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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EPISTOL AE.
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                    <pb o="393" rhead="EPISTOL AE." n="405" file="0405" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0405"/>
                  ta fuit vt
                    <var>.m.t.</var>
                  ad
                    <var>.t.n.</var>
                  idcirco ex .11. quinti ita erit ipſius fruſti
                    <var>.a.e.</var>
                  ad ſectionem
                    <var>.d.b.
                      <lb/>
                    e.</var>
                  vt tres quintę ipſius
                    <var>.f.g.</var>
                  ad
                    <var>.i.r</var>
                  .</s>
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                  <note xlink:label="note-0404-04" xlink:href="note-0404-04a" position="left" xml:space="preserve">β</note>
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                <p>
                  <s xml:id="echoid-s4661" xml:space="preserve">Inquit deinde quod proportio corporis iam ſupradicti, quod pro ſua baſi habeat
                    <lb/>
                  quadratum ipſius
                    <var>.a.f.</var>
                  altitudinem verò compoſitam ex duplo ipſius
                    <var>.d.g.</var>
                  cum ſimplo
                    <lb/>
                    <var>a.f.</var>
                  ad cubum ipſius
                    <var>.a.f.</var>
                  eadem erit quæ dupli ipſius
                    <var>.d.g.</var>
                  cum ſimplo
                    <var>.a.f.</var>
                  ad
                    <var>.a.f</var>
                  . </s>
                  <s xml:id="echoid-s4662" xml:space="preserve">Quod
                    <lb/>
                  quidem verum eſt ex .33. vndecimi & ex prima ſexti.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4663" xml:space="preserve">Sed ſuperius (vbi. α.) iam probauimus eandem proportio nem eſſe inter
                    <var>.m.n.</var>
                  &
                    <lb/>
                    <var>n.x.</var>
                  quæ inter
                    <var>.a.f.</var>
                  et
                    <var>.d.g.</var>
                  ideo ex conuerſa pro portion alitate ita erit ipſius
                    <var>.x.n.</var>
                  ad
                    <var>.n.
                      <lb/>
                    m.</var>
                  vt ipſius
                    <var>.d.g.</var>
                  ad
                    <var>.a.f.</var>
                  ſed dupli
                    <var>.x.n.</var>
                  ad ſimplum
                    <var>.x.n.</var>
                  eſt vt dupli
                    <var>.d.g.</var>
                  ad
                    <var>.d.g</var>
                  . </s>
                  <s xml:id="echoid-s4664" xml:space="preserve">Qua
                    <lb/>
                  re ex .22. quinti dupli
                    <var>.x.n.</var>
                  ad
                    <var>.m.n.</var>
                  erit vt dupli
                    <var>.d.g.</var>
                  ad
                    <var>.a.f.</var>
                  & ex .18. eiuſdem ita erit
                    <lb/>
                  dupli
                    <var>.x.n.</var>
                  cum ſimplo
                    <var>.m.n.</var>
                  ad
                    <var>.m.n.</var>
                  vt dupli
                    <var>.d.g.</var>
                  cum ſimplo
                    <var>.a.f.</var>
                  ad
                    <var>.a.f</var>
                  . </s>
                  <s xml:id="echoid-s4665" xml:space="preserve">Quare ſolidi
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0405-01a" xlink:href="fig-0405-01"/>
                  </s>
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