Stevin, Simon, Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis, 1605

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          <pb o="186" file="527.01.186" n="186" rhead="A*DDITAMENTI* S*TATICÆ* P*ARS QVARTA*"/>
        </div>
        <div xml:id="echoid-div714" type="section" level="1" n="513">
          <head xml:id="echoid-head546" xml:space="preserve">1 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s5112" xml:space="preserve">Scaporum inverſuris aſperitatem neque augeri neque
              <lb/>
            leniri.</s>
            <s xml:id="echoid-s5113" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5114" xml:space="preserve">I*LLVSTRISSIMVS* P*RINCEPS* haud ignarus hos, qui ſcaporum in-
              <lb/>
            verſuras, tribus punctis R, H, S eodem loco manentibus, frenorum aſperita-
              <lb/>
            ti lenitudinive quidquam momenti afferre credunt, falſos opinionis & </s>
            <s xml:id="echoid-s5115" xml:space="preserve">veri va-
              <lb/>
            nos eſſe. </s>
            <s xml:id="echoid-s5116" xml:space="preserve">eoſdem quoque his rationibus ſolet refellere. </s>
            <s xml:id="echoid-s5117" xml:space="preserve">Affigas enim, ajebat,
              <lb/>
            ſcapo directo, cujus figuram ſupra expreſſimus, laminam aliquam ferream,
              <lb/>
            quæ ſcapum tanquam majuſculis inverſuris deformatum exhibeat. </s>
            <s xml:id="echoid-s5118" xml:space="preserve">jam ſi quis
              <lb/>
            eſt ab hac mente, ut inde aſperitatem augeri ſuſpicetur: </s>
            <s xml:id="echoid-s5119" xml:space="preserve">id perinde foret ac ſi
              <lb/>
            credat inductam illam lamellam occulta quadam vi (magnetis inſtar) vel preſ-
              <lb/>
            ſim vel punctim aliquid agere. </s>
            <s xml:id="echoid-s5120" xml:space="preserve">porrò ſi qui pertinacius affirmĕt id re ipſa uſuq́;
              <lb/>
            </s>
            <s xml:id="echoid-s5121" xml:space="preserve">comprobari, iſtos negando facile eſt refutare: </s>
            <s xml:id="echoid-s5122" xml:space="preserve">quid enim habent dicere@ Cæ-
              <lb/>
            terum ſi equiſones, χαλινέρ{γα}{πο
              <unsure/>
            }, quique ὶ{πω}ικ{ὴν} ſolo uſu tractant, tritum il-
              <lb/>
            lud, tanquam ex Apollinis tripode nobis occinant. </s>
            <s xml:id="echoid-s5123" xml:space="preserve">Luam quiſque novit ar-
              <lb/>
            tem, in hac fidem ei habendam. </s>
            <s xml:id="echoid-s5124" xml:space="preserve">illi ſciant hoc in ſe ipſos quadrare maximè. </s>
            <s xml:id="echoid-s5125" xml:space="preserve">
              <lb/>
            nam de ſtaticis effectionibus ſentĕtiam ferunt, quarum tamen ſint ignariſſimi. </s>
            <s xml:id="echoid-s5126" xml:space="preserve">
              <lb/>
            ex hac enim facile docerentur mutationem omnem & </s>
            <s xml:id="echoid-s5127" xml:space="preserve">varietatem exiſtere ab
              <lb/>
            tribus punctis R H S. </s>
            <s xml:id="echoid-s5128" xml:space="preserve">quibus eodem loco manentibus, & </s>
            <s xml:id="echoid-s5129" xml:space="preserve">propter eas lineis
              <lb/>
            imaginariis R H, H S ſede ſua haud emotis, anguloq́ue R H S invariato, ea-
              <lb/>
            dem & </s>
            <s xml:id="echoid-s5130" xml:space="preserve">par ſemper eritab ſcapo aſperitas. </s>
            <s xml:id="echoid-s5131" xml:space="preserve">niſi fortè quid momenti afferat la-
              <lb/>
            mellæ affixæ ponduſculum. </s>
            <s xml:id="echoid-s5132" xml:space="preserve">verum id à propoſita quæſtione alienum eſt. </s>
            <s xml:id="echoid-s5133" xml:space="preserve">& </s>
            <s xml:id="echoid-s5134" xml:space="preserve">ſi
              <lb/>
            hoc urgeant, eares forte non magis eorum ſententiæ patrocinabitur, quam
              <lb/>
            adverſabitur.</s>
            <s xml:id="echoid-s5135" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5136" xml:space="preserve">Præterea animadverſione dignum eſt, non latus V W in ſcapi capitello, ſed
              <lb/>
            rectam imaginariam H S ad generalis cujuſdam theorematis ordinationem,
              <lb/>
            unde inflexurarum modus capiatur, aliquid momenti afferre. </s>
            <s xml:id="echoid-s5137" xml:space="preserve">nam latitudo
              <lb/>
            ocelli diverſa, diverſos quoque effectus inducit.</s>
            <s xml:id="echoid-s5138" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div715" type="section" level="1" n="514">
          <head xml:id="echoid-head547" xml:space="preserve">2 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s5139" xml:space="preserve">Scapi quo breviores tanto ſuntaſperiores.</s>
            <s xml:id="echoid-s5140" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5141" xml:space="preserve">Cauſa ejus rei ferè gemina. </s>
            <s xml:id="echoid-s5142" xml:space="preserve">prima quod adductis tantundem habenis ſcapi
              <lb/>
            breviores plus commoveantur quam longiores. </s>
            <s xml:id="echoid-s5143" xml:space="preserve">cujus veritatem diagramma-
              <lb/>
            te demonſtrabo. </s>
            <s xml:id="echoid-s5144" xml:space="preserve">A B ſcapus longior, A C brevior, quo-
              <lb/>
            rum ſit idem capitellum A D, ejuſque ocelli contactus D:
              <lb/>
            </s>
            <s xml:id="echoid-s5145" xml:space="preserve">
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            adductis habenis in ſcapo breviore aſſurgat annelli conta-
              <lb/>
            ctus in E per peripheriam C E, & </s>
            <s xml:id="echoid-s5146" xml:space="preserve">ocelli contactus D de-
              <lb/>
            ſcendat in F per peripheriam D F. </s>
            <s xml:id="echoid-s5147" xml:space="preserve">Conſimiliter in ſcapo
              <lb/>
            longiore annelli contactus adducatur ad G, ut peripheriæ
              <lb/>
            C E, B G æquales ſint, hîc D deſcendet ſolummodo in H
              <lb/>
            per peripheriam D H. </s>
            <s xml:id="echoid-s5148" xml:space="preserve">ſed D F major eſt quàm D H, ſunt
              <lb/>
            enim inter ſe rationeſcaporum inverſa, id eſt, quemadmo-
              <lb/>
            dum longior ſcapus A B ad breviorem A C. </s>
            <s xml:id="echoid-s5149" xml:space="preserve">Itaque pſellia
              <lb/>
            ocellis affixa minoribus ſcapis moventur validius. </s>
            <s xml:id="echoid-s5150" xml:space="preserve">verum
              <lb/>
            quantum pſellia moventur magis, hoc mandibula à lupo,
              <lb/>
            mentumq́ue à pſellio preſsius premitur conſtringiturq́ue. </s>
            <s xml:id="echoid-s5151" xml:space="preserve">unde eſſicitur ut
              <lb/>
            ſcapi breviores longioribus ſint aſperiores.</s>
            <s xml:id="echoid-s5152" xml:space="preserve"/>
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