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-div533" type="section" level="3" n="11">
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                <p>
                  <s xml:id="echoid-s3428" xml:space="preserve">
                    <pb o="274" rhead="IO. BAPT. BENED." n="286" file="0286" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0286"/>
                  quam in altero
                    <var>.i.b.</var>
                  et
                    <var>u.b.</var>
                  correſpondebit ipſi
                    <var>.A.E.</var>
                  et
                    <var>.b.n.</var>
                  ipſi
                    <var>.E.V.</var>
                  et
                    <var>.b.a.</var>
                  ipſi
                    <var>.E.I.</var>
                    <lb/>
                  quapropter iubeo, vt quæras quantum ſit latus
                    <var>.b.n.</var>
                  ex regula de tribus, dicens ſi
                    <var>.a.e.</var>
                    <lb/>
                  tribuit mihi
                    <var>.e.u.</var>
                  quid mihi dabit
                    <var>.u.b</var>
                  ? </s>
                  <s xml:id="echoid-s3429" xml:space="preserve">eo quod
                    <var>.a.e.u.</var>
                  ſimile eſt
                    <var>.u.b.n.</var>
                  reperto autem
                    <lb/>
                  latere
                    <var>.b.n.</var>
                  ex quo dempto
                    <var>.b.a.</var>
                  breuioris diſtantię, reſiduum reſpondebit ipſi
                    <var>.I.V.</var>
                  vt
                    <lb/>
                  ſcis, vnde proſequendo operationem tibi cognitam, obtinebis intentum, hoc eſt co
                    <lb/>
                  gnoſces reliqua interualla. </s>
                  <s xml:id="echoid-s3430" xml:space="preserve">Nihil enim miror demonſtrationem Tartaleæ circa hu
                    <lb/>
                  iuſmodi operationem te minime ſatisfeciſſe.</s>
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                <p>
                  <s xml:id="echoid-s3431" xml:space="preserve">Quod autem quarta propoſitio illius ſcriptoris, de quo nuper
                    <reg norm="mecum" type="context">mecũ</reg>
                  locutus es, vt
                    <lb/>
                  mihi dixiſti, tua ſit, hoc enimego, nec affirmare, nec negare audeo, quamuis in mul
                    <lb/>
                  tis cum tua manuſcripta concordet. </s>
                  <s xml:id="echoid-s3432" xml:space="preserve">Nam ſępæ cogitationes hominum in idem co-
                    <lb/>
                  incidunt, vt pluries cenſuit Ariſto.</s>
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                  <image file="0286-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0286-01"/>
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                <head xml:id="echoid-head410" style="it" xml:space="preserve">Demonstrationes quorundam problematum Nicolai Tartalea
                  <lb/>
                cum
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                operationibus circa eadem ſubiecta.</head>
                <head xml:id="echoid-head411" xml:space="preserve">AD EVNDEM.</head>
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                  <s xml:id="echoid-s3433" xml:space="preserve">AMor erga te meus ſanè ſingularis, nullo modo
                    <reg norm="permittit" type="simple">ꝑmittit</reg>
                  , vt ea quæ Tartaleę ſcri
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                  pta
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                  inuenerim, non tibi
                    <reg norm="communicem" type="context">cõmunicem</reg>
                  . </s>
                  <s xml:id="echoid-s3434" xml:space="preserve">Hæc autem ſunt circa quæ
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                  dam illius Authoris problemata, quorum primum ab ipſo Tartalea
                    <lb/>
                  ſcriptum in .3. quæſito libr .4. tale eſt, is vult locare .3500. homines, eodem modo,
                    <lb/>
                  quo præſupponit locatos eſſe .1000. ita vt quilibet hominum ordo ſiue vt vulgo di-
                    <lb/>
                  citur filtia ſit .49. quapropter multiplicat quadratum ipſius .49. quod eſt .2401.
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  numero .3500. propoſito, productum verò .8403500. diuidit per .1000. vt proue-
                    <lb/>
                  niat .8403. cuius radix quadrata eſt .91. pro numero hominum vniuſcuiuſque ordinis
                    <lb/>
                  propoſiti numeri .3500.</s>
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                <p>
                  <s xml:id="echoid-s3435" xml:space="preserve">Pro cuius operationis ratione, cogitemus rectangulum
                    <var>.a.b.</var>
                  1000. hominum, et
                    <var>.d.
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                    b.</var>
                  ſit vna filtia ſiue ordo .49.
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                  , cuius
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                  ſit
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                  2401. imaginemur
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                  re
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                  ctangulum
                    <var>.A.B.</var>
                  3500. hominum, quod ſupponemus ſimile rectangulo
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                  et
                    <var>.B.C.</var>
                  </s>
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