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-div533" type="section" level="3" n="11">
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                <p>
                  <s xml:id="echoid-s3414" xml:space="preserve">
                    <pb o="272" rhead="IO. BAPT. BENED." n="284" file="0284" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0284"/>
                  ſtea egeat ipſa ualde calefacta. </s>
                  <s xml:id="echoid-s3415" xml:space="preserve">Quod Tartalea in quinto quęſito non animaduer-
                    <lb/>
                  terat.</s>
                </p>
              </div>
              <div xml:id="echoid-div535" type="letter" level="4" n="3">
                <head xml:id="echoid-head408" style="it" xml:space="preserve">Solutiones aliqua, circa altimetriam.</head>
                <head xml:id="echoid-head409" xml:space="preserve">AD EVNDEM.</head>
                <p>
                  <s xml:id="echoid-s3416" xml:space="preserve">TVas literas accepi,
                    <reg norm="tuasque" type="simple">tuasq́;</reg>
                  dubitationes conſideraui, quas quidem non inutiles
                    <lb/>
                  inueni, quo uerò ad primam, dico te oportere illud Theorema ſpeculari or
                    <lb/>
                  dine huiuſmodi methodi, uidelicet quod
                    <reg norm="quotieſcunque" type="simple">quotieſcunq;</reg>
                  habuerimus
                    <reg norm="angulum" type="context">angulũ</reg>
                    <reg norm="aliquem" type="context">aliquẽ</reg>
                    <lb/>
                  cuiufuis amplitudinis, puta
                    <var>.A.R.V.</var>
                  cuius duo latera
                    <var>.R.A.</var>
                  et
                    <var>.R.V.</var>
                  indeterminata
                    <lb/>
                  intelligantur, ſi ab aliquo puncto inter ipſas poſito, puta
                    <var>.u.</var>
                  quod etiam uocetur
                    <var>.i.</var>
                  du
                    <lb/>
                  ctę fuerint .4. lineę ipſis dictis lateribus, hac ſcilicet
                    <reg norm="conditione" type="context">cõditione</reg>
                  ,
                    <reg norm="quod" type="wordlist">qđ</reg>
                  duę ex dictis .4. ſint
                    <lb/>
                  parallelę ipfis
                    <reg norm="lateribus" type="simple">lateribꝰ</reg>
                  , puta
                    <lb/>
                    <figure xlink:label="fig-0284-01" xlink:href="fig-0284-01a" number="310">
                      <image file="0284-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0284-01"/>
                    </figure>
                    <var>u.e.</var>
                  et
                    <var>.u.E.</var>
                  reliquę uero duę
                    <lb/>
                  ſeccent ipſa latera, ut
                    <var>V.u.
                      <lb/>
                    a.</var>
                  et
                    <var>.I.u.A</var>
                  . </s>
                  <s xml:id="echoid-s3417" xml:space="preserve">Dico nunc pro-
                    <lb/>
                  portionem
                    <var>.e.A.</var>
                  ad
                    <var>.e.a.</var>
                  ean
                    <lb/>
                  dem eſſe, quę
                    <var>.E.V.</var>
                  ad
                    <var>.E.I.</var>
                    <lb/>
                  Nam ſcimus proportionem
                    <lb/>
                    <var>E.i.</var>
                  ad
                    <var>.E.i.</var>
                  eandem eſſe quę
                    <lb/>
                    <var>e.i.</var>
                  ad
                    <var>.e.A.</var>
                  ex fimilitudine
                    <lb/>
                    <reg norm="triangulorum" type="context">triangulorũ</reg>
                  , ſimiliter
                    <reg norm="propor" type="simple">ꝓpor</reg>
                    <lb/>
                    <reg norm="tionem" type="context">tionẽ</reg>
                    <var>.E.u.</var>
                  ad
                    <var>.E.V.</var>
                    <reg norm="eandem" type="context context">eãdẽ</reg>
                  quę
                    <lb/>
                    <var>e.a.</var>
                  ad
                    <var>.e.u.</var>
                  </s>
                  <s xml:id="echoid-s3418" xml:space="preserve">quare aggregata
                    <lb/>
                  ex iſtis erunt inuicem
                    <reg norm="aequa- lia" type="simple">ęqua-
                      <lb/>
                    lia</reg>
                  , uel ſi mauis ex ęqua pro
                    <lb/>
                  portionalitate, quod idem
                    <lb/>
                  eſt, ita ſe habebit
                    <var>.E.I.</var>
                  ad
                    <var>.
                      <lb/>
                    E.V.</var>
                  ut
                    <var>.e.a.</var>
                  ad
                    <var>.e.A</var>
                  .</s>
                </p>
                <p>
                  <s xml:id="echoid-s3419" xml:space="preserve">Suppoſito nunc plano orizontali
                    <var>.V.E</var>
                  . </s>
                  <s xml:id="echoid-s3420" xml:space="preserve">
                    <reg norm="Altitudineque" type="simple">Altitudineq́;</reg>
                  inacceſſibili
                    <var>.A.E</var>
                  . </s>
                  <s xml:id="echoid-s3421" xml:space="preserve">Duę ue-
                    <lb/>
                  rò ſtationes oculorum ſint
                    <var>.V.</var>
                  et
                    <var>.I.</var>
                  lineę autem uiſuales ſint
                    <var>.V.A.</var>
                  et
                    <var>.I.A</var>
                  . </s>
                  <s xml:id="echoid-s3422" xml:space="preserve">Et quadra-
                    <lb/>
                  tum geometricum ſit
                    <var>.b.e</var>
                  . </s>
                  <s xml:id="echoid-s3423" xml:space="preserve">Supponatur nunc pro prima dubitatione, quod in am-
                    <lb/>
                  babus ſtationibus filum perpendiculare ſeccet latus
                    <var>.e.c.</var>
                  non autem
                    <var>.b.c.</var>
                  (nam quan-
                    <lb/>
                  do in ambabus ſtationibus filum ſecat latus
                    <var>.b.c.</var>
                  nullum tibi dubium oritur, imo ma
                    <lb/>
                  nifeſtè patent partes lateris
                    <var>.b.c.</var>
                  terminatas à
                    <var>.b.</var>
                  & à filo proportionales eſſe
                    <var>.V.E.</var>
                  &
                    <lb/>
                    <var>I.E.</var>
                  ſumpto
                    <var>.E.</var>
                  pro
                    <var>.b.</var>
                  et
                    <var>.I.V.</var>
                  pro punctis ſecatis à filo, ex
                    <reg norm="euidenti" type="context">euidẽti</reg>
                  ſimilitudine trian-
                    <lb/>
                  gulorum quadrati cum triangulis
                    <var>.A.E.V.</var>
                  et
                    <var>.A.E.I.</var>
                  ) Sed cum in pręſenti caſu repe-
                    <lb/>
                  riatur triangulum
                    <var>.u.e.a.</var>
                  minus, in ſtatione remotiori, ſimile triangulo maiori
                    <var>.V.E.
                      <lb/>
                    A.</var>
                  & triangulum maius
                    <var>.i.e.a.</var>
                  proximioris ſtationis, ſimile triangulo minori
                    <var>.I.E.A.</var>
                    <lb/>
                  (quod in alio iam dicto, caſu non accidit, ut unum triangulorum, minus ſcilicet, ſi-
                    <lb/>
                  mile ſit uno triangulorum, maiori ſcilicet & è conuerſo) Non omnino abſque ratio
                    <lb/>
                  ne dubitas quo pacto fieri poſſit ut
                    <var>.a.e.</var>
                  remotioris ſtationis ad
                    <var>.a.e.</var>
                  propinquioris ita
                    <lb/>
                  ſe habeat quema dmodum
                    <var>.I.E.</var>
                  ad
                    <var>.E.V</var>
                  . </s>
                  <s xml:id="echoid-s3424" xml:space="preserve">Quapropter ſi pręcedentem figuram dili- </s>
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