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<?xml version="1.0"?>
<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd">
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink">      <info>
        <author>Pseudo Euclid</author>
        <title>de ponderoso et levi</title>
        <date>1537</date>
        <place>Paris</place>
       <translator></translator>
        <lang>la</lang>
        <cvs_file>eucli_ponde_056_la_1537.xml</cvs_file>
        <cvs_version/>
        <locator>056.xml</locator>
</info>      <text>
<pb xlink:href="056/01/001.jpg" /><front><section><p type="head">
<s id="id.000001">EVCLIDIS DE LEVI ET PONDEROSO FRAGMENTUM.</s></p></section></front><body><chap><p type="margin">
<s id="id.000002"><arrow.to.target n="marg1"/><margin.target id="marg1"/><emph type="italics"/>Diffini<lb/>tiones.<emph.end type="italics"/></s></p><p type="main">
<s id="id.000003">1 &AElig;qua magnitudine corpora &longs;unt, qu&aelig; loca replent &aelig;qua.</s>
<s id="id.000004"> 2 Di&shy;<lb/>uer&longs;a magnitudine corpora &longs;unt, qu&aelig; loca replent non &aelig;qua.</s>
<s id="id.000005"> 3 Gr<expan abbr="&atilde;">an</expan>dio<lb/>ra magnitudine <expan abbr="dic&utilde;tur">dicuntur</expan> corpora, qu&aelig; loco &longs;unt ampliore.</s>
<s id="id.000006"> 4 &AElig;qua po<lb/>tentia corpora &longs;unt, quor<expan abbr="&utilde;">um</expan> &amp; tempore &amp; a&euml;re aqu&aacute;ve media &aelig;quabilis &amp; <lb/>per &aelig;qualia interualla &aelig;quales &longs;unt motus.</s>
<s id="id.000007"> 5 Diuer&longs;a potentia corpo&shy;<lb/>ra &longs;unt, quorum, t<expan abbr="&etilde;">em</expan>pore diuer&longs;o motus &longs;unt &aelig;quales.</s>
<s id="id.000008"> 6 Diuer&longs;or<expan abbr="&utilde;">um</expan> <expan abbr="pot&etilde;tia">poten<lb/>tia</expan> corporum, maius id potentia dicitur, quod mouendo temporis in&longs;um&shy;<lb/>p&longs;it minus: minus autem <expan abbr="pot&etilde;tia">potentia</expan>, quod temporis amplius.</s>
<s id="id.000009"> 7 Generis <lb/>eiu&longs;dem corpora &longs;unt, qu&aelig; cum &aelig;qua magnitudine &longs;int, etiam &longs;unt poten&shy;<lb/>tia.</s>
<s id="id.000010"> 8 Diuer&longs;a genere corpora &longs;unt, qu&aelig; cum &aelig;qua magnitudine &longs;int, <lb/>potentia non &longs;unt, per idem licet medium <expan abbr="moue&atilde;">moueantur</expan>.</s>
<s id="id.000011"> 9 Diuer&longs;orum<lb/>genere corporum, potentius id dicitur quod e&longs;t &longs;olidius.</s></p><p type="margin">
<s id="id.000012"><arrow.to.target n="marg2"/><margin.target id="marg2"/><emph type="italics"/>Theore&shy;<lb/>mata.<emph.end type="italics"/></s></p><p type="head">
<s id="id.000013"><emph type="italics"/>Theorema primum<emph.end type="italics"/></s></p><p>
<s id="id.000014">Diuer&longs;orum potentia corporum, quod &longs;patium amplius moue&shy;<lb/><arrow.to.target n="marg2"/><lb/>tur, habet amplius potenti&aelig;.</s></p><pb xlink:href="056/01/002.jpg" pagenum="586"/><p>
<s id="id.000015">Sint a &amp; b corpora dio, &longs;int gd &amp; ef, &longs;patia duo, gd maius per quod a, ef, minus  per <lb/>quod b mouetur re&longs;ecabo &agrave; &longs;patio gd, gr, &longs;pa<lb/>tium, &longs;ic ut &longs;it ef &longs;patio <expan abbr="&longs;pati&utilde;">&longs;patium</expan> gr &aelig;quale.</s>
<s id="id.000016"> C&aelig;te<lb/>ra &longs;ponte patent.</s><figure id="id.056.01.002.1.jpg" xlink:href="056/01/002/1.jpg"/></p><p type="head">
<s id="id.000017"><emph type="italics"/>Theorema &longs;ecundum<emph.end type="italics"/></s></p><p>
<s id="id.000018">EOrundem genere corpor<expan abbr="&utilde;">um</expan><lb/>&longs;i ip&longs;a inter &longs;e erunt multiplicia, erunt &aelig;que ip&longs;orum potenti&aelig; <lb/>multiplices.</s></p><p>
<s id="id.000019">Sit corpus ag, eodem genere corpori d duplum, dico.<lb/><figure id="id.056.01.002.2.jpg" xlink:href="056/01/002/2.jpg"/>etiam potentia duplum e&longs;&longs;e.</s>
<s id="id.000020"> Sit enim ag, quidem cor&shy;<lb/>poris potentia eh, d uero &amp; ag iuxta multiplicis ex&shy;<lb/>ce&longs;&longs;um in ab &amp; bg, diuidatur, &longs;ic ut utriu&longs;que potentia,<lb/>ip&longs;ius d corporis pot<expan abbr="&etilde;">en</expan>ti&aelig; qu&aelig; erat c &aelig;qualis, fiat rur&longs;us <lb/>ut ag corpus in partes ab, bg corpori d &aelig;quas diui&longs;imus.</s>
<s id="id.000021"> &longs;ic eh, potentiam in partes <lb/>er &amp; rh, &aelig;quas c potentia diuidamus.</s>
<s id="id.000022"> Liquidum e&longs;t eh potenti<expan abbr="&atilde;">am</expan> duplum potenti&aelig; c <lb/>euadere.</s></p><p type="head">
<s id="id.000023"><emph type="italics"/>Theorema tertium<emph.end type="italics"/></s></p><p>
<s id="id.000024">EOrund<expan abbr="&etilde;">em</expan> genere corpor<expan abbr="&utilde;">um</expan>, proportio, &amp; magnitudine, &amp; potentia <lb/>e&longs;t eadem.</s></p><figure id="id.056.01.002.3.jpg" xlink:href="056/01/002/3.jpg"/><p>
<s id="id.000025">Sit &agrave; corpus<lb/>corporis eo&shy;<lb/>dem genere b duplum, di&shy;<lb/>co ut a corpus ad b cor<lb/>pus e&longs;t, &longs;ic corporis a <expan abbr="pot&etilde;tia">poten<lb/>tia</expan> g ad corporis b potentiam d e&longs;&longs;e.</s>
<s id="id.000026"> Patet &longs;i ut corpora &longs;ic potentias &aelig;que utrinque <lb/>multipliciter diuidamus.</s></p><p type="head">
<s id="id.000027"><emph type="italics"/>Theorema quartum<emph.end type="italics"/></s></p><p type="main">
<s id="id.000028">QU&aelig; corpora, &aelig;qua potentia eiu&longs;dem generis corpori &longs;unt, eiu&longs;d<expan abbr="&etilde;">em</expan><lb/>&longs;unt inter &longs;e generis, ablatis enim &aelig;qualibus illi tertio, er<expan abbr="&utilde;">un</expan>t ip&longs;o&shy;<lb/>rum uirtutes &aelig;quales, quia potenti&aelig; tertij &aelig;quales.</s></p><p>
<s id="id.000029">Quor<expan abbr="&utilde;">um</expan> corpor<expan abbr="&utilde;">um</expan> &amp; magnitudo &amp; potentia proportio una e&longs;t, ip&longs;a generis eiu&longs;d<expan abbr="&etilde;">em</expan> erunt.<lb/></s>
<s id="id.000030"> Sit ut a corpus ad corpus b, &longs;ic corpus a potentia ad corporis b potenti<expan abbr="&atilde;">am</expan> d, dico a. b. <lb/>corpora generis eiu&longs;d<expan abbr="&etilde;">em</expan> e&longs;&longs;e.</s>
<s id="id.000031">Statuamus <expan abbr=".n.">enim</expan> a. corpus, &aelig;quale corpori cuius potentia &longs;it <lb/>r. </s>
<s id="id.000032">Erunt igitur ut b ad a, &longs;ic r ad potentiam ip&longs;ius a qu&aelig; e&longs;t g.</s>
<s id="id.000033"> Reliqua pat<expan abbr="&etilde;">en</expan>t. </s></p></chap></body></text></archimedes>
author	Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date	Thu, 02 May 2013 11:38:23 +0200
parents	22d6a63640c6
children