Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <pb pagenum="429" xlink:href="026/01/463.jpg"/>
            <p id="N29DF4" type="main">
              <s id="N29DF6">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              20.
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              </s>
            </p>
            <p id="N29E02" type="main">
              <s id="N29E04">
                <emph type="italics"/>
              Sectoris minoris quadrante determinari poteſt centrum percuſſionis, cum
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              ſcilicet voluitur in plano, cui eiuſdem planum eſt parallelum
                <emph.end type="italics"/>
              ; </s>
              <s id="N29E0F">ſit enim
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              quadrans BAI; </s>
              <s id="N29E15">ducatur BI, ſit pyramis cuius baſis ſit ſectio cylindri,
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              erectis, ſcilicet perpendicularibus tranſuerſis ſupra arcum BTI, eo
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              modo, quo ſuprà iam ſæpè diximus; </s>
              <s id="N29E1D">v.g. ducta ſit Tangens ZT, diuiſa bi­
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              fariam in C, puncto ſcilicet contactus, quæ tandiu voluatur circa CA,
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              dum ſecet arcum ad angulos rectos: </s>
              <s id="N29E27">idem fiat in alijs punctis arcus; </s>
              <s id="N29E2B">de­
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              nique ad extremitates Tangentium ducantur vtrimque à centro A rectæ,
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              & habebitur prædicta pyramis mixta, cuius centrum grauitatis inuen­
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              tum dabit centrum percuſſionis; </s>
              <s id="N29E35">quod vt meliùs oculo ſubijciatur, ſit
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              triangulum ZTA, voluatur circa CA, donec eius planum ſecet ad an­
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              gulos iectos planum quadrantis BAI; </s>
              <s id="N29E3D">tùm in eo ſitu voluatur axis AC
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              per totum arcum BI, & habebitur ſolidum quæſitum, cuius centrum gra­
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              uitatis ita poteſt inueniri; </s>
              <s id="N29E45">ducatur BI, tùm AC diuidens BI bifariam
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              in E, centrum grauitatis eſt in AC; </s>
              <s id="N29E4D">aſſumatur GE 1/4 totius AE; </s>
              <s id="N29E51">certè G
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              eſt centrum grauitatis pyramidis ABEI; </s>
              <s id="N29E57">ſit autem D centrum grauitatis
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              reliqui ſolidi BEIC, ſitque vt hoc ſolidum ad pyramidem ABEI, ita
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              GF ad FD: dico F eſſe centrum grauitatis per p. </s>
              <s id="N29E5F">7. ducatur FK perpen­
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              dicularis in AC, K eſt centrum percuſſionis per Th.17. </s>
            </p>
            <p id="N29E65" type="main">
              <s id="N29E67">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N29E73" type="main">
              <s id="N29E75">Colligo primò; </s>
              <s id="N29E78">prædictam pyramidem mixtam eſſ 2/3 ſectoris cylindrj; </s>
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              ſit enim triangulum ACZ erectum, atque îta voluatur per totam pe­
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              ripheram IBPVI. fiet ſolidum cauum, cuius cauitas erit conus, cuius
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              altitudo erit CZ, & baſis orbis BPVI; </s>
              <s id="N29E85">ſed hic conus eſt 1/3 cylindri, ſub
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              eadem baſi, & altitudine; </s>
              <s id="N29E8B">igitur ſolidum, quod ſupereſt, continet 2/3 cy­
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              lindri ſub altitudine CZ, & baſi BPVI; </s>
              <s id="N29E91">ſed cauum BAI de quo ſuprà
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              eſt 1/3 totius; igitur reliquum continet 2/3 ſectoris cylindri BA, ſub alti­
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              tudine CT. </s>
            </p>
            <p id="N29E99" type="main">
              <s id="N29E9B">Secundò colligo, ſi aſſumatur ſemicirculus PBI momentum quadran­
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              tis PBA, æquale eſſe momento quadrantis IA
                <foreign lang="grc">β</foreign>
              , vt conſtat; nam I, per
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              IM, idem præſtat quod P, per PQ, & S per SR, idem quod L,
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              per LV, &c. </s>
            </p>
            <p id="N29EA9" type="main">
              <s id="N29EAB">Tertiò, ſi voluatur tantùm triangulum ABI, ducaturque GX per­
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              pendicularis in AC punctum X erit centrum percuſſionis; quid mirum
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              igitur, ſi addito ſegmento BCIE, ſit in K? </s>
            </p>
            <p id="N29EB3" type="main">
              <s id="N29EB5">Quartò, ſi quadrans AI
                <foreign lang="grc">β</foreign>
              trahat deorſum adducto filo ex K, certè in
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              K erit centrum percuſſionis, vt conſtat. </s>
            </p>
            <p id="N29EBE" type="main">
              <s id="N29EC0">Quintò, ſi vterque quadrans BI
                <foreign lang="grc">β</foreign>
              A ſimul cadat, centrum percuſſio­
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              nis erit in K, ſed duplò maior ictus. </s>
            </p>
            <p id="N29EC9" type="main">
              <s id="N29ECB">Sexto, ſi ſemicirculus APBI cadar, centrum etiam percuſſionis erit
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              in K, quia quadrans PBA æquiualet quadranti A
                <foreign lang="grc">β</foreign>
              I. </s>
            </p>
            <p id="N29ED5" type="main">
              <s id="N29ED7">Septimò, ſi aſſumatur ſector maior quadrante, ſed minor ſemicirculo,
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              v.g. ASBI, ſit BAC æqualis BAS; </s>
              <s id="N29EDF">inueniatur centrum grauitatis BA </s>
            </p>
          </chap>
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