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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page |< < (315) of 445 > >|
EPISTOL AE.
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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div606" type="section" level="3" n="23">
              <div xml:id="echoid-div611" type="letter" level="4" n="3">
                <p>
                  <s xml:id="echoid-s3863" xml:space="preserve">
                    <pb o="315" rhead="EPISTOL AE." n="327" file="0327" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0327"/>
                  ad
                    <var>.o.d.</var>
                  hoc eſt vt
                    <var>.z.</var>
                  ad
                    <var>.l.</var>
                  hoc eſt vt
                    <var>.c.</var>
                  ad
                    <var>.y</var>
                  . </s>
                  <s xml:id="echoid-s3864" xml:space="preserve">quare
                    <reg norm="triangulum" type="context">triangulũ</reg>
                    <var>.p.q.o.</var>
                  ita erit proportio
                    <lb/>
                    <reg norm="natum" type="context">natũ</reg>
                  triangulo
                    <var>.o.q.b.</var>
                  vt
                    <var>.c.</var>
                  ad
                    <var>.y.</var>
                  conſtituo deinde ex .25. fexti duo triangula ſimi-
                    <lb/>
                  lia duobus
                    <var>.p.q.o.</var>
                  et
                    <var>.o.q.b.</var>
                    <reg norm="æqualiaque" type="simple">æqualiaq́</reg>
                    <var>.c.</var>
                  et
                    <var>.y.</var>
                  quę ſint
                    <var>.a.i.u.</var>
                  et
                    <var>.n.t.x.</var>
                  ſecetur poſtea
                    <var>.q.
                      <lb/>
                    g.</var>
                  in puncto
                    <var>.æ.</var>
                  ita, quod
                    <var>.q.æ.</var>
                  æqualis ſit
                    <var>.i.a.</var>
                  duco poſtea
                    <var>.æ.e.</var>
                  æquidiſtantem. ad
                    <var>.p.b.</var>
                    <lb/>
                  & ſic habebimus duo triangula
                    <var>.q.x.æ.</var>
                  ct
                    <var>.q.x.</var>
                  e, vt quærebantur, quamuis duo trian
                    <lb/>
                  gula
                    <var>.a.i.u.</var>
                  et
                    <var>.t.n.x.</var>
                  eaſdem habeant conditiones.</s>
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                  <figure xlink:label="fig-0326-01" xlink:href="fig-0326-01a">
                    <image file="0326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0326-01"/>
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            <div xml:id="echoid-div614" type="section" level="3" n="24">
              <div xml:id="echoid-div614" type="letter" level="4" n="1">
                <head xml:id="echoid-head475" xml:space="preserve">DE IMPERFECTA SOLVTIONE PROBLE-
                  <lb/>
                matis Nicolai Tartaleæ ad Cardanum. De animad-
                  <lb/>
                uerſione in Ptolomeum. Deincendio carbo-
                  <lb/>
                num à vento.</head>
                <head xml:id="echoid-head476" style="it" xml:space="preserve">Clariβimo Dominico Moreſino.</head>
                <p>
                  <s xml:id="echoid-s3865" xml:space="preserve">
                    <emph style="sc">SCio</emph>
                  propoſitam tibi quæſtionem te diu agitauiſſe, nectamen ſolutio-
                    <lb/>
                  nem aſſequi potuiſſe, aduerte igitur ipſam falſam, ideſt impoſſibilem
                    <lb/>
                  eſſe, quemadmodum etiam decimumoctauum quæſitum propoſitum à
                    <lb/>
                  Cardano Tartaleæ, ab ipſo Tarralea ſolutum minimè fuit. </s>
                  <s xml:id="echoid-s3866" xml:space="preserve">Quiquidem
                    <lb/>
                  Tartalea vult circulum deſcribi circa triangulum per quintam libri quarti Euclidis,
                    <lb/>
                  vt in fine ferè quintæ partis ſuarum menſurarum affirmat, neque videt in quinta
                    <lb/>
                  quarti Euclidem vti vndecima primi, & in vndecima primi, quarta aut octaua eiuſ-
                    <lb/>
                  dem, quas, ipſe Euclides oſtenſiuè non demonſtrauit. </s>
                  <s xml:id="echoid-s3867" xml:space="preserve">Quapropter oportebat Tar-
                    <lb/>
                  taleam demonſtraſſe omnes propoſitiones ad hoc neceſſarias oſtenſiuè
                    <reg norm="vſque" type="simple">vſq;</reg>
                  ad pri-
                    <lb/>
                  mas indemonſtrabiles, quia ad demonſtrandam ſcientificè
                    <reg norm="aliquam" type="context">aliquã</reg>
                  propoſitionem,
                    <lb/>
                  aut à propoſitione in propoſitionem vſque ad prima principia vniuerſalia ( vt ali-
                    <lb/>
                  quando ego feci) eſt retrogradandum, aut ab ipſis principijs incipiendum ſucceſſi-
                    <lb/>
                  uè eouſque progrediendo donec ad propoſitionem quam demonſtrare volumus
                    <lb/>
                  perueniamus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3868" xml:space="preserve">Quod ad Ptolomeum in geographia attinet, dico eum mihi non ſatisfacere, cum
                    <lb/>
                  ſumit portionem arcus circuli maioris inter vnam ciuitatem, & aliam, ea ratione
                    <lb/>
                  quam deſcribit. </s>
                  <s xml:id="echoid-s3869" xml:space="preserve">Quod ſi vſus fuiſſet modo Menelai, ab ipſomet deinde in
                    <reg norm="ſuum" type="context">ſuũ</reg>
                  Al-
                    <lb/>
                  mageſtum vſurpato, aut Monteregij triangulorum ſphęricorum, quem Copernicus
                    <lb/>
                  adhibuit (qui tamen modus, tempore Ptolomei, nondum fortaſſe in lucem vene-
                    <lb/>
                  rat) bene egiſſet.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3870" xml:space="preserve">Quod deinde ad ſuum illud inſtrumentum geometricum attinet, eſt
                    <reg norm="imperfectum" type="context">imperfectũ</reg>
                  ,
                    <lb/>
                  vt oſtendi domino Pandulfo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3871" xml:space="preserve">Motum autem aeris, aut mauis ventum, accendere ignem, non ſolum ratione an
                    <lb/>
                  tiperiſtaſis, quam affers euenit, ſed etiam quia à carbonibus accenſis totam excre
                    <lb/>
                  mentitiam materiam, quæ eos circundat, auferat.</s>
                </p>
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              <div xml:id="echoid-div615" type="letter" level="4" n="2">
                <head xml:id="echoid-head477" style="it" xml:space="preserve">Alia dilucidatio propoſitionis .25. lib. 2. Monteregij.</head>
                <head xml:id="echoid-head478" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3872" xml:space="preserve">SCribiste non intelligere .25. propoſitionem lib. 2. Monteregij. cum necſcias
                    <lb/>
                  reperire diametrum circuli circunſcriptibilis circa propoſitum triangu- </s>
                </p>
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