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-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div533" type="section" level="3" n="11">
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                <p>
                  <s xml:id="echoid-s3435" xml:space="preserve">
                    <pb o="275" rhead="EPISTOL AE." n="287" file="0287" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0287"/>
                  ſit quadratum ipſius
                    <var>.D.B</var>
                  . </s>
                  <s xml:id="echoid-s3436" xml:space="preserve">Nunc ſupponendo
                    <var>.A.B.</var>
                  ſimile
                    <var>.a.b.</var>
                  clarum erit ex diffini-
                    <lb/>
                  tione ſimilium figurarum, quod eadem proportio erit
                    <var>.A.D.</var>
                  ad
                    <var>.D.B.</var>
                  quę
                    <var>.a.d.</var>
                  ad
                    <var>.d.
                      <lb/>
                    b.</var>
                  hoc eſt
                    <var>.A.D.</var>
                  ad
                    <var>.D.C.</var>
                  vt
                    <var>.a.d.</var>
                  ad
                    <var>.d.c.</var>
                  hoc eſt
                    <var>.A.B.</var>
                  ad
                    <var>.B.c.</var>
                  vt
                    <var>.a.b.</var>
                  ad
                    <var>.b.c.</var>
                  ex prima
                    <lb/>
                  ſexti, vel .18. ſeu .19. ſeptimi, </s>
                  <s xml:id="echoid-s3437" xml:space="preserve">tunc cum dixerimus ſi
                    <var>.a.b.</var>
                  ita reſpondet ad
                    <var>.b.c.</var>
                  ergo
                    <var>.A.
                      <lb/>
                    B.</var>
                  correſpondet etiam ita ad
                    <var>.B.C.</var>
                  </s>
                  <s xml:id="echoid-s3438" xml:space="preserve">quare ex regula de tribus rectè fit multiplicando
                    <var>.
                      <lb/>
                    A.B.</var>
                  per
                    <var>.b.c.</var>
                  productum verò diuidendo per
                    <var>.a.b.</var>
                  ex .15. ſexti vel .20. ſeptimi, cuius
                    <lb/>
                  prouentus radix quadrata erit quod quærebatur.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3439" xml:space="preserve">Sed aliter idem poſſe fieri ſpeculatus ſum, hoc eſt multiplicando numerum .49.
                    <lb/>
                  ordinis .1000. hominum
                    <reg norm="cum" type="context">cũ</reg>
                  radice quadrata numeri .3500. propoſiti, productum ve-
                    <lb/>
                  rò diuidere per radicem quadratam ipſius .1000. vnde prouentus .91. erit numerus
                    <lb/>
                  vnius ordinis .3500. numeri
                    <reg norm="propoſiti" type="simple">ꝓpoſiti</reg>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3440" xml:space="preserve">Cuius
                    <reg norm="operationis" type="simple">oꝑationis</reg>
                  ſpeculatio eſt iſta.
                    <lb/>
                    <figure xlink:label="fig-0287-01" xlink:href="fig-0287-01a" number="314">
                      <image file="0287-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0287-01"/>
                    </figure>
                  </s>
                  <s xml:id="echoid-s3441" xml:space="preserve">Sit
                    <var>.a.b.</var>
                  quadratum .1000. et
                    <var>.a.c.</var>
                  ſua
                    <lb/>
                  radix et
                    <var>.a.d.</var>
                  rectangulum propoſi-
                    <lb/>
                  tum ipſius .1000. et
                    <var>.a.e.</var>
                  vnus ordo.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s3442" xml:space="preserve">Sit etiam
                    <var>.A.B.</var>
                  quadratum .3500. &
                    <lb/>
                    <var>A.C.</var>
                  eius radix et
                    <var>.A.D.</var>
                    <reg norm="rectangulum" type="context">rectangulũ</reg>
                    <lb/>
                  ipſius numeri .3500. propoſiti, ſimile
                    <lb/>
                  tamen rectangulo
                    <var>.a.d.</var>
                  et
                    <var>.A.E.</var>
                  eius
                    <lb/>
                  vnus ordo. </s>
                  <s xml:id="echoid-s3443" xml:space="preserve">
                    <reg norm="Cum" type="context">Cũ</reg>
                  enim
                    <var>.a.b.</var>
                  æquale ſit
                    <lb/>
                    <var>a.d.</var>
                  et
                    <var>.A.B</var>
                  :
                    <var>A.D.</var>
                    <reg norm="tunc" type="context">tũc</reg>
                    <var>.a.c.</var>
                  erit media
                    <lb/>
                  proportionalis inter
                    <var>.a.e.</var>
                  et
                    <var>.e.d.</var>
                  & ſic
                    <lb/>
                    <var>A.C.</var>
                  erit etiam media proportiona
                    <lb/>
                  lis inter
                    <var>.A.E.</var>
                  et
                    <var>.E.D.</var>
                  per .16. ſexti,
                    <lb/>
                  ſeu .20. ſeptimi, & quia proporrio. A
                    <lb/>
                  E. ad
                    <var>.E.D.</var>
                  æqualis eſt proportioni
                    <var>.
                      <lb/>
                    a.e.</var>
                  ad
                    <var>.e.d.</var>
                  cum
                    <var>.A.D.</var>
                  ſupponatur ſi-
                    <lb/>
                  mile
                    <var>.a.d.</var>
                  ergo proportio
                    <var>.A.E.</var>
                  ad
                    <var>.A
                      <lb/>
                    C.</var>
                  ęqualis erit proportioni
                    <var>.a.e.</var>
                  ad
                    <var>.a.
                      <lb/>
                    c.</var>
                  quę medietates ſunt
                    <reg norm="totorum" type="context">totorũ</reg>
                  æqua-
                    <lb/>
                  lium, rectè igitur fiet ſi procedamus
                    <lb/>
                  ex regula de tribus, dicendo ſi
                    <var>.a.c.</var>
                    <lb/>
                    <reg norm="correſpondet" type="context">correſpõdet</reg>
                    <var>.a.e.</var>
                  tùc
                    <var>.A.C.</var>
                    <reg norm="correſpon" type="context">correſpõ</reg>
                    <lb/>
                  det
                    <var>.A.E.</var>
                  ex ſupradictis .15. ſexti. vel
                    <lb/>
                  20. ſeptimi.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3444" xml:space="preserve">Ratio verò quarti quæſiti per ſe
                    <lb/>
                  patet, quod eſt inuenire
                    <reg norm="pauimentum" type="context">pauimentũ</reg>
                    <lb/>
                  ſeu aream quadratam, in qua poſſint
                    <lb/>
                  locari quot homines volueris, ita in
                    <lb/>
                  ter ſe ſiti, ut vnuſquiſque occupet
                    <num value="7">.
                      <lb/>
                    7.</num>
                  pedes ipſius areę in longitudinem
                    <lb/>
                  et .3. per latitudinem à lateribus.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3445" xml:space="preserve">Seu ex propoſito hominum nume
                    <lb/>
                  ro inuenire numerum ipſorum loca-
                    <lb/>
                  bilem in aliqua area quadrata, ita,
                    <lb/>
                  vt vnuſquiſque occupet .21. pedes
                    <lb/>
                  quadratos ipſius areæ.</s>
                </p>
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