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 Notes

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            <div xml:id="echoid-div676" type="section" level="3" n="30">
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                <p>
                  <s xml:id="echoid-s4232" xml:space="preserve">
                    <pb o="352" rhead="I O. BAPT. BENED." n="364" file="0364" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0364"/>
                  habes in circulo .ω vbi fateris te non videre qua ratione eadem proportio ſit qua-
                    <lb/>
                  drati
                    <var>.u.o.</var>
                  ad quadratum
                    <var>.o.n.</var>
                  vt lineæ
                    <var>.o.a.</var>
                  ad lineam
                    <var>.o.e.</var>
                  partes diametri
                    <var>.o.i.</var>
                  ipſius
                    <lb/>
                  circuli, terminatæ à perpendicularibus
                    <var>.u.a.</var>
                  et
                    <var>.n.e</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4233" xml:space="preserve">Hoc neceſſario contingit, propterea quod cum fuerint protractæ
                    <var>.u.i.</var>
                  et
                    <var>.n.i.</var>
                    <reg norm="tunc" type="context">tũc</reg>
                    <lb/>
                  habebimus ad partem
                    <var>.o.u.i.</var>
                  triangulum
                    <var>.o.u.i.</var>
                  diuiſum in duo triangula ſimilia ipſi
                    <lb/>
                  totali triangulo. </s>
                  <s xml:id="echoid-s4234" xml:space="preserve">Idem etiam dico ad partem
                    <var>.o.n.i.</var>
                  vnde ex tali ſimilitudine habe-
                    <lb/>
                  bimus
                    <var>.o.u.</var>
                  mediam proportionalem inter
                    <var>.o.i.</var>
                  et
                    <var>.o.a.</var>
                  et ſic
                    <var>.o.n.</var>
                  erit media proportio
                    <lb/>
                  nalis inter
                    <var>.o.i.</var>
                  et
                    <var>.o.e.</var>
                  </s>
                  <s xml:id="echoid-s4235" xml:space="preserve">quare ex .16. ſexti, quadratum
                    <var>.o.u.</var>
                  æquale erit producto ipſius
                    <lb/>
                    <var>o.i.</var>
                  in
                    <var>.o.a.</var>
                  & quadratum
                    <var>.o.n.</var>
                  æquale producto
                    <var>.o.i.</var>
                  in
                    <var>.o.e.</var>
                  ſed ex prima eiuſdem, ea
                    <lb/>
                  dem proportio eſt ipſius
                    <var>.o.a.</var>
                  ad
                    <var>.o.e.</var>
                  quæ producti ipſius
                    <var>.o.i.</var>
                  in
                    <var>o.a.</var>
                  ad productum
                    <var>.o.
                      <lb/>
                    i.</var>
                  in
                    <var>.o.e.</var>
                  </s>
                  <s xml:id="echoid-s4236" xml:space="preserve">quare, ex
                    <reg norm="communi" type="context">cõmuni</reg>
                  conceptu, ita erit quadrati
                    <var>.o.u.</var>
                  ad quadratúm.o.n. </s>
                  <s xml:id="echoid-s4237" xml:space="preserve">Et hęc
                    <lb/>
                  eſt alia circuli paſſio.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4238" xml:space="preserve">Reliqua verò difficultas quam te habere ſcribis, eſt, quare cum duæ lineę
                    <lb/>
                    <var>a.u.</var>
                  et
                    <var>.b.s.i.</var>
                  ſint inuicem ęquales, diuiſæ verò non æquali modo, ſed tali, quod
                    <var>.a.</var>
                    <lb/>
                  maior ſit quam
                    <var>.u.</var>
                  et
                    <var>.b.s.</var>
                  maior quam
                    <var>.i.</var>
                  quomodo poteſt fieri, quod ſi
                    <var>.u.</var>
                  maior fue-
                    <lb/>
                  rit
                    <var>.i.</var>
                  proportio
                    <var>.a.</var>
                  ad
                    <var>.i.</var>
                  maior ſit quam ipſius
                    <var>.b.s.</var>
                  ad
                    <var>.u</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4239" xml:space="preserve">Hoc etiam ex neceſſitate cuenit, eo
                    <lb/>
                  quod ſi accepta fuerit
                    <var>.t.n.</var>
                  æqualis
                    <var>.u.</var>
                  ab
                    <lb/>
                    <figure xlink:label="fig-0364-01" xlink:href="fig-0364-01a" number="401">
                      <image file="0364-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0364-01"/>
                    </figure>
                    <reg norm="ipſaque" type="simple">ipſaq́;</reg>
                  abſciſa fuerit
                    <var>.t.</var>
                  æqualis
                    <var>.i.</var>
                  & ab
                    <var>.
                      <lb/>
                    b.s.</var>
                  abſciſa
                    <var>.s.</var>
                  æqualis
                    <var>.n.</var>
                  habebimus
                    <var>.a.</var>
                  et
                    <lb/>
                  b. inuicem æ quales, vnde habebis ma-
                    <lb/>
                  iorem propor tionem ipſius
                    <var>.b.</var>
                  ad
                    <var>.t.</var>
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                  s. ad
                    <var>.n.</var>
                  quod cum clarum per ſe ſit, tibi
                    <lb/>
                  relinquo. </s>
                  <s xml:id="echoid-s4240" xml:space="preserve">ſed ex .27. quinti, proportio
                    <lb/>
                  b. ad. s, maior erit quam
                    <var>.t.</var>
                  ad
                    <var>.n.</var>
                  & ex
                    <lb/>
                  28.
                    <reg norm="eiuſdem" type="context">eiuſdẽ</reg>
                    <reg norm="proportio" type="simple">ꝓportio</reg>
                    <var>.b.s.</var>
                  ad
                    <var>.s.</var>
                  maior erit,
                    <lb/>
                  quam
                    <var>.t.n.</var>
                  ad
                    <var>.n.</var>
                  & ex .27. maior propor
                    <lb/>
                  tio erit ipſius
                    <var>.b.s.</var>
                  ad
                    <var>.n.t.</var>
                  quam
                    <var>.s.</var>
                  ad
                    <var>.n.</var>
                    <lb/>
                  ergo ex .33. maior erit ipſius
                    <var>.b.</var>
                  ad
                    <var>.t.</var>
                    <reg norm="quam" type="context">quã</reg>
                    <lb/>
                    <var>b.s.</var>
                  ad
                    <var>.n.t.</var>
                  hoc eſt maior ipſius
                    <var>.a.</var>
                  ad
                    <lb/>
                  i. quam
                    <var>.b.s.</var>
                  ad
                    <var>.u.</var>
                  quod eſt propo-
                    <lb/>
                  ſitum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4241" xml:space="preserve">Id verò de quo me interrogas
                    <reg norm="nempe" type="context">nẽpe</reg>
                  de
                    <lb/>
                  diſtinctione orbium cęleſtium, ortum
                    <lb/>
                  habet à communi opinione motuum
                    <lb/>
                  fixarum. </s>
                  <s xml:id="echoid-s4242" xml:space="preserve">Nam cum putauerint philo-
                    <lb/>
                  ſophi ipſas moueri, ſemper eandem
                    <reg norm="ſeruando" type="context">ſeruãdo</reg>
                  inuicem diſtantiam, non ſine ratione
                    <lb/>
                  crediderunt eas fixas eſſe eodem in orbe, idem etiam poſtea de planetis opinaue-
                    <lb/>
                  runt. </s>
                  <s xml:id="echoid-s4243" xml:space="preserve">Hoc eſt, vnumquemque, aliquo in orbe, fixo exiſtere.</s>
                </p>
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