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-div698" type="section" level="3" n="33">
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                <p>
                  <s xml:id="echoid-s4321" xml:space="preserve">
                    <pb o="361" rhead="EPISTOL AE." n="373" file="0373" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0373"/>
                  ni ſcicntia. </s>
                  <s xml:id="echoid-s4322" xml:space="preserve">Quare maior proportio erit acus
                    <var>.b.c.a.</var>
                  ad arcum
                    <var>.b.d.c.</var>
                  quam ad arcum
                    <lb/>
                    <var>b.i.c.</var>
                  ex .8. quinti. </s>
                  <s xml:id="echoid-s4323" xml:space="preserve">Vnde ex vltima ſexti et .12. quinti, proportio anguli
                    <var>.a.e.b.</var>
                  ad an-
                    <lb/>
                  gulum
                    <var>.c.e.b.</var>
                  maior erit quam chordæ, ſiue baſis
                    <var>.a.b.</var>
                  ad chordam ſiue baſim
                    <var>.c.b</var>
                  .</s>
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            <div xml:id="echoid-div701" type="section" level="3" n="34">
              <div xml:id="echoid-div701" type="letter" level="4" n="1">
                <head xml:id="echoid-head532" xml:space="preserve">DE CAVSA SVSPENSIONIS NVBIVM
                  <lb/>
                in aere contra Antonium Bergam.</head>
                <head xml:id="echoid-head533" style="it" xml:space="preserve">Clarißimo Franciſco Venerio.</head>
                <p>
                  <s xml:id="echoid-s4324" xml:space="preserve">EGo enim non tantum miror ea quæ mihi ſcripſiſti de opinione Ortenſij
                    <lb/>
                  quantum quod Antonius Berga putat nubes à Sole ſupenſas teneri, id pla
                    <lb/>
                  nè falſum eſt, vera cauſa huiuſmodi effectus, alia nulla eſt, niſi earundem
                    <lb/>
                  raritas hoc eſt, cum rariores ſint ipſo aere ſubiecto, </s>
                  <s xml:id="echoid-s4325" xml:space="preserve">propterea ſupra
                    <reg norm="ipsum" type="context">ipsũ</reg>
                    <lb/>
                  natant & ſtant ſub eo qui rarior ipſis eſt, eo quod corpora rariora poſita in medio
                    <lb/>
                  non tam raro, aſcendunt, & denſiora in medio minus denſo deſcendunt. </s>
                  <s xml:id="echoid-s4326" xml:space="preserve">Nam ſi
                    <lb/>
                  Sol ipſas nubes ſuſpenſas in aere teneret, hoc interdiu tantummodo fieret, ſed no
                    <lb/>
                  ctu, cur non deſcendunt vſque ad terram, & in eodem loco ſemper manent? </s>
                  <s xml:id="echoid-s4327" xml:space="preserve">Scien-
                    <lb/>
                  dum igitur eſt nubes aſcendere in altum quouſque inueniant aerem eiuſdem ra-
                    <lb/>
                  ritatis cuius ipſæ ſunt. </s>
                  <s xml:id="echoid-s4328" xml:space="preserve">Raritas enim & denſitas non ſunt res viſibiles niſi per acci-
                    <lb/>
                  dens, quemadmodum etiam leuitas, & grauitas, opacitas verò & diaphaneitas ma
                    <lb/>
                  gis
                    <reg norm="compræhenduntur" type="context">compræhendũtur</reg>
                  , opacitas enim ex reflexione radiorum luminoſorum, diapha
                    <lb/>
                  neitas verò compræhenditur ex penetratione ipſorum radiorum, opacitas autem nu
                    <lb/>
                  bis non eſt denſitas, cum valde diuerſa ſit denſitas ab opacitate, ſicut raritas ab dia-
                    <lb/>
                  phaneitate, vt aliàs dixi. </s>
                  <s xml:id="echoid-s4329" xml:space="preserve">Et quando dicit, quod Sol calefaciendo aerem ipſam nu
                    <lb/>
                  bem ambientem, rarefaciat eum magis quam ipſam nubem reſpondeo, hoc verum
                    <lb/>
                  non eſſe, proptere
                    <unsure/>
                  a quodradius Solis non multum calefacit ea corpora, quæ ip ſi per
                    <lb/>
                  mittunt liberum tranſitum. </s>
                  <s xml:id="echoid-s4330" xml:space="preserve">vnde corpora quanto magis diaphana ſunt tanto minus
                    <lb/>
                  ab ipſo radio luminoſo calefiunt, ſed ea quæ magis opaca ſunt, magis etiam calefiunt
                    <lb/>
                  & per conſequens magis rarefiunt, cum calidi ſit per ſe rarefacere, & non attrahere,
                    <lb/>
                  vt ipſe & ferè omnes alij putant.</s>
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            <div xml:id="echoid-div703" type="section" level="3" n="35">
              <div xml:id="echoid-div703" type="letter" level="4" n="1">
                <head xml:id="echoid-head534" xml:space="preserve">DE RATIONE EXTENSIONIS FVNIS
                  <lb/>
                cuiuſdam libramenti, & de quadam ſimboleita-
                  <lb/>
                te circuli cum ellipſi.</head>
                <head xml:id="echoid-head535" style="it" xml:space="preserve">Angelo Ferrario Serenißimi Ducis Sabaudia
                  <lb/>
                Agrimenſori expertißimo.</head>
                <p>
                  <s xml:id="echoid-s4331" xml:space="preserve">
                    <emph style="sc">TIbi</emph>
                  in mentem veniet, quod cum ſuperioribus diebus in villa lucenti, in
                    <lb/>
                  qua degebat Sereniſſimus Dux noſter, dum viridarium ad æquilibrium
                    <lb/>
                  reducebas, eſſemus, à te quæſiui an ſcires vnde fieret, vt ſtante libramen-
                    <lb/>
                  to ad angulos rectos ſupra ſuum pedem, funis quæ extrema eiuſdem li-
                    <lb/>
                  bramenti cum pede in formam trianguli æquicruris coniungit, magis diſtentus exi-
                    <lb/>
                  ſteret, quam cum dictum libramentum cum pede obliquum remanet, ita vt huiuſ- </s>
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