01
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xlink:href
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ſius
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. </
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<
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xml:space
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>
incidentiæ, recta
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incederet ſub
<
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>.c.e.</
var
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efficeret angulum
<
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>.e.d.h.</
var
>
<
lb
/>
æqualem angulo
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>.c.d.a.</
var
>
eius contrapoſito,
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ſed quia impeditur ipſæ radius ab opacitate
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/>
ipſius ſpeculi
<
var
>.c.e.</
var
>
ne vlterius incedat, propte
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rea reflectitur ab ipſa ſuperficie ſpeculi, con-
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/>
ſtituens cum ipſa angulum
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>.e.d.b.</
var
>
æqualem
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/>
angulo
<
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>.e.d.h.</
var
>
ſed quia angulus
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>.c.d.a.</
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>
eſt
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type
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<
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ęqualis ipſi angulo
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>
propterea angulus
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>.e.d.b.</
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ęqualis exiſtit angulo
<
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>.c.d.</
var
>
a; </
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<
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xml:space
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">per
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accidens igitur ſequitur
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et
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>.d.b.</
var
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ſimul ſumptas, breuiorem facere longiludinem
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omni alia, quæ ab ipſa ſuperficie
<
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>.c.e.</
var
>
ad eadem puncta
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>.a.b.</
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>
ducta eſſet, </
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<
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xml:space
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">quare natu-
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ræintentio eſt efficere angulum
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>.e.d.b.</
var
>
æqualem angulo
<
var
>.e.d.h.</
var
>
vnde ex accidenti po
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/>
ſtea ſequitur, ipſum æqualem eſſe angulo
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var
>.c.d.a.</
var
>
& deinde
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lineæ
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>.a.d.</
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>
et
<
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>.d.b.</
var
>
con-
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ſtituant longitudinem breuiorem. </
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>
<
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xml:space
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">Quare illud quod omnes putabant eſſe primum
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& perſe, vltimum eſt, & exaccidenti.</
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<
s
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xml:space
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">Quare vero ſuperficies, quæ vocatur reflexionis, in qua ſunt duæ lineę, hoc eſt
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incidentię,
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, ſemper ſit perpendicularis ſuperficiei ipſius ſpeculi: </
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xml:space
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eſt ratio, quia cum quilibet radius incidentiæ, perpendicularis ipſi ſuperficiei ſpe-
<
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culi, in ſeipſo reflectit, ex ijſdem dictis rationibus, hoc eſt, quia cum tali angulo vult
<
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/>
reflecti, cum quali tranſiret, ita etiam purandum eſt, quodradius incidens obliquus,
<
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/>
cum in ſeipſum non poſſit redire, quia non eſt perpendicularis ſuperficiei ſpeculi,
<
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/>
reflectitur tamen per planum erectum ipſi ſuperficiei ſpeculi, vt in eo, cui magis re-
<
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ſiſtit ſuperficies corporis opaci, quàm alicui alij plano ipſius infiniti inclinatorum
<
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/>
planorum, ab vtraque parte ipſius plani perpendicularis, quod vnum etiam tan-
<
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tummodo eſt, & in quo, radius maiorem vim obtinet reflectendi, ſeu in eo, in quo
<
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radius ipſe cum maiori reſiſtentia repercutitur à ſuperficie corporis opaci.</
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<
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vnde oriatur,
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>
rei viſibilis imago, à ſpeculo plano reflexa, ſem
<
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per in catheto incidentiæ videatur.</
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>
</
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<
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<
s
xml:id
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xml:space
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preserve
">Pro cuius rei ratione cognoſcendum primò eſt, quo modo fit perfecta
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ſimplexque
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">ſimplexq́;</
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<
lb
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viſio, & non reflexa, deinde proſequemur ad reliqua huius tertiæ propoſitionis.</
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<
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<
s
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">Animaduertendum igitur eſt, quod
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obiectum aliquod viſibile aſpi
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cimus, nos nunquam perfectè illud comprehendere poſſumus, niſi in puncto con-
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curſus, ſeu interſectionis axium viſualium, ſeu radialium ( vt ita loquar )
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quam
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<
reg
norm
="
inter- ſectionem
"
type
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">inter-
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ſectionẽ</
reg
>
, nos efficimus ope reuolutionis oculorum
<
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adinuicem
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type
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">adinuicẽ</
reg
>
, hoc eſt voluendo vnum
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verſus alium, ita vt in ſitu ipſius obiecti, ſeinuicem ſecent axes iam dicti, </
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>
<
s
xml:id
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xml:space
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">tunc enim
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vtroque oculo mediante, exacte rem perſpicimus, cęteris .8. circunſtantijs non ob-
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ſtantibus.</
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</
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<
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<
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xml:id
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xml:space
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">Vnde ſtantibus oculis in tali ſitu, altero reſpectu alterius, ſi eorum alter tectus;
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</
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<
s
xml:id
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xml:space
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">ſeu velatus fuerit, tune alio tantummodo oculo mediante, videbimus obiectum,
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in ea diſtantia, exactius, quam in quauis alia propinquiori, & remotiori.</
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