Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

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          <chap id="N24CC8">
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            <p id="N24D65" type="main">
              <s id="N24D67">
                <emph type="center"/>
                <emph type="italics"/>
              Axioma
                <emph.end type="italics"/>
              1.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24D74" type="main">
              <s id="N24D76">
                <emph type="italics"/>
              Illa partes mouentur velociùs, quæ tempore aquali maius ſpatium acquirunt
                <lb/>
              tardiùs verò, que minus ſpatium, clariſſimum eſt, nec maiori indiget expli­
                <lb/>
              catione.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N24D82" type="main">
              <s id="N24D84">
                <emph type="center"/>
                <emph type="italics"/>
              Axioma
                <emph.end type="italics"/>
              2.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24D91" type="main">
              <s id="N24D93">
                <emph type="italics"/>
              Cum vtraque determinatio motus ad
                <expan abbr="eãdem">eandem</expan>
              partem ſpectat, acquiritur
                <lb/>
              maius ſpatium; </s>
              <s id="N24D9F">tum verò ad diuerſas partes minus, at que ita prorata
                <emph.end type="italics"/>
              ; hoc
                <lb/>
              etiam Axioma certum eſt. </s>
            </p>
            <p id="N24DA8" type="main">
              <s id="N24DAA">
                <emph type="center"/>
                <emph type="italics"/>
              Hypotheſis.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24DB6" type="main">
              <s id="N24DB8">
                <emph type="italics"/>
              Rotæ circa idem centrum mobilis ſemicirculi oppoſiti in partes contrarias
                <lb/>
              feruntur, motu ſcilicet orbis per arcus ſcilicet æquales
                <emph.end type="italics"/>
              ; </s>
              <s id="N24DC7">nam anguli oppoſiti
                <lb/>
              æquales ſunt; ſed arcus ſunt vt anguli. </s>
            </p>
            <p id="N24DCD" type="main">
              <s id="N24DCF">
                <emph type="center"/>
                <emph type="italics"/>
              Poſtulatum.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24DDB" type="main">
              <s id="N24DDD">
                <emph type="italics"/>
              Liceat rotare orbem in plana ſuperficie, in conuexa, in concaua, in æquali. </s>
              <s id="N24DE4">
                <lb/>
              inæquali, ita vt motus orbis conueniat cum motu centri, vel ab eo diuerſus ſit.
                <emph.end type="italics"/>
              </s>
            </p>
            <p id="N24DEA" type="main">
              <s id="N24DEC">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              1.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24DF9" type="main">
              <s id="N24DFB">
                <emph type="italics"/>
              Rota, quæ mouetur in ſuperficie plana, mouetur motu mixto ex recto centri
                <lb/>
              & circulari orbis
                <emph.end type="italics"/>
              ; </s>
              <s id="N24E0A">ſit enim AQLZ incubans plano AD in quo rotatur,
                <lb/>
              ſitque AD recta æqualis arcui
                <expan abbr="Aq;">Aque</expan>
              certè poſito quod motus orbis ſit æ­
                <lb/>
              qualis motui centri, id eſt poſito quod æqualibus temporibus ſegmentum
                <lb/>
              plani percurratur motu centri v.g. QE vel AD æquale arcui, qui circa
                <lb/>
              centrum O conuoluitur motu orbis, v.g. arcui AQ, quodlibet punctum
                <lb/>
              peripheriæ rotæ mouebitur motu mixto ex recto, & circulari v. g. pun­
                <lb/>
              ctum L motu centri fertur verſus V & motu orbis verſus Q; ſi enim
                <lb/>
              eſſet tantum motus centri verſus E, omnes partes mouerentur motu recto
                <lb/>
              v.g. L per rectam LV, A per rectam AD; </s>
              <s id="N24E30">ſi verò eſſet tantùm motus
                <lb/>
              orbis, omnes partes mouerentur tantùm motu circulari v. g. L, per ar­
                <lb/>
              cum LZ; A per arcum AZ; </s>
              <s id="N24E3C">at cum ſimul ſit vterque motus, id eſt vtraque
                <lb/>
              determinatio, certè vtraque confert de ſuo; igitur eſt motus mixtus. </s>
            </p>
            <p id="N24E42" type="main">
              <s id="N24E44">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              2.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24E51" type="main">
              <s id="N24E53">
                <emph type="italics"/>
              Vnicum tantùm punctum rotæ mouetur metu recto, ſcilicet centrum, cætera
                <lb/>
              per lineam curuam
                <emph.end type="italics"/>
              ; </s>
              <s id="N24E60">de centro conſtat, quia cùm ſemper æqualiter diſter
                <lb/>
              à planis AD & LV, ſcilicet eodem radio OL, ON; </s>
              <s id="N24E66">certè percurrit OE
                <lb/>
              parallelam vtrique; ſed parallela vtrique eſt recta, punctum verò L mo­
                <lb/>
              uetur per lineam curuam, vt conſtabit ex illius deſcriptione, quàm tra­
                <lb/>
              demus infrà. </s>
            </p>
            <p id="N24E72" type="main">
              <s id="N24E74">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              4.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24E81" type="main">
              <s id="N24E83">
                <emph type="italics"/>
              Si diuidatur arcus LQ in tres arcus aquales & planum AD in tres par­
                <lb/>
              tes æquales, poteſt aſſignari punctum, in quo ſit L decurſo prime arcu LK
                <emph.end type="italics"/>
              ; </s>
              <s id="N24E92">ſi
                <lb/>
              enim eſſet tantùm
                <expan abbr="coętri">centri</expan>
              , eſſet in
                <foreign lang="grc">μ</foreign>
              , ſi motus orbis eſſet in K; </s>
              <s id="N24E9C">igitur
                <lb/>
              ſit recta MI parallela LV, ſitque KI æqualis AB, vel L
                <foreign lang="grc">μ</foreign>
              ; </s>
              <s id="N24EA6">haud dubiè erit </s>
            </p>
          </chap>
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    </archimedes>
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