Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

Table of contents

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[121.] COMMENTARIVS.
[122.] COMMENTARIVS.
[123.] DE AMBITV TERRAE.
[124.] COMMENTARIVS.
[125.] COMMENTARIVS.
[126.] VIÆ AD INVESTIGANDVM AMBITVM TERRÆ commodiores, quàm ea, quæ ab auctore tradita eſt.
[127.] COMMENTARIVS.
[128.] REGVLA, QVA DI AMETER EX CIRCVNFE-rentia, & circumferentia ex diametro inueniatur.
[129.] REGVLAE, QVIBVSET SVPERFICIES MA-ximi circuli in orbe terreno, uel etiam in quacunque ſphæra, & ſuperficies conuexa eiuſdem orbis terreni, uel etiam cuiuſque ſpære, immo, & tota ſoliditas inueniatur.
[130.] DE VARIIS MENSVRIS Mathematicorum.
[131.] VARIÆ SENTENTIÆ AVCTORVM in ambitu terræ præfiniendo.
[132.] DISTANTIÆ COELORVM A TERRA, craſſitudinesq́ue, & Ambitus eorundem.
[133.] DIGRESSIO DE ARENAE NVMERO.
[134.] PRIMI CAPITIS FINIS.
[135.] CAPVT SECVNDVM DE CIRCVLIS, EX QVIBVS SPHAERA materialis componitur, & illa ſupercæleſtis, quæ per iſtam repræſentatur, componi intelligitur.
[136.] COMMENTARIVS.
[138.] II.
[139.] III.
[140.] IIII.
[142.] VI.
[143.] VII.
[144.] VIII.
[145.] IX.
[146.] DE AEQVINOCTI ALI CIRCVLO.
[147.] COMMENTARIS.
[148.] COMMENTARIVS.
[149.] COMMENTARIVS.
[150.] OFFICIA ÆQVINOCTIALIS CIRCVLI. I.
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          <p>
            <s xml:id="echoid-s4529" xml:space="preserve">
              <pb o="93" file="129" n="130" rhead="Ioan. de Sacro Boſco."/>
            vna linea, deſcripto. </s>
            <s xml:id="echoid-s4530" xml:space="preserve">& </s>
            <s xml:id="echoid-s4531" xml:space="preserve">quadrato ex K M, M H, tanquam ex una linea deſcri-
              <lb/>
            pto, hoc eſt, quadrato K H, vtriuſque ſimul. </s>
            <s xml:id="echoid-s4532" xml:space="preserve">Ablato ergo communi quadrato
              <lb/>
            K H, erit quadratum ex F K, G H, tanquam ex una linea, deſcriptum maius
              <lb/>
            quadrato ex B K, D H, tanquam ex una linea, deſcripto; </s>
            <s xml:id="echoid-s4533" xml:space="preserve">ideòque maiores e-
              <lb/>
            runt rectæ linea F K, G H, ſimul rectis B K, D H, ſimnl: </s>
            <s xml:id="echoid-s4534" xml:space="preserve">Ac propterea, demptis
              <lb/>
            communibus B K, G H, erit F B, reliqua maior quàm reliqua D G. </s>
            <s xml:id="echoid-s4535" xml:space="preserve">Eſt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">K C, maior quàm H C, eò quòd tota A C, cuius dimidium eſt K C, maior
              <lb/>
            ponitur, quam tota C E,
              <lb/>
              <figure xlink:label="fig-129-01" xlink:href="fig-129-01a" number="31">
                <image file="129-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/129-01"/>
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            cuius dimidium eſt H C.
              <lb/>
            </s>
            <s xml:id="echoid-s4537" xml:space="preserve">Qua propter rectangulũ
              <lb/>
            ſub F B, K C, contentum,
              <lb/>
            maius erit rectangulo
              <lb/>
            ſub D G, H C, contẽto. </s>
            <s xml:id="echoid-s4538" xml:space="preserve">
              <lb/>
            Et quoniam triangulum
              <lb/>
            F B C, dimidium eſt re,
              <lb/>
            ctanguli ſub F B, K C, con
              <lb/>
            tenti; </s>
            <s xml:id="echoid-s4539" xml:space="preserve">(Nam ſi ſuper F B,
              <lb/>
            conſtituatur rectangu--
              <lb/>
            lum altitudinem habens
              <lb/>
            K C, ita ut triangulum,
              <lb/>
            & </s>
            <s xml:id="echoid-s4540" xml:space="preserve">rectangulum inter eaſ-
              <lb/>
            dem ſint parallelas; </s>
            <s xml:id="echoid-s4541" xml:space="preserve">erit
              <lb/>
              <note position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">41. primi.</note>
            triangulum parallelo--
              <lb/>
            grammi dimidium. </s>
            <s xml:id="echoid-s4542" xml:space="preserve">quod
              <lb/>
            quidem parallelogram-
              <lb/>
            mum idem eſt, quod re-
              <lb/>
            ctangulum ſub F B, K C,
              <lb/>
            contentum, ut conſtat.
              <lb/>
            </s>
            <s xml:id="echoid-s4543" xml:space="preserve">Triangulum uero D G C, dimidium eſt rectanguli contenti ſub, D G, H C; </s>
            <s xml:id="echoid-s4544" xml:space="preserve">(ſi
              <lb/>
            enim ſuper D G, conſtituatur rectangulum altitudinem habens H C, ita vt
              <lb/>
            triangulum, & </s>
            <s xml:id="echoid-s4545" xml:space="preserve">rectangulum inter eaſdem ſint parallelas; </s>
            <s xml:id="echoid-s4546" xml:space="preserve">erit triangulum pa-
              <lb/>
            rallelogrammi dimidium. </s>
            <s xml:id="echoid-s4547" xml:space="preserve">quod quidem parallelogrammum idem eſt, quod
              <lb/>
              <note position="right" xlink:label="note-129-02" xlink:href="note-129-02a" xml:space="preserve">41. primi.</note>
            rectangulum ſub D H, H C, contentum, ut conſtat. </s>
            <s xml:id="echoid-s4548" xml:space="preserve">(erit quoque triangulum
              <lb/>
            FBC, maius triangulo D G C, ac propterea duplum trianguli F B C, nimirũ
              <lb/>
            rectilineum A F C B A, maius erit duplo trianguli D G C, ut pote rectilineo
              <lb/>
            erunt triangula A F C, C G E, utraque ſimul maiora triangulis A B C, C D E,
              <lb/>
            utriuſque ſimul. </s>
            <s xml:id="echoid-s4549" xml:space="preserve">Duo ergo triangula Iſoſcelia ſimilia ſuper inæqualibus baſi-
              <lb/>
            bus conſtituta, &</s>
            <s xml:id="echoid-s4550" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4551" xml:space="preserve">quod oſtendendum erat.</s>
            <s xml:id="echoid-s4552" xml:space="preserve"/>
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        <div xml:id="echoid-div247" type="section" level="1" n="85">
          <head xml:id="echoid-head89" style="it" xml:space="preserve">THEOR. 10. PROPOS. 52</head>
          <note position="right" xml:space="preserve">Inter Iſope-
            <lb/>
          rimetras fi-
            <lb/>
          guras ęqua-
            <lb/>
          lia numero
            <lb/>
          habentes la
            <lb/>
          tera maxi-
            <lb/>
          ma & æqui
            <lb/>
          latera eſt,
            <lb/>
          & æquian-
            <lb/>
          gula.</note>
          <p style="it">
            <s xml:id="echoid-s4553" xml:space="preserve">ISOPERIMETR ARVM figur arum latera numero ęqualia ha-
              <lb/>
            bentium maxima & </s>
            <s xml:id="echoid-s4554" xml:space="preserve">æqualiter eſt, & </s>
            <s xml:id="echoid-s4555" xml:space="preserve">æquiangula.</s>
            <s xml:id="echoid-s4556" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4557" xml:space="preserve">
              <emph style="sc">Esto</emph>
            figura quotcunq; </s>
            <s xml:id="echoid-s4558" xml:space="preserve">laterum ABCDEF, maxima inter omnes totidem
              <lb/>
            laterum ſibi iſoperimetras; </s>
            <s xml:id="echoid-s4559" xml:space="preserve">ita ut maior dari non poſſit. </s>
            <s xml:id="echoid-s4560" xml:space="preserve">Dico eam eſſe æquila-
              <lb/>
            terã, & </s>
            <s xml:id="echoid-s4561" xml:space="preserve">æquiãgulã. </s>
            <s xml:id="echoid-s4562" xml:space="preserve">Sit enim, ſi fieri poteſt, primũ nõ æquilatera, ſed ſint </s>
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