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

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          <pb o="138" file="527.01.138" n="138" rhead="4 L*IBER* S*TATICÆ*"/>
          <p>
            <s xml:id="echoid-s4113" xml:space="preserve">Similiter in cæteris, nam ad numerum qui ipſi 7 inſcribatur inveniendum,
              <lb/>
            addes nomen 9 ad 7, totus 16 eſt nomen novum, cuiſuperſcribes 14 à 9 & </s>
            <s xml:id="echoid-s4114" xml:space="preserve">5 (qui
              <lb/>
            ſunt numerus nomenq́ue {5/9}) compoſitum. </s>
            <s xml:id="echoid-s4115" xml:space="preserve">atque ita {14/16} erit numerus debitus ipſi
              <lb/>
            7, ut infra vides:</s>
            <s xml:id="echoid-s4116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4117" xml:space="preserve">{1/4} {5/9} {14/36}</s>
          </p>
          <p>
            <s xml:id="echoid-s4118" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4119" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4120" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4121" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4122" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4123" xml:space="preserve">11.</s>
            <s xml:id="echoid-s4124" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4125" xml:space="preserve">Qua ratione in cæteris continuata, numeros ipſis 9 & </s>
            <s xml:id="echoid-s4126" xml:space="preserve">11 inſcribendos inve-
              <lb/>
            neris. </s>
            <s xml:id="echoid-s4127" xml:space="preserve">quales hic vides:</s>
            <s xml:id="echoid-s4128" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4129" xml:space="preserve">{1/4} {5/9} {14/36} {30/29} {55/36}.</s>
            <s xml:id="echoid-s4130" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4131" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4132" xml:space="preserve">3. </s>
            <s xml:id="echoid-s4133" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4134" xml:space="preserve">7. </s>
            <s xml:id="echoid-s4135" xml:space="preserve">9. </s>
            <s xml:id="echoid-s4136" xml:space="preserve">11.</s>
            <s xml:id="echoid-s4137" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4138" xml:space="preserve">Quibus intellectis, ſi quæratur quo punctum L aſcendat fundo in quinque
              <lb/>
            ęquas partes diſtributo. </s>
            <s xml:id="echoid-s4139" xml:space="preserve">Sumito numerum quinto loco, hoceſt ipſi 9 inſcriptum
              <lb/>
            is erit {30/25} ſeu in minimis terminis {6/5}, hic indicabit L F talis fundi quinque-partiti
              <lb/>
            fore {6/5} menſuræ cognominis partibus, in quas fundum tributũ erit. </s>
            <s xml:id="echoid-s4140" xml:space="preserve">Sed eam mi-
              <lb/>
            norem eſſe quam {1/3} E F, punctumq́ue ejus ſummũ L hærere infra K demõſtra-
              <lb/>
            bitur hoc modo. </s>
            <s xml:id="echoid-s4141" xml:space="preserve">{6/5} partis unius in quas fundũ ſecatur hoc eſt {6/5} {6/5} ſunt totius EF
              <lb/>
            {6/25} quas {1/3} excedit {7/75} ejuſdem. </s>
            <s xml:id="echoid-s4142" xml:space="preserve">tantoq́ue intervallo tunc L punctum in citra K
              <lb/>
            conſiſtet. </s>
            <s xml:id="echoid-s4143" xml:space="preserve">porro ut in eadem ſectionelocum ipſius M invenias, addito integram
              <lb/>
            menſuram ad ſui {6/5} ſumma erit {11
              <unsure/>
            /9}, quæ ſunt {11/25} totius E F & </s>
            <s xml:id="echoid-s4144" xml:space="preserve">majores quam {1/3}
              <lb/>
            ejuſdem, nam de {11/28
              <unsure/>
            } deducta {1/3} relinquitur {8/75}, tantumq́ue M punctum ſupra K
              <lb/>
            conſiſtet, punctumq́ue hoc ſupernate M cadet ab K {1
              <unsure/>
            /75} diſtantius quam in-
              <lb/>
            fernate L. </s>
            <s xml:id="echoid-s4145" xml:space="preserve">atque ita in cæteris omnibus. </s>
            <s xml:id="echoid-s4146" xml:space="preserve">ut cum A B C D ſecabitur in partes
              <lb/>
            40, F L deprehen detur {20550/1600} unius menſuræ hoc eſt unius quadrageſimæ ipſius
              <lb/>
            E F. </s>
            <s xml:id="echoid-s4147" xml:space="preserve">Quo ratiocinio infinitè continuato punctorum L, M acceſſio ad K infi-
              <lb/>
            nitè quoque vicinior invenietur, quæ tamen nunquam eo pertingat. </s>
            <s xml:id="echoid-s4148" xml:space="preserve">cujus
              <lb/>
            neceſſitas ſuperiore exemplo γραμμικως demonſtrata eſt. </s>
            <s xml:id="echoid-s4149" xml:space="preserve">Cauſam compendii
              <lb/>
            hujus noſtri, is facilè animadvertet, qui modum 2 propoſ. </s>
            <s xml:id="echoid-s4150" xml:space="preserve">1 lib. </s>
            <s xml:id="echoid-s4151" xml:space="preserve">Elem. </s>
            <s xml:id="echoid-s4152" xml:space="preserve">Static.
              <lb/>
            </s>
            <s xml:id="echoid-s4153" xml:space="preserve">factione prolixa perſequetur. </s>
            <s xml:id="echoid-s4154" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s4155" xml:space="preserve">Itaque ſi parallelogrammi ad
              <lb/>
            horizontem inclinati, & </s>
            <s xml:id="echoid-s4156" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4157" xml:space="preserve"/>
          </p>
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          <head xml:id="echoid-head442" xml:space="preserve">13 THEOREMA. 19 PROPOSITIO.</head>
          <p>
            <s xml:id="echoid-s4158" xml:space="preserve">Si parallelogrammi ad horizontem inclinati ſummum
              <lb/>
            latus horizonti parallelum intra aquam abditum recta & </s>
            <s xml:id="echoid-s4159" xml:space="preserve">
              <lb/>
            ipſum & </s>
            <s xml:id="echoid-s4160" xml:space="preserve">latus oppoſitũ biſecet; </s>
            <s xml:id="echoid-s4161" xml:space="preserve">preſſus gravitatis centrum
              <lb/>
            in iſto fundo collecti partem dictæ rectæ inter ſui ſemiſ-
              <lb/>
            ſem & </s>
            <s xml:id="echoid-s4162" xml:space="preserve">trientem inferiorem interjectam ita ſecat, ut pars
              <lb/>
            trienti inferiori vicina ad reliquam ſit, quemadmodum per-
              <lb/>
            pendicularis à ſupero fundi latere uſque ad aquæ ſuperfi-
              <lb/>
            ciem ſummam, ad ſemiſſem perpendicularis indidem de-
              <lb/>
            miſſæ in planum per imum latus horizonti parallelum.</s>
            <s xml:id="echoid-s4163" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4164" xml:space="preserve">D*ATVM*. </s>
            <s xml:id="echoid-s4165" xml:space="preserve">Fundum A B C D ad horizontem inclinatum, ejuſq́ue ſupe-
              <lb/>
            rum latus A B intra aquam E F deliteſcens horizonti parallela eſt, unde G A
              <lb/>
            perpendicularis eſt in ſuperam aquæ ſuperficiem, eademq́ue continuata deor-
              <lb/>
            ſum in ſuperficiem per D C horizonti parallelam ſit A H, ſemiſſis A I, </s>
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