Fabri, Honoré, Tractatus physicus de motu locali, 1646

Page concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1137F">
            <pb pagenum="42" xlink:href="026/01/074.jpg"/>
            <p id="N13BA6" type="main">
              <s id="N13BA8">
                <emph type="center"/>
                <emph type="italics"/>
              Corollarium
                <emph.end type="italics"/>
              5.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N13BB5" type="main">
              <s id="N13BB7">Ex dictis etiam colliges diuerſas percuſſionum rationes ſuppoſita di­
                <lb/>
              uerſa ratione ponderum globi percutientis, & percuſſi; </s>
              <s id="N13BBD">cum enim impe­
                <lb/>
              tus productus ſit æqualis per ſe impetui producenti, per Th.60. modò
                <lb/>
              debita fiat applicatio, de qua in Th.50. ſi percutiens ſit duplus percuſſi,
                <lb/>
              ſuppoſita eadem materia, motus percuſſi erit duplò velocior; quia im­
                <lb/>
              petus erit duplò intenſior, vt conſtat ex Th. 61. ſi verò ſit quadruplus,
                <lb/>
              quadruplo, &c. </s>
              <s id="N13BCB">Igitur velocitates motuum ſunt in ratiòne ponderum
                <lb/>
              permutando. </s>
            </p>
            <p id="N13BD0" type="main">
              <s id="N13BD2">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              68.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N13BDE" type="main">
              <s id="N13BE0">
                <emph type="italics"/>
              Si corpus percuſſum ſit oblongum, & percuſſio fiat in centro grauitatis eiuſ­
                <lb/>
              dem corporis; </s>
              <s id="N13BE8">producitur impetus in percuſſio æqualis impetui percutientis
                <emph.end type="italics"/>
              ; </s>
              <s id="N13BEF">ſed
                <lb/>
              opus eſt aliqua figura: </s>
              <s id="N13BF5">Sit corpus AD, parallelipedum; </s>
              <s id="N13BF9">diuidatur æqua­
                <lb/>
              liter in E ita vt E ſit centrum grauitatis; </s>
              <s id="N13BFF">ſi percuſſio fiatin E per lineam
                <lb/>
              perpendicularem HE, producetur impetus in corpore AD æqualis im­
                <lb/>
              petui corporis percutientis; </s>
              <s id="N13C07">quia ſcilicet à corpore AD non poteſt maius
                <lb/>
              eſſe impedimentum; igitur agit quantùm poteſt impetus corporis per­
                <lb/>
              cutientis per Th.50. igitur producit æqualem per Th.69. </s>
            </p>
            <p id="N13C0F" type="main">
              <s id="N13C11">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              69.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N13C1D" type="main">
              <s id="N13C1F">
                <emph type="italics"/>
              Si percuſſio fiat in
                <emph.end type="italics"/>
              F
                <emph type="italics"/>
              per lineam perpendicularem
                <emph.end type="italics"/>
              IF,
                <emph type="italics"/>
              minus erit impedi­
                <lb/>
              mentum, quàm per
                <emph.end type="italics"/>
              HE, Quia ſi per HE, moueri tantùm poteſt motu
                <lb/>
              recto, ſi per IF, etiam motu circulari circa aliquod centrum; </s>
              <s id="N13C38">ſed hic
                <lb/>
              motus eſt facilior quam ille; </s>
              <s id="N13C3E">igitur minus eſt impedimentum; </s>
              <s id="N13C42">(ſuppono
                <lb/>
              autem cylindrum BC vtroque modo moueri poſſe ab applicata potentia)
                <lb/>
              igitur minùs impetus producitur, ſi percuſſio fiat per IF, quàm ſi fiat
                <lb/>
              per LK: </s>
              <s id="N13C4C">In qua verò proportione ſit minus impedimentum, & minori
                <lb/>
              opus impetu, poſito eodem potentiæ niſu, determinabimus facilè aliàs;
                <lb/>
              vt etiam demonſtrabimus circa quod centrum hic circularis motus fieri
                <lb/>
              debeat. </s>
            </p>
            <p id="N13C56" type="main">
              <s id="N13C58">
                <emph type="center"/>
                <emph type="italics"/>
              Scholium.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N13C64" type="main">
              <s id="N13C66">Ex duobus capitibus minus eſſe poteſt impedimentum; </s>
              <s id="N13C6A">primum eſt,
                <lb/>
              quod petitur à puncto contactus, ſecundum à linea incidentiæ; </s>
              <s id="N13C70">v. g. ſi
                <lb/>
              accipiatur punctum E, in quo eſt centrum grauitatis corporis AD, & in
                <lb/>
              eo fiat percuſſio; </s>
              <s id="N13C7C">maximum eſt impedimentum ratione puncti conta­
                <lb/>
              ctus, in quo fit percuſſio; </s>
              <s id="N13C82">ſi verò percuſſio fiat per lineam perpendicu­
                <lb/>
              larem HE, maximum eſt impedimentum, ratione lineæ; </s>
              <s id="N13C88">ſi autem ex
                <lb/>
              vtroque capite ſimul accidat impedimentum, maximum eſt omnium; </s>
              <s id="N13C8E">
                <lb/>
              iam verò ſi accipiatur punctum E, & linea percuſsionis ME; </s>
              <s id="N13C93">minor eſt
                <lb/>
              percuſsio ratione lineæ non puncti; </s>
              <s id="N13C99">accipiatur punctum N, & linea
                <lb/>
              percuſsionis MN, minor eſt percuſsio ratione puncti non lineæ, acci­
                <lb/>
              piatur punctum N, & linea IN, minor eſt percuſsio ratione vtriuſque; </s>
              <s id="N13CA1">
                <lb/>
              ſi demum accipiatur punctum E, & linea ME, minor eſt percuſsio ra­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum