Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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          <p>
            <s xml:id="echoid-s8404" xml:space="preserve">
              <pb o="207" file="243" n="244" rhead="Ioan. de Sacro Boſco."/>
            bet circuli ad diametrum; </s>
            <s xml:id="echoid-s8405" xml:space="preserve">erit conuertendo, eadẽ proportio 7. </s>
            <s xml:id="echoid-s8406" xml:space="preserve">ad 22. </s>
            <s xml:id="echoid-s8407" xml:space="preserve">quæ dia-
              <lb/>
            metri ad circun ferentiam. </s>
            <s xml:id="echoid-s8408" xml:space="preserve">Quare ſi diameter, ideſt, tertius numerus regulæ
              <lb/>
            proportionum, multiplicetur per 2. </s>
            <s xml:id="echoid-s8409" xml:space="preserve">nimirum per ſecundum numerum eiuſdẽ
              <lb/>
            regulæ, productusque numerus per primum numerũ, hoc eſt, per 7. </s>
            <s xml:id="echoid-s8410" xml:space="preserve">diuidatur,
              <lb/>
            reperiretur quartus eiuſdem regulæ numerus, ideſt, circunferentia circuli. </s>
            <s xml:id="echoid-s8411" xml:space="preserve">Vt
              <lb/>
            in proximo exemplo, ſi diameter 490. </s>
            <s xml:id="echoid-s8412" xml:space="preserve">mnltiplicetur per 22. </s>
            <s xml:id="echoid-s8413" xml:space="preserve">numerusque pro-
              <lb/>
            ductus per 7. </s>
            <s xml:id="echoid-s8414" xml:space="preserve">diuidatur, reperietur circunferentia 1540. </s>
            <s xml:id="echoid-s8415" xml:space="preserve">ut prius. </s>
            <s xml:id="echoid-s8416" xml:space="preserve">Duplex au-
              <lb/>
            tem hoc præceptum continetur his carminibus.</s>
            <s xml:id="echoid-s8417" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8418" xml:space="preserve">Circuitus circi per ſeptem multiplicetur,
              <lb/>
            Per duo uiginti productum deinde ſecato:
              <lb/>
            </s>
            <s xml:id="echoid-s8419" xml:space="preserve">Hinc numerus, Quotiens qui dicitur, eſt diametrus.</s>
            <s xml:id="echoid-s8420" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s8421" xml:space="preserve">Per duo uiginti ſi multiplices diametrum,
              <lb/>
            Per ſeptemq́ ſeces numerum, quiprodijt inde:
              <lb/>
            </s>
            <s xml:id="echoid-s8422" xml:space="preserve">Circuitum circi Quotiens numerus tibi reddet.</s>
            <s xml:id="echoid-s8423" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8424" xml:space="preserve">
              <emph style="sc">Hinc</emph>
            facile intelligitur modus, quo uſus eſt Franciſcus Maurolycus in
              <lb/>
            inueſtigando terreni orbis ambitu. </s>
            <s xml:id="echoid-s8425" xml:space="preserve">Prius enim uia Geometrica didicit quãti
              <lb/>
            tatem diametri terræ, ex qua poſtea iuxta hanc proportionem diametri ad cir-
              <lb/>
            cunferentiam demonſtratam ab Archimede, venatus eſt circunferentiam maxi
              <lb/>
            mi circuli per terrę centrum deſcripti.</s>
            <s xml:id="echoid-s8426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8427" xml:space="preserve">
              <emph style="sc">Caetervm</emph>
            circunferentia circuli cuiuslibet ad eius diametrum non
              <lb/>
            habet præciſe eam proportionem, quam 22. </s>
            <s xml:id="echoid-s8428" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8429" xml:space="preserve">ſed paulo minorem. </s>
            <s xml:id="echoid-s8430" xml:space="preserve">Vt enim
              <lb/>
            Archimedes in libello de Dimenſione acutiſſime demõſtrauit. </s>
            <s xml:id="echoid-s8431" xml:space="preserve">Cuiuslibet cir-
              <lb/>
            culi circunferentia ad ſuam diametrum proportionẽ minorem quidem habe
              <unsure/>
            t
              <lb/>
            tripla ſeſquiſeptima, ſeu (quod idem eſt) tripl@@ſuperdecupartiente ſeptuageſi-
              <lb/>
            mas: </s>
            <s xml:id="echoid-s8432" xml:space="preserve">maiorem uero tripla ſuperdecupartiente ſeptuageſimas primas. </s>
            <s xml:id="echoid-s8433" xml:space="preserve">Itaque ſi
              <lb/>
            ſumatur diameter ter cum ſeptima parte, hoc eſt, cum {10/70}. </s>
            <s xml:id="echoid-s8434" xml:space="preserve">efficietur linea
              <lb/>
            paulo maior, quàm circunferentia: </s>
            <s xml:id="echoid-s8435" xml:space="preserve">At uero ſi ſumatur diameter cum {10/70}.
              <lb/>
            </s>
            <s xml:id="echoid-s8436" xml:space="preserve">cõficietur linea paulò minor, quàm circũſerentia. </s>
            <s xml:id="echoid-s8437" xml:space="preserve">Adeo ut uera proportio cir-
              <lb/>
            cunferentiæ ad diametrum conſiſtat) licet occulta ſit) inter duas, quarũ deno-
              <lb/>
            minatores ſun 3 {10/70}. </s>
            <s xml:id="echoid-s8438" xml:space="preserve">3 {10/71}. </s>
            <s xml:id="echoid-s8439" xml:space="preserve">Communis tamen uſus artificum obtinuit, ut
              <lb/>
              <note position="right" xlink:label="note-243-01" xlink:href="note-243-01a" xml:space="preserve">Ex regulis
                <lb/>
              ſuperiori-
                <lb/>
              bus reperi-
                <lb/>
              tur circũfe-
                <lb/>
              rẽtia maior
                <lb/>
              exdiame@@o
                <lb/>
              nota diame
                <lb/>
              ter uero mi
                <lb/>
              nor ex nota
                <lb/>
              circunferen
                <lb/>
              tia, quàmr
                <unsure/>
              e
                <lb/>
              ipſa ſit.</note>
            prior proportio, nempe tripla ſeſquiſeptima, potius uſurpetur tanquam uera,
              <lb/>
            quàm illa, cuius denominator eſt {10/71}. </s>
            <s xml:id="echoid-s8440" xml:space="preserve">Sumunt enim diametrũ ter cum ſepti-
              <lb/>
            ma eius parte, ut circunferentię lineam rectam æqualem exhibeant; </s>
            <s xml:id="echoid-s8441" xml:space="preserve">quoniam
              <lb/>
            uidelicet parũ à uero deficit, & </s>
            <s xml:id="echoid-s8442" xml:space="preserve">facilior fit operatio per 3 {1/7}. </s>
            <s xml:id="echoid-s8443" xml:space="preserve">quam per 3 {10/71}.
              <lb/>
            </s>
            <s xml:id="echoid-s8444" xml:space="preserve">proptereaq́ nobis eadẽ proportione uti quoq; </s>
            <s xml:id="echoid-s8445" xml:space="preserve">licebit, dummodo memores ſi
              <lb/>
            mus, per documẽta ſuperiora ex diametro nota inueniri circunferentiã paulo
              <lb/>
            maiorem, diametrum uero ex nota circunferentia paulo minorem, quàm uere
              <lb/>
            ſit. </s>
            <s xml:id="echoid-s8446" xml:space="preserve">Nam cum ſecundum Archimedem minor ſit proportio circunferentiæ ad
              <lb/>
            diametrũ, quàm tripla ſeſquiſeptima, hoc eſt, quàm 22. </s>
            <s xml:id="echoid-s8447" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8448" xml:space="preserve">fit, ſi diameter fue
              <lb/>
            rit 7. </s>
            <s xml:id="echoid-s8449" xml:space="preserve">circunferentiam eſſe paulo minorem quàm 22. </s>
            <s xml:id="echoid-s8450" xml:space="preserve">Numerus enim minor,
              <lb/>
            quàm 22. </s>
            <s xml:id="echoid-s8451" xml:space="preserve">minorem proportionem habet ad 7. </s>
            <s xml:id="echoid-s8452" xml:space="preserve">quàm 22. </s>
            <s xml:id="echoid-s8453" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8454" xml:space="preserve">Vnde cum ſecun-
              <lb/>
            dum regulam ſuperiorem, ſi diameter fuerit 7. </s>
            <s xml:id="echoid-s8455" xml:space="preserve">circunferentia reperiatur 22. </s>
            <s xml:id="echoid-s8456" xml:space="preserve">li
              <lb/>
            quido conſtat, maiorem inuenir
              <unsure/>
            i circunferentiam ex diametro nota, quàm re
              <lb/>
            ipſa ſit. </s>
            <s xml:id="echoid-s8457" xml:space="preserve">Rurſus efficiatur, ſi circunferentia fuerit 22. </s>
            <s xml:id="echoid-s8458" xml:space="preserve">diametrum eſſe paulo mi-
              <lb/>
            norem, quàm 7. </s>
            <s xml:id="echoid-s8459" xml:space="preserve">Numerus enaim 22. </s>
            <s xml:id="echoid-s8460" xml:space="preserve">d numer um maiorem, quàm 7. </s>
            <s xml:id="echoid-s8461" xml:space="preserve">minor
              <unsure/>
            em
              <lb/>
            habet proportionem, quam ad 7. </s>
            <s xml:id="echoid-s8462" xml:space="preserve">Quare cum iuxta ſuperiorem regulam, ſi cir-
              <lb/>
            cunferentia fuerit 22. </s>
            <s xml:id="echoid-s8463" xml:space="preserve">diameter reperiatur 7. </s>
            <s xml:id="echoid-s8464" xml:space="preserve">perſpicuum eſt, minorem reperi-
              <lb/>
            ri diametrum ex nota circunfereutia, quàm re ipſa ſit.</s>
            <s xml:id="echoid-s8465" xml:space="preserve"/>
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