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annotate texts/XML/archimedes/la/varro_demot_044_la_1584_old.xml @ 6:22d6a63640c6

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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
author casties
date Fri, 07 Dec 2012 17:05:22 +0100
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1 <?xml version="1.0"?>
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2 <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" >
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3 <info>
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4 <author>Varro, Michel</author>
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5 <title>De motu tractatus, old version (54 pages)</title>
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6 <date>1584</date>
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7 <place>Geneva</place>
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8 <translator></translator>
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9 <lang>la</lang>
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10 <cvs_file>varro_demot_044_la_1584.xml</cvs_file>
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11 <cvs_version></cvs_version>
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12 <locator>044.xml</locator>
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13 <echodir>/permanent/archimedes/varro_demot_044_la_1584</echodir>
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14 </info>
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15 <text>
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16 <front>
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17 <section>
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18 <pb xlink:href="044/01/001.jpg"></pb>
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19 <p type="head">
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20 <s>TERRA <lb></lb> MACHINIS MOTA <lb></lb> DISSERTATIONES <lb></lb> GEOMETRICAE, MECHANICAE
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21 <lb></lb> PHYSICAE, HYDROSTATICAE <lb></lb> In quibus <lb></lb> Machinarum Coniugatarum
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22 uires inter ſe comparantur: <lb></lb> Multiplici Noua Methodo Terrae
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23 magnitudo et <lb></lb> Grauitas inueſtigatur: ARCHIMEDES <lb></lb> terrae
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24 motionem ſpondens ab arrogantia <lb></lb> ſuſpicione
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25 uindicatur. <lb></lb></s>
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26 <s>AVTHORE <lb></lb> PAVLO CASATO <lb></lb> E SOCIETATE IESV. <lb></lb></s>
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27 <s>ROMAE. <lb></lb></s>
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28 <s>Ex Typographia Ignatij de Lazaris.</s>
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29 <s>M.DC.LVIII.<lb></lb></s>
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30 <s>SVPERIORVM PERMISSV.<lb></lb></s>
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31 </p>
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32 <pb xlink:href="044/01/002.jpg"></pb>
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33 <pb xlink:href="044/01/003.jpg" id="p.0001"></pb>
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34 <p type="head">
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35
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36
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37 <s>ILLVSTRI ET IN <lb></lb> PRIMIS GENEROSO DOMINO, <lb></lb> DOMINO CAROLO BARONI <lb></lb>
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38 Azerotin, Nameſtij Roſicij <lb></lb> Brandeiſij Domino, <lb></lb>
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39 MICH. VARRO. S. P. D.</s>
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40 </p>
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41 <p type="main">
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42
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43
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44 <s><emph type="italics"></emph>CVM ab Ineunte ætate in Ma­<lb></lb> thematicis
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45 me exercuiſſem, ſem­<lb></lb> per animo meo in
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46 hæſit hoc deſide­<lb></lb> rium, vt quæ de Archimede
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47 Syra­<lb></lb> cuſano referuntur, ea &amp; ratione <lb></lb>
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48 demonſtrare &amp; experimento comprobare poſſem. <lb></lb>
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49 </s>
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50 <s>Cumque multa in eo genere meditatus eſſem, poſt­<lb></lb>
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51 quam ad iuris ciuilis ſtudium tranſii, ac tandem <lb></lb> ad
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52 Rempub. nunquam mihi tantum otii contigit, <lb></lb> vt ea in
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53 ordinem redigere potuerim. </s>
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54 <s>At cum pau­<lb></lb> cis retrò annis ſatis longam peregrinationem
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55 per <lb></lb> Sarmatiam ſuſcepiſſem,
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56 eſſetque vacuus curis a-<emph.end type="italics"></emph.end>
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57 <pb xlink:href="044/01/004.jpg"></pb><emph type="italics"></emph>nimus, atque ad earum
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58 rerum meditationem me <lb></lb> impelleret genius meus, cœpi aliquid de
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59 his ſcribe­<lb></lb> re, quantum ipſe iter faciendo meo marte
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60 aſſequi <lb></lb> potui cum libris deſtituerer. </s>
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61 <s>Scriptum illud cum <lb></lb> in maximè ardua &amp; difficìli
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62 contemplatione ver<lb></lb> ſetur, nec ab eo tempore ex quo
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63 adſolitas occupa­<lb></lb> tiones redii ei extremam manum apponere
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64 mihi <lb></lb> licuerit, decreueram inter priuatas meas muſas <lb></lb>
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65 aſſeruare Verebar enim vulgi <expan abbr="iudiciũ">iudicium</expan>, (cuius <expan abbr="ta-mẽ">ta­<lb></lb>
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66 men</expan> rationem viro politico <expan abbr="habendã">habendam</expan> eſſe cenſeo) ne­<lb></lb> que
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67 ſolum vulgi, verum etiam <expan abbr="eorũ">eorum</expan> qui
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68 doctorum <lb></lb> nomine gaudent, cum inaudita quædam interdum <lb></lb>
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69 quæque ab eorum opinione recedere <expan abbr="videãtur">videantur</expan> at­<lb></lb> tingam. </s>
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70 <s><expan abbr="Cupiebã">Cupiebam</expan> etiam in eo argumento
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71 vlteriùs <lb></lb> progredi, antè quam quidquam ederem, atque ea <lb></lb>
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72 quæ in meis aduerſariis ea de re ſparſa habeo, iis
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73 <lb></lb> quæ <expan abbr="congeſſerã">congeſſeram</expan> ſubiicere, vt iuſtum <expan abbr="volumẽ">volumen</expan> fieret.<emph.end type="italics"></emph.end></s>
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74 </p>
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75 <p type="main">
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76
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77 <s><emph type="italics"></emph>Poſtquam verò te diſceſſum
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78 ex hac nostra ci­<lb></lb> uitate parare intellexi, in qua dum
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79 verſatus es. <lb></lb>
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80 </s>
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81 <s>non ſolùm ei <expan abbr="ornamẽto">ornamento</expan>
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82 fuiſti, ſed etiam optimos <lb></lb> quoſque virtutum tuarum
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83 admiratione tibi con­<lb></lb> ciliasti: mihi verò peculiariter
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84 innumera beneuo-<emph.end type="italics"></emph.end>
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85 <pb xlink:href="044/01/005.jpg"></pb><emph type="italics"></emph>lentiæ
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86 ſigna exhibuiſti, non potui tantum virum, <lb></lb> meíque
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87 <expan abbr="amãtem">amantem</expan> ſine aliquo munere
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88 aut<emph.end type="italics"></emph.end>
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89 <foreign lang="grc">μνημοσύνῳ</foreign><lb></lb>
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90 <emph type="italics"></emph>dimittere. </s>
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91 <s>Itaque libellum hunc tibi dicare, &amp; <lb></lb> ſub tuo nomine in
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92 publicum edere ſtatui. </s>
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93 <s>Squalli­<lb></lb> dus quidem prodit, &amp; rudis, mole etiam
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94 perexi­<lb></lb> guus: ſplendidius aliquid &amp; magis elaboratum
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95 <lb></lb> postularet tua dignitas. </s>
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96 <s>Atqui ea eſt argumenti <lb></lb> illius magnitudo, vt in eo aliquid
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97 voluiſſe ſatis <lb></lb> ſit. </s>
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98 <s>Militare ſanè munus eſt, eóque nomine tibi <lb></lb>
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99 conueniens: ſi quis enim hac cognitione inſtructus <lb></lb> fuerit,
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100 non minùs ea in re bellica vti poterit, <lb></lb> quam Archimedes in
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101 Syracuſis defendendis <lb></lb> aduerſus Marcum Marcellum vſus
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102 est. </s>
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103 <s>Eá­<lb></lb> que mirari deſinet quæ de eo Plutarchus
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104 nar­<lb></lb> rat. </s>
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105 <s>Id lucidius <expan abbr="demõſtrare">demonſtrare</expan>
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106 potuiſſem, ſi mihi hæc <lb></lb> vlterius
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107 perſequendi otium fuiſſet: Jeiuna enim <lb></lb> per ſe
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108 videntur, niſi quis ſuccum qui ſub corti­<lb></lb> ce
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109 latet, eliciat. </s>
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110 <s>Malui tamen hoc veluti pro­<lb></lb> gymnaſmate alios quibus plus est
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111 otii &amp; in­<lb></lb> genii ad eiuſmodi inquiſitionem hortari
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112 &amp; ac­<lb></lb> cendere, quàm præclaram illam
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113 cognitio­<lb></lb> nem diutius ſepultam relinquere cum ne-<emph.end type="italics"></emph.end>
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114 <pb xlink:href="044/01/006.jpg"></pb>
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115 <emph type="italics"></emph>minem hodie animaduertam qui ei inſudet, <lb></lb>
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116 neque mihi ſpes vlla affulgeat diuturni otii, cuius <lb></lb> ope in hoc
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117 ſtadio pergere poßim: Quòd ſi fortè <lb></lb> mihi
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118 aliquando contingat, riuos plurimos ex his <lb></lb> fontibus me educturum;
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119 <expan abbr="cõfido">confido</expan>; quibus multum <lb></lb>
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120 <expan abbr="cõmoditàtis">commoditàtis</expan> rebus humanis
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121 accedat. </s>
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122 <s>Quæ enim <lb></lb> hic traduntur, ad motus omnes atque ad omnis ge<lb></lb>
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123 neris virium comparationes accommodari poſ­<lb></lb> ſunt ad
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124 fines propoſitos aſſequendos. </s>
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125 <s>Quod quàm <lb></lb> latè pateat, dici non poteſt. </s>
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126 <s>Eſt enim eorum vſus <lb></lb> non ſolùm in mechanicis, in
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127 quibus tamen eſt ma <lb></lb> ximus, ſed etiam in politicis &amp;
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128 œconomicis: ſunt <lb></lb> enim in illis motus, ſunt vires
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129 &amp; reſistentiæ. </s>
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130 <s>In <lb></lb> arte medica &amp; reliquis phyſices partibus pra­<lb></lb>
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131 cticis, quantus ſit, nemo fando exprimere poßit. <lb></lb>
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132 </s>
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133 <s>Quia vero ea quæ praxim docent gratiora ſunt <lb></lb> ipſa
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134 contemplatione, &amp; cauſæ propter effecta in­<lb></lb>
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135 quirantur,<emph.end type="italics"></emph.end>
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136 <foreign lang="grc">Ἀλφήστας</foreign>
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137 <emph type="italics"></emph>omnes hortor vt quod ego in­<lb></lb> numeris aliis
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138 cur is implicitus addere non poſ­<lb></lb> ſum, ipſi
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139 addant. </s>
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140 <s>Abundat nunc Europa præ­<lb></lb> ſtantibus ingeniis, ſi
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141 Mœcenates adeſſent. <lb></lb>
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142 </s>
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143 <s>Ea autem quæ præter hæc meditatus ſum, ac fer-<emph.end type="italics"></emph.end><pb xlink:href="044/01/007.jpg"></pb>
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144 <emph type="italics"></emph>mè parata habeo, hæc ſunt. </s>
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145 <s>Tractatus de iactu. <lb></lb>
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146 </s>
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147 <s>De continuitate eiuſque ſolutione. </s>
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148 <s>De <expan abbr="cõdenſa-tione">condenſa­<lb></lb>
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149 tione</expan> &amp; rarefactione earumque cauſis &amp;
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150 effecti­<lb></lb> bus: <expan abbr="Itẽ">Item</expan> in Mechanicis,
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151 tractatus de variis ma­<lb></lb> chinis ad motus <expan abbr="ciẽdos">ciendos</expan>, ac de perfectißimæ
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152 cuiuſ­<lb></lb> que ad id quod propoſitum fuerit moliendum
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153 in­<lb></lb> ueſtigatione. </s>
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154 <s>Nonnulla <expan abbr="etiã">etiam</expan> de <expan abbr="Rerumpublicarũ">Rerumpublicarum</expan>
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155 <lb></lb> motu tum interno <expan abbr="tũ">tum</expan> externo notaui,
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156 quæ <expan abbr="eodẽ">eodem</expan> or­<lb></lb> dine tradere
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157 optarem: quorum omnium principia <lb></lb> hic ſi quis diligenter
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158 animaduertat tradita ſunt. <lb></lb>
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159 </s>
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160 <s>Si quis mihi in his <expan abbr="palmã">palmam</expan> præripuerit,
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161 meque an­<lb></lb> teuerterit ei maximas gratias agam. </s>
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162 <s>Sunt tamen <lb></lb> inter hæc quædam quæ vulgò pandere
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163 nephas est. <lb></lb>
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164 </s>
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165 <s>Itaque theoriæ magis inſiſtendum puto, in qua ſi <lb></lb>
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166 quis exercitatus fuerit, nullo negotio illam in opus <lb></lb> educere poterit,
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167 idque ſine periculo fiet, cum vul­<lb></lb> go non pateat. </s>
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168 <s>Alioqui <expan abbr="periculũ">periculum</expan> eſt, ne ſi
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169 particu­<lb></lb> laria tradantur iis contenti homines, vt fieri
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170 ſolet <lb></lb> vniuerſalem cognitionem &amp; cauſarum
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171 inquiſi­<lb></lb> tionem negligant, pereatque ſcientia. </s>
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172 <s>Eaque de <lb></lb> cauſa nihil quicquam de his quæ fecerat
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173 Archi-<emph.end type="italics"></emph.end>
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174 <pb xlink:href="044/01/008.jpg"></pb>
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175 <emph type="italics"></emph>medes ſcriptum relinquere voluit. </s>
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176 <s><expan abbr="Exiſtimãs">Exiſtimans</expan> eos <lb></lb> qui in
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177 iis quæ<emph.end type="italics"></emph.end>
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178 <foreign lang="grc">θεωρητικῶς</foreign>
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179 <emph type="italics"></emph>tradiderat, diligentem ope­<lb></lb> ram ponere
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180 <expan abbr="vellẽt">vellent</expan>, multò maiora quoties
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181 opus fo­<lb></lb> ret præſtituros. </s>
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182 <s>Equidem mihi perſuadeo non de­<lb></lb> futuros qui varia iudicia de
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183 hoc noſtro ſcripto fe­<lb></lb> rant &amp; quaſi nouum
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184 athletam in arenàm pro­<lb></lb> deuntem mirentur. </s>
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185 <s>Quibus vno verbo reſpon­<lb></lb> ſum volo, me nullius vnquam in
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186 verba ma­<lb></lb> gistri iuraſſe, ſed liberrimè
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187 ſemper philoſo­<lb></lb> phatum eſſe: ita vt etiam
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188 in principia ab aliis <lb></lb> ſtatuta animaduertere mihi licere
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189 putauerim. <lb></lb>
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190 </s>
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191 <s>Quod eò liberiùs feci, poſtquam magnam <expan abbr="partẽ">partem</expan>
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192 <lb></lb> vulgo receptarum opinionum falſam eſſe re ipſa
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193 <lb></lb> deprehendi. </s>
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194 <s>Omnibus placuero, ſi tibi placuero. </s>
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195 <s>Si <lb></lb> quid in his obſcurius fuerit, habes <expan abbr="clarißimũ">clarißimum</expan> vi­<lb></lb> rum
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196 Wenceſlaum lauinium tuum, abſtruſioris <lb></lb>
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197 philoſophiæ indagatorem <expan abbr="ſummũ">ſummum</expan>, qui tibi omnia <lb></lb> explicabit. </s>
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198 <s>Hoc igitur <expan abbr="munuſculũ">munuſculum</expan> vt
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199 ſerena <expan abbr="frõ-te">fron­<lb></lb> te</expan>
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200 ſuſcipias rogo. </s>
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201 <s>Vale. </s>
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202 <s>V I. </s>
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203 <s>K al. Jun. Anno <lb></lb> Christi Domini<emph.end type="italics"></emph.end> M. D. LXXXIV. </s>
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204
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205
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206
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207 </p>
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208 </section>
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209 <pb xlink:href="044/01/009.jpg" pagenum="1"></pb>
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210 <section>
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211 <p type="head">
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212
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213 <s>M. VARRONIS DE <lb></lb> MOTV TRACTATVS.</s>
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214 </p>
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215 </section>
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216 </front>
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217 <body>
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218 <chap>
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219 <p type="head">
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220
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221 <s><emph type="italics"></emph>PROBLEMA.<emph.end type="italics"></emph.end></s>
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222 </p>
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223 <p type="head">
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224
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225 <s><emph type="italics"></emph>Data vi datum pondus mouere.<emph.end type="italics"></emph.end></s>
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226 </p>
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227 <p type="main">
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228
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229 <s>Hoc problema prima quidem <lb></lb> fronte mirabile videtur, vt ſcilicet
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230 <lb></lb> pondus vel maximum viribus ta­<lb></lb> men minimis, vt puta ſi
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231 dicas vnius <lb></lb> hominis, vel etiam imbecillioris a­<lb></lb> licuius
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232 animalis viribus totum ter­<lb></lb> ræ globum loco moueri
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233 poſſe. </s>
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234 <s>Quod Archimedem <lb></lb> Syracuſanum iactaſſe referunt hoc
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235 dicto, <foreign lang="grc">δὸς ποῦ στῷ <lb></lb> τὰν γὰν κινῷ.
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236 </foreign></s>
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237 <s>Si quis tamen in Geometrico puluere <lb></lb> verſatus fuerit,
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238 preſertim verò in iis quæ ab ipſo in <lb></lb> ſuo
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239 <foreign lang="grc">ἰσοροπικῶν</foreign> libello <expan abbr="tradũtur">traduntur</expan>. </s>
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240 <s>Illud cæteráque eiuſ­<lb></lb> modi, ludicra Geometriæ,
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241 vt &amp; ipſe facere ſolitus di<lb></lb> citur, appellabit. </s>
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242 <s>Ex huius autem problematis expli<lb></lb> catione, omnium machinarum quę ad
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243 motus cien­<lb></lb> dos excogitari poſſunt, ratio pendet. </s>
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244 <s>Etſi verò <expan abbr="totũ">totum</expan>
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245 <lb></lb> Geometrica demonſtratione expediri poſſit, quo­
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246 <pb xlink:href="044/01/010.jpg" pagenum="2"></pb>niam tamen hęc
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247 conſideratio, quæ Græcis <foreign lang="grc">σταθμικὴ</foreign> di<lb></lb> citur Geometriæ tantùm eſt
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248 <foreign lang="grc">ὑπάλληλος</foreign> mixta ſcili­<lb></lb>
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249 cet ex phyſica &amp; Geometrica eo quòd illius
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250 ſubie­<lb></lb> ctum ſit motus. </s>
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251 <s>Ideò paulò craſſiori Minerua &amp; <lb></lb> præter
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252 Geometricam ſimplicitatem <foreign lang="grc">φυσικῶς</foreign>
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253 etiam <lb></lb> tractanda eſt: alioqui Archimedicis
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254 demonſtratio­<lb></lb> nibus ſtandum eſſet,
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255 quæ in eo mancæ ſunt, quòd il­<lb></lb> læ
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256 propoſitiones quæ ex phyſicis peti debent, inde­<lb></lb>
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257 monſtratæ manent, nec explicantur, ſed pro
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258 confeſ­<lb></lb> ſis principiorum loco poſtulantur. </s>
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259 <s>Eas igitur, qua­<lb></lb> tenus ad huius problematis explicationem faciunt,
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260 <lb></lb> hic diſcutiemus. </s>
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261 <s>Neque enim Euclidis <expan abbr="librũ">librum</expan> de
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262 gra­<lb></lb> ui &amp; leui, in quo hoc argumentum perſequi
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263 voluiſ­<lb></lb> ſe videtur, integrum habemus. </s>
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264 <s>Ariſtoteles verò in <lb></lb> eo quod ab ipſo ſcriptum
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265 extat de Mechanicis fra­<lb></lb> gmento pręter ſuum morem,
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266 cùm alio qui in omni­<lb></lb> bus exactiſſimus ſit,
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267 hanc quæſtionem potiùs nota­<lb></lb> uit quàm
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268 explicuit in ſexto &amp; ſeptimo phyſicorum <lb></lb> libro
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269 multa prætermiſit. </s>
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270 <s>Vt igitur ad rem aggredia­<lb></lb> mur, primùm voces, quibus vtendum
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271 eſt, definie­<lb></lb> mus, vt intelligatur quo ſenſu eas
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272 accipiamus. </s>
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273 </p>
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274 <p type="head">
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275
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276 <s>DEFINITIO I.</s>
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277 </p>
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278 <p type="main">
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279
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280 <s>Vis dicitur agendi aut agenti reſiſtendi <expan abbr="potẽtia">potentia</expan>, <lb></lb> præſertim
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281 verò mouendi &amp; mouenti reſiſtendi. </s>
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282 </p>
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283 <p type="head">
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284
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285 <s>II.</s>
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286 </p>
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287 <p type="main">
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288
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289 <s>Vis ſubiectum dicitur id quod vis mouet, vel <pb xlink:href="044/01/011.jpg" pagenum="3"></pb>quod à vi mouetur. </s>
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290 </p>
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291 <p type="main">
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292
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293 <s>Hîc non agimus de vi primaria quæ virium o­<lb></lb> mnium
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294 principium eſt, mouétque omnia, nec <expan abbr="tamẽ">tamen</expan>
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295 <lb></lb> mouetur, ſed de ea, quę dum mouet, <expan abbr="etiã">etiam</expan> cum ſub­<lb></lb> iecto, cui ineſt, mouetur.
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296 </s>
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297 </p>
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298 <p type="main">
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299
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300 <s>Subiecta verò quæ nullam vim habent, nec mo­<lb></lb> uentur, nec
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301 mouenti <expan abbr="reſiſtũt">reſiſtunt</expan>: ſi qua verò vis illis
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302 ac­<lb></lb> cedat, tum ab ea ſe moueri patiuntur. </s>
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303 </p>
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304 <p type="main">
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305
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306 <s>Etſi autem plura ſint virium genera, tot ſcilicet, <lb></lb>
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307 quot ſunt in rerum natura contrariorum, actionem <lb></lb> &amp;
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308 paſſionem recipientium, vt leue graue, rarum <expan abbr="dẽ-ſum">den­<lb></lb> ſum</expan>, plenum
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309 vacuum, durum molle, &amp; cætera eiuſ­<lb></lb> modi, quoniam
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310 tamen ea omnia hîc perſequi noſtri <lb></lb> non eſt
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311 inſtituti, cùm de ea tantùm qua motus fit a­<lb></lb> gere
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312 ſtatuerimus. </s>
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313 </p>
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314 <p type="head">
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315
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316 <s>III.</s>
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317 </p>
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318 <p type="main">
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319
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320 <s>Cùm de motu hîc agemus motum ad locum, <lb></lb> quem Græci
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321 <foreign lang="grc">φορὰν</foreign> vocant, intelligi volumus. </s>
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322 </p>
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323 <p type="head">
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324
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325 <s>IIII.</s>
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326 </p>
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327 <p type="main">
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328
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329 <s>Linea autem recta quæ eſt ab eo loco à quo mo­<lb></lb> tus
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330 fieri incipit ad illum ad quem tendit. </s>
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331 <s>Illius vis <lb></lb> quæ motum efficit, nutus dicetur. </s>
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332 </p>
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333 <p type="main">
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334
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335 <s><expan abbr="Eadẽ">Eadem</expan> verò linea <expan abbr="cõſiderata">conſiderata</expan> à loco ad
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336 <expan abbr="quẽ">quem</expan>
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337 <expan abbr="tẽdit">tendit</expan> vis <lb></lb> ad <expan abbr="illũ">illum</expan> à quo motus fieri incipit, contra
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338 <expan abbr="nutũ">nutum</expan> dicitur. </s>
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339 </p>
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340 <p type="main">
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341
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342 <s>Itidem &amp; omnes illi parallelæ. </s>
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343 </p>
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344 <p type="main">
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345
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346 <s>Quæ verò lineæ vel rectæ, vel curuæ, nutus <expan abbr="lineã">lineam</expan>
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347 <pb xlink:href="044/01/012.jpg" pagenum="4"></pb>ad angulos inæquales
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348 ſecant, illæ obliquè nutum <lb></lb> verſus, vel contra
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349 nutum ferri <expan abbr="dicũtur">dicuntur</expan>, habita
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350 ratio­<lb></lb> ne partium, quas ſpectant. </s>
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351 </p>
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352 <p type="main">
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353
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354 <s>Plurimùm autem à ſitu corporis humani deno­<lb></lb>
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355 minationem accipiunt illæ partes, vt ſurſum,
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356 deor­<lb></lb> ſum, dextrorſum, ſiniſtrorſum,
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357 antè vel ponè di­<lb></lb> cantur. </s>
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358 <s>Quæ verò lineæ, nutus lineam ad angulos <lb></lb> rectos
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359 ſecant, neque verſus nutum, neque contra <lb></lb> nutum ferri
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360 dicuntur, ſed æquè diſtant à loco natu­<lb></lb>
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361 rali. </s>
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362 </p>
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363 </chap>
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364 <chap>
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365 <p type="head">
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366
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367 <s><emph type="italics"></emph>Virium diuiſio.<emph.end type="italics"></emph.end></s>
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368 </p>
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369 <p type="main">
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370
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371 <s>Vis autem omnis aut naturalis eſt, aut non natu­<lb></lb> ralis, aut
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372 mixta. </s>
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373 <s>Naturalis vis eſt, qua res quælibet <lb></lb> natura ſua
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374 mouetur, aut mouenti reſiſtit habita ra­<lb></lb> tione tum
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375 loci ſui naturalis, tum etiam ſitus ſuarum <lb></lb> partium. </s>
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376 <s>Non naturalis eſt quæ nec ratione loci ſui <lb></lb> naturalis,
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377 nec ſitus partium mouet. </s>
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378 <s>Eſt autem hæc <lb></lb> duplex, fortuita ſcilicet &amp;
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379 voluntaria: illa vt vis ven­<lb></lb> torum &amp; ſpirituum
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380 intellectu carentium, hæc vt a­<lb></lb> nimalium &amp;
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381 ſpirituum intelligentium &amp; ſimilium. <lb></lb>
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382 </s>
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383 <s>Mixta dicitur, quæ partim naturalis eſt, partim non <lb></lb>
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384 naturalis. </s>
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385 </p>
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386 <p type="main">
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387
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388 <s>Locus autem naturalis cuiuſque rei eſt, in quo <lb></lb>
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389 exiſtens ipſa quieſcit, &amp; ſi inde remota
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390 ſit, vis ei à na<lb></lb> tura inſita eam illuc impellit. </s>
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391 <s>Huius verò motus aut <lb></lb> quietis cauſſa nulla alia
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392 aſſignari poteſt præter pri- <pb xlink:href="044/01/013.jpg" pagenum="5"></pb>mam illam rerum omnium
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393 conditricem, quę, ne o­<lb></lb> mnia in omnibus eſſent
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394 ſingulis partibus vniuerſi <lb></lb> ſingula loca attribuit
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395 circa quæ conglobantur, &amp; i­<lb></lb> bi hærent. </s>
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396 <s>Quicquid enim terreum eſt, in terræ glo­<lb></lb> bum <expan abbr="cõfluxit">confluxit</expan>. </s>
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397 <s>Ita quicquid ſoli homogenes in Solis <lb></lb> corpus, lunaria omnia in
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398 lunam, &amp; ſic de cæteris cor<lb></lb> poribus vniuerſi. </s>
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399 <s>Singulæ autem eorum partes ſuis <lb></lb> totis adhærent, nec
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400 inde ſponte <expan abbr="mouẽtur">mouentur</expan>: ſi
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401 verò in­<lb></lb> de motæ fuerint, eò redire nituntur. </s>
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402 <s>Quod enim in <lb></lb> terra fieri videmus, idem &amp; in reliquis corporibus
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403 v­<lb></lb> niuerſi fieri dicere poſſumus, ſcilicet
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404 quod vnita cir<lb></lb> ca locum ſuum naturalem maneant: ſi enim
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405 partes <lb></lb> eorum ſponte ſepararentur, &amp; vi ab ipſis
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406 ſeparatæ <lb></lb> ad locum ſuum non redirent, ſtatim
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407 tota diſſolue­<lb></lb> rentur. </s>
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408 </p>
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409 <p type="main">
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410
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411 <s>Vis igitur illa in loco ſuo quieſcendi grauitas di­<lb></lb>
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412 citur, cuius contrarium eſt leuitas. </s>
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413 <s>Res autem nulla <lb></lb> per ſe leuis dicitur, ſed <expan abbr="tãtùm">tantùm</expan> habita ratione alterius <lb></lb>
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414 loci, quàm ſui naturalis: vt puta ſi pars aliqua Solis
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415 <lb></lb> vi quapiam in terram inuecta eſſet, ſuóque
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416 arbitrio <lb></lb> committeretur, illa ſtatim Solem peteret: ita ſi
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417 ter­<lb></lb> ræ pars in Solem inuecta eſſet,
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418 ſuóque arbitrio com<lb></lb> mitteretur, ſtatim à
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419 ſole euolaret, &amp; ſe per cælum <lb></lb> terram verſus
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420 proriperet. </s>
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421 <s>Vt igitur terræ partes in <lb></lb> terra graues ſunt: ſic Solis
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422 partes in ſole graues ſunt: <lb></lb> in terra verò leues,
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423 terræ verò partes in Sole leues <pb xlink:href="044/01/014.jpg" pagenum="6"></pb>ſunt. </s>
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424 <s>Idem de cæteris corporibus vniuerſi dici po­<lb></lb> teſt. </s>
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425 <s>Neque enim faciliùs ex globo lunæ particulam <lb></lb> abſtrahas,
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426 quàm ex terra glebam. </s>
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427 </p>
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428 <p type="main">
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429
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430 <s>Aer autem nullum proprium habet locum natu<lb></lb> ralem, ſed vbique
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431 eſſe poteſt, cùm rerum omnium <lb></lb> locus
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432 vniuerſalis eſſe videatur: de quo dubitari po­<lb></lb>
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433 teſt an ſit infinitus, cùm omnia contineat, à nulla re
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434 <lb></lb> verò totus comprehendatur, ſed hæc diſputatio
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435 non <lb></lb> eſt huius loci. </s>
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436 </p>
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437 <p type="main">
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438
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439 <s>Etſi autem nullum proprium habet locum natu<lb></lb> ralem, neque leuis aut
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440 grauis ſit: leuis tamen eſſe vi­<lb></lb> detur, cùm
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441 grauis non ſit, nec ægrè ſe moueri patia­<lb></lb>
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442 tur. </s>
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443 <s>Itaque ſi quo modo ita conſtitutus ſit, vt rem a­<lb></lb>
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444 liquam, quò minùs ad locum ſuum naturalem per­<lb></lb>
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445 uenire poſſit, impediat, tum per expreſſionem
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446 ſeu <lb></lb>
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447 <foreign lang="grc">ἔκθλιψιν</foreign>, ab ea eiicietur, in
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448 eiúſque locum ſuccedet, <lb></lb> vt fit in aqua, cùm ei
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449 introducitur. </s>
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450 <s>Quæ quidem <foreign lang="grc">ἔκ­<lb></lb> θλιψις</foreign> iis
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451 etiam accidit quæ loco naturali gaudent, <lb></lb> cùm
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452 ſeſe mutuò impediunt, ne ad illum ferantur. <lb></lb>
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453 </s>
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454 <s>Præſertim verò in liquidis locum habet, quorum <lb></lb> partes
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455 facilius mouentur, quàm rerum <expan abbr="cohærentiũ">cohærentium</expan>
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456 <lb></lb> &amp; compactarum. </s>
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457 <s>Inde accidit vt quicquid liquidis <lb></lb> immergitur, tantò fiat in illis
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458 leuius quàm grauius, <lb></lb> eſt moles eiuſdem liquoris
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459 ipſorum moli æqualis. <lb></lb>
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460 </s>
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461 <s>Sed hæc de loco naturali fuſiùs à nobis alibi
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462 medita­<lb></lb> ta, obiter hîc attigiſſe ſufficiat,
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463 vt intelligatur quid <pb xlink:href="044/01/015.jpg" pagenum="7"></pb>ſit
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464 vis naturalis. </s>
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465 </p>
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466 <p type="main">
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467
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468 <s>Vis autem voluntaria nullum certum nutum <lb></lb> habet, ſed illum
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469 tantùm in quo mouentis voluntas <lb></lb> conquieſcit. </s>
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470 <s>Cúmque vis naturalis vnum tantùm <lb></lb> nutum habeat, ſcilicet
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471 à loco à naturali requie re­<lb></lb> moto, ad ipſam
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472 naturalem requiem, illa infinitos nu <lb></lb> tus habet &amp; indeterminatos
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473 per ſe ac voluntatis tan <lb></lb> tùm decreto determinabiles. </s>
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474 </p>
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475 <p type="main">
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476
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477 <s>Fortuita verò ipſo tantùm caſu determinabilem <lb></lb>
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478 nutum habet: quò enim ipſa tendit, eo munere dici­<lb></lb> tur
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479 ſiue ſurſum, ſiue deorſum, ſiue ad
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480 latera. </s>
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481 <s>Itaque <lb></lb> &amp; hic &amp; ille nutus <foreign lang="grc">ἀδιόριστος</foreign> dicitur. </s>
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482 <s>Quemadmodum <lb></lb> &amp; is quem habent vires illæ, quibus res à
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483 ſitu <expan abbr="partiũ">partium</expan>
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484 <lb></lb> naturali remotæ ad illum redeunt: prout enim ab <lb></lb> eo
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485 motæ ſunt, ita ad illum redeunt, prout etiam huc <lb></lb> aut illuc
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486 obuerſæ ſunt, vt vis arcus aut baliſtæ. </s>
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487 </p>
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488 <p type="head">
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489
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490 <s>DEFIN. V.</s>
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491 </p>
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492 <p type="main">
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493
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494 <s>Vires autem contrariæ dicuntur, quæ contrarios <lb></lb> motus ciere
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495 poſſunt, vt ea <expan abbr="quę">quæ</expan>
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496 ſurſum mouet &amp; <expan abbr="quę">quæ</expan><lb></lb>
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497 deorſum, &amp; ſic de cæteris. </s>
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498 </p>
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499 <p type="main">
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500
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501 <s>Conſideratur autem in vi <expan abbr="quãtitas">quantitas</expan>,
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502 tum eo quòd <lb></lb> vis partibus ſuis conſtet, in quas in
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503 infinitum diuidi <lb></lb> poteſt, &amp; rurſus additione aut
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504 multiplicatione au­<lb></lb> geri, tum quòd æqualitatis
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505 exceſſus &amp; defectus <expan abbr="cõ-parationem">con­<lb></lb> parationem</expan> recipiat. </s>
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506 </p>
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507
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508
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509 <pb xlink:href="044/01/016.jpg" pagenum="8"></pb>
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510 <p type="main">
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511
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512 <s>Ac quoniam vis eſt mouendi potentia, vis par­<lb></lb> tes erunt
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513 quæ motus partes efficient, &amp; quæ erit mo<lb></lb> tus partium,
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514 menſura eadem erit &amp; vis partium. </s>
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515 <s>Et <lb></lb> motus quidem propria menſura eſt linea ſeu <expan abbr="ſpatiũ">ſpatium</expan>. <lb></lb>
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516 </s>
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517 <s>Quantum enim res quæpiam mota, ſpatij percur­<lb></lb> rit,
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518 tantùm mota eſſe dicitur. </s>
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519 <s>Quoniam verò in mo<lb></lb> mento vel inſtanti quod inſtar
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520 puncti eſt, &amp; magni­<lb></lb> tudine caret, nullus motus fieri
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521 poteſt, ſed motus o­<lb></lb> mnis in tempore fit. </s>
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522 <s>Ideò ad motus menſuram tem­<lb></lb> pus etiam adhibere oportet. </s>
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523 <s>Illud enim cum ſpatio <lb></lb> vel linea, motus dici facit æquales
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524 aut inæquales. </s>
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525 </p>
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526 <p type="head">
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527
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528 <s>DEFIN. VI.</s>
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529 </p>
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530 <p type="main">
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531
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532 <s>Æquales igitur motus dicuntur, qui æqualibus <lb></lb> temporibus
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533 æqualia ſpatia percurrunt. </s>
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534 </p>
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535 <p type="main">
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536
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537 <s>Qui autem æqualibus temporibus æqualia ſpa­<lb></lb> tia
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538 permeant, illi iidem proportionales ſunt: hoc <lb></lb> eſt,
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539 quæ eſt ratio temporis, quo alter eorum fit ad <lb></lb> tempus quo
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540 fit alter, eadem eſt ſpatij quod percurrit <lb></lb> alter ad
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541 ſpatium quod reliquus percurrit. </s>
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542 <s>Si enim <lb></lb> duorum quorum ſinguli vna hora miliaris vnius
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543 i­<lb></lb> ter conficiunt, alter eodem motu per tria miliaria <lb></lb> ferri
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544 pergat, alter verò per duo <expan abbr="tãtùm">tantùm</expan>. </s>
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545 <s>Ille tribus ho­<lb></lb> ris ea abſoluet, hic verò duabus, &amp;
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546 æquè celeriter <lb></lb> ferri dicentur, licet ſpatia
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547 inæqualia <expan abbr="percurrãt">percurrant</expan>,
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548 quo­<lb></lb> niam illa ſunt temporibus proportionalia. </s>
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549 </p>
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550
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551
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552 <pb xlink:href="044/01/017.jpg" pagenum="9"></pb>
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553 <p type="head">
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554
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555 <s>VII.</s>
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556 </p>
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557 <p type="main">
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558
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559 <s>Inæquales autem motus dicuntur, quorum tem­<lb></lb> pora non
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560 ſunt ſpatiis proportionalia. </s>
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561 <s>Eorum autem <lb></lb> maior ille dicitur, cuius maior erit ratio ſpatij ad
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562 ſpa<lb></lb> tium, quàm temporis ad tempus, quibus fiunt illi <lb></lb>
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563 motus. </s>
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564 <s>Ex quo intelligitur etiam quis minor dica­<lb></lb> tur. </s>
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565 <s>Maior igitur dicetur qui celeriùs feretur, minor, <lb></lb> qui
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566 tardiùs. </s>
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567 </p>
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568 <p type="head">
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569
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570 <s>VIII.</s>
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571 </p>
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572 <p type="main">
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573
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574 <s>Æquales igitur vires dicentur, quæ æqualibus <lb></lb> motibus
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575 ſubiecta ſua mouebunt. </s>
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576 <s>Maior verò quæ <lb></lb> ſubiectum ſuum magis vel
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577 celeriùs mouebit. </s>
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578 <s>Mi­<lb></lb> nor, quæ minùs vel tardiùs. </s>
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579 </p>
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580 </chap>
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581 <chap>
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582 <p type="head">
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583
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584 <s><emph type="italics"></emph>Motuum diuiſio.<emph.end type="italics"></emph.end></s>
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585 </p>
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586 <p type="main">
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587
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588 <s>Comparantur autem motus ſecundum omnes <lb></lb> comparationis gradus, hoc
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589 eſt, æqualitatem, exceſ­<lb></lb> ſum &amp;
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590 defectum: tum ſibi ipſis, cùm totus ſuis
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591 par­<lb></lb> tibus confertur, tum alij aliis. </s>
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592 </p>
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593 <p type="main">
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594
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595 <s>Quatenus autem ſibi ipſi motus <expan abbr="cõparatur">comparatur</expan>, aut <lb></lb> eſt <foreign lang="grc">ὁμοιομερὴς</foreign> ſeu æquabilis aut <foreign lang="grc">ἀνομοιομερὴς</foreign>, id eſt inæ­<lb></lb>
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596 quabilis. </s>
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597 <s>Aequabilis, cuius omnes partes tum mini­<lb></lb> mæ tum maiores
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598 tempora habent ſpatiis per quæ <lb></lb> cientur proportionalia. </s>
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599 <s>Inæquabilis verò, in quo illa <lb></lb> non ſunt proportionalia.
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600 </s>
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601 </p>
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602 <p type="main">
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603
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604 <s>Inæquabilium autem motuum duo ſunt genera, <pb xlink:href="044/01/018.jpg" pagenum="10"></pb>creſcens ſcilicet
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605 &amp; decreſcens, ídque vel continuè, <lb></lb> vel per
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606 interualla, ordinatim vel <foreign lang="grc">ἀτακτῶς. </foreign></s>
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607 </p>
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608 <p type="main">
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609
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610 <s>Creſcens dicitur, quando partium poſteriorum <lb></lb> ipſius
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611 maior eſt celeritas, quàm priorum: <expan abbr="decreſcẽs">decreſcens</expan>, <lb></lb> quando
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612 minor. </s>
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613 </p>
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614 <p type="main">
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615
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616 <s>Continuè, quando nulla pars illius vel minima <lb></lb> alteri parti
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617 eſt æqualis ſeu ſibi ipſi æquabilis. </s>
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618 </p>
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619 <p type="main">
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620
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621 <s>Per interualla verò, quando partes quidem illius <lb></lb> ſibi
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622 ipſis æquabiles ſunt, aliæ verò aliis
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623 comparatæ <lb></lb> inæquabiles. </s>
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624 </p>
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625 <p type="main">
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626
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627 <s>Ordinatim, quando incrementum aut <expan abbr="decremẽ-tum">decremen­<lb></lb> tum</expan> illud certa aliqua proportionis
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628 progreſſione <lb></lb> fit, vt ſi in motu continuè
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629 creſcente, diuiſo toto mo<lb></lb> tus ſpatio in aliquot
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630 partes æquales eadem ſit ratio <lb></lb> celeritatis, finis primi
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631 ſpatij ad celeritatem finis ſe­<lb></lb> cundi, quæ finis
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632 ſecundi ad finem tertij, &amp; ſic dein­<lb></lb> ceps: vel
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633 ſi finis ſecundi ſpatij duplo citiùs feratur, <lb></lb>
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634 quàm finis primi &amp; finis tertij, triplo quàm primi: <lb></lb>
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635 finis verò quarti quadruplo, &amp; ſic deinceps. </s>
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636 <s>Idem ſi <lb></lb> in quauis alia proportionis progreſſione
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637 illarum <lb></lb> partium celeritas, aliarum ad alias ſe habeat. </s>
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638 <s>In mo­<lb></lb> tu verò per interualla creſcente <expan abbr="augmẽtum">augmentum</expan> illud or­<lb></lb> dinatim
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639 fieri dicetur, ſi interuallorum proportio a­<lb></lb> liquem
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640 progreſſionis ordinem ſeruet: puta ſi <expan abbr="primũ">primum</expan>
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641 <lb></lb> interuallum duplo tardiùs <expan abbr="ſecũdo">ſecundo</expan> moueatur, triplo <lb></lb> verò tardiùs
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642 tertio, &amp;c. </s>
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643 </p>
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644
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645
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646 <pb xlink:href="044/01/019.jpg" pagenum="11"></pb>
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647 <p type="main">
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648
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649 <s>Inordinatè autem creſcere vel decreſcere dicetur <lb></lb>
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650 motus, ſi incrementum illud aut decrementum nul<lb></lb> la certa &amp;
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651 ordinata proportione fiat. </s>
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652 </p>
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653 <p type="main">
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654
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diff changeset
655 <s>Comparantur autem motus alij aliis, æquabiles <lb></lb> ſcilicet &amp;
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656 inæquabiles ordinatim progredientes: de <lb></lb> inordinatorum enim tum
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657 inter ſe, tum cum aliis <expan abbr="cõ||">com</expan><lb></lb>
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658 paratione nihil certò ſtatui poteſt. </s>
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659 </p>
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660 <p type="main">
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661
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662 <s>Comparantur igitur æquabiles cum æquabili­<lb></lb> bus aut cum
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663 inæquabilibus, ac etiam inæquabiles <lb></lb> cum inæquabilibus.
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664 </s>
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665 </p>
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666 <p type="main">
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667
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668 <s>Æquabiles autem cum æquabilibus compara­<lb></lb> tionibus
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669 ſuis partibus correſpondentibus ſunt pro­<lb></lb>
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670 portionales. </s>
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671 <s>Si enim <expan abbr="proponãtur">proponantur</expan> duo motus
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672 æqua­<lb></lb> biles, quorum alter altero maior ſit, quæ
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673 erit ratio <lb></lb> dimidiæ partis vnius ad dimidiam partem alterius,
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674 <lb></lb> eadem erit tertiæ ad tertiam, &amp; ſic deinceps. </s>
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675 </p>
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676 <p type="main">
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677
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678 <s>Æquabilium verò motuum cum inæquabilibus, <lb></lb> cum iis
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679 ſcilicet qui per interualla creſcunt, compa­<lb></lb> ratio fit
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680 tanquam cum pluribus diuerſis motibus æ­<lb></lb> quabilibus,
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681 ſunt enim interuallorum <expan abbr="illorũ">illorum</expan>
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682 motus <lb></lb> æquabiles. </s>
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683 <s>At cum continuè <expan abbr="creſcẽtibus">creſcentibus</expan> aut decre­<lb></lb> ſcentibus
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684 difficile eſt comparationis modum defi­<lb></lb> nire, cùm ne
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685 momento quidem ſtabilis maneat par<lb></lb> tium illarum quantitas. </s>
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686 <s>Eſt tamen motus æquabilis <lb></lb> illorum menſura: tanti enim
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687 eſſe dicuntur, quanti <lb></lb> forent, ſi in ea celeritatis
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688 menſura ad quam perue­ <pb xlink:href="044/01/020.jpg" pagenum="12"></pb>nerunt, æquabiliter pergerent. </s>
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689 </p>
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690 <p type="main">
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691
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692 <s>Creſcentes verò cum creſcentibus continuè, <expan abbr="cõ-parati">con­<lb></lb> parati</expan> ſiquidem eadem
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693 progreſſionis proportione <lb></lb> creſcant, æqualia
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694 ſpatia ab eorum principiis nume­<lb></lb> rata, æqualibus
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695 temporibus emenſa habebunt, idem <lb></lb> in decreſcentibus. </s>
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696 <s>Sed hęc hactenus inquiſiuiſſe ſuf­<lb></lb>
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697 ficiat: ſi quis enim particulatim omnia <expan abbr="expẽdere">expendere</expan> vel­<lb></lb> let, in infinitum ſeſe
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698 extenderet hęc partium &amp; pro­<lb></lb> portionum motuum
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699 ſupputatio. </s>
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700 </p>
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701 <p type="main">
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702
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703 <s>Iam videamus quæ vires quos horum motuum <lb></lb> cieant. </s>
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704 <s>Et vis quidem ea qua res quælibet ad ſitum <lb></lb> naturalem
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705 ſuarum partium redit, motu <expan abbr="cõtinuè">continuè</expan> de­<lb></lb> creſcente mouet: quo enim
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706 propiùs ad ſitum natu­<lb></lb> ralem partium accedit, eo
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707 tardior &amp; languidior eſt. <lb></lb>
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708 </s>
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709 <s>Arcus enim cùm primùm laxari incipit, celeriùs <lb></lb> mouetur,
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710 quàm cùm motus ſui finis propior eſt. </s>
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711 </p>
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712 <p type="main">
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713
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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714 <s>Vis verò naturalis, qua res quęlibet ad <expan abbr="locũ">locum</expan> ſuum <lb></lb> naturalem tendit, ſubiectum
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diff changeset
715 ſuum, motu continuè <lb></lb> &amp; ordinatim creſcente, mouet. </s>
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716 <s>Illius autem motus <lb></lb> cauſa eſt quòd faciliùs id
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717 moueatur, quod in motu <lb></lb> eſt, quàm quod quieſcit. </s>
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718 <s>Vis igitur eadem, <expan abbr="ſubiectũ">ſubiectum</expan>
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diff changeset
719 <lb></lb> quod iam in motu eſt premens, illud magis moue­<lb></lb> bit,
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diff changeset
720 quàm ſi quieſcat, &amp; magis motum, magis etiam <lb></lb>
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721 mouebit: ita vt eadem vis motione maior fiat, quàm <lb></lb> per ſe
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722 ſit. </s>
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723 <s>Et hæc eſt cauſa cur ictus, quo magis ab al­<lb></lb> tero
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diff changeset
724 venit, eo vehementior ſit. </s>
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725 <s>Motus autem huius <pb xlink:href="044/01/021.jpg" pagenum="13"></pb>ſpatia
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726 hanc celeritatis proportionem ſeruant, vt <expan abbr="quę">quæ</expan>
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727 <lb></lb> eſt ratio totius ſpatij, per quod fit ille motus ad
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728 par­<lb></lb> tem ipſius (vtriuſque initio inde ſumpto,
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729 vbi eſt mo<lb></lb> tus initium) eadem ſit celeritatis ad
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730 celeritatem. <lb></lb>
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731 <figure id="id.044.01.021.1.jpg" xlink:href="044/01/021/1.jpg"></figure><lb></lb>
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732 Exempli gratia, ſi vis aliqua per lineam ABC <lb></lb> mouerit,
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733 ſitque AB illius lineæ pars, quæ erit <lb></lb> ratio AC ad AB,
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734 eadem erit celeritatis motus <lb></lb> in puncto C ad <expan abbr="celeritatẽ">celeritatem</expan> motus in puncto B. <lb></lb>
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735 </s>
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736 <s>Cuiuſmodi proportio obſeruatur in paralle­<lb></lb> lis
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737 triangulum ſecantibus. </s>
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738 <s>Vt enim ſe habet <lb></lb>
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739 <figure id="id.044.01.021.2.jpg" xlink:href="044/01/021/2.jpg"></figure><lb></lb> AC ad
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740 AB, ſic CG ad BF, &amp; vt AD ad <lb></lb> AC, ſic DH ad CG.
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741 </s>
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742 <s>Itaque ſi in ſpatia ali­<lb></lb> quot æqualia diuidatur
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diff changeset
743 totius motus ſpa<lb></lb> tium, finis ſecundi duplo citiùs
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744 feretur, <lb></lb> quàm finis primi: finis verò tertijtriplo <lb></lb>
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diff changeset
745 citiùs quàm finis primi, &amp; ſic deinceps. <lb></lb>
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746 </s>
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747 <s>Hac autem ratione fit, vt ſpatiorum illo­<lb></lb> rum initio maxima
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diff changeset
748 ſit celeritatis <expan abbr="differẽ-tia">differen­<lb></lb>
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749 tia</expan>: progreſſu verò ſemper minuatur, ac
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750 tandem fer­<lb></lb> mè eadem ſit, vt fit in trianguli
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751 lateribus, quæ lon­<lb></lb> giſſimè producta
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752 æquè diſtare videntur. </s>
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753 <s>Eáque eſt <lb></lb> ratio cur Solis &amp; Lunæ radij,
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754 etiamſi concurrant (in <lb></lb> ipſorum ſcilicet corporibus,
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755 aut vltra res quas <expan abbr="illu-ſtrãt">illu­<lb></lb>
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756 ſtrant</expan>) paralleli <expan abbr="tamẽ">tamen</expan>
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757 <expan abbr="appareãt">appareant</expan>. </s>
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758 <s><expan abbr="Eadẽ">Eadem</expan>
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759 <expan abbr="etiã">etiam</expan> cauſa eſt cur <lb></lb>
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760 lineę omnes ad <expan abbr="perpẽdiculũ">perpendiculum</expan> in <expan abbr="terrã">terram</expan>
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761 cadentes, paral­<lb></lb> lelæ videantur, cùm <expan abbr="tamẽ">tamen</expan> in centro terræ <expan abbr="cõcurrant">concurrant</expan>. </s>
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762 </p>
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763
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764
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765 <pb xlink:href="044/01/022.jpg" pagenum="14"></pb>
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766 <p type="main">
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767
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768 <s>Hunc igitur motum vis naturalis efficit, modò <lb></lb> nulla quies
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769 intercedat. </s>
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770 </p>
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771 <p type="main">
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772
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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773 <s>Vis autem voluntaria motum omnem ciere apta <lb></lb> eſt. </s>
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774 <s>Fortuita verò inordinatum tantùm motum effi­<lb></lb> cit. </s>
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775 <s>Et hæc de variis virium motibus, <expan abbr="eorúmq;">eorúmque</expan> pro­<lb></lb> portione &amp; partibus. </s>
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776 </p>
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777 <p type="main">
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778
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779 <s>Eſt verò etiam virium partitio quædam, quæ ex <lb></lb>
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780 eorum quibus <expan abbr="inhærẽt">inhærent</expan>
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781 ſubiectorum diuiſione, aut <lb></lb> alterius ad alterum proportione
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782 reſultat. </s>
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783 <s>In ſubie­<lb></lb> ctis enim, quæ <foreign lang="grc">ὁμοιομερῆ</foreign> ſunt, vis naturalis æqualiter <lb></lb>
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784 per omnes partes diffuſa eſt: ita vt quæ eſt ratio
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785 mo­<lb></lb> lis ad molem ſub eadem figura, <expan abbr="eadẽ">eadem</expan> ſit vis ad vim: <lb></lb> vt ſi globus alicuius
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786 metalli, ad alium globum eiuſ­<lb></lb> dem metalli mole quadruplus
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787 ſit, illius quoque <expan abbr="põ-dus">pon­<lb></lb>
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788 dus</expan> ad huius pondus quadruplum erit. </s>
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789 </p>
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790 <p type="main">
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791
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792 <s>Hactenus vim <expan abbr="cõſiderauimus">conſiderauimus</expan> quatenus mouet, <lb></lb> ſupereſt
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793 vt eam conſideremus, quatenus mouenti <lb></lb> reſiſtit. </s>
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794 <s>Habet autem locum reſiſtentia, vbi duæ vi­<lb></lb> res
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795 contrariæ committuntur: ſi enim vtraque <expan abbr="eodẽ">eodem</expan>
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796 <lb></lb> motu moueat, nulla erit reſiſtentia, ſed altera
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797 alteri <lb></lb> addita maiorem vim conſtituet. </s>
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798 </p>
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799 <p type="main">
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800
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801 <s>Committi autem dicuntur vires, quando ita ap­<lb></lb> plicantur &amp;
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802 <expan abbr="connectũtur">connectuntur</expan>, vt altera nutu
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803 ſuo moueri <lb></lb> non poſſit, quin altera contra nutum
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804 ſuum mouea­<lb></lb> tur. </s>
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805 <s>Viribus autem ita connexis, accidit vt altera in <lb></lb> alterius
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806 ſubiectum agat, &amp; altera in ſubiecto ſuo exi- <pb xlink:href="044/01/023.jpg" pagenum="15"></pb>ſtens, alteri in altero
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807 ſubiecto exiſtenti reſiſtat, ita vt <lb></lb> eorum
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808 ſubiecta quodammodo reciproca fiant. </s>
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809 </p>
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810 <p type="head">
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811
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812 <s>CONCLVSIO I.</s>
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813 </p>
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814 <p type="main">
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815
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816 <s>Illam autem reſiſtentiam vi momenti in eodem <lb></lb> ſubiecto
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817 æqualem, aut eandem cum ea eſſe, ex ipſius <lb></lb>
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818 definitione conſtat. </s>
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819 <s>Eſt enim reſiſtere <expan abbr="nõ">non</expan> pati
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820 ſe mo­<lb></lb> ueri. </s>
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821 <s>Quantum autem vis quælibet <expan abbr="ſubiectũ">ſubiectum</expan> ſuum <lb></lb> nutu ſuo mouet, tantum
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822 illud contra nutum ſuum <lb></lb> moueri non patitur. </s>
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823 <s>Mouendi igitur &amp; <expan abbr="mouẽti">mouenti</expan>
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824 re­<lb></lb> ſiſtendi potentia in eodem ſubiecto
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825 æquales ſunt. </s>
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826 </p>
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827 <p type="head">
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828
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829 <s>II.</s>
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830 </p>
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831 <p type="main">
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832
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833 <s>Quemadmodum autem in eodem ſubiecto ma­<lb></lb> ior vis
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834 ineſſe dicitur, in quo eſt maioris motus po­<lb></lb>
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diff changeset
835 tentia, ſic maior reſiſtentia erit maioris motus
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diff changeset
836 con­<lb></lb> trarij impatientia. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
837 <s>Eadem igitur vis magis mouere <lb></lb> nitenti <expan abbr="cõtra">contra</expan> ipſius nutum magis reſiſtet, minus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
838 ve­<lb></lb> rò nitenti minùs reſiſtet. </s>
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diff changeset
839 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
840 <p type="head">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
841
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
842 <s>III.</s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
843 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
844 <p type="main">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
845
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
846 <s>Et quo maior erit motus contrarius, eo magis re­<lb></lb>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
847 ſiſtet: id eſt, quo celerius vis quælibet à nutu
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
848 ſuo re­<lb></lb> uelletur, eo magis reſiſtet. </s>
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diff changeset
849 <s>Duplo igitur citiùs re­<lb></lb> uellenti duplo reſiſtet,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
850 triplo citius triplo reſiſtet, &amp; <lb></lb> ſic <foreign lang="grc">ἀναλόγως</foreign> in omni proportione. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
851 <s>Quæ igitur erit <lb></lb> ratio motus ad motum, contra nutum eadem erit
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diff changeset
852 <lb></lb> in vna &amp; eadem vi ratio reſiſtentiæ ad
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diff changeset
853 reſiſtentiam. </s>
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854 </p>
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diff changeset
855 <p type="main">
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856
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
857 <s>Si verò plures vires comparentur. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
858 </p>
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diff changeset
859
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
860
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
861 <pb xlink:href="044/01/024.jpg" pagenum="16"></pb>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
862 <p type="head">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
863
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
864 <s>IIII.</s>
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diff changeset
865 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
866 <p type="main">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
867
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
868 <s>Æqualium quidem virium æqualibus motibus <lb></lb> æquales erunt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
869 reſiſtentiæ. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
870 <s>Si enim æquales vires æ­<lb></lb> qualiter à ſuis
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
871 nutibus reuellantur, æqualiter reſi­<lb></lb> ſtent. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
872 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
873 <p type="head">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
874
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
875 <s>V.</s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
876 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
877 <p type="main">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
878
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
879 <s>Inæqualibus verò motibus, earum reſiſtentię
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
880 in­<lb></lb> æquales erunt, &amp; motuum proportionem
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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881 ſequen­<lb></lb> tur. </s>
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882 <s>Exempli gratia, ſint duæ vires A &amp; B, quarum v­<lb></lb>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
883 traque vna hora miliare vnum percurrat, illæ æqua­<lb></lb> les
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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884 erunt. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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885 <s>Si igitur vtraque quarta parte vnius milia­<lb></lb> ris, vel dimidio
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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886 miliari à ſuo nutu eodem tempore <lb></lb> reuellatur, eadem erit
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diff changeset
887 vtriuſque illi motui reſiſten­<lb></lb> tia. </s>
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888 <s>Sin verò altera quidem quarta parte vnius milia­<lb></lb> ris à
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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889 nutu ſuo reuellatur, altera verò eodem tempo­<lb></lb> re
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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890 integro miliari reuellatur: hæc reſiſtentia ad
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
891 il­<lb></lb> lam quadrupla erit, &amp; ſic de cæteris motuum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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892 pro­<lb></lb> portionibus. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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893 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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894 <p type="head">
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895
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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896 <s>VI.</s>
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897 </p>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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898 <p type="main">
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899
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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900 <s>Inæqualium verò virium reſiſtentiæ æqualibus
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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901 <lb></lb> motibus ipſarum virium proportionem ſequentur. <lb></lb>
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902 </s>
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903 <s>Quo maior enim eſt vis, eo magis eodem tempore <lb></lb> eodémque
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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904 ſpatio contra nutum mouenti reſiſtit. <lb></lb>
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905 </s>
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906 <s><expan abbr="Exẽpli">Exempli</expan> gratia, ſit vis A quadrupla
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907 ad vim B, vis A mo­<lb></lb> uenti ſe vno miliari quadruplo
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parents:
diff changeset
908 reſiſtet, quàm B mo­<lb></lb> uenti ſe vno miliari
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909 eodem tempore. </s>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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910 </p>
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911
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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912
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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913 <pb xlink:href="044/01/025.jpg" pagenum="17"></pb>
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914 <p type="main">
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915
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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916 <s>Inæqualium verò virium inæqualibus motibus <lb></lb>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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917 reſiſtentiæ, quando motus eam inter ſe
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918 proportio­<lb></lb> nem ſeruabunt, quæ eſt inter eas
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919 <foreign lang="grc">ἀντιπεπονθῶς</foreign>, ſeu <lb></lb>
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920 reciprocè, æquales erunt. </s>
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921 <s>Sit enim vis A quæ ad vim <lb></lb> B eandem habeat <expan abbr="rationẽ">rationem</expan> quam C ad D, puta quam <lb></lb> 3 ad
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922 1, aut 4 ad 1, aut quæcunque alia ſit, <expan abbr="moueatúrq;">moueatúrque</expan>
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923 <lb></lb> vtraque ſpatio E contra nutum ſuum eodem tem­<lb></lb>
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924 pore, reſiſtentia A ad reſiſtentiam B ſe
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925 habebit, vt C <lb></lb> ad D per proximam concluſionem. </s>
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926 <s>Si verò B moue­<lb></lb> atur eodem tempore ſpatio aliquo quod
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927 ſe habeat <lb></lb> ad ſpatium E vt C ad D, reſiſtentia
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928 B huic motui ſe <lb></lb> habebit ad reſiſtentiam priori
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929 motui, vt C ad D per <lb></lb> quartam <expan abbr="concluſionẽ">concluſionem</expan>. </s>
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930 <s>Duæ ergo reſiſtentiæ ad ean­<lb></lb> dem, eandem
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931 habebunt rationem, ergo æquales e­<lb></lb> runt per <emph type="italics"></emph>9<emph.end type="italics"></emph.end> prop. <emph type="italics"></emph>5.<emph.end type="italics"></emph.end> Elem. Eucl.
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932 </s>
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933 </p>
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934 <p type="head">
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935
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936 <s>VIII.</s>
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937 </p>
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938 <p type="main">
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939
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940 <s>Si verò motuum virium inæqualium proportio <lb></lb> non ſit
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941 eadem quæ eſt ipſarum virium reciprocè, vis <lb></lb>
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942 illius quæ ad alteram maiorem habebit rationem, <lb></lb> quàm motus
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943 alterius ad motum ipſius, reſiſtentia <lb></lb> maior erit,
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944 altera verò minor. </s>
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945 <s>Exempli gratia, ſi vis <lb></lb> A ſit tripla ad vim B, &amp; motus
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946 quo B à nutu ſuo reuel<lb></lb> letur, ſit minor quàm
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diff changeset
947 triplus ad motum A, reſiſten­<lb></lb> tia A erit maior
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948 quàm reſiſtentia B. </s>
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949 <s>Idem erit, ſi ma­<lb></lb> ior ſit ratio A ad B, quàm 3
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950 ado, motus verò B ad mo­ <pb xlink:href="044/01/026.jpg" pagenum="18"></pb>tum A ſit triplus. </s>
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951 <s>Contrà verò ſi A ad B ſit tripla: mo­<lb></lb> tus
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952 verò B ad motum A ſit maior quàm triplus, ma­<lb></lb> ior
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953 erit reſiſtentia B quàm A. </s>
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954 <s>Idem accidet, ſi A ad B <lb></lb> ratio minor ſit quàm 3 ad 1,
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955 motus verò B ad motum <lb></lb> A ſit triplus. </s>
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956 <s>Hunc autem exceſſum &amp; defectum <expan abbr="nõ">non</expan>
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957 <lb></lb> vlteriùs ſcrutabimur, vt ipſius quantitatis <expan abbr="menſurã">menſuram</expan>
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958 <lb></lb> aſſequamur: alioqui in infinitum fieret
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959 progreſſus. </s>
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960 </p>
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961 <p type="main">
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962
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963 <s>Ex his colligimus <expan abbr="reſiſtẽtias">reſiſtentias</expan> tribus modis æqua­<lb></lb> les
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964 aut inæquales dici, per ſe ſcilicet aut motione, aut <lb></lb>
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965 vtroque modo. </s>
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966 <s>Per ſe quidem cùm ſubiectorum <lb></lb> vires ſunt
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967 æquales (id eſt æqualiter ſua ſubiecta
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968 mo­<lb></lb> uent) aut inæquales. </s>
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969 <s>Motione verò quando per ſe <lb></lb> quidem in æquales
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970 ſunt, motione verò æquales <expan abbr="fiũt">fiunt</expan>: <lb></lb> aut quando per ſe æquales ſunt,
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971 motione verò inæ­<lb></lb> quales <expan abbr="fiũt">fiunt</expan> eo, quo dictum eſt, modo. </s>
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972 <s>Vtroque mo <lb></lb> do æquales aut inæquales <expan abbr="dicũtur">dicuntur</expan>, quando tum per <lb></lb> ſe,
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973 tum motione tales fiunt. </s>
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974 <s>His explicatis videamus <lb></lb> quis eorum ſit effectus, vbi vires
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975 committentur. </s>
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976 </p>
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977 <p type="head">
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978
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979 <s>IX.</s>
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980 </p>
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981 <p type="main">
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982
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983 <s>Primùm ex prima concluſione ſequitur quę erit <lb></lb>
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984 ratio reſiſtentiæ ad reſiſtentiam, eandem fore
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985 reſi­<lb></lb> ſtentiæ ad vim cuius eſt altera
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986 reſiſtentia: ſunt enim <lb></lb> vis &amp; <expan abbr="reſiſtẽtia">reſiſtentia</expan> in
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987 <expan abbr="eodẽ">eodem</expan> ſubiecto æquales. </s>
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988 <s>Ergo mul­<lb></lb> to magis ſequitur, ſi <expan abbr="reſiſtẽtia">reſiſtentia</expan>
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989 altera maior, altera mi <lb></lb> nor fuerit, illam huius vi <expan abbr="maiorẽ">maiorem</expan> fore, vel illius vim <lb></lb> hac
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990 reſiſtentia maiorem, ſi æqualis æqualem. </s>
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991 </p>
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992
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993
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994 <pb xlink:href="044/01/027.jpg" pagenum="19"></pb>
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995 <p type="head">
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996
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997 <s>X</s>
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998 </p>
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999 <p type="main">
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1000
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1001 <s>Reſiſtentia autem vi contrariæ commiſſa <expan abbr="tãtum">tantum</expan>
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1002 <lb></lb> de ea tollit quanta eſt ipſa reſiſtentia. </s>
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1003 <s>Sublata autem <lb></lb> vi tollitur motus: ſublata verò
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1004 reſiſtentia, ſi vis adſit, <lb></lb> ſequitur
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1005 motus. </s>
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1006 <s>Vbi igitur vis &amp; reſiſtentia inęqua­<lb></lb> les
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1007 committentur, ſi vis maior ſit quàm
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1008 reſiſtentia, <lb></lb> fiet motus ſecundum vis illius nutum,
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1009 &amp; contra nu­<lb></lb> tum vis illius quæ reſiſtit. </s>
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1010 <s>Si verò reſiſtentia maior <lb></lb> fuerit, tum ipſa fiet
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1011 vis mouens, &amp; vim contrariam <lb></lb> contra nutum ipſius mouebit,
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1012 dum ipſa nutu ſuo <lb></lb> mouebitur. </s>
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1013 <s>Hinc ſequuntur duo theoremata, circa <lb></lb> quæ totius huius
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1014 conſiderationis cardo vertitur. </s>
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1015 </p>
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1016 <p type="head">
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1017
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1018 <s>THEOREMA I.</s>
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1019 </p>
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1020 <p type="main">
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1021
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1022 <s>Duarum virium connexarum, quarum (ſi mo­<lb></lb> ueantur) motus erunt
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1023 ipſis <foreign lang="grc">ἀντιπεπονθῶς</foreign>
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1024 proportiona­<lb></lb> les neutra alteram mouebit, ſed
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diff changeset
1025 æquilibrium <expan abbr="faciẽt">facient</expan>. </s>
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1026 </p>
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1027 <p type="main">
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1028
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1029 <s>Sit vis A commiſſa cum vi B, ſitque vis A ad vim <lb></lb> B
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1030 ratio per ſe, vt C ad D <expan abbr="quæcũque">quæcunque</expan> illa ſit, ſiue dupla, <lb></lb>
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1031 ſiue tripla, ſiue alia. </s>
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1032 <s>Sit etiam <expan abbr="eadẽ">eadem</expan> ratio motus quo <lb></lb> B
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1033 mouebitur, ſi ita, vt connexa ſunt, moueantur) ad <lb></lb> motum
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1034 quo A mouebitur, quæ eſt C ad D, dico mo­<lb></lb> tum non
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1035 ſequuturum, ſed factum iri æquilibrium. <lb></lb>
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1036 </s>
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1037 <s>Aut enim A &amp; B vires per ſe erunt æquales aut
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1038 inæ­<lb></lb> quales: ſi æquales, ergo &amp; ipſarum
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1039 motus æquales e­<lb></lb> runt: ſunt enim ex hypotheſi
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1040 ipſis proportionales: <pb xlink:href="044/01/028.jpg" pagenum="20"></pb>ergo per quartam concluſionem earum reſiſtentiæ
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1041 <lb></lb> æquales erunt, ergo per decimam concluſionem <expan abbr="nõ">non</expan>
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1042 <lb></lb> fiet motus. </s>
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1043 <s>Si verò ſunt inæquales, cùm earum mo­<lb></lb> tus ex
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1044 hypotheſi ſint <foreign lang="grc">ἀντιπεπονθῶς</foreign>
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1045 proportionales per <lb></lb> ſeptimam concluſionem æquales
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1046 erunt etiam reſi­<lb></lb> ſtentiæ. </s>
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1047 <s>Ergo nec motus fiet: nullo igitur modo fiet <lb></lb> earum motus. </s>
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1048 <s>Quod demonſtrandum erat. </s>
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1049 </p>
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1050 <p type="head">
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1051
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1052 <s>THEOREMA II.</s>
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1053 </p>
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1054 <p type="main">
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1055
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1056 <s>Quarum verò ita connexarum (ſi <expan abbr="moueãtur">moueantur</expan>) mo<lb></lb> tus, ipſis proportionales non erunt:
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1057 illa alteram mo­<lb></lb> uebit, cuius ad alteram ratio maior erit,
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1058 quàm huius <lb></lb> motus ad illius motum. </s>
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1059 </p>
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1060 <p type="main">
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1061
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1062 <s>Sit vis A cum vi B commiſſa, ſitque A ad B ratio <lb></lb> per
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1063 ſe, vt C ad D: ita verò connexæ ſint, vt ſi
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1064 mouean­<lb></lb> tur, minor ſit ratio motus quo B mouebitur ad
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1065 mo­<lb></lb> tum, quo A mouebitur, quum C ad D dico A motu­<lb></lb> ram
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1066 B: erit enim per octauam concluſionem reſi­<lb></lb>
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1067 ſtentia B minor reſiſtentia A: ergo per nonam
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1068 con­<lb></lb> cluſionem reſiſtentia B minor vi A: vis
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1069 igitur A vim <lb></lb> B mouebit per vndecimam concluſionem. </s>
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1070 <s>Quod <lb></lb> demonſtrandum erat. </s>
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1071 </p>
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1072 <p type="main">
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1073
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1074 <s>Hinc poſſemus ad problematis noſtri demon­<lb></lb>
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1075 ſtrationem rectà pergere: ante tamen craſſiùs
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1076 ali­<lb></lb> quanto hæc explicanda ſunt, vt à quouis
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1077 faciliùs in­<lb></lb> telligantur. </s>
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1078 <s>Duæ ſunt motus menſuræ, locus ſcilicet <lb></lb>
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1079 &amp; tempus: vtroque igitur, tempore videlicet &amp; loco <pb xlink:href="044/01/029.jpg" pagenum="21"></pb>maior, minor aut æqualis
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1080 dicitur: &amp; quo minori <expan abbr="tẽ-pore">tem­<lb></lb>
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1081 pore</expan> idem ſpatium abſoluitur, eo maior eſt,
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1082 vel quo <lb></lb> maius ſpatium eodem tempore. </s>
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1083 </p>
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1084 <p type="main">
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1085
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1086 <s>Vt igitur motus magnus dicatur, perinde eſt ſi <lb></lb> paruo
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1087 tempore fiat, aut magno ſpatio. </s>
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1088 </p>
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1089 <p type="main">
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1090
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1091 <s>Quod autem maiorem <expan abbr="motũ">motum</expan> ciere poteſt
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1092 illud, <lb></lb> vis maior dicitur, quòd minorem minor. </s>
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1093 </p>
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1094 <p type="main">
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1095
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1096 <s>Vis autem ſeu mouendi potentia in eodem ſub­<lb></lb> iecto
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1097 certa &amp; finita eſt. </s>
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1098 <s>Quęlibet enim res vi natura­<lb></lb> li prędita, ſi
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1099 à loco naturali abſit, ſuóque arbitrio <expan abbr="cõ-mittatur">con­<lb></lb> mittatur</expan>, certo tempore
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1100 eò redit. </s>
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1101 <s>Eſt enim certum <lb></lb> in rerum natura quanto tempore libræ vnius
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1102 <expan abbr="põdus">pondus</expan>
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1103 <lb></lb> deorſum ſponte ſua delatum, miliare vnum aut duo
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1104 <lb></lb> conficiat pro ratione materię, vel quantum ſpatij
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1105 v­<lb></lb> na vel duabus horis percurrat. </s>
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1106 <s>Id verò quantum ſit, <lb></lb> hominum induſtria nondum quod
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1107 ſciam explora­<lb></lb> tum eſt: aliâs autem id
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1108 demonſtrare conabimur. </s>
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1109 </p>
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1110 <p type="main">
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1111
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1112 <s>Mouendi verò potentia in alieno ſubiecto infi­<lb></lb> nita
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1113 eſt, hoc eſt, in <expan abbr="infinitũ">infinitum</expan>
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1114 augeri vel minui poteſt, <lb></lb> quoniam in finita auctione &amp;
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1115 diminutione eſt reſi­<lb></lb> ſtentia: tanta enim
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1116 eſt, quanta eſt in eodem ſubiecto <lb></lb> vis: <expan abbr="quantúſq;">quantúſque</expan> motus illius
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1117 eſt vis alterius reſpectu. <lb></lb>
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1118 </s>
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1119 <s>Quo igitur vis quæ alienum ſubiectum mouere ni­<lb></lb> titur,
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1120 illud magis mouere nitetur, eo minùs illud <lb></lb> mouere poterit, maior
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1121 enim erit illius reſiſtentia. <lb></lb>
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1122 </s>
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1123 <s>Quemadmodum enim quod magis nutu ſuo mo­ <pb xlink:href="044/01/030.jpg" pagenum="22"></pb>uetur, maiorem vim mouendi
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1124 habet. </s>
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1125 <s>Ita illud idem <lb></lb> quod magis contra nutum ſuum mouetur, <expan abbr="maiorẽ">maiorem</expan>
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1126 <lb></lb> vim reſiſtendi habet. </s>
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1127 <s>E contrario verò quo vis quæ­<lb></lb> libet minorem motum in
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1128 alieno ſubiecto ciere ni­<lb></lb> tetur, eo faciliùs illud
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1129 mouebit. </s>
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1130 </p>
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1131 <p type="main">
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1132
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1133 <s>Tarditate igitur motus, reſiſtentia in infinitum <lb></lb> minui
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1134 poteſt: minuta verò reſiſtentia vis contrariæ
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1135 <lb></lb> effectus augetur, ita vt vis quæ per ſe minima eſt,
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1136 in <lb></lb> contrariam cui plurimum diminuta ſit, reſiſtentia
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1137 <lb></lb> maximè agat. </s>
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1138 <s>Perinde igitur eſt, ſi vis mouens ma­<lb></lb> gna ſit,
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1139 mouenda verò parua, ac ſi illa celeriter fera­<lb></lb> tur,
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1140 hæc verò tardè: <expan abbr="quãtum">quantum</expan>
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1141 enim vis mouens ſi ma­<lb></lb> gna fuerit in mouendam minorem
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1142 poterit, tantum <lb></lb> vis parua celeriter mota in magnam tardè motam
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1143 <lb></lb> poterit. </s>
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1144 <s>Si igitur velimus vt vis parua magnam mo­<lb></lb> ueat, eas ita collocare
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1145 oportet, vt quantum magna <lb></lb> paruam ſuperat, tantum illi de motus
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1146 celeritate de­<lb></lb> trahatur, &amp; aliquid ampliùs. </s>
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1147 <s>Si enim tanta ſit tardi­<lb></lb> tas motus vis vnius, reſpectu
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1148 motus vis alterius, <expan abbr="quã-ta">quan­<lb></lb> ta</expan>
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1149 eſt proportio vis illius, ad hanc non fiet motus: vt <lb></lb> ſi
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1150 pondus A quatuor librarum cum pondere B libræ <lb></lb> vnius committatur:
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1151 ſintque ita connexa, vt dum <lb></lb> A vno ſpatio mouebitur, B
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1152 quatuor ſpatiis mouea­<lb></lb> tur, ita vt motus A quadruplo tardior
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1153 ſit motu B <expan abbr="nõ">non</expan>
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1154 <lb></lb> fiet motus, quia quantum A excedit B pondere tan­<lb></lb> tùm
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1155 deficit motus tarditate. </s>
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1156 </p>
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1157
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1158
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1159 <pb xlink:href="044/01/031.jpg" pagenum="23"></pb>
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1160 <p type="main">
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1161
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1162 <s>Tantum enim eſt libram vnam quatuor ſpatiis <lb></lb> moueri, quantum
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1163 libras quatuor vno ſpatio eodem <lb></lb> tempore: ſi igitur
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1164 alterutri eorum ita <expan abbr="conſtitutorũ">conſtitutorum</expan>, <lb></lb> vel momentum vis addatur, id cui
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1165 additum fuerit, <lb></lb> alterum mouebit. </s>
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1166 <s>Idem fiet ſi A ita connectatur vt <lb></lb> vel momento citiùs
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1167 quàm moueri poſitum eſt, mo<lb></lb> ueatur vel B tardiùs.
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1168 </s>
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1169 </p>
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1170 <p type="main">
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1171
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1172 <s>Id etiam alia ratione oſtendi poteſt, ſi vis A
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1173 qua­<lb></lb> drupla ſit ad vim B, erunt in A quatuor partes,
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1174 ipſi B <lb></lb> æquales. </s>
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1175 <s>Si igitur B cum ſingulis illis committatur, <lb></lb> ita vt æqualiter
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1176 moueantur, non fiet motus: ſi verò <lb></lb> alterutri aut ipſi
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1177 B, aut ſingulis illis partibus vis vel <lb></lb> motus momentum adiiciatur
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1178 vel detrahatur, illa cui <lb></lb> adiectum fuerit, aut cui non detractum
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1179 fuerit, nutu <lb></lb> ſuo mouebitur, &amp; aliam contra nutum eius
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1180 moue­<lb></lb> bit. </s>
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1181 <s>Addito igitur ipſi B momento, dum vno ſpatio <lb></lb> mouebitur,
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1182 ſingulas illas partes vno ſpatio moue­<lb></lb> bit. </s>
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1183 <s>Vbi igitur ſingulas ſemel mouerit, ipſa quater <lb></lb> mota
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1184 erit. </s>
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1185 <s>Dum verò ſingulæ ſemel motæ erunt, to­<lb></lb>
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1186 tum ex illis conſtans ſemel motum intelligetur: po­<lb></lb>
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1187 terit igitur B addito ipſi momento, dum quater mo<lb></lb> uebitur,
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1188 ſemel totum A mouere. </s>
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1189 </p>
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1190 <p type="main">
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1191
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1192 <s>Tertio modo id ipſum concludere poſſumus. </s>
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1193 <s>Si <lb></lb> duæ vires æquales connectantur, ita vt motæ,
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1194 æqua­<lb></lb> liter moueantur, altera in <expan abbr="alterã">alteram</expan> non aget. </s>
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1195 <s>Si verò ita <lb></lb> connectantur vt motæ inæqualiter moueantur,
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1196 <pb xlink:href="044/01/032.jpg" pagenum="24"></pb>quantum altera alteram
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1197 celeritate ſuperabit, <expan abbr="tãtum">tantum</expan>
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1198 <lb></lb> &amp; vi ſuperabit. </s>
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1199 <s>Vt ſi vis A vi B æqualis ſit, ac ita <expan abbr="con-nectãtur">con­<lb></lb> nectantur</expan>, vt B quatuor
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1200 ſpatiis moueatur, dum A vno <lb></lb> ſpatio mouebitur, B quadruplam
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1201 vim habebit ad A, <lb></lb> quia eam in motibus ſuis proportionem
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1202 ſeruant, <lb></lb> quam ſi <expan abbr="ſeruarẽt">ſeruarent</expan> arbitrio ſuo commiſſæ, B
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1203 ad A qua­<lb></lb> drupla eſſet. </s>
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1204 <s>Si igitur illis ita connexis, ipſi A adda­<lb></lb> tur vis triplo
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diff changeset
1205 maior quàm ipſa ſit, B illis quatuor re­<lb></lb>
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diff changeset
1206 ſiſtet, nec fiet motus. </s>
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1207 </p>
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diff changeset
1208 <p type="main">
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1209
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diff changeset
1210 <s>Duarum igitur virium comparatarum, quanto <lb></lb> altera ſubiectum
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diff changeset
1211 ſuum celeriùs mouebit, quàm al­<lb></lb> tera: tanto illa
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diff changeset
1212 hanc celeriùs mouere poterit, quàm <lb></lb> ipſa moueatur,
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diff changeset
1213 ſi illi vis <expan abbr="momẽtum">momentum</expan> additum
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diff changeset
1214 fuerit. <lb></lb>
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1215 </s>
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1216 <s>Ita vt quæ erit proportio vis ad vim, eadem ſit mo­<lb></lb> tus,
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diff changeset
1217 quem illa in hac ciere poteſt ad motum quo ipſa <lb></lb> mouebitur. </s>
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diff changeset
1218 <s>Et è conuerſo quæ erit ratio motus ad <lb></lb> motum, eadem erit
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diff changeset
1219 vis cui additum fuerit momen­<lb></lb> tum ad eam quam ipſa mouere
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diff changeset
1220 poterit ratio reci­<lb></lb> procè. </s>
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diff changeset
1221 <s>Iam ad problematis noſtri demonſtratio­<lb></lb> nem veniamus.
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1222 </s>
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diff changeset
1223 </p>
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1224 </chap>
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diff changeset
1225 <chap>
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1226 <p type="head">
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1227
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diff changeset
1228 <s><emph type="italics"></emph>Propoſiti problematis
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diff changeset
1229 demonſtratio.<emph.end type="italics"></emph.end></s>
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diff changeset
1230 </p>
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diff changeset
1231 <p type="main">
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1232
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diff changeset
1233 <s>Sit data vis A quantacunque illa ſit magna vel <lb></lb> parua: datum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1234 verò pondus B quantumquantum il­<lb></lb> lud ſit, dico me vi A
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diff changeset
1235 pondus B tollere poſſe. </s>
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diff changeset
1236 <s>Id ſic de­<lb></lb> monſtro. </s>
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diff changeset
1237 </p>
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diff changeset
1238
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diff changeset
1239
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1240 <pb xlink:href="044/01/033.jpg" pagenum="25"></pb>
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diff changeset
1241 <p type="main">
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1242
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diff changeset
1243 <s>Primùm enim ex doctrina ſecundi <expan abbr="lẽmatis">lemmatis</expan>, quod <lb></lb> inferiùs demonſtrabitur,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1244 ſciam proportionem pro­<lb></lb> ximè maiorem, quàm
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diff changeset
1245 ſit A ad B proportio. </s>
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diff changeset
1246 <s>Deinde <lb></lb> ex doctrina primi lemmatis ita connectam A &amp; B, <lb></lb> vt
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diff changeset
1247 quando ambo mouebuntur, nunc ſit ratio motus <lb></lb> quo B mouebitur ad
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diff changeset
1248 <expan abbr="motũ">motum</expan> quo A mouebitur, quàm <lb></lb>
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diff changeset
1249 ſit A ad B. </s>
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1250 <s>His peractis ſequitur vim A pondus B mo­<lb></lb> turam ex
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diff changeset
1251 ſecundo ſuperiùs demonſtrato theorema­<lb></lb> te. </s>
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1252 <s>Quod erat propoſitum. </s>
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1253 </p>
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1254 <p type="head">
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1255
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1256 <s>LEMMA I.</s>
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1257 </p>
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1258 <p type="main">
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1259
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1260 <s>Duas vires ita connectere, vt ſi moueantur, <expan abbr="earũ">earum</expan>
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1261 <lb></lb> motus, in data ratione alter ad alterum ſe habeant <lb></lb> vires
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1262 contrariæ, aut medio aliquo, aut per ſe abſque <lb></lb> vllo
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1263 medio committuntur. </s>
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1264 <s>Si abſque medio com­<lb></lb> mittant, eodem motu mouebuntur, maior
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diff changeset
1265 enim mi<lb></lb> norem eodem motu, quo ipſa moueri poterit, mo­<lb></lb>
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1266 uebit: aut æquilibrium <expan abbr="faciẽt">facient</expan>,
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1267 ſi æquales ſint: vt ſi le­<lb></lb> ue graui
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1268 committatur, ſiquidem leuitas grauitate <lb></lb> maior ſit,
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1269 attolletur graue: ſin verò grauitas maior <lb></lb> ſit, leue
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1270 deprimetur: ſi æqualia ſint, non mouebun­<lb></lb> tur.
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1271 </s>
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1272 </p>
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1273 <p type="main">
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1274
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1275 <s>Si verò medio aliquo connectantur mediorum <lb></lb> varia ſunt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1276 genera. </s>
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1277 <s>Aut enim medium eſt flexibile &amp; <lb></lb>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1278 <foreign lang="grc">ὁμοιομερὲς</foreign>, vt funis, catena, &amp;c. </s>
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1279 <s>aut eſt inflexibile, il­<lb></lb> lúdque aut rectum, aut curuum,
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1280 vt recta linea vel <lb></lb> curua vel angulus. </s>
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1281 <s>Atque hæc omnia aut continua <pb xlink:href="044/01/034.jpg" pagenum="26"></pb>ſunt aut diuiſa, ſimplicia aut
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1282 compoſita. </s>
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1283 </p>
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1284 <p type="main">
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1285
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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1286 <s>Horum autem mediorum opera fit vt vires illis <lb></lb> applicatæ, quarum
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1287 iidem ſunt nutus, contrariis mo­<lb></lb> tibus moueantur. </s>
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1288 <s>Id <expan abbr="autẽ">autem</expan> fit cùm in mediis illis inter <lb></lb>
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1289 <expan abbr="eorũ">eorum</expan> extrema interiacet quies vna vel
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1290 plures. </s>
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1291 <s><expan abbr="Exẽpli">Exempli</expan>
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1292 <lb></lb> gratia, ſi duo pondera funis extremitatibus alligata <lb></lb>
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1293 ſint, &amp; funis clauo fixo &amp; immobili incumbat pro­<lb></lb>
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1294 pter illam quietem inter <expan abbr="vtrumq;">vtrumque</expan> pondus
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1295 <expan abbr="poſitã">poſitam</expan>
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1296 <expan abbr="nõ">non</expan>
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1297 <lb></lb> poterit <expan abbr="alterũ">alterum</expan> deorſum
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1298 moueri, quin <expan abbr="alterũ">alterum</expan> ſurſum
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diff changeset
1299 <lb></lb> moueatur. </s>
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diff changeset
1300 <s><expan abbr="Idẽ">Idem</expan> fiet in linea recta, ſi enim
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1301 illius extre­<lb></lb> mitatibus pondera duo annexa ſint, &amp; inter
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1302 ea ſit in <lb></lb> illa <expan abbr="punctũ">punctum</expan>
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diff changeset
1303 aliquod quieſcens, dum alterum ex illis <lb></lb> ponderibus deorſum
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diff changeset
1304 feretur, alterum aſcendet. </s>
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1305 <s><expan abbr="Pũ-ctum">Pun­<lb></lb> ctum</expan> autem illud
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diff changeset
1306 quieſcens in linea illa recta, Gręcis <lb></lb> hypomochlium
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1307 dicitur, eò quòd vecti, quem <foreign lang="grc">μόχλον</foreign><lb></lb> vocant, ſubiiciatur. </s>
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1308 <s>Huius autem hypomochlij, in <lb></lb> recta linea ſe vecte collocatio
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1309 faciet, vt lineæ extre­<lb></lb> ma ſecundum datam rationem
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1310 moueantur. </s>
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1311 <s>Si enim <lb></lb> recta linea in datam rationem diuiſa fuerit, hoc
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diff changeset
1312 eſt, <lb></lb> vt pars altera ad <expan abbr="alterã">alteram</expan>
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diff changeset
1313 eam habeat <expan abbr="rationẽ">rationem</expan>, <expan abbr="quã">quam</expan> quis <lb></lb> voluerit. (Quod <expan abbr="quidẽ">quidem</expan> quo modo fiat docet Euc.) &amp; <lb></lb>
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diff changeset
1314 in puncto diuiſionis collocetur <expan abbr="hypomochliũ">hypomochlium</expan>, illius <lb></lb> lineæ extrema ſecundum
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1315 <expan abbr="illã">illam</expan>
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diff changeset
1316 <expan abbr="rationẽ">rationem</expan> mouebuntur: <lb></lb> ſiue
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diff changeset
1317 enim conſideretur <expan abbr="circulorũ">circulorum</expan>,
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diff changeset
1318 quos illa extrema <lb></lb> deſcribent, proportio ſiue ſpatium
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diff changeset
1319 quod illa in linea <lb></lb> perpendiculari notabunt vtroque modo illi motus,
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diff changeset
1320 <pb xlink:href="044/01/035.jpg" pagenum="27"></pb><expan abbr="partiũ">partium</expan>
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1321 <expan abbr="illarũ">illarum</expan>
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diff changeset
1322 <expan abbr="proportionẽ">proportionem</expan>
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1323 <expan abbr="ſeruabũt">ſeruabunt</expan>. </s>
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diff changeset
1324 <s>Sit <expan abbr="exẽpli">exempli</expan> gratia <lb></lb> linea AB,
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1325 quæ in puncto C in datam rationem ſecta <lb></lb> ſit, puta vt
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diff changeset
1326 pars AC quadrupla ſit ad partem CB, mo­<lb></lb> ueatúrque circa
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diff changeset
1327 centrum C, punctum A deſcribet cir<lb></lb> culum <expan abbr="quadruplũ">quadruplum</expan> ad illum quem B <lb></lb>
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1328 deſcribet. </s>
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parents:
diff changeset
1329 <s>Eſt enim <expan abbr="eadẽ">eadem</expan> ratio in
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diff changeset
1330 cir­<lb></lb> culo diametri ad <expan abbr="diametrũ">diametrum</expan>, quæ eſt <lb></lb> circunferentiæ ad
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1331 <expan abbr="circunferentiã">circunferentiam</expan> (vt <lb></lb>
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1332 alibi demonſtrauimus.) Hac igitur <lb></lb> ratione A puncti motus
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1333 quadruplus <lb></lb>
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1334 <figure id="id.044.01.035.1.jpg" xlink:href="044/01/035/1.jpg"></figure><lb></lb> erit
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diff changeset
1335 ad puncti B <expan abbr="motũ">motum</expan>. </s>
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1336 <s>Si verò ponamus AD <expan abbr="perpen-dicularẽ">perpen­<lb></lb> dicularem</expan> eſſe, &amp; linea AB
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1337 illi primùm <expan abbr="coincidẽs">coincidens</expan> circa
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1338 <lb></lb> punctum C, moueatur donec A ad D perueniat: tum <lb></lb>
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1339 <expan abbr="eodẽ">eodem</expan> momento B perueniet ad E: motum
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1340 igitur erit <lb></lb> A in linea <expan abbr="perpẽdiculari">perpendiculari</expan> tota circuli maioris diame­<lb></lb> tro,
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1341 quæ eſt AD:B verò in <expan abbr="eadẽ">eadem</expan>
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1342 linea, minoris <expan abbr="tãtùm">tantùm</expan>
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1343 <lb></lb> circuli diametro <expan abbr="motũ">motum</expan> erit,
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1344 quę eſt BE. </s>
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1345 <s>Atqui diame<lb></lb> ter AD quadrupla eſt ad BE, quia ex hypotheſi
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1346 <expan abbr="ſemi-diametrorũ">ſemi­<lb></lb>
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1347 diametrorum</expan>
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1348 <expan abbr="illorũ">illorum</expan>
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1349 <expan abbr="circulorũ">circulorum</expan> proportio eſt, vt 4
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1350 ad 1. <lb></lb> Motus igitur <expan abbr="pũcti">puncti</expan> in linea A
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1351 <expan abbr="perpẽdiculari">perpendiculari</expan> ad <expan abbr="motũ">motum</expan>
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1352 <lb></lb>
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1353 <expan abbr="pũcti">puncti</expan> B quadruplus erit: <expan abbr="Idẽ">Idem</expan> dicetur ſi in data aliqua <lb></lb>
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1354 alia ratione ſecta ſit linea AB. <expan abbr="Demõſtratũ">Demonſtratum</expan> igitur
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1355 eſt <lb></lb> quomodo fieri poſſit vt rectæ lineę
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1356 extrema <expan abbr="ſecũdũ">ſecundum</expan>
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1357 <lb></lb>
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1358 <expan abbr="datã">datam</expan>
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1359 <expan abbr="rationẽ">rationem</expan> moueantur. </s>
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1360 <s>Si igitur illis extremis duæ <lb></lb> vires applicentur, <expan abbr="mouebũtur">mouebuntur</expan>
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1361 <expan abbr="eodẽ">eodem</expan> ipſo motu: ergo <lb></lb>
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1362 ſecundum datam vel propoſitam rationem. </s>
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1363 <s>Quod <lb></lb> aſſumptum erat. </s>
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1364 </p>
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1365
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1366
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1367 <pb xlink:href="044/01/036.jpg" pagenum="28"></pb>
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1368 <p type="main">
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1369
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1370 <s>Quod autem in vecte demonſtratum eſt, illud e­<lb></lb> tiam in
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1371 reliquis mediis demonſtrandum erit, etſi <lb></lb> lemmati
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1372 ſatisfactum eſt, dum in vno exemplo id <lb></lb> probatum eſt. </s>
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1373 <s>Ante igitur ſecundum lemma de­<lb></lb> monſtrabimus. </s>
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1374 </p>
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1375 <p type="head">
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1376
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1377 <s>LEMMA II.</s>
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1378 </p>
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1379 <p type="main">
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1380
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1381 <s>Proportionem proximè maiorem vel minorem, <lb></lb> quàm ſit
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1382 datæ vis ad datum pondus proportio, de­<lb></lb> terminare vis
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1383 cuiuslibet quantitas ex motu ciere po|| <lb></lb> teſt, metienda
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1384 eſt. </s>
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1385 <s>Motum autem ciere poteſt vel in <lb></lb> ſubiecto ſuo, vel in
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1386 alieno. </s>
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1387 <s>Vis autem menſura non <lb></lb> ſumitur ex eo motu quem in
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1388 ſubiecto ſuo ciere po­<lb></lb> teſt, eo quòd licet
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1389 vis quælibet certum motum ha­<lb></lb> beat &amp; <expan abbr="determinatũ">determinatum</expan> quo ſubiectum
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1390 ſuum mouet, <lb></lb> illius tamen quantitas, vt ſuprà diximus,
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1391 nondum <lb></lb> demonſtrata eſt. </s>
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1392 <s>Supereſt igitur vt vires motu illo <lb></lb> metiamur, quem in alieno
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1393 ſubiecto ciere poſſunt, vt <lb></lb> id fiat, quærenda
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1394 nobis ſunt ſubiecta quæ in homi­<lb></lb> num
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1395 poteſtate ſint, &amp; cum vi qualibet committi <lb></lb>
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1396 poſſint. </s>
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1397 <s>Omnium autem mobilium ſubiectorum, <lb></lb> maximè in hominum
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1398 poteſtate ſunt grauia: leuia e­<lb></lb> nim coercere vix
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1399 poſſumus. </s>
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1400 <s>Ideo vires illis metiri <lb></lb> ſolemus, ſed grauibus quæ vel
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1401 vel figuris ſuis &amp; com<lb></lb> page vel vaſe aliquo coercentur. </s>
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1402 <s>Itaque vſus homi­<lb></lb> num certas quaſdam ponderum
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1403 menſuras ſibi ſta <lb></lb> tui, ponderibus ſcilicet
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1404 quibuſdam certa <expan abbr="quãtitate">quantitate</expan>
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1405 <pb xlink:href="044/01/037.jpg" pagenum="29"></pb>conſtantibus inditis
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1406 nominibus, vt eſſent <expan abbr="ponderũ">ponderum</expan>
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1407 <lb></lb> omnium communes menſuræ, vt ſunt libræ, vncia, <lb></lb>
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1408 <expan abbr="drachmę">drachmæ</expan>, &amp;c. </s>
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1409 <s>quas famoſas menſuras <expan abbr="vocãt">vocant</expan>. </s>
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1410 <s>Quem­<lb></lb> admodum igitur numeros numeris, ſic pondera <expan abbr="põ-deribus">pon­<lb></lb> deribus</expan> metimur. </s>
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1411 <s><expan abbr="Tãtum">Tantum</expan> enim pondus eſſe dicitur,
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1412 <lb></lb> quot libras vncias drachmas æqualiter mouere po­<lb></lb>
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1413 teſt dempto momento. </s>
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1414 <s>Nec tantum pondera hoc <lb></lb> modo metimur, ſed etiam alias omnes vires
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1415 motum <lb></lb> ad locum cientes. </s>
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1416 <s>Quot enim libras vir aut aliud a­<lb></lb> nimal vel <expan abbr="vẽtus">ventus</expan> aut ignis, aut aliqua alia vis dempto
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1417 <lb></lb> momento mouere poterit, tot libris illam æqualem <lb></lb>
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1418 eſſe dicemus. </s>
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1419 <s>Si igitur data vel propoſita vis metien­<lb></lb> da ſit,
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1420 ſiquidem naturalis ſit, quoniam docuimus <lb></lb> vim naturalem per
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1421 totum ſubiectum diffuſam eſſe <lb></lb> in rebus
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1422 homogeneis: id eſt, vt quæ eſt proportio <lb></lb> molis ad
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1423 molem, eadem ſit ponderis ad pondus: ſu­<lb></lb> memus partem
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1424 aliquam illi homogeneam, aut ex i­<lb></lb> pſo ſubiecto, aut
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1425 ex alio ipſi homogeneo, eámque <lb></lb> famoſa aliqua
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1426 menſura metiemur, vtramque ſcili­<lb></lb> cet committendo
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1427 &amp; obſeruando, quem motum al­<lb></lb> tera in altera ciere
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1428 poſſit, vbi enim æquilibrium fa­<lb></lb> cient motibus
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1429 extremorum, quibus affixæ fuerint, <lb></lb> proportionales erunt per 1
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1430 theorema: motus autem <lb></lb> illi linearum dimenſione quam Geometria
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1431 docet, <lb></lb> noti erunt, &amp; eorum proportio, nota igitur erit &amp; <lb></lb>
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1432 virium proportio. </s>
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1433 <s>Atqui menſuræ famoſæ nota, per <pb xlink:href="044/01/038.jpg" pagenum="30"></pb>ſe eſt quantitas:
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1434 duorum autem proportione cogni­<lb></lb> ta &amp; alterius quantitate,
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1435 ſtatim &amp; reliqui quantitas <lb></lb> innoteſcit per
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1436 ſecundam da. Eu. nota igitur vis
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1437 <expan abbr="quã-titate">quan­<lb></lb> titate</expan> quæ
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1438 parti illi ineſt, noſcetur &amp; vis <expan abbr="quãtitas">quantitas</expan>
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1439 <expan abbr="quę">quæ</expan><lb></lb> toti inerit: quæ enim
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1440 erit ratio molis ſubiecti vis da­<lb></lb> tæ ad molem
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1441 particulę ſumptę, eadem erit vis totius <lb></lb> ad vim
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1442 partis. </s>
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1443
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1444
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1445
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1446
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1447
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1448 <s>Hîc igitur erunt quatuor proportio­<lb></lb> nalia, ſcilicet vt
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1449 moles ad molem: ſic vis ad vim ex <lb></lb> quibus tria nota erunt: moles
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1450 enim metiri Geome­<lb></lb> tria nos docuit, præterea vis partis, vt
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1451 demonſtraui­<lb></lb> mus, nota eſt, ergo &amp; vis totius
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1452 quantitas per deci­<lb></lb> mam ſeptimam ſeptimi Elem. Eucl.
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1453 </s>
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1454 </p>
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1455 <p type="main">
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1456
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1457 <s>Si verò ſubiectum non ſit homogeneum, vi ta­<lb></lb> men
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1458 naturali ſit præditum, ſi quidem data vis quam <lb></lb> metiri
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1459 volumus, ea ſitque motum ciere volumus, <lb></lb> tum conſiderabimus
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1460 quæ pars in illa, vis minimum <lb></lb> habeat: &amp; ex ea totam
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1461 ipſius molem æſtimabimus: <lb></lb> ſi verò
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1462 ſit vis mouenda, ſtatuemus quaſi tota ſit
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1463 ho­<lb></lb> mogenea ipſius parti, quæ vis plurimum in ſe
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1464 habe­<lb></lb> bit, &amp; ex ea totam ipſius molem
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1465 æſtimabimus. </s>
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1466 <s>Ita­<lb></lb> que tum illius quanta minima, tum huius quanta <lb></lb> maxima
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1467 eſſe poteſt, vis quantitas nobis nota erit per <lb></lb>
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1468 proximè demonſtratam rationem. </s>
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1469 <s>Notis autem vi­<lb></lb> rium quantitatibus, nota erit &amp; earum
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1470 proportio: <lb></lb> ergo &amp; proportio ipſa proximè maior vel
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1471 mi­<lb></lb> nor: addita enim vel detracta ipſius denomi- <pb xlink:href="044/01/039.jpg" pagenum="31"></pb>nationi, vnitate erit
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1472 proximè maior vel mi­<lb></lb> nor. </s>
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1473 </p>
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1474 <p type="main">
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1475
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1476 <s>Si verò vis data non ſit naturalis, <expan abbr="voluntariã">voluntariam</expan> qui­<lb></lb> dem ita æſtimare
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diff changeset
1477 poſſumus, qualis vt plurimum <lb></lb> eſt, &amp; ſi
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diff changeset
1478 quidem ea ſit, qua mouere volumus, eam <lb></lb> ſtatuemus, quanta
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diff changeset
1479 minima in eiuſdem generis ſub­<lb></lb> iecto eſſe
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diff changeset
1480 poteſt, vt ſi vim hominis quinquaginta li­<lb></lb> bris
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diff changeset
1481 æqualem ponamus, vim equi centum: ſi verò <lb></lb> ea ſit
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diff changeset
1482 quam mouere volumus, ſtatuemus eam <expan abbr="quã-ta">quan­<lb></lb> ta</expan> maxima eſſe poteſt, vt vim
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diff changeset
1483 hominis 300 libra­<lb></lb> rum, vim equi 500 librarum, &amp; ſic
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1484 dé cæteris: ita vt <lb></lb> nullum ſit dubium quin illa minor
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1485 ſit, quam ſtatue­<lb></lb> rimus, hæc verò maior.
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1486 </s>
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1487 </p>
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1488 <p type="main">
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1489
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1490 <s>Vis verò fortuitæ quantitatem nulla certa con­<lb></lb> iectura
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diff changeset
1491 aſſequi poſſumus: ita vt quaſcunque
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1492 ma­<lb></lb> chinas ei aptemus, modò moueat, modò non
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1493 mo­<lb></lb> ueat, neque ad noſtrum <expan abbr="inſtitutũ">inſtitutum</expan> magnoperè
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diff changeset
1494 per­<lb></lb> tinet illa inquiſitio: cum fortuitorum nulla ſit
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1495 diſci­<lb></lb> plina. </s>
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1496 </p>
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1497 <p type="main">
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1498
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1499 <s>His igitur modis virium duarum datarum pro­<lb></lb> portio proximè
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1500 maior nota fiet, quod in ſecundo <lb></lb> lemmate demonſtrandum
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1501 ſumpſeramus. </s>
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1502 </p>
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1503 <p type="main">
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1504
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1505 <s>Iam redeamus ad mediorum, quibus vi­<lb></lb> res annectuntur,
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diff changeset
1506 conſide­<lb></lb> rationem. </s>
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1507 </p>
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1508
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1509
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1510 <pb xlink:href="044/01/040.jpg" pagenum="32"></pb>
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1511 <figure id="id.044.01.040.1.jpg" xlink:href="044/01/040/1.jpg"></figure>
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1512 <p type="main">
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1513
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1514 <s>Docuimus quis ſit ſimplicis ve­<lb></lb> ctis effectus,
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diff changeset
1515 ſimplex autem ve­<lb></lb> ctis ſemicirculi conuerſione
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1516 ſuam <lb></lb> operationem abſouit, ita vt ſi <lb></lb>
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1517 vlteriùs F moueatur in in alio ſe­<lb></lb> micirculo motus
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diff changeset
1518 prioribus contra­<lb></lb> rios cieat: vt exempli gratia, ſit <lb></lb>
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1519 vectis AB, cuius hypomochium <lb></lb> ſit C, dum A punctum
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1520 deſcribet ſemicirculum AFD, <lb></lb> motus ille deorſum erit:
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1521 interea verò B punctum <lb></lb> deſcribet ſemicirculum BGE
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1522 aſcendendo: ſi verò A <lb></lb> tranſcendat, D incipiet
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1523 aſcendere: B verò tranſcen­<lb></lb> dens, E <expan abbr="deſcẽdet">deſcendet</expan>: ideo excogitata
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1524 eſt vectis ratio per­<lb></lb> petua ex plurium vectium
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1525 ſucceſſione circa idem <lb></lb> hypomochlium: eſt autem
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1526 illa tum in ergatis aut ſu­<lb></lb> culis, tum in duorum tympanorum
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1527 homocentrico­<lb></lb> rum, ſeu eadem axe transfixorum in planis
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1528 parallelis <lb></lb> aptatione, quorum ſemidiametri ſint in eadem
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diff changeset
1529 pro­<lb></lb> portione quæ in vecte ad propoſitum motum
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1530 cien­<lb></lb> dum neceſſaria eſt: centrum verò
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1531 eorum ſeu axis fi­<lb></lb> xa ſit, ac ita vires aptentur, vt
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diff changeset
1532 maior minorem, mi­<lb></lb> nor verò maiorem tympanum impellat. </s>
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1533 <s>Quemad­<lb></lb> modum autem horum tympanorum homocentri­<lb></lb> corum
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diff changeset
1534 opera vectis perpetui ratio <expan abbr="inuẽta">inuenta</expan>
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diff changeset
1535 eſt, ita eo­<lb></lb> rum multiplicatione motus, &amp; mouentis &amp;
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1536 <expan abbr="mouẽ-di">mouen­<lb></lb> di</expan>, proportio in
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diff changeset
1537 infinitum augeri poteſt. </s>
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1538 <s>Cuius rei <pb xlink:href="044/01/041.jpg" pagenum="33"></pb>maximus eſt
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1539 vſus: nec enim materia ad vectem, cu­<lb></lb> ius longitudo
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1540 ſtadij vnius requireretur, idonea in­<lb></lb> ueniri
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1541 poſſet: plurium autem tympanorum propor­<lb></lb> tionalium
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1542 aptatione fiet machina tractabilis, cuius <lb></lb> vis maior erit quàm
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diff changeset
1543 vectis, cuius longitudo ſtadij v­<lb></lb> nius eſſet. </s>
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1544 <s>Si enim duo tympani homocentrici a­<lb></lb> ptentur, quorum proportio
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1545 ſit alterius ad alterum, <lb></lb> decupla, vis quæ libram vnam
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1546 æquabit, vim decem <lb></lb> libris æqualem dempto momento mouebit,
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1547 ſi con­<lb></lb> gruè illis tympanis aptentur: ſi
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1548 verò adhuc duo alij <lb></lb> tympani fiant, quorum alterius ad alterum
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1549 decupla <lb></lb> ſit proportio, ac minor <expan abbr="illorũ">illorum</expan> ita aptetur, vt <expan abbr="maiorẽ">maiorem</expan>
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1550 <lb></lb> ex prioribus moueat, appendatur deinde minori ex <lb></lb> prioribus
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1551 tympanis vis centum libris æqualis, maio­<lb></lb> ri verò ex
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1552 poſterioribus vis vni libræ æqualis, tum <lb></lb> hæc
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1553 illam mouebit, &amp; ſic in infinitum motus extre­<lb></lb> morum
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1554 proportio multiplicari poteſt. </s>
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1555 <s>Flexibili ve­<lb></lb> rò medio quies ita aptari poteſt, vt duo
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1556 eius extre­<lb></lb> ma diuerſis motibus moueantur, &amp; quidem
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1557 ſecun­<lb></lb> dum datam rationem. </s>
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1558 <s>Exemplum habemus in orga <lb></lb> nis polyſpactis, ſeu trochleis, in
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1559 quibus altero funis <lb></lb> extremo immobili manente, reliquum funis circa
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1560 <lb></lb> plures trochleas conuoluitur, quarum aliæ centris <lb></lb>
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diff changeset
1561 immobilibus fixæ ſunt, aliæ verò ipſis
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diff changeset
1562 contrariæ cen <lb></lb> tris mobilibus. </s>
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diff changeset
1563 <s>Atque ita circa illas conuoluitur fu­<lb></lb> nis, vt inter eas ſit
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diff changeset
1564 ſpatium tantum, quanta eſt linea, <pb xlink:href="044/01/042.jpg" pagenum="34"></pb>per quam motum ciere volumus. </s>
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diff changeset
1565 <s>Quoties igitur fu­<lb></lb> nis extremum quod moueri poteſt, trahitur,
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diff changeset
1566 <expan abbr="ſingulę">ſingulæ</expan><lb></lb>
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diff changeset
1567 reuolutiones æqualiter minuuntur, eáque ratione, <lb></lb>
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diff changeset
1568 <expan abbr="diſtãtia">diſtantia</expan> quæ eſt
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diff changeset
1569 inter trochleas contrarias minuitur, <lb></lb> ita ſcilicet vt quot
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diff changeset
1570 ſunt reuolutiones, in tot partes <lb></lb> diſtributum ſit
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diff changeset
1571 motus ſpatium. </s>
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diff changeset
1572 <s>Quot igitur reuolu<lb></lb> tiones erunt, totuplex erit motus extremitatis funis
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diff changeset
1573 <lb></lb> ad motum trochlearum mobilium verſus fixas. </s>
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diff changeset
1574 <s>Si i­<lb></lb> gitur motus iſtius extrema conſtituantur, alterum <lb></lb>
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diff changeset
1575 <expan abbr="quidẽ">quidem</expan> funis illa extremitas quæ
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diff changeset
1576 mouetur, <expan abbr="alterũ">alterum</expan> ve­<lb></lb> rò
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diff changeset
1577 terminus ſpatij illius, quod eſt à trochleis fixis ad <lb></lb>
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diff changeset
1578 mobiles contrarias: quæ erit proportio numeri con­<lb></lb> uolutionum
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diff changeset
1579 funis ad vnitatem, eadem erit motus, <lb></lb> quo funis extremum mouebitur ad
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diff changeset
1580 motum quo al­<lb></lb> terum extremum mouebitur: poteſt autem in
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diff changeset
1581 infi­<lb></lb> nitum augeri conuolutionum numerus, ergo &amp; mo<lb></lb> tus
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1582 illius proportio. </s>
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1583 </p>
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1584 <p type="main">
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1585
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diff changeset
1586 <s>Angulus autem ad motum ciendum ita ad­<lb></lb> hibetur. </s>
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1587 <s>Diximus motus menſuram in nutus li­<lb></lb> nea ſumi, quantum
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diff changeset
1588 igitur vis aliqua per eam verſus <lb></lb> locum naturalem mouetur, tanta
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diff changeset
1589 eſt, quantum verò <lb></lb> per eam à loco naturali reuellitur,
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1590 tanta eſt eius reſi­<lb></lb> ſtentia. </s>
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1591 <s>Quod verò per lineam à loco naturali æquè <lb></lb>
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1592 diſtantem (id eſt, per eam quæ nutus lineas ſecat ad
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1593 <lb></lb> angulos rectos) mouetur, illud mouenti non reſi­<lb></lb>
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1594 ſtit, omnium autem linearum inter illas intercepta- <pb xlink:href="044/01/043.jpg" pagenum="35"></pb>rum, ac cum illis in earum
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1595 interſectionis puncto <expan abbr="cõ-currentium">con­<lb></lb>
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1596 currentium</expan>, quæ obliquè nutum verſus, aut contra
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1597 <lb></lb> nutum ferri dicuntur, quo propiùs quælibet ad nu­<lb></lb>
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1598 tus lineam accedit, per illam rei motæ vis aut <expan abbr="reſiſtẽ-tia">reſiſten­<lb></lb>
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1599 tia</expan> maior eſt: quò verò propiùs ad lineam
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1600 à loco na­<lb></lb> turali æqui diſtantem accedit, eò
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1601 minor eſt. </s>
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1602 <s><expan abbr="Omniũ">Omnium</expan>
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1603 <lb></lb> autem maxima eſt in nutus linea, æquidiſtans
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1604 verò <lb></lb> à loco naturali motui per lineam nutus omnino op<lb></lb>
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1605 poſita eſt, obliquæ verò non ita quia ſecundum
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1606 illas <lb></lb>
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1607 <expan abbr="eodẽ">eodem</expan> ſpatio delata vis propiùs
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1608 ad <expan abbr="locũ">locum</expan>
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1609 <expan abbr="naturalẽ">naturalem</expan> acce­<lb></lb> dit, aut ab
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1610 eo recedit, quàm eſſet, cùm moueri cœpit. </s>
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1611 </p>
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1612 <figure id="id.044.01.043.1.jpg" xlink:href="044/01/043/1.jpg"></figure>
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1613 <p type="main">
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1614 <s>Sit exempli gratia AB linea <lb></lb> nutus, vis alicuius, puta ponde­<lb></lb>
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1615 ris, ſitque A ſurſum &amp; contra nu<lb></lb> tum: B verò
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parents:
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1616 deorſum &amp; nutum <lb></lb> verſus, deſcribatúrque
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1617 circulus, <lb></lb> cuius AB ſit diameter, quàm CD, <lb></lb> alia
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parents:
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1618 diameter ſecet ad angulos <lb></lb> rectos in centro E: omnes igitur <lb></lb>
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1619 lineæ à centro E ad circunferentiam circuli ductæ, <lb></lb>
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1620 quæ <expan abbr="cadẽt">cadent</expan> intra <expan abbr="ſemicirculũ">ſemicirculum</expan> CAD, contra
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1621 <expan abbr="nutũ">nutum</expan>
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1622 <expan abbr="aſcẽ-dere">aſcen­<lb></lb> dere</expan>
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1623 dicentur, quatenus circunferentiam ſpectant: <lb></lb> quatenus verò
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1624 centrum ſpectant, deſcendere dicen­<lb></lb> tur: <expan abbr="cõtra">contra</expan> verò omnes in ſemicirculo
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1625 CBD à centro <lb></lb> ad circunferentiam ductæ deſcendere
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parents:
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1626 circunferen­<lb></lb> tiam verſus, &amp; centrum verſus
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1627 aſcendere dicentur: <pb xlink:href="044/01/044.jpg" pagenum="36"></pb>illæ igitur erunt, quæ obliquè nutum verſus aut
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1628 con<lb></lb> tra nutum ferri <expan abbr="dicũtur">dicuntur</expan>: linea
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1629 verò CED, neque <expan abbr="aſcẽ-det">aſcen­<lb></lb> det</expan>, neque deſcendet: lineæ
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1630 verò in ipſam ad angu­<lb></lb> los rectos incidentes nutus
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1631 lineæ erunt, quoniam li­<lb></lb> neæ AB parallelæ erunt:
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parents:
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1632 ſi igitur à centro E <expan abbr="ducãtur">ducantur</expan>
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1633 <lb></lb> lineæ ad circunferentiam inter A &amp; D, puta EF, EG, <lb></lb> EH,
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1634 quarum EF ſit proxima lineæ AB:EH verò pro­<lb></lb> xima
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1635 lineæ CD, ac per illas moueantur contra <expan abbr="nutũ">nutum</expan>
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1636 <lb></lb> tres vires æquales eodem tempore, ita vt prima per <lb></lb> lineam
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1637 EF perueniat ad punctum F: ſecunda verò <lb></lb> per EG perueniat ad
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1638 G, tertia per EH perueniat ad H, <lb></lb> dico vis motæ per EF maiorem
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1639 fore reſiſtentiam, <lb></lb> quàm illius quæ per EG aut
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1640 EH, mouebitur &amp; illius <lb></lb> quæ per EG mouebitur, maiorem
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1641 quàm eius quæ <lb></lb> per EH mouebitur. </s>
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1642 <s>Ducantur enim à punctis FGH <lb></lb> in lineam ED perpendiculares FK, GL,
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1643 HM, illæ <expan abbr="erũt">erunt</expan>
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1644 <lb></lb> nutus lineæ: quanta igitur erit FK, tantum vis prima <lb></lb> mota
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1645 cenſebitur, quanta verò GH, tantum vis ſecun<lb></lb> da:
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diff changeset
1646 quanta verò HM, tantum vis tertia mota cenſebi­<lb></lb> tur: at
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diff changeset
1647 qui quæ eſt ratio motus ad motum in viribus <lb></lb> æqualibus,
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diff changeset
1648 per quartam <expan abbr="cõcluſionem">concluſionem</expan>
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diff changeset
1649 huius tracta­<lb></lb> tus, eadem eſt reſiſtentiæ ad
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diff changeset
1650 reſiſtentiam: quæ igitur <lb></lb> erit ratio linearum illarum
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diff changeset
1651 perpendicularium, inter <lb></lb> ſe eadem erit &amp; <expan abbr="reſiſtẽtiarum">reſiſtentiarum</expan> virium per lineas ob­<lb></lb>
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diff changeset
1652 liquas motarum, à quibus illæ perpendiculares du­<lb></lb>
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diff changeset
1653 ctæ ſunt, atqui quo lineæ illæ perpendiculares pro- <pb xlink:href="044/01/045.jpg" pagenum="37"></pb>piùs ad AB circuli
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diff changeset
1654 diametrum accedunt, eò ſunt ma<lb></lb> iores per decimam quartam
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diff changeset
1655 tertij Elem. Eu. ergo &amp; <lb></lb> vires per eas lineas delatę à
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diff changeset
1656 <expan abbr="quarũ">quarum</expan> extremitatibus du<lb></lb>
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parents:
diff changeset
1657 <expan abbr="cẽtur">centur</expan>, maiores <expan abbr="reſiſtẽtias">reſiſtentias</expan>
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diff changeset
1658 <expan abbr="habebũt">habebunt</expan>: at qui quò magis <lb></lb> ad
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diff changeset
1659 AB, accedunt eo magis ab ED recedunt: quò igi­<lb></lb> tur magis ad
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diff changeset
1660 ED accedent, eò minores erunt <expan abbr="reſiſtẽ-tiæ">reſiſten­<lb></lb> tiæ</expan>, hinc ſequitur
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diff changeset
1661 tanquam corollarium. </s>
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diff changeset
1662 <s>Si duæ vi­<lb></lb> res perſe æquales triangulo rectangulo
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diff changeset
1663 aptentur, cu<lb></lb> ius latus alterum, angulum rectum <expan abbr="conſtituẽtium">conſtituentium</expan>: <lb></lb>
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diff changeset
1664 ſit earum nutus linea, ac per illud vis altera mouea­<lb></lb> tur,
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diff changeset
1665 altera verò per latus angulo recto oppoſitum, <lb></lb> quæ erit
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diff changeset
1666 ratio huius lateris ad illud, eadem erit reſi­<lb></lb> ſtentia
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diff changeset
1667 vis illius ad vis huius <expan abbr="reſiſtẽtiam">reſiſtentiam</expan>. </s>
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diff changeset
1668 <s>Atqui duo­<lb></lb> rum illorum laterum proportio in infinitum
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diff changeset
1669 auge­<lb></lb> ri vel minui poteſt, ergo &amp;
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parents:
diff changeset
1670 reſiſtentia virium illis ap<lb></lb> plicatarum. </s>
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diff changeset
1671 <s>Hoc igitur modo poſſumus vti angulo <lb></lb> ſeu triangulo ad
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diff changeset
1672 motus ciendos, nempe eo immoto <lb></lb> vires per eius latera mouendo. </s>
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1673 </p>
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diff changeset
1674 <p type="main">
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parents:
diff changeset
1675
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parents:
diff changeset
1676 <s>Sed &amp; alia ratione eo vti poſſumus, ipſum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
1677 ſcilicet <lb></lb> triangulum mouendo, qui tunc cuneus dicitur. </s>
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diff changeset
1678 <s>Vt <lb></lb> autem eo hac ratione vtamur, vires ita diſponere o­<lb></lb>
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diff changeset
1679 portet, vt altera illarum vni ex lateribus angulum <lb></lb> rectum
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diff changeset
1680 conſtituentibus incumbat, altera verò lateri <lb></lb> ipſum
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diff changeset
1681 ſubtendenti. </s>
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diff changeset
1682 <s>Illa enim tantùm mouebitur, <lb></lb> quantum latus cui altera incumbit. </s>
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diff changeset
1683 <s>Sit exempli gra­ <pb xlink:href="044/01/046.jpg" pagenum="38"></pb><figure id="id.044.01.046.1.jpg" xlink:href="044/01/046/1.jpg"></figure><lb></lb> tia
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diff changeset
1684 triangulus ABC, cuius angulus B <lb></lb> rectus ſit, latus verò
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parents:
diff changeset
1685 illum ſubtendens <lb></lb> ſit AC, incumbátque vis D lateri AB,
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1686 <lb></lb> vis verò E lateri AC, ſitque vis D nutus <lb></lb> linea BC,
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parents:
diff changeset
1687 vis verò E nutus ſit linea AB, erigatúrque à <lb></lb>
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1688 puncto C linea CF <expan abbr="perpẽdicularis">perpendicularis</expan> ad BC æqualis AB, <lb></lb> à qua vis E
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diff changeset
1689 <expan abbr="nõ">non</expan> diſcedat. </s>
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1690 <s>Si triangulum illud in plano <lb></lb> fixo moueatur, donec AB perueniat ad CF,
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diff changeset
1691 mota e­<lb></lb> rit vis D nutu ſuo tantùm, quanta eſt
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diff changeset
1692 linea BC, vis ve­<lb></lb> rò E tantum, quanta eſt linea AB.
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1693 </s>
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diff changeset
1694 <s>Cùm autem poſſit <lb></lb> in infinitum augeri &amp; minui,
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diff changeset
1695 laterum illorum pro­<lb></lb> portio, poſſunt etiam duorum
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1696 illorum <expan abbr="extremorũ">extremorum</expan>
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diff changeset
1697 <lb></lb> motus in data ratione conſtitui. </s>
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1698 <s>Quanta enim erit <lb></lb> BC ad AB, tantus erit motus vis D ad motum vis E:
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
1699 <lb></lb> ergo &amp; in hoc medio primum lemma noſtrum de­<lb></lb>
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parents:
diff changeset
1700 monſtratum eſt. </s>
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1701 </p>
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diff changeset
1702 <p type="main">
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1703
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
1704 <s>In hoc autem medij genere hoc diuerſum ab <lb></lb> aliis mediis accidit,
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diff changeset
1705 quòd non tam facilè vtrin­<lb></lb> que motus eo cietur, ac in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1706 illis, in quibus ſi virium <lb></lb> proportio momento vel ſuperet,
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diff changeset
1707 vel minor ſit pro­<lb></lb> portione motus <expan abbr="extremorũ">extremorum</expan> medij, tum motus hinc <lb></lb>
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diff changeset
1708 vel inde cietur. </s>
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parents:
diff changeset
1709 <s>Atqui in hoc propter ſuperficie­<lb></lb> rum contactum, quarum pori
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1710 vel aſperitates ſe­<lb></lb> ſe mutuò
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diff changeset
1711 ſubingrediuntur, &amp; ita inuicem adhæ­<lb></lb> rent, fit vt
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1712 ægriùs cieatur motus, faciliùs ve- <pb xlink:href="044/01/047.jpg" pagenum="39"></pb>rò mouebuntur, ſi
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1713 illæ ſuperficies leues fue­<lb></lb> rint, vt ſi pinguibus
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diff changeset
1714 inungantur, vel ex materia <lb></lb> leui conſtent. </s>
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1715 <s>Ideò enim reliqua faciliùs mo­<lb></lb> uentur, quòd circa
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parents:
diff changeset
1716 puncta veluti quædam mo­<lb></lb> ueantur. </s>
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1717 </p>
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1718 <p type="main">
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1719
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1720 <s>Simplicis autem trianguli rectilinei aut cu­<lb></lb> nei in diuturnis
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1721 motibus ciendis rarus eſt vſus, <lb></lb> tum ob illud quod
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1722 notauimus incommodum ex <lb></lb> vitio materiæ, quo fit vt in eo
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1723 quaſſatione opus <lb></lb> ſit, tum etiam quòd breui eius
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1724 operatio termine­<lb></lb> tur. </s>
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1725 <s>Ideo illo vtimur aut cùm ſolutionem con­<lb></lb> tinui molimur,
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1726 quæ breui tempore fit, vel <lb></lb> cùm aliquid diſtendere aut
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1727 aliquid figere volu­<lb></lb> mus. </s>
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1728 </p>
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1729 <p type="main">
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1730
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1731 <s>Anguli verò curui linei magnus eſt vſus, præ­<lb></lb>
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diff changeset
1732 ſertim helicis cylindricæ. </s>
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diff changeset
1733 <s>Nihil enim aliud eſt he­<lb></lb> lix quàm triangulus curuus:
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diff changeset
1734 ſi enim alteram ex <lb></lb> lineis rectis angulum conſtituentibus,
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diff changeset
1735 cylindri <lb></lb> baſi ipſi lineæ æquali obuolueris,
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diff changeset
1736 reliquam ve­<lb></lb> rò ſeruato eodem quem conſtituunt
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parents:
diff changeset
1737 angulo, ſu­<lb></lb> per cylindri ſuperficiem curuaueris,
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diff changeset
1738 habebis he­<lb></lb> licem cylindricam, quam ſi iterum ſeruato
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diff changeset
1739 eo­<lb></lb> dem angulo in rectum extendas, habebis trian­<lb></lb> gulum
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diff changeset
1740 rectilineum. </s>
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diff changeset
1741 <s>Hæc autem helix commo­<lb></lb> diſſima eſt, tum
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diff changeset
1742 quòd in parua mole triangulum <pb xlink:href="044/01/048.jpg" pagenum="40"></pb>longiſſimum obuolutum contineat tum quod
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diff changeset
1743 par­<lb></lb> tes eius omnes ſibi inuicem <expan abbr="cõgruant">congruant</expan>: omnes enim <lb></lb> partes helicis cylindricæ, aut
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diff changeset
1744 circa eundem, aut circa <lb></lb> æquales cylindros deſcriptæ,
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diff changeset
1745 ſeruato eodem angulo <lb></lb> ſibi inuicem
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diff changeset
1746 ſuppoſitæ congruunt. </s>
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diff changeset
1747 <s>Quo fit, vt ſi ca­<lb></lb> ui cylindri interiori ſuperficiei
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diff changeset
1748 impreſſa ſit helix, a­<lb></lb> lia verò cylindri
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diff changeset
1749 ſuperficiei connexę ipſi cauę æqua­<lb></lb>
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diff changeset
1750 li, ſeruato eodem qui in illo eſt, angulo, ſibi
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diff changeset
1751 inui­<lb></lb> cem &amp; omnes vnius omnibus alterius partibus con<lb></lb>
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diff changeset
1752 gruant. </s>
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diff changeset
1753 </p>
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diff changeset
1754 <p type="main">
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diff changeset
1755
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diff changeset
1756 <s>Huius autem medij cùm plures ſint partes, con<lb></lb> ſtat enim
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diff changeset
1757 duabus ſuperficiebus, pluribus etiam mo<lb></lb> dis variari poteſt. </s>
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parents:
diff changeset
1758 <s>In ſumma autem eius affectus hic <lb></lb> eſt, vt cylindri
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parents:
diff changeset
1759 baſi in ſuperficie immobili circum a­<lb></lb> xem
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parents:
diff changeset
1760 conuerſa, vis mouenda helicem premat: dum <lb></lb> enim cylindrus circum
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
1761 axem conuertetur, vis mo­<lb></lb> uenda qualibet reuolutione tantùm
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parents:
diff changeset
1762 ſecundum cy­<lb></lb> lindri longitudinem mouebitur, quanta eſt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1763 diſtan­<lb></lb> tia duarum helicis ſpirarum. </s>
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diff changeset
1764 <s>Quæ igitur erit propor<lb></lb> tio circunferentiæ circuli baſim
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diff changeset
1765 cylindri <expan abbr="conſtituẽ-tis">conſtituen­<lb></lb> tis</expan> ad illam <expan abbr="diſtãtiam">diſtantiam</expan>, eadem erit motus
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parents:
diff changeset
1766 orbicularis <lb></lb> cuiuſlibet puncti in cylindri ſuperficie
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parents:
diff changeset
1767 ſignati ad mo<lb></lb> tum rectum vis helicem prementis. </s>
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diff changeset
1768 </p>
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diff changeset
1769 <p type="main">
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1770
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parents:
diff changeset
1771 <s>Illud igitur medium ex duobus compoſitum eſt, <lb></lb> recto
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diff changeset
1772 ſcilicet &amp; curuo: ita igitur vires illi aptandæ <lb></lb>
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diff changeset
1773 ſunt, vt eius quam mouere volumus, nutus linea ſit <pb xlink:href="044/01/049.jpg" pagenum="41"></pb>cylindri longitudo: illa
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
1774 verò qua mouere volumus, <lb></lb> in orbem moueatur, aut ſi eius
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diff changeset
1775 nutus linea recta ſit, <lb></lb> circa cylindrum fluens illum moueat
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1776 contingendo. </s>
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1777 </p>
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diff changeset
1778 <p type="main">
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1779
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diff changeset
1780 <s>Et hæc quidem de mediis in ſuo genere <expan abbr="conſiſtẽ-tibus">conſiſten­<lb></lb> tibus</expan>. </s>
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1781 <s>Poſſunt autem fieri eorum Syzygiæ vectis
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diff changeset
1782 ſci­<lb></lb> licet cum trochleis, helicis cum vecte, aut cum
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diff changeset
1783 tro­<lb></lb> chleis, aut <expan abbr="omniũ">omnium</expan>
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diff changeset
1784 ſimul. </s>
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diff changeset
1785 <s>Vectis cum trochleis ſi fu­<lb></lb> nis illud extremum, quod mouetur
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diff changeset
1786 in trochleis, er­<lb></lb> gatis aut ſuculis inuoluatur: helix cum
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diff changeset
1787 vecte <expan abbr="coniũ-getur">coniun­<lb></lb> getur</expan>,
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diff changeset
1788 ſi tympanus circum axem moueatur, ſitque i­<lb></lb> ta
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diff changeset
1789 denticulatus, vt dentes ipſius helicem in cylindro <lb></lb> excauatam
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1790 ingrediantur, quam machinam helicem <lb></lb> perpetuam vulgò vocant,
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1791 eò quòd eius conuerſio <lb></lb> perpetua eſſe
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1792 poſſit, cum helicis ſimplicis operatio <lb></lb> non excedat
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1793 ipſius longitudinem. </s>
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1794 <s>Quorum <expan abbr="omniũ">omnium</expan>
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diff changeset
1795 <lb></lb> tum inter ſe, tum ad ſubiecta mouenda accommo­<lb></lb>
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diff changeset
1796 datio adeò varia eſt, vt ſcripto <expan abbr="cõprehẽdi">comprehendi</expan> vix poſſit.
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1797 <lb></lb>
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1798 </s>
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1799 <s>Ex his autem quæ dicta ſunt, mediocris ingenij me­<lb></lb>
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1800 chanicus poterit ea prout ipſi neceſſe erit aptare. </s>
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1801 <s>In <lb></lb> machinis autem omnibus hæc cautio <expan abbr="adhibẽda">adhibenda</expan> eſt, <lb></lb> vt earum ſtructura firma
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1802 ſit, præſertim verò vbi cir­<lb></lb> cum axes
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1803 aliquas fit motus, deinde vt vincula, qui­<lb></lb> bus illis vires <expan abbr="affingũtur">affinguntur</expan>, valida ſint, illarum
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1804 enim o­<lb></lb> mnium vis in ſuo ſtatu manendi vtrique vi
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1805 aptandæ <lb></lb> æqualis eſſe debet: aget enim in illas
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1806 vis <expan abbr="vtraq;">vtraque</expan>, quòd <lb></lb> ſi medium
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1807 firmum non ſit, motus in ipſa machina <pb xlink:href="044/01/050.jpg" pagenum="42"></pb>ciebitur. </s>
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1808 <s>Itaque diſſoluetur, ideò manca videtur pe­<lb></lb> titio
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1809 illa Archimedis in hoc problemate <foreign lang="grc">δὸς ποῦ στῶ τὰν
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1810 <lb></lb> γὰν κινῶ</foreign>, quòd locum <expan abbr="tãtùm">tantùm</expan> in quo conſiſtat,
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1811 ſibi da­<lb></lb> ri poſtulet, cùm pręterea vincula
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1812 quibus terra à loco <lb></lb> ſuo naturali remota
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1813 ſuſtineri poſſet, petere debue­<lb></lb> rit: id
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1814 <expan abbr="autẽ">autem</expan> vt &amp; ea quæ de motu in
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1815 infinitum augen­<lb></lb> do vel minuendo diximus, ita intelligenda
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1816 ſunt, vt <lb></lb> ſciamus infinita hominum poteſtati,
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1817 quacunque ar­<lb></lb> te iuuetur, non ſubeſſe: quamuis
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1818 enim Geometri­<lb></lb> ca conſideratio in infinitum ſeſe
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diff changeset
1819 <expan abbr="extẽdat">extendat</expan>, ſunt ta­<lb></lb>
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diff changeset
1820 men certi fines, vltra quos natura rerum nos pro­<lb></lb> gredi non
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diff changeset
1821 patitur: ſunt præterea vitia materiæ, <lb></lb> quæ
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diff changeset
1822 Geometra non conſiderat, illa tamen non <lb></lb> obſtant quò
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diff changeset
1823 minùs id quod proponitur, <expan abbr="verũ">verum</expan>
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diff changeset
1824 ſit in <lb></lb> intellectu. </s>
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diff changeset
1825 <s>An verò id quod proponitur tale ſit, vt in <lb></lb> opus educi
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diff changeset
1826 poſſit, conſiderabit Geometer habita ra­<lb></lb> tione
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diff changeset
1827 circunſtantiarum, præſertim verò temporis, <lb></lb> quod
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diff changeset
1828 ipſi præſcribetur, &amp; ſumptuum quos facere <lb></lb>
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diff changeset
1829 poterit is qui aliquid faciendum proponet, quæ ſi <lb></lb>
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diff changeset
1830 abundè ſuppetant, nihil non fieri poterit. </s>
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diff changeset
1831 </p>
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diff changeset
1832 <p type="main">
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1833
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diff changeset
1834 <s>Vt igitur hunc tractatulum concludamus, ac ve­<lb></lb> lut in ſummam
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parents:
diff changeset
1835 contrahamus: In motibus ciendis <lb></lb> tria ſunt conſideranda. </s>
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diff changeset
1836 <s>Vis qua motum ciere volu­<lb></lb> mus, vis quam mouere volumus, &amp; motum
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diff changeset
1837 quo <lb></lb> mouere volumus: duo enim quælibet ex illis ter­<lb></lb>
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diff changeset
1838 tium determinant. </s>
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diff changeset
1839 <s>Si enim vi parua vim magnam <pb xlink:href="044/01/051.jpg" pagenum="43"></pb>mouere volumus, id nonniſi paruo motu facere <lb></lb>
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diff changeset
1840 poſſumus: ſi verò vim aliquam magno motu
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diff changeset
1841 mo­<lb></lb> uere velimus, vi magna mouente ad id opus eſt. </s>
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diff changeset
1842 <s>Si <lb></lb> vi parua magnum motum ciere volumus, mini­<lb></lb> mam vim
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diff changeset
1843 mouendam eſſe oportet: vt puta, ſi libra <lb></lb> vna centum
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diff changeset
1844 libras mouere velimus, oportet motum <lb></lb> illius, motu huius <expan abbr="cẽtuplo">centuplo</expan> maiorem eſſe. </s>
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diff changeset
1845 <s>Si verò ve­<lb></lb> limus libra vna aliam vim ita mouere, vt ea
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diff changeset
1846 cen­<lb></lb> tuplo citiùs moueatur, quàm libræ illius
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diff changeset
1847 pondus, il­<lb></lb> lam centeſimam tantùm libræ vnius
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diff changeset
1848 partem eſſe ne­<lb></lb> ceſſe eſt: ſi
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diff changeset
1849 verò libram vnam ita mouere velimus, vt <lb></lb> centuplo citius moueatur,
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diff changeset
1850 quàm vis quæ illam mo­<lb></lb> uebit, vi centum libris maiore ad
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diff changeset
1851 id opus erit. </s>
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1852 <s><expan abbr="Neq;">Neque</expan>
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diff changeset
1853 <lb></lb> patitur natura ſibi in his vim fieri: ſi enim
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diff changeset
1854 eiuſmodi <lb></lb> proportio aliquo modo infringi poſſet,
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1855 ſtatim da­<lb></lb> retur <foreign lang="grc">αὐτώμα
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1856 ἐνδέλεχες</foreign>, vel vt <expan abbr="vocãt">vocant</expan>,
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diff changeset
1857 motus perpetuus <lb></lb> in perpetua materia. </s>
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1858 </p>
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1859 <p type="main">
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1860
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1861 <s>Ex his igitur fundamentis inuentæ ſunt machinæ <lb></lb> omnes,
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1862 quotquot antehac ſunt excogitatę, &amp; quot­<lb></lb> quot
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1863 poſthac excogitari poterunt, ad ea referentur. </s>
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1864 </p>
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1865 <p type="main">
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1866
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1867 <s>Itaque ſi propoſitæ cuiuſcunque machinæ
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1868 effe­<lb></lb> ctum ſcire velimus, conſideranda ſunt duo
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1869 eius <lb></lb> extrema, quibus vires applicantur: quæ enim erit <lb></lb> ratio
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1870 motus vnius ex illis extremis, ad motum <lb></lb> alterius eadem erit &amp;
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1871 virium, quæ illis extre­<lb></lb> mis ad motum ciendum applicari
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1872 poterunt, <pb xlink:href="044/01/052.jpg" pagenum="44"></pb>addito aut dempto
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1873 momento, vt ſi dum <expan abbr="alterũ">alterum</expan>
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1874 ma­<lb></lb> chinæ extremum palmo vno mouetur, alterum cen<lb></lb> tum
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1875 palmis moueatur vis quælibet huic annexa, al­<lb></lb> teram alteri
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1876 annexam centuplam momento minùs, <lb></lb> mouebit: ſed motu
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1877 centuplo: mouebit autem &amp; re­<lb></lb> liquas omnes vires, quæ
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1878 infra centuplam proportio­<lb></lb> nem ad eam habebunt: ſi verò
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1879 non vim centuplam <lb></lb> mouere, ſed in data vi motum centuplum ciere
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1880 veli­<lb></lb> mus, eam quidem in extremo quod centuplo citiùs <lb></lb>
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1881 mouetur, locare oportebit, alteram verò alteri extre<lb></lb> mo centuplo
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1882 maiorem adhibere neceſſe erit. </s>
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1883 </p>
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1884 <p type="main">
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1885
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1886 <s>Hinc oriuntur tria problemata, videlicet data vi <lb></lb> datum pondus mouere,
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1887 quod iam <expan abbr="demõſtrauimus">demonſtrauimus</expan>: <lb></lb> item data vi datum motum ciere, quod ex
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1888 <expan abbr="præcedẽ-tis">præceden­<lb></lb>
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1889 tis</expan> demonſtratione abſoluitur: tertium, datam vim,
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1890 <lb></lb> dato motu mouere, quod quidem faciliùs demon­<lb></lb>
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1891 ſtratur, quàm abſoluitur. </s>
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1892 <s>Scimus enim, vt id fiat, <lb></lb> vim aliam proportionalem (vt docuimus)
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1893 requiri, <lb></lb> quo modo autem illam habere poſſimus, explicare
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1894 <lb></lb> hoc opus, hic labor eſt. </s>
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1895 <s>Non enim quemadmodum <lb></lb> organa ad motus in data proportione ciendos
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1896 ha­<lb></lb> bere poſſumus: ita &amp; vires infinitæ
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1897 magnitudinis po<lb></lb> teſtati noſtræ ſubſunt.
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1898 </s>
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1899 </p>
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1900 <p type="main">
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1901
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1902 <s>Quod enim ad vires in grauitatis &amp; leuitatis gene<lb></lb> re
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1903 conſiſtentes attinet, eas vt moueant antè moueri <lb></lb>
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1904 oportet à loco vel ſitu naturali, vi <expan abbr="autẽ">autem</expan> aliqua id fie- <pb xlink:href="044/01/053.jpg" pagenum="45"></pb>ri oportet, quæ iam in promptu ſit. </s>
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1905 <s>Quæ ſi tanta eſt, <lb></lb> vt poſſit motum
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1906 propoſitum ciere, fruſtrà fiat, ſi alij <lb></lb> à
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1907 loco naturali remouendæ, qua poſtea ad motum <lb></lb> vtendum
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1908 ſit, adhibeatur. </s>
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1909 </p>
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1910 <p type="main">
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1911
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1912 <s>Nullum igitur ex eiuſmodi viribus commodum <lb></lb> percipi poteſt,
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1913 niſi quis in futurum ſibi proſpiciens, <lb></lb> multa à
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1914 loco vel ſitu naturali ex otio remoueat, vt <lb></lb> iis, cùm opus
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1915 erit ad motus ciendos vtatur. </s>
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1916 <s>Hac ra­<lb></lb> tione quantas vires in promptuario habebit, tantos <lb></lb>
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1917 motus ciere poterit. </s>
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1918 <s>Præcipuum igitur quod ad hu­<lb></lb> ius problematis
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1919 conſtructionem pertinet, eſt, vt vi­<lb></lb> res quàm
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1920 maximas poteſtati noſtræ ſubiiciamus, vo<lb></lb>
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1921 luntariis aut fortuitis viribus naturales præparando, <lb></lb> aut à
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1922 natura præparatas, quæ poteſtati noſtræ
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1923 ſub­<lb></lb> ſunt, accipiendo. </s>
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1924 <s>Qualia multa ſi mortales aduerte­<lb></lb> rent, fieri
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1925 poſſent, vt aliàs, Deo duce, docebimus. </s>
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1926 </p>
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1927 <p type="main">
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1928
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1929 <s>Earum autem virium quæ in raritatis &amp; denſita­<lb></lb> tis
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1930 proportione conſiſtunt, ſubiecta plurimùm in <lb></lb>
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1931 noſtra poteſtate ſunt: multa enim ſunt naturalia
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1932 ſub <lb></lb> iecta actu, denſa potentia verò rara. </s>
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1933 <s>Si quod igitur <lb></lb> eorum potentia proxima ſit rariſſimum,
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1934 ita vt nullo <lb></lb> negotio actus ille raritatis induci poſſit,
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1935 <expan abbr="concluda-túrq;">concluda­<lb></lb>
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1936 túrque</expan> loco aliquo anguſto, poſtea inducatur
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1937 ille a­<lb></lb> ctus, cùm rara <expan abbr="maiorẽ">maiorem</expan> locum occupent, quum den­<lb></lb> ſa, fiet vt
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1938 locus in omnem partem diſtendatur, illius <lb></lb> autem partes
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1939 minùs cohærentes, tantum impellen­ <pb xlink:href="044/01/054.jpg" pagenum="46"></pb>tur, quanta eſt
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1940 proportio molis rei rarefactæ ad mo­<lb></lb> lem illius cùm
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1941 denſa eſſet: illa autem raritatis po­<lb></lb> tentia
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1942 proxima eſt in compoſitione ſulphuris <lb></lb> &amp; nitri:
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1943 ea igitur &amp; ſimilibus ſubiectis, <lb></lb> in data vi datus
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1944 motus <lb></lb> cieri poteſt. </s>
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1945 </p>
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1946 <p type="head">
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1947
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1948 <s>FINIS.</s>
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1949 </p>
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1950 <p type="head">
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1951
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1952 <s>Errata quæ inter imprimendum irrepſerunt, <lb></lb> ſic
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1953 corrigito.</s>
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1954 </p>
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1955 <p type="main">
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1956
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1957 <s><emph type="italics"></emph>Pagina<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>linea<emph.end type="italics"></emph.end> 10, <emph type="italics"></emph>munere, lege nuere. </s>
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1958
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1959 <s>pag.<emph.end type="italics"></emph.end> 11. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 12, <emph type="italics"></emph>comparationibus, lege
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1960 comparati, omni­<lb></lb> bus. </s>
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1961
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1962 <s>pag.<emph.end type="italics"></emph.end> 12. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 16. <emph type="italics"></emph>finis, lege fini. </s>
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1963
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1964 <s>pag. eadem. lin. penult. Altero, lege Alto.</s>
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1965
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1966 <s>pag.<emph.end type="italics"></emph.end> 20. <lb></lb>
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1967 <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 16. <emph type="italics"></emph>quum<emph.end type="italics"></emph.end> C <emph type="italics"></emph>ad<emph.end type="italics"></emph.end> L. <emph type="italics"></emph>lege quam. </s>
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1968
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1969 <s>pag.<emph.end type="italics"></emph.end> 25. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>nunc ſit ratio, lege
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1970 minor ſit. </s>
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1971
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1972 <s>linea<emph.end type="italics"></emph.end> 13. <emph type="italics"></emph>Vi­<lb></lb> res
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1973 maiori litera<emph.end type="italics"></emph.end> (<emph type="italics"></emph>eſt
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1974 enim ſectionis initium. </s>
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1975
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1976 <s>lin.<emph.end type="italics"></emph.end> 15. <emph type="italics"></emph>mittant, lege
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1977 mittantur. </s>
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1978
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1979 <s>pag.<emph.end type="italics"></emph.end> 27. <emph type="italics"></emph>li.<emph.end type="italics"></emph.end> 20. <lb></lb>
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1980 <emph type="italics"></emph>puncti in linea<emph.end type="italics"></emph.end> A, <emph type="italics"></emph>lege puncti<emph.end type="italics"></emph.end> A <emph type="italics"></emph>in linea. </s>
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1981
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1982 <s>pag.<emph.end type="italics"></emph.end> 28. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 9. <emph type="italics"></emph>vis, lege Vis, maiori
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1983 litera<emph.end type="italics"></emph.end> (<emph type="italics"></emph>eſt enim
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1984 <lb></lb> ſectionis initium. </s>
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1985
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1986 <s>lin. e. motu ciere, leg. motu quem ciere. </s>
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1987
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1988 <s>lin.<emph.end type="italics"></emph.end> 23. <emph type="italics"></emph>metiri
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1989 ſolemus, lege non <lb></lb> ſolemus. </s>
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1990
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1991 <s>lin. vlt. ſtatui, lege ſtatuit.</s>
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1992
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1993 <s>pag.<emph.end type="italics"></emph.end> 32. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 4. <emph type="italics"></emph>abſouit, lege
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1994 abſoluit. </s>
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1995
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1996 <s>lin.<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>dele<emph.end type="italics"></emph.end> F. </s>
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1997
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1998 <s><emph type="italics"></emph>lin.<emph.end type="italics"></emph.end><lb></lb> 12. <emph type="italics"></emph>&amp;<emph.end type="italics"></emph.end> 13, <emph type="italics"></emph>pone virgulam poſt<emph.end type="italics"></emph.end> D <emph type="italics"></emph>&amp;<emph.end type="italics"></emph.end> E.</s>
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1999
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2000 <s>
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2001 <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 8. <emph type="italics"></emph>hypomochium, lege hypomochlium. </s>
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2002
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2003 <s>pag.<emph.end type="italics"></emph.end> 37. <emph type="italics"></emph>li.<emph.end type="italics"></emph.end><lb></lb> 13. <emph type="italics"></emph>reſiſtentia,
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2004 lege reſiſtentiæ. </s>
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2005
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2006 <s>pag.<emph.end type="italics"></emph.end> 39. <emph type="italics"></emph>lin.<emph.end type="italics"></emph.end> 3. <emph type="italics"></emph>leui, lege læui. </s>
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2007
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2008 <s>pag.<emph.end type="italics"></emph.end> 40. <emph type="italics"></emph>linea<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>ſuppoſitæ,
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2009 lege <lb></lb> ſuperpoſitæ</s>
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2010
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2011 <s>li.<emph.end type="italics"></emph.end> 7. <emph type="italics"></emph>connexæ, lege
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2012 conuexæ. </s>
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2013
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2014 <s>lin.<emph.end type="italics"></emph.end> 13. <emph type="italics"></emph>affectus, lege
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2015 effectus.<emph.end type="italics"></emph.end></s>
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2016 </p>
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2017 </chap>
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2018 </body>
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2019 <back></back>
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2020 </text>
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2021 </archimedes>