Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of handwritten notes

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              <pb o="206" file="242" n="243" rhead="Comment. in I. Cap. Sphæræ"/>
              <figure xlink:label="fig-242-01" xlink:href="fig-242-01a" number="75">
                <image file="242-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/242-01"/>
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            gula, qua præcipit ex ambitu terreno diametrum, ſiue profunditatem terræ
              <lb/>
            explorare.</s>
            <s xml:id="echoid-s8351" xml:space="preserve"/>
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        <div xml:id="echoid-div405" type="section" level="1" n="128">
          <head xml:id="echoid-head133" style="it" xml:space="preserve">REGVLA, QVA DI AMETER EX CIRCVNFE-
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          rentia, & circumferentia ex diametro inueniatur.</head>
          <p>
            <s xml:id="echoid-s8352" xml:space="preserve">Ex eadem hac proportione circũferentiæ circuli ad eius diametrum, quam
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            nimirum habent 22. </s>
            <s xml:id="echoid-s8353" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8354" xml:space="preserve">alij ſcriptores hanc eliciunt regulam, & </s>
            <s xml:id="echoid-s8355" xml:space="preserve">multo com
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            modiorem regula noſtri auctoris, ad inquirendam diametrum ex circunferen
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            tia cognita, uel contra, ad inueniendam circunferentiam ex nota diametro.
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            </s>
            <s xml:id="echoid-s8356" xml:space="preserve">Prima pars regulæ, qua ex circunferentia cognita diameter eruitur, hæc eſt.</s>
            <s xml:id="echoid-s8357" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8358" xml:space="preserve">
              <emph style="sc">Dividatvr</emph>
            circunferentia per 3 {7/1}. </s>
            <s xml:id="echoid-s8359" xml:space="preserve">nimirum per denominatorem
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              <note position="left" xlink:label="note-242-01" xlink:href="note-242-01a" xml:space="preserve">Diameter
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              circuli quo
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              pacto ex cir
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              cunferentia
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              nota elicia-
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              @ut.</note>
            proportionis triplæ ſeſquiſeptimæ, quam habere diximus, ſecundum Ar
              <unsure/>
            chime
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            dem, circunferentiam ad diamet@ũ. </s>
            <s xml:id="echoid-s8360" xml:space="preserve">Numerus enim in tali diuiſione exiens erit
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            diameter circuli. </s>
            <s xml:id="echoid-s8361" xml:space="preserve">Vt ſi circũferentia alicuius circuli cõtinens. </s>
            <s xml:id="echoid-s8362" xml:space="preserve">palmos 1540. </s>
            <s xml:id="echoid-s8363" xml:space="preserve">di-
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            uidatur per 3 {1/7}. </s>
            <s xml:id="echoid-s8364" xml:space="preserve">prodibunt palmi 490 pro magnitudine diametri. </s>
            <s xml:id="echoid-s8365" xml:space="preserve">Quæ regula
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            ita quoque proponi poteſt. </s>
            <s xml:id="echoid-s8366" xml:space="preserve">Multipliciter circũferentia per 7. </s>
            <s xml:id="echoid-s8367" xml:space="preserve">productusq́. </s>
            <s xml:id="echoid-s8368" xml:space="preserve">nu-
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            merus diuidatur per 22. </s>
            <s xml:id="echoid-s8369" xml:space="preserve">inuenieturq́ue diameter. </s>
            <s xml:id="echoid-s8370" xml:space="preserve">Quoniam enim, quæ propor
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            tio eſt 22. </s>
            <s xml:id="echoid-s8371" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8372" xml:space="preserve">ea eſt circunferentiæ cuiuſl bet circuli ad diametrum, ut Archi
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            medes demonſtrauit: </s>
            <s xml:id="echoid-s8373" xml:space="preserve">fit, ut ſi circunferentia, hoceſt, tertius numerus regulæ
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            proportionum, multiplicetur per 7. </s>
            <s xml:id="echoid-s8374" xml:space="preserve">nempe per ſecundum numerum eiuſdẽ re
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            gulæ, productusq́ numerus per primum numerum, ideſt, per 22. </s>
            <s xml:id="echoid-s8375" xml:space="preserve">diuidatur, pro
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            quarto numero regulæ proportionũ reperiatur diameter. </s>
            <s xml:id="echoid-s8376" xml:space="preserve">Vt in proximo exem
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            plo, ſi circunferentia 1540. </s>
            <s xml:id="echoid-s8377" xml:space="preserve">multiplicetur per 7. </s>
            <s xml:id="echoid-s8378" xml:space="preserve">productusq́ numerus per 22.
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            </s>
            <s xml:id="echoid-s8379" xml:space="preserve">diuidatur, reperietur diameter 490. </s>
            <s xml:id="echoid-s8380" xml:space="preserve">ut prius. </s>
            <s xml:id="echoid-s8381" xml:space="preserve">Hac ratione, ſi ambitum terræ ſe-
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            cundum Eratoſthenem, nempe ſtadia 252000. </s>
            <s xml:id="echoid-s8382" xml:space="preserve">multiplicemus per 7 producen
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            tur 1764000. </s>
            <s xml:id="echoid-s8383" xml:space="preserve">quibus d@uiſis per 22. </s>
            <s xml:id="echoid-s8384" xml:space="preserve">prodibunt 80181. </s>
            <s xml:id="echoid-s8385" xml:space="preserve">& </s>
            <s xml:id="echoid-s8386" xml:space="preserve">{18/22}. </s>
            <s xml:id="echoid-s8387" xml:space="preserve">hoc eſt {9/11}. </s>
            <s xml:id="echoid-s8388" xml:space="preserve">pro
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            diametro terræ, ſicuti prius iuxta auctoris regulam. </s>
            <s xml:id="echoid-s8389" xml:space="preserve">Poſterior autem regulæ
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            pars, qua ex diametro nota viciſſim circunferentia elicitur, ita ſe habet.</s>
            <s xml:id="echoid-s8390" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8391" xml:space="preserve">
              <emph style="sc">Mvltiplicetvr</emph>
            diameter per 3 {1/7}. </s>
            <s xml:id="echoid-s8392" xml:space="preserve">nempe per denominatorem
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              <note position="left" xlink:label="note-242-02" xlink:href="note-242-02a" xml:space="preserve">Circunferẽ-
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              tia circuli
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              quo pacto
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              ex diame-
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              tro nota in-
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              ueniatur.</note>
            proportionis triplæ ſeſquiſeptimæ, quàm ſecundum Archimedem, circũferen-
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            tia habet ad diametrum. </s>
            <s xml:id="echoid-s8393" xml:space="preserve">Productus namque numerus indicabit illico circunfe
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            rentiam. </s>
            <s xml:id="echoid-s8394" xml:space="preserve">Vt ſi diameter alicuius circuli habens palmos 490. </s>
            <s xml:id="echoid-s8395" xml:space="preserve">multiplicetur per
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            3 {1/7}. </s>
            <s xml:id="echoid-s8396" xml:space="preserve">inuenietur circunferentia palmorum 1540. </s>
            <s xml:id="echoid-s8397" xml:space="preserve">Quæ etiam regula hoc modo
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            proponi poteſt. </s>
            <s xml:id="echoid-s8398" xml:space="preserve">Multiplicetur diameter per 22. </s>
            <s xml:id="echoid-s8399" xml:space="preserve">productusq́ue numerus per 7.
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            </s>
            <s xml:id="echoid-s8400" xml:space="preserve">diuidatur, prouenietq́. </s>
            <s xml:id="echoid-s8401" xml:space="preserve">quantitas circunferentiæ. </s>
            <s xml:id="echoid-s8402" xml:space="preserve">Quoniam enim, ut ab Archi
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            mede demonſtratũ eſt, quæ proportio eſt 22. </s>
            <s xml:id="echoid-s8403" xml:space="preserve">ad 7. </s>
            <s xml:id="echoid-s8404" xml:space="preserve">ea eſt circunferentiæ </s>
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