Fabri, Honoré, Tractatus physicus de motu locali, 1646

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          <chap id="N22A20">
            <pb pagenum="319" xlink:href="026/01/353.jpg"/>
            <p id="N23FBC" type="main">
              <s id="N23FBE">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23FCA" type="main">
              <s id="N23FCC">Hinc manifeſta ratio, cur funependulum poſt vibrationem deſcenſus
                <lb/>
              non perueniat in aſcenſu ad tantam altitudinem; </s>
              <s id="N23FD2">nec eſt quod aliqui di­
                <lb/>
              cant aëra interceptum efficere, ne ad æqualem altitudinem aſcendat,
                <lb/>
              cùm aër non minùs reſiſtat deſcenſui, quàm aſcenſui; quod quomodo
                <lb/>
              fiat, iam alibi explicuimus. </s>
            </p>
            <p id="N23FDC" type="main">
              <s id="N23FDE">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              20.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23FEA" type="main">
              <s id="N23FEC">
                <emph type="italics"/>
              Maioris vibrationis aſcenſus imminuitur in maiori proportione, quàm mi­
                <lb/>
              noris
                <emph.end type="italics"/>
              ; </s>
              <s id="N23FF7">certa experientia, cuius ratio eſt, quia in arcu ſuperiore plùs im­
                <lb/>
              petus deſtruitur, in inferiore minùs; </s>
              <s id="N23FFD">igitur plùs ſpatij detrahitur maiori
                <lb/>
              vibrationi, quàm minori, ſcilicet in aſcenſu; </s>
              <s id="N24003">hæc ratio demonſtratiua eſt,
                <lb/>
              quia quò minùs impetus deſtruitur ſingulis inſtantibus, plùs ſpatij ac­
                <lb/>
              quiritur, vt conſtat ex planis inclinatis; </s>
              <s id="N2400B">ſit enim in eadem figura pla­
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              num inclinatum DO, & verticale DA; </s>
              <s id="N24011">imprimatur impetus mobili ex D,
                <lb/>
              certè cum eodem impetu aſcendet per DA & per DO, vt demonſtraui­
                <lb/>
              mus cum de planis inclinatis; </s>
              <s id="N24019">igitur ſingulis inſtantibus minùs impetus
                <lb/>
              in DO deſtruitur, quàm in DA; </s>
              <s id="N2401F">vnde maius ſpatium conficitur; </s>
              <s id="N24023">eſt enim
                <lb/>
              DO maior DA: </s>
              <s id="N24029">ita prorſus accidit in arcu aſcenſus funependuli; </s>
              <s id="N2402D">ſit enim
                <lb/>
              arcus aſcenſus DH æqualis arcui deſcenſus oppoſiti; </s>
              <s id="N24033">certè tantillùm im­
                <lb/>
              petus deſtruetur; </s>
              <s id="N24039">igitur arcus aſcenſus ferè accedet ad A; </s>
              <s id="N2403D">ſi vetò arcus
                <lb/>
              deſcenſus ſit æqualis DL, plùs impetus deſtruetur in aſcenſu; igitur ar­
                <lb/>
              cus aſcenſus habebit minorem proportionem ad DL, quàm prior ad DH,
                <lb/>
              & hæc eſt veriſſima ratio luculentiſſimi experimenti, quod ferè omnibus
                <lb/>
              notum eſt. </s>
            </p>
            <p id="N24049" type="main">
              <s id="N2404B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              21.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N24057" type="main">
              <s id="N24059">
                <emph type="italics"/>
              Si proijciatur mobile per ipſum perpendiculum DA cum eo impetu, quo
                <lb/>
              ex D feratur in A motu naturaliter retardato; </s>
              <s id="N24061">certè cum eodem impetu fere­
                <lb/>
              tur in O per DO, & per arcum DLO:
                <emph.end type="italics"/>
              probatur quia ex A in D, vel ex O
                <lb/>
              in D ſiue per chordam OD, ſiue per arcum OHD æqualis impetus ac­
                <lb/>
              quiritur per Lemma 11. ſed cum eodem impetu, quo ex A fertur in D.
                <lb/>
              vel ex O in D motu naturaliter accelerato, ex D ferri poteſt in A vel in
                <lb/>
              O: </s>
              <s id="N24072">dixi cum eodem impetu, ita vt tot gradus impetus concurrant ad aſ­
                <lb/>
              cenſum, quot ad deſcenſum; </s>
              <s id="N24078">ſi enim aliquis gradus concurrens ad deſ­
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              cenſum, non concurreret ad aſcenſum; </s>
              <s id="N2407E">haud dubiè non perueniret mo­
                <lb/>
              bile ad
                <expan abbr="eãdem">eandem</expan>
              altitudinem; quod autem æquale ſpatium reſpondeat
                <lb/>
              aſcenſui, & deſcenſui ſuppoſito æquali impetu, iam demonſtratum eſt ſu­
                <lb/>
              prà l. 3. & 5. ſed iam examinandæ ſunt proportiones huius deſtructio­
                <lb/>
              nis impetus in maioribus, & minoribus vibrationibus. </s>
            </p>
            <p id="N24090" type="main">
              <s id="N24092">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              22.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2409E" type="main">
              <s id="N240A0">
                <emph type="italics"/>
              Poteſt determinari in qua parte arcus deſinat motus ſurſum in aſcenſu
                <lb/>
              vibrationis, ſi cognoſcatur ad quam altitudinem ferretur mobile per ipſum
                <lb/>
              perpendiculum
                <emph.end type="italics"/>
              ; </s>
              <s id="N240AD">fit cum punctum infimum D, ſitque in pendule ille impe­
                <lb/>
              tus, haud dubiè per arcum ferretur in
                <foreign lang="grc">α</foreign>
              , ducatur
                <foreign lang="grc">α</foreign>
              Q parallela AO; </s>
              <s id="N240B7">haud </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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