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

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              <pb o="126" file="527.01.126" n="126" rhead="4 L*IBER* S*TATICÆ*"/>
            colligendæ compendium infra damus) erit {499500/1000000}: </s>
            <s xml:id="echoid-s3681" xml:space="preserve">Similiter mille ponduſcula
              <lb/>
            graviora {1/1000000}, {2/1000000}, {3/1000000}, &</s>
            <s xml:id="echoid-s3682" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3683" xml:space="preserve">quorum noviſſimum {1000/100000}, in ſummam colle-
              <lb/>
            cta efficiunt {500500/1000000}. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">Quamobrem fundo inſidet põdus majus quàm {499500/1000000}, minus
              <lb/>
            autem quàm {500500/1000000} unius pedis cubici, atqui {499500/1000000} abeſt duntaxat {1/1000} ab {1/27}, quare
              <lb/>
            pondus quod inſidet fundo ACDE deficit à dimidio pede defectu minore
              <lb/>
            quam fit {1/10000}; </s>
            <s xml:id="echoid-s3685" xml:space="preserve">ſic {500500/1000000} excedit {1/2} pedis ſemiſſem {1/1000}, itaq; </s>
            <s xml:id="echoid-s3686" xml:space="preserve">ipſi non inſidet pon-
              <lb/>
            dus {1/1000} dimidium pedem excedens. </s>
            <s xml:id="echoid-s3687" xml:space="preserve">Simile ratiocinium inſtitues in cæteris,
              <lb/>
            etiam poſitis quibuſliber quam minimis particulis. </s>
            <s xml:id="echoid-s3688" xml:space="preserve">Quare evidens eſt difſeten-
              <lb/>
            tiam (ſi quæ tamen eſſet) inter aquam fundo ACDE inſidentem, & </s>
            <s xml:id="echoid-s3689" xml:space="preserve">cubici
              <lb/>
            aquei pedis dimidium, minorem eſſe qualibet quæ animo concipi aut cogita-
              <lb/>
            tione comprehendi poſſit. </s>
            <s xml:id="echoid-s3690" xml:space="preserve">Vnde ſyllogiſmum inſtituo.</s>
            <s xml:id="echoid-s3691" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3692" xml:space="preserve">Pondere, quod ab aquæ dimidio pede abeſt, aliud minore ab eo differentia distans
              <lb/>
            exhiberi poteſt:</s>
            <s xml:id="echoid-s3693" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3694" xml:space="preserve">Sed pondere aqueo fundo A C D E inſidente, nullum ab aquæ pede dimidio minus
              <lb/>
            differens exhiberi poteſt:</s>
            <s xml:id="echoid-s3695" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3696" xml:space="preserve">Itaque pondus aquæ inſidens fundo A C D E, à dimidio aquæ pede nihil differt.</s>
            <s xml:id="echoid-s3697" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3698" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s3699" xml:space="preserve">Itaque fundi regularis, cujus ſummum punctum in aquæ
              <lb/>
            conſiſtit, &</s>
            <s xml:id="echoid-s3700" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3702" xml:space="preserve">CAuſa cur ſemiſſis iſte inter duos numeros perpetuò magis vicinos, nun-
              <lb/>
            quam tamen concurrentes conſiſtar, hujuſmodi theoremate exprimitur.</s>
            <s xml:id="echoid-s3703" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3704" xml:space="preserve">Numeris quotcunqueab unitate deinceps continuatis,
              <lb/>
            dimidius noviſsimi numeri quadratus cedat ſummæom-
              <lb/>
            nium, eandemq́ue noviſsimo numero multatam excedit.</s>
            <s xml:id="echoid-s3705" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3706" xml:space="preserve">SEd ut fidem exſolvam, & </s>
            <s xml:id="echoid-s3707" xml:space="preserve">compendium in tanta numerorum multitudine
              <lb/>
            addenda nunc explicem, ita habe. </s>
            <s xml:id="echoid-s3708" xml:space="preserve">primùm partium iſtarum nomen unum
              <lb/>
            eſſe & </s>
            <s xml:id="echoid-s3709" xml:space="preserve">commune, quare hoc poſthabito ipſarum numeris animũ intendamus,
              <lb/>
            ii igitur ab unitate continuò progreſſu unitate mutuò ſe ſuperant. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">Itaque ad fa-
              <lb/>
            ctum à noviſſimo in ſui ſemiſſem multiplicato, is ipſe ſemiſſis additus dabit
              <lb/>
            optatam ſummam. </s>
            <s xml:id="echoid-s3711" xml:space="preserve">Exemplum hujuſmodi eſto; </s>
            <s xml:id="echoid-s3712" xml:space="preserve">quæritur ſumma numerorum
              <lb/>
            1, 2, 3, 4, 5, 6. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">Factus à noviſſimo 6 in ſuũ ſemiſſem 3 ad eundem 3 additus dabit
              <lb/>
            21 optatam ſummam. </s>
            <s xml:id="echoid-s3714" xml:space="preserve">Vel ſi noviſſimus ſit impar, ut 1, 2, 3, 4, 5, 6, 7: </s>
            <s xml:id="echoid-s3715" xml:space="preserve">7 in ſuum ſe-
              <lb/>
            miſſem 2 {1/2} ductus facit 24 {1/2}, qui cum ſemiſſe 3 {1/2} compoſitus dat 28 optatũ ſum-
              <lb/>
            mæ totius numerum. </s>
            <s xml:id="echoid-s3716" xml:space="preserve">At cum noviſſimus iſle impar erit, quî partium numeratio
              <lb/>
            declinetur, unitatead noviſſimum addito eodemq́; </s>
            <s xml:id="echoid-s3717" xml:space="preserve">noviſſimo per hujus ſemiſ-
              <lb/>
            ſem multiplicato commodius abſolves. </s>
            <s xml:id="echoid-s3718" xml:space="preserve">utſi in eodem exemplo 1, 2, 3, 4, 5, 6, 7,
              <lb/>
            quæratur ſumma; </s>
            <s xml:id="echoid-s3719" xml:space="preserve">adde 1 ad 7 fit 8, cujus ſemiſsis 4 cum noviſsimo 7 multipli-
              <lb/>
            catus dabit 28 ut priùs. </s>
            <s xml:id="echoid-s3720" xml:space="preserve">atque ita in cæteris.</s>
            <s xml:id="echoid-s3721" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div518" type="section" level="1" n="371">
          <head xml:id="echoid-head388" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s3722" xml:space="preserve">Luia ſupraſcriptus columnæ ſemißis, æquatur integræ item columnæ cujus baſis ſit
              <lb/>
            fundum datum, altitudo autem ſemißis perpendicularis à ſummo fundi puncto, in pla-
              <lb/>
            num per imum eius punctum borizonti parallelum demiſſæ; </s>
            <s xml:id="echoid-s3723" xml:space="preserve">11 pr opoſhoc modo quoque
              <lb/>
            enuntiari poterit.</s>
            <s xml:id="echoid-s3724" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3725" xml:space="preserve">Si fundi regularis ſupremum punctũ ſit in ſumma </s>
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