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">
              <div xml:id="echoid-div538" type="letter" level="4" n="4">
                <pb o="276" rhead="IO. BAPT. BENED." n="288" file="0288" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0288"/>
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                  <s xml:id="echoid-s3446" xml:space="preserve">Sed aliter idem fieri poſſe inueni, hoc eſt
                    <reg norm="multiplicando" type="context">multiplicãdo</reg>
                  radicem quadratam pro-
                    <lb/>
                  poſiti numeri hominum per .21. & productum item multiplicando per eandem radi
                    <lb/>
                  cem, & huiuſmodi producti radicem diuiden do per .3. vnde prouentus eſſet nume-
                    <lb/>
                  rus hominum vnius ordinis. </s>
                  <s xml:id="echoid-s3447" xml:space="preserve">
                    <reg norm="Exempli" type="context">Exẽpli</reg>
                  gratia proponu
                    <unsure/>
                  ntur .3600. homines, multiplica
                    <lb/>
                  bimus huiuſmodi numeri radicem
                    <lb/>
                  quadratam hoc eſt .60. per .21. hoc
                    <lb/>
                    <figure xlink:label="fig-0288-01" xlink:href="fig-0288-01a" number="315">
                      <image file="0288-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0288-01"/>
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                  eſt per productum quod fit ex .7.
                    <reg norm="cum" type="context">cũ</reg>
                    <lb/>
                  3. & reſultabit nobis .1260. quod ſi
                    <lb/>
                  multiplicabitur, per .60. hoc eſt per
                    <lb/>
                  eandem radicem, reſultabit nobis
                    <num value="75600">.
                      <lb/>
                    75600.</num>
                  cuius producti radix qua-
                    <lb/>
                  drata eſt ferè .275. qua diuiſa per .3
                    <lb/>
                  proueniet nobis .91. pro hominum
                    <lb/>
                  numero vnius ordinis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3448" xml:space="preserve">Cuiusratio eſt iſta, cogitemus nu
                    <lb/>
                  merum .3600. propoſitum eſſe qua
                    <lb/>
                  dratum
                    <var>.a.b.</var>
                  (ſed non areæ) cuius ra
                    <lb/>
                  dix .60. ſit
                    <var>.a.c.</var>
                  & quia hic numerus
                    <num value="60">.
                      <lb/>
                    60.</num>
                  intelligitur eſſe hominum, quo-
                    <lb/>
                  rum
                    <reg norm="vnuſquiſque" type="simple">vnuſquiſq;</reg>
                  occupat .21. pedes
                    <lb/>
                  quadratos ſuperficiales ex ſuppoſi-
                    <lb/>
                  to, </s>
                  <s xml:id="echoid-s3449" xml:space="preserve">& propterea multiplicatur, 60.
                    <lb/>
                  cum .21. vnde nobis veniat .1260.
                    <lb/>
                  quadrati ſuperficiales pro vnoquo-
                    <lb/>
                  que ordine, &
                    <reg norm="quia" type="simple">ꝗa</reg>
                  .b.c. vt. latus qua-
                    <lb/>
                  drati
                    <var>.a.b.</var>
                  habet tot ordines homi-
                    <lb/>
                  num ſimiliter, hoc eſt .60. igi-
                    <lb/>
                  tur multiplicando .60. cum .1260.
                    <lb/>
                  habebimus totalem ſuperficiem
                    <var>.a.
                      <lb/>
                    b.</var>
                  ex .75600. quadratis ſuperficiali-
                    <lb/>
                  bus, quæ quadrata imaginemur lo-
                    <lb/>
                  cata eſſe in quodam totali quadra-
                    <lb/>
                  to, quod ſit
                    <var>.e.f.</var>
                  cuius radix ſit
                    <var>.e.</var>
                  g
                    <num value="275">.
                      <lb/>
                    275.</num>
                  pedum qui diuidantur per .3.
                    <lb/>
                  hoc eſt per numerum pedum latitu-
                    <lb/>
                  dinis & prouenient nobis .91. pro
                    <lb/>
                  numero
                    <reg norm="hominum" type="context">hominũ</reg>
                    <reg norm="vniuſcuiuſque" type="simple">vniuſcuiuſq;</reg>
                  ordi-
                    <lb/>
                  nis, diuidendo poſtea latus
                    <var>.f.g.</var>
                  per
                    <lb/>
                  numerum ſpatij inter vnum, &
                    <reg norm="alium" type="context">aliũ</reg>
                    <lb/>
                  ordinem, quod eſt .7. proueniet
                    <lb/>
                  nobis .39. pro numero ordinum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s3450" xml:space="preserve">Aliter, & breuius etiam poſſumus idem inuenire, hoc eſt multiplicando
                    <reg norm="nume- rum" type="context">nume-
                      <lb/>
                    rũ</reg>
                    <reg norm="propoſitum" type="context">propoſitũ</reg>
                    <reg norm="hominum" type="context">hominũ</reg>
                    <reg norm="cum" type="context">cũ</reg>
                  rectangulo .21. vnde venietnobis
                    <reg norm="productum" type="simple context">ꝓductũ</reg>
                  .75600 quod pro
                    <lb/>
                    <reg norm="ductum" type="context">ductũ</reg>
                  ſi accipiemus vt
                    <reg norm="quadratum" type="context">quadratũ</reg>
                  , cuius radix erit .275. quæ diuidatur
                    <reg norm="per" type="simple">ꝑ</reg>
                  .3. habebi-
                    <lb/>
                  mus
                    <reg norm="propofitum" type="simple context">ꝓpofitũ</reg>
                  . </s>
                  <s xml:id="echoid-s3451" xml:space="preserve">Cuius ratio
                    <reg norm="pendet" type="context">pẽdet</reg>
                  à ſupradicta, eo
                    <reg norm="quod" type="wordlist">qđ</reg>
                  loco
                    <reg norm="multiplicandi" type="context">multiplicãdi</reg>
                    <var>.a.c.</var>
                  (hoc eſt
                    <num value="60">. </num>
                  </s>
                </p>
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