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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163
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DE MECHAN.
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">PRo intelligenda vera, & intrinſeca ratione, vnde fiat ut multitudo rotularum in
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trochleis cauſa ſit, ut exigua vis ſurſum moueat, aut attollat
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magna. </
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<
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">Ima
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ginemur duas hîc ſubſcriptas trochlæas explicatas tranſuerſaliter in hunc modum,
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ideſt ſit
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fixum &
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orizonti. cui ſint rotulæ appenſe ab infe
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riori parte ad ſuperiorem
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type
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è regione
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ſit aliud
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type
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quod moueri
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poſſit ab imo ad ſumum, ſuper quod totidem ſint rotulæ aut radij,
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annexa poſtea
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fuerit funis puncto
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fixo, eam faciendo pertranſire per rotulas tam à parte ſupe-
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riore, quam ab inferiore; </
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<
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xml:space
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">& appenſum deinde cum erit paruo illi tigno
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>
mobili
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pondus
<
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>.E.</
var
>
ducendo poſtmodum extremum
<
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>.f.</
var
>
funis tranſeuntis per rotulas, idem pla
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nè fiet quod à trochlęis ſimul unitis fieri ſolet. </
s
>
<
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xml:space
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preserve
">Cuius quidem effectus ratio ſub no-
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ſtram cognitionem cadet facilius in huiuſmodi figura. </
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<
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teram
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>
cuius
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ſit
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ita ſitum, ut brachium
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>
ſit duplum ad brachium
<
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>.K.
<
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h.</
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>
ſupponendo igitur in puncto
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>
pondus, aut virtutem mouentem unius libræ, & in
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h. duarum librarum,
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dubio hæ duæ uirtutes in huiuſmodi diſtantijs à centro
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ęquales
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, ob rationes prioribus capitibus iam allatas, & ſtatera orizontalis
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manebit. </
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">Vnde clarum erit,
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quæuis etiam exigua virtus adiuncta ipſi
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>
mouebit
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ſtateram extra orizontalem ſitum. </
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xml:space
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ex æquo medio inter
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et
<
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>.K.</
var
>
<
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/>
applicata erit virtus ipſius
<
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>.h.</
var
>
non amplius conſiderato brachio
<
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>.K.h.</
var
>
inclinante uirtu-
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/>
te ipſius
<
var
>.i.</
var
>
eandem partem verſus, in quam inclinabat, quando erat in
<
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>.h.</
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>
ſed uirtus ip
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/>
ſius
<
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>.g.</
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>
inclinet contrario modo,
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ab eo, quo inclinabat prius; </
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erit, communi conceptu, & ob ea, quæ cap .5. huius tractatus ſunt dicta
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ſemper
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in eodem ſitu abſque motu manſuram,
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ſtateram appellabimus mobilem, &
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primam. </
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<
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xml:space
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>.e.</
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>
fixo deſcendere funem
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>
quæ fulciat pun
<
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/>
ctum
<
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>.K.</
var
>
extremum diametri
<
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>
quam intelligo pro diametro vnius ex rotulis infe
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rioribus trochleæ; </
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>
<
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xml:space
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">& ſit
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>
diameter vnius ex rotulis ſuperioribus alterius parui
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tigni defixi à parte inclinationis ipſius
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>
& parallela diametro
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>.g.K.</
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>
cuius diametri
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centrum fixum ſit
<
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>.l.</
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>
& ſit coniunctum
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>.g.</
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>
punctum, à fune cum puncto
<
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>.m.</
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>
quæ
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per-
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pendicularis ſit primo diametro
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>
quàm ſecundo
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ideſt ita vt anguli
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