Newton, Isaac Philosophia naturalis principia mathematica 1713

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<p type="margin"> <s><margin.target id="note441"/>DE MUNDI <lb/>
SYSTEMATE</s></p>

<p type="main"> <s><emph type="center"/>PROPOSITIO XXXII. PROBLEMA XIII.<emph.end type="center"/></s></p>

<p type="main"> <s><emph type="center"/><emph type="italics"/>Invenire motum medium Nodorum Lun&aelig;.<emph.end type="italics"/><emph.end type="center"/></s></p>

<p type="main"> <s>Motus medius annuus e&longs;t &longs;umma motuum omnium horariorum <lb/>
mediocrium in anno. </s> <s>Concipe Nodum ver&longs;ari in <emph type="italics"/>N,<emph.end type="italics"/>&amp; &longs;ingulis <lb/>
horis completis retrahi in locum &longs;uum priorem, ut non ob&longs;tante <lb/>
motu &longs;uo proprio, datum &longs;emper &longs;ervet &longs;itum ad Stellas Fixas. </s> <s><lb/>
Interea vero Solem <emph type="italics"/>S,<emph.end type="italics"/>per motum Terr&aelig;, progredi a Nodo, &amp; <lb/>
cur&longs;um annuum apparentem uniformiter complere. </s> <s>Sit autem <lb/>
<emph type="italics"/>Aa<emph.end type="italics"/>arcus datus quam minimus, quem recta <emph type="italics"/>TS<emph.end type="italics"/>ad Solem &longs;emper <lb/>
ducta, inter&longs;ectione &longs;ui &amp; circuli <emph type="italics"/>NAn,<emph.end type="italics"/>dato tempore quam mi&shy;<lb/>
nimo de&longs;cribit: &amp; motus horarius mediocris (per jam o&longs;ten&longs;a) <lb/>
erit ut <emph type="italics"/>AZq,<emph.end type="italics"/>id e&longs;t (ob proportionales <emph type="italics"/>AZ, ZY<emph.end type="italics"/>) ut rectan&shy;<lb/>
gulum &longs;ub <emph type="italics"/>AZ<emph.end type="italics"/>&amp; <emph type="italics"/>ZY,<emph.end type="italics"/>hoc e&longs;t, ut area <emph type="italics"/>AZYa.<emph.end type="italics"/>Et &longs;umma om&shy;<lb/>
nium horariorum motuum mediocrium ab initio, ut &longs;umma om&shy;<lb/>
nium arearum <emph type="italics"/>aYZA,<emph.end type="italics"/>id e&longs;t, ut area <emph type="italics"/>NAZ.<emph.end type="italics"/>E&longs;t autem maxima <lb/>
<figure id="id.039.01.440.1.jpg" xlink:href="newto_philo_039_la_1713/039-01-figures/039.01.440.1.jpg"/><lb/>
<emph type="italics"/>AZYa<emph.end type="italics"/>&aelig;qualis rectangulo &longs;ub arcu <emph type="italics"/>Aa<emph.end type="italics"/>&amp; radio circuli; &amp; prop&shy;<lb/>
terea &longs;umma omnium rectangulorum in circulo toto ad &longs;ummam <lb/>
totidem maximorum, ut area circuli totius ad rectangulum &longs;ub <lb/>
circumferentia tota &amp; radio; id e&longs;t, ut 1 ad 2. Motus autem ho&shy;<lb/>
rarius, rectangulo maximo re&longs;pondens, erat 16&Prime;. </s> <s>16&prime;. </s> <s>37<emph type="sup"/>iv<emph.end type="sup"/>. </s> <s>42<emph type="sup"/>v<emph.end type="sup"/>. </s> <s>Et <lb/>
hic motus, anno toto &longs;idereo dierum 365. <emph type="italics"/>hor.<emph.end type="italics"/>6. <emph type="italics"/>min.<emph.end type="italics"/>9 fit <lb/>
39<emph type="sup"/>gr.<emph.end type="sup"/> 38&prime;. </s> <s>7&Prime;. </s> <s>50&prime;. </s> <s>Ideoque hujus dimidium 19<emph type="sup"/>gr.<emph.end type="sup"/> 49&prime;. </s> <s>3&Prime;. </s> <s>55&prime;. </s> <s>e&longs;t mo-