Fabri, Honoré, Tractatus physicus de motu locali, 1646

Page concordance

< >
Scan Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N15AC3">
            <pb pagenum="90" xlink:href="026/01/122.jpg"/>
            <p id="N169D1" type="main">
              <s id="N169D3">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              40.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N169DF" type="main">
              <s id="N169E1">
                <emph type="italics"/>
              Collectio ſpatiorum eſt ſumma terminorum huius progreſſionis arithmeticæ
                <emph.end type="italics"/>
              ;
                <lb/>
              </s>
              <s id="N169EB">Cùm enim ratio ſpatiorum ſit vt ratio velocitatum; </s>
              <s id="N169EF">dum ſcilicet hæc
                <lb/>
              progreſſio accipitur in inſtantibus, & ratio velocitatum vt ratio incre­
                <lb/>
              menti impetuum; vt conſtat ex dictis, & hæc ſequatur ſimplicem
                <lb/>
              progreſſionem 1. 2. 3. 4. &c. </s>
              <s id="N169F9">certè collectio ſpatiorum eſt ſumma ter­
                <lb/>
              minorum. </s>
            </p>
            <p id="N169FE" type="main">
              <s id="N16A00">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              41.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16A0C" type="main">
              <s id="N16A0E">
                <emph type="italics"/>
              Hinc cognito primo termino, & vltimo, id eſt ſpatio quod per curritur primo
                <lb/>
              inſtanti & ſpatio quod percurritur vltimo instanti, cognoſcitur ſumma, id eſt
                <lb/>
              collectio ſpatiorum, id eſt, totum ſpatium confectum.
                <emph.end type="italics"/>
              v.g.ſi primus terminus,
                <lb/>
              ſecundus S.igitur ſumma eſt 36. quippe vltimus terminus indicat nume­
                <lb/>
              rum terminorum, quia primus eſt ſemper vnitas, & progreſſiuus etiam
                <lb/>
              vnitas. </s>
            </p>
            <p id="N16A20" type="main">
              <s id="N16A22">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              42.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16A2E" type="main">
              <s id="N16A30">
                <emph type="italics"/>
              Hinc cognita ſumma & vltimo termino cognoſcitur etiam numerus inſtan­
                <lb/>
              tium æqualium, qui ſemper est idem cum numero terminorum, cognoſcitur
                <lb/>
              etiam primus terminus, id eſt ſpatium quod primo instanti percurritur, cogno­
                <lb/>
              ſcuntur etiam gradus velocitatis
                <emph.end type="italics"/>
              ; </s>
              <s id="N16A3F">quippe hæc omnia ſunt in eadem ratio­
                <lb/>
              ne; </s>
              <s id="N16A45">quæ omnia conſtant ex regulis arithmeticis præter alia multa data,
                <lb/>
              quæ lubens omitto; </s>
              <s id="N16A4B">tùm quia Phyſicam non ſapiunt, tùm quia hypothe­
                <lb/>
              ſis illa eſt impoſſibilis phyſicè; quis enim ſenſu percipere poſſit & di­
                <lb/>
              ſtinguere vnum temporis inſtans, vel ſpatij punctum? </s>
              <s id="N16A53">licèt recenſenda
                <lb/>
              fuerit hæc accelerati motus proportio in inſtantibus, vt ad ſua phyſica
                <lb/>
              principia reduceretur. </s>
            </p>
            <p id="N16A5A" type="main">
              <s id="N16A5C">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              43.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16A68" type="main">
              <s id="N16A6A">
                <emph type="italics"/>
              Data ſumma progreſſionis huius ſimplicis, inuenietur numerus terminorum,
                <lb/>
              ſi inueniatur numerus, per quem diuidatur, qui ſuperet tantùm vnitate du­
                <lb/>
              plum quotientis
                <emph.end type="italics"/>
              ; </s>
              <s id="N16A77">quippe habebis in duplo quotientis numerum termino­
                <lb/>
              rum v.g. ſit ſumma 10. diuiſor ſit 5. quotiens 2. duplus 4. hic eſt nume­
                <lb/>
              rus terminorum datæ ſummæ; </s>
              <s id="N16A81">ſit alia ſumma 21. diuiſor ſit 7.quotiens 3.
                <lb/>
              numerus terminorum 6. ſit alia ſumma 36. diniſor ſit 9. quotiens 4. nu­
                <lb/>
              merus terminorum 8. ſit alia ſumma 45. partitor ſit 10. quotiens 4 1/2,
                <lb/>
              numerus terminorum 9. quomodo verò hic partitor inueniri poſſit, vi­
                <lb/>
              derint Arithmetici; </s>
              <s id="N16A8D">nec enim eſt huius loci, quamquam datâ ſummâ
                <lb/>
              huius progreſſionis ſimplicis facilè cognoſci poteſt numerus termino­
                <lb/>
              rum; duplicetur enim, & radix 9. neglecto reſiduo dabit numerum ter­
                <lb/>
              minorum v.g. ſit ſumma 21. duplicetur, erit 42. rad. </s>
              <s id="N16A99">9. 6. dat numerum
                <lb/>
              terminorum; ſit ſumma 36. duplicetur, erit 72.rad.9.8. dabit numerum
                <lb/>
              terminorum. </s>
            </p>
            <p id="N16AA1" type="main">
              <s id="N16AA3">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              44.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N16AAF" type="main">
              <s id="N16AB1">
                <emph type="italics"/>
              Semper decreſcit proportio incrementi velocitatis, id est maior est proportio
                <lb/>
              velocitatis ſecundi inſtantis ad primum quàm tertij ad ſecundum, & maior
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum