Fabri, Honoré
,
Dialogi physici in quibus de motu terrae disputatur
,
1665
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in YD, in ratione compoſita, ex ratione Quadrati ab ad differentiam
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Quadrati BD & ex permutata Quadrati ſub chorda arcus EY ad differen
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tiam Quadrati ſub chorda arcus ED, vel ex ratione Quadrati LB, ad Qua
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dratum bD, plus bis rectangulum ſub LbD, ſeu ad rectangulum ſub bD,
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& aD, & Lc. ad cE &c. </
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Auguſtin.
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<
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"> Non intelligo hæc Geometrica, tam enim jejunè illa pro
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ponis; cùm tamèn abſtruſas demonſtrationes contineant; vix ea curtim &
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raptim indicata potiùs quàm expoſita quiſquam mente capiat. </
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Antim.
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<
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id
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"> Suppono ea, quæ jam aliàs demonſtravi, ſcilicet circulum ſub
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radio, æquali chordæ, æqualem eſſe portioni ſuperficiei Sphæræ, quam
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metitur, vel gignit arcus, cujus eſt chorda, v. g. ſi accipiatur circulus ſub
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radio æquali chordæ ſubtenſæ arcui EY, erit æqualis portioni ſuperficiei
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Sphæræ,
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metitur, vel gignit arcus EY revolutus ſcilicet circa axem EC,
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hinc chorda ſubtenſa arcui ED eſt æqualis radio circuli æqualis ſuperficiei
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Hemiſphærij; demonſtratum eſt item, portionem ſuperficiei genitæ ab arcu
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YE eſſe ad genitam ab arcu YD, vt Ec, ad cL; præterea lumina inci
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dentia, per parallelas, ſunt vt baſes, ſi conſiderentur in ſe; ſi verò conſi
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derentur in ſubjecto, id eſt in diverſa ſuperficie, cui incidunt, ſi ſint
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æqualia lumina, erunt in ſubjecto, vt ſuperficies illuſtratæ permutando; v.
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g. ſi eadem vis, ſeu quantitas luminis, (ſic enim vocare liceat) incidat in
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ſuperficiem duplam alterius, erit lumen, vel luminis intenſio ſuperficiei
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duplæ ad aliam, vt 1.ad 2. Si verò ſuperficies ſunt æquales, ſed lumina inæ
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qualia, erunt intenſiones, vt ipſa lumina; ſi demum & ſuperficies inæqua
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les ſunt, erunt intenſiones in ratione compoſita luminum & ſuperficierum
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permutando; jam applica. </
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Auguſtin.
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<
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"> Satis eſt, probe intelligo; inde autem conſtat, quod jam
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ſubindicare viſus es, vim Solis potiſſimum effectum habere circa Polum
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Hemiſphærij Lunaris ab eo illuſtrati, v. g. circa E, intra arcum Zy, vltra
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verò versùs B & D parum valet; hinc etiam ſimilis ratio ducitur, cur Sol
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Oriens vel Occidens, terræ ſuperficiem parum afficiat, plus verò de meri
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die, plus demum, quò Sol propiùs ad punctum verticale accedit; hinc vis
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debilior radij obliqui, non tantùm à radij reflexi carentia petenda eſt; vt
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aliqui faciunt. </
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Chryſocom.
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<
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"> Ex iis, quæ dicis, Antime, ſequeretur Lunaris diſci, vel
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Hemiſphærij extremitates, minùs ſplendidas & illuſtratas videri; nul
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lum tamen ego diſcrimen obſervo; oculis autem meis magis credo, quàm
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veſtris demonſtrationibus. </
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Antim.
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<
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"> Demonſtratio, Chryſocome, nunquam fallit, nec fallere poteſt
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ſtatue igitur oculum in A; Lunam, licèt Sphærica ſit, vt planum diſcum
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aſpicis, cujus diameter eſt BD, paulò minor; & Ba, ſegmentum ſcilicet
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apparentis Semidiametri, vides ſub angulo BAa; aL verò ſub angulo
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aAL; ſed ob parvitatem anguli BAL, qui vix eſt 16.minutorum, anguli
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ſub quibus videntur ſegmenta aB, aL, ſunt vt ipſa ſegmenta; igitur tanta
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lux videtur in aB quanta in aL; quia in eadem ratione videtur contra
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ctior, in qua primùm incidit diſtractior; vt enim rem in plano tantùm, </
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