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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[4.28.] Occultam fuiße grauisſimo Stagirit & canſam ſcintilla-tionis ſtellarum. CAP. XXVIII.
[4.29.] Daricontinuum infinitum motum ſuper rectam at que finitam lineam. CAP. XXIX.
[4.30.] Non eſſe ſolis calorem à motu localι ipſius corporis ſolaris, ut Ariſtoteli placuit. CAP. XXX.
[4.31.] Vnde caloris ſolis prode at incrementum & state, et byeme decrementum. CAP. XXXI.
[4.32.] Nullum corpus ſenſus expers à ſono offendi, præterquam Aristoteles crediderit. CAP. XXXII.
[4.33.] Pytagoreorum opinionem de ſonitu corporum cælestium non fuiſſe ab Aristotele ſublatam. CAP. XXXIII.
[4.34.] Deraro et denſo nonnulla, minus diligenter à Peripateticis perpenſa. CAP. XXXIIII.
[4.35.] Motum rectum curuo poſſe comparari etiam diſentiente Ariſtotele. CAP. XXXV.
[4.36.] Minus ſufficienter exploſam fuiſſe ab Ariſtotele opinionem cre-dentium plures mundos exiſtere. CAP. XXXVI.
[4.37.] Anrectè loquutus ſit Phyloſopbus de extenſione luminis per uacuum. CAP. XXXVII.
[4.38.] An rectè phyloſophiœ penus Ariſtoteles ſenſerit de loco im-pellendo à pyramide. CAP. XXXVIII.
[4.39.] Examinatur quam ualida ſit ratio Aristotelis de inalterabilitate Cœli. CAP. XXXIX.
[5.] IN QVINTVM EVCLIDIS LIBRVM
[Item 5.1.]
[5.1.1.] Horum autem primum est.
[5.1.2.] SECVNDVM.
[5.1.3.] TERTIVM. Quę est εuclidis ſeptima propoſitio.
[5.1.4.] QVARTVM. εuclidis uerò nona propoſitio.
[5.1.5.] QVINTVM. Euclidis uerò octaua propoſitio.
[5.1.6.] SEXTVM. εuclidis uerò decima propoſitio.
[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.
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            <div xml:id="echoid-div680" type="section" level="3" n="31">
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                <pb o="355" rhead="EPISTOL AE." n="367" file="0367" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0367"/>
                <p>
                  <s xml:id="echoid-s4265" xml:space="preserve">Inueniatur nunc quadratum
                    <var>.u.n.</var>
                  æquale ſextæ parti ſuperficiei
                    <var>.f.i.g.h.</var>
                  quod per
                    <lb/>
                  ſe facile erit, </s>
                  <s xml:id="echoid-s4266" xml:space="preserve">deinde accipiatur altitudo corporis
                    <var>.f.x.</var>
                  ducendo vnam perpendicula
                    <lb/>
                  rem à puncto
                    <var>.m.</var>
                  ad baſim
                    <var>.f.g.h.</var>
                  quę ſit
                    <var>.n.e.</var>
                  qua mediante, cum quadrato
                    <var>.u.n.</var>
                  fabri
                    <lb/>
                  cetur ſolidum parallelepepidum
                    <var>.u.e.</var>
                  quod erit æquale dictæ pyramidi ex .33. vnde-
                    <lb/>
                  cimi Euclid.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4267" xml:space="preserve">Repertæ nunc ſint duæ mediæ proportionales
                    <var>.r.s.</var>
                  inter
                    <var>.n.e.</var>
                  et
                    <var>.n.p.</var>
                  quarum
                    <var>.s.</var>
                  ſit
                    <lb/>
                  proximior ipſi
                    <var>.u.p.</var>
                  ex qua
                    <var>.s.</var>
                  ſi conſtitutus fuerit cubus, habebimus propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4268" xml:space="preserve">Pro cuius rei ratione, cogitemus corpus
                    <var>.u.e.</var>
                  productum eſſe vſque ad
                    <var>.a.o.</var>
                  per lon-
                    <lb/>
                  gitudem
                    <var>.s.</var>
                  latus dicti cubi, qui quidem cubus ſit
                    <var>.d.b.</var>
                  vnde proportio corporis
                    <var>.u.e.</var>
                    <lb/>
                  ad corpus
                    <var>.e.o.</var>
                  erit, vt ſuperficiei
                    <var>.p.e.</var>
                  ad ſuperficiem
                    <var>.t.e.</var>
                  ex .33. undecimi, ipſæ verò
                    <lb/>
                  ſuperficies ſibi inuicem erunt vt
                    <var>.n.e.</var>
                  ad
                    <var>.e.a.</var>
                  ex prima ſexti, </s>
                  <s xml:id="echoid-s4269" xml:space="preserve">quare proportio corpo
                    <lb/>
                  ris
                    <var>.u.e.</var>
                  ad corpus
                    <var>.e.o.</var>
                  dupla erit proportioni ipſius
                    <var>.s.</var>
                  ad
                    <var>.n.p.</var>
                  ſed cum ex .33 vndeci-
                    <lb/>
                  mi, proportio cubi
                    <var>.d.b.</var>
                  ad corpus
                    <var>.e.o.</var>
                  ſit vt
                    <reg norm="quadratum" type="context">quadratũ</reg>
                    <var>.q.b.</var>
                  ad quadratum
                    <var>.o.a.</var>
                  & cum
                    <lb/>
                  proportio
                    <var>.q.b.</var>
                  ad
                    <var>.o.a.</var>
                  dupla ſit ei quæ
                    <var>.q.o.</var>
                  ad
                    <var>.o.t.</var>
                  ex .18. ſexti, erit igitur proportio
                    <lb/>
                  cubi
                    <var>.d.b.</var>
                  ad corpus
                    <var>.e.o.</var>
                  dupla ei quæ
                    <var>.q.o.</var>
                  ad
                    <var>.o.t.</var>
                  hoc eſt ei quæ
                    <var>.s.</var>
                  ad
                    <var>.n.p.</var>
                  ſed ita erat
                    <lb/>
                  corporis
                    <var>.u.e.</var>
                  ad corpus
                    <var>.e.o.</var>
                  </s>
                  <s xml:id="echoid-s4270" xml:space="preserve">quare ex .9. quinti, cubus
                    <var>.d.b.</var>
                  æqualis erit corpor
                    <unsure/>
                  i.u.e.
                    <lb/>
                  hoc eſt pyramidi propoſitæ.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4271" xml:space="preserve">Sed ſi oportebit cubum maiorem vel minorem ipſa pyramide reperire, in qua
                    <lb/>
                  proportione tibi placuerit, </s>
                  <s xml:id="echoid-s4272" xml:space="preserve">tunc opus erit aliud quadratum inuenire, quod in ea
                    <lb/>
                  proportione ſe habeat ad quadratum
                    <var>.u.n.</var>
                  quam volueris, quo mediante ſimul cum
                    <lb/>
                  altitudine pyramidis conſequemur propoſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4273" xml:space="preserve">Aduertendum tamen quod fabri-
                    <lb/>
                  care ipſum corpus ſerratile
                    <var>.k.f.h.</var>
                  & ſo
                    <lb/>
                    <figure xlink:label="fig-0367-01" xlink:href="fig-0367-01a" number="404">
                      <image file="0367-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0367-01"/>
                    </figure>
                  lidum
                    <var>.f.x.</var>
                  neceſſarium non eſt, niſi pro
                    <lb/>
                  demonſtratione. </s>
                  <s xml:id="echoid-s4274" xml:space="preserve">
                    <reg norm="idemque" type="simple">idemq́;</reg>
                  dico de alijs
                    <lb/>
                  ſolidis, nam pro ſimplici operatione
                    <lb/>
                  huiuſmodi problematis, abſque ali-
                    <lb/>
                  qua re neceſſaria ad ſpeculandum, ita
                    <lb/>
                  faciendum erit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4275" xml:space="preserve">Data pyramide
                    <var>.m.f.g.h.</var>
                  accipe
                    <reg norm="eius" type="simple">eiꝰ</reg>
                    <lb/>
                  alitudinem à
                    <reg norm="puncto" type="context">pũcto</reg>
                    <var>.m.</var>
                  vſque ad ſuper
                    <lb/>
                  ficiem baſis
                    <var>.f.g.h.</var>
                  quæ ſit
                    <var>.n.e.</var>
                  accipe
                    <lb/>
                  deinde latus letragonicum quadrati
                    <var>.
                      <lb/>
                      <figure xlink:label="fig-0367-02" xlink:href="fig-0367-02a" number="405">
                        <image file="0367-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0367-02"/>
                      </figure>
                    u.n.</var>
                  æqualis tertiæ partis ipſius baſis
                    <var>.f.
                      <lb/>
                    g.h.</var>
                  quod latus ſit
                    <var>.n.p.</var>
                  inter quod, et
                    <var>.
                      <lb/>
                    n.e.</var>
                  inuentæ cum fuerint duæ lineæ
                    <lb/>
                  mediæ proportiona es
                    <var>.s.</var>
                  et
                    <var>.r.</var>
                    <reg norm="quarum" type="context">quarũ</reg>
                    <var>.
                      <lb/>
                    s.</var>
                  proximior ſit
                    <var>.n.p.</var>
                  quæ
                    <reg norm="quidem" type="context">quidẽ</reg>
                    <var>.s.</var>
                  erit
                    <lb/>
                  latus cubi quæſiti.</s>
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