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

Table of contents

< >
[121.] 2 C*ONSECTARIUM*.
Page: 30 (30)
[122.] 7 THEOREMA. 15 PROPOSITIO.
Page: 31 (31)
[123.] DECLARATIO.
Page: 31 (31)
[124.] 8 THEOREMA. 16 PROPOSITIO.
Page: 31 (31)
[125.] DEMONSTRATIO.
Page: 31 (31)
[126.] 9 THEOREMA. 17 PROPOSITIO.
Page: 32 (32)
[127.] DEMONSTRATIO.
Page: 32 (32)
[128.] C*ONSECTARIUM*.
Page: 33 (33)
[129.] 10 THEOREMA. 18 PROPOSITIO.
Page: 33 (33)
[130.] C*ONSECTARIUM*.
Page: 34 (34)
[131.] HACTENVS RECTORVM PONDERVM GENERA DICTA SVNT; OBLI-QVORVM PROPRIETATES DEINCEPS deſcribendæ ſunt, quarum omnium genera-lem veritatem tanquam fundamentum istud theoremata complectitur. 11 THEOREMA. 19 PROPOSITIO.
Page: 34 (34)
[132.] DEMONSTRATIO.
Page: 35 (35)
[133.] 1 C*ONSECTARIUM*.
Page: 35 (35)
[134.] 2 C*ONSECTARIUM*.
Page: 35 (35)
[135.] 3 C*ONSECTARIUM*.
Page: 35 (35)
[136.] 4 C*ONSECTARIUM*.
Page: 36 (36)
[137.] 5 C*ONSECTARIUM*.
Page: 36 (36)
[138.] 6 C*ONSECTARIUM*.
Page: 36 (36)
[139.] 7 C*ONSECTARIUM*.
Page: 38 (38)
[140.] 8 C*ONSECTARIUM*.
Page: 38 (38)
[141.] 9 C*ONSECTARIUM*.
Page: 39 (39)
[142.] 10 C*ONSECTARIUM*.
Page: 40 (40)
[143.] 11 C*ONSECTARIUM*.
Page: 40 (40)
[144.] 12 C*ONSECTARIUM*.
Page: 40 (40)
[145.] 12 THE OREMA. 20 PROPOSITIO.
Page: 41 (41)
[146.] NOTATO
Page: 42 (42)
[147.] 13 THEOREMA. 21 PROPOSITIO.
Page: 42 (42)
[148.] DEMONSTRATIO.
Page: 42 (42)
[149.] 9 PROBLEMA. 22 PROPOSITIO.
Page: 43 (43)
[150.] PRAGMATIA.
Page: 43 (43)
< >
page |< < (128) of 197 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div521" type="section" level="1" n="374">
          <p>
            <s xml:id="echoid-s3754" xml:space="preserve">
              <pb o="128" file="527.01.128" n="128" rhead="4 L*IBER* S*TATICÆ*"/>
            æquari columnæbaſis A B C D, altitudinis GE,
              <lb/>
              <figure xlink:label="fig-527.01.128-01" xlink:href="fig-527.01.128-01a" number="177">
                <image file="527.01.128-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.128-01"/>
              </figure>
            patebit demiſſa O Q perpendiculari in planum
              <lb/>
            A B C D: </s>
            <s xml:id="echoid-s3755" xml:space="preserve">nam priſma A B C D P O M N æqua-
              <lb/>
            le eſt ſolido cujus baſis A B C D altitudo O Q:
              <lb/>
            </s>
            <s xml:id="echoid-s3756" xml:space="preserve">ſed quia rectæ A H, O C, itemq́ue anguli HAE,
              <lb/>
            C O Q ſunt æquales, & </s>
            <s xml:id="echoid-s3757" xml:space="preserve">AE plano per H, E, pun-
              <lb/>
            cta trajecto perpendicularis, item O Q ei quod
              <lb/>
            per C, Q, propterea A E & </s>
            <s xml:id="echoid-s3758" xml:space="preserve">æquatur ipſi O Q: </s>
            <s xml:id="echoid-s3759" xml:space="preserve">
              <lb/>
            ideoq́ue parallelepipedum A B C D P O M N,
              <lb/>
            parallelepipedo in baſin A B C D altitudine
              <lb/>
            A E inſiſtente erit æquale. </s>
            <s xml:id="echoid-s3760" xml:space="preserve">At (quemadmodum
              <lb/>
            jam 11 propoſ. </s>
            <s xml:id="echoid-s3761" xml:space="preserve">demonſtratum fuit) priſma
              <lb/>
            M N P O K L æquatur parallelepipedo baſis
              <lb/>
            A B C D altitudinis A G. </s>
            <s xml:id="echoid-s3762" xml:space="preserve">quare duo iſta ſolida
              <lb/>
            addita conſtituunt priſma A B C D L K N M æquale parallelepipedo dictæ
              <lb/>
            baſis A B C D, altitudinis autem G E.</s>
            <s xml:id="echoid-s3763" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div523" type="section" level="1" n="375">
          <head xml:id="echoid-head392" xml:space="preserve">ALTERA DEMONSTRATIO.</head>
          <p>
            <s xml:id="echoid-s3764" xml:space="preserve">Si per A B agas planum horizonti parallelum ipſi A B C D ſimile & </s>
            <s xml:id="echoid-s3765" xml:space="preserve">æquale;
              <lb/>
            </s>
            <s xml:id="echoid-s3766" xml:space="preserve">huic incumbet per 10 prop. </s>
            <s xml:id="echoid-s3767" xml:space="preserve">põdus aquæ æquale columnæ baſis A B C D, altitu-
              <lb/>
            dinis AE: </s>
            <s xml:id="echoid-s3768" xml:space="preserve">atqui minimùm tantũ põderis inſidet cuilibet fundo humiliori ipſiq́; </s>
            <s xml:id="echoid-s3769" xml:space="preserve">
              <lb/>
            æquali: </s>
            <s xml:id="echoid-s3770" xml:space="preserve">primùm igitur fundo A B C D incumbit columna baſis dictæ A B C D,
              <lb/>
            altitudinis A E. </s>
            <s xml:id="echoid-s3771" xml:space="preserve">remota igitur aqua iſta quæ ſuperiori fundo inſidet quodque
              <lb/>
            ipſi A B C D formavimus æquale, erit A B in reliquę aqu@ ſummitate, atque
              <lb/>
            ideo per 11 prop. </s>
            <s xml:id="echoid-s3772" xml:space="preserve">dicto fundo A B C D inſidebit aquea columna baſis A B C D
              <lb/>
            altitudinis A B; </s>
            <s xml:id="echoid-s3773" xml:space="preserve">quæ ad ſuperiorem addita cõſtituet columnam baſis A B C D,
              <lb/>
            altitudinis autem E G, quæ quantitas eſt ponderis fundo A B C D inſidentis.</s>
            <s xml:id="echoid-s3774" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div524" type="section" level="1" n="376">
          <head xml:id="echoid-head393" xml:space="preserve">2 Exemplum.</head>
          <figure number="178">
            <image file="527.01.128-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.128-02"/>
          </figure>
          <p>
            <s xml:id="echoid-s3775" xml:space="preserve">Fundi regularis A B ſupremum punctum A in aquæ
              <lb/>
            ſummo, B ſit in imo; </s>
            <s xml:id="echoid-s3776" xml:space="preserve">perpendicularis A C ab A ſurſum
              <lb/>
            ad C aquæ ſuperficiem extimam, & </s>
            <s xml:id="echoid-s3777" xml:space="preserve">deorſum in D ad
              <lb/>
            planum per B imum punctum horizonti parallelũ con-
              <lb/>
            tinuata, continuationisq́ue inferioris ſemiſſis eſto A E.
              <lb/>
            </s>
            <s xml:id="echoid-s3778" xml:space="preserve">Ajo tantum pondus fundo inſidere, quantum eſt colum-
              <lb/>
            næ baſis A B altitudinis C E. </s>
            <s xml:id="echoid-s3779" xml:space="preserve">cujus demonſtratio ante-
              <lb/>
            cedenti ſimilis eſt.</s>
            <s xml:id="echoid-s3780" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3781" xml:space="preserve">C*ONCLVSIO*. </s>
            <s xml:id="echoid-s3782" xml:space="preserve">Itaqueſi fundi regularis ſupremum
              <lb/>
            punctum, &</s>
            <s xml:id="echoid-s3783" xml:space="preserve">c.</s>
            <s xml:id="echoid-s3784" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div525" type="section" level="1" n="377">
          <head xml:id="echoid-head394" xml:space="preserve">NOTATO.</head>
          <p style="it">
            <s xml:id="echoid-s3785" xml:space="preserve">Hoc T heoremate, adhibita perpendiculari per ſummum fundipunctum educta, quan-
              <lb/>
            tum eſſet pondus regulari plano inſidens demonſtr avimus, ſed fundo non regulari pon-
              <lb/>
            dus hoc istiuſmodi perpendiculari non invenitur. </s>
            <s xml:id="echoid-s3786" xml:space="preserve">Certum eſt ipſi pondus inſidere æquale
              <lb/>
            aqueæ columnæ, cuius baſis iſtud ſit fundum, & </s>
            <s xml:id="echoid-s3787" xml:space="preserve">altituào perp endicularis à ſupremo cius
              <lb/>
            fundi puncto ad aquæ ſub qua deliteſcit ſummitatem educta, ſedpræterea jamreliguum
              <lb/>
            @llud pondus non æquatur alteri, columnæ cuius baſis ſit idem fundum altitudo dimidiæ
              <lb/>
            perpendicularis ab altiſsimo fundi puncto in planum per infimum punctum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum