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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                <pb o="285" rhead="EPISTOL AE." n="297" file="0297" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0297"/>
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                <head xml:id="echoid-head418" xml:space="preserve">DE MOTV MOLAE, ET TROCHI, DE AMPVL-
                  <lb/>
                lis aquæ, de claritate aeris, & Lunæ noctu fulgentis, de æter-
                  <lb/>
                nitate temporis, & infinito ſpacio extra
                  <lb/>
                Cœlum, Cœ
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                figura.</head>
                <head xml:id="echoid-head419" style="it" xml:space="preserve">Illust. Ioanni Paulo Capra Nouarienſi Sabaudia Ducis boſpicij
                  <lb/>
                Magistro, viro ingeny praſtantia, & morum cando-
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                re, non minus quam familia nobili-
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                tate conſpicuo.</head>
                <p>
                  <s xml:id="echoid-s3536" xml:space="preserve">SI vera eſſet animorum illa tranſmigratio quam ſibi Italicæ ſapientiæ Pa-
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                  ter Pythagoras effinxerat, tuam,
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                  exiſtimarem animam canis,
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                  quandoque venatici fuiſſe.</s>
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                <p>
                  <s xml:id="echoid-s3537" xml:space="preserve">Quæris à me literis tuis, an motus circularis alicuius molæ molendina
                    <lb/>
                  rie, ſi ſuper aliquod punctum, quaſi
                    <reg norm="mathematicum" type="context">mathematicũ</reg>
                  , quieſceret, poſſet eſſe perpetuus,
                    <lb/>
                  cum aliquando eſſet mota, ſupponendo etiam eandem eſſe perfectè rotundam, &
                    <lb/>
                  lęuigatam. </s>
                  <s xml:id="echoid-s3538" xml:space="preserve">Reſpondeo huiuſmodi motum nullo modo futurum perpetuum, nec
                    <lb/>
                  etiam multum duraturum, quia præterquam quod ab aere qui ei circumcirca
                    <reg norm="aliquam" type="context">aliquã</reg>
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                  reſiſtentiam facit ſtringitur, eſt etiam reſiſtentia partium illius corporis moti, quæ
                    <lb/>
                  cum motæ ſunt, natura, impetum habent efficiendi iter directum, vnde cum ſimul
                    <lb/>
                  iunctæ ſint, & earum vna continuata cum alia. </s>
                  <s xml:id="echoid-s3539" xml:space="preserve">dum circulariter mouentur patiuntur
                    <lb/>
                  violentiam, & in huiuſmodi motu per vim vnitæ manent, quia quanto magis mo-
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                  uentur, tanto magis in ijs creſcit naturalis inclinatio recta eundi, vnde tanto magis
                    <lb/>
                  contra ſuammet naturam voluuntur, ita vt ſecundum naturam quieſcant, quia cum
                    <lb/>
                  eis proprium ſit, quando ſunt motæ, eundi recta, quanto violentius voluuntur, tan-
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                  to magis vna reſiſtit alteri, & quaſi retrò reuocat eam, quam antea reperitur habere.</s>
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                <p>
                  <s xml:id="echoid-s3540" xml:space="preserve">Ab eiuſmodi inclinatione rectitudinis motus partium alicuius corporis rotundi
                    <lb/>
                  fit, vt per aliquod temporis ſpacium, trochus cum magna violentia ſeipſum circun-
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                  agens, omninò rectus quieſcat ſuper illam cuſpidem ferri quam habet, non incli-
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                  nans ſe verſus mundi centrum, magis ad vnam
                    <reg norm="partem" type="context">partẽ</reg>
                  , quam ad aliam, cum quælibet
                    <lb/>
                  ſuarum partium in huiuſmodi motu non inclinet omnino verſus
                    <reg norm="mundi" type="context">mũdi</reg>
                  centrum, ſed
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                  multo magis per tranſuerſum ad angulos rectos cum linea directionis, aut verticali,
                    <lb/>
                  aut orizontis axe, ita vt neceſſariò huiuſmodi corpus rectum ſtare debeat. </s>
                  <s xml:id="echoid-s3541" xml:space="preserve">Et quod
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                  dico ipſas partes non omninò inclinare verſus mundi centrum, id ea ratione dico,
                    <lb/>
                  quia non abſolutè ſunt unquam priuatæ huiuſmodi inclinatione, quę efficit vt ipſum
                    <lb/>
                  corpus eo puncto nitatur. </s>
                  <s xml:id="echoid-s3542" xml:space="preserve">Verum tamen eſt, quod quanto magis eſt velox, tan-
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                  to minus premit ipſum punctum, imò ipſum corpus
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                  magis leue remanet. </s>
                  <s xml:id="echoid-s3543" xml:space="preserve">Id
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                  apertè patet
                    <reg norm="ſumendo" type="context">ſumẽdo</reg>
                    <reg norm="exemplum" type="context context">exẽplũ</reg>
                  pilę alicuius arcus, aut
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                  alterius
                    <reg norm="inſtrumenti" type="context">inſtrumẽti</reg>
                  , ſeu ma
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                  chinæ miſſilis, quæ pila quanto eſt velocior, in motu violento, tanto maiorem pro-
                    <lb/>
                  penſionem habet rectius eundi, vnde verſus mundi centrum tanto minus inclinat,
                    <lb/>
                  & hanc ob cauſam leuior redditur. </s>
                  <s xml:id="echoid-s3544" xml:space="preserve">Sed ſi clarius, hanc veritatem videre cupis,
                    <lb/>
                  cogita illud corpus, Trochum ſcilicet, dum velociſſime circunducitur ſecari, ſeu
                    <lb/>
                  diuidi in multas partes, vnde uidebis illas omnes, non illico uerſus mundi centrum </s>
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