Clavius, Christoph, Geometria practica

Table of handwritten notes

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[Handwritten note 45]
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          <pb o="181" file="211" n="211" rhead="LIBER QVARTVS."/>
          <p>
            <s xml:id="echoid-s7636" xml:space="preserve">POST hæc, quia eſt, vt ſinus huius anguliinuenti, nimirum ſemiſsis
              <note symbol="a" position="right" xlink:label="note-211-01" xlink:href="note-211-01a" xml:space="preserve">4. triang re-
                <lb/>
              ctil.</note>
            4338837. </s>
            <s xml:id="echoid-s7637" xml:space="preserve">lateris ex ſuperiori tabula excerpti, ad {1/2}. </s>
            <s xml:id="echoid-s7638" xml:space="preserve">ſemiſſem lateris, id eſt, ita ſi-
              <lb/>
            nus complementi eiuſdem anguliinuenti, hoc eſt, ita ſinus grad. </s>
            <s xml:id="echoid-s7639" xml:space="preserve">64. </s>
            <s xml:id="echoid-s7640" xml:space="preserve">min. </s>
            <s xml:id="echoid-s7641" xml:space="preserve">17. </s>
            <s xml:id="echoid-s7642" xml:space="preserve">ſec.
              <lb/>
            </s>
            <s xml:id="echoid-s7643" xml:space="preserve">9. </s>
            <s xml:id="echoid-s7644" xml:space="preserve">(adhibita quoque parte proportionali, propter ſecunda.) </s>
            <s xml:id="echoid-s7645" xml:space="preserve">nimirum 9011398. </s>
            <s xml:id="echoid-s7646" xml:space="preserve">
              <lb/>
            ad perpendicularem huic complemento inuenti anguli oppoſitam in triangulo
              <lb/>
            rectangulo: </s>
            <s xml:id="echoid-s7647" xml:space="preserve">Inuenta eſt hæc perpendicularis {9011398/8677678} quæ tandem ducta in {7/2}. </s>
            <s xml:id="echoid-s7648" xml:space="preserve">
              <lb/>
            ſemiſſem ambitus heptagoni produxit aream heptagoni 3 {11014442/17355348}. </s>
            <s xml:id="echoid-s7649" xml:space="preserve">velin mino-
              <lb/>
            ribus numeris 3 {5507221/3677674} At que hac eadem ratione aream cuiuſcunque figurære-
              <lb/>
            gularis latus habentis 1. </s>
            <s xml:id="echoid-s7650" xml:space="preserve">dummodo numerus laterum maior non ſit, quam 80. </s>
            <s xml:id="echoid-s7651" xml:space="preserve">
              <lb/>
            reperies: </s>
            <s xml:id="echoid-s7652" xml:space="preserve">Ex qua deinde aream ſimilis figuræ latus habentis maius, quam 1. </s>
            <s xml:id="echoid-s7653" xml:space="preserve">per
              <lb/>
            regulam Num. </s>
            <s xml:id="echoid-s7654" xml:space="preserve">5. </s>
            <s xml:id="echoid-s7655" xml:space="preserve">vel 6. </s>
            <s xml:id="echoid-s7656" xml:space="preserve">traditam elicies.</s>
            <s xml:id="echoid-s7657" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7658" xml:space="preserve">
              <emph style="sc">Eodem</emph>
            tamen artificio hoc Num. </s>
            <s xml:id="echoid-s7659" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7660" xml:space="preserve">expoſito aream cuiuſuis figuræ regu-
              <lb/>
            laris, etiamſi latus habeat maius, quam 1. </s>
            <s xml:id="echoid-s7661" xml:space="preserve">(ſi placet) colligere licebit, quamuis
              <lb/>
            non reperiatur prius area figuræ ſimilis, cuius latus ſit 1. </s>
            <s xml:id="echoid-s7662" xml:space="preserve">ſi nimirum loco {1/2}. </s>
            <s xml:id="echoid-s7663" xml:space="preserve">ſemiſ-
              <lb/>
            ſis lateris 1. </s>
            <s xml:id="echoid-s7664" xml:space="preserve">accipiatur ſemiſsis lateris dati, quod maius ſit quam 1. </s>
            <s xml:id="echoid-s7665" xml:space="preserve">vt perſpicuum
              <lb/>
            eſt.</s>
            <s xml:id="echoid-s7666" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7667" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7668" xml:space="preserve">Cognita area figuræ regularis, cuius numerus laterum maior non ſit, quã
              <lb/>
              <note position="right" xlink:label="note-211-02" xlink:href="note-211-02a" xml:space="preserve">Ex area co-
                <lb/>
              gnita quo pa-
                <lb/>
              cto lat{us} erua-
                <lb/>
              tur.</note>
            12. </s>
            <s xml:id="echoid-s7669" xml:space="preserve">cognoſcetur eius latus hoc modo. </s>
            <s xml:id="echoid-s7670" xml:space="preserve">Fiat vt area figuræ ſimilis latus habentis
              <lb/>
            1. </s>
            <s xml:id="echoid-s7671" xml:space="preserve">ex præce dentitabula deſumpta ad aream figuræ propoſitæ: </s>
            <s xml:id="echoid-s7672" xml:space="preserve">Ita 1. </s>
            <s xml:id="echoid-s7673" xml:space="preserve">quadratum
              <lb/>
            lateris 1. </s>
            <s xml:id="echoid-s7674" xml:space="preserve">ad aliud. </s>
            <s xml:id="echoid-s7675" xml:space="preserve">Productus enim numerus erit quadratus lateris quæſiti. </s>
            <s xml:id="echoid-s7676" xml:space="preserve">Ra-
              <lb/>
            dix ergo eius qua drata dabit latus quæſitum. </s>
            <s xml:id="echoid-s7677" xml:space="preserve">Nam ita eſt area ad aream, vt qua-
              <lb/>
            dratum lateris ad quadratum lateris; </s>
            <s xml:id="echoid-s7678" xml:space="preserve"> quod vtraque proportio ſit
              <note symbol="b" position="right" xlink:label="note-211-03" xlink:href="note-211-03a" xml:space="preserve">10. vel 20.
                <lb/>
              ſexti.</note>
            nis laterum duplicata.</s>
            <s xml:id="echoid-s7679" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7680" xml:space="preserve">
              <emph style="sc">Qvod</emph>
            ſi area cognita ſit figuræ regularis plura latera habentis, quam 12. </s>
            <s xml:id="echoid-s7681" xml:space="preserve">nõ
              <lb/>
            plura tamen, quam 80. </s>
            <s xml:id="echoid-s7682" xml:space="preserve">inuenienda primum erit area figuræ ſimilis latus habentis
              <lb/>
            1. </s>
            <s xml:id="echoid-s7683" xml:space="preserve">beneficio ſuperioris tabulæ laterum, vt Num. </s>
            <s xml:id="echoid-s7684" xml:space="preserve">7. </s>
            <s xml:id="echoid-s7685" xml:space="preserve">docuimus. </s>
            <s xml:id="echoid-s7686" xml:space="preserve">Deinde latus ex-
              <lb/>
            quirendum, vt hoc Num. </s>
            <s xml:id="echoid-s7687" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7688" xml:space="preserve">declaratum eſt. </s>
            <s xml:id="echoid-s7689" xml:space="preserve">Et ſi tabula ſuperior laterum exten-
              <lb/>
            ſa eſſet ad plura latera, inueniretur eodem modo latus figuræ plurium laterum,
              <lb/>
            quam 80. </s>
            <s xml:id="echoid-s7690" xml:space="preserve">ex eius area. </s>
            <s xml:id="echoid-s7691" xml:space="preserve">Exempli gratia. </s>
            <s xml:id="echoid-s7692" xml:space="preserve">Sit area alicuius trianguliæ quilateri 15 {3/5}.
              <lb/>
            </s>
            <s xml:id="echoid-s7693" xml:space="preserve">Et quia area æquilateritrianguli, cuiuslatus eſt 1. </s>
            <s xml:id="echoid-s7694" xml:space="preserve">inuenta eſt ſupra {13/30}. </s>
            <s xml:id="echoid-s7695" xml:space="preserve">ſi fiat vt
              <lb/>
            {13/30}. </s>
            <s xml:id="echoid-s7696" xml:space="preserve">ad aream propoſitam. </s>
            <s xml:id="echoid-s7697" xml:space="preserve">15 {3/5}. </s>
            <s xml:id="echoid-s7698" xml:space="preserve">ita 1. </s>
            <s xml:id="echoid-s7699" xml:space="preserve">quadratum lateris 1. </s>
            <s xml:id="echoid-s7700" xml:space="preserve">ad aliud, reperietur qua-
              <lb/>
            dratum lateris quæſiti 36. </s>
            <s xml:id="echoid-s7701" xml:space="preserve">cuius radix quadrata 6. </s>
            <s xml:id="echoid-s7702" xml:space="preserve">dabit latus, quod quæritur.</s>
            <s xml:id="echoid-s7703" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div483" type="section" level="1" n="176">
          <head xml:id="echoid-head182" xml:space="preserve">De dimenſione circuli ex Archimede.</head>
          <head xml:id="echoid-head183" xml:space="preserve">
            <emph style="sc">Capvt</emph>
          VI.</head>
          <p>
            <s xml:id="echoid-s7704" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7705" xml:space="preserve">VT circulum quemlibet propoſitum, eiuſq; </s>
            <s xml:id="echoid-s7706" xml:space="preserve">partes metiri poſsimus, ne-
              <lb/>
            ceſſe eſt probè noſſe, quæ Archimedes de circuli dimenſione tradidit.
              <lb/>
            </s>
            <s xml:id="echoid-s7707" xml:space="preserve">Non absre ergo erit, ſi eius libellum de circuli dimenſione acutiſsimũ
              <lb/>
            ſane, & </s>
            <s xml:id="echoid-s7708" xml:space="preserve">ſubtiliſsimum hic interſeram, tum quia breuiſsimus eſt, quippe quitri-
              <lb/>
            bus duntaxat propoſitionibus conſtet: </s>
            <s xml:id="echoid-s7709" xml:space="preserve">tum ne ſtudio ſus, vt rem tam vtilem,
              <lb/>
            atque apud omnes artifices peruulgatam intelligat, Archimedem ipſum adire
              <lb/>
            cogatur: </s>
            <s xml:id="echoid-s7710" xml:space="preserve">tum vero maximè, quod cum Archimedis ſcripta ob affectatam bre-
              <lb/>
            uitatem, ſint paulo obſcuriora, illis nos lucem aliquam allaturos ſperamus. </s>
            <s xml:id="echoid-s7711" xml:space="preserve"/>
          </p>
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