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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IO. BAPT. BENED.
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clarum erit ex rationibus ſupradictis nos ipſam videre in
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concurſu ipſorum
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axium viſualium, qui axes cum reperiantur vnà cum ipſis radijs reflexis
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et
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ex neceſſitate ſeinuicem
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in catheto
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cum extendantur in ipſis ſuperficie-
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bus reflexionum, quæ ſuperficies nihil aliud commune inuicem habent, quam cathe
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tum dictum
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ſit igitur in puncto
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.</
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<
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<
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xml:space
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">Ex his dictis alia oritur neceſſitas, hoc eſt, quod quotieſcunque vnam tantummo
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do imaginem obiecti
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videmus, dato quod duæ ſuperficies reflexionis ſint, & non
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vna tantum, tunc angulos
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et
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ſemper inuicem æquales eſſe oportebit. </
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xml:space
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cus
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et
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ex neceſſitate inuicem æquales erunt.</
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<
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xml:space
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">Scimas enim ex .3. ſexti Euclid. quod eadem proportio erit ipſius
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ad
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d.</
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quę ipſius
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ad
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& ipſius
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ad
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ſimiliter, </
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">quare ipſiusb
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ad
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d.</
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erit vt ipſius
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ad
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. </
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xml:space
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">Vnde ſequitur
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æqualem eſſe ipſi
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et
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ipſi
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vt à medio circulo
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potes videre, quamuis etiam
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non eſſet extremum
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diametri, ſed vbicunque volueris in ipſo diametro, vel
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protracta, eo quod pun-
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ctum
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& punctum
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in eodem ſemicirculo, vel in æqualibus ſemicirculis, non
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aliter in ipſa circunferentia locari,
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ſeruando proportionem
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ad
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vt
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>.b.
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t.</
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ad
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</
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<
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xml:space
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">propterea quod in omni alio ſitu exiſtente puncto
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ipſa
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eſſet aut maior
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aut minor ipſa
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et
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aut minor, aut maior ipſa
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ex .7. & 14. tertij Eucli. </
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aut maior, aut minor proportio eſſet ipſius
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ad
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quam ipſius
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ad
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& non
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eadem.</
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<
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xml:space
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">Nunc è conuerſo ſi
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et
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ſunt ſibi inuicem æquales, & ſic
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cum
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ſequi-
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tur ex .8. primi Eucli. angulos
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et
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inuicem æquales eſſe.</
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<
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xml:space
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">Ab ijſdem ſpeculationibus potes etiam videre vnde accidat quod partes ſuperio
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res alicuius obiecti reflexæ à tali ſpeculo concauo videntur nobis inferiores eſſe, &
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inferiores appareant ſuperiores, & dextræ ſiniſtræ, & ſiniſtræ dextræ. </
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<
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xml:space
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">quod autem
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hucuſque demonſtraui de ſpeculis planis, & ſphæricis concauis, ratiocinare tu ijſdem
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medijs circa ſphærica conuexa, vbi clarè videbis puncta huiuſmodi ſpeculi conuexi,
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à quibus reflectitur imago obiecti ad ambos oculos, ſemper oportere æquidiſtantia
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eſſe à
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communi ipſius ſuperficiei ſpeculi, & catheto incidentiæ, dum unam tan
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tummodo imaginem ipſius obiecti videmus, & à diuerſis ſuperficiebus reflexionum.</
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<
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xml:space
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">Nolo etiam prætermittere, quod nunc mihi ſuccurrit, hoc eſt quod poſſet ali-
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quis duos ſitus inuenire, vnum pro oculo, alterum verò pro obiecto, reſpectu alicu-
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ius ſpeculi concaui, ſphęroidis prolatæ, vt reflexio ipſius obiecti videretur, vt linea
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diuidens per æqualia ipſum ſpeculum. </
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<
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xml:space
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">Reſpectu verò alicuius ſpeculi concaui ſphæ-
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roidis oblongæ, vt reflexio obiecti ad oculum veniret à tota ſuperficie ipſius ſpecu-
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li, vnde tota ſuperficies ipſius ſpeculi videretur colorata illo colore cuius eſſet
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obiectum, quæ quidem paſſiones
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à .48. tertij lib. ipſius Pergei, vt ex te ipſo fa
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cile videre potes, propter æqualitatem angulorum reflexionis, & incidentiæ.</
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<
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xml:space
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">Opinio autem mea, quam ſcire cupis de imagine obiecti reflexa, quam putas eſ-
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ſe in ſuperficie ſpeculi, hæc eſt, quod nec in ſuperficie, nec ultra, nec citra eam eſt ip
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ſa imago, quod autem vltra non ſit, hoc puto nulli dubium eſſe. </
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<
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xml:space
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">eadem etiam ra-
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tione non erit citra ſuperficiem ſpeculi concaui, quamuis ipſam nos compræhenda-
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mus in concurſu radiorum viſualium, tam ab vno ſpeculo quam ab alio reflexione
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facta. </
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<
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xml:space
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">Sed quòd ipſa neque ſit in ipſa ſpeculi ſuperficie, manifeſtum erit ex hoc,
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duo ſpectantes in eodem ſpeculo, duas diuerſas imagines vident, tres,
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tres, qua-
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tuor, quatuor, & ſic deinceps, vnde tot eſſent imagines ſupra ſuperficiem ſpeculi,
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quot obiecta,
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tamen ita non eſt, nec plus eſt in vno loco ipſa imago, quam in alio, </
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