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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338
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0338
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<
s
xml:id
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xml:space
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">Nunc verò cum duo puncta alicuius horarię lineæ inuenta fuerint, quæ à Solis ſi-
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tu in diuerſis parallelis efficiuntur, ſi voluerimus ipſam lineam
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ducere, ſcien
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dum primò eſt ipſam lineam horariam eſſe communem ſectionem circuli horarij,
<
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illius horæ cum ſuperficie cyllindrica, </
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>
<
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xml:space
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">& propterea ellipticam, vt oſtendit Serenus
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in .19. primi lib. quod etiam ellicere poſſumus ab eo, quod Archimedes in .10. pro-
<
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poſitione libr. de conoidalibus, ſcribit. </
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<
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xml:space
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">Quapropter oporter nos inſtrumen-
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tum prius componere, modo circini, ſed trium crurum, quæ omnia in eadem
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plana ſuperficie ſint, ea tamen arte factum, vt quodlibet illorum poſſimus pro-
<
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/>
longare, necnon contrahere, ut cum duo extrema firmata fuerint, media poſ-
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ſit circunduci circa centrum, ſeu punctum commune illarum interſectionum
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>
<
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poſſit produci, necnon abbreuiari vel augeri, & diminui, vt mediante ſua extremi-
<
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/>
tate inſeriori poſſimus delineare gyrum ellipticum horarium, dum
<
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centrum
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ipſorum
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crurum adhæreat extremitati gnomonis, reliquæ vero extremitates ipſorum
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crurum
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type
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ſint ſupra puncta inuenta ipſius horæ. </
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<
s
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xml:space
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">oportet etiam vt hoc inſtrumentum à tergo
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ipſorum crurum habeat in ſuperiori parte ſuperficiem quandam
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, quę
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ſit vice vnius partis illius ſuperficiei, in qua ſupponuntur omnia crura inſtrumenti,
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& hoc quantum fieri poteſt, quod quidem fieri debet, ne crus medium, hoc eſt mo
<
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/>
bile, exeat à tali ſuperficie, ſeu declinet ab ea, quæ ſemper ſupponitur in ſitu circuli
<
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horarij talis horæ. </
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>
<
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xml:space
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">oportet etiam, vt iuxta circunferentiam dimidij circuli ſint duo
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gyri eiuſdem materiæ inter ſe parum diſtantes, ita ut crura poſſint moueri, intra hos
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gyros, & dimidium circulum, & quod inter hos gyros locatæ ſint duæ cochleæ, ſeu
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duo helices, vt quando voluerimus, poſſimus fir-
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mare ipſa crura extrema, dum eorum extremitates
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fuerint ſupra puncta inuenta illius horæ, </
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dorſo iſtius inſtrumenti, circa centrum coniunctio
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nis, rectè factum erit ſi aliqua concauitas fuerit, in
<
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/>
qua, extremitas gnomonis poſſit locari, dum duce-
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/>
re voluerimus aliquam horariam lineam.</
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>
</
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<
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<
s
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xml:space
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">Tale inſtrumentum excogitaui ad fugiendum
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tædium inueniendi dictam ellipticam ex punctis.</
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</
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<
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<
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xml:space
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">Nunc autem ſciendum eſt, quod vnus tantum-
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modo gnomon ſufficiens non erit pro tota die æſti-
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/>
ua, neque duo, niſi valde breues fuerint reſpectu
<
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/>
ſemidiametri cyllindri, & in ſitu medio quartarum
<
lb
/>
meridionalium noſtro orizonti, quorum autem
<
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/>
longitudo ita inuenienda eſſet.</
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>
</
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<
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<
s
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xml:space
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>
cyllindri ori
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zontis vice,
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à duobus diametris
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>
et
<
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>.c.
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f.</
var
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quarum
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ſit pro meridiana: </
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e. punctus orientalis: </
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verò
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autem meridionalis. et
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var
>
ſeptentrionalis,
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maxima.
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</
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<
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xml:space
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verſus
<
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quæ terminetur ab
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>
ita
<
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<
var
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minor ſit
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graduum .45. aliter impoſſibile eſſet duobus
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gnomonibus mediantibus
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tota die æſtiua horas videre.</
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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
">Quo facto ducatur ab .q:
<
var
>q.p.</
var
>
contingens circulum & à centro circuli
<
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>.o.</
var
>
per pun-
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ctum
<
var
>.u.</
var
>
medium quartæ ducatur
<
var
>.o.u.i.</
var
>
vſque ad contingentem
<
var
>.q.p.</
var
>
vnde
<
var
>.u.i.</
var
>
longitu
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do erit vniuſcuiuſque gnomonis, qui gnomones infixi erunt in medio dictarum
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quartarum.</
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