Archimedes, Archimedis De insidentibvs aqvae

Table of contents

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[Item 1.]
[2.] ARCHIMEDIS DE INSIDENTIBVS AQV AE. LIBER PRIMVS.
[3.] CVM PRIVILEGIO. TROIANO CVRTIO
[4.] VENETIIS, APVD CVRTIVM TROIANVM. M D LXV►
[5.] FABRITIO DENORES FILIO IACOBI COMITIS TRIPOLIS VCRTIVS TROIANVS S. P. D.
[6.] ARCHIMEDIS DE INSIDENTIBVS AQV AE. LIBER PRIMVS. Suppoſitio prima.
[7.] Theorema primum. Propoſitio prima.
[8.] Theorema ij. Propoſitio ij.
[9.] Theorema iij. Propoſitio iij.
[10.] Theorema iiij. Propoſitio iiij.
[11.] Theorema v. Propoſitio v.
[12.] Theorema vj. Propoſitio vj.
[13.] Theorema vij. Propoſitio vij.
[14.] Suppoſitio ſecunda.
[15.] Theorema viij. Propoſitio viij.
[16.] AR CHIM EDIS DE INSIDENTIBVS AQV AE.
[17.] LIBER SECVNDVS. TROIANO CVRTIO VENETIIS, APVD TROIANVM CVRTIVM. M D L X V
[18.] FABRITIO DENORES FILIO IACOBI COMITIS TRIPOLIS CVRTIVS TROIANVS S. P. D.
[19.] INSIDENTIBVS AQV AE. LIB. II. PRIMVS.
[20.] SECVNDVS.
[21.] TERTIVS.
[22.] QVARTVS.
[23.] QVINTVS.
[24.] SEXTVS.
[25.] SEPTIMVS.
[26.] OCTAVVS.
[27.] NONVS.
[28.] DECIMVS.
[29.] Archimedis de inſidentibus in bumido li-ber ſecundus explicit, ad laudem Dei.
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            <s xml:id="echoid-s488" xml:space="preserve">
              <pb file="0032" n="32" rhead="DE INSIDENTIBVS AQVAE"/>
            ipſius c, d. </s>
            <s xml:id="echoid-s489" xml:space="preserve">Ipſius autem o, i, dupla eſt, quæ ***, propter ſeptimum tbeore-
              <lb/>
            ma primi libri elementorum conoycorum A pollonij. </s>
            <s xml:id="echoid-s490" xml:space="preserve">Eſt ergo quæ o, i,
              <lb/>
            minor, quàm x, b. </s>
            <s xml:id="echoid-s491" xml:space="preserve">Quare quæ i, ***, eſt maior, quàm x, r, quæ autem x, r,
              <lb/>
            eſt æqualis ipſi f, maior ergo _est_, quæ i, ***, quàm f. </s>
            <s xml:id="echoid-s492" xml:space="preserve">Et quoniam ſupponi
              <lb/>
            tur portio ad humidum iu grauitate habere per portionem, quàm tetra-
              <lb/>
            gonum, quod ab f, q, ad tetragonum, quod a, b, d. </s>
            <s xml:id="echoid-s493" xml:space="preserve">Quam autem propor-
              <lb/>
            tionem, habet proportio ad humidum in grauitate, hanc habet propor-
              <lb/>
            tionem pars ipſius demerſa ad totam portionem, quam autem pars de-
              <lb/>
            merſa ad totam hanc habet tetragonum, quod a, p, m, a tetragonum,
              <lb/>
            quod ab o, n. </s>
            <s xml:id="echoid-s494" xml:space="preserve">Quam ergo proportionem babet tetragonum, quod a, b, f, q.
              <lb/>
            </s>
            <s xml:id="echoid-s495" xml:space="preserve">ad tetragonum, quod a, b, d, hanc proportionem habet tetragonum, quod
              <lb/>
            a, b, m, b, ad tetragonum quod a, b, o, n, æqualis ergo eſt, quæ f, q, ipſi p,
              <lb/>
            m. </s>
            <s xml:id="echoid-s496" xml:space="preserve">Quæ autem p, b, demonstrata eſt eſſe maior, quàm f, palam ergo, quòd
              <lb/>
            quæ p, m, eſt minor, quàm dupla ipſius b, m. </s>
            <s xml:id="echoid-s497" xml:space="preserve">Sit igitur quæ p, Z, dupla ip
              <lb/>
            ſius Z. </s>
            <s xml:id="echoid-s498" xml:space="preserve">m, erit autem t, quidem centrum grauitatis ſolidi, eius auté, quod
              <lb/>
            intra bumidum Z. </s>
            <s xml:id="echoid-s499" xml:space="preserve">Reliquam autem magnitudinis centrum grauitatis
              <lb/>
            erit in linea Z, t. </s>
            <s xml:id="echoid-s500" xml:space="preserve">Copulata, & </s>
            <s xml:id="echoid-s501" xml:space="preserve">educta, & </s>
            <s xml:id="echoid-s502" xml:space="preserve">educatur ad g, demonſtrabitur
              <lb/>
            autem ſimiliter quæ t, b, perpendicularis exiſtens ad ſuperficiem humi-
              <lb/>
            di, & </s>
            <s xml:id="echoid-s503" xml:space="preserve">portio quidem quæ intra humidum fertur ad extra humidi, ſecun
              <lb/>
            dum perpendicularem ducta per Z, ſuperficiem humidi. </s>
            <s xml:id="echoid-s504" xml:space="preserve">Quæ autem ex-
              <lb/>
            tra humidum ferretur intra humidum, ſecundum ea, quæ per g, non ma-
              <lb/>
            net autem portio, ſecundum ſuppoſitam inclinationem, nec etiam in re-
              <lb/>
            ctum restituetur. </s>
            <s xml:id="echoid-s505" xml:space="preserve">palam enim propter hoc quoniam, quæ producuntur
              <lb/>
            per Z, g. </s>
            <s xml:id="echoid-s506" xml:space="preserve">perpendiculares. </s>
            <s xml:id="echoid-s507" xml:space="preserve">quæ quidem per Z, perducit ipſi g,
              <lb/>
            l, ad eaſdem partes cadit ad quas eſt, & </s>
            <s xml:id="echoid-s508" xml:space="preserve">ſecundum g. </s>
            <s xml:id="echoid-s509" xml:space="preserve">Quæ autem per
              <lb/>
            g, ad eaſdem ipſi Z, g. </s>
            <s xml:id="echoid-s510" xml:space="preserve">palam quòd propter prædicta Z, quidem centrũ
              <lb/>
            ſurſum ferretur:</s>
            <s xml:id="echoid-s511" xml:space="preserve">g, autem deorſum. </s>
            <s xml:id="echoid-s512" xml:space="preserve">Quare totius magnitudinis, quæ ex
              <lb/>
            parte a, deorſum ferretur, hoc antem erat inutile ad demonstrandum.</s>
            <s xml:id="echoid-s513" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s514" xml:space="preserve">Supponatur rurſum alia quidem eadem axis autem portionis ad ſu-
              <lb/>
            perficiem humidi faciat angulum minorem eo, qui apud b, minorem au-
              <lb/>
            tem proportionem habet tetragonum, quod a, p, i, ad tetragonum, quod
              <lb/>
            ab i, ***, quàm ad a, b, x, ad id, quod a, x, b, & </s>
            <s xml:id="echoid-s515" xml:space="preserve">quæ K, r, ergo ad ***, i, mi
              <lb/>
            norem proportionem habet, quàm medietas ipſius K, r, ad x, b. </s>
            <s xml:id="echoid-s516" xml:space="preserve">Eſt ergo
              <lb/>
            quæ i, ***, maiorem quàm dupla ipſius x, b, ergo quæ ***, i, minor ipſius
              <lb/>
            autem o, i, dupla ergo ***, eſt, quæ o, i, ipſus x, b, eſt autem, & </s>
            <s xml:id="echoid-s517" xml:space="preserve">to
              <lb/>
            ta, quæ ***, t, æqualis ipſi r, b, & </s>
            <s xml:id="echoid-s518" xml:space="preserve">reliqua minor eſt, quàm ***, r, erit ergo,
              <lb/>
            & </s>
            <s xml:id="echoid-s519" xml:space="preserve">quæ p, h, minor, quàm f. </s>
            <s xml:id="echoid-s520" xml:space="preserve">Quæ autem m, p, ipſi f, q, eſt æqualis: </s>
            <s xml:id="echoid-s521" xml:space="preserve">palam
              <lb/>
            quòd p, m, eſt maior, quàm emiolia ipſius p, b, quæ autẽ p, h, minor, quàm
              <lb/>
            dupla ipſius h, m. </s>
            <s xml:id="echoid-s522" xml:space="preserve">Sit igitur, quæ p, z, ipſius z, m, dupla igitur rurſum. </s>
            <s xml:id="echoid-s523" xml:space="preserve">to
              <lb/>
            tius quidem cétrum grauitatis erit t, eius autem quod intra humidũ Z.</s>
            <s xml:id="echoid-s524" xml:space="preserve"/>
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