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1 <?xml version="1.0"?>
2 <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info>
3
4 <author>Jordanus de Nemore</author>
5
6 <title>Liber de ponderibus, old version (31 p.)</title>
7
8
9
10 <date>1533</date>
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12
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14 <place>Nuremberg</place>
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16
17
18 <translator></translator>
19
20
21
22 <lang>la</lang>
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26 <cvs_file>jorda_ponde_050_la_1533.xml</cvs_file>
27
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30 <cvs_version></cvs_version>
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34 <locator>050.xml</locator>
35 <echodir>permanent/archimedes/jorda_ponde_050_la_1533</echodir>
36 </info>
37
38
39
40 <text><front><section><pb xlink:href="050/01/001.jpg"></pb>
41 <p type="head">
42 <s><emph type="center"></emph>LIBER IORDANI <lb></lb>
43 NEMORARII VIRI CLARISSIMI, <emph.end type="center"></emph.end></s>
44 </p>
45
46 <p type="head">
47 <s><emph type="center"></emph>DE PONDERIBUS PROPOSITIONES XIII.<emph.end type="center"></emph.end></s>
48 </p>
49
50 <p type="head">
51 <s><emph type="center"></emph>&amp; earundem demonſtrationes, mul­<lb></lb>tarumque rerum rationes ſanè <lb></lb>pulcherrimas comple­<lb></lb>ctens, nunc in lu­<lb></lb>cem editus.<emph.end type="center"></emph.end></s>
52 </p>
53
54 <p type="head">
55 <s><emph type="center"></emph>Cum gratia &amp; priuilegio Imperiali, Petro Apiano Ma<lb></lb>thematico Ingolſtadiano ad xxx. annos conceſſo.<emph.end type="center"></emph.end></s>
56 </p>
57
58 <figure></figure>
59
60 <p type="main">
61 <s><emph type="center"></emph>M. D. XXXIII.<emph.end type="center"></emph.end></s>
62 </p>
63
64 <pb xlink:href="050/01/002.jpg"></pb><p type="main"><s>[empty page]</s></p></section></front>
65
66 <body><chap><pb xlink:href="050/01/003.jpg"></pb><p type="main"><s>[dedication not transcribed]</s></p><pb xlink:href="050/01/004.jpg"></pb><p type="main"><s>[dedication not transcribed]</s></p><pb xlink:href="050/01/005.jpg"></pb><p type="main"><s>[dedication not transcribed]</s></p></chap><chap><pb xlink:href="050/01/006.jpg"></pb><p type="main">
67
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70 <s id="id.0.0.02.00">LIBER DE PON­<lb></lb>DERIBVS IORDANI NEMORARII.<lb></lb></s>
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74 <s id="id.0.0.02.01">Cum scientia de ponderibus sit subalternata tam Ge<lb></lb>ometriæ quam philosophiæ, oportet in hac sci­<lb></lb>entia quædam geometrice, quædam phyſice proba­<lb></lb>re.</s>
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78 <s id="id.0.0.02.02">Primii ergo oportet scire, quod brachium descenden<lb></lb>do in libra, describit <expan abbr="circulũ">circulu</expan>, cuius circuli semidia­<lb></lb>meter, est semper æqualis brachio libræ.</s>
79
80
81
82 <s id="id.0.0.02.03">Secundo <lb></lb>oportet ostendere, quod maior arcus eiusdem circuli, <lb></lb>est magis curvus minore, et quod talis minor plus cur­<lb></lb>vatur, quam in circulo maiore.</s>
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84
85
86 <s id="id.0.0.02.04">Primum probatur, quia minus de corda, quæ<lb></lb>est recta linea, correspondet proportionaliter arcui maiori, quam minori, <lb></lb>non enim arcui duplo correspondet corda dupla, sed minus ea.</s>
87
88
89
90 <s id="id.0.0.02.05">Secun­<lb></lb>dum patet sic, quia si sumantur de circulo maiori et minori arcus æqua­<lb></lb>les, corda arcus maioris circuli longior est, propterea posset ex hoc osten­<lb></lb>di, quod pondus in libra tanto sit levius, quanto plus descendit in semicircu<lb></lb>lo.</s>
91
92
93
94 <s id="id.0.0.03.02">Incipiat igitur mobile descendere a summo semicirculi, et descendat <lb></lb>continue, dico tunc quod maior arcus circuli plus contrariatur rectæ lineæ <lb></lb>quam minor, et casus gravis per arcum maiorem, plus contrariatur casui gra<lb></lb>vis, qui per rectam fieri debet, quam casus per arcum minorem, patet, ergo ma­<lb></lb>ior est violentia in motu secundum arcum maiorem, quam secundum minorem, <lb></lb>aliter enim non fieret motus magis gravis.</s>
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96
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98 <s id="id.0.0.03.05">Cum ergo plus in ascensu ascensu aliquod mo<lb></lb>vetur violentie, patet, quam maior est gravitas secundum hunc situm, et quia secundum <lb></lb>situationem talium sic fit, dicatur gravitas secundum situm in futu­<lb></lb>ro processu.</s>
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100
101
102 <s id="id.0.0.04.01">Ita enim, syllogisando de motu, tamquam motus sit causa gravita­<lb></lb>tis et levitatis, potius contrarium concludimus per causam huius contrari<lb></lb>etatis, plus contrariam, id est plus habere violentiæ, quod si grave descen­<lb></lb>dat, hoc est a natura, sed per lineam curvam, hoc est contra naturam, ideo <lb></lb>iste descensus est mixtus ex descensu naturæ et violento.</s>
103
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106 <s id="id.0.0.04.03">In ascensu vero <lb></lb>ponderis, cum ibi nihil sit secundum naturam, licet argumentari sicut <lb></lb>de igne, qui naturaliter ascendit.</s>
107
108
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110 <s id="id.0.0.04.04">De igne enim argumentatur in ascensu, <lb></lb>sicut de gravi in descensu, ex quo sequitur, Quanto grave plus sic ascen­<lb></lb>dit, tanto minus habet de levitate secundum situm, et sic plus habet de <lb></lb>gravitate secundum situm.</s>
111
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113
114 <s id="id.0.0.05.01">Diceret forte aliquis, quod non oportet propter <lb></lb>prædicta, grave in parte circuli inferiori fieri secundum situm levius, pa<lb></lb>tet unum non esse motum, sed quietem, tunc nihil contrarium naturæ acqui­<lb></lb>ritur.</s>
115
116
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118 <s id="id.0.0.05.02">Sed contra illud obijcitur sic, possibile fuit hanc quiætem fuisse ter­<lb></lb>minum motus intrinsecum motus, sicut albationis albedo, cum igitur motus<pb xlink:href="050/01/007.jpg"></pb>non contrarientur, nisi quia termini contrariantur eorum.</s><s>Et est propor<lb></lb>tio quietum inter se, et motuum inter se per locum a proportione, sequi­<lb></lb>tur tantam esse contrarietatem in quiescendo, sicut in movendo.</s>
119
120
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122 <s id="id.0.0.05.03">In termi<lb></lb>no enim cuiuscumque motus intenditur, intenditur et viget tota natura <lb></lb>in actu, qui in motu sit quasi in potentia, secundum quem fiebat contra­<lb></lb>rietatis suæ oppositio.</s>
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124
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126 <s id="id.0.0.05.04">Grave igitur in parte inferiori, sive moveatur si­<lb></lb>ve quiescat, levius est secundum situm.</s></p><p type="main">
127
128
129
130 <s id="id.0.0.06.01">Atque eodem syllogismo necesse <lb></lb>est pondus gravius esse quodam modo et velocius descendere, quod move<lb></lb>tur in circulo maiori, quia ut prius probatur, minus obliquatur, quam in <lb></lb>circulo minori, et per consequens minus habet violentiæ, quia igitur mi<lb></lb>nus distat descensus in circulo maiori a descensu naturali, qui sit per rectam <lb></lb>lineam, quam qui est in circulo minori.</s><s>Dicatur descensus rectior, id est plus <lb></lb>tendens ad rectitudinem, atque in circulo minori, ob rationem oppositam, <lb></lb>obliquior descensus.</s>
131
132
133
134 <s id="id.0.0.06.03">Quare vero superius dictum est in quiete esse con­<lb></lb>trarietatem, sicut in motu potest esse dubitatio, quia in eodem situ, ubi <lb></lb>est illa dependentia quietis obliquitatis, potest et rectitudinis, sicut si la<lb></lb>pis suspendatur in tecto domus ad locum ponderis, et quod pendeat in li­<lb></lb>bra.</s>
135
136
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138 <s id="id.0.0.06.04">Sed dicendum ad hoc, quod varietas violentiæ, facit varietatem quietum <lb></lb>secundum formam, quod manifestum est ex motuum ad quietes varia­<lb></lb>tione.</s>
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142 <s id="id.0.0.06.05">Ex eadem enim violentia sit totus ad quietem motus, et ipsa quies, <lb></lb>sicut patet ex prædictis, unde idem forte sit locus quietum naturaliter di­<lb></lb>versarum.</s></p><p type="main">
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146 <s id="id.0.0.07.01">Istis igitur notis, sequuntur suppositiones libri Ponderum <lb></lb>et dicuntur suppositiones, quia per istam scientiam non debent probari, <lb></lb>sed supponuntur, probari tamen ex iam dictis quædam indigent proba­<lb></lb>tione, sicut post apparebit.</s>
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150 <s id="id.0.0.07.04">Sunt itaque suppositiones septem.</s></p></chap><chap><p type="main">
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154 <s id="id.0.0.09.01.post">Prima <lb></lb>est, Omnis ponderosi motum ad medium esse.</s></p><p type="main">
155
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158 <s id="id.0.0.10.01.post">Secunda, Quanto gra­<lb></lb>vius tanto velocius descendere.</s></p><p type="main">
159
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162 <s id="id.0.0.11.01.post">Tertia, Gravius ess in descendendo,<lb></lb> quanto eiusdem motus ad medium est rectior.</s></p><p type="main">
163
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166 <s id="id.0.0.12.01.post">Quarta, Secundum si­<lb></lb>tum gravius esse, quanto in eodem situ minus obliquus est descensus.<lb></lb></s></p><p type="main">
167
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170 <s id="id.0.0.13.01.post">Quinta, Obilquiorem autem descensum minus capere de directo, in eadem <lb></lb>quantitate.</s></p><p type="main">
171
172
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174 <s id="id.0.0.14.01.post">Sexta, Minus grave aliud alio esse secundum situm, quan­<lb></lb>to descensus alterius consequitur contrario motu.</s></p><p type="main">
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178 <s id="id.0.0.15.01.post">Septima, Situm<lb></lb> æqualitatis esse æquidistantiam superficiei orizontis.</s></p><p type="main">
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182 <s id="id.0.0.16.01">Omnes autem <lb></lb>suppositiones sunt satis manifestæ, sicut patet per prædicta, et ideo pro­<lb></lb>positiones prosequi licet, et dicuntur propositiones, quia, ut probentur, <lb></lb>proponuntur.</s>
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186 <s id="id.0.0.16.03">Sunt itaque tredecim.</s></p><pb xlink:href="050/01/008.jpg"></pb></chap><chap><p type="main">
187
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190 <s id="id.0.0.18.01.prop">PROPOSITIO PRIMA.<lb></lb></s><s>Inter quælibet duo gravia est velocitas descenden<lb></lb>do proprie, et ponderum eodem ordine sumpta pro<lb></lb>portio, descensus autem, et contrarii motus, proportio eadem, sed permutata.<lb></lb></s></p><p type="main">
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194 <s id="id.0.0.19.01"><figure id="id.050.01.008.1.jpg" xlink:href="050/01/008/1.jpg"></figure>Dicitur proprie, ut excludantur omnes velocitates, quoquo modo <lb></lb>præter naturam acquisitæ.</s>
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198 <s id="id.0.0.19.02">Prima pars patet, quia cum velocitatis pro­<lb></lb>prie precisa causa sit pondus, patet, quo ad multiplicationem ponderis <lb></lb>sequitur velocitatis multiplicatio.</s>
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202 <s id="id.0.0.19.03">Secunda pars patet, quia eadem est <lb></lb>proportio descensus et ascensus, sed contrarie sumitur proportio hic <lb></lb>et ibi, propter quod dicitur permutata.</s>
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206 <s id="id.0.0.19.04">Sicut enim se habet in descensu <lb></lb>pondus, ita aliud pondus in ascensu, quia eiusdem proportionis est di­<lb></lb>stantia gravis in descendendo in circulo superiori, sicut ascensus ab infe<lb></lb>riori, eadem igitur est proportio, sed permutata.</s>
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210 <s id="id.0.0.19.05">Oportet enim, quanto illud exce­<lb></lb>dit, tanto id isto excedi.</s><s>Et per consequens, quanto illud quod est gravi­<lb></lb>us, velocius ascendit, tanto levius movetur contrarie.</s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/009.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.009.1.jpg" xlink:href="050/01/009/1.jpg"></figure><pb xlink:href="050/01/010.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/011.jpg"></pb></chap><chap><p type="main"><s>[commentary not transcribed]</s></p><p type="main">
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214 <s id="id.0.0.20.01.prop">PROPOSITIO SECUNDA.<lb></lb></s><s> Cum fuerit æquilibris positio æqualis, æquis pon<lb></lb>deribus appensis, ab æqualitate non discedet, etsi ab <lb></lb>æquidistantia separetur, ad æqualitatis situm revertetur.<lb></lb></s></p><p type="main">
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218 <s id="id.0.0.21.01">Primum patet, quia sunt equæ gravia.</s>
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222 <s id="id.0.0.21.02">Secundum patet per quartam suppositi­<lb></lb>onem quartam, vocatur autem illud situs, quod circulus dicitur, sicut patet per <lb></lb>prædicta.<figure id="id.050.01.011.1.jpg" xlink:href="050/01/011/1.jpg"></figure></s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/012.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.012.1.jpg" xlink:href="050/01/012/1.jpg"></figure><pb xlink:href="050/01/013.jpg"></pb></chap><chap><p type="main">
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226 <s id="id.0.0.22.00"><figure id="id.050.01.013.1.jpg" xlink:href="050/01/013/1.jpg"></figure>PROPOSITIO III.<lb></lb></s>
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230 <s id="id.0.0.22.01.prop">Cum fuerint appen­<lb></lb>sorum pondera æqua<lb></lb>lia, non motum faciet in<lb></lb>æquilibri appendicu­<lb></lb>lorum inæqualitas.</s></p><p type="main">
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234 <s id="id.0.0.23.01">Non debet hic sumi inæ­<lb></lb>qualitas appendiculorum pon­<lb></lb>dere, sed longitudine proba­<lb></lb>tur sic.</s><s>Si fiat motus in una par<lb></lb>te, ergo pars alia est minus gra­<lb></lb>vis, per suppositionem secundam, <lb></lb>sed positum est prius appenso<lb></lb>rum pondera esse æqualia; ergo.<lb></lb></s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/014.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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238 <s id="id.0.0.24.00">PROPOSITIO QUARTA.<lb></lb></s>
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242 <s id="id.0.0.24.01.prop">Quodlibet pondus in quamcumque partem discedat secundum situm sit levius.<lb></lb></s></p><p type="main">
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246 <s id="id.0.0.25.01">Manifestum est hoc per suppositionem quartam.</s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/015.jpg"></pb><figure id="id.050.01.015.1.jpg" xlink:href="050/01/015/1.jpg"></figure><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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250 <s id="id.0.0.26.00">PROPOSITIO QUINTA.</s>
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254 <s id="id.0.0.26.01.prop">Si fuerint brachia æquilibris inæqualia, æquali­<lb></lb>bus ponderibus appensis, ex parte longioris fiet motus.<lb></lb></s></p><p type="main">
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258 <s id="id.0.0.27.01">Brachia inæqualia longitudine non pondere, probatur sic.</s>
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262 <s id="id.0.0.27.02">Ex parte <lb></lb>longioris describitur circulus maior, et sic patet per suppositionem tertiam <lb></lb>quod pondus secundum situm est gravius.</s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/016.jpg"></pb><figure id="id.050.01.016.1.jpg" xlink:href="050/01/016/1.jpg"></figure><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.016.2.jpg" xlink:href="050/01/016/2.jpg"></figure><pb xlink:href="050/01/017.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.017.1.jpg" xlink:href="050/01/017/1.jpg"></figure><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/018.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/019.jpg"></pb><figure id="id.050.01.019.1.jpg" xlink:href="050/01/019/1.jpg"></figure><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.019.2.jpg" xlink:href="050/01/019/2.jpg"></figure><pb xlink:href="050/01/020.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.020.1.jpg" xlink:href="050/01/020/1.jpg"></figure></chap><chap><p type="main">
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266 <s id="id.0.0.28.00">PROPOSITIO SEXTA.<lb></lb></s>
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270 <s id="id.0.0.28.01.prop">Cum unius ponderis sint appensa, et a centro mo­<lb></lb>tus inæqualiter distent, et si remotum secundum di­<lb></lb>stantiam propinquius accesserit ad directionem, alio <lb></lb>non moto secundum situm, illo levius fiet.<lb></lb></s></p><p type="main">
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274 <s id="id.0.0.29.01">Centrum motus dicitur hic punctus in brachio libræ circa quem bra­<lb></lb>chia libræ vertuntur.</s>
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278 <s id="id.0.0.29.02">Si igitur unum pondus ponderat in brachio, plus <lb></lb>distante a centro motus illo alio dependente in alio brachio, et sint æque <lb></lb>gravia, si tunc remotius appropinquat ad distantiam, vel at directionem, <lb></lb>moto appensili ad situm æqualem, quod prius in remotiori parte fue­<lb></lb>rit æque grave, nunc est levius, quia tunc a se ipso, quam prius est levius, quia<pb xlink:href="050/01/021.jpg"></pb>obliquior est descensus.</s>
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282 <s id="id.0.0.29.03">Est enim semicirculus minor, quem tunc fuit.</s></p><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.021.1.jpg" xlink:href="050/01/021/1.jpg"></figure><pb xlink:href="050/01/022.jpg"></pb></chap><chap><p type="main">
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286 <s id="id.0.0.30.00">PROPOSITIO SEPTIMA.<lb></lb></s>
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290 <s id="id.0.0.30.01.prop">Aequis ponderibus in æquilibri appensis, si æqua<lb></lb>lia sint appensibilia, alterum autem circum <lb></lb>volubile appenditur, graviua erit secundum situm.<lb></lb></s></p><p type="main">
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294 <s id="id.0.0.31.01">Circumvolubile dicitur, quando perpendiculum potest habere decli<lb></lb>nationem plus largam, quam brachia libræ, ut sit, quando in circulo pendet <lb></lb>secundum angulum rectum fixum, dicitur, quando nullam contingit habere de­<lb></lb>clinationem perpendiculorum, nisi secundum brachium, et est in situ æqua­<lb></lb>litatis inter brachium et perpendiculum angulus rectus, probatur.</s><s>Sint <lb></lb>appensa æqualia, ut vult positio, in pondere, sed non in longitudine, tunc <lb></lb>illud quod est circumvolubile, maiorem circulum constituit in causa, <lb></lb>quia plus declinat propter circumvolutionem, et sic pondus ibi gravius <lb></lb>est secundum situm, cum eius descensus sit rectior.</s></p><p type="main">
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298 <s id="id.0.0.32.01">Illa propositio fuit inventa <lb></lb>de quodam experimento facto ad probationem partis secundæ.</s>
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302 <s id="id.0.0.32.02">Cum enim <lb></lb>aliquis voluit experiri, an ita esset; posuit in æquilibri pondera æqua<lb></lb>lia, cuius appendentia erunt filo composita, quæ motum habent a bra­<lb></lb>chiis alienum, etiam propter perpendiculorum flexus incognitis experimentum<lb></lb><figure id="id.050.01.022.1.jpg" xlink:href="050/01/022/1.jpg"></figure>fallax, quare experiens ve­<lb></lb>ritatis irrisorem, et acce­<lb></lb>pto cum casu, quod secundum <lb></lb>æquidistantiam a medio mo­<lb></lb>tus propter perpendicula, <lb></lb>ex terminis brachiorum li­<lb></lb>neæ sic describuntur utrumque <lb></lb>intelligit, quod prius nega­<lb></lb>vit, quod est, quia preter mu­<lb></lb>tationes brachiorum alii non <lb></lb>erunt flexus, et ex hoc non <lb></lb>conclusit secundum rectos <lb></lb>angulos idem congruere, cum <lb></lb>motus brachiorum simili­<lb></lb>ter contingit.</s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/023.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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306 <s id="id.0.0.33.00">PROPOSITIO OCTAVA.<lb></lb></s>
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310 <s id="id.0.0.33.01.prop">Si fuerint brachia libræ proportionalia ponderi­<lb></lb>bus appensorum, ita, ut in breviori gravius appenda<lb></lb>tur, æque gravia erunt secundum situm.<lb></lb></s></p><p type="main">
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314 <s id="id.0.0.34.01">Si pondus gravius tantum valet in termino breviori, quantum bra­<lb></lb>chium libræ longius in suo loco, et similiter pondus minus in breviori, <lb></lb>tunc dico, sic valebunt secundum situm, quando non essent sic secundum <lb></lb>naturam, necessario erunt pondera secundum situm æqualia, quia pon­<lb></lb>dus et brachium hic valet per oppositum totum reliquum, quia propter neu<lb></lb>trum pondus declinat, sicut patet propositione huius prima.</s></p><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.023.1.jpg" xlink:href="050/01/023/1.jpg"></figure><pb xlink:href="050/01/024.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/025.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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318 <s id="id.0.0.35.00">PROPOSITIO NONA.<lb></lb></s>
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322 <s id="id.0.0.35.01.prop">Si duo oblonga unius grossiciei per totum ſimilia <lb></lb>et pondere et quantitate æqualia, appendantur, ita, <lb></lb>ut alterum erigatur, et alterum orthogonaliter depen<lb></lb>deat, ita etiam, ut termini dependentis, et medii alte­<lb></lb>rius, eadem sit a centro distantia, secundum hunc situm<lb></lb>æque gravia fient.<lb></lb></s></p><p type="main">
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326 <s id="id.0.0.36.01">Unum pondus secet brachium transversum, et aliud pondus de­<lb></lb>pendeat descensu verso, et sit terminus illius inæquali distantia a centro <lb></lb>motus cum medio alterius, quia sicut illius extremum plus a centro di­<lb></lb>stat, ita istius medium.</s>
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330 <s id="id.0.0.36.02">probatur sic, Gravitas naturalis est æqualis utro<lb></lb>bique propositum ut violentum, similiter, quia semicirculi sunt æquales, <lb></lb>ergo æque gravia secundum situm sunt appensa.</s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/026.jpg"></pb><figure id="id.050.01.026.1.jpg" xlink:href="050/01/026/1.jpg"></figure><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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334 <s id="id.0.0.37.00">PROPOSITIO DECIMA.<lb></lb></s>
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338 <s id="id.0.0.37.01.prop">Si canonium fuerit symmetrum magnitudine, et sub<lb></lb>stantiæ eiusdem, dividitaturque in duas partes inæqua­<lb></lb>les, et suspendatur in termino minoris portionis pon<lb></lb>dus, quod faciat canonium paralellum epipedo ori­<lb></lb>zontis, proportio ponderis illius, ad superabundan­<lb></lb>tiam ponderis maioris portionis canonii ad minorem,<pb xlink:href="050/01/027.jpg"></pb> est sicut proportio totius canonii ad duplum longitu<lb></lb>dinis minoris portionis.</s></p><p type="main">
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342 <s id="id.0.0.38.01">Canonium est idem quod brachium libræ, quia est regula, Symmetrum <lb></lb>est proportionale id est brachium æquale brachio, zona et magnitudine eius<lb></lb>dem in quantitate et pondere, et parallelum id est æquidistans, epipedo, id est su­<lb></lb>perficiei, probatur sic.</s><s>Sit æquilibra æquilonga, et omnia æqualia, et<lb></lb>in omni parte æque grossum, sit utrumque et æque grave.</s>
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346 <s id="id.0.0.38.06">Sit ergo longi­<lb></lb>tudo uniuscuiusque sex palmorum, et tollantur post hoc quatuor palmi de <lb></lb>uno Manifestum itaque, quoniam brachium longius, est gravius triplici <lb></lb>gravitate, sicut etiam longius gravius dicitur naturaliter, quia brevius <lb></lb>tantum duos palmos, sicut sit, pro ponderositate cuiusque appendatur <lb></lb>pondus sex ad terminum brevioris partis.</s>
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350 <s id="id.0.0.38.10">Arguitur sic, Illud pondus <lb></lb>facit canonium parallelum epipedo orizontis, sicut patet, quia cum li­<lb></lb>nea recta perpendicularis erecta fuerit a superiori plano orizontis ad ca<lb></lb>nonium constituit angulos rectos, manifestum est propositione prima <lb></lb>per Euclidem, canonium sæpe parallelum empipedo, si altera pars esset <lb></lb>gravior altera, alia eam sequeretur, sicut aliud canonium motu contra­<lb></lb>rio, patet suppositione sexta, ergo æque graves sunt partes alternarum se<lb></lb>cundum situm, quod si sic est, tunc additio addatur ponderi, tunc minor erit <lb></lb>canonii inclinatio.</s>
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354 <s id="id.0.0.38.13">Sicut ista probatur geometrice, ita possunt omnes pro­ba<lb></lb>ri per missæ per proportionem illarum linearum, et angulorum suorum constructorum.<lb></lb></s></p><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.027.1.jpg" xlink:href="050/01/027/1.jpg"></figure><pb xlink:href="050/01/028.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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358 <s id="id.0.0.39.00">PROPOSITIO UNDECIMA.<lb></lb></s>
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362 <s id="id.0.0.39.01.prop">Si fuerit proportio ponderis in termino minoris<lb></lb>portionis suspensi ad superabundantiam ponderis ma­<lb></lb>ioris portionis ad minorem, sicut proportio totius lon<lb></lb>gitudinis canonii ad duplam longitudinem minoris por<lb></lb>tionis, erit canonium paralellum empipedo orizontis.</s></p><p type="main">
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366 <s id="id.0.0.40.01">Commentum prius probatum est, quod ad equidistantiam canonii a superficie o­<lb></lb>rizontis, oportet esse pondus iam dictum, ex quibus sequitur conversa sci­<lb></lb>licet, quod talis æquidistantia semper sit tali pondere, quia si non sit æquidi­<lb></lb>stantia, sequitur, quod quæ æquantur, pondere non æquantur.</s>
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370 <s id="id.0.0.40.03">Prius enim osten­<lb></lb>debatur, brachio longiori pondus in situ coæquari, vel correspondere, <lb></lb>igitur per suppositionem sextam, neque brachium pondus, neque pondus bra­<lb></lb>chium sequitur motu contrario.</s></p><p type="main"><s>[commentary not transcribed]</s></p><pb xlink:href="050/01/029.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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374 <s id="id.0.0.41.00">PROPOSITIO DUODECIMA.<lb></lb></s>
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378 <s id="id.0.0.41.01.prop">Ex iis manifestum est, quoniam si fuerit canonium sim<lb></lb>metrum magnitudine, et zona eiusdem notum longitudine <lb></lb>et pondere, et dividatur in duas partes inæquales da­<lb></lb>tas, tunc possibile est nobis invenire pondus, quod <lb></lb>cum suspensum fuerit a termino minoris portionis, fa<lb></lb>ciet canonium paralellum empipedo orizontis.</s></p><p type="main">
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382 <s id="id.0.0.42.01">Illa probatio satis patet ex prædictis.</s></p><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.029.1.jpg" xlink:href="050/01/029/1.jpg"></figure><pb xlink:href="050/01/030.jpg"></pb><p type="main"><s>[commentary not transcribed]</s></p></chap><chap><p type="main">
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386 <s id="id.0.0.43.00">PROPOSITIO TREDECIMA.<lb></lb></s>
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390 <s id="id.0.0.43.01.prop">Si fuerit canonium datum longitudine, spissitudi<lb></lb>ne, et gravitate, et dividatur in duas partes inæqua­<lb></lb>les, fueritque suspensum a termino minoris portionis <lb></lb>pondus datum, quod faciet canonium paralellum <lb></lb>empipedo orizontis, longitudo uniuscuiusque portio <lb></lb>data erit.</s></p><p type="main">
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394 <s id="id.0.0.44.01">Probatur sic, Longitudine totius canonii nota, et pondere noto, pone <lb></lb>pedem circini in centro medii motus, et constitue circulum super mino­<lb></lb>rem portionem, quæ secabit per diffinitionem circuli æqualem de bra­<lb></lb>chio longiori, parti autem reliquæ æquatur portio ablata a termino ubi<pb xlink:href="050/01/031.jpg"></pb>pendet pondus, quia ex hac exceditur brachium brachio, unde sequitur<lb></lb>quæsitum.</s></p><p type="main"><s>[commentary not transcribed]</s></p><figure id="id.050.01.031.1.jpg" xlink:href="050/01/031/1.jpg"></figure></chap><chap><p type="main">
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398 <s id="id.0.0.45.01">Excussum Norimbergæ per<gap></gap>.<gap></gap>,<lb></lb>Anno domini M. D. XXXIII.</s></p></chap></body></text>
399
400 </archimedes>