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-div354" type="section" level="3" n="8">
              <p>
                <s xml:id="echoid-s1791" xml:space="preserve">
                  <pb o="150" rhead="IO. BAPT. BENED." n="162" file="0162" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0162"/>
                lus
                  <var>u.A.C.</var>
                æqualis ſit
                  <lb/>
                angulo
                  <var>.K.B.T.</var>
                & an-
                  <lb/>
                gulus
                  <var>.C.A.F.</var>
                æqua-
                  <lb/>
                lis angulo
                  <var>.T.B.Z.</var>
                  <reg norm="nunc" type="context">nũc</reg>
                  <lb/>
                comparatio eſt inter
                  <lb/>
                angulum
                  <var>.D.B.F.</var>
                & an
                  <lb/>
                gulum
                  <var>.K.B.Z.</var>
                miſtili-
                  <lb/>
                neos, qui quidem duo
                  <lb/>
                anguli,
                  <reg norm="communem" type="context">cõmunem</reg>
                ha-
                  <lb/>
                bent angulum miſtili
                  <lb/>
                neum
                  <var>.K.B.F.</var>
                quapro-
                  <lb/>
                  <figure xlink:label="fig-0162-01" xlink:href="fig-0162-01a" number="220">
                    <image file="0162-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0162-01"/>
                  </figure>
                pter ſi angulus
                  <var>.K.B.Z.</var>
                  <lb/>
                miſtilineus maior eſt
                  <lb/>
                angulo
                  <var>.D.B.F.</var>
                miſti-
                  <lb/>
                lineo per angulum
                  <var>.
                    <lb/>
                  K.B.Z.</var>
                contingentiæ,
                  <lb/>
                circulorum ergo angu
                  <lb/>
                lus miſtilineus com-
                  <lb/>
                munis
                  <var>.K.B.F.</var>
                æqualis
                  <lb/>
                erit miſtilineo, angu-
                  <lb/>
                lo
                  <var>.D.B.F.</var>
                pars vide-
                  <lb/>
                licet ſui toto. </s>
                <s xml:id="echoid-s1792" xml:space="preserve">Omnis
                  <lb/>
                autem error in quem
                  <lb/>
                Tartalea,
                  <reg norm="Iordanusque" type="simple">Iordanusq;</reg>
                  <lb/>
                lapſi fuerunt ab eo,
                  <reg norm="quod" type="simple">ꝙ</reg>
                  <lb/>
                  <handwritten xlink:label="hd-0162-01" xlink:href="hd-0162-01a" number="10"/>
                lineas inclinationum
                  <lb/>
                pro parallelis viciſſim
                  <lb/>
                ſumpſerunt, emana-
                  <lb/>
                uit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1793" xml:space="preserve">Septima propoſitio Tartaleæ, quæ eſt
                  <reg norm="quinta" type="simple">ꝗnta</reg>
                quæſtio Iordani mihi
                  <reg norm="videtur" type="simple">videt̃</reg>
                excipien-
                  <lb/>
                da riſu, cum pondus ipſius
                  <var>.A.</var>
                ponderi ipſius
                  <var>.B.</var>
                exiſtens æquale, grauius ſit pondere
                  <lb/>
                eiuſdem
                  <var>.B.</var>
                ratione minoris aperturæ anguli contingentiæ in
                  <var>.A.</var>
                quam in
                  <var>.B.</var>
                in quo
                  <lb/>
                idem error committitur, qui in præcedenti committebatur, cum ſcilicet ipſe putet
                  <lb/>
                lineas
                  <var>.A.E.</var>
                et
                  <var>.B.D.</var>
                figuræ ab eo confictæ ſibi inuicem eſſe parallelas, quæ etiam ſi
                  <lb/>
                æquidiſtantes eſſent (vnde angulus
                  <var>.E.A.G.</var>
                minor eſſet angulo
                  <var>.D.B.F.</var>
                ) non eam ta
                  <lb/>
                men ob cauſam huiuſmodiangulorum differentia cauſa eſſet differentiæ
                  <reg norm="grauitatum" type="context">grauitatũ</reg>
                  <lb/>
                ipſorum
                  <var>.A.</var>
                et
                  <var>.B.</var>
                ob ea quæ cap .4. huius tractatus poſui.</s>
              </p>
              <p>
                <s xml:id="echoid-s1794" xml:space="preserve">Octaua autem propoſitio, quæ eſt .6. quæſtio Iordani Iongè melius demonſtratur
                  <lb/>
                ab Archi. in .6. lib. primi de ponderibus, cum nec à Iordano, nec à Tartalæa probata
                  <lb/>
                fuerit, cum ijdem non probauerint præcedentes, quas in dicta .8. </s>
                <s xml:id="echoid-s1795" xml:space="preserve">Tartalęa citat, qui
                  <lb/>
                neque etiam probat nonam .10. 11. 12. et .13. cum ad pręcedentes probandas mini
                  <lb/>
                mè acceſſerit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1796" xml:space="preserve">Quartadecima verò, quæ eſt .10. quęſtio Iordani, duas ob cauſas eſt falſa, quarum
                  <lb/>
                vna eſt,
                  <reg norm="quod" type="simple">ꝙ</reg>
                (ſupponendo
                  <var>.A.D.E.G.B.</var>
                eſſe vnum brachium librę et
                  <var>.A.</var>
                punctum
                  <reg norm="centri" type="context">cẽtri</reg>
                  <lb/>
                eiuſdem, et
                  <var>.D.</var>
                pondus ęquale ponderi
                  <var>.E.</var>
                & lineas inclinationum
                  <var>.D.K.</var>
                et
                  <var>.E.M.</var>
                ) an
                  <lb/>
                guli
                  <var>.K.D.E.</var>
                et
                  <var>.M.E.G.</var>
                ſibi
                  <reg norm="inuicem" type="context">inuicẽ</reg>
                  <reg norm="non" type="context">nõ</reg>
                ſunt ęquales; </s>
                <s xml:id="echoid-s1797" xml:space="preserve">
                  <reg norm="cum" type="context">cũ</reg>
                ille angulus ſit intrinſecus, hic
                  <lb/>
                verò extrinſecus & oppoſitus dicto intrinſeco
                  <reg norm="vnius" type="simple">vniꝰ</reg>
                  <reg norm="trianguli" type="context">triãguli</reg>
                terminati à.
                  <var>D.E.</var>
                à
                  <var>.D.K.</var>
                </s>
              </p>
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