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]

Table of contents

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[5.1.7.] SEPTIMVM. Euclidis uerò undecima propoſitio.
[5.1.8.] OCTAVVM. εuclidis uerò duodecima propoſitio.
[5.1.9.] NONVM. Euclidis uero tertiadecima propoſitio.
[5.1.10.] DECIMVM.
[5.1.11.] VNDECIMVM.
[5.1.12.] DVODECIMVM.
[Item 5.2.]
[5.2.1.] THEOR.I. II. ET III.
[5.2.2.] THEOREM. IIII.
[5.2.3.] THEOR.V. ET VI.
[5.2.4.] THEOR. VII. VIII. IX.X. XI. XII. XIII.
[5.2.5.] THEOREM. XIIII.
[5.2.6.] THEOR. XV.
[5.2.7.] THEOREM. XVI.
[5.2.8.] THEOR. XVII.
[5.2.9.] THEOREM. XVIII.
[5.2.10.] THEOREM. XIX.
[5.2.11.] THEOREM. XX.
[5.2.12.] THEOREM. XXI.
[5.2.13.] THEOREM. XXII. XXIII.
[6.] PHYSICA, ET MATHEMATICA RESPONSA. FO. BAPTISTAE BεNεDICTI PATRITII Veneti, Philoſophi Mathematici.
[Item 6.1.]
[Item 6.2.]
[Item 6.3.]
[Item 6.4.]
[Item 6.5.]
[Item 6.6.]
[Item 6.7.]
[Item 6.8.]
[Item 6.9.]
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                  hoc eſt .6. dabit .4. integra cum
                    <num value="86">.
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                    86.</num>
                  centeſimis, ſed nos vellemus no-
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                  bis prouenire tria, eo
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                  ita eſt
                    <var>.f.h.</var>
                    <lb/>
                  qua propter deſcendere nos oporte-
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                  bit à nouem ad .8. & ab .8. ad .7. & à.
                    <lb/>
                  7. ad .6. </s>
                  <s xml:id="echoid-s3334" xml:space="preserve">tunc inueniemus
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                  oporte-
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                  re eſſe circiter quinque cum duabus
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                  tertijs,
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                  poſtea ex regula de
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                  <s xml:id="echoid-s3335" xml:space="preserve">tunc nouem cum tertia parte integri
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                  dabit .2.
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                  296. de .300. hoc eſt .2.
                    <lb/>
                  cum circa .49. quinquageſimis, quæ
                    <lb/>
                  quidem quantitas, cum propinquiſſi
                    <lb/>
                  ma ſit lineæ
                    <var>.f.h.</var>
                  trium integrorum di
                    <lb/>
                  cemus
                    <var>.c.x.</var>
                  eſſe quinque integrorum
                    <lb/>
                  cum duabus tertijs partibus vnius in
                    <lb/>
                  tegri, et
                    <var>.e.x.</var>
                  reſiduum, hoc eſt axem
                    <lb/>
                  quæſitum portionis
                    <var>.i.e.t.</var>
                  eſſe circa .4
                    <lb/>
                  integra cum tertia parte vnius inte-
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                  gri.</s>
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                <head xml:id="echoid-head398" xml:space="preserve">DE ERRORIBVS THOMAE PORCACHII
                  <lb/>
                & Benedicti Bordonij in eorum inſularijs.</head>
                <head xml:id="echoid-head399" style="it" xml:space="preserve">Excellentißimo D. lo. Baptiſtæ Fæmello Ciui
                  <reg norm="Decurionique" type="simple">Decurioniq́ꝫ</reg>
                Tau-
                  <lb/>
                rinenſi Philoſopho, Medico, & in Accademia eius
                  <lb/>
                Ciuitatis Medicinæ Practicæ Ordinario,
                  <reg norm="Pri- marioque" type="simple">Pri-
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                  marioq́ꝫ</reg>
                profeßori celeberrimo.</head>
                <p>
                  <s xml:id="echoid-s3336" xml:space="preserve">DIj perdant tuas adeo moleſtas, & aſſiduas curas, quæ te nimis à ſuauiori-
                    <lb/>
                  bus ſtudijs diſtrahunt, & à nobis longius abducunt. </s>
                  <s xml:id="echoid-s3337" xml:space="preserve">Nam, ut tibi
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                  ,
                    <lb/>
                  ita mihi ingentem adimunt voluptatem. </s>
                  <s xml:id="echoid-s3338" xml:space="preserve">Sed ne in aliquo erga te defi-
                    <lb/>
                  cere videar, quæ tibi olim promiſi, nunc mitto.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3339" xml:space="preserve">Negari quidem non poteſt, quin fuerit laborioſum opus Porcachij, & Benedicti
                    <lb/>
                  Bordonij, hoc eſt inſularium, qui rectè etiam feciſſent, cum loqui eos oportebat de
                    <lb/>
                  terminis ſphæræ ratione ſitus locorum, ſi ſeipſos alicuius excellentis Coſmographi
                    <lb/>
                  conſilio ſubmiſiſſent. </s>
                  <s xml:id="echoid-s3340" xml:space="preserve">Conſidera quæſo, quomodo admitti poſſit, id quod ait Por-
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                  cachius initio ſui operis, ideſt Iſlandiam ſub Polo arctico iacere, inter auſtrum, &
                    <lb/>
                  boream: </s>
                  <s xml:id="echoid-s3341" xml:space="preserve">omittamus etiam quod idem in Proęmio lib. ſecundi, vbi ait Biarmiam,
                    <lb/>
                  (& non Iſlandiam) eſſe ſub dicto polo arctico: </s>
                  <s xml:id="echoid-s3342" xml:space="preserve">in
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                  principio repetit ipſam
                    <lb/>
                  Iſlandiam inter auſtrum, & boream per centum leucas Germanicas extendi, dein-
                    <lb/>
                  de verſus occidentem, ea duo ſtupenda miracula conſpici. </s>
                  <s xml:id="echoid-s3343" xml:space="preserve">Vide quæſo, quomodo
                    <lb/>
                  incolę ſub aliquo ex polis, habere poſſint occidentem, orientem, magiſtrum,
                    <reg norm="auſtrum" type="context">auſtrũ</reg>
                  , </s>
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