Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

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          <chap id="N22A20">
            <pb pagenum="305" xlink:href="026/01/339.jpg"/>
            <p id="N231BC" type="main">
              <s id="N231BE">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              10.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N231CA" type="main">
              <s id="N231CC">
                <emph type="italics"/>
              Velocitas acquiſita in duabus chordis EIB eſt æqualis acquiſitæ in EB
                <emph.end type="italics"/>
              ; </s>
              <s id="N231D5">
                <lb/>
              quia acquiſita in EI eſt æqualis acquiſitæ in GI; </s>
              <s id="N231DA">ſunt enim eiuſdem al­
                <lb/>
              titudinis; </s>
              <s id="N231E0">igitur acquiſita in EIB æqualis acquiſitæ in GB: </s>
              <s id="N231E4">ſed acqui­
                <lb/>
              ſita in GB eſt æqualis acquiſitæ in EIB; </s>
              <s id="N231EA">igitur acquiſita in EB eſt æqua­
                <lb/>
              lis acquiſitæ in EIB, itemque acquiſita in ELB acquiſitæ in EB: </s>
              <s id="N231F0">immò
                <lb/>
              acquiſita in tribus EILB eſt æqualis acquiſitæ in EB; </s>
              <s id="N231F6">quia acquiſita in
                <lb/>
              EIL eſt æqualis acquiſitæ in EL; </s>
              <s id="N231FC">igitur acquiſita in EILB æqualis
                <lb/>
              acquiſitæ in ELB: </s>
              <s id="N23202">ſed acquiſita in ELB eſt æqualis acquiſitæ in EB; igi­
                <lb/>
              tur acquiſita in EB æqualis acquiſitæ in EILB idem dico de 5. chordis,
                <lb/>
              6.7. atque ita deinceps. </s>
            </p>
            <p id="N2320B" type="main">
              <s id="N2320D">Quod certè mirabile eſt, & quaſi paradoxon; </s>
              <s id="N23211">præſertim cùm duplici
                <lb/>
              motu acquiratur æqualis velocitas in ſpatiis inæqualibus, quorum mauis
                <lb/>
              citiùs percurritur; </s>
              <s id="N23219">Equidem in AB, EB acquiritur æqualis velocitas,
                <lb/>
              vel impetus, ſed breuius ſpatium, ſcilicet AB citius percurritur; </s>
              <s id="N2321F">at verò
                <lb/>
              in EB, & ELB acquiritur æqualis velocitas; </s>
              <s id="N23225">licèt ſpatium longius ELB
                <lb/>
              percurratur citiùs, quàm EB; ſimiliter EILB velociùs, quam ELB & EB. </s>
            </p>
            <p id="N2322C" type="main">
              <s id="N2322E">Hinc ſuprà velocitas acquiſita in perpendiculari ſeu radio quadrantis
                <lb/>
              non eſt ad velocitatem acquiſitam in toto arcu quadrantis vt quadratum
                <lb/>
              ſub radio ad ipſum quadrantem, quia ſcilicet velocitas acquiſita per ar­
                <lb/>
              cum ELB eſt æqualis acquiſitæ per omnes chordas facto initio motus
                <lb/>
              ab E; ſed velocitas acquiſita in 6. chordis. </s>
              <s id="N2323A">v. g. eſt æqualis acquiſitæ in
                <lb/>
              5. 4. 3. 2. 1. igitur velocitas acquiſita in EB eſt æqualis acquiſitæ in ar­
                <lb/>
              cu ELB, & in ipſa perpendiculari ER. </s>
            </p>
            <p id="N23245" type="main">
              <s id="N23247">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              11.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23253" type="main">
              <s id="N23255">
                <emph type="italics"/>
              Hinc Lemma vniuerſaliſſimum ſtatuitur, ſcilicet ab eodem puncto altitudi­
                <lb/>
              nîs ad
                <expan abbr="eãdem">eandem</expan>
              horizontalem, vel ab eadem horizontali ad idem punctum
                <lb/>
              deorſum, vel ab eadem horizontali ad aliam horizontalem aquales acquiri
                <lb/>
              velocitates, ſiue plures ſint lineæ, ſine vnica, ſiue ſimplices, ſiue compoſitæ, ſiue
                <lb/>
              recta, ſiue curua
                <emph.end type="italics"/>
              ; quæ omnia ex Lemmate decimo manifeſta redduntur. </s>
            </p>
            <p id="N2326A" type="main">
              <s id="N2326C">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              12.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23278" type="main">
              <s id="N2327A">
                <emph type="italics"/>
              Velocitas acquiſita in toto arcu quadrantis ELB non debet aſſumi in area
                <lb/>
              tota quadrantis AEB, ſed in linea recta æquali toti arcui ELB, ductis ſci­
                <lb/>
              licet lineis rectis tranſuerſis, qua ſint ipſis ſinubus rectis æquales, cuius conſtru­
                <lb/>
              ctionis
                <emph.end type="italics"/>
              ; </s>
              <s id="N23289">ſit enim linea AN æqualis arcui quadrantis, & NT radio; </s>
              <s id="N2328D">igi­
                <lb/>
              tur totum triangulum mixtum ex rectis AN, NT, & curua TQH, eſt
                <lb/>
              velocitas acquiſita in toto arcu quadrantis; ſit autem A
                <foreign lang="grc">σ</foreign>
              æqualis lateri
                <lb/>
              quadrati inſcripti qua eſt ad AN proximè vt 10. ad 11. eſt enim AB ra­
                <lb/>
              dix quad. </s>
              <s id="N2329D">98. ſitque AE ſinus rectus quad. </s>
              <s id="N232A0">45. certè rectangulum NE
                <lb/>
              eſt velocitas acquiſita in chorda A
                <foreign lang="grc">σ</foreign>
              , ſed hæc eſt æqualis acquiſitæ in
                <lb/>
              toto arcu quadrantis AN; </s>
              <s id="N232AC">igitur rectangulum NE eſt æquale triangulo
                <lb/>
              mixto NTOA, denique velocitas acquiſita in radio A 4. æquali AF,
                <lb/>
              eſt vt quadratum 4 F, ſed quadratum 4. F eſt æquale rectangulo BE, vt
                <lb/>
              conſtat, nam A
                <foreign lang="grc">σ</foreign>
              eſt dupla AE; </s>
              <s id="N232BA">igitur rectangulum eſt ſubduplum qua-</s>
            </p>
          </chap>
        </body>
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    </archimedes>
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