Biancani, Giuseppe
,
Aristotelis loca mathematica
,
1615
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illa, qua ad vaporum altitudines indagandas vtuntur Alhazenus, Vitellio,
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& Clauius, in qua terræ globus eſt F L G E, regiò vaporum, & exhalatio
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num M X N T. horizon aſtronomicus O P. phyſicus Q R, tangens terram
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in puncto F, vbi etiam ponendus eſt huius horizontis habitator, vnà cum.
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</
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<
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">Caucaſo F V. </
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<
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">Sol A B C, qui initio Crepuſculi infra horizontem O P, depri
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mitur gr. 18. vti ab Aſtronomis compertum eſt, hoc eſt, arcum D P, eſſe
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grad. 18. radius autem C I K, tangens terram, incipit illuminare halitus,
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qui ſunt ad K, in extremo horizonte ſenſibili F K. quique poſſunt videri ab
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oculo in F, ideſt ab huius horizontis habitatore. </
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<
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s.001802
">Cæterùm prædicti autho
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res poſt longam ratiocinationem ex calculo planorum
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triangulorũ
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tandem
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oſtendunt in triangulo H F K, latus H K, continere milliaria 3631. ex quo
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detracta H L, ſemidiametro terræ, quæ eſt milliar. 3579. reliqua L K, ſum
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ma halituum eleuatio relinquatur 52. milliar. </
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<
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">quibus ab ipſis demonſtra
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tis, ſi H F, terræ ſemidiameter, quæ continet milliar. 3579. ponatur ſinus
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totus 100000. & latus F K, ponatur tangens anguli ad H, quem prędicti au
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thores probant eſſe grad. 8. 54. erit F K, tangens partium 15659. fiat igi
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tur per 2. pro. </
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<
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<
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<
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>vt H F, ſinus totus,</
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<
cell
>ad milliar.</
cell
>
<
cell
>ita tangens F K,</
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>
<
cell
>ad milliar.</
cell
>
</
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<
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<
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>100000.</
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>
<
cell
>3579.</
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>
<
cell
>15659.</
cell
>
<
cell
>560.</
cell
>
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<
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">& inueniemus per auream regulam latus F K, continere milliar. </
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<
s
id
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s.001808
">560. quan
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ta ſcilicet eſt diſtantia ab oculo noſtro ad exhalationes Crepuſculi initium
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efficientes. </
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<
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id
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">Conſideremus iam triangulum F K V, vt ipſius latus F V, quæ
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eſt Caucaſi altitudo, in milliaribus innoteſcat. </
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>
<
s
id
="
s.001810
">iam ipſius latus F K, inno
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tuit, angulus verò ad F, eſt rectus; at angulus ad K, ſic manifeſtabitur; in
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quadrilatero F K I H, quatuor anguli ſunt æquales 4. rectis ex 32. primi. </
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<
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">duo
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autem F, & I, ſunt recti ex 18. 3. ergo reliqui duo H, & K, æquales erunt duo
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bus rectis, quorum alter H, eſt gr. 17. 48. vt præditi Mathematici
<
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oſtẽdunt
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,
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reliquus igitur ad K, erit gr. 162. 12. vt compleat duos rectos. </
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<
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">qui ſi detra
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hatur à duobus rectis, qui ſunt deinceps ad lineam F K, reliquus angulus
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F K V, erit gr. 17. 48. ſi ergo latus F K, notum ponatur ſinus totus 100000.
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latus verò F V, tangens anguli noti, erit ipſa 32100. fiat igitur,
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<
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<
cell
>vt F K, ſinus totus,</
cell
>
<
cell
>ad milliar.</
cell
>
<
cell
>ita F V, tangens</
cell
>
<
cell
>ad milliar.</
cell
>
</
row
>
<
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>
<
cell
>100000.</
cell
>
<
cell
>560.</
cell
>
<
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>32100.</
cell
>
<
cell
>180.</
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>
</
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<
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inueniemusq́
">inueniemusque</
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; latus F V, continere milliar. </
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<
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">180. cuius pars F X, quæ eſt in
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fra habituum altitudinem continet milliar. </
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<
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">52. quibus detractis ex 180. re
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manent 128. pro tota X V, quæ tota eſt ſupra vapores, nondum tamen illu
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minata. </
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<
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id
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">vnde patet Mazonium erraſſe in colligenda hoc modo Caucaſi al
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titudine, ex prima Crepuſculi illuminatione in horizonte Caucaſi facta,
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cum ex præmiſſo calculo conſtet partem montis F V, totam tunc temporis
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eſſe tenebroſam, quamuis ſuperet multò regionem vaporum, contrà quàm
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ipſe putabat, ſuperat enim eam milliar. </
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<
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">128. quare duæ tertiæ montis erunt
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non 52. mill. vt ipſe ait, ſed mill. 180. & proinde tota altitudo erit mill. 270.
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quod ſanè ridiculum eſt, cum nullius montis altitudo ſeſquimilliare tran
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ſcendat. </
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<
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">Quod ſi ſequamur alteram expoſitionem, vt nimirum Ariſtot. lo
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quatur non de tertia montis parte, ſed noctis, ita vt dicat, circa initium
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tertiæ partis noctis apicem montis illuſtrari, altitudo eius erit </
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