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-div737" type="section" level="3" n="42">
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                <p>
                  <s xml:id="echoid-s4542" xml:space="preserve">
                    <pb o="383" rhead="EPISTOLAE." n="395" file="0395" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0395"/>
                  cum ſit
                    <var>.f.x.</var>
                  æqualis ipſi
                    <var>.u.i.</var>
                  vt tibi probaui, & inuicem parallelæ ideo
                    <var>.f.i.</var>
                  parallela
                    <lb/>
                  erit ipſi
                    <var>.x.u.</var>
                  ex .33. primi Euclidis. </s>
                  <s xml:id="echoid-s4543" xml:space="preserve">Vnde ex .30. eiuſdem, parallela erit etiam ipſi
                    <var>.a.
                      <lb/>
                    c.</var>
                  ſed cum
                    <var>.x.u.</var>
                  diuiſa ſit ab
                    <var>.d.b.</var>
                  per æqualia, eo quod diuidit
                    <var>.a.c.</var>
                  eodem modo, quę
                    <lb/>
                  ipſi parallela eſt ex .2. ſexti. </s>
                  <s xml:id="echoid-s4544" xml:space="preserve">Reliqua tibi conſideranda relinquo. </s>
                  <s xml:id="echoid-s4545" xml:space="preserve">cum verò ambæ
                    <var>.f.
                      <lb/>
                    x.</var>
                  et
                    <var>.u.i.</var>
                  parallelæ ſint ipſi
                    <var>.b.d.</var>
                  ſequitur quod cum ex .34. primi
                    <reg norm="vnaquæque" type="simple">vnaquæq;</reg>
                    <var>.f.m.</var>
                  et
                    <var>.m.
                      <lb/>
                    i.</var>
                  æqualis ſit medietati ipſius
                    <var>.x.u.</var>
                  erunt inuicem æquales.</s>
                </p>
                <figure position="here" number="435">
                  <image file="0395-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0395-01"/>
                </figure>
                <p>
                  <s xml:id="echoid-s4546" xml:space="preserve">Minime dubitabam tibi non ſatisfacere Eutocium in .3. propoſitione ſecundi
                    <lb/>
                  lib. de centris Grauium Archimedis, cum citet .6. librum de elementis conicis, ad-
                    <lb/>
                  de quod ſi aliud in ipſo .6. libro ab eo citato non eſſet magis ad propoſitum, quàm
                    <lb/>
                  ca quæ ab ipſo citata ſunt, nihilominus adhuc irreſolutus maneres.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4547" xml:space="preserve">Conſidera igitur eandem ipſam figuram præcedentem; </s>
                  <s xml:id="echoid-s4548" xml:space="preserve">pro alia verò parabola ſi
                    <lb/>
                  mili dictæ, accipe ſecundam figuram ipſius tertiæ dictæ propoſitionis. </s>
                  <s xml:id="echoid-s4549" xml:space="preserve">Deinde ima
                    <lb/>
                  ginabis duo latera
                    <var>.o.x.</var>
                  et
                    <var>.o.p.</var>
                  diuiſa eſſe per æqualia in punct is
                    <var>.g.</var>
                  et
                    <var>.K.</var>
                    <reg norm="protractisque" type="simple">protractisq́;</reg>
                    <lb/>
                  diametris
                    <var>.g.y.</var>
                  et
                    <var>.K.u.</var>
                  quæ, vt in præcedenti probaui, ſunt inuicem æquales, ſcire
                    <lb/>
                  debes quod ſimiles parabolæ inuicem aliæ non poſſunt eſſe, niſi eæ quæ diametros
                    <lb/>
                  proportionales ſuis baſibus habeant,
                    <reg norm="ſimiliterque" type="simple">ſimiliterq́;</reg>
                  poſitæ, hoc eſt, ut proportio ipſius
                    <lb/>
                    <var>b.d.</var>
                  ad
                    <var>.a.c.</var>
                  ſit eadem quæ ipſius
                    <var>.o.r.</var>
                  ad
                    <var>.x.p.</var>
                  & quod anguli ad
                    <var>.r.</var>
                  ſint æquales angulis
                    <lb/>
                  circa
                    <var>.d</var>
                  . </s>
                  <s xml:id="echoid-s4550" xml:space="preserve">Notentur ergo primum puncta communia ip ſius
                    <var>.o.g.</var>
                  cum
                    <var>.y.t.</var>
                  & ipſius
                    <var>.b.</var>
                  x
                    <lb/>
                  cum
                    <var>.f.m.</var>
                  characteribus. ω
                    <unsure/>
                  . et
                    <var>.n</var>
                  . </s>
                  <s xml:id="echoid-s4551" xml:space="preserve">Nunc igitur ſcimus
                    <var>.f.m.</var>
                  æqualem eſſe
                    <var>.m.i.</var>
                  tota
                    <reg norm="mque" type="simple">mq́;</reg>
                    <var>.f.
                      <lb/>
                    i.</var>
                  parallelam eſſe ipſi
                    <var>.a.c</var>
                  . </s>
                  <s xml:id="echoid-s4552" xml:space="preserve">Idem dico de
                    <var>.y.t.u.</var>
                    <reg norm="triangulique" type="simple">trianguliq́;</reg>
                    <var>.x.f.n.</var>
                  et
                    <var>.g.y.</var>
                  ω
                    <unsure/>
                  . eſſe ſimiles
                    <lb/>
                  triangulis
                    <var>.n.m.b.</var>
                  et. ω
                    <unsure/>
                    <var>.t.o.</var>
                  quod ita probatur, nam ex .15. primi Euclid. anguli ad
                    <var>.n.</var>
                    <lb/>
                  ſunt inuicem æquales, ex .29. verò eiuſdem anguli
                    <var>.f.x.n.</var>
                  et
                    <var>.n.b.m.</var>
                  ſimiliter æquales
                    <lb/>
                  ita etiam
                    <var>.n.f.x.</var>
                  et
                    <var>.n.m.b</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s4553" xml:space="preserve">Idem dico in ſecunda figura, vnde ex .4. ſexti Eucli. proportio
                    <var>.n.f.</var>
                  ad
                    <var>.m.n.</var>
                  erit ea
                    <lb/>
                  dem quę
                    <var>.f.x.</var>
                  ad
                    <var>.b.m.</var>
                  & ipſius
                    <var>.n.f.</var>
                  ad
                    <var>.x.f.</var>
                  vt
                    <var>.n.m.</var>
                  ad
                    <var>.m.b.</var>
                  ex .16. quinti. </s>
                  <s xml:id="echoid-s4554" xml:space="preserve">Quare ex .11.
                    <lb/>
                    <figure xlink:label="fig-0395-02" xlink:href="fig-0395-02a" number="436">
                      <image file="0395-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0395-02"/>
                    </figure>
                  </s>
                </p>
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