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-div367" type="section" level="3" n="14">
              <p>
                <s xml:id="echoid-s1878" xml:space="preserve">
                  <pb o="158" rhead="IO. BAPT. BENED." n="170" file="0170" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0170"/>
                figuris rectilineis tam paris, quàm diſparis numeri. </s>
                <s xml:id="echoid-s1879" xml:space="preserve">Sed aliam quandam maiorem
                  <lb/>
                inęqualitatem habent hæ figuræ numeri diſparis, quæ eſt, quòd
                  <reg norm="quando" type="context">quãdo</reg>
                linea
                  <var>.t.i.</var>
                tam
                  <lb/>
                  <var>.u.q.</var>
                quàm ipſi
                  <var>.i.p.</var>
                  <lb/>
                  <figure xlink:label="fig-0170-01" xlink:href="fig-0170-01a" number="231">
                    <image file="0170-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0170-01"/>
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                  <reg norm="perpendicularis" type="simple context">ꝑpẽdicularis</reg>
                fuerit,
                  <lb/>
                ideſt
                  <reg norm="quando" type="context">quãdo</reg>
                  <var>.t.i.</var>
                cum
                  <lb/>
                dictis partibus funis
                  <lb/>
                angulos rectos con-
                  <lb/>
                ſtituerit,
                  <reg norm="tunc" type="context">tũc</reg>
                ratione
                  <lb/>
                  <reg norm="longitudinis" type="context">lõgitudinis</reg>
                ipſius
                  <var>.c.
                    <lb/>
                  i.</var>
                maioris quam
                  <var>.t.
                    <lb/>
                  c.</var>
                (quia cum ſit
                  <var>.c.i.</var>
                  <reg norm="ae- qualis" type="simple">ę-
                    <lb/>
                  qualis</reg>
                ipſi
                  <var>.c.a.</var>
                et
                  <var>.c.a.</var>
                  <lb/>
                maior ipſa
                  <var>.c.t</var>
                :
                  <var>c.i.</var>
                  <lb/>
                etiam maior ſit ipſa
                  <var>.
                    <lb/>
                  c.t.</var>
                ) pondus aut vis
                  <lb/>
                ipſius
                  <var>.p.</var>
                ſuperabit
                  <reg norm="eam" type="context">eã</reg>
                  <lb/>
                quæ eſt ipſius
                  <var>.q.</var>
                ſed
                  <lb/>
                quando
                  <var>.t.</var>
                erit in oppoſita parte, et
                  <var>.i.</var>
                in ea, quæ eſt
                  <lb/>
                ipſius .t: q.
                  <reg norm="eandem" type="context">eãdem</reg>
                ob cauſam ſuperabit
                  <var>.p.</var>
                & ſic mo
                  <lb/>
                  <figure xlink:label="fig-0170-02" xlink:href="fig-0170-02a" number="232">
                    <image file="0170-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0170-02"/>
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                tum faciet irregularem, &
                  <reg norm="non" type="context">nõ</reg>
                vniformem; </s>
                <s xml:id="echoid-s1880" xml:space="preserve">& obid
                  <lb/>
                etiam perarduum, præter ictus, quos infligunt an-
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                guli in partem pendentem
                  <reg norm="aſcendentem" type="context">aſcendẽtem</reg>
                funis,
                  <reg norm="quan- do" type="context">quã-
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                  do</reg>
                vnum exlateribus vnitur cum fune.</s>
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              <p>
                <s xml:id="echoid-s1881" xml:space="preserve">Aliam inęqualitatem habent figuræ pares, quæ
                  <lb/>
                etiam in imparibus cernitur, etſi aliquantulum di-
                  <lb/>
                uerſa; </s>
                <s xml:id="echoid-s1882" xml:space="preserve">quæ ab eo oritur, quod funes ſit modò ma-
                  <lb/>
                gis, modo minus propinquę centro; </s>
                <s xml:id="echoid-s1883" xml:space="preserve">quæ inæqualis
                  <lb/>
                diſtantia, maiorem
                  <reg norm="minoremque" type="simple">minoremq́;</reg>
                vim ſuper dictum
                  <lb/>
                centrum ob rationes in ſecunda parte cap. decimi
                  <lb/>
                huius tractatus propoſitas, gignit. </s>
                <s xml:id="echoid-s1884" xml:space="preserve">Nulla autem
                  <lb/>
                ex ijs inæqualitatibus circulari figuræ contingit. </s>
                <s xml:id="echoid-s1885" xml:space="preserve">Illud verò, quod de pentagonis fi-
                  <lb/>
                guris dixi, omnibus aliis figuris diſparibus accommodari poteſt.</s>
              </p>
              <p>
                <s xml:id="echoid-s1886" xml:space="preserve">Secundus modus eſt earum rotarum, in quibus aliquod animal incedit, quæ ſi cir-
                  <lb/>
                culares non eſſent, tantò difficilius voluerentur, quantò pauciores angulos haberent.
                  <lb/>
                </s>
                <s xml:id="echoid-s1887" xml:space="preserve">quod cum per ſe pateat, non demonſtrabo. </s>
                <s xml:id="echoid-s1888" xml:space="preserve">Si ergo quantò plures angulos habebit
                  <lb/>
                dicta figura, tantò ad circunuoluendum hoc modo agilior erit. </s>
                <s xml:id="echoid-s1889" xml:space="preserve">Circularis igitur fi-
                  <lb/>
                  <handwritten xlink:label="hd-0170-01" xlink:href="hd-0170-01a" number="14"/>
                gura, quæ ex infinitis angulis efficitur, omnium agillima erit.</s>
              </p>
              <p>
                <s xml:id="echoid-s1890" xml:space="preserve">Tertius modus eſt earum rotarum, quæ manubrium habent, quæ etiam quantò
                  <lb/>
                pauciores angulos habebunt, tanto
                  <reg norm="quoque" type="simple">quoq;</reg>
                difficiliores reddentur, tam ratione inimi
                  <lb/>
                citiæ: </s>
                <s xml:id="echoid-s1891" xml:space="preserve">quam exercet cum vacuo natura, quàm
                  <reg norm="violentię" type="context">violẽtię</reg>
                , quam anguli aeri faciunt, eum
                  <lb/>
                expellendo, vt ipſi occupent locum, quem ipſe
                  <reg norm="aer" type="conjecture">aér</reg>
                implebat. </s>
                <s xml:id="echoid-s1892" xml:space="preserve">Quod nullo modo po
                  <lb/>
                teſt euenire circulari figuræ.</s>
              </p>
              <p>
                <s xml:id="echoid-s1893" xml:space="preserve">Nunc nobis ad dicendum reſtat de ſpecie reuolutionis rotarum, quæ parallelæ
                  <lb/>
                ſunt orizonri, quibus accidit poſſe volui primo
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                modo ſecundę ſpeciei, & ob
                  <lb/>
                id ſi circulares non erunt, eadem ſubibunt incommoda, de quibus in ſecunda illa ſpe
                  <lb/>
                cie loquuti ſumus. </s>
                <s xml:id="echoid-s1894" xml:space="preserve">ſed circulares rotæ huius tertiæ ſpeciei ad reuoluendum erunt re-
                  <lb/>
                liquis eò faciliores,
                  <reg norm="quod" type="simple">ꝙ</reg>
                vno
                  <reg norm="ſolum" type="context">ſolũ</reg>
                polo nituntur; </s>
                <s xml:id="echoid-s1895" xml:space="preserve">Quod alijs nequaquam conceditur.</s>
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