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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<div xml:id="echoid-div477" type="chapter" level="2" n="6">
<div xml:id="echoid-div630" type="section" level="3" n="26">
<div xml:id="echoid-div630" type="letter" level="4" n="1">
<p>
<s xml:id="echoid-s3965" xml:space="preserve">Nunc verò cum duo puncta alicuius horarię lineæ inuenta fuerint, quæ à Solis ſi-
<lb/>
tu in diuerſis parallelis efficiuntur, ſi voluerimus ipſam lineam
<reg norm="horariam" type="context">horariã</reg>
ducere, ſcien
<lb/>
dum primò eſt ipſam lineam horariam eſſe communem ſectionem circuli horarij,
<lb/>
illius horæ cum ſuperficie cyllindrica, </s>
<s xml:id="echoid-s3966" xml:space="preserve">& propterea ellipticam, vt oſtendit Serenus
<lb/>
in .19. primi lib. quod etiam ellicere poſſumus ab eo, quod Archimedes in .10. pro-
<lb/>
poſitione libr. de conoidalibus, ſcribit. </s>
<s xml:id="echoid-s3967" xml:space="preserve">Quapropter oporter nos inſtrumen-
<lb/>
tum prius componere, modo circini, ſed trium crurum, quæ omnia in eadem
<lb/>
plana ſuperficie ſint, ea tamen arte factum, vt quodlibet illorum poſſimus pro-
<lb/>
longare, necnon contrahere, ut cum duo extrema firmata fuerint, media poſ-
<lb/>
ſit circunduci circa centrum, ſeu punctum commune illarum interſectionum
<reg norm="ſimulque" type="simple">ſimulq́;</reg>
<lb/>
poſſit produci, necnon abbreuiari vel augeri, & diminui, vt mediante ſua extremi-
<lb/>
tate inſeriori poſſimus delineare gyrum ellipticum horarium, dum
<reg norm="centrum" type="context">cẽtrum</reg>
ipſorum
<lb/>
crurum adhæreat extremitati gnomonis, reliquæ vero extremitates ipſorum
<reg norm="crurum" type="context">crurũ</reg>
<lb/>
ſint ſupra puncta inuenta ipſius horæ. </s>
<s xml:id="echoid-s3968" xml:space="preserve">oportet etiam vt hoc inſtrumentum à tergo
<lb/>
ipſorum crurum habeat in ſuperiori parte ſuperficiem quandam
<reg norm="ſemicircularem" type="context">ſemicircularẽ</reg>
, quę
<lb/>
ſit vice vnius partis illius ſuperficiei, in qua ſupponuntur omnia crura inſtrumenti,
<lb/>
& hoc quantum fieri poteſt, quod quidem fieri debet, ne crus medium, hoc eſt mo
<lb/>
bile, exeat à tali ſuperficie, ſeu declinet ab ea, quæ ſemper ſupponitur in ſitu circuli
<lb/>
horarij talis horæ. </s>
<s xml:id="echoid-s3969" xml:space="preserve">oportet etiam, vt iuxta circunferentiam dimidij circuli ſint duo
<lb/>
gyri eiuſdem materiæ inter ſe parum diſtantes, ita ut crura poſſint moueri, intra hos
<lb/>
gyros, & dimidium circulum, & quod inter hos gyros locatæ ſint duæ cochleæ, ſeu
<lb/>
duo helices, vt quando voluerimus, poſſimus fir-
<lb/>
mare ipſa crura extrema, dum eorum extremitates
<lb/>
</figure>
fuerint ſupra puncta inuenta illius horæ, </s>
<s xml:id="echoid-s3970" xml:space="preserve">deinde in
<lb/>
dorſo iſtius inſtrumenti, circa centrum coniunctio
<lb/>
nis, rectè factum erit ſi aliqua concauitas fuerit, in
<lb/>
qua, extremitas gnomonis poſſit locari, dum duce-
<lb/>
re voluerimus aliquam horariam lineam.</s>
</p>
<p>
<s xml:id="echoid-s3971" xml:space="preserve">Tale inſtrumentum excogitaui ad fugiendum
<lb/>
tædium inueniendi dictam ellipticam ex punctis.</s>
</p>
<p>
<s xml:id="echoid-s3972" xml:space="preserve">Nunc autem ſciendum eſt, quod vnus tantum-
<lb/>
modo gnomon ſufficiens non erit pro tota die æſti-
<lb/>
ua, neque duo, niſi valde breues fuerint reſpectu
<lb/>
ſemidiametri cyllindri, & in ſitu medio quartarum
<lb/>
meridionalium noſtro orizonti, quorum autem
<lb/>
longitudo ita inuenienda eſſet.</s>
</p>
<p>
<s xml:id="echoid-s3973" xml:space="preserve">Sit exempli gratia circulus
<var>.a.b.e.u.</var>
cyllindri ori
<lb/>
zontis vice,
<reg norm="diuiſusque" type="simple">diuiſusq́;</reg>
à duobus diametris
<var>.d.e.</var>
et
<var>.c.
<lb/>
f.</var>
quarum
<var>.c.f.</var>
ſit pro meridiana: </s>
<s xml:id="echoid-s3974" xml:space="preserve">d.e. autem pro verticali,
<reg norm="ſitque" type="simple">ſitq́;</reg>
e. punctus orientalis: </s>
<s xml:id="echoid-s3975" xml:space="preserve">d.
<lb/>
verò
<reg norm="occidentalis" type="context">occidẽtalis</reg>
<var>.f.</var>
autem meridionalis. et
<var>.c.</var>
ſeptentrionalis,
<reg norm="computeturque" type="simple">computeturq́;</reg>
maxima.
<lb/>
</s>
<s xml:id="echoid-s3976" xml:space="preserve">Solis amplitudo ab
<var>.f.</var>
verſus
<var>.e.</var>
quæ terminetur ab
<var>.q.</var>
ita
<reg norm="quodarcus" type="simple">quodarcꝰ</reg>
<var>.f.q.</var>
minor ſit
<reg norm="quam" type="context">quã</reg>
<lb/>
graduum .45. aliter impoſſibile eſſet duobus
<reg norm="tantummodo" type="context">tantũmodo</reg>
gnomonibus mediantibus
<lb/>
tota die æſtiua horas videre.</s>
</p>
<p>
<s xml:id="echoid-s3977" xml:space="preserve">Quo facto ducatur ab .q:
<var>q.p.</var>
contingens circulum & à centro circuli
<var>.o.</var>
per pun-
<lb/>
ctum
<var>.u.</var>
medium quartæ ducatur
<var>.o.u.i.</var>
<var>.q.p.</var>
vnde
<var>.u.i.</var>
longitu
<lb/>
do erit vniuſcuiuſque gnomonis, qui gnomones infixi erunt in medio dictarum
<lb/>
quartarum.</s>
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