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-div634" type="letter" level="4" n="2">
                <pb o="330" rhead="IO. BAPT. BENED." n="342" file="0342" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0342"/>
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            <div xml:id="echoid-div639" type="section" level="3" n="27">
              <div xml:id="echoid-div639" type="letter" level="4" n="1">
                <head xml:id="echoid-head493" xml:space="preserve">QVAEDAM NOTATV DIGNA IN
                  <lb/>
                Ptolomeum.</head>
                <head xml:id="echoid-head494" style="it" xml:space="preserve">Bartolomeo Christino Serenißimi Sabaudiœ Ducis apparitore.</head>
                <p>
                  <s xml:id="echoid-s4003" xml:space="preserve">EX tuis literis cognoui quo erga me animo eſſes,
                    <reg norm="qualique" type="simple">qualiq́;</reg>
                  voluntate, ſed ne
                    <lb/>
                  tua pulcherrima ſtudia aliquo modo imperfecta
                    <reg norm="relinquantur" type="simple">relinquant̃</reg>
                  , vel ego tibi
                    <lb/>
                  deeſſe videar, dum Problemata geographica Magni Ptolomei conſi-
                    <lb/>
                  deras, aduerte, quod ſi putares in figura .6. cap. libr .7. geographię eiuſ-
                    <lb/>
                  dem (vt multi credunt) lineam
                    <var>.V.*.</var>
                  ſecare circunferentiam
                    <var>.A.D.</var>
                  in puncto
                    <var>.G.</var>
                  ita
                    <lb/>
                  vt punctus
                    <var>.G.</var>
                  ſit tropici æſtiui, ideſt arcum
                    <var>.D.G.</var>
                  eſſe graduum .24. cum illis inci-
                    <lb/>
                  deres in maximum errorem. </s>
                  <s xml:id="echoid-s4004" xml:space="preserve">Quapropter conſidera quæ nunc tibi ſcribo.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4005" xml:space="preserve">Sit circulus
                    <var>.A.B.C.D.</var>
                  huius centrum
                    <var>.E.</var>
                    <reg norm="ſupponaturque" type="simple">ſupponaturq́;</reg>
                  ſemidiameter
                    <var>.E.D.</var>
                  eſſe
                    <lb/>
                  partium 120. quarum
                    <var>.E.Z.</var>
                  in alio ſemidiametro
                    <var>.C.E.</var>
                  ei orthogonaliter coniuncto,
                    <lb/>
                  talium ſit .17. in ſemidiametro vero
                    <var>.E.A.</var>
                  accipiatur
                    <var>.E.S.</var>
                  talium .24. et
                    <var>.E.V.</var>
                  64. vn
                    <lb/>
                  de
                    <var>.S.V.</var>
                  erit partium 40. ſimilium.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4006" xml:space="preserve">Erigatur deinde
                    <var>.S.*.</var>
                  ad rectos cum
                    <var>.E.A.</var>
                  in puncto
                    <var>.S.</var>
                  quæ terminetur ab inter-
                    <lb/>
                  ſectione lineę ductæ per puncta
                    <var>.Z.D.</var>
                  in puncto
                    <var>.*.</var>
                  ducatur demum
                    <var>.V.*.</var>
                  quæ ſeca-
                    <lb/>
                  bit circunf rentiam
                    <var>.A.D.</var>
                  in puncto
                    <var>.G</var>
                  . </s>
                  <s xml:id="echoid-s4007" xml:space="preserve">Quæratur nunc quantitas ipſius
                    <var>.G.D.</var>
                    <lb/>
                  Ad quod efficiendum quærenda primum eſt quantitas ipſius
                    <var>.S.*.</var>
                  quam illico co
                    <lb/>
                  gnoſcemus ex regula de tribus, cum dixerimus, ſi@ 17. dat nobis .120. quid dabit .41.
                    <lb/>
                  (nam duo triangula
                    <var>.Z.E.D.</var>
                  et
                    <var>.Z.S.*.</var>
                  ſunt inuicem ſimilia, cum
                    <var>.S.*.</var>
                  parallela ſit
                    <lb/>
                  ipſi
                    <var>.E.D.</var>
                  ) vnde
                    <var>.S.*.</var>
                  proueniet nobis ex ſimilibus partibus .289. cum fracto, quod
                    <lb/>
                  r
                    <unsure/>
                  eijciamus ob minorem laborem.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4008" xml:space="preserve">Producantur poſtea
                    <var>.V.*.</var>
                  et
                    <var>.E.D.</var>
                  vſque ad eorum concurſum in puncto
                    <var>.ω.</var>
                  quæ-
                    <lb/>
                    <reg norm="remusque" type="simple">remusq́;</reg>
                  quanta ſit
                    <var>.E.ω.</var>
                  ex eadem regula, cum dixerimus, ſi .40. dat nobis .289. quid
                    <lb/>
                    <figure xlink:label="fig-0342-01" xlink:href="fig-0342-01a" number="366">
                      <image file="0342-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0342-01"/>
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