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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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div703" type="section" level="3" n="35">
              <div xml:id="echoid-div703" type="letter" level="4" n="1">
                <p>
                  <s xml:id="echoid-s4343" xml:space="preserve">
                    <pb o="363" rhead="EPISTOL AE." n="375" file="0375" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0375"/>
                  & qua drato
                    <var>.a.c.</var>
                  ex
                    <reg norm="eadem" type="context">eadẽ</reg>
                  . </s>
                  <s xml:id="echoid-s4344" xml:space="preserve">Nunc videndum eſt
                    <reg norm="vtrum" type="context">vtrũ</reg>
                    <reg norm="duplum" type="context">duplũ</reg>
                  quadrati
                    <var>.a.e.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  duplo qua
                    <lb/>
                  drati
                    <var>.b.a.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  duplo quadrati
                    <var>.b.c.</var>
                  ſit æquale duplo quadrati
                    <var>.a.e.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  quadrato
                    <var>.a.d.</var>
                  &
                    <lb/>
                  cum quadrato
                    <var>.a.c</var>
                  . </s>
                  <s xml:id="echoid-s4345" xml:space="preserve">Sed quia tam ex vna parte quàm ex alia habemus duplum qua-
                    <lb/>
                  drati
                    <var>.a.e</var>
                  . </s>
                  <s xml:id="echoid-s4346" xml:space="preserve">Videndum igitur erit vtrum duplum quadrati
                    <var>.a.b.</var>
                  ſimul cum duplo qua-
                    <lb/>
                  drati
                    <var>.b.c.</var>
                  ęquale ſit quadrato
                    <var>.a.c.</var>
                  cum quadrato
                    <var>.a.d.</var>
                  ſed hoc manifeſtum eſt .ex .10.
                    <lb/>
                  ſecundi Euclidis, dato quod
                    <reg norm="punctum" type="context">punctũ</reg>
                    <var>.a.</var>
                  ſit inter
                    <var>.f.</var>
                  et
                    <var>.d.</var>
                  ſed ſi fuerit inter
                    <var>.d.</var>
                  et
                    <var>.b.</var>
                  hoc
                    <lb/>
                  manifeſtum erit ex .9. ſecundi dicti, nihilominus accipe hunc alium modum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4347" xml:space="preserve">Sit hic ſubſcriptum quadratum
                    <var>.D.</var>
                  ex
                    <var>.a.c.</var>
                  in ſeipſa producta, cuius diameter ſit
                    <lb/>
                    <var>a.n.</var>
                    <reg norm="protrahanturque" type="simple">protrahanturq́</reg>
                  parallelę
                    <var>.d.h</var>
                  :
                    <var>b.K</var>
                  :
                    <var>l.m.o.</var>
                  et
                    <var>.r.q.s.</var>
                    <reg norm="eique" type="simple">eiq́;</reg>
                  addatur
                    <var>.c.p.</var>
                  ad
                    <var>.a.c.</var>
                  æqua-
                    <lb/>
                  lis tamen
                    <var>.d.a.</var>
                    <reg norm="ſitque" type="simple">ſitq́;</reg>
                  protracta
                    <var>.p.u.</var>
                  vſque ad
                    <var>.m.o.u.</var>
                  vnde habebimus
                    <var>.a.n.</var>
                  pro totali
                    <lb/>
                  quadrato, et
                    <var>.p.s.</var>
                  pro partiali, & æquali quadrato lineæ
                    <var>.a.d</var>
                  . </s>
                  <s xml:id="echoid-s4348" xml:space="preserve">Videndum nunc eſt,
                    <reg norm="vtrum" type="context">vtrũ</reg>
                    <lb/>
                  hęc duo quadrata æqualia ſint duobus quadratis lineæ
                    <var>.a.b.</var>
                  & duobus lineæ
                    <var>.b.c.</var>
                    <reg norm="Nam" type="context">Nã</reg>
                    <lb/>
                  duo quadrata lineæ
                    <var>.b.c.</var>
                  ſint
                    <var>.K.o.</var>
                  et
                    <var>.h.l.</var>
                  videndum nunc eſt utrum reſiduum ęquale
                    <lb/>
                  ſit duobus quadratis lineę
                    <var>.a.b.</var>
                  quorum vnum ſit
                    <var>.m.b.</var>
                  alterum verò
                    <var>.l.p.</var>
                  quod ſupe-
                    <lb/>
                  rat
                    <var>.l.c.</var>
                  et
                    <var>.s.p.</var>
                  figuræ
                    <var>.D.</var>
                  per ſupplementum
                    <var>.o.t.</var>
                  cui æquale eſt parallelogrammum
                    <var>.h.
                      <lb/>
                    m.</var>
                  figuræ
                    <var>.D.</var>
                  ſed ſi punctus
                    <var>.a.</var>
                  poſitus fuerit inter
                    <var>.d.</var>
                  et
                    <var>.b.</var>
                  conſtituto quadrato
                    <var>.d.u.</var>
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  omnibus parallelis, vtin figura
                    <var>.C.</var>
                  viderelicet, in qua figura videbimus quadrata
                    <var>.r.
                      <lb/>
                    n.</var>
                  et
                    <var>.d.r.</var>
                  ęquari duplo quadratorum
                    <var>.l.n.</var>
                  et
                    <var>.r.l.</var>
                  nam in quadrato
                    <var>.r.n.</var>
                  ipſa duo quadra-
                    <lb/>
                  ta
                    <var>.l.n.</var>
                  et
                    <var>.r.l.</var>
                  capiuntur, reliquum eſt igitur vt videamus an duo ſupplementa
                    <var>.l.t.</var>
                  et
                    <var>.l.
                      <lb/>
                    s.</var>
                  cum quadrato
                    <var>.d.r.</var>
                  ſint æqualia dictis
                    <reg norm="quadratis" type="typo">q́uadratis</reg>
                    <var>.l.n.</var>
                  et
                    <var>.r.l.</var>
                  ſed quadratum
                    <var>.d.l.</var>
                  æ qua-
                    <lb/>
                  tur quadrato
                    <var>.l.n.</var>
                  videndum igitur eſt,
                    <lb/>
                  an duo ſupplementa
                    <var>.l.t.</var>
                  et
                    <var>.l.s.</var>
                  cum qua
                    <lb/>
                    <anchor type="figure" xlink:label="fig-0375-01a" xlink:href="fig-0375-01"/>
                  drato
                    <var>.d.r.</var>
                  ſint æqualia duobus quadra
                    <lb/>
                  tis
                    <var>.d.l.</var>
                  et
                    <var>.r.l.</var>
                  ſed quadratum
                    <var>.d.l.</var>
                  æqua-
                    <lb/>
                  tur quadrato
                    <var>.d.r.</var>
                  & ſupplemento
                    <var>.l.t.</var>
                    <lb/>
                  mediante
                    <var>.q.l.</var>
                  & ſupplemento
                    <var>.r.b.</var>
                  ſup-
                    <lb/>
                  plementum verò
                    <var>.l.s.</var>
                  ſuperat
                    <reg norm="ſupplemem" type="context">ſupplemẽ</reg>
                    <lb/>
                  tum
                    <var>.r.b.</var>
                  per quantitatem
                    <reg norm="æqualem" type="context">æqualẽ</reg>
                  qua-
                    <lb/>
                  drato
                    <var>.r.l.</var>
                  </s>
                  <s xml:id="echoid-s4349" xml:space="preserve">quare duo ſupplementa
                    <var>.l.t.</var>
                    <lb/>
                  et
                    <var>.l.s.</var>
                  cum quadrato
                    <var>.d.r.</var>
                  æquantur qua
                    <lb/>
                  drato
                    <var>.d.l.</var>
                    <reg norm="cum" type="context">cũ</reg>
                  quadrato
                    <var>.l.r.</var>
                  verum igitur eſt duas
                    <var>.d.e.e.c.</var>
                  figuræ
                    <var>.A.</var>
                  æquales eſſe in
                    <lb/>
                  potentia duabus
                    <var>d.e.e.c.</var>
                  figurę
                    <var>.D.</var>
                  quæ quidem affectio circuli, à nemine fuit adhuc
                    <lb/>
                  (quod ſciam) detecta.</s>
                </p>
                <div xml:id="echoid-div705" type="float" level="5" n="3">
                  <figure xlink:label="fig-0375-01" xlink:href="fig-0375-01a">
                    <image file="0375-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0375-01"/>
                  </figure>
                </div>
              </div>
            </div>
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