Mercurial > hg > mpdl-xml-content
annotate texts/XML/archimedes/ar/heron_mecha_096_ar_1900.xml @ 10:d7b79f6537bb
Version vom 2009-02-14
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
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| date | Thu, 02 May 2013 11:08:12 +0200 |
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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>Heron Alexandrinus</author> |
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5 <title>Mechanica</title> |
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6 <date>1900</date> |
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7 <place>Leipzig</place> |
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8 <translator>Qusta ibn Luqa</translator> |
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9 <lang>ar</lang> |
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10 <cvs_file>heron_mecha_096_ar_1900.xml</cvs_file> |
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11 <locator>096.xml</locator> |
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12 </info> |
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13 <text> |
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14 <body> |
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15 <chap n="0"> |
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16 <p n="0"> |
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17 <s id="A18-0|00|00"></s> |
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18 <s id="A18-0|00|01">كِتاب ٓايرُن في رَفع اَل۪أَشياء اَل۪ثَقيلَة</s> |
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19 <s id="A18-0|00|04"></s> |
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20 </p> |
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21 </chap> |
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22 <chap n="1"> |
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23 <p n="0"> |
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24 <s id="A18-1|00|00"></s> |
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25 <s id="A18-1|00|01"><pb n="3"></pb> بِ۪اِسم ٓاللَه اَل۪رَحمٰن اَل۪رَحيم رَبّ يَسِّر بِ۪رَحمَتِكَ</s> |
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26 <s id="A18-1|00|02">اَل۪مَقالَة اَل۪ولا مِن كِتاب ٓايرُن في رَفع اَل۪أَشياء اَل۪ثَقيلَة</s> |
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27 <s id="A18-1|00|03">أَمَرَ بِ۪إِخراجِهِ مِن اَل۪لُغَة اَل۪يونانِيَّة إِلى اَل۪لُغَة اَل۪عَرَبِيَّة ٓأَبو اَل۪عٓابّاس ٓأَحمَد اِبن اَل۪ٓمُعتَصِم وَ۪تَوَلّى تَرجَمَتَهُ ٓقُسطا اِبن ٓلوقا اَل۪ٓبَعلَبَكّي</s> |
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28 </p> |
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29 <p n="1"> |
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30 <s id="A18-1|01|00"></s> |
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31 <s id="A18-1|01|01">نُريد اَن نُحَرِّك اَل۪ثِقل اَل۪مَعلوم بِ۪اَل۪قُوَّة اَل۪مَعلومَة بِ۪تَراكيب فِلَك ذات أَسنان </s> |
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32 <s id="A18-1|01|02">فَ۪يُعمَل شَكل ثابِت شَبيه بِ۪اَل۪صُندوق وَ۪ل۪يَكُن في حيطانِهِ اَل۪طِوال اَل۪مُتَوازِيَة مَحاوِر مُتَوازِيَة وَ۪يَكون بُعدُها بِ۪اَل۪قَدر اَلَّذي تَتَراكِب اَل۪أَسنان اَلَّتي لِ۪أَحَدِها في اَل۪أَسنان اَلَّتي لِ۪ل۪آخَر كَما سَنُبَيِّن </s> |
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33 <s id="A18-1|01|03">فَ۪ل۪يَكُن هٰذا اَل۪شَكل صُندوق عَلَيهِ ٓآبٓغٓد وَ۪ل۪يَكُن فيهِ مِحوَر مَوضوع تَكون حَرَكَتُهُ سَلِسَة وَ۪هُوَ ٓeٓز وَ۪ل۪تَكُن عَلَيهِ فَلكَة مُسَنَّنَة ثابِتَة عَلَيهِ وَ۪هِيَ فَلَكَة ٓهٓت </s> |
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34 <s id="A18-1|01|04">وَ۪ل۪يَكُن مَثَلاً قُطرُها خَمسَة أَمثال قُطر مِحوَر ٓeٓز وَ۪ل۪اَن يَكون عَمَلُنا مُمَثَّلاً نُصَيِّر اَل۪ثِقل اَلَّذي نُريد اَن نَجُرَّهُ أَلف قِنطار وَ۪اَل۪قُوَّة اَل۪مُحَرِّكَة خَمسَة قَناطير <pb n="5"></pb> أَعني اَل۪رَجُل اَل۪مُحَرِّك أَو اَل۪صَبي اَلَّذي يُمكِنُهُ اَن يُحَرِّك بِ۪نَفسِهِ بِلا حيلَة خَمسَة قَناطير </s> |
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35 <s id="A18-1|01|05">فَ۪إِذا أَدخَلنا اَل۪قُلوس اَل۪مَشدودَة في اَل۪حَمل مِن ثُقب ما في حائِط ٓآب حَتّى تَلتِفّ عَلى مِحوَر ٓeٓز فَ۪إِنَّهُ بِ۪دَور فَلكَة ٓهٓت وَ۪بِ۪إِلتِفاف اَل۪قُلوس يَتَحَرَّك اَل۪حَمل </s> |
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36 <s id="A18-1|01|06">وَ۪ل۪اَن تَتَحَرَّك فَلكَة ٓهٓت يَحتاج مِن اَل۪قُوَّة إِلى مِئَتَي قِنطار لِ۪أَنَّ قُطر اَل۪فَلَكَة خَمسَة أَمثال قُطر اَل۪مِحوَر عَلى ما فَرَضناهُ وَ۪ذٰلِكَ قَد تَبَيَّنَ في بَراهين اَل۪خَمس قُوى </s> |
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37 <s id="A18-1|01|07">وَ۪لَكِنَ لَيسَ لَنا قُوَّة مِئَتَي قِنطار فَ۪إِذاً اَل۪فَلكَة لا تَتَحَرَّك </s> |
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38 <s id="A18-1|01|08">فَ۪نَعمَل مِحوَراً آخَر مُوازِياً لِ۪مِحوَر ٓeٓز وَ۪هُوَ مِحوَر ٓكٓل وَ۪ل۪تَكُن عَلَيهِ فَلكَة ثابِتَة ذات أَسنان وَ۪هِيَ فَلكَة ٓمٓن وَ۪ل۪تَكُن فَلكَة ٓهٓت أَيضاً ذات أَسنان تَتَراكِب عَلى أَسنان فَلكَة ٓمٓن وَ۪ل۪تَكُن عَلى مِحوَر ٓكٓل فَلكَة أُخرا ثابِتَة وَ۪هِيَ ٓسْٓ يَكون قُطرُها خَمسَة أَمثال قُطر ٓمٓن فَ۪يُحتاج مِن اَل۪قُوَّة في اَن نُحَرِّك اَل۪ثِقل بِ۪فَلكَة ٓسْٓ إِلى أَربَعين قِنطاراً لِ۪أَنَّ خُمس اَل۪مِئَتَي قِنطار أَربَعون قِنطاراً </s> |
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39 <s id="A18-1|01|09">وَ۪أَيضاً نُرَكِّب عَلى فَلكَة ٓسْٓ فَلكَة أُخرا وَ۪هِيَ فَلكَة ٓفٓق ثابِتَة عَلى مِحوَر آخَر وَ۪هُوَ مِحوَر ٓيٓc وَ۪ل۪تَكُن عَلى هٰذا اَل۪مِحوَر فَلكَة أُخرا ثابِتَة عَلَيهِ يَكونُ قُطرُها خَمسَة أَمثال قُطر فَلكَة ٓفٓق وَ۪هِيَ فَلكَة ٓرٓخ فَ۪تَكون اَل۪قُوَّة اَلَّتي تُحَرِّك اَل۪ثِقل عِندَ عَلامَة ٓرٓخ ثَمانِيَة قَناطير وَ۪لَكِنَ اَل۪قُوَّة اَل۪مَفروضَة لَنا إِنَّما هِيَ قُوَّة خَمسَة قَناطير </s> |
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40 <s id="A18-1|01|10">فَ۪ل۪نُرَكِّب فَلكَة أُخرا ذات أَسنان وَ۪هِيَ فَلكَة ِٓٓة وَ۪ل۪يَكُن قُطرُها مِثلَي قُطر فَلكَة <pb n="7"></pb> ٓرٓخ وَ۪تَكون ثابِتَة عَلى مِحوَر آخَر وَ۪هُوَ مِحوَر ٓهٓذ فَ۪تَكون فَلكَة ِٓٓة تَحتاج مِن اَل۪قُوَّة إِلى أَربَعَة قَناطير وَ۪اَل۪قُوَّة اَل۪مَفروضَة لَنا خَمسَة قَناطير فَ۪يَكونُ في هٰذِهِ اَل۪قُوَّة زِيادَة قِنطار يُستَظهَر بِهِ لَمّا عَسى اَن يَعرِض مِن عُسر اَل۪فِلَك</s> |
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41 <s id="A18-1|01|11">فَ۪قَد تَبَيَّنَ مِمّا وَصَفنا أَنَّ اَل۪مُحَرِّك إِذا حَرَّكَ فَلكَة ِٓٓة دارَ مِحوَر ٓخٓذ وَ۪دارَ بِ۪دَورانِهِ فَلكَة ٓرٓخ وَ۪دارَ لِ۪ذٰلِكَ مِحوَر ٓيٓc فَ۪دارَت فَلكَة ٓفٓق وَ۪دارَت فَلكَة ٓسْٓ مَعَها وَ۪دارَ لِ۪ذٰلِكَ مِحوَر ٓكٓل وَ۪دارَت فَلكَة ٓمٓن وَ۪أَدارَت فَلكَة ٓهٓت وَ۪دارَ لِ۪ذٰلِكَ مِحوَر ٓeٓز فَ۪إِلتَفَّت اَل۪قُلوس عَلى اَل۪مِحوَر وَ۪إِرتَفَعَ اَل۪ثِقل </s> |
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42 <s id="A18-1|01|12">فَ۪قَد رَفَعنا بِ۪قُوَّة خَمسَة قَناطير ثِقلاً مَبلَغُهُ أَلف قِنطار بِ۪هٰذِهِ اَل۪حيلَة اَلَّتي وَصَفناها وَ۪ذٰلِكَ ما أَرَدنا اَن نُبَيِّن</s> |
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43 <s id="A18-1|01|13">حاشِيَة يَنبَغي اَن يَخرُج مِحوَر ٓذٓخ إِلى ٓض وَ۪يُقام عَلَيهِ عَمود ٓضٓظ مُساوِياً لِ۪نِصف قُطر فَلكَة ِٓٓة أَو أَكثَر مِنهُ وَ۪ٓاللَه أَعلَم</s> |
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44 </p> |
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45 <p n="2"> |
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46 <s id="A18-1|02|00"></s> |
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47 <s id="A18-1|02|01">في اَل۪دَوائِر </s> |
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48 <s id="A18-1|02|02">إِنَّ اَل۪دَوائِر اَل۪ثابِتَة عَلى مِحوَر واحِد تَكون حَرَكَتُها أَبَداً إِلى جِهَة واحِدَة وَ۪هِيَ اَل۪جِهَة اَلَّتي يَتَحَرَّك إِلَيها اَل۪مِحوَر </s> |
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49 <s id="A18-1|02|03">وَ۪اَل۪دَوائِر اَلَّتي تَكون عَلى مِحوَرَين وَ۪يَتَراكِب بَعضُها في بَعض بِ۪دَندانجات تَكون حَرَكَتُها إِلى جِهَتَين مُختَلِفَتَين فَ۪تَكون إِحداهُما إِلى ناحِيَة اَل۪يَمين وَ۪اَل۪أُخرا إِلىناحِيَة اَل۪شِمال</s> |
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50 <s id="A18-1|02|04">وَ۪إِذا كانَت اَل۪دائِرَتان مُتَساوِيَتَين إِستَوفَت دَورَة إِحداهِما إِلى اَل۪يَمين دَورَة اَل۪أُخرا إِلى اَل۪يَسار وَ۪إِذا كانَتا غَير مُتَساوِيَتَين فَ۪كانَت إِحداهِما <pb n="9"></pb> أَعظَم مِن اَل۪أُخرا دارَت اَل۪صُغرى مَرّات إِلى اَن تَدور اَل۪كُبرى مَرَّة عَلى حَسَب ما فيهِما مِن اَل۪عُظم </s> |
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51 </p> |
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52 <p n="3"> |
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53 <s id="A18-1|03|00"></s> |
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54 <s id="A18-1|03|01">وَ۪إِذ قَد بانَ ذٰلِكَ في هٰذِهِ اَل۪مُقَدِّمَة فَ۪ل۪نُدِر دائِرَتَين مُتَساوِيَتَين ولاهُما ٓهٓeٓكٓد وَ۪اَل۪ثانِيَة ٓزٓغٓتٓe عَلى مَركَزَي ٓآب وَ۪تَتَماسّان عَلى نُقطَة ٓe </s> |
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55 <s id="A18-1|03|02">وَ۪إِذا تَحَرَّكَتا مِن نُقطَة ٓe في زَمان واحِد مِقدار اَل۪نِصف مِنهُما فَ۪في ذٰلِكَ اَل۪زَمان عَلامَة ٓe تَجوز قَوس ٓeٓهٓد وَ۪تَصير إِلى عَلامَة ٓد مُتَحَرِّكَة مِثلَ حَرَكَة عَلامَة ٓغ عَلى قَوس ٓهٓتٓe </s> |
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56 <s id="A18-1|03|03">فَ۪إِذاً قَد يُمكِن اَن تَتَحَرَّك عَلامات ما في جِهَة واحِدَة وَ۪يُمكِن اَن تَتَحَرَّك بِ۪اَل۪تَضادّ </s> |
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57 <s id="A18-1|03|04">أَمّا ما يَكون مِنها في جِهَة واحِدَة فَ۪يَتَحَرَّك بِ۪اَل۪تَضادّ وَ۪أَمّا ما يَكون مِنها نَظائِر فَ۪في جِهَة واحِدَة </s> |
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58 <s id="A18-1|03|05">وَ۪قَد يُمكِن اَن يَكون ما يُقال لَهُ إِنَّهُ يَتَحَرَّك بِ۪اَل۪تَضادّ يَتَحَرَّك في جِهَة واحِدَة لِ۪أَنَّ اَل۪عَلامات اِن تَحَرَّكَت وَ كانَت حَرَكَتُها مِن عَلامَة واحِدَة وَ۪هِيَ عَلامَة ٓه وَ۪تَوَهَّمنا خَطَّي ٓزٓآت ٓهٓبٓك قائِمَين عَلى خَطّ ٓغٓد تَكون اَل۪حَرَكَة اَلَّتي عَلى قَوس ٓeٓز ضِدّ اَل۪حَرَكَة اَلَّتي عَلى قَوس ٓeٓه لِ۪أَنَّ إِحداهِما تَتَحَرَّك إِلى اَل۪جِهَة اَل۪يُمنى وَ۪اَل۪أُخرا إِلى اَل۪يُسرى</s> |
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59 <s id="A18-1|03|06">وَ۪قَد يُمكِن اَن تَكون اَل۪حَرَكَة في جِهَة واحِدَة إِذا تَوَهَّمنا بُعد اَل۪عَلامات <pb n="11"></pb> مُتَساوِياً عَن ٓزٓه وَ۪أَيضاً إِذا كانَت اَل۪حَرَكَة عَلى قَوسَي ٓزٓغ ٓهٓد إِلى ٓغٓد كانَت مُتَساوِيَة وَ۪هٰذا مِمّا يَنبَغي اَن نَتَوَهَّمَهُ عَلى قَوسَي ٓغٓت ٓدٓك وَ۪عَلى قَوسَي ٓتٓe ٓكٓe </s> |
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60 <s id="A18-1|03|07">وَ۪أَيضاً نَقول إِنَّهُ يُمكِن اَن تَتَحَرَّك في جِهَة واحِدَة فَ۪نَقول إِنَّ عَلامَتَي ٓدٓe تَتَحَرَّك في جِهَة واحِدَة إِذا كانَت عَلامَة ٓe تَتَحَرَّك عَلى قَوس ٓeٓزٓغ وَ۪عَلامَة ٓد عَلى قَوس ٓدٓكٓe وَ۪كانَ بُعدُهُما مِن عَلامَتَي ٓزٓك مُتَساوِياً وَ۪قُربُهُما مِنهُما مُتَساوِياً فَ۪هٰذِهِ اَل۪حَرَكَة تُسَمّي اَل۪مُتَضادَّة </s> |
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61 <s id="A18-1|03|08">فَ۪ل۪ذٰلِكَ صارَ اَل۪مُتَضادّ وَ۪اَل۪مُماثِل مِن اَل۪مُضاف فَ۪يَنبَغي اَن تُمَيَّز في كُلّ حَرَكَة اَل۪حَرَكَة اَلَّتي تُماثِل وَ۪اَلَّتي تُضادّ </s> |
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62 <s id="A18-1|03|09">وَ۪قَولُنا هٰذا يَنبَغي اَن نَتَوَهَّم في اَل۪دَوائِر اَل۪مُتَساوِيَة فَ۪أَمّا في اَل۪دَوائِر اَل۪مُختَلِفَة فَ۪فيما بَعدَ هٰذا نُبَيِّنُهُ</s> |
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63 </p> |
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64 <p n="4"> |
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65 <s id="A18-1|04|00"></s> |
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66 <s id="A18-1|04|01">وَ۪ل۪تَكُن اَل۪دَوائِر غَير مُتَساوِيَة وَ۪ل۪تَكُن مَراكِزُها عَلى عَلامَتَي ٓآب وَ۪ل۪يَكُن أَعظَم اَل۪دائِرَتَين اَل۪دائِرَة اَلَّتي مَركَزُها عَلى عَلامَة ٓأَة فَ۪في هٰذِهِ اَل۪دَوائِر لا يَتِمّ اَل۪تَرتيب اَلَّذي في اَل۪دَوائِر اَل۪مُتَساوِيَة </s> |
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67 <s id="A18-1|04|02">فَ۪ل۪نَفرِض عَلامَتَين نُدِرهِما مِن عَلامَة ٓe وَ۪ل۪اَن نُمَثِّل ذٰلِكَ نُصَيِّر قُطر ٓغٓe ضِعف قُطر ٓeٓد فَ۪إِذاً يَكون قَوس ٓeٓزٓغ ضِعف قَوس ٓeٓهٓد فَ۪إِنَّ ذٰلِكَ قَد بَرهَنَهُ ٓأَرشِميدِس </s> |
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68 <s id="A18-1|04|03">فَ۪إِذاً في اَل۪زَمان اَلَّذي تَجوز فيهِ عَلامَة ٓe قَوس ٓeٓز مُتَحَرِّكَة <pb n="13"></pb> في جِهَة ٓغ في ذٰلِكَ اَل۪زَمان تَجوزُ عَلامَة ٓe قَوس ٓeٓهٓد وَ۪هِيَ مُتَحَرِّكَة حَرَكَة مُتَضادَّة </s> |
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69 <s id="A18-1|04|04">وَ۪أَيضاً في اَل۪زَمان اَلَّذي تَبتَدِئ فيهِ عَلامَة ٓe مِن ٓز فَ۪تَجوز قَوس ٓزٓغ في ذٰلِكَ اَل۪زَمان تَبتَدِئ عَلامَة ٓe مِن ٓد فَ۪تَجوز قَوس ٓدٓكٓe وَ۪تَصير إِلى عَلامَة ٓe</s> |
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70 <s id="A18-1|04|05">فَ۪تَكون اَل۪عَلامَة اَلَّتي تَجوز عَلى قَوس ٓeٓهٓدٓكٓe مَرَّة تُضادّ حَرَكَة اَل۪عَلامَة اَلَّتي تَجوز عَلى قَوس ٓeٓزٓغ وَ۪مَرَّة تَكون مُماثِلَة لَها</s> |
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71 <s id="A18-1|04|06">وَ۪أَيضاً في اَل۪زَمان اَلَّذي تَجوز فيهِ عَلامَة ٓغ قَوس ٓغٓتٓe فيهِ تَجوز عَلامَة ٓe قَوس ٓeٓهٓدٓكٓe مَرَّة في جِهَة ٓغ وَ۪مَرَّة مُضادَّة لَها </s> |
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72 <s id="A18-1|04|07">فَ۪اِن كانَت اَل۪قَوس ثَلاثَة أَمثال اَل۪قَوس أَو في نِسبَة أُخرا أَيّ نِسبَة كانَت فَ۪إِنَّنا نُبَيِّن أَنَّ اَل۪عَلامات اَل۪مُتَحَرِّكَة مَرَّة تَتَحَرَّك في جِهَة واحِدَة وَ۪مَرَّة تَتَحَرَّك في جِهات مُتَضادَّة وَ۪ٓاللَه اَل۪مُوَفِّق</s> |
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73 </p> |
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74 <p n="5"> |
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75 <s id="A18-1|05|00"></s> |
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76 <s id="A18-1|05|01">فَ۪اِن تَوَهَّمنا دائِرَة مَوضوعَة تُماسّ اَل۪دائِرَة اَلَّتي مَركَزُها عَلامَة ٓب عَلى عَلامَة ٓك فَ۪إِنّا نُبَيِّن ما ذَكَرنا في اَل۪دائِرَة اَل۪ولا في اَل۪دائِرَة اَل۪ثالِثَة لِ۪أَنَّهُ إِذا كانَت اَل۪دائِرَة اَل۪ولا تَتَحَرَّك حَرَكَة تُضادّ اَل۪دائِرَة اَل۪ثانِيَة وَ۪كانَت اَل۪دائِرَة اَل۪ثانِيَة تَتَحَرَّك حَرَكَة تُضادّ اَل۪دائِرَة اَل۪ثالِثَة فَ۪إِنَّ حَرَكَة اَل۪دائِرَة اَل۪ولا تَكون مُماثِلَة لِ۪حَرَكَة اَل۪دائِرَة اَل۪ثالِثَة</s> |
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77 <s id="A18-1|05|02">فَ۪اِن تَحَرَّكَ شَيء ما حَرَكَة مُماثِلَة لِ۪حَرَكَة شَيء آخَر وَ۪كانَت تِلكَ تَتَحَرَّك حَرَكَة مُتَضادَّة لِ۪حَرَكَة أَشياء اُخَر فَ۪إِنَّ اَل۪ولا تَتَحَرَّك حَرَكَة مُضادَّة لِ۪حَرَكَة اَل۪أَشياء اَل۪ثالِثَة </s> |
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78 <s id="A18-1|05|03">فَ۪اِن كانَت أَيضاً دائِرَة رابِعَة بَيَّنّا ذٰلِكَ <pb n="15"></pb> أَيضاً عَلى هٰذا وَ۪بِ۪اَل۪جُملَة إِنَّ اَلَّذي يَعرِض في اَل۪ثَلاث اَل۪دَوائِر هُوَ يَعرِض في كُلّ اَل۪دَوائِر اَلَّتي جُملَتُها أَفراد وَ۪اَلَّذي يَعرِض في اَل۪دائِرَتَين هُوَ يَعرِض في كُلّ اَل۪دَوائِر اَلَّتي جُملَتُها أَزواج </s> |
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79 <s id="A18-1|05|04">وَ۪قَد تَرى اَل۪حَرَكَة تَكون مَرَّة مُماثِلَة وَ۪مَرَّة مُضادَّة لَيسَ في دائِرَتَين وَ۪أَكثَر مِنهُما فَقَط لَكِنَ في اَل۪دائِرَة اَل۪واحِدَة قَد تَرى اَل۪عَلامَة اَل۪واحِدَة مَرَّة تَتَحَرَّك في جِهَة ما وَ۪مَرَّة تَتَحَرَّك في ضِدّ تِلكَ اَل۪جِهَة</s> |
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80 <s id="A18-1|05|05">فَ۪إِنَّ تِلكَ اَل۪عَلامَة اَل۪مُتَحَرِّكَة إِذا إِبتَدَأَت بِ۪اَل۪حَرَكَة مِن عَلامَة ما لا تَزال تَتَحَرَّك في جِهَة واحِدَة إِلى اَن تَجوز نِصف دائِرَة فَ۪أَمّا إِذا جازَت قَوس نِصف اَل۪دائِرَة اَل۪ثاني فَ۪إِنَّها تَتَحَرَّك حَرَكَة مُضادَّة لِ۪تِلكَ اَل۪حَرَكَة</s> |
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81 </p> |
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82 <p n="6"> |
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83 <s id="A18-1|06|00"></s> |
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84 <s id="A18-1|06|01">وَ۪أَيضاً لَيسَ تَكون اَل۪دَوائِر اَل۪عِظام أَبَداً أَسرَع حَرَكَة مِن اَل۪دَوائِر اَل۪صِغار لَكِنَ قَد تَكون أَيضاً اَل۪دَوائِر اَل۪صِغار أَسرَع مِن اَل۪كِبار لِ۪أَنَّهُ إِذا كانَت اَل۪دَوائِر عَلى مَركَز واحِد ثابِتَة عَلَيهِ فَ۪إِنَّ اَل۪دَوائِر اَل۪كِبار تَتَحَرَّك أَسرَع مِن اَل۪صِغار </s> |
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85 <s id="A18-1|06|02">فَ۪اِن كانَت اَل۪دَوائِر مُتَباعِدَ وَ۪كانَت في جِسم واحِد أَعني عَلى غَير مِحوَر واحِد كَما قَد يَكون في اَل۪عَجَل اَل۪كَثيرَة اَل۪فِلَك فَ۪إِنَّ اَل۪دَوائِر اَل۪صِغار تَتَحَرَّك أَسرَع مِن اَل۪دَوائِر اَل۪كِبار لِ۪أَنَّ حَرَكَتَها واحِدَة وَ۪في اَل۪زَمان اَل۪واحِد كُلّ واحِدَة مِنها تَتَحَرَّك فَ۪تَحتاج اَل۪دائِرَة اَل۪صُغرى اَن تَدور دَورات كَثيرَة إِلى اَن تَدور اَل۪كَبيرَة دَورَة واحِدَة فَ۪ل۪دالِكَ صارَت اَل۪صُغرى أَسرَع حَرَكَة </s> |
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86 </p> |
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87 <p n="7"> |
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88 <s id="A18-1|07|00"></s> |
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89 <s id="A18-1|07|01"><pb n="17"></pb> وَ۪قَد يُمكِن اَن تَكون حَرَكَة اَل۪دائِرَة اَل۪صُغرى وَ۪اَل۪كُبرى مُتَساوِيَة اَل۪سُرعَة وَ۪اِن كانَت اَل۪دَوائِر ثابِتَة مُتَحَرِّكَة عَلى مَركَز واحِد </s> |
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90 <s id="A18-1|07|02">فَ۪ل۪نَتَوَهَّم دائِرَتَين ثابِتَتَين عَلى مَركَز واحِد وَ۪هُوَ مَركَز ٓأَة وَ۪ل۪يَكُن خَطّ ما يُماسّ اَل۪دائِرَة اَل۪كُبرى وَ۪هُوَ خَطّ ٓبٓب </s> |
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91 <s id="A18-1|07|03">وَ۪ل۪نَصِل عَلامَتَي ٓآب فَ۪يَكون خَطّ ٓآب قائِماً عَلى خَطّ ٓبٓب وَ۪خَطّ ٓبٓب يُوازي خَطّ ٓغٓغ فَ۪إِذاً خَطّ ٓغٓغ يُماسّ اَل۪دائِرَة اَل۪صُغرى </s> |
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92 <s id="A18-1|07|04">وَ۪أَيضاً فَ۪ل۪نُخرِج عَلى عَلامَة ٓأَة خَطّاً يُوازي هٰذِهِ اَل۪خُطوط وَ۪هُوَ خَطّ ٓآا فَ۪اِن تَوَهَّمنا اَل۪دائِرَة اَل۪عُظمى مُتَدَحرِجَة عَلى خَطّ ٓبٓب فَ۪إِنَّ اَل۪دائِرَة اَل۪صُغرى تَتَدَحرِج جائِزَة عَلى خَطّ ٓغٓغ </s> |
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93 <s id="A18-1|07|05">فَ۪اِن كانَت اَل۪دائِرَة اَل۪عُظمى قَد دارَت دَورَة واحِدَة يَظهَر لَنا أَنَّ اَل۪دائِرَة اَل۪صُغرى قَد دارَت دَورَة واحِدَة فَ۪يَكون وَضع اَل۪دَوائِر وَضع اَل۪دَوائِر اَلَّتي مَركَزُها عَلى ٓأَة وَ۪يَكون وَضع خَطّ ٓآب اَل۪وَضع اَلَّذي لِ۪خَطّ ٓآب وَ۪ل۪ذٰلِكَ يَكون خَطّ ٓبٓب مُساوِياً لِ۪خَطّ ٓغٓغ </s> |
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94 <s id="A18-1|07|06">وَ۪خَطّ ٓبٓب هُوَ اَل۪خَطّ اَلَّذي تَتَدَحرِج عَلَيهِ اَل۪دائِرَة اَل۪عُظمى إِذا دارَت دَورَة واحِدَة وَ۪خَطّ ٓغٓغ هُوَ اَل۪خَطّ اَلَّذي تَلتِفّ عَلَيهِ اَل۪دائِرَة اَل۪صُغرى إِذا دارَت دَورَة واحِدَة فَ۪إِذاً اَل۪دائِرَة اَل۪صُغرى حَرَكَتُها مُساوِيَة اَل۪سُرعَة لِ۪حَرَكَة اَل۪دائِرَة اَل۪عُظمى لِ۪أَنَّ خَطّ ٓبٓب يُساوي خَطّ ٓغٓغ </s> |
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95 <s id="A18-1|07|07">وَ۪اَل۪أَشياء اَلَّتي تَجوز في اَل۪أَزمان اَل۪مُتَساوِيَة أَبعاداً مُتَساوِيَة فَ۪إِنَّ حَرَكَتَها مُتَساوِيَة اَل۪سُرعَة </s> |
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96 <s id="A18-1|07|08">وَ۪لَعَلَّ هٰذا اَل۪قَول يُظَنّ <pb n="19"></pb> بِهِ أَنَّهُ مُحال لِ۪أَنَّهُ لا يُمكِن اَن تَكون قَوس اَل۪دائِرَة اَل۪عُظمى مُساوِيَة لِ۪قَوس اَل۪دائِرَة اَل۪صُغرى </s> |
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97 <s id="A18-1|07|09">فَ۪نَقول إِنَّ قَوس اَل۪دائِرَة اَل۪صُغرى لَم تَتَدَحرِج عَلى خَطّ ٓغٓغ فَقَط لَكِنَ اَل۪دائِرَة اَل۪صُغرى تَجوز مَجاز اَل۪دائِرَة اَل۪كُبرى مَعاً فَ۪يَعرِض اَن تَتَحَرَّك اَل۪دائِرَة اَل۪صُغرى حَرَكَة مُتَساوِيَة اَل۪سُرعَة لِ۪حَرَكَة اَل۪دائِرَة اَل۪كُبرى بِ۪حَرَكَتَين لِ۪أَنّا إِذا تَوَهَّمنا اَل۪دائِرَة اَل۪كُبرى مُتَدَحرِجَة وَ۪اَل۪دائِرَة اَل۪صُغرى غَير مُتَدَحرِجَة بَل ثابِتَة عَلى عَلامَة ٓغ وَحدَها فَ۪إِنَّها في مِثلَ ذٰلِكَ اَل۪زَمان تَجوز خَطّ ٓغٓغ فَ۪إِذاً مَركَز ٓأَة في ذٰلِكَ اَل۪زَمان يَجوز خَطّ ٓآا </s> |
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98 <s id="A18-1|07|10">وَ۪هُوَ مُساوٍ لِ۪خَطَّي ٓبٓب ٓغٓغ فَ۪إِذاً لَيسَ يَنفَع في اَل۪حَرَكَة تَدَحرُج إِلتِفاف اَل۪دائِرَة اَل۪صُغرى كَثير شَيء وَ۪عَلَيهِ طول مَسافَة اَل۪دائِرَة اَل۪كُبرى اَلَّتي تُحَرِّك اَل۪دائِرَة اَل۪صُغرى فَ۪إِنّا قَد نَرى اَل۪مَركَز وَ۪هُوَ لا يَتَدَحرِج بَتَّة يَسلُك ذٰلِكَ اَل۪بُعد بِ۪اَل۪حَرَكَة اَلَّتي تُحَرَّك بِها اَل۪دائِرَة اَل۪عُظمى </s> |
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99 </p> |
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100 <p n="8"> |
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101 <s id="A18-1|08|00"></s> |
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102 <s id="A18-1|08|01">فَ۪أَمّا اِن تَكون اَل۪عَلامَة اَل۪واحِدَة إِذا تَحَرَّكَت بِ۪حَرَكَتَين مُتَساوِيَتَي اَل۪سُرعَة يُمكِنُها اَن تَجوز خُطوطاً غَير مُتَساوِيَة فَ۪إِنّا اَل۪آن نُبَيِّن ذٰلِكَ </s> |
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103 <s id="A18-1|08|02">فَ۪ل۪يُفرَض سَطح مُرَبَّع مُتَوازي اَل۪أَضلاع قائِم اَل۪زَوايا وَ۪هُوَ سَطح ٓآبٓغٓد وَ۪ل۪يَكُن قُطرُهُ خَطّ ٓآد وَ۪ل۪تَكُن عَلامَة ٓأَة جائِزَة مَجازاً مُعتَدِلاً عَلى خَطّ ٓآب وَ۪ل۪يَكُن خَطّ ٓآب مُتَحَرِّكاً عَلى خَطَّي ٓآغ ٓبٓد حَرَكَة مُعتَدِلَة لِ۪يَكُن أَبَداً مُوازِياً لِ۪خَطّ ٓغٓد وَ۪ل۪يَكُن اَل۪زَمان اَلَّذي يَجوز <pb n="21"></pb> فيهِ نُقطَة ٓأَة إِلى ٓب مُساوِياً لِ۪ل۪زَمان اَلَّذي يَجوز فيهِ خَطّ ٓآب إِلى ٓغٓد فَ۪أَقول إِنَّ عَلامَة ٓأَة في اَل۪زَمان اَل۪واحِد تَتَحَرَّك عَلى خَطَّين غَير مُتَساوِيَين </s> |
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104 <s id="A18-1|08|03">بُرهان ذٰلِكَ أَنَّهُ إِذا تَحَرَّكَ خَطّ ٓآب في زَمان ما فَ۪صارَ مَوضِعُهُ عَلى خَطّ ٓeٓز فَ۪إِنَّ عَلامَة ٓأَة اَل۪مُتَحَرِّكَة عَلى خَطّ ٓآب تَكون في ذٰلِكَ اَل۪زَمان عَلى خَطّ ٓeٓز فَ۪تَكون نِسبَة واحِدَة </s> |
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105 <s id="A18-1|08|04">نِسبَة خَطّ ٓآغ إِلى خَطّ ٓآب أَعني إِلى خَطّ ٓغٓد كَ۪نِسبَة خَطّ ٓآe إِلى اَل۪خَطّ اَلَّذي مِن عَلامَة ٓe إِلى اَل۪عَلامَة اَل۪مُتَحَرِّكَة عَلَيهِ </s> |
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106 <s id="A18-1|08|05">وَ۪ل۪خَطّ ٓآغ إِلى خَطّ ٓغٓد نِسبَة هِيَ نِسبَة ٓآe إِلى ٓeٓه فَ۪إِذاً اَل۪عَلامَة اَل۪مُتَحَرِّكَة عَلى خَطّ ٓآب تَصير عِندَ ٓه عَلى خَطّ ٓآد اَلَّذي هُوَ اَل۪قُطر </s> |
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107 <s id="A18-1|08|06">وَ۪بِ۪مِثلَ ذٰلِكَ بِ۪تَبَيٌّ أَنَّ اَل۪عَلامَة اَلَّتي تَجوز عَلى خَطّ ٓآب هِيَ أَبَداً جائِزَة عَلىخَطّ ٓآد وَ۪في ذٰلِكَ اَل۪زَمان تَتَحَرَّك عَلى كُلّ واحِد مِن خَطَّي ٓآد ٓآب وَ۪خَطّا ٓآد ٓآب مُختَلِفان فَ۪إِذاً اَل۪عَلامَة اَل۪مُتَحَرِّكَة حَرَكَة مُعتَدِلَة في اَل۪زَمان اَل۪واحِد تَجوز عَلى خَطَّين غَير مُتَساوِيَين </s> |
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108 <s id="A18-1|08|07">وَ۪لَكِنَ كَما قُلنا حَرَكَة اَل۪عَلامَة عَلى خَطّ ٓآب مَبسوطَة وَ۪حَرَكَتُها اَلَّتي عَلى قُطر ٓآد مُؤَلَّفَة مِن حَرَكَة ٓآب عَلى خَطَّي ٓآغ ٓبٓد وَ۪مِن حَرَكَة ٓأَة عَلى خَطّ ٓآب فَ۪إِذاً عَلامَة ٓأَة في اَل۪زَمان اَل۪واحِد بِ۪اَل۪حَرَكَة اَل۪مُعتَدِلَة تَجوز عَلى خَطَّين غَير مُتَساوِيَين وَ۪ذٰلِكَ ما أَرَدنا اَن نُبَيِّنۦ</s> |
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109 </p> |
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110 <p n="9"> |
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111 <s id="A18-1|09|00"></s> |
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112 <s id="A18-1|09|01"><pb n="23"></pb> فَ۪أَمّا كَيفَ نَزيد عَلى اَل۪أَشكال اَل۪بَسيطَة وَ۪اَل۪مُجَسَّمَة وَ۪كَيفَ نُنَقِّص مِنها عَلى اَل۪نِسبَة اَل۪مَعلومَة فَ۪إِنّا اَل۪آن نُخَبِّر بِ۪ذٰلِكَ لِ۪يُمكِنُنا اَن نَزيد في اَل۪ذِراع مَثَلاً في اَل۪أَشكال اَل۪مُجَسَّمَة وَ۪اَل۪بَسيطَة عَلى نِسبَة واحِدَة </s> |
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113 <s id="A18-1|09|02">وَ۪أَوَّل ذٰلِكَ في اَل۪أَشكال اَل۪بَسيطَة فَ۪ل۪نَفرِض خَطّاً ما مَعلوم اَل۪نَوع </s> |
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114 <s id="A18-1|09|03">فَ۪نُريد اَن نَجِد خَطّاً آخَر يَكون اَل۪شَكلَين اَل۪مَرسومَين عَلى اَل۪خَطَّين اَل۪مُتَشابِهَين لِ۪أَحَدِهِما إِلى اَل۪آخَر نِسبَة مِثلَ اَل۪نِسبَة اَل۪مَعلومَة </s> |
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115 <s id="A18-1|09|04">فَ۪ل۪يَكُن لِ۪ل۪خَطّ اَل۪مَعلوم إِلى خَطّ آخَر نِسبَة مَعلومَة وَ۪ل۪نَفرِض بَينَ اَل۪خَطَّين اَل۪مَعلومَين نِسبَة خَطّ آخَر وَ۪هُوَ اَل۪خَطّ اَل۪مَطلوب لِ۪أَنَّهُ إِذا كانَت ثَلاثَة خُطوط مُتَناسِبَة تَكون مِثلَ نِسبَة اَل۪أَوَّل إِلى اَل۪ثالِث كَ۪ذٰلِكَ نِسبَة صورَة اَل۪أَوَّل إِلى صورَة اَل۪ثاني اَل۪مُتَشابِهَة اَل۪مَخطوطَة بِ۪اَل۪تَشابُه</s> |
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116 </p> |
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117 <p n="10"> |
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118 <s id="A18-1|10|00"></s> |
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119 <s id="A18-1|10|01">وَ۪لَكِنَ هُنا نُريد اَن نَجِد خَطّاً آخَر تَكون اَل۪أَشكال اَل۪مُجَسَّمَة اَلَّتي مِن خَطَّين اَل۪مُتَشابِهَة اَل۪مَرسومَة بِ۪اَل۪تَشابُه لِ۪بَعضِها إِلى بَعض نِسبَة مَعلومَة</s> |
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120 <s id="A18-1|10|02">فَ۪ل۪يَكُن خَطّ ما لَهُ إِلى خَطّ آخَر نِسبَة ما مَعلومَة </s> |
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121 <s id="A18-1|10|03">وَ۪نَفرِض بَينَ هٰذَين اَل۪خَطَّين خَطَّين آخَرَين في اَل۪نِسبَة اَل۪مُتَّصِلَة فَ۪إِذا فَعَلنا ذٰلِكَ فَحَصنا عَن مَطلوبِنا لِ۪أَنَّهُ إِذا كانَت أَربَعَة خُطوط في نِسبَة مُتَّصِلَة تَكون مِثلَ نِسبَة اَل۪أَوَّل إِلى اَل۪رابِع كَ۪ذٰلِكَ نِسبَة اَل۪صورَة اَل۪مُجَسَّمَة اَلَّتي مِن اَل۪خَطّ اَل۪أَوَّل إِلى اَل۪شَكل اَل۪مُجَسَّم اَلَّذي مِن اَل۪خَطّ اَل۪ثاني اَل۪مُتَشابِه اَل۪مَخطوط عَلى اَل۪مُشابَهَة</s> |
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122 </p> |
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123 <p n="11"> |
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124 <s id="A18-1|11|00"></s> |
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125 <s id="A18-1|11|01"><pb n="25"></pb> فَ۪أَمّا كَيفَ نَستَخرِج خَطَّين مُتَناسِبَين بَينَ خَطَّين مَفروضَين فَ۪إِنّا نُبَيِّن ذٰلِكَ بِ۪آلَة لِ۪أَنّا لا نَحتاج في ذٰلِكَ إِلى اَل۪مُجَسَّمَة وَ۪ل۪نَضَع في ذٰلِكَ ما كانَ في اَل۪عَمَل أَكثَر سُهولَة </s> |
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126 <s id="A18-1|11|02">فَ۪ل۪يَكُن اَل۪خَطّان اَل۪مَفروضان خَطَّي ٓآب ٓبٓغ وَ۪ل۪يَكُن أَحَدُهُما قائِماً عَلى اَل۪آخَر وَ۪هُما اَل۪خَطّان اَلَّذان نُريد اَن نَجِد خَطَّين مُتَوَسِّطَين بَينَهُما </s> |
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127 <s id="A18-1|11|03">فَ۪نَتِمّ مُرَبَّع ٓآبٓغٓد وَ۪نُخرِج خَطَّي ٓدٓغ ٓدٓا وَ۪نَصِل ٓبٓد ٓغٓا وَ۪نُرَكِّب عَلى عَلامَة ٓب قانوناً يَقطَع خَطَّي ٓدٓe ٓآز وَ۪نُديرُهُ حَتّى يَكون اَل۪خَطّ اَل۪خارِج مِن عَلامَة ٓه إِلى تَقاطُع ٓغٓe مُساوِياً لِ۪ل۪خَطّ اَل۪خارِج مِن عَلامَة ٓه إِلى تَقاطُع ٓآز </s> |
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128 <s id="A18-1|11|04">وَ۪ل۪يَكُن وَضع اَل۪قانون عَلى ٓeٓبٓز وَ۪خَطّا ٓeٓه ٓهٓز مُتَساوِيان فَ۪أَقول إِنَّ خَطَّي ٓآز ٓغٓe مُتَوَسِّطَين مُتَناسِبَين بَينَ خَطَّي ٓآب ٓبٓغ وَ۪أَوَّلُها ٓآب وَ۪اَل۪ثاني ٓزٓا وَ۪اَل۪ثالِث ٓغٓe وَ۪اَل۪رابِع ٓغٓب </s> |
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129 <s id="A18-1|11|05">بُرهان ذٰلِكَ مِن أَجل أَنَّ مُرَبَّع ٓآبٓغٓد مُتَوازي اَل۪أَضلاع قائِم اَل۪زَوايا فَ۪إِنَّ اَل۪أَربَعَة خُطوط اَلَّتي هِيَ ٓدٓه ٓهٓا ٓهٓب ٓهٓغ مُتَساوِيَة وَ۪مِن أَجل أَنَّ خَطّ ٓهٓد مُساوٍ لِ۪خَطّ ٓهٓا وَ۪قَد أُخرِج خَطّ ٓهٓز </s> |
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130 <s id="A18-1|11|06">فَ۪إِنَّ مَضروب ٓدٓز في ٓزٓا مَعَ مَضروب ٓآه في نَفسِهِ مُساوٍ لِ۪مَضروب ٓهٓز في نَفسِهِ وَ۪كَ۪ذٰلِكَ أَيضاً مَضروب ٓدٓe في ٓeٓغ مَعَ مَضروب ٓغٓه في نَفسِهِ مُساوٍ لِ۪مَضروب ٓهٓe في نَفسِهِ </s> |
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131 <s id="A18-1|11|07">وَ۪خَطّا ٓeٓه ٓهٓز مُتَساوِيان فَ۪إِذاً مَضروب ٓدٓز في ٓزٓا مَعَ <pb n="27"></pb> مَضروب ٓآه في نَفسِهِ مُساوٍ لِ۪مَضروب ٓدٓe في ٓeٓغ مَعَ مَضروب ٓهٓغ في نَفسِهِ </s> |
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132 <s id="A18-1|11|08">وَ۪مَضروب ٓهٓغ في نَفسِهِ مُساوٍ لِ۪مَضروب ٓآه في نَفسِهِ فَ۪إِذاً مَضروب <pb n="maSrwb"></pb> ٓدٓe في ٓeٓغ اَل۪باقي مُساوٍ لِ۪مَضروب ٓدٓز في ٓآز اَل۪باقي </s> |
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133 <s id="A18-1|11|09">فَ۪إِذاً خَطّ ٓeٓد عِندَ ٓدٓز كَ۪خَطّ ٓزٓا عِندَ ٓغٓe وَ۪خَطّ ٓeٓد عِندَ ٓدٓز كَ۪خَطّ ٓبٓا عِندَ ٓآز وَ۪كَ۪خَطّ ٓeٓغ عِندَ ٓغٓب فَ۪إِذاً خَطّ ٓزٓا عِندَ ٓغٓe وَ۪خَطّ ٓغٓe عِندَ ٓبٓغ كَ۪خَطّ ٓبٓا عِندَ ٓآز </s> |
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134 <s id="A18-1|11|10">فَ۪قَد أَلقَينا بَينَ خَطَّي ٓآب ٓبٓغ خَطَّين مُتَوَسِّطَين مُتَناسِبَين هُما خَطّا ٓآز ٓغٓe وَ۪ذٰلِكَ ما أَرَدنا اَن نُبَيِّن</s> |
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135 </p> |
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136 <p n="12"> |
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137 <s id="A18-1|12|00"></s> |
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138 <s id="A18-1|12|01">فَ۪أَمّا كَيفَ يَنبَغي اَن نَزيد وَ۪نُنَقِّص في اَل۪أَشكال اَل۪مُرَتَّبَة سُطوحِيَّة كانَت أَو مُجَسَّمَة عَلى اَل۪نِسبَة اَل۪مَعلومَة فَ۪قَد أَخبَرنا بِ۪ذٰلِكَ </s> |
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139 <s id="A18-1|12|02">وَ۪قَد يَجِب بِ۪إِضطِرار اَن نَحتال في غَير اَل۪مُرَتَّبَة اَل۪بَسيطَة وَ۪اَل۪مُجَسَّمَة بِ۪حيلَة يُمكِنُنا بِها اَن نَعمَل مِثلَ ذٰلِكَ اَل۪عَمَل </s> |
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140 <s id="A18-1|12|03">وَ۪لَكِنَنا نُقَدِّم أَوَّلاً ما يَصلُح لِ۪تَسهيل مَعرِفَة هٰذا ثُمَّ نُتبِعُهُ بَيان ذٰلِكَ </s> |
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141 <s id="A18-1|12|04">يُقال إِنَّ اَل۪أَشكال مُتَشابِهَة مُتَساوِيَة بَسيطَة وَ۪مُجَسَّمَة مُرَتَّبَة كانَت أَو غَير مُرَتَّبَة إِذا أَمكَنَنا اَن نُرَسِّم في أَحَدِها مِن اَل۪أَشكال اَل۪مُستَقيمَة اَل۪خُطوط شَكلاً مُساوِياً مُشابِهاً اَلَّذي نُرَسِّمُهُ في اَل۪آخَر وَ۪اَل۪أَشكال يُقال إِنَّها مُتَشابِهَة إِذا أَمكَنَنا اَن نُرَسِّم في أَحَدِها مِن اَل۪أَشكال اَل۪مُستَقيمَة اَل۪خُطوط أَشكالاً ما يُمكِنُنا اَن نُرَسِّم أَشكالاً مُشابِهَة لَها في اَل۪آخَر </s> |
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142 </p> |
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143 <p n="13"> |
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144 <s id="A18-1|13|00"></s> |
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145 <s id="A18-1|13|01"><pb n="29"></pb> إِذا كانَ خَطّ ما مُتَحَرِّكاً عَلى نُقطَة ما وَ۪فُرِضَ عَلى ذٰلِكَ اَل۪خَطّ عَلامَتان تَقسِمان اَل۪خَطّ فيما يَلي اَل۪عَلامَة اَل۪ثابِتَة عَلى اَل۪نِسبَة اَل۪مَعلومَة فَ۪إِنَّ اَل۪عَلامَتَين أَلَّتَين تَتَحَرَّكان عَلى ذٰلِكَ اَل۪خَطّ تَرسُمان أَشكالاً مُتَشابِهَة</s> |
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146 <s id="A18-1|13|02">فَ۪اِن كانَ اَل۪خَطّ يَتَحَرَّك عَلى سَطح فَ۪إِنَّهُ تَكون اَل۪أَشكال اَل۪مَرسومَة بَسيطَة </s> |
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147 <s id="A18-1|13|03">فَ۪اِن لَم يَكُن اَل۪خَطّ مُتَحَرِّكاً عَلى سَطح لَكِنَهُ كانَ عَلى مُجَسَّم فَ۪إِنَّ اَل۪أَشكال اَل۪مَرسومَة تَكون مُجَسَّمَة إِذا تَوَهَّمنا اَل۪عَلامات بِ۪تَقارُبِها تَرسُم بَسائِط اَل۪أَشكال لِ۪أَنَّهُ لَيسَ بِ۪مُمتَنَع اَن نَتَوَهَّم في اَل۪مَحسوسات هٰذا اَل۪وَضع وَ۪ذٰلِكَ في اَل۪مَعقولات أَكثَر صِدقاً وَ۪أَصَحّ </s> |
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148 <s id="A18-1|13|04">وَ۪عَلى جِهَة أُخرا تُسَمّي اَل۪أَشكال مُتَشابِهَة إِذا كانَ إِذا رُسِمَ أَحَدُهُما في اَل۪آخَر وَ۪فُرِضَت عَلامَة ما تَكون اَل۪خُطوط اَل۪خَرّاجَة مِن اَل۪عَلامَة إِلى نِهايات اَل۪أَشكال خُطوطاً كانَت أَو سُطوحاً تَقطَعُها نِهايات اَل۪أَشكال في تِلكَ اَل۪نِسبَة</s> |
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149 </p> |
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150 <p n="14"> |
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151 <s id="A18-1|14|00"></s> |
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152 <s id="A18-1|14|01">فَ۪إِذ قَد قَدَّمنا هٰذا نُبَيِّن أَنَّهُ يُمكِنُنا اَن نَجِد شَكلاً مُشابِهاً لِ۪كُلّ شَكل مَفروض وَ۪لَهُ إِلَيهِ نِسبَة مَعلومَة </s> |
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153 <s id="A18-1|14|02">وَ۪أَوَّل ذٰلِكَ نُبَيِّنُهُ في اَل۪سُطوح </s> |
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154 <s id="A18-1|14|03">فَ۪ل۪نَفرِض خَطّاً ما هُوَ خَطّ ٓآب ثابِتاً عَلى عَلامَة ٓأَة مُتَحَرِّكاً عَلى سَطح وَ۪ل۪تَكُن عَلَيهِ عَلامَتان وَ۪هُما عَلامَتا ٓبٓه تَجوزان عَلى اَل۪خَطّ </s> |
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155 <s id="A18-1|14|04">وَ۪ل۪تُرَسِّم عَلامَة ٓب في <pb n="31"></pb> اَل۪سَطح خَطّ ٓبٓغٓدٓeٓز وَ۪عَلامَة ٓه تُرَسِّم خَطّ ٓهٓتٓكٓلٓم فَ۪نَقول إِنَّ شَكلَي ٓبٓغٓدٓeٓز ٓهٓتٓكٓلٓم مُتَشابِهان </s> |
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156 <s id="A18-1|14|05">بُرهان ذٰلِكَ أَنّا نُرَسِّم في ٓبٓغٓدٓeٓز شَكلاً مُستَقيم اَل۪خُطوط وَ۪هُوَ شَكل ٓبٓغٓدٓeٓز وَ۪أَيضاً نُرَسِّم شَكل ٓهٓتٓكٓلٓم وَ۪نَصِل مِن عَلامَة ٓأَة إِلى عَلامات ٓبٓغٓدٓeٓز خُطوطاً وَ۪هِيَ اَل۪خُطوط اَلَّتي قَد أَخرَجناها وَ۪أَيضاً نَصِل ٓهٓتٓكٓلٓم وَ۪مِن أَجل أَنَّ خُطوط ٓبٓا ٓغٓا ٓدٓا ٓeٓا ٓآز قَد قُسِمَت قِسمَة مُتَشابِهَة عَلى عَلامات ٓهٓتٓكٓلٓم لِ۪ما فَرَضنا فَ۪إِنَّ اَل۪شَكل اَل۪مُستَقيم اَل۪خُطوط اَلَّذي هُوَ ٓبٓغٓدٓeٓز مُشابِه لِ۪ل۪شَكل اَل۪مُستَقيم اَل۪خُطوط اَلَّذي هُوَ ٓهٓتٓكٓلٓم </s> |
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157 <s id="A18-1|14|06">وَ۪بِ۪مِثلَ ذٰلِكَ نُبَيِّن أَنَّهُ قَد يُمكِنُنا اَن نُرَسِّم في شَكل ٓهٓتٓكٓلٓم شَكلاً مُستَقيم اَل۪خُطوط يُشابِه كُلّ شَكل مُستَقيم اَل۪خُطوط يُرَسَّم في شَكل ٓبٓغٓدٓeٓز لِ۪أَنَّ اَل۪أَشكال اَلَّتي رَسَمَتها اَل۪عَلامَتان مُتَشابِهَة</s> |
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158 </p> |
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159 <p n="15"> |
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160 <s id="A18-1|15|00"></s> |
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161 <s id="A18-1|15|01">وَ۪ل۪نُبَيِّن اَل۪آن كَيفَ نَجِد شَكلاً مُشابِهاً لِ۪ل۪شَكل اَل۪مُسَطَّح اَل۪مَعلوم بِ۪آلَة تَكون لَهُ إِلَيهِ نِسبَة مَعلومَة </s> |
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162 <s id="A18-1|15|02">فَ۪نَعمَل صَفيحَتَين عَلى مَركَز واحِد ثابِتَة عَلَيهِ ذَوات أَسنان مُهَندَمَة عَلى مِحوَر واحِد مُتَحَرِّكَة في اَل۪سَطح اَلَّذي فيهِ اَل۪شَكل اَلَّذي نُريد اَن نَعمَل مِثلَهُ وَ۪ل۪تَكُن نِسبَة اَل۪صَفائِح بَعضِها إِلى بَعض تِلكَ اَل۪نِسبَة اَل۪مَعلومَة </s> |
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163 <s id="A18-1|15|03">وَ۪ل۪يَكُن عَلى كُلّ واحِدَة مِن <pb n="33"></pb> اَل۪صَفائِح قانون ذو أَسنان في تِلكَ اَل۪جِهَة وَ۪ل۪تَكُن أَسنانُها مُرَكَّبَة عَلى أَسنان اَل۪صَفائِح </s> |
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164 <s id="A18-1|15|04">وَ۪ل۪تَكُن هٰذِهِ اَل۪قَوانين في حَفر ميزابي مِن قانون آخَر مُتَحَرِّك عَلى مِحوَر اَل۪صَفائِح بِ۪ثُقب مُستَدير </s> |
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165 <s id="A18-1|15|05">وَ۪ل۪يَكُن عَلى أَطراف اَل۪قَوانين اَل۪مُضَرَّسَة مَراكِز تَكون لِ۪خَطّ اَل۪أَشكال اَل۪مُتَشابِهَة وَ۪ل۪تَكُن هٰذِهِ اَل۪مَراكِز تَجوز عَلى خَطّ مُستَقيم عَلى مَركَز اَل۪صَفائِح </s> |
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166 <s id="A18-1|15|06">وَ۪ل۪اَن يَكونا كِلاهُما أَبَداً مُتَحَرِّكَين حَرَكَة مُستَقيمَة عَلى مَركَز اَل۪صَفائِح وَ۪تَعمَل اَل۪ثَلاث عَلامات عَمَلاً واحِداً وَ۪تَكون أَبَداً عَلى خَطّ واحِد مُستَقيم يَنبَغي اَن نَعمَل اَل۪مَراكِز اَلَّتي في اَل۪قَوانين اَل۪مُسَنَّنَة بَعيدَة عَن مَركَز اَل۪صَفائِح قَدر اَل۪بُعد اَل۪أَصغَر اَلَّذي لِ۪مَركَز كُلّ واحِدَة مِن اَل۪صَفيحَتَين عَن أَطراف اَل۪قانونَين </s> |
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167 <s id="A18-1|15|07">ثُمَّ نُعَوِّجُها لِ۪تَنال اَل۪سَطح اَلَّذي نُريد اَن نُرَسِّم فيهِ اَل۪أَشكال اَل۪مُتَشابِهَة </s> |
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168 <s id="A18-1|15|08">فَ۪اِن مَدَّة أَحَد مَركَزاً ما فَ۪صَيَّرَهُ عَلى اَل۪خَطّ اَلَّذي يُحيط بِ۪ذٰلِكَ اَل۪شَكل وَ۪باعَدَ اَل۪آخَر عَنهُ اَل۪بُعد اَلَّذي يَكون ما بَينَهُ وَ۪بَينَ مَركَز اَل۪صَفائِح عِندَ اَل۪بُعد اَلَّذي بَينَهُ وَ۪بَينَ اَل۪مَركَز اَل۪آخَر كَ۪نِسبَة أَقطار اَل۪صَفائِح اَل۪مُسَنَّنَة بَعضِها إِلى بَعض وَ۪صَيَّرَ اَل۪قانون اَلَّذي فيهِ اَل۪حَفر اَل۪ميزابي مُقَوَّساً <pb n="35"></pb> قَليلاً لِ۪يَكون اَل۪مَركَز اَلَّذي عَلى اَل۪خَطّ اَلَّذي ذَكَرناهُ جائِزاً عَلى هٰذا اَل۪خَطّ فَ۪إِنَّ اَل۪مَركَز اَل۪آخَر يَرسُم اَل۪شَكل اَل۪مُشابِه لِ۪ل۪شَكل اَل۪أَوَّل وَ۪يَرسُمُهُ أَيضاً عَلى اَل۪نِسبَة اَل۪مَعلومَة لِ۪أَنَّ اَل۪صَفائِح اَل۪مُسَنَّنَة لِ۪إِحداهِما إِلى اَل۪أُخرا هٰذِهِ اَل۪نِسبَة</s> |
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169 </p> |
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170 <p n="16"> |
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171 <s id="A18-1|16|00"></s> |
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172 <s id="A18-1|16|01">أَمّا اَل۪شَكل اَلَّذي يُشابِه اَل۪شَكل اَل۪مَعلوم اَلَّذي لَهُ إِلَيهِ نِسبَة مَعلومَة فَ۪قَد عَمَلناهُ في اَل۪مَوضِع اَلَّذي هُوَ فيهِ وَ۪اَلَّذي نُريد اَن نَعمَل اَل۪شَكل اَل۪مُشابِه لَهُ فيهِ </s> |
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173 <s id="A18-1|16|02">فَ۪اِن أَرادَ أَحَد اَن لا يَعمَل اَل۪شَكل اَل۪مَوجود في ذٰلِكَ اَل۪مَوضِع لَكِنَ في مَوضِع آخَر حَيثُ يُريد واضِعَهُ فَ۪إِنّا نَستَعمِل فيهِ هٰذا اَل۪عَمَل </s> |
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174 <s id="A18-1|16|03">فَ۪ل۪يَكُن اَل۪شَكل اَل۪مُشابِه لِ۪ل۪شَكل اَل۪مَعلوم شَكل ٓآبٓغٓدٓeٓز وَ۪ل۪يَكُن اَل۪مَوضِع اَلَّذي نُريد اَن نَعمَلَهُ فيهِ ما يَلي عَلامَة ٓه </s> |
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175 <s id="A18-1|16|04">وَ۪ل۪نَفرِض في داخِل شَكل ٓآبٓغٓدٓeٓز عَلامَة ما وَ۪هِيَ عَلامَة ٓت وَ۪ل۪نَرسُم عَلى عَلامَتَي ٓهٓت دائِرَتَين مُتَساوِيَتَين في اَل۪سَطح وَ۪ل۪نُقَسِّمهِما بِ۪أَقسام مُتَساوِيَة اَل۪كَثرَة عَلى عَلامات ٓكٓلٓمٓنٓسْٓ ٓفٓقٓرٓخِٓٓة وَ۪ل۪نَصِلها وَ۪نُخرِجها مِن اَل۪مَراكِز إِلى اَل۪فُصول وَ۪نُخرِج خُطوطاً مُساوِيَة لِ۪ل۪خُطوط اَلَّتي أُخرِجَت في شَكل ٓآبٓغٓدٓeٓز مِن عَلامَة ٓه وَ۪ل۪يَكُن خَطّ ٓآك مُساوِياً لِ۪خَطّ ٓقٓذ <pb n="37"></pb> وَ۪ٓلٓب لِ۪خَطّ ٓرٓض وَ۪ٓمٓغ لِ۪خَطّ ٓخٓث وَ۪ٓنٓد لِ۪خَطّ ِٓٓc وَ۪ٓسٓe لِ۪خَطّ ٓةٓت وَْ۪ٓٓز لِ۪خَطّ ٓفٓخ </s> |
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176 <s id="A18-1|16|05">وَ۪ل۪نُخرِج عَلى عَلامات ٓخٓذٓضٓثٓcٓظ وَ۪اَل۪عَلامات اَل۪مُشابِهَة لَها خُطوطاً فَ۪اِن قُسِمَت اَل۪دَوائِر اَل۪مُتَساوِيَة اَلَّتي عَلى مَركَزَي ٓتٓه بِ۪أَقسام أَكثَر فَ۪إِنَّ كُلَّما كانَت اَل۪عَلامات مُتَقارِبَة كانَ اَل۪خَطّ اَل۪مَرسوم أَكثَر صِحَّة وَ۪إِستِقصاء </s> |
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177 <s id="A18-1|16|06">فَ۪ل۪نَرسُم خَطّ ٓخٓذٓضٓثٓcٓظ فَ۪يَكون هٰذا اَل۪خَطّ مُساوِياً وَ۪مُشابِهاً لِ۪خَطّ ٓآبٓغٓدٓeٓز لِ۪أَنَّ اَل۪سُطوح اَل۪مُتَشابِهَة اَل۪مُتَساوِيَة يَتَراكِب بَعضُها عَلى بَعض</s> |
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178 </p> |
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179 <p n="17"> |
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180 <s id="A18-1|17|00"></s> |
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181 <s id="A18-1|17|01">وَ۪في اَل۪أَشكال اَل۪مُجَسَّمَة أَيضاً اَل۪مُرَتَّبَة وَ۪غَير اَل۪مُرَتَّبَة يَنبَغي اَن نَتَوَهَّم اَل۪نُقلَة مُتَشابِهَة أَعني اَن تَكون كُرَة بَدَلَة اَل۪دائِرَة اَلَّتي تُعمَل أَو فيها أَو خارِجها أَشكال ما اُخَر مُتَساوِيَة مُتَشابِهَة </s> |
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182 <s id="A18-1|17|02">فَ۪نَفرِض عَلَيها عَلامات مُتَشابِهَة اَل۪وَضع وَ۪نُخرِج مِنها إِلى عَلامات اُخَر مَوضوعَة في أَوساط اَل۪أَشكال خُطوطاً وَ۪نُخرِجها</s> |
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183 <s id="A18-1|17|03">فَ۪إِنّا إِذا فَعَلنا ذٰلِكَ كانَ مِن هٰذِهِ اَل۪خُطوط شَكل مُجَسَّم مُساوٍ مُشابِه لِ۪ل۪شَكل اَل۪مَوضوعَة أَوَّلاً</s> |
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184 </p> |
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185 <p n="18"> |
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186 <s id="A18-1|18|00"></s> |
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187 <s id="A18-1|18|01">فَ۪أَمّا اَل۪مُجَسَّمات فَ۪إِنّا نَعمَلُها عَلى هٰذِهِ اَل۪جِهَة نَتَّخِذ لَوحَين مِن خَشَب سُطوحِيَّة مُتَحَرِّكَة عَلى خَطّ مُشتَرَك يَكون اَل۪خَطّ اَل۪مُشتَرَك في كُلّ حَرَكَة خَطّاً واحِداً وَ۪ذٰلِكَ يَتَهَيَّأ إِذا كانَت مَراكِز اَل۪هَرماوُجات اَلَّتي تَتَحَرَّك عَلَيها اَل۪أَلواح عَلى هٰذا اَل۪خَطّ اَل۪مُشتَرَك </s> |
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188 <s id="A18-1|18|02">وَ۪ل۪يَكُن عُظم اَل۪أَلواح <pb n="39"></pb> عَلى قَدر أَعظَم اَل۪شَكلَين اَل۪مُتَشابِهَين اَل۪مُجَسَّمَين </s> |
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189 <s id="A18-1|18|03">وَ۪أَمّا صَنعَة اَل۪آلَة وَ۪اَل۪حاجَة إِلَيها فَ۪اَل۪آن نُعَلِّمُها وَ۪ل۪نَتَّخِذ شَكلَين مِن حَديد يُشابِهان اَل۪حَرف اَلَّذي يُسَمّي هولا فَ۪ل۪تَكُن أَجزاء كُلّ واحِد مِنهُما اَل۪مَمدودَة مُتَساوِيَة </s> |
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190 <s id="A18-1|18|04">وَ۪ل۪نُعَوِّج أَطرافَها تَعويجاً لَهُ حِدَّة وَ۪ل۪تَكُن مِن تَعويج إِثنَين مِنها صورَة مُثَلَّث </s> |
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191 <s id="A18-1|18|05">وَ۪ل۪تَكُن اَل۪نِسبَة اَل۪مَعلومَة اَلَّتي لِ۪أَحَد اَل۪مُجَسَّمَين إِلى اَل۪آخَر ثَلاثَة أَمثال اَل۪نِسبَة اَلَّتي لِ۪أَضلاع اَل۪مُثَلَّثَين بَعضِها إِلى بَعض فَ۪ل۪نَتَوَهَّم ذٰلِكَ إِلى خُطوط ٓآب ٓآغ ٓآد وَ۪اَل۪خُطوط اَلَّتي قَد عُوِّجَت ٓغٓe ٓبٓز ٓدٓه وَ۪اَل۪شَكل اَل۪آخَر خُطوط ٓتٓك ٓتٓل ٓتٓم وَ۪ل۪تَكُن اَل۪خُطوط اَلَّتي قَد عُوِّجَت خُطوط ٓكٓن ٓلٓس ٓمْٓ وَ۪ل۪يَكُن اَل۪مُثَلَّثان اَل۪مُتَشابِهان ٓهٓeٓز ٓنْٓٓس </s> |
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192 <s id="A18-1|18|06">وَ۪ل۪نَرسُم عَلى اَل۪خَطّ اَل۪مُشتَرَك اَلَّذي لِ۪ل۪لَوحَين اَل۪مُتَحَرِّكَين في أَحَد اَل۪لَوحَين شَكلاً مُساوِياً مُشابِهاً لِ۪ل۪شَكل اَل۪حَديد وَ۪ل۪نُخرِج عَلى أَحَد خُطوط اَل۪مُثَلَّث خَطّاً مُوازِياً لِ۪قاعِدَة اَل۪مُثَلَّث يُحيط بِ۪مُثَلَّث آخَر مُساوٍ لِ۪ل۪مُثَلَّث اَلَّذي مِن حَديد اَلَّذي يُشابِه حَرف هولا </s> |
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193 <s id="A18-1|18|07">وَ۪ل۪يَكُن عَلى كُلّ واحِد مِن أَشكال هولا قَضيب مِن رَصاص مُلصَق بِهِ وَ۪ل۪يَكُن طَرَفُهُ مُحَدَّداً قَوِياً لِ۪يَكُن إِذا عُوِّجَ أَيّ تَعويج كانَ وَ۪تُرِكَ يَسكٌ أَعني لا يَرتَعِدَ <pb n="41"></pb> كَما قَد تَكون اَل۪قُضبان اَل۪رَصاص اَلَّتي تُعمَل لِ۪ل۪تَماثيل اَل۪إِنسِيَّة </s> |
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194 <s id="A18-1|18|08">وَ۪ل۪تَكُن صورَة هٰذا اَل۪حَرف اَلَّذي يُسَمّي هولا مُشابِهاً لِ۪ل۪أَدات اَلَّتي تُسَمّي غَلا أَغرا وَ۪ل۪تَكُن اَل۪أَلواح اَلَّتي ذَكَرنا مُتَحَرِّكَة إِلى بَعضِها بَعض اَل۪حَرَكَة اَلَّتي إِذا سَكَنَت ثَبَتَت وَ۪كانَت غَير مُتَزَعزِعَ كَ۪اَل۪سَراطين </s> |
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195 <s id="A18-1|18|09">أَمّا صَنعَة اَل۪آلَة فَ۪هِيَ هٰذِهِ وَ۪اَلَّذي نُريد اَن نُخَبِّرَهُ بَعدَ هٰذا هُوَ إِستِعمالُها</s> |
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196 <s id="A18-1|18|10">فَ۪إِذا أَرَدنا اَن نَعمَل شَكلاً مُجَسَّماً مُشابِهاً لِ۪شَكل آخَر مَعلوم مُجَسَّم وَ۪لَهُ إِلَيهِ نِسبَة كَ۪اَل۪نِسبَة اَل۪مَعلومَة فَ۪إِنّا نُقَرِّب بَسيط اَل۪شَكل اَل۪مُجَسَّم إِلى شَكل هولا لِ۪تَماسّ اَل۪مَراكِز اَل۪بَسيط مِن كُلّ جِهَة وَ۪نُقَرِّب أَيضاً اَل۪شَكل اَل۪آخَر اَل۪مُشابِه هولا لِ۪ل۪شَكل اَلَّذي نُريد اَن نَعمَلَهُ </s> |
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197 <s id="A18-1|18|11">فَ۪اِن أَرَدنا اَن نَعمَلَهُ أَكبَر مِن اَل۪شَكل اَل۪مَنظور أَتَينا بِ۪اَل۪شَكل اَل۪أَعظَم إِلى اَل۪مُثَلَّث اَل۪أَعظَم وَ۪اَل۪آخَر إِلى اَل۪باقي </s> |
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198 <s id="A18-1|18|12">فَ۪ل۪يَكُن نُريد اَن نَعمَل اَل۪شَكل اَل۪مُشابِه في حَجَر أَو خَشَب أَو آلَة أُخرا وَ۪نُصَيِّر عَلى كُلّ جِسم عَلامات اَل۪مَراكِز </s> |
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199 <s id="A18-1|18|13">وَ۪ل۪تَكُن اَل۪عَلامات اَل۪مَفروضَة مَوضوعَة عَلى اَل۪أَجسام وَضعاً مُتَشابِهاً وَ۪ل۪نَعمَل اَل۪أَجزاء اَل۪اُخَر عَلى هٰذا اَل۪عَمَل </s> |
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200 <s id="A18-1|18|14">وَ۪ل۪يَكُن اَل۪تَعليم ظاهِراً نَفرِض كَ۪أَنّا نُريد اَن نَرسُم عَيناً في مِثال إِنسان أَو مِثال آخَر غَيرِهِ </s> |
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201 <s id="A18-1|18|15">فَ۪نَضَع مَراكِز هولا عَلى اَل۪مَعمول أَعني اَل۪مَوضوع لَنا اَلَّذي نُريد اَن نَعمَل شَكلاً <pb n="43"></pb> مُشابِهاً لَهُ وَ۪نُعَوِّج طَرَف اَل۪قَضيب اَل۪رَصاص اَلَّذي عِندَ هولا حَتّى يَنال طَرَفُهُ اَل۪عَين اَلَّذي نُريد ثُمَّ نَرفَع هولا وَ۪نُرَكِّبُهُ عَلى اَل۪مُثَلَّث اَلَّذي قَد رُسِمَ في اَل۪لَوح ثُمَّ نَخفَض أَو نَرفَع اَل۪لَوح اَل۪آخَر اَلَّذي لَيسَ فيهِ رَسم حَتّى يَنالُهُ طَرَف اَل۪قَضيب بِ۪إِنخِفاضِهِ أَو بِ۪إِرتِفاعِهِ </s> |
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202 <s id="A18-1|18|16">ثُمَّ نَرفَع هولا وَ۪نَصِل خَطَّين مِن اَل۪عَلامَة اَلَّتي يَنالُها اَل۪قَضيب اَل۪رَصاص عَلى اَل۪لَوح في نِهايات ضِلع اَل۪مُثَلَّث اَلَّذي عَلى اَل۪خَطّ اَل۪مُشتَرَك لِ۪ل۪لَوحَين وَ۪ل۪نَحفَظ كُلّ واحِد مِن اَل۪لَوحَين غَير مُتَحَرِّك إِلى اَل۪آخَر وَ۪نُخرِج عَلى اَل۪عَلامَة اَل۪أُخرا اَلَّتي عَلى اَل۪خَطّ اَل۪مُشتَرَك لِ۪ل۪لَوحَين خَطّاً مُوازِياً لِ۪ل۪خُطوط اَل۪عِظام اَلَّتي عِندَ اَل۪خَطّ اَل۪مُوازي لِ۪ل۪قاعِدَة حَتّى يَقطَع اَل۪خَطّ اَل۪مُخرَج اَل۪آخَر </s> |
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203 <s id="A18-1|18|17">ثُمَّ نَأخُذ هولا اَل۪آخَر وَ۪نُرَكِّب أَطراف اَل۪أَسنان اَلَّتي قَد عُوِّجَت اَل۪حادَّة عَلى اَل۪مُثَلَّث اَلَّذي في اَل۪لَوح اَل۪مُساوي لِ۪ل۪مُثَلَّث اَل۪مَعمول مِن أَطراف تِلكَ اَل۪أَجزاء وَ۪نُعَوِّج اَل۪قَضيب اَل۪رَصاص حَتّى يَنال اَل۪عَلامَة اَلَّتي رَسَمَها اَل۪خَطّ اَل۪مُوازي في اَل۪لَوح اَل۪آخَر وَ۪نَرفَع هولا وَ۪نَضَعُهُ عَلى اَل۪عَلامات اَل۪مَفروضَة في اَل۪شَكل اَلَّذي لَم نَستَعمِلهُ </s> |
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204 <s id="A18-1|18|18">فَ۪عَلى أَيّ عَلامَة تَراكَبَة طَرَف اَل۪قَضيب في اَل۪جِسم تِلكَ اَل۪عَلامَة تَكون اَل۪مَوضوعَة عَلى مَوضِع عَين اَل۪مِثال اَل۪مُشابِهَة اَل۪وَضع اَلَّتي تُعَوِّج عَلَيها اَل۪قَضيب اَل۪أَوَّل </s> |
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205 <s id="A18-1|18|19">وَ۪كَ۪ذٰلِكَ <pb n="45"></pb> أَيضاً نُعَوِّج اَل۪قَضيب عَلى أَجزاء اَل۪بُنيَة اَل۪اُخَر فَ۪نَرسُم اَل۪مُتَشابِهات اَل۪وَضع عَلى اَل۪حَجَر ثُمَّ نَعمَل اَل۪بَسيط عَلى اَل۪عَلامات اَل۪مَفروضَة وَ۪هِيَ اَل۪عَلامات اَلَّتي تَعمَل اَل۪شَكل مُشابِهاً لِ۪ل۪شَكل اَلَّذي تَقَدَّمَ وَضُهُ وَ۪تَصير لَهُ إِلَيهِ نِسبَة هِيَ اَل۪نِسبَة اَل۪مَذكورَة </s> |
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206 <s id="A18-1|18|20">فَ۪أَمّا اَل۪خَطّ اَل۪مُوازي اَلَّذي ذَكَرناهُ فَ۪إِنَّهُ يُرسَم في اَل۪لَوح اَل۪آخَر بِ۪سُهولَة إِذا رَسَمنا عَلى اَل۪لَوح خَطّاً ما مُوازِياً لِ۪ل۪خَطّ اَل۪مُشتَرَك</s> |
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207 <s id="A18-1|18|21">أَمّا اَن تَكون اَل۪أَشكال اَل۪مَعمولَة عَلى هٰذا اَل۪عَمَل مُتَشابِهَة فَ۪ذٰلِكَ ظاهِر لِ۪أَنَّها مِن أَشكال نارِيَّة مُتَشابِهَة مُتَشابِهَة اَل۪وَضع قَواعِدُها اَل۪مُثَلَّثات اَلَّتي رَسَمَها هولا في اَل۪أَجسام رُؤوسُها اَل۪عَلامات اَلَّتي رَسَمَتها أَطراف اَل۪قُضبان في كُلّ واحِد مِن اَل۪أَجسام </s> |
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208 <s id="A18-1|18|22">فَ۪أَمّا اَن تَكون لِ۪بَعضِها إِلى بَعض نِسبَة مَعلومَة فَ۪ذٰلِكَ ظاهِر لِ۪أَنَّ اَل۪أَشكال اَل۪نارِيَّة اَلَّتي مِنها عُمِلَت اَل۪أَجسام نِسبَتُها ثَلاثَة أَمثال نِسبَة اَل۪أَضلاع اَل۪مُتَناسِبَة لِ۪أَنَّ أَضلاع اَل۪مُثَلَّثَين اَل۪مُتَشابِهَين كَذا فُرِضَت </s> |
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209 <s id="A18-1|18|23">فَ۪إِذاً اَل۪مُجَسَّمات لِ۪بَعضِها إِلى بَعض هٰذِهِ اَل۪نِسبَة اَل۪مَعلومَة</s> |
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210 </p> |
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211 <p n="19"> |
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212 <s id="A18-1|19|00"></s> |
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213 <s id="A18-1|19|01">فَ۪اِن أَرَدنا اَن نَعمَل ما خَلف اَل۪أَجسام اَل۪مُتَشابِهَة فَ۪إِنّا نَستَعمِل بِ۪هٰذِهِ اَل۪حيلَة </s> |
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214 <s id="A18-1|19|02">نَتَوَهَّم في جِهَة خَلف ثَلاث عَلامات في كُلّ واحِد مِن اَل۪أَشكال مَوضوعَة وَضعاً مُتَشابِهاً <pb n="47"></pb> وَ۪فاعِلاً مِن اَل۪خُطوط اَلَّتي تَصِلُها مُثَلَّثَين مُساوِيَين لِ۪ل۪مُثَلَّثات اَل۪مَعمولَة مِن حَرف هولا أَعني اَل۪مَرسومَة في اَل۪لَوح اَل۪واحِد وَ۪نَنقُل كِلَيهِما في جِهَة خَلف وَ۪نَفرِض عَلامات مُتَّصِلَة نَعمَل بِها أَجزاء اَل۪جِسم اَل۪مَذكورَة </s> |
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215 <s id="A18-1|19|03">فَ۪اِن أَرَدنا اَن نَعمَل تَماثيل يُخالِف بَعضُها بَعضاً حَتّى يَكون إِذا قَدَّمَ أَحَدُها اَل۪رِجل اَل۪يُمنى يُقَدِّم اَل۪آخَر اَل۪رِجل اَل۪يُسرى قَدَمَ تُشابِه رِجل اَل۪آخَر اَل۪يُمنى وَ۪عَلى هٰذا في اَل۪أَعضاء اَل۪اُخَر فَ۪إِنّا نَعمَل هَكَذا </s> |
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216 <s id="A18-1|19|04">نَنقُل اَل۪عَلامَة اَل۪مَفروضَة في اَل۪لَوح اَل۪آخَر إِلى اَل۪جِهَة اَل۪أُخرا حَتّى تَكون مَوضوعَة وَضعاً مُتَشابِهاً أَعني اَن يَكون اَل۪عَمود اَل۪خارِج مِن اَل۪عَلامَة اَل۪مَذكورَة عَلى اَل۪خَطّ اَل۪مُشتَرَك بَعيداً مِن اَل۪طَرَف اَل۪واحِد اَل۪بُعد اَلَّذي أَحاطَ بِهِ اَل۪خَطّ اَل۪آخَر مِن اَل۪عَلامَة اَل۪أُخرا في اَل۪جِهَة اَل۪أُخرا وَ۪يَكون مُساوِياً لِ۪ل۪عَمود اَل۪آخَر </s> |
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217 <s id="A18-1|19|05">أَعني اَن يَكون اَل۪خَطّ اَل۪مُشتَرَك لِ۪ل۪لَوحَين خَطّ ٓآب وَ۪تَكون نِهايات ضِلع اَل۪مُثَلَّث عَلامَتَي ٓغٓد وَ۪اَل۪عَلامَة اَل۪مَفروضَة عَلامَة ٓe وَ۪ل۪نُخرِج عَلى خَطّ ٓغٓد عَموداً وَ۪هُوَ عَمود ٓeٓز وَ۪ل۪نُخرِج خَطّ ٓدٓه مُساوِياً لِ۪خَطّ ٓغٓز وَ۪ل۪يَكُن خَطّ ٓهٓت اَل۪مُساوي لِ۪خَطّ ٓeٓز اَل۪قائِم عَلَيهِ </s> |
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218 <s id="A18-1|19|06">فَ۪طَرَف اَل۪قَضيب لَيسَ نُعَوِّجُهُ إِلى ما يَلي <pb n="49"></pb> عَلامَة ٓe وَ۪لَكِنَ إِلى ما يَلي عَلامَة ٓت </s> |
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219 <s id="A18-1|19|07">وَ۪كَ۪ذٰلِكَ نُدَبِّرُها بِ۪نَقلِها إِلى اَل۪جِهَة اَل۪أُخرا فَ۪نَعمَل أَعضاء اَل۪أَجسام مُتَخالِفَة </s> |
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220 <s id="A18-1|19|08">فَ۪أَمّا كَيفَ نَعمَل لِ۪صَفيحَة ما أَسناناً تَكون مَعلومَة اَل۪كَثرَة وَ۪تَتَراكِب عَلى لَولَب مَعلوم فَ۪إِنّا نُبَيِّن ذٰلِكَ لِ۪أَنَّ ذٰلِكَ كَثير اَل۪مَنفَعَة فيما نُريد اَن نُخَبِّر بِهِ بَعدَ هٰذا </s> |
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221 <s id="A18-1|19|09">فَ۪ل۪يَكُن اَل۪لَولَب عَلى ٓآب وَ۪ل۪تَكُن اَل۪دَوائِر اَل۪لَولَبِيَّة غَير عَدَسِيَّة وَ۪ل۪تَكُن أَبعاد هٰذِهِ اَل۪دَوائِر اَل۪لَولَبِيَّة قَدر ٓغٓد ٓدٓe ٓeٓز فَ۪تَكون هٰذِهِ اَل۪ثَلَثَة اَل۪خُطوط مُتَساوِيَة فَ۪نُريد اَن نَجِد صَفيحَة تَكون ذات عِشرين سِنّاً تَتَراكِب عَلى اَل۪دَوائِر اَل۪لَولَبِيَّة اَلَّتي عَلى اَل۪لَولَب </s> |
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222 <s id="A18-1|19|10">فَ۪ل۪نَفرِض دائِرَة ما تَكون في عُظمِها عَلى اَل۪قَدر اَلَّذي نُريد وَ۪هِيَ دائِرَة ٓهٓتٓك وَ۪ل۪يَكُن مَركَزُها عَلى عَلامَة ٓل وَ۪نُقَسِّم مُحيط اَل۪دائِرَة بِ۪عِشرين جُزأاً مُتَساوِيَة وَ۪ل۪يَكُن أَحَد هٰذِهِ اَل۪عِشرين جُزأاً قَوس ٓهٓت </s> |
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223 <s id="A18-1|19|11">وَ۪ل۪نَصِل عَلامات ٓهٓت ٓلٓت ٓلٓه وَ۪ل۪نَفرِض خَطّ ٓهٓم مُساوِياً لِ۪أَحَد خُطوط ٓغٓد ٓدٓe ٓeٓز وَ۪ل۪نُخرِج مِن عَلامَة ٓل خَطّاً مُوازِياً لِ۪خَطّ ٓهٓت وَ۪هُوَ خَطّ ٓلٓن وَ۪ل۪يَكُن هٰذا اَل۪خَطّ مُساوِياً لِ۪خَطّ ٓهٓم وَ۪ل۪نَصِل عَلامَتَي ٓمٓن بِ۪خَطّ ٓمٓن فَ۪إِنَّهُ يُقاطِع خَطّ ٓلٓت فَ۪ل۪يَكُن اَل۪تَقاطُع عَلى عَلامَة ٓس </s> |
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224 <s id="A18-1|19|12">وَ۪نَرسُم عَلى مَركَز ٓل بِ۪بُعد ٓلٓس <pb n="51"></pb> دائِرَة ٓسْٓٓف فَ۪يَظهَر لَنا أَنَّ قَوس ٓسْٓ جُزء مِن عِشرين جُزأاً مِن دائِرَة ٓسْٓٓف لِ۪أَنَّ قَوس ٓهٓت جُزء مِن عِشرين مِن مُحيط دائِرَة ٓهٓتٓك </s> |
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225 <s id="A18-1|19|13">وَ۪دائِرَة ٓسْٓٓف هِيَ اَل۪دائِرَة اَل۪داخِلَة فَ۪تَكون هِيَ اَل۪دائِرَة اَل۪مَحدودَة إِذا زَدنا عَلى خَطّ ٓلٓس خَطّاً يَكون بِ۪قَدر عَمق اَل۪دَوائِر اَل۪لَولَبِيَّة وَ۪رَسَمنا بِ۪بُعد ذٰلِكَ اَل۪خَطّ كُلِّهِ دائِرَة عَلى مَركَز ٓل </s> |
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226 <s id="A18-1|19|14">وَ۪قَد يَنبَغي اَن نَعلَم أَنَّ قِسمَة خارِج اَل۪دائِرَة يَنبَغي اَن تَتَراكِب في عَمق اَل۪لَولَب لِ۪أَنَّ ٓسْٓ مُساوٍ لِ۪ٓغٓد </s> |
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227 <s id="A18-1|19|15">أَمّا عَلى اَل۪حَقيقَة فَ۪إِنَّها لا تَتَراكِب لِ۪أَنَّ بُعد ظاهِر اَل۪دَوائِر اَل۪لَولَبِيَّة مُساوٍ لِ۪بُعد اَل۪دائِرَة اَل۪لَولَبِيَّة اَل۪داخِل فَ۪أَمّا اَل۪أَسنان فَ۪إِنَّ اَل۪بُعد اَلَّذي بَينَ أَعلاها اَل۪خارِج أَكبَر مِن اَل۪بُعد اَلَّذي بَينَ أَسفَلِها اَل۪داخِل وَ۪ل۪أَنَّ اَل۪إِختِلاف في ذٰلِكَ غَير مَحسوس لا يَكون مِنهُ إِمتِناع فِعل </s> |
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228 <s id="A18-1|19|16">وَ۪أَيضاً يَنبَغي اَن يَكون اَل۪حَفر اَلَّذي لِ۪ل۪أَسنان اَلَّتي في بَسيط حافَّة اَل۪فَلَكَة لَيسَ بِ۪قائِمَة كَما قَد نُعَلِّمُهُ في اَل۪فِلَك اَلَّتي نُريد اَن نُرَكِّب أَسنان بَعضَها عَلى بَعض لَكِنَنا نُصَيِّرُها مائِلَة لِ۪تَتَراكِب اَل۪أَسنان أَبَداً عَلى كُلّ مَوضِع حَفر اَل۪لَولَب </s> |
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229 <s id="A18-1|19|17">وَ۪ذٰلِكَ يَظهَر لَنا إِذا قَسَّمنا دائِرَة <pb n="53"></pb> عَلى حافَّة اَل۪فَلكَة بِ۪عِشرين جُزأاً أَقساماً مُتَساوِيَة وَ۪نُخرِج عَلى عَلامَة أَحَد اَل۪أَقسام خَطّاً مائِلاً عَلى قَدر مَيل اَل۪دَوائِر اَل۪لَولَبِيَّة وَ۪نُقَسِّم ما يَلي اَل۪جِهَة اَل۪أُخرا مِن اَل۪فَلكَة بِ۪مِثلَ هٰذِهِ اَل۪أَقسام وَ۪نَصِل هٰذِهِ اَل۪عَلامات بِ۪خُطوط تَكون عَلى بَسيط حافَّة اَل۪فَلكَة ثُمَّ نَحفِر اَل۪أَسنان فَ۪تَكون اَل۪دَوائِر اَل۪لَولَبِيَّة مُهَندَمَة فَ۪تَتَراكِب عَلَيها أَسنان اَل۪فَلكَة</s> |
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230 <s id="A18-1|19|18">فَ۪أَمّا كَيفَ يَنبَغي اَن يَكون تَعويج اَل۪أَسنان اَلَّتي في حافَّة اَل۪فَلكَة عِندَ اَل۪تَدوير فَ۪إِنّا نَعمَل مَيل اَل۪أَسنان اَلَّتي عَلى بَسيط حافَّة اَل۪فَلكَة مَيلاً يَتَراكِب في حَفر اَل۪دَوائِر اَل۪لَولَبِيَّة فَ۪إِنّا اَل۪آن نُبَيِّنُهُ </s> |
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231 <s id="A18-1|19|19">فَ۪ل۪نَفرِض فَلكَة وَ۪ل۪يَكُن اَل۪بُعد اَلَّذي لِ۪أَحَد اَل۪أَسنان خَطّ ٓآب وَ۪ل۪يَكُن اَل۪حَفر اَل۪لَولَبي اَلَّذي عَلى اَل۪لَولَب خَطّ ٓغٓد بَينَ خَطَّين مُوازِيَين لِ۪قاعِدَة اَل۪شَكل اَل۪أُسطُواني وَ۪هُما ٓغٓز ٓeٓد </s> |
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232 <s id="A18-1|19|20">وَ۪ل۪نَفرِض خَطَّين يَقوم أَحَدُهُما عَلى اَل۪آخَر عَلى زاوِيَة قائِمَة وَ۪هُما خَطّا ٓهٓت ٓتٓك وَ۪ل۪يَكُن خَطّ ٓدٓe مُساوِياً لِ۪خَطّ ٓهٓت وَ۪خَطّ ٓغٓe مُساوِياً لِ۪خَطّ ٓتٓك </s> |
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233 <s id="A18-1|19|21">وَ۪ل۪نَصِل عَلامَتَي ٓهٓك وَ۪نُخرِج مِن عَلامَة ٓأَة خَطّاً قائِماً عَلى اَل۪فَلكَة في ثُخن اَل۪فَلكَة وَ۪هُوَ خَطّ ٓآل فَ۪يَكون خَطّ ٓآل ثُخن اَل۪فَلكَة </s> |
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234 <s id="A18-1|19|22">وَ۪ل۪يَكُن <pb n="55"></pb> خَطّ ٓتٓم مُساوِياً لِ۪خَطّ ٓآل وَ۪نُخرِج خَطّ ٓمٓن مُوازِياً لِ۪خَطّ ٓهٓك وَ۪ل۪يَكُن خَطّ ٓلٓس مُساوِياً لِ۪خَطّ ٓتٓن في دائِرَة اَل۪فَلكَة اَل۪أُخرا وَ۪نَصِل عَلامَتَي ٓسٓا وَ۪نُقَسِّم دائِرَة ٓلٓس مِن عَلامَة ٓس بِ۪عَدَد كَثرَة اَل۪أَسنان وَ۪ل۪يَكُن ٓسْٓ قِسماً واحِداً وَ۪ل۪نَصِل ْٓٓب فَ۪يَكون حَفر اَل۪سِنّ عَلى خَطَّي ٓآس ٓبْٓ فَ۪ل۪تَكُن كَ۪ذٰلِكَ اَل۪أَسنان اَل۪اُخَر</s> |
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235 </p> |
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236 <p n="20"> |
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237 <s id="A18-1|20|00"></s> |
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238 <s id="A18-1|20|01">وَ۪قَد ظَنَّ قَوم أَنَّ اَل۪أَثقال اَل۪مَوضوعَة عَلى اَل۪أَرض تُحَرَّك بِ۪قُوَّة مُعادِلَة لَها بِ۪إِستِعمالِهِم اَل۪أَراء اَل۪كاذِبَة </s> |
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239 <s id="A18-1|20|02">فَ۪ل۪نُبَيِّن أَنَّ اَل۪أَثقال اَلَّتي وَضعَها عَلى ما وَصَفنا تَتَحَرَّك بِ۪قُوَّة أَقَلّ مِن كُلّ اَل۪قُوَّة اَل۪مَعلومَة وَ۪نوضِح اَل۪عِلَّة اَلَّتي لَها صارَ ذٰلِكَ غَير ظاهِر في اَل۪عَمَل </s> |
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240 <s id="A18-1|20|03">فَ۪ل۪نَتَوَهَّم حَملاً ما مَوضوعاً عَلى اَل۪أَرض وَ۪ل۪يَكُن مُعتَدِلاً أَملَس مُجتَمِعاً بَعضُهُ إِلى بَعض وَ۪ل۪يَكُن اَل۪سَطح اَلَّذي اَل۪ثِقل عَلَيهِ يُمكِن اَن يَميل إِلى كُلّ اَل۪جِهَتَين أَعني اَل۪يُمنى وَ۪اَل۪يُسرى </s> |
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241 <s id="A18-1|20|04">فَ۪ل۪يَكُن أَوَّلاً مائِلاً إِلى اَل۪يُمنى فَ۪يَظهَر لَنا أَنَّ اَل۪ثِقل اَل۪مَفروض يَميل إِلى اَل۪جِهَة اَل۪يُمنى لِ۪أَنَّ اَل۪أَثقال طَبيعَتُها اَن تَتَحَرَّك إِلى اَل۪سُفل اِن لَم يَدعَمُها شَيء فَ۪يَمنَعُها مِن اَل۪حَرَكَة وَ۪أَيضاً إِذا أُستُقِلَّت اَل۪جِهَة اَل۪مائِلَة إِلى اَل۪سَطح وَ۪صارَ مُعتَدِلاً فَ۪إِنَّهُ يَصير اَل۪ثِقل بِ۪هٰذا مَحفوظاً </s> |
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242 <s id="A18-1|20|05">فَ۪اِن مالَ إِلى اَل۪جِهَة اَل۪أُخرا أَعني إِلى اَل۪جِهَة اَل۪يُسرى فَ۪إِنَّ اَل۪ثِقل أَيضاً يَنحِطّ إِلى اَل۪جِهَة اَل۪مائِلَة وَ۪اِن كانَ اَل۪مَيل يَسيراً جِدّاً فَ۪لا يَحتاج اَل۪ثِقل إِلى قُوَّة تُحَرِّكُهُ لَكِنَ <pb n="57"></pb> يَحتاج إِلى قُوَّة تَدعَمُهُ لِ۪أَة۪لا يَتَحَرَّك </s> |
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243 <s id="A18-1|20|06">فَ۪إِذا صارَ اَل۪ثِقل أَيضاً مُعتَدِلاً غَير مائِل إِلى جِهَة مِن اَل۪جِهات فَ۪إِنَّهُ بِ۪هٰذا بِ۪لا اَن تَكون لَهُ قُوَّة تَدعَمُهُ فَ۪لا يَزال هادِناً إِلى اَن يَميل اَل۪سَطح إِلى أَيّ جِهَة كانَت فَ۪إِنَّهُ يَميل إِلى تِلكَ اَل۪جِهَة </s> |
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244 <s id="A18-1|20|07"> فَ۪اَل۪ثِقل اَل۪مُتَهَيِّئ لِ۪ل۪ذَهاب إِلى كُلّ جِهَة كَيفَ لا تَكون حاجَتُهُ في اَن يَتَحأَرَّك إِلى قُوَّة يَسيرَة قَدر اَل۪قُوَّة اَلَّتي تُمَيِّلُهُ فَ۪إِذاً اَل۪ثِقل يَتَحَرَّك بِ۪كُلّ قُوَّة يَسيرَة</s> |
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245 </p> |
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246 <p n="21"> |
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247 <s id="A18-1|21|00"></s> |
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248 <s id="A18-1|21|01">فَ۪اَل۪مِياه اَلَّتي عَلى اَل۪سُطوح غَير اَل۪مائِلَة فَ۪إِنَّها تَكون غَير سائِلَة بَل تَكون ثابِتَة لا تَميل إِلى جِهَة مِن اَل۪جِهات </s> |
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249 <s id="A18-1|21|02">فَ۪إِذا نالَها أَقَلّ مَيل فَ۪إِنَّ جَميعُها يَميل إِلى تِلكَ اَل۪جِهَة حَتّى لا يَبقى أَقَلّ جُزء مِن اَل۪ماء ثابِتاً عَلَيهِ إِلّا اَن يَكون في اَل۪سَطح أَغوار فَ۪تَبقى أَجزاء يَسيرَة في قَعر اَل۪أَغوار كَما قَد يَعرِض في اَل۪آنِيَة </s> |
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250 <s id="A18-1|21|03">وَ۪لَكِنَ اَل۪ماء قَد نالَهُ هٰذا لِ۪أَنَّ أَجزاءَهُ غَير مُتَّصِلَة شَديدَة اَل۪تَحَلُّل </s> |
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251 <s id="A18-1|21|04">وَ۪أَمّا اَل۪أَجساد اَل۪مُتَّصِلَة فَ۪مِن أَجل أَنَّها في طَبعِها غَير مَلِسَة في بَسائِطِها وَ۪لا يُمَلِّسُها سَهل فَ۪إِنَّهُ يَعرِض مِن خُشونَة اَل۪أَجساد اَن يَدعَم بَعضُها بَعضاً فَ۪يَعرِض مِن ذٰلِكَ اَن يَستَنِد أَحَدُها بِ۪اَل۪آخَر كَ۪اَل۪أَضراس فَ۪تَمنَع مِن ذٰلِكَ لِ۪أَنَّها إِذا تَكاثَرَت وَ۪إِتَّصَلَت بِ۪إِجتِماع بَعضِها إِلى بَعض تَحتاج إِلى إِجتِماع قُوَّة عَظيمَة</s> |
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252 <s id="A18-1|21|05">فَ۪مِن اَل۪تَجرِبَة صارَ لَهُم مُعَلِّم صاروا يَرصُفون تَحت اَل۪لَجآت خَشَباً تَكون بَسائِطُها في هَيئَة اَل۪أَساطين <pb n="59"></pb> فَ۪لا تَماسّ مِن اَل۪سَطح إِلّا جُزأاً يَسيراً وَ۪لا يَعرِض مِن ذٰلِكَ مِن اَل۪خُشونَة إِلّا أَقَلّ ذٰلِكَ وَ۪يَستَعمِلون اَل۪أَوتاد فَ۪يَتَحَرَّك اَل۪ثِقل عَلَيها بِ۪سُهولَة عَلى أَنَّهُ قَد زيدَ عَلى اَل۪ثِقل ثِقل اَل۪أَدات </s> |
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253 <s id="A18-1|21|06">وَ۪أَقوام يَرُصّون عَلى اَل۪سَطح أَلواحاً مَنحوتَة لِ۪مَلاسَتِها وَ۪يَطلونَها بِ۪دَسَم لِ۪اَن تَتَمَلَّس اَل۪خُشونَة اَلَّتي عَلَيها فَ۪يُحَرِّكون اَل۪ثِقل بِ۪أَيسَر قُوَّة </s> |
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254 <s id="A18-1|21|07">فَ۪أَمّا اَل۪أَساطين فَ۪إِنَّها إِذا كانَت ثِقالاً وَ۪كانَت مُلقات عَلى اَل۪أَرض حَتّى لا يَنال اَل۪أَرض مِنها إِلّا ضِلع واحِد فَ۪إِنَّها تَتَحَرَّك بِ۪سُهولَة وَ۪كَ۪ذٰلِكَ أَيضاً اَل۪أُكَر وَ۪هٰذِهِ قَد تَقَدَّمَ في قَولِنا</s> |
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255 </p> |
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256 <p n="22"> |
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257 <s id="A18-1|22|00"></s> |
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258 <s id="A18-1|22|01">فَ۪اِن أَرَدنا اَن نَحمِل اَل۪ثِقل إِلى جِهَة عُليا فَ۪إِنّا عِندَ ذٰلِكَ نَحتاج إِلى قُوَّة مُساوِيَة لِ۪ل۪ثِقل </s> |
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259 <s id="A18-1|22|02">فَ۪ل۪نَتَوَهَّم حِنايَة مُتَعالِيَة مُتَحَرِّكَة قائِمَة عَلى سَطح وَ۪ل۪تَكُن مُتَحَرِّكَة عَلى مَراكِز عَلى مِحوَر حَرَكَة سَهلَة وَ۪ل۪يَكُن عَلى بَسيط حافَّتِهِ حَبل يَكون أَحَد طَرَفَيهِ مَشدوداً بِ۪اَل۪حَمل وَ۪طَرَفُهُ اَل۪آخَر عِندَ اَل۪قُوَّة اَل۪جاذِبَة فَ۪أَقول إِنَّ ذٰلِكَ اَل۪ثِقل يَتَحَرَّك بِ۪قُوَّة مُساوِيَة لَهُ </s> |
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260 <s id="A18-1|22|03">وَ۪لا يَكون عِندَ طَرَف اَل۪حَبل اَل۪آخَر قُوَّة بَل۪يَكون ثِقل آخَر مَشدوداً فيهِ فَ۪يَظهَر لَنا أَنَّ اَل۪أَثقال إِذا كانَت مُتَساوِيَة فَ۪إِنَّ اَل۪حِنايَة لا تَميل إِلى جِهَة مِن اَل۪جِهات وَ۪لا يَقوا اَل۪ثِقل اَل۪أَوَّل عَلى اَل۪ثِقل اَل۪مُرتَبِط اَل۪ثاني وَ۪لا اَل۪ثِقل عَلى اَل۪حَمل لِ۪أَنَّ اَل۪ثِقل اَل۪مَشدود اَل۪ثاني مُساوٍ لِ۪ل۪حَمل اَل۪أَوَّل </s> |
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261 <s id="A18-1|22|04">فَ۪إِذا زيدَ في اَل۪ثِقل قَدر ما يَسير فَ۪إِنَّ اَل۪ثِقل اَل۪آخَر يَنجَبِذ إِلى اَل۪جِهَة <pb n="61"></pb> اَل۪عُليا فَ۪اَل۪قُوَّة إِذاً اَل۪مُحَرِّكَة لِ۪ل۪حَمل اِن كانَت أَعظَم مِن اَل۪حَمل فَ۪إِنَّها تَقوى عَلَيهِ وَ۪تُحَرِّكُهُ إِلّا اَن تَعرِض خُشونَة في تَدوير اَل۪حِنايَة أَو صَلابَة في اَل۪قُلوس فَ۪يَكون مِن ذٰلِكَ إِمتِناع اَل۪حَرَكَة</s> |
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262 </p> |
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263 <p n="23"> |
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264 <s id="A18-1|23|00"></s> |
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265 <s id="A18-1|23|01">فَ۪أَمّا اَل۪أَثقال اَلَّتي عَلى اَل۪سُطوح اَل۪مائِلَة فَ۪إِنَّ طَبيعَتُها اَن تَميل إِلى اَل۪سُفل أَيضاً كَما قَد تَكون حَرَكَة جَميع اَل۪أَجسام فَ۪اِن لَم يَكُن هٰذا كَما ذَكَرنا فَ۪يَنبَغي اَن نَتَوَهَّم فيهِ أَيضاً اَل۪عِلَّة اَلَّتي ذَكَرناها قَبلَ هٰذا </s> |
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266 <s id="A18-1|23|02">فَ۪ل۪نَفرِض إِنّا نُريد اَن نُحَرِّك ثِقلاً ما عَلى سَطح مائِل إِلى ما يَلي اَل۪عُلُوّ وَ۪ل۪تَكُن أَرضُهُ لَيِّنَة مَلِسَة وَ۪كَ۪ذٰلِكَ أَيضاً جُزء اَل۪ثِقل اَلَّذي تَدعَمُهُ </s> |
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267 <s id="A18-1|23|03">فَ۪نَحتاج في هٰذا اَن نَكتَسِب قُوَّة ما أَو ثِقلاً ما مِن اَل۪جِهَة اَل۪أُخرا لِ۪يَقوا أَوَّلاً عَلى اَل۪ثِقل أَعني اَن يُعادِلَهُ لِ۪تَكون اَل۪قُوَّة اَل۪زائِدَة عَلَيهِ تَقوى عَلى اَل۪ثِقل فَ۪تَرفَعُهُ إِلى ما فَوقَ </s> |
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268 <s id="A18-1|23|04">وَ۪ل۪اَن يَصِحّ قَولُنا نُبَيِّن ذٰلِكَ في أُسطُوانَة مَوضوعَة فَ۪إِنَّ اَل۪أُسطُوانَة مِن أَجل أَنَّهُ لا يَنال اَل۪أَرض مِنها كَبير جُزء فَ۪إِنَّها في طَبيعَتِها اَن تَتَدَحرِج إِلى أَسفَل </s> |
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269 <s id="A18-1|23|05">فَ۪ل۪نَتَوَهَّم سَطحاً ما خارِجاً عَلى اَل۪ضِلع اَلَّذي يُماسّ اَل۪أَرض قائِماً عَلى تِلكَ اَل۪أَرض فَ۪يَظهَر لَنا أَنَّ ذٰلِكَ اَل۪سَطح يَجوز عَلى مِحوَر اَل۪أُسطُوانَة وَ۪يَقطَعُها بِ۪نِصفَين لِ۪أَنَّهُ إِذا كانَت دائِرَة ما يُماسُّها خَطّ وَ۪أُخرِجَ مِن عَلامَة اَل۪مُماسَّة خَطّ عَلى زاوِيَة قائِمَة فَ۪إِنَّ ذٰلِكَ اَل۪خَطّ يَقَع عَلى مَركَز اَل۪دائِرَة </s> |
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270 <s id="A18-1|23|06">وَ۪أَيضاً نُخرِج عَلى <pb n="63"></pb> ذٰلِكَ اَل۪ضِلع أَعني ضِلع اَل۪أُسطُوانَة سَطحاً آخَر قائِماً عَلى اَل۪أُفُق فَ۪إِنَّهُ لا يَكون اَل۪سَطح اَل۪مُخرَج اَل۪أَوَّل وَ۪يُقسَم اَل۪أُسطُوانَة بِ۪قِسمَين مُختَلِفَين يَكون أَصغَرُهُما مِمّا يَلي اَل۪جِهَة اَل۪عُليا وَ۪أَعظَمُهُما مِمّا يَلي اَل۪جِهَة اَل۪سُفلى فَ۪يَقوا أَعظَمُهُما عَلى أَصغَرِهِما ذ كانَ أَعظَم مِنهُ فَ۪تَدَحرَجَ اَل۪أُسطُوانَة</s> |
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271 <s id="A18-1|23|07"> فَ۪اِن تَوَهَّمنا في اَل۪جِهَة اَل۪أُخرا مِن اَل۪سَطح اَل۪مُخرَج اَل۪قائِم عَلى اَل۪أُفُق أَنَّهُ قَد نُقِصَ مِن اَل۪قِسم اَل۪أَعظَم قَدر زِيادَتِهِ عَلى اَل۪قِسم اَل۪أَصغَر فَ۪إِنَّ اَل۪قِسمَين يَعتَدِلان فَ۪يَكون ثِقل جَميعِهِما ثابِتاً عَلى ذٰلِكَ اَل۪ضِلع اَل۪مُماسّ لِ۪ل۪أَرض فَ۪لا يَميل إِلى جِهَة مِن اَل۪جِهات أَعني لا إِلى ما يَلي اَل۪عُلُوّ وَ۪لا ما يَلي اَل۪سُفل </s> |
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272 <s id="A18-1|23|08">فَ۪نَحتاج حَينَئِذٍ إِلى قُوَّة مُعادِلَة لَهُ تُقاوِمُهُ فَ۪إِذا زيدَ عَلى تِلكَ اَل۪قُوَّة زِيادَة ما يَسيرَة قَوِيَت عَلى اَل۪ثِقل</s> |
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273 </p> |
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274 <p n="24"> |
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275 <s id="A18-1|24|00"></s> |
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276 <s id="A18-1|24|01">وَ۪قَد أَرى أَنَّهُ يَجِب بِ۪إِضطِرار اَن نُخَبِّر مُتَعَلِّمي صِناعات اَل۪حِيَل ماذا اَل۪مَيل وَ۪ما مَركَز اَل۪ثِقل في جِسم كانَ ذٰلِكَ أَو في غَير جِسم</s> |
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277 <s id="A18-1|24|02">وَ۪أَمّا اِن يَكون اَل۪مَيل وَ۪اَل۪إِنحِراف لا يُقال بِ۪اَل۪إِستِحقاق إِلّا في اَل۪أَجسام فَ۪إِنَّ ذٰلِكَ لَيسَ يَدفَعُهُ أَحَد </s> |
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278 <s id="A18-1|24|03">ٓفَ۪اِن قُلنا في اَل۪أَشكال اَل۪مِساحِيَّة اَل۪مُجَسَّمَة وَ۪اَل۪سُطوحِيَّة أَنَّ مَركَز اَل۪مَيل وَ۪مَركَز اَل۪ثِقل عَلامَة ما فَ۪إِنَّ دالِكَ قَد أَوضَحَهُ ٓأَرشِميدِس بِما فيهِ كِفايَةۥ </s> |
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279 <s id="A18-1|24|04">فَ۪يَنبَغي اَن يُفهَم هٰذا عَلى ما هُوَ ذا نُخَبِّر بِهِ إِنَّ ٓبوسِدونيوس اَلَّذي مِن أَصحاب اَل۪رِواق قَد حَدَّ مَركَز اَل۪مَيل وَ۪اَل۪ثِقل <pb n="65"></pb> بِ۪حَدّ طَبيعي فَ۪قالَ إِنَّ مَركَز اَل۪ثِقل أَو اَل۪مَيل هُوَ عَلامَة ما إِذا عُلِّقَ اَل۪ثِقل بِها كانَ مُنقَسِماً بِ۪قِسمَين مُتَساوِيَين</s> |
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280 <s id="A18-1|24|05">ٓفَ۪مِن أَجل ذٰلِكَ ٓأَرشِميدِس وَ۪مَن إِقتَدى بِهِ مِن أَهل صِناعَة اَل۪حِيَل مَيَّزوا هٰذا اَل۪قَول وَ۪فَصَلوا بَينَ اَل۪عِلاقَة وَ۪بَينَ مَركَز اَل۪مَيل </s> |
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281 <s id="A18-1|24|06">أَمّا اَل۪عِلاقَة فَ۪إِنَّها عَلامَة ما عَلى اَل۪جِسم أَو غَير اَل۪جِسم إِذا عُلِّقَ بِها اَل۪مُعَلَّق تَعادَلَت أَجزاؤُهُ أَعني بِ۪ذٰلِكَ اَن لا يَتَرَجَّح وَ۪لا يَميل</s> |
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282 <s id="A18-1|24|07">ٓفَ۪إِنَّ اَل۪مُعادَلَة هِيَ إِذا عادَلَ شَيء شَيئاً كَما قَد يَعرِض في اَل۪مَوازين إِذا كانَت مُضطَرِبَة مُوازِيَة لِ۪سَطح اَل۪أُفُق أَو سَطح ما كانَ مُوازِياً لَهُ كَما قالَ ٓأَرشِميدِس إِنَّ اَل۪أَثقال تَكون غَير مائِلَة عَلى خَطّ وَ۪عَلامَة </s> |
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283 <s id="A18-1|24|08">أَمّا عَلى خَطّ إِذا كانَ اَل۪ثِقل عَلى عَلامَتَين مِن ذٰلِكَ اَل۪خَطّ فَ۪لَم يَكُن يَميل اَل۪خَطّ وَ۪كانَ اَل۪سَطح اَل۪خارِج عَلى ذٰلِكَ اَل۪خَطّ اَل۪قائِم عَلى اَل۪أُفُق كَيفَ حُوِّلَ اَل۪خَطّ كانَ قائِماً فَ۪إِنَّهُ لا يَميلُ اَل۪ثِقل عَلى اَل۪خَطّ بَتَّة</s> |
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284 <s id="A18-1|24|09">فَ۪أَمّا إِذا قُلنا اَل۪ثِقل مائِل فَ۪إِنّا إِنَّما نُريد إِنحِطاطَهُ إِلى اَل۪سُفل أَي حَرَكَتَهُ إِلى ما يَلي اَل۪أَرض</s> |
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285 <s id="A18-1|24|10">وَ۪أَمّا اَل۪مُعادَلَة اَلَّتي تَكون عَلى اَل۪عَلامَة فَ۪إِنَّها قَد تَكون إِذا كانَ اَل۪ثِقل مُعَلَّقاً بِها وَ۪كانَ اَل۪جِسم في كُلّ حَرَكَة تَحَرَّكَ مُتَساوِيَة أَجزاؤُهُ بَعضُها بِ۪بَعض </s> |
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286 <s id="A18-1|24|11">وَ۪اَل۪ثِقل يُعادِل ثِقلاً آخَر إِذا كانَ عِندَ تَعليقِهِما عَلى عَلامَتَين مِن خَطّ مَقسوم بِ۪نِصفَين وَ۪عَلى اَل۪عَلامَة اَلَّتي قُسِمَ عَلَيها كانَ اَل۪خَطّ مُوازِياً لِ۪ل۪أُفُق بَعد اَن تَكون أَقدار اَل۪أَثقال بَعضِها إِلى بَعض <pb n="67"></pb> كَ۪قَدر أَبعادِها اَل۪مُبادَلَة مِن اَل۪عَلامات اَلَّتي هِيَ مُعَلَّقَة عَلَيها </s> |
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287 <s id="A18-1|24|12">أَمّا اِن تَكون اَل۪أَثقال اَل۪مُعَلَّقَة عَلى هٰذِهِ اَل۪جِهَة مُتَعادِلَة اَل۪مَيل فَ۪إِنَّ ٓأَرشِميدِس قَد بَيَّنَ ذٰلِكَ في كُتُبِهِ في اَل۪مُعادَلات في اَل۪أَشكال اَلَّتي تُستَعمَل فيها اَل۪أَمخال</s> |
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288 <s id="A18-1|24|13">وَ۪قَد يَعرِض لِ۪ل۪عِلاقات وَ۪اَل۪قَوائِم شَيء واحِد لِ۪أَنَّ اَل۪عِلاقَة وَ۪اَل۪قائِمَة بِ۪اَل۪قُوَّة هُما شَيء واحِد فَ۪إِنَّ اَل۪قَوائِم اَلَّتي يَتَعَلَّق فيها اَل۪ثِقل هِيَ اَلَّتي تَحمِل اَل۪ثِقل</s> |
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289 <s id="A18-1|24|14">وَ۪قَد يَعرِض اَن تَكون هٰذِهِ اَل۪قَوائِم كَثيرَة جِدّاً غَير مُتَناهِيَت اَل۪كَثرَة فَ۪أَمّا مَركَز اَل۪مَيل فَ۪إِنَّهُ في كُلّ واحِد مِن اَل۪أَجسام عَلامَة ما واحِدَة تَميلُ إِلَيها اَل۪قَوائِم اَلَّتي مِن اَل۪عِلاقات وَ۪قَد تَكون مَراكِز اَل۪مَيل في بَعض اَل۪أَجسام خارِجاً مِن جَواهِرِها كَما قَد يَعرِض في اَل۪حِنايات وَ۪اَل۪أَسوِرَ</s> |
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290 <s id="A18-1|24|15">أَمّا اِن تَكون خُطوط اَل۪عِلاقات تَجتَمِع إِلى نُقطَة واحِدَة مُشتَرَكَة لَها فَ۪إِنَّ ذٰلِكَ يَتَبَيّاً لَنا إِذا تَوَهَّمنا سَتحاً ما قائِماً عَلى اَل۪أُفُق وَ۪كانَ يَقطَع جِسماً ما بِ۪إِعتِدال فَ۪إِنَّهُ يَظهَر لَنا أَنَّ ذٰلِكَ اَل۪سَطح يُقسَم بِهِ اَل۪جِسم بِ۪نِصفَين فَ۪إِنَّهُ إِذاً يَنفُذ في اَل۪جِسم</s> |
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291 <s id="A18-1|24|16">فَ۪إِذا تَوَهَّمنا أَيضاً سَطحاً آخَر يَقطَع اَل۪جِسم مِثلَ ذٰلِكَ اَل۪سَطح فَ۪إِنَّهُ يَنفُذ فيهِ كَ۪نَفاذ هٰذا اَل۪سَطح وَ۪يَتَقاطَعان اَل۪سَطحان عَلى خَطّ فَ۪اِن وَقَعَ اَل۪تَقاطُع عَلى غَير اَل۪عِلاقَة عَرَضَ مِن ذٰلِكَ اَن تَكون اَل۪أَجسام مُتَعادِلَة وَ۪غَير مُتَعادِلَة</s> |
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292 <s id="A18-1|24|17">وَ۪ل۪نَنقُل اَل۪آن هٰذا اَل۪قَول إِلى اَل۪قَوائِم وَ۪نَتَوَهَّم جِسماً قائِماً عَلى خَطّ قائِم عَلى سَطح وَ۪ل۪يَكُن اَل۪جِسم مُعتَدِل اَل۪أَجزاء قائِماً <pb n="69"></pb> عَلى ذٰلِكَ اَل۪خَطّ فَ۪إِذا أُخرِجَ ذٰلِكَ اَل۪خَطّ فَ۪إِنَّهُ يَنفُذ في اَل۪جِسم </s> |
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293 <s id="A18-1|24|18">فَ۪اِن وَقَعَ اَل۪خَطّ اَل۪مُخرَج خارِج اَل۪جِسم فَ۪إِنَّ اَل۪سَطح اَل۪مُخرَج عَلَيهِ يَقَع أَيضاً خارِج اَل۪جِسم وَ۪ذٰلِكَ قَد ظَهَرَ أَنَّهُ غَير مُمكِن فَ۪إِذاً اَل۪خَطّ يَنفُذ في اَل۪جِسم وَ۪يُقَسِّمُهُ بِ۪قِسمَين مُعتَدِلَين</s> |
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294 <s id="A18-1|24|19">فَ۪اِن تَوَهَّمنا عَلامَة اَل۪إِعتِدال عَلامَة أُخرا أَيضاً غَير تِلكَ فَ۪إِنَّهُ قَد يَعرِض في ذٰلِكَ أَيضاً مِثلَ اَلَّذي عَرَضَ في اَل۪أَوَّل أَعني اَن يَكون اَل۪خَطّ اَل۪مُخرَج عَلى تِلكَ اَل۪عَلامَة يَنفُذ في وَسَط اَل۪جِسم فَ۪يَكون اَل۪خَطّان مُتَبايِنَين فَ۪إِذا أُخرِجَ عَلَيهِما سَطحان لَم يَتَقاطَعا فَ۪إِنَّهُ قَد يُمكِن اَن يُخرَج عَلى خَطَّين سَطحان لا يَتَقاطَعان فَ۪يَعرِض في هٰذا مِثلَ اَلَّذي عَرَضَ في اَل۪أَوَّل فَ۪يَكون هٰذا غَير مُمكِن </s> |
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295 <s id="A18-1|24|20">فَ۪مِن أَجل هٰذا نَعلَم أَنَّ اَل۪سُطوح تَتَقاطَع وَ۪اَل۪خُطوط تَتَلاقا فَ۪تَكون في سَطح واحِد فَ۪إِذا أُخرِجَ ذٰلِكَ اَل۪سَطح إِلى بَسيط اَل۪جِسم فَ۪إِنَّهُ يَفعَل خَطّاً عَلى عَلامات اَل۪تَقاطُع فَ۪تَكون عَلامَة ثالِثَة واقِعَة خارِجاً عَن هٰذا اَل۪خَطّ </s> |
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296 <s id="A18-1|24|21">وَ۪نَتَوَهَّم هٰذِهِ اَل۪عَلامَة عَلامَة اَل۪مُعادَلَة أَيضاً يَكون اَل۪جِسم مُعتَدِلاً عَلَيها وَ۪نُخرِج مِن اَل۪عَلامَة خَطّاً في وَسَط اَل۪جِسم فَ۪ل۪اَلَّذي تَقَدَّمَ مِن قَولِنا إِذا أُخرِجَ هٰذا اَل۪خَطّ يَقَع عَلى ذٰلِكَ اَل۪خَطَّين أَلَّذَين أُخرِجَ اَل۪سَطح عَلَيهِما وَ۪لا يَقَع عَلى عَلامَة أُخرا غَير عَلامَة تَلاقيهِما لِ۪أَنَّهُ إِذا لاقا خَطّا ما خَطَّين مُتَقاطِعَين وَ۪هُوَ في سَطح آخَر فَ۪إِنَّهُ يُلاقيهِما عَلى عَلامَة تَقاطُعِهِما فَ۪اِن لَم تَكُن <pb n="71"></pb> مُلاقاتُهُ لَهُما عَلى عَلامَة تَقاطُعِهِما يَجِب اَن يَكون بَعض اَل۪خَطّ في سَطح وَ۪باقيهِ في سَطح آخَر فَ۪إِذاً جَميع اَل۪خُطوط اَلَّتي لِ۪ل۪عِلاقَة تَجتَمِع إِلى عَلامَة واحِدَة وَ۪هِيَ اَلَّتي تُسَمّي مَركَز اَل۪مَيل وَ۪اَل۪ثِقل</s> |
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297 </p> |
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298 <p n="25"> |
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299 <s id="A18-1|25|00"></s> |
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300 <s id="A18-1|25|01">وَ۪قَد يَجِب بِ۪إِضطِرار اَن نوضِح شَيئاً في اَل۪كَبس وَ۪اَل۪نَقل وَ۪اَل۪حَمل عَلى جِهَة اَل۪كَمِّيَّة ما يَكون يُصلِح لِ۪ل۪مَدخَل </s> |
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301 <s id="A18-1|25|02">فَ۪إِنَّ ٓأَرشِميدِس قَد إِستَعمَلَ في هٰذا اَل۪جُزء صِناعَة مُتقَنَ في كِتابِهِ اَل۪مُسَمّى كِتاب اَل۪قَوائِم </s> |
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302 <s id="A18-1|25|03">وَ۪نَحنُ نَضَع ما نَحتاج إِلَيهِ مِنهُ في أَشياء آخَر وَ۪أَمّا اَل۪آن فَ۪إِنّا نَستَعمِل مِن ذٰلِكَ ما كانَ عَلى قَدر اَل۪كَمِّيَّة عَلى ما يَصلُح لِ۪ل۪مُتَعَلِّمين </s> |
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303 <s id="A18-1|25|04">وَ۪اَل۪جِهَة في ذٰلِكَ هِيَ هٰذِهِ</s> |
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304 <s id="A18-1|25|05">إِذا كانَت أَساطين كَم كانَت وَ۪كانَت عَلَيها عَوارِض أَو حائِط ما وَ۪كانَ مَوضوعاً عَلَيها وَضعاً مُتَساوِياً أَو كانَ مُختَلِف اَل۪وَضع عَلى أَطرافِها وَ۪كانَ زائِداً عَلى أَحَد اَل۪طَرَفَين أَو عَلى اَل۪طَرَفَين جَميعاً وَ۪كانَ اَل۪بُعد اَلَّذي بَينَ اَل۪أَساطين مُتَساوِياً أَو مُختَلِفاً فَ۪إِنّا نُريد اَن نَعرِف كَم يَنال كُلّ واحِد مِن اَل۪أَساطين مِن اَل۪ثِقل </s> |
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305 <s id="A18-1|25|06">مِثال ذٰلِكَ أَنَّهُ إِذا كانَت خَشَبَة طَويلَة مُجتَمِعَة اَل۪ثِقل وَ۪كانَ رِجال يَحمِلونَها مُتَساوِيين في طول اَل۪خَشَبَة وَ۪في أَطرافِها وَ۪يَكون أَحَد أَطرافِها فاضِلاً أَو جَميعُها فَ۪إِنّا نُريد اَن نَعرِف كُلّ واحِد مِن اَل۪رِجال كَم يَنالُهُ مِن اَل۪ثِقل فَ۪إِنَّ اَل۪مَطلوب في جَميعِها واحِد</s> |
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306 </p> |
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307 <p n="26"> |
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308 <s id="A18-1|26|00"></s> |
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309 <s id="A18-1|26|01"><pb n="73"></pb> فَ۪ل۪يَكُن ثِقل مُساوي اَل۪ثُخن مُتَساوي اَل۪أَجزاء عَلى اَل۪أَساطين وَ۪هُوَ ٓآب </s> |
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310 <s id="A18-1|26|02">وَ۪ل۪يَكُن مَوضوعاً عَلى أُسطُوانَتَين وَ۪هُما ٓآغ ٓبٓد فَ۪تَكون كُلّ واحِدَة مِن أُسطُوانَتَي ٓآغ ٓبٓد يَنالُها نِصف ثِقل ٓآب </s> |
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311 <s id="A18-1|26|03">فَ۪ل۪تَكُن أَيضاً أُسطُوانَة أُخرا وَ۪هِيَ ٓeٓز وَ۪تَفصِل بُعد ٓآب كَيفَ ما وَقَعَ فَ۪نُريد اَن نَعرِف كُلّ واحِدَة مِن أَساطين ٓآغ ٓeٓز ٓبٓد كَم يَنالُها مِن اَل۪ثِقل </s> |
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312 <s id="A18-1|26|04">فَ۪ل۪نَتَوَهَّم ثِقل ٓآب مَقسوماً عَلى عَلامَة ٓe قِسمَة عَلى خَطّ قائِم عَلى أُسطُوانَة فَ۪يَظهَر لَنا أَنَّ جِهَة ٓآe يَنال كُلّ واحِدَة مِن أُسطُوانَتَي ٓآغ ٓeٓز نِصف ثِقلِها وَ۪جِهَة ٓeٓب يَنال كُلّ واحِدَة مِن أُسطُوانَتَي ٓeٓز ٓبٓد نِصف ثِقلِها لِ۪أَنَّهُ لا يَكون إِختِلاف فيما يُنال اَل۪أَساطين إِذا كانَ اَل۪مَوضوع عَلَيها مُتَّصِلاً أَو كانَ مُنفَصِلاً لِ۪أَنَّهُ مُتَّصِلاً كانَ أَو مُنفَصِلاً فَ۪إِنَّ جَميعَهُ عَلى اَل۪أُسطُوانَة </s> |
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313 <s id="A18-1|26|05">فَ۪إِذاً أُسطُوانَة ٓeٓز يَنالُها نِصف ثِقل ٓeٓب وَ۪نِصف ثِقل ٓآe أَعني نِصف جَميع ثِقل ٓآب وَ۪أُسطُوانَة ٓآغ يَنالُها نِصف ثِقل ٓآe وَ۪أُسطُوانَة ٓبٓد يَنالُها نِصف ثِقل ٓeٓب </s> |
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314 <s id="A18-1|26|06">فَ۪اِن قَسَّمنا نِصف ٓآب عَلى نِسبَة بُعد ٓآe إِلى بُعد ٓeٓب فَ۪إِنَّ ثِقل اَل۪قِسم اَل۪مُشابِه لِ۪نِسبَة ٓآe يَنال ٓآغ وَ۪اَل۪ثِقل اَل۪مُناسِب لِ۪بُعد ٓeٓب يَنال ٓبٓد </s> |
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315 <s id="A18-1|26|07">وَ۪أَيضاً فَ۪ل۪نَضَع أُسطُوانَة أُخرا وَ۪هِيَ ٓهٓت فَ۪يَظهَر لَنا أَنَّ ٓآغ يَنالُها نِصف ٓآe وَ۪ٓبٓد يَنالُها نِصف ٓهٓب وَ۪ٓeٓز يَنالُها نِصف <pb n="75"></pb> ٓآه وَ۪ٓهٓت يَنالُها نِصف ٓeٓب </s> |
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316 <s id="A18-1|26|08">وَ۪نِصف ٓآe وَ۪نِصف ٓهٓب وَ۪نِصف ٓآه وَ۪نِصف ٓeٓب هُوَ جَميع ٓآب وَ۪هُوَ اَل۪مَوضوع عَلى جَميع اَل۪أَساطين </s> |
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317 <s id="A18-1|26|09">وَ۪اِن كانَت اَل۪أَساطين أَكثَر فَ۪إِنّا بِ۪هٰذا اَل۪عَمَل نَعرِف كَم يَنال كُلّ واحِدَة مِنها مِن اَل۪ثِقل </s> |
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318 </p> |
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319 <p n="27"> |
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320 <s id="A18-1|27|00"></s> |
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321 <s id="A18-1|27|01">وَ۪إِذا كانَ هٰذا هَكَذا فَ۪ل۪نَفرِض قَوائِم ٓآب ٓغٓد مُتَساوِيَة اَل۪وَضع </s> |
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322 <s id="A18-1|27|02">وَ۪ل۪يَكُن عَلَيها جِسم ما مُتَساوي اَل۪عُظم وَ۪اَل۪ثِقل وَ۪هُوَ ٓآغ </s> |
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323 <s id="A18-1|27|03">وَ۪قَد كُنّا قُلنا أَنَّ كُلّ واحِدَة مِن قائِمَتَي ٓآب ٓغٓد يَنالُها نِصف ثِقل ٓآغ </s> |
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324 <s id="A18-1|27|04">فَ۪ل۪نَنقُل قائِمَة ٓغٓد وَ۪نُقَرِّبُهُ إِلى ٓآب وَ۪ل۪يَكُن مَوضِع ٓeٓز وَ۪نُريد اَن نَعلَم أَيضاً أَيّ شَيء يَنال ٓآب ٓeٓز مِن اَل۪ثِقل </s> |
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325 <s id="A18-1|27|05">فَ۪نَقول إِنَّ بُعد ٓآe إِمّا اَن يَكون مُساوِياً لِ۪بُعد ٓeٓغ وَ۪إِمّا اَن يَكون أَصغَر مِنهُ وَ۪إِمّا اَن يَكون أَعظَم مِنهُ </s> |
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326 <s id="A18-1|27|06">فَ۪ل۪يَكُن أَوَّلاً مُساوِياً لَهُ فَ۪يَظهَر لَنا أَنَّ ثِقل ٓآe يُعادِل ثِقل ٓeٓغ </s> |
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327 <s id="A18-1|27|07">فَ۪اِن نَحنُ أَخرَجنا قائِمَة ٓآب يُقيم ثِقل ٓآغ ثابِتاً عَلى حالِهِ فَ۪يَظهَر لَنا أَنَّ قائِمَة ٓآب لَم يَكُن يَنالُها مِن اَل۪ثِقل شَيء وَ۪إِنَّما كانَ ثِقل ٓآغ عَلى ٓeٓز وَحدَها </s> |
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328 <s id="A18-1|27|08">فَ۪اِن كانَ بُعد ٓغٓe أَعظَم مِن بُعد ٓeٓا فَ۪إِنَّ ثِقل ٓآغ يَنحِطّ إِلى ما يَلي ٓغ </s> |
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329 <s id="A18-1|27|09">فَ۪ل۪يَكُن بُعد ٓeٓغ أَصغَر مِن بُعد ٓeٓا وَ۪ل۪يَكُن ٓغٓe مُساوِياً لِ۪ٓeٓه فَ۪إِذاً ٓغٓه يَكون مُعتَدِلاً عَلى ٓeٓز وَحدَها </s> |
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330 <s id="A18-1|27|10">وَ۪ل۪نَضَع رُكناً ما عَلى ٓهٓت فَ۪اِن تَوَهَّمنا أَنَّ جَميع اَل۪ثِقل قَد فُصِلَت عَلى عَلامَة ٓه فَ۪إِنَّ <pb n="77"></pb> ٓهٓغ يَكون ثابِتاً عَلى ٓeٓز وَحدَها وَ۪يَكون نِصف ٓآه عَلى كُلّ واحِدَة مِن قائِمَتَي ٓآب ٓهٓت </s> |
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331 <s id="A18-1|27|11">فَ۪إِذا نَقَّصنا قائِمَة ٓهٓت تَكون لِ۪عَلامَة ٓه قُوَّة اَل۪قائِمَة بَعدَ اَن يَكون اَل۪جِسم مُلتَحِماً فَ۪تَكون ٓآب يَنالُها نِصف ثِقل ٓهٓا وَ۪ٓeٓز يَنالُها اَل۪باقي أَعني ٓغٓه وَ۪نِصف ٓآه أَعني إِذا تَوَهَّمنا ٓآغ مَفصولاً بِ۪نِصفَين عَلى عَلامَة ٓك يَكون ٓكٓe نِصف ٓآه </s> |
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332 <s id="A18-1|27|12">فَ۪إِذا كانَت اَل۪قائِمَة اَلَّتي كانَت أَوَّلاً عِندَ ٓe تَحتَ عَلامَة ٓك فَ۪إِنَّهُ يَنالُها ثِقل جَميع ٓآغ </s> |
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333 <s id="A18-1|27|13">وَ۪كُلَّما تَباعَدَت اَل۪قائِمَة مِن اَل۪فَصل اَلَّذي يَقسِم اَل۪ثِقل بِ۪نِصفَين فَ۪إِنَّ بِ۪ذٰلِكَ اَل۪قَدر يَنال ٓآب مِن اَل۪ثِقل وَ۪يَكون باقي اَل۪ثِقل عَلى اَل۪قائِمَة اَل۪أُخرا </s> |
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334 </p> |
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335 <p n="28"> |
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336 <s id="A18-1|28|00"></s> |
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337 <s id="A18-1|28|01">وَ۪إِذا كانَ هٰذا هَكَذا فَ۪ل۪نَفرِض قائِمَتَين هُما ٓآب ٓeٓز مَوضوعَة اَل۪وَضع اَلَّذي ذَكَرناهُ قَبلَ هٰذا وَ۪ل۪يَكُن ثِقل ٓeٓغ فاضِلاً </s> |
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338 <s id="A18-1|28|02">وَ۪ل۪نُقَسِّم ٓآغ بِ۪نِصفَين عَلى عَلامَة ٓك فَ۪قَد بَيَّنّا أَنَّ قائِمَة ٓآب يَنالُها ثِقل ٓكٓe وَ۪قائِمَة ٓeٓز يَنالُها باقي ثِقل ٓآغ </s> |
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339 <s id="A18-1|28|03">وَ۪ل۪نَفرِض تَحتَ عَلامَة ٓغ قائِمَة وَ۪هِيَ قائِمَة ٓغٓد فَ۪يَتَبَيّاً أَيضاً أَنَّ قائِمَة ٓآب يَنالُها نِصف ثِقل ٓeٓا وَ۪قائِمَة ٓدٓغ يَنالُها نِصف ثِقل ٓeٓغ وَ۪قائِمَة ٓeٓز يَنالُها نِصف ثِقل ٓآغ </s> |
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340 <s id="A18-1|28|04">وَ۪مِن قَبلَ اَن نَضَع قائِمَة ٓغٓد بَيَّنّا كَم يَنال كُلّ واحِدَة مِن ٓآب ٓeٓز مِن اَل۪ثِقل </s> |
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341 <s id="A18-1|28|05">فَ۪ظاهِر لَنا أَنَّ قائِمَة ٓغٓد لَمّا اَن صيرَت تَحتَ <pb n="79"></pb> اَل۪ثِقل صارَ اَلَّذي يَنال قائِمَة ٓآب مِن اَل۪ثِقل أَكثَر مِمّا كانَ يَنالُها قَبلَ ذٰلِكَ بِ۪قَدر نِصف ٓeٓه أَعني بِ۪قَدر نِصف ٓeٓغ وَ۪صارَ اَلَّذي يَنال ٓeٓز أَقَلّ مِمّا كانَ يَنالُها أَوَّلاً بِ۪قَدر ٓeٓغ </s> |
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342 <s id="A18-1|28|06">فَ۪يَكون اَلَّذي يَنال ٓدٓغ مِن اَل۪ثِقل عَلى هٰذا اَل۪قَول نِصف ٓeٓغ لِ۪أَنَّ اَل۪قائِمَة اَلَّتي زيدَت تَحتَ اَل۪ثِقل نَقَّصَت مِمّا يَنال ٓeٓز قَدراً مُساوِياً لِ۪ثِقل ٓeٓغ وَ۪زادَت عَلى قائِمَة ٓآب ثِقلاً مُساوِياً لِ۪نِصف ٓeٓغ فَ۪تَكون ٓغٓد يَنالُها نِصف ثِقل ٓeٓغ اَل۪باقي </s> |
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343 <s id="A18-1|28|07">وَ۪قَد كانَ هٰذا اَل۪مِقدار يَنالُها عَلى اَل۪عَمَل اَل۪آخَر </s> |
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344 <s id="A18-1|28|08">فَ۪مِن هاهُنا يَظهَر لَنا أَنَّهُ إِذا كانَ ثِقل ما عَلى قَوائِم تَحمِلُهُ وَ۪زيدَ عَلى تِلكَ اَل۪قَوائِم قائِمَة أُخرا فَ۪إِنَّ إِحدا اَل۪قَوائِم اَل۪ولا اَلَّتي هِيَ اَل۪ولا يَنالُها مِن اَل۪ثِقل أَكثَر مِمّا كانَ يَنالُها قَبلَ اَل۪زِيادَة وَ۪اَل۪قائِمَة اَل۪أُخرا يَنالُها مِن اَل۪ثِقل أَقَلّ مِمّا كانَ يَنالُها قَبلَ اَل۪زِيادَة </s> |
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345 <s id="A18-1|28|09">وَ۪مِن أَجل أَنَّهُ لَمّا كانَت اَل۪قَوائِم ٓآب ٓeٓز ٓغٓد كانَ اَلَّذي يَنال ٓآب نِصف ٓآe وَ۪لَمّا نُقِصَ ٓغٓد كانَ اَلَّذي يَنال ٓآب نِصف ثِقل ٓآه ظَهَرَ لَنا أَنَّ ٓeٓغ لَمّا اِن تَعَلَّقَ صارَ في هَيئَة مُخل فَ۪حَمَلَ بَعض اَل۪ثِقل اَلَّذي كانَ عَلى ٓآب وَ۪زادَ عَلى ٓeٓز أَكثَر مِمّا كانَ عَلَيها مِن اَل۪ثِقل أَوَّلاً وَ۪ثِقل ٓآغ ثابِت في مَكانِهِ</s> |
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346 </p> |
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347 <p n="29"> |
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348 <s id="A18-1|29|00"></s> |
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349 <s id="A18-1|29|01">فَ۪أَمّا إِنَّهُ لا يُمكِن اَن تُحَرِّك اَل۪قُوى اَل۪يَسيرَة أَثقالاً عِظاماً بِ۪لا حيلَة تُستَعمَل فيها فَ۪إِنَّ ذٰلِكَ قَد تَبَيَّنَ مِن <pb n="81"></pb> اَل۪أَشياء اَل۪ظاهِرَة فَ۪إِنَّ اَل۪رَجُلَين يُحَرِّكان ثِقلاً ما بِ۪سُهولَة لا يُحَرِّكُهُ اَل۪رَجُل اَل۪واحِد وَ۪لَو إِستَعمَلَ قُوَّتَهُ كُلَّها</s> |
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350 <s id="A18-1|29|02">فَ۪يَظهَر لَنا أَنَّ اَل۪ثِقل إِنَّما تَحَرَّكَ لَمّا زيدَت قُوَّة اَل۪رَجُل اَل۪ثاني </s> |
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351 <s id="A18-1|29|03">فَ۪أَمّا إِنَّ اَل۪رَجُل اَل۪ثاني وَحدَهُ لا يُحَرِّك اَل۪ثِقل فَ۪إِنَّ ذٰلِكَ ظاهِر لِ۪أَنَّهُ اِن سَخا اَل۪رَجُل اَل۪أَوَّل وَ۪تَرَكَهُ عَلى اَل۪ثاني وَحدِهِ لَم يُحَرِّكهُ </s> |
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352 <s id="A18-1|29|04">فَ۪اِن قُسِمَ اَل۪ثِقل بِ۪نِصفَين فَ۪إِنَّ اَل۪رَجُل اَل۪أَوَّل وَحدَهُ يُحَرِّك نِصف اَل۪ثِقل وَ۪يَبقى اَل۪نِصف اَل۪آخَر ثابِتاً </s> |
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353 <s id="A18-1|29|05">فَ۪يَظهَر لَنا أَنَّ اَل۪نِصف اَلَّذي حَرَّكَهُ اَل۪رَجُل اَل۪واحِد كانَ يَجتَبِذُهُ اَل۪نِصف اَل۪آخَر قَبلَ اَن يُفصَل مِنهُ </s> |
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354 <s id="A18-1|29|06">وَ۪كَ۪ذٰلِكَ أَيضاً إِذا كانَت قُوى كَثيرَة تُحَرِّك ثِقلاً ما وَ۪نُقِصَ مِن تِلكَ اَل۪قُوى قُوَّة واحِدَة فَ۪إِنَّ جَميع اَل۪قُوى بَعدَ اَن نُنَقِّص اَل۪قُوَّة اَل۪واحِدَة لا تُحَرِّك اَل۪ثِقل </s> |
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355 <s id="A18-1|29|07">فَ۪اِن إِبتَدَأَت اَل۪قُوَّة اَل۪مُجتَمِعَة اَن تُقِلّ ذٰلِكَ اَل۪ثِقل فَ۪إِنَّ عِندَ زِيادَة اَل۪قُوَّة اَل۪مَفروضَة اَل۪باقِيَة يَتَحَرَّك اَل۪ثِقل حَرَكَة سَهلَة </s> |
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356 <s id="A18-1|29|08">وَ۪قَد يَظهَر لَنا ذٰلِكَ أَيضاً في اَل۪ضَرَبات لِ۪أَنَّ اَل۪شَيء اَلَّذي يَتَهَشَّم بِ۪اَل۪ضَرَبات اَل۪كَثيرَة إِذا زيدَت عَلَيهِ ضَربَة واحِدَة رَضَّتهُ لَيسَ بِ۪إِجتِماع تِلكَ فَقَط لَكِنَ بِها أَيضاً وَحدِها </s> |
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357 <s id="A18-1|29|09">وَ۪ذٰلِكَ قَد يَظهَر في اَل۪مَحسوسات لِ۪أَنَّهُ إِذا كُنّا نَحمِل ثِقلاً ما وَ۪كانَ في ثِقلِهِ ما نَقوى عَلَيهِ لَكِنَ بَعدَ تَعب وَ۪أَلَم فَ۪يَظهَر لَنا أَنَّ قُوَّتَنا قَدر ذٰلِكَ اَل۪ثِقل </s> |
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358 </p> |
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359 <p n="30"> |
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360 <s id="A18-1|30|00"></s> |
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361 <s id="A18-1|30|01">فَ۪ل۪نَفرِض قَوائِم ٓآب ٓغٓد وَ۪عَلَيها جِسم ما مُتَساوي اَل۪ثِقل وَ۪اَل۪ثُخن وَ۪هُوَ ٓeٓز وَ۪ل۪يَكُن عَلى كُلّ واحِدَة مِن اَل۪قَوائِم <pb n="83"></pb> فاضِلاً </s> |
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362 <s id="A18-1|30|02">وَ۪نُريد اَن۪نَعلَم كُلّ واحِدَة مِن اَل۪قَوائِم كَم يَنالُها مِن اَل۪ثِقل </s> |
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363 <s id="A18-1|30|03">لِ۪أَنّا قَد بَيَّنّا أَنَّهُ إِذا كانَ ثِقل ٓآز مَوضوعاً عَلى ٓغٓد ٓآب فَ۪إِنَّ ٓغٓد يَنالُها مِن اَل۪ثِقل أَكثَر مِن ٓآب بِ۪قَدر ضِعف ٓغٓز وَ۪إِذا كانَ ٓغٓe مَوضوعاً عَلى ٓغٓد ٓآب فَ۪إِنَّ ٓآب يَنالُها مِن اَل۪ثِقل أَكثَر مِن ٓغٓد بِ۪قَدر ضِعف ٓآe فَ۪يَظهَر لَنا أَنَّ ٓغٓد يَنالُها مِن اَل۪ثِقل أَكثَر مِمّا يَنال ٓآب بِ۪قَدر زِيادَة ضِعف ٓغٓز عَلى ضِعف ٓآe </s> |
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364 <s id="A18-1|30|04">فَ۪اِن كانَ ٓغٓز ٓeٓا مُتَساوِيَين فَ۪إِنَّ اَلَّذي يَنال كُلّ واحِدَة مِن ٓغٓد ٓآب مِن اَل۪ثِقل مُتَساوٍ </s> |
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365 <s id="A18-1|30|05">فَ۪بِ۪اَل۪قَدر اَلَّذي يَكون اَل۪بُعد أَعظَم بِ۪ذٰلِكَ اَل۪قَدر يَنال تِلكَ اَل۪قائِمَة مِن زِيادَة اَل۪ثِقل</s> |
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366 <s id="A18-1|30|06">وَ۪مِمّا تَقَدَّمَ مِن قَولِنا يَظهَر لَنا أَنَّهُ إِذا كانَ عَلى أَساطين أَو قَوائِم عَوارِض أَو حائِط مُتَساوي اَل۪ثُخن وَ۪اَل۪ثِقل وَ۪كانَت اَل۪أَبعاد اَلَّتي بَينَها مُختَلِفَة كَيفَ كانَت فَ۪إِنَّهُ قَد يُمكِنُنا اَن نَعلَم أَيُّما مِن اَل۪قَوائِم يَنالُها ثِقل أَعظَم وَ۪كَم زِيادَة اَل۪ثِقل </s> |
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367 <s id="A18-1|30|07">فَ۪اِن كانَ عَلى اَل۪قَوائِم عَوارِض أَو غَير ذٰلِكَ فَ۪إِنَّهُ يَظهَر لَنا أَيضاً بِ۪هٰذا اَل۪عَمَل </s> |
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368 <s id="A18-1|30|08">وَ۪كَ۪ذٰلِكَ أَيضاً إِذا كانَ عود أَو حَجَر يَحمِلُهُ إِناس عَلى أَعضادِهِم أَو عَلى وَهق وَ۪كانَ بَعضُهُم في وَسَطِهِ وَ۪بَعضُهُم في طَرَفِهِ وَ۪اِن كانَ اَل۪ثِقل فاضِلاً مِن جِهَة واحِدَة أَو مِن جِهَتَين فَ۪إِنَّهُ قَد يَظهَر لَنا كَم يَنال كُلّ واحِد مِن اَل۪حامِلين مِن اَل۪ثِقل</s> |
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369 </p> |
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370 <p n="31"> |
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371 <s id="A18-1|31|00"></s> |
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372 <s id="A18-1|31|01"><pb n="85"></pb> وَ۪ل۪يَكُن ثِقل ما آخَر أَيضاً مُتَساوي اَل۪أَجزاء وَ۪اَل۪ثِقل وَ۪هُوَ ٓآب وَ۪ل۪يَكُن عَلى قَوائِم مُتَساوِيَة اَل۪وَضع هُما ٓآغ ٓبٓد </s> |
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373 <s id="A18-1|31|02">فَ۪يَظهَر لَنا أَنَّ كُلّ واحِدَة مِن اَل۪قَوائِم يَنالُها نِصف ثِقل ٓآب</s> |
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374 <s id="A18-1|31|03">فَ۪ل۪نُعَلِّق ثِقلاً عَلى ٓآب مِن عَلامَة ٓe </s> |
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375 <s id="A18-1|31|04">فَ۪اِن كانَت عَلامَة ٓe تَفصِل ٓآب بِ۪نِصفَين فَ۪يَظهَر لَنا أَنَّ كُلّ واحِدَة مِن اَل۪قَوائِم يَنالُها نِصف ثِقل ٓآب وَ۪نِصف اَل۪ثِقل اَل۪مُعَلَّق عَلى عَلامَة ٓe أَو اَل۪مَوضوع عَلَيها </s> |
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376 <s id="A18-1|31|05">فَ۪اِن لَم تَكُن عَلامَة ٓe تَفصِلُهُ بِ۪نِصفَين وَ۪فُصِلَ اَل۪ثِقل بِ۪قِسمَين عَلى نِسبَة ٓبٓe إِلى ٓآe فَ۪إِنَّ ثِقل اَل۪جُزء اَل۪مُناسِب ٓeٓب يَنال ٓآغ وَ۪ثِقل اَل۪جُزء اَل۪مُناسِب ٓeٓا يَنال ٓبٓد وَ۪أَيضاً كُلّ واحِدَة مِن اَل۪قَوائِم يَنالُها نِصف ٓآب </s> |
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377 <s id="A18-1|31|06">فَ۪اِن عَلَّقنا ثِقلاً آخَر عَلى عَلامَة ٓز وَ۪قَسَّمناهُ بِ۪نِسبَة ٓآز إِلى ٓزٓب فَ۪إِنَّ ٓدٓب يَنالُها ثِقل اَل۪جُزء اَل۪مُناسِب ٓآز وَ۪ٓآغ يَنالُها ثِقل اَل۪جُزء اَل۪مُناسِب ٓزٓب فَ۪يَنال كُلّ واحِدَة مِن اَل۪قَوائِم نِصف ٓآب </s> |
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378 <s id="A18-1|31|07">وَ۪ٓزٓب عِندَ ٓآغ مَلفوظ </s> |
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379 <s id="A18-1|31|08">وَ۪قَد كانَت اَل۪أَثقال اَلَّتي يَنالُها قَبلَ اَن تُعَلَّق اَل۪أَثقال اَلَّتي عُلِّقَت عَلى ٓزٓe مَلفوظَة </s> |
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380 <s id="A18-1|31|09">فَ۪إِذاً جَميع اَلَّذي يَنال قائِمَتَي ٓآغ ٓبٓد مَلفوظ </s> |
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381 <s id="A18-1|31|10">وَ۪أَيضاً اِن عُلِّقَت أَثقال اُخَر فَ۪بِ۪هٰذا اَل۪عَمَل تَخرُج لَنا مَعرِفَة كَم يَنال كُلّ واحِدَة مِنها مِن اَل۪ثِقل</s> |
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382 </p> |
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383 <p n="32"> |
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384 <s id="A18-1|32|00"></s> |
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385 <s id="A18-1|32|01">وَ۪قَد تَوَهَّمَ قَوم في اَل۪مَوازين أَنَّهُ إِذا عادَلَت اَل۪أَثقال اَل۪أَثقال فَ۪إِنَّ تِلكَ اَل۪نِسبَة تَكون لِ۪ل۪أَثقال إِلى اَل۪أَبعاد <pb n="87"></pb> بِ۪إِنقِلاب </s> |
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386 <s id="A18-1|32|02">وَ۪قَد يَنبَغي اَن لا يُقال هٰذا قَولاً مُرسَلاً بَل۪يُمَيِّز تَمييزاً أَحساً </s> |
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387 <s id="A18-1|32|03">فَ۪ل۪نَفرِض عَمود ميزان مُتَساوي لِ۪ثِقل وَ۪اَل۪ثُخن وَ۪هُوَ ٓآب وَ۪ل۪تَكُن عِلاقَتُهُ اَلَّتي هِيَ عَلامَة ٓغ في وَسَط اَل۪عَمود </s> |
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388 <s id="A18-1|32|04">وَ۪ل۪يُعَلَّق عَلى عَلامات ما أَيّ عَلامات كانَت وَ۪هِيَ عَلامَتا ٓدٓe حِبال تَكون حَبلَي ٓدٓز ٓeٓه وَ۪ل۪نُعَلِّق عَلَيها ثِقلَين وَ۪ل۪يَكُن اَل۪ميزان بَعدَ تَعليق اَل۪ثِقل مُعتَدِلاً </s> |
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389 <s id="A18-1|32|05">وَ۪ل۪نَتَوَهَّم اَل۪حَبلَين مُخرَجَين عَلى عَلامَتَي ٓتٓك فَ۪يَكون عِندَ إِعتِدال اَل۪ميزان كَ۪بُعد ٓتٓغ عِندَ بُعد ٓغٓك كَ۪ذٰلِكَ ثِقل ٓه عِندَ ثِقل ٓز </s> |
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390 <s id="A18-1|32|06">فَ۪إِنَّ هٰذا قَد بَيَّنَهُ ٓأَرشِميدِس في كُتُبِهِ اَلَّتي تُسَمّي كُتُب اَل۪أَمخال </s> |
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391 <s id="A18-1|32|07">فَ۪اِن فَصَلنا مِن عَمود اَل۪ميزان ما يَلي اَل۪جِهَتَين جَميعاً أَعني ٓتٓا ٓكٓب فَ۪إِنَّ اَل۪ميزان لا يَعتَدِل </s> |
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392 </p> |
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393 <p n="33"> |
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394 <s id="A18-1|33|00"></s> |
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395 <s id="A18-1|33|01">وَ۪قَد ظَنَّ قَوم أَنَّ اَل۪مُناسَبَة اَلَّتي تَكون بِ۪اَل۪مُبادَلَة ۦۦۦ </s> |
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396 <s id="A18-1|33|02">فَ۪ل۪نَفرِض أَيضاً عَمود ميزان مُختَلِف اَل۪ثِقل وَ۪اَل۪ثُخن مِن أَيّ جِسم كانَ وَ۪ل۪يَكُن مُعتَدِلاً إِذا عُلِّقَ مِن عَلامَة ٓغ </s> |
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397 <s id="A18-1|33|03">وَ۪مَعنانا في هٰذا اَل۪مَوضِع في اَل۪إِعتِدال سُكون اَل۪عَمود وَ۪ثَباتُهُ وَ۪اِن كانَ مائِلاً إِلى جِهَة مِن اَل۪جِهات </s> |
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398 <s id="A18-1|33|04">ثُمَّ نُعَلِّق أَثقالاً ما عَلى عَلامات أَيّ عَلامات كانَت وَ۪هِيَ عَلامات <pb n="89"></pb> ٓدٓe وَ۪ل۪يَكُن أَيضاً بَعدَ تَعليق اَل۪أَثقال اَل۪عَمود مُعتَدِلاً </s> |
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399 <s id="A18-1|33|05">فَ۪قَد بَرهَنَ ٓأَرشِميدِس أَنَّ نِسبَة اَل۪ثِقل إِلى اَل۪ثِقل في هٰذا أَيضاً كَ۪نِسبَة اَل۪بُعد إِلى اَل۪بُعد بِ۪اَل۪مُبادَلَة </s> |
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400 <s id="A18-1|33|06">فَ۪أَمّا في اَل۪أَجسام غَير اَل۪مُرَتَّبَة اَل۪مائِلَة اَل۪بُعد فَ۪إِنَّهُ يَنبَغي اَن نَتَوَهَّم فيها هٰذا </s> |
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401 <s id="A18-1|33|07">نُخرِج اَل۪حَبل اَلَّذي مِن عَلامَة ٓغ إِلى ما يَلي عَلامَة ٓز </s> |
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402 <s id="A18-1|33|08">وَ۪نُخرِج خَطّاً وَ۪نَتَوَهَّم أَنَّهُ يَخرُج عَلى عَلامَة ٓز مُساوِياً لِ۪خَطّ ٓزٓهٓت وَ۪ل۪يَكُن ثابِتاً أَعني اَن يَكون عَلى زاوِيَة قائِمَة عَلى اَل۪حَبل </s> |
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403 <s id="A18-1|33|09">فَ۪إِذا كانَ اَل۪حَبلان اَلَّذان مِن عَلامَتَي ٓدٓe هَكَذا أَعني <pb n="91"></pb> حَبلَي ٓدٓه ٓتٓe فَ۪إِنَّ اَل۪بُعد اَلَّذي بَينَ خَطّ ٓغٓز وَ۪بَينَ اَل۪ثِقل اَلَّذي عِندَ عَلامَة ٓe أَعني ٓزٓت يَكون عِندَ سُكون اَل۪ميزان كَما ٓزٓه عِندَ ٓزٓت كَ۪ذٰلِكَ اَل۪ثِقل اَل۪مُعَلَّق عَلى عَلامَة ٓe عِندَ اَل۪ثِقل اَل۪مُعَلَّق عَلى عَلامَة ٓد فَ۪إِنَّ هٰذا قَد تَبَيَّنَ فيما تَقَدَّمَ</s> |
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404 </p> |
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405 <p n="34"> |
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406 <s id="A18-1|34|00"></s> |
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407 <s id="A18-1|34|01">فَ۪ل۪تَكُن فَلكَة أَو بَكرَة مُتَحَرِّكَة عَلى مِحوَر عَلى مَركَز ٓأَة وَ۪ل۪يَكُن قُطرُها خَطّ ٓبٓغ مُوازِياً لِ۪ل۪أُفُق </s> |
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408 <s id="A18-1|34|02">وَ۪ل۪نُعَلِّق عَلى عَلامَتَي ٓبٓغ حَبلَين وَ۪هُما ٓزٓد ٓغٓe وَ۪ل۪نُعَلِّق فيهِما أَثقالاً مُتَساوِيَة فَ۪يَظهَر لَنا أَنَّ اَل۪بَكرَة لا تَميل إِلى جِهَة مِن اَل۪جِهات لِ۪أَنَّ اَل۪ثِقلَين مُتَساوِيان وَ۪اَل۪بُعدان اَلَّذان مِن عَلامَة ٓأَة مُتَساوِيان </s> |
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409 <s id="A18-1|34|03">فَ۪ل۪يَكُن اَل۪ثِقل اَلَّذي عِندَ ٓد أَعظَم مِن اَل۪ثِقل اَلَّذي عِندَ ٓe فَ۪يَظهَر لَنا أَنَّ اَل۪فَلكَة تَميل إِلى جِهَة ٓب وَ۪تَنحِطّ عَلامَة ٓب مَعَ اَل۪ثِقل </s> |
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410 <s id="A18-1|34|04">فَ۪يَنبَغي لَنا اَن نَعلَم إِلى أَيّ مَوضِع إِذا إِنحَطَّ ثِقل ٓد اَل۪أَعظَم تَسكٌ </s> |
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411 <s id="A18-1|34|05">فَ۪ل۪نَحُطّ عَلامَة ٓب وَ۪نُصَيِّرُها عَلى عَلامَة ٓز وَ۪ل۪يَكُن حَبل ٓبٓد عَلى حَبل ٓزٓه فَ۪يَسكٌ اَل۪ثِقل </s> |
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412 <s id="A18-1|34|06">فَ۪يَظهَر لَنا أَنَّ حَبل ٓغٓe يَلتِفّ عَلى حافَّة اَل۪فَلكَة وَ۪يَكون مُعَلَّقاً عَلى اَل۪ثِقل عَلى عَلامَة ٓغ لِ۪أَنَّ ما كانَ مِنهُ مُلتَفّاً لَيسَ هُوَ مُتَعَلِّق </s> |
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413 <s id="A18-1|34|07">فَ۪نُخرِج ٓزٓه إِلى عَلامَة ٓت فَ۪مِن أَجل أَنَّ اَل۪ثِقلَين مُعتَدِلان تَكون نِسبَة اَل۪ثِقل إِلى اَل۪ثِقل كَ۪نِسبَة اَل۪بُعد اَلَّذي بَينَ <pb n="93"></pb> عِلاقَة ٓأَة وَ۪بَينَ اَل۪حِبال فَ۪يَكون كَما ٓآغ عِندَ ٓآت كَ۪ذٰلِكَ اَل۪ثِقل اَلَّذي عِندَ ٓه إِلى اَل۪ثِقل اَلَّذي عِندَ ٓe </s> |
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414 <s id="A18-1|34|08">فَ۪إِذا صَيَّرنا نِسبَة ٓغٓا إِلى ٓآت كَ۪نِسبَة اَل۪ثِقل إِلى اَل۪ثِقل وَ۪أَخرَجنا عَلامَتَي ٓبٓغ نَحوَ ٓزٓت عَلى زَوايا قائِمَة يَظهَر لَنا أَنَّ اَل۪فَلكَة تَحَرَّكَت مِن عَلامَة ٓب إِلى عَلامَة ٓز وَ۪تَسكُنوَ۪هٰذا اَل۪قَول أَيضاً في اَل۪أَثقال اَل۪اُخَر </s> |
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415 <s id="A18-1|34|09">فَ۪إِذاً قَد يُمكِن اَن يُعادِل كُلّ ثِقل ثِقلاً أَصغَر مِنهُ عَلى هٰذِهِ اَل۪جِهَة </s> |
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416 <s id="A18-1|34|10">أَمّا في أَوَّل اَل۪قَول مِن مَداخِل صِناعَة اَل۪حِيَل فَ۪يَكفي بِ۪هٰذا </s> |
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417 <s id="A18-1|34|11">وَ۪أَمّا في اَلَّذي يَتلوهُ فَ۪إِنّا نُخَبِّر عَن اَل۪خَمس قُوى اَلَّتي تُحَرَّك بِها اَل۪أَثقال وَ۪نَشرَح عِلَّتَها وَ۪اَل۪فِعل اَل۪طَبيعي فيها </s> |
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418 <s id="A18-1|34|12">وَ۪نُخَبِّر بِ۪أَشياء اُخَر تَكون كَثيرَة اَل۪مَنفَعَة في حَمل اَل۪أَثقال وَ۪رَفعِها </s> |
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419 <s id="A18-1|34|13">تَمَّت اَل۪مَقالَة اَل۪ولا مِن كِتاب ٓايرُن في رَفع اَل۪أَشياء اَل۪ثَقيلَة </s> |
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420 </p> |
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421 </chap> |
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422 <chap n="2"> |
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423 <p n="0"> |
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424 <s id="A18-2|00|00"></s> |
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425 <s id="A18-2|00|01"><pb n="95"></pb> اَل۪مَقالَة اَل۪ثانِيَة مِن كِتاب ٓايرُن في رَفع اَل۪أَشياء اَل۪ثَقيلَة</s> |
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426 </p> |
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427 <p n="1"> |
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428 <s id="A18-2|01|00"></s> |
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429 <s id="A18-2|01|01">إِنَّهُ لَمّا كانَت اَل۪قُوى اَلَّتي تُحَرَّك بِها اَل۪ثِقل اَل۪مَعلوم بِ۪اَل۪قُوَّة اَل۪مَعلومَة خَمساً يَجِب بِ۪إِضطِرار اَن نَضَع أَشكالَها وَ۪إِستِعمالاتَها وَ۪أَسماءَها لِ۪أَنَّ هٰذِهِ اَل۪قُوى مَنسوبَة إِلى طَبيعَة واحِدَة وَ۪هِيَ مُختَلِفَة في أَشكالِها إِختِلافاً كَثيراً</s> |
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430 <s id="A18-2|01|02">فَ۪أَمّا أَسماؤُها فَ۪هِيَ هٰذِهِۦ مِحوَر داخِل في فَلكَةۦ مُخلۦ بَكرَةۦ إِسفينۦ لَولَب</s> |
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431 <s id="A18-2|01|03">أَمّا اَل۪مِحوَر اَل۪مُرَكَّب في فَلكَة فَ۪إِنَّهُ يُعمَل عَلى هٰذِهِ اَل۪صَنعَة </s> |
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432 <s id="A18-2|01|04">يُؤخَذ عود صُلب مُرَبَّع في هَيئَة اَل۪خَشَبَة فَ۪تُمَلَّس أَطرافُهُ وَ۪يُدَوَّر وَ۪تُرَكَّب عَلَيها سَنغات مِن نُحاس مُهَندَمَة لا يَجوز غِلَظ اَل۪مِحوَر لِ۪تَكون إِذا رُكِّبَت في ثُقَب مُستَديرَة مُلَبَّسَة نُحاساً في رُكن ثابِت غَير مُتَحَرِّك تُدَوَّر تَدويراً سَهلاً</s> |
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433 <s id="A18-2|01|05">فَ۪هٰذا اَل۪عود إِذا عُمِلَ عَلى هٰذِهِ اَل۪صِفَة سُمِّيَ مِحوَراً </s> |
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434 <s id="A18-2|01|06">ثُمَّ نُرَكِّب في وَسَط اَل۪مِحوَر فَلكَة مَثقوبَة ثُقباً مُرَبَّعَة بِ۪قَدر وَسَط اَل۪مِحوَر مُهَندَمَة عَلى قَدر اَل۪مِحوَر لِ۪تَكُن إِذا رُكِّبَت اَل۪فَلكَة في اَل۪مِحوَر دارَت اَل۪فَلكَة <pb n="97"></pb> وَ۪اَل۪مِحوَر مَعاً</s> |
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435 <s id="A18-2|01|07">وَ۪هٰذِهِ اَل۪فَلَكَة تُسَمّي بِرِطرُكين وَ۪تَأويلُهُ اَل۪مُحيطَة </s> |
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436 <s id="A18-2|01|08">فَ۪إِذا فَعَلنا ذٰلِكَ فَرَّضنا في اَل۪مِحوَر عَن جَنبَي اَل۪فَلكَة فَرضاً مُتَعَكِّشاً لِ۪يَكون ذٰلِكَ اَل۪فَرض مِلَفَّة تَلتِفّ اَل۪قُلوس عَلَيها </s> |
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437 <s id="A18-2|01|09">وَ۪نَثقُب في ظاهِر اَل۪فَلكَة أَعني في مُحيطِها ثُقَباً تَكون في كَثرَتِها عَلى قَدر ما يَدعو اَل۪حاجَة إِلَيهِ وَ۪ل۪تَكُن مُهَندَمَة حَتّى تَكون إِذا رُكِّبَت فيها أَوتاد تَدور بِ۪تِلكَ اَل۪أَوتاد اَل۪فَلكَة وَ۪اَل۪مِحوَر</s> |
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438 <s id="A18-2|01|10">وَ۪قَد بَيَّنّا كَيفَ يَنبَغي اَن يُعمَل اَل۪مِحوَر فَ۪أَمّا اَل۪عَمَل بِهِ فَ۪اَل۪آن نَشرَحُهُ</s> |
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439 <s id="A18-2|01|11">إِذا أَرَدتَ اَن تُحَرِّك ثِقلاً عَظيماً بِ۪قُوَّة أَقَلّ مِنهُ تَشُدّ اَل۪قُلوس اَل۪مُرتَبِطَة في اَل۪ثِقل في اَل۪مَوضِع اَل۪مَفروض مِن اَل۪مِحوَر عَن جَنبَي اَل۪فَلكَة</s> |
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440 <s id="A18-2|01|12">ثُمَّ تُرَكِّب في اَل۪ثُقَب اَلَّتي ثَقَبنا في اَل۪فَلكَة أَوتاداً وَ۪تُكَبِّس اَل۪أَوتاد في جِهَة اَل۪إِنخِفاض حَتّى تُدير اَل۪فَلكَة فَ۪يَتَحَرَّك اَل۪ثِقل بِ۪قُوَّة يَسيرَة وَ۪تَلتِفّ اَل۪قُلوس عَلى اَل۪مِحوَر أَو نُرَكِّب بَعضَها بَعضاً لِ۪اَن لا تَلتِفّ جَميعاً عَلى اَل۪مِحوَر</s> |
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441 <s id="A18-2|01|13">فَ۪يَنبَغي اَن يَكون عُظم هٰذِهِ اَل۪آلَة عَلى قَدر عُظم اَل۪أَجسام اَلَّتي تُريد اَن تَنقُلَها بِها </s> |
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442 <s id="A18-2|01|14">وَ۪أَمّا تَقديرُها فَ۪يَنبَغي اَن يَكون عَلى قَدر نِسبَة اَل۪ثِقل اَلَّذي نُريد حَرَكَتَهُ إِلى اَل۪قُوَّة اَلَّتي تُحَرِّكُها وَ۪ذٰلِكَ سَنُبَيِّنُهُ فيما يَستَأنِف</s> |
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443 </p> |
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444 <p n="2"> |
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445 <s id="A18-2|02|00"></s> |
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446 <s id="A18-2|02|01">اَل۪قُوَّة اَل۪ثانِيَة</s> |
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447 <s id="A18-2|02|02">فَ۪أَمّا اَل۪قُوَّة اَل۪ثانِيَة فَ۪إِنَّها اَلَّتي تُدعي <pb n="99"></pb> اَل۪مُخل وَ۪لَعَلَّ هٰذِهِ اَل۪قُوَّة هِيَ أَوَّل ما فُكِرَ فيهِ في حَرَكَة اَل۪أَجسام اَل۪مُفرِطَة اَل۪ثِقل </s> |
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448 <s id="A18-2|02|03">لِ۪أَنَّ قَوماً لَمّا أَرادوا اَن يُحَرِّكوا جِسماً ثَقيلاً مُفرِط اَل۪ثِقل مِن أَجل أَنَّ أَوَّل ما إِحتاجوا إِلَيهِ في حَرَكَتِهِ اَن يُقِلّوهُ عَن اَل۪أَرض وَ۪لَم تَكُن لَهُم مَقابِض يَقبِضونَها مِنهُ لِ۪أَنَّ جَميع أَجزاء اَل۪قاعِدَة تَكون عَلى اَل۪أَرض إِحتاجوا إِلى اَن إِحتالوا في ذٰلِكَ فَ۪حَفَروا تَحتَ اَل۪جِسم اَل۪ثَقيل في اَل۪أَرض حَفراً يَسيراً وَ۪أَخَذوا عوداً طَويلاً فَ۪أَدخَلوا طَرَفَهُ في ذٰلِكَ اَل۪حَفر وَ۪كَبَّسوا اَل۪طَرَف اَل۪آخَر فَ۪أُستُقِلَّ اَل۪ثِقل </s> |
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449 <s id="A18-2|02|04">ثُمَّ وَضَعوا تَحتَ هٰذا اَل۪عود حَجَراً سَمّوهُ إِبومُخلِيّون وَ۪تَأويلُهُ اَل۪مَوضوع تَحتَ اَل۪مُخل وَ۪كَبَّسوهُ أَيضاً فَ۪أُستُقِلَّ اَل۪ثِقل أَكثَر </s> |
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450 <s id="A18-2|02|05">فَ۪لَمّا ظَهَرَت هٰذِهِ اَل۪قُوَّة عُلِمَت أَنَّهُ قَد يُمكِن اَن تُحَرَّك بِ۪هٰذِهِ اَل۪جِهَة أَثقال عَظيمَة </s> |
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451 <s id="A18-2|02|06">وَ۪هٰذا اَل۪عود يُسَمّي مُخلاً مُدَوَّراً كانَ أَو مُرَبَّعاً </s> |
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452 <s id="A18-2|02|07">وَ۪كُلَّما قُرِّبَ اَل۪حَجَر اَلَّذي يوضَع تَحتَهُ مِن اَل۪ثِقل اَلَّذي يُحَرَّك كانَ أَهوَن لِ۪حَرَكَتِهِ عَلى ما سَنُبَيِّنُهُ فيما يَستَأنِف</s> |
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453 </p> |
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454 <p n="3"> |
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455 <s id="A18-2|03|00"></s> |
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456 <s id="A18-2|03|01">اَل۪قُوَّة اَل۪ثالِثَة</s> |
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457 <s id="A18-2|03|02">فَ۪أَمّا اَل۪قُوَّة اَل۪ثالِثَة فَ۪إِنَّها اَلَّتي تُدعي اَل۪كَثيرَة اَل۪رَفع </s> |
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458 <s id="A18-2|03|03">فَ۪إِنّا إِذا أَرَدنا اَن نَرفَع ثِقلاً أَيّ ثِقل كانَ رَبَطنا اَل۪قُلوس في ذٰلِكَ اَل۪ثِقل وَ۪أَرَدنا اَن نَمُدّ اَل۪قُلوس حَتّى نَرفَعَهُ </s> |
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459 <s id="A18-2|03|04">وَ۪يُحتاج في ذٰلِكَ إِلى قُوَّة مُوازِيَة لِ۪ل۪ثِقل اَلَّذي نُريد اَن نَرفَعَهُ </s> |
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460 <s id="A18-2|03|05">فَ۪اِن نَحنُ حَلَّلنا اَل۪قُلوس مِن اَل۪حَمل وَ۪رَبَطنا أَحَد <pb n="101"></pb> طَرَفَيهِ في عارِضَة ثابِتَة وَ۪أَدخَلنا اَل۪طَرَف اَل۪آخَر في بَكرَة مَشدودَة في وَسَط اَل۪حَمل وَ۪مَدَّدنا اَل۪قُلوس كانَ تَحريكُنا لِ۪ذٰلِكَ اَل۪ثِقل أَسهَل </s> |
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461 <s id="A18-2|03|06">وَ۪اِن نَحنُ رَبَطنا في اَل۪عارِضَة اَل۪ثابِتَة بَكرَة أُخرا وَ۪أَدخَلنا طَرَف اَل۪قَلس فيها وَ۪مَدَّدناهُ كانَ تَحريكُنا لِ۪ذٰلِكَ اَل۪ثِقل أَكثَر سُهولَة </s> |
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462 <s id="A18-2|03|07">وَ۪أَيضاً اِن نَحنُ شَدَّدنا عَلى ذٰلِكَ اَل۪ثِقل بَكرَة أُخرا وَ۪أَدخَلنا طَرَف اَل۪حَبل فيها زادَنا ذٰلِكَ سُهولَة في حَرَكَة اَل۪ثِقل</s> |
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463 <s id="A18-2|03|08">وَ۪عَلى هٰذا اَل۪عَمَل كُلَّما زَدنا في اَل۪عارِضَة اَل۪ثابِتَة مِن اَل۪بِكَر وَ۪في اَل۪ثِقل اَلَّذي نُريد اَن نَحمِلَهُ وَ۪أَدخَلنا أَحَد طَرَفَي اَل۪قَلس في اَل۪بَكرَة اَلَّتي في اَل۪عارِضَة اَل۪ثابِتَة وَ۪في اَل۪بَكرَة اَل۪مُرتَبِطَة عَلى اَل۪حَمل وَ۪صَيَّرنا مَجرا اَل۪قُلوس يَمتَدّ إِلَيهِ زَدنا في سُهولَة رَفع ذٰلِكَ اَل۪ثِقل </s> |
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464 <s id="A18-2|03|09">وَ۪كُلَّما تَكاثَرَت اَل۪بِكَر اَلَّتي تَجري عَلَيها اَل۪قُلوس كانَ أَسهَل لِ۪رَفع ذٰلِكَ اَل۪ثِقل </s> |
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465 <s id="A18-2|03|10">وَ۪يَنبَغي اَن يَكون طَرَف اَل۪قَلس اَل۪واحِد ثابِتاً مَشدوداً في اَل۪عارِضَة اَل۪ثابِتَة وَ۪يَكون اَل۪قَلس يَجري مِنها إِلى اَل۪ثِقل </s> |
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466 <s id="A18-2|03|11">فَ۪أَمّا اَل۪بِكَر اَلَّتي في اَل۪عارِضَة اَل۪ثابِتَة فَ۪إِنَّهُ يَنبَغي اَن تَكون مَشدودَة عَلى خَشَبَة أُخرا وَ۪تَكون دائِرَة عَلى مِحوَر واحِد </s> |
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467 <s id="A18-2|03|12">وَ۪يُدعي ذٰلِكَ اَل۪مِحوَر مَنغَنُن</s> |
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468 <s id="A18-2|03|13">وَ۪تَكون تِلكَ اَل۪خَشَبَة مَشدودَة عَلى اَل۪عارِضَة اَل۪ثابِتَة بِ۪قُلوس اُخَر </s> |
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469 <s id="A18-2|03|14">وَ۪أَمّا اَل۪بِكَر اَل۪مَشدودَة عَلى اَل۪حَمل فَ۪إِنَّها تَكون عَلى مِحوَر آخَر مُساوٍ لِ۪ذٰلِكَ اَل۪مِحوَر مَربوط بِ۪اَل۪حَمل </s> |
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470 <s id="A18-2|03|15">وَ۪قَد يَجِب اَن <pb n="103"></pb> تُرَكَّب اَل۪بِكَر عَلى اَل۪مِحوَر تَركيباً لا يُمكِن بَعضُها يُلاقي بَعضاً لِ۪أَنَّها إِذا تَلاقَت صَعُبَ تَدويرُها </s> |
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471 <s id="A18-2|03|16">فَ۪أَمّا لِ۪ما إِذا صارَت اَل۪زِيادَة في اَل۪بِكَر نَزيد في سُهولَة اَل۪رَفع وَ۪ل۪ما صارَ طَرَف اَل۪قَلس يُربَط في اَل۪عارِضَة اَل۪ثابِتَة فَ۪إِنّا سَنُخَبِّر بِهِ فيما بَعدَ هٰذا</s> |
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472 </p> |
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473 <p n="4"> |
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474 <s id="A18-2|04|00"></s> |
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475 <s id="A18-2|04|01">اَل۪قُوَّة اَل۪رابِع</s> |
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476 <s id="A18-2|04|02">فَ۪أَمّا اَل۪قُوَّة اَل۪رابِع اَلَّتي تَتلوا هٰذِهِ فَ۪إِنَّها اَل۪قُوَّة اَلَّتي تُدعي بِ۪اَل۪إِسفين </s> |
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477 <s id="A18-2|04|03">وَ۪هِيَ تُستَعمَل في بَعض آلات اَل۪طيب وَ۪في إِلصاق ما جَلَّ مِن أَعمال اَل۪نَجّارَة </s> |
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478 <s id="A18-2|04|04">وَ۪كَثيرَة أَعمالُها وَ۪أَكثَر إِستِعمالِنا لَها إِذا أَرَدنا اَن نَفري أَسفَل اَل۪حَجَر اَلَّذي نُريد اَن نَقطَعَهُ وَ۪قَد فَصَلنا جَوانِبَهُ مِن اَل۪جَبَل اَلَّذي نَقطَعُهُ مِنهُ </s> |
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479 <s id="A18-2|04|05">فَ۪إِنَّ في هٰذا اَل۪باب لَيسَ يَعمَل شَيء مِن تِلكَ اَل۪قُوى اَل۪اُخَر فَ۪لا لَو إِجتَمَعَت كُلُّها </s> |
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480 <s id="A18-2|04|06">فَ۪أَمّا اَل۪إِسفين فَ۪إِنَّهُ وَحدَهُ يَفعَل في ذٰلِكَ </s> |
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481 <s id="A18-2|04|07">وَ۪فِعلُهُ بِ۪اَل۪ضَربَة اَلَّتي تَنالُهُ أَيّ ضَربَة كانَت وَ۪لَيسَ يَبطُل مِن فِعلِهِ بَعدَ سُكون اَل۪ضَربَة </s> |
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482 <s id="A18-2|04|08">وَ۪ذٰلِكَ ظاهِر لَنا إِنَّهُ بِ۪لا اَن يُضرَب كَثيراً ما يَكون لَهُ صَوت وَ۪قَلع لِ۪ما يَشُقّ بِ۪قُوَّتِهِ </s> |
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483 <s id="A18-2|04|09">وَ۪كُلَّما كانَت زاوِيَة اَل۪إِسفين أَصغَر فَ۪إِنَّ اَل۪عَمَل بِهِ يَكون أَسهَل كَما سَنُبَيِّن </s> |
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484 </p> |
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485 <p n="5"> |
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486 <s id="A18-2|05|00"></s> |
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487 <s id="A18-2|05|01"><pb n="105"></pb> اَل۪قُوَّة اَل۪خامِسَة</s> |
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488 <s id="A18-2|05|02">وَ۪هِيَ اَلَّتي تُسَمّي اَل۪لَولَب </s> |
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489 <s id="A18-2|05|03">أَمّا اَل۪آلات اَلَّتي ذَكَرنا فَ۪إِنَّ مَعانيها ظاهِرَة تَتِمّ بِ۪ذاتِها وَ۪ذٰلِكَ ظاهِر لَنا في أَشياء كَثيرَة مِن إِستِعمالاتِها فَ۪أَمّا اَل۪لَولَب فَ۪إِنَّ في عَمَلِهِ وَ۪إِستِعمالِهِ صُعوبَ كانَ هُوَ اَلَّذي يَعمَل وَحدُهُ أَو كانَ قُوَّة أُخرا تَعمَل مَعَهُ </s> |
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490 <s id="A18-2|05|04">إِلّا أَنَّهُ لَيسَ بِ۪شَيء آخَر إِلّا إِسفين مُلتَوٍ لا يَنالُهُ ضَرب بَل يَتَحَرَّك بِ۪اَل۪مُخل </s> |
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491 <s id="A18-2|05|05">وَ۪ذٰلِكَ يَتَبَيّاً بِ۪ما نَحنُ ذاكِرون </s> |
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492 <s id="A18-2|05|06">فَ۪نَقول إِنَّ طَبيعَة اَل۪خَطّ اَل۪مَرسوم عَلَيهِ هِيَ هٰذِهِ إِذا فُرِضَ ضِلع مِن أَضلاع شَكل أُسطُواني مُتَحَرِّك عَلى بَسيط اَل۪أُسطُوانَة وَ۪فُرِضَت نُقطَة ما في نِهايَة ذٰلِكَ اَل۪ضِلع تَتَحَرَّك عَلى اَل۪ضِلع وَ۪تَنفُذ عَلَيهِ كُلِّهِ في اَل۪زَمان اَلَّذي يَدور اَل۪ضِلع عَلى بَسيط اَل۪شَكل اَل۪أُسطُواني كُلِّهِ دَورَة واحِدَة وَ۪يَرجَع إِلى اَل۪مَوضِع اَلَّذي مِنهُ إِبتَدَأَت تَتَحَرَّك فَ۪إِنَّ اَل۪خَطّ اَلَّذي تَرسُمُهُ تِلكَ اَل۪نُقطَة عَلى بَسيط اَل۪شَكل اَل۪أُسطُواني يَكون دائِرَة لَولَبِيَّة وَ۪هِيَ اَلَّتي تُسَمّي اَل۪لَولَب </s> |
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493 <s id="A18-2|05|07">فَ۪إِذا أَرَدنا اَن نَرسُم هٰذا اَل۪خَطّ عَلى بَسيط اَل۪أُسطُوانَة فَ۪إِنّا نَستَعمِل هٰذا اَل۪عَمَل أَنّا إِذا فَرَضنا عَلى سَطح ما خَطَّين أَحَدُهُما قائِم عَلى اَل۪آخَر عَلى زاوِيَة قائِمَة كانَ أَحَد اَل۪خَطَّين مُساوِياً لِ۪ضِلع اَل۪أُسطُوانَة وَ۪اَل۪آخَر مُساوِياً لِ۪دائِرَة اَل۪أُسطُوانَة أَعني دائِرَة قاعِدَتِها وَ۪وَصَلنا طَرَفَي اَل۪خَطَّين اَل۪مُحيطَين بِ۪اَل۪زاوِيَة اَل۪قائِمَة بِ۪خَطّ يُوَتِّر اَل۪زاوِيَة اَل۪قائِمَة ثُمَّ رَكَّبنا اَل۪خَطّ <pb n="107"></pb> اَل۪مُساوي لِ۪ضِلع اَل۪أُسطُوانَة عَلى ضِلع اَل۪أُسطُوانَة وَ۪اَل۪خَطّ اَل۪مُساوي لِ۪دائِرَة قاعِدَة اَل۪أُسطُوانَة عَلى دائِرَة قاعِدَة اَل۪أُسطُوانَة فَ۪إِنَّ اَل۪خَطّ اَل۪مُوَتِّر لِ۪ل۪زاوِيَة اَل۪قائِمَة يَلتِفّ عَلى بَسيط اَل۪أُسطُوانَة فَ۪تَكون عَلَيهِ دائِرَة لَولَبِيَّة</s> |
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494 <s id="A18-2|05|08">وَ۪قَد يُمكِنُنا اَن نُقَسِّم ضِلع اَل۪أُسطُوانَة في اَل۪أَجزاء اَل۪مُتَساوِيَة بِ۪كَم أَرَدنا وَ۪نَرسُم عَلى كُلّ جُزء مِنها دائِرَة لَولَبِيَّة فَ۪تَكون عَلى اَل۪أُسطُوانَة دَوائِر كَثيرَة لَولَبِيَّة وَ۪تَكون اَل۪أُسطُوانَة لَولَباً</s> |
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495 <s id="A18-2|05|09">وَ۪تُسَمّي اَل۪أُسطُوانَة اَلَّتي قَد إِلتَفَّ عَلَيها وَتَر زاوِيَة واحِدَة لَولَباً ذا دَورَة واحِدَة أَعني إِذا كانَ ضِلع اَل۪أُسطُوانَة لا يُحيط إِلّا بِ۪خَطّ واحِد يَبتَدِئ مِن إِحدا نِهايَتَيهِ وَ۪يَنتَهي إِلى اَل۪أُخرا </s> |
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496 <s id="A18-2|05|10">فَ۪إِذا أَرَدنا إِستِعمال اَل۪لَولَب حَفَرنا عَلى هٰذا اَل۪خَطّ اَل۪مُلتَفّ عَلى اَل۪أُسطُوانَة حَفراً عَميقاً يَصِل إِلى قَعر اَل۪أُسطُوانَة حَتّى يُمكِنَنا اَن نُرَكِّب في ذٰلِكَ اَل۪حَفر اَل۪خَشَبَة اَلَّتي تُسَمّي طولُس </s> |
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497 <s id="A18-2|05|11">ثُمَّ نَستَعمِل اَل۪لَولَب عَلىهٰذِهِ اَل۪جِهَة </s> |
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498 <s id="A18-2|05|12">نُدير طَرَفَيهِ تَدويراً مُمَلَّساً وَ۪نُرَكِّبُهُما في ثُقَب مُستَديرَة مِن أَركان ثابِتَة لِ۪يَكون تَدويرُهُ في تِلكَ اَل۪ثُقَب سَلِساً </s> |
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499 <s id="A18-2|05|13">وَ۪نُرَكِّب اَل۪خَشَبَة اَلَّتي تُسَمّي قانون قائِمَة مُوازِيَة لِ۪خَشَبَة اَل۪لَولَب </s> |
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500 <s id="A18-2|05|14">وَ۪ل۪يَكُن في هٰذا اَل۪قانون حَفر ميزابي عَميق ظاهِر في بَسيط اَل۪خَشَبَة في اَل۪جِهَة اَلَّتي تَلي اَل۪لَولَب </s> |
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501 <s id="A18-2|05|15">ثُمَّ نُرَكِّب طَرَف اَل۪عود اَلَّذي يُسَمّي طولُس <pb n="109"></pb> في حَفر اَل۪لَولَب وَ۪طَرَفَهُ اَل۪آخَر في حَفر اَل۪قانون </s> |
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502 <s id="A18-2|05|16">فَ۪إِذا أَرَدنا اَن نَرفَع حَملاً ثَقيلاً بِ۪هٰذِهِ اَل۪آلَة نَأخُذ قَلساً مِن اَل۪قُلوس اَلَّتي تُسَمّي سِلاح وَ۪نَشُدّ أَحَد طَرَفَيهِ في اَل۪حَمل اَلَّذي نُريد اَن نَرفَعَهُ وَ۪اَل۪آخَر في اَل۪عود اَلَّذي يُسَمّي طولُس وَ۪نَكون قَد ثَقَبنا في طَرَف اَل۪لَولَب ثُقَباً مُخالِفَة </s> |
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503 <s id="A18-2|05|17">فَ۪نُرَكِّب في هٰذِهِ اَل۪ثُقَب أَوتاداً وَ۪نُدير اَل۪لَولَب بِ۪هٰذِهِ اَل۪أَوتاد فَ۪يَرتَفِع هٰذا اَل۪طولُس بِ۪حَرَكَتِهِ في اَل۪حَفر اَلَّذي في اَل۪لَولَب وَ۪يَرتَفِع بِ۪إِرتِفاعِهِ اَل۪حَبل فَ۪يُقِلّ اَل۪ثِقل اَل۪مُرتَبِط فيهِ</s> |
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504 <s id="A18-2|05|18">وَ۪قَد يُمكِنُنا اَن نُرَكِّب بَدَلَة اَل۪أَوتاد مُرَبَّعَة ذات مَقابِض في طَرَف اَل۪لَولَب اَل۪خارِج عَن اَل۪رُكن اَل۪ثابِت فَ۪نُدير اَل۪لَولَب بِ۪هٰذِهِ اَل۪مُرَبَّعَة وَ۪يَرتَفِع اَل۪حَمل</s> |
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505 <s id="A18-2|05|19">فَ۪أَمّا اَل۪حَفر اَل۪لَولَبي اَلَّذي يَكون عَلى اَل۪أُسطُوانَة فَ۪إِنَّهُ رُبَّما كانَ مُرَبَّعاً وَ۪رُبَّما كانَ عَدَسِيّاً</s> |
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506 <s id="A18-2|05|20">فَ۪أَمّا اَل۪مُرَبَّع فَ۪هُوَ اَل۪قائِم اَل۪حَفر اَلَّذي يَنتَهي حَفرُهُ إِلىخَطَّين وَ۪أَمّا اَل۪عَدَسي فَ۪هُوَ اَلَّذي حَفرُهُ مائِل وَ۪يَنتَهي إِلىخَطّ واحِد </s> |
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507 <s id="A18-2|05|21">فَ۪يُسَمّي هٰذا عَدَسِيّاً وَ۪اَل۪آخَر يُسَمّي مُرَبَّعاً</s> |
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508 </p> |
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509 <p n="6"> |
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510 <s id="A18-2|06|00"></s> |
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511 <s id="A18-2|06|01">فَ۪اَل۪لَولَب إِذا كانَ يُستَعمَل مُفرَداً وَحدَهُ فَ۪عَلى هٰذِهِ اَل۪جِهَة يُستَعمَل </s> |
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512 <s id="A18-2|06|02">وَ۪أَمّا اِن يُستَعمَل إِستِعمالاً آخَر بِ۪مُشارَكَتِهِ <pb n="111"></pb> قُوَّة أُخرا وَ۪هِيَ اَلَّتي تُفعَل بِ۪اَل۪مِحوَر اَلَّذي عَلَيهِ فَلكَة مُرَكَّبَة فَ۪هِيَ تَكون عَلى هٰذِهِ اَل۪جِهَة </s> |
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513 <s id="A18-2|06|03">نَتَوَهَّم لِ۪ل۪فَلكَة اَلَّتي عَلى اَل۪مِحوَر أَوتاداً وَ۪لَولَب ما مُحاذي اَل۪فَلكَة إِمّا قائِم عَلى اَل۪أَرض وَ۪إِمّا مُوازٍ لِ۪سَطح اَل۪أَرض</s> |
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514 <s id="A18-2|06|04">وَ۪ل۪تَكُن اَل۪أَوتاد مُرَكَّبَة في اَل۪حَفر اَل۪لَولَبي وَ۪أَطراف اَل۪لَولَب تَكون في ثُقبَين مُستَديرَين مِن رُكنَين ثابِتَين عَلى ما وَصَفنا فيما تَقَدَّمَ</s> |
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515 <s id="A18-2|06|05">وَ۪ل۪يَكُن طَرَف اَل۪لَولَب فيهِ فَضل خارِج عَن اَل۪رُكن اَل۪ثابِت مُرَكَّب فيهِ مُرَبَّعَة ذات مَقابِض أَو نَثقُب في ذٰلِكَ اَل۪فَضل اَل۪خارِج ثُقباً لِ۪نُرَكِّب فيها أَوتاداً نُدَوِّر اَل۪لَولَب بِها </s> |
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516 <s id="A18-2|06|06">فَ۪إِذا أَرَدنا اَن نَرفَع ثِقلاً ما بِ۪هٰذِهِ اَل۪آلَة نَشُدّ اَل۪قُلوس اَل۪مُرتَبِطَة بِ۪اَل۪حَمل عَلى اَل۪مِحوَر مِن جَنبَتَي اَل۪فَلكَة </s> |
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517 <s id="A18-2|06|07">وَ۪نُدير اَل۪لَولَب اَلَّذي قَد رَكَّبنا فيهِ أَوتاد اَل۪فَلكَة فَ۪تَدور اَل۪فَلكَة وَ۪اَل۪مِحوَر وَ۪يُستَقَلّ ذٰلِكَ اَل۪ثِقل</s> |
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518 </p> |
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519 <p n="7"> |
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520 <s id="A18-2|07|00"></s> |
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521 <s id="A18-2|07|01">أَمّا صَنعَة اَل۪خَمس قُوى اَلَّتي تَقَدَّمَ وَصفُها وَ۪اَل۪عَمَل بِها فَ۪قَد أَتَينا عَلى ذِكرِهِ وَ۪شَرحِهِ </s> |
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522 <s id="A18-2|07|02">وَ۪أَمّا اَل۪عِلَّة اَلَّتي بِها صارَت كُلّ واحِدَة مِن هٰذِهِ اَل۪آلات تُحَرِّك أَثقالاً عِظاماً بِ۪قُوَّة يَسيرَة فَ۪إِنّا اَل۪آن نُخَبِّر بِهِ هَكَذا </s> |
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523 <s id="A18-2|07|03">نَفرِض دائِرَتَين عَلى مَركَز واحِد وَ۪هُوَ عَلامَة ٓأَة وَ۪ل۪يَكُن قُطراهُما خَطَّي ٓبٓغ ٓدٓe </s> |
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524 <s id="A18-2|07|04">وَ۪ل۪تَكُن اَل۪دائِرَتان مُتَحَرِّكَتَين عَلى عَلامَة ٓأَة اَلَّتي هِيَ مَركَزُهُما وَ۪ل۪تَكُن اَل۪دائِرَتان قائِمَتَين عَلى اَل۪أُفُق </s> |
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525 <s id="A18-2|07|05">وَ۪ل۪نُعَلِّق عَلى عَلامَتَي <pb n="113"></pb> ٓبٓغ ثِقلَين مُتَساوِيَين وَ۪هُما عَلامَتا ٓزٓه فَ۪يَظهَر لَنا أَنَّ اَل۪دَوائِر لا تَميل إِلى جِهَة مِن اَل۪جِهات لِ۪أَنَّ ثِقلَي ٓزٓه مُتَساوِيان وَ۪بُعدَي ٓبٓا ٓآغ مُتَساوِيان فَ۪يَكون ٓبٓغ عَمود ميزان يَتَحَرَّك عَلى عِلاقَة هِيَ عَلامَة ٓأَة</s> |
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526 <s id="A18-2|07|06">فَ۪اِن نَقَلنا اَل۪ثِقل اَلَّذي عَلى ٓغ فَ۪عَلَّقناهُ عَلى ٓe يَميل إِلى ما أَسفَل مُنحَطّاً ثِقل ٓز وَ۪يُدير اَل۪دَوائِر </s> |
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527 <s id="A18-2|07|07">فَ۪إِذا زَدنا في ثِقل ٓت سَيُعادِل ثِقل ٓز وَ۪تَكون نِسبَة ثِقل ٓت إِلى ثِقل ٓز كَ۪نِسبَة بُعد ٓبٓا إِلى بُعد ٓآe فَ۪نَتَوَهَّم خَطّ ٓبٓe ميزاناً يَتَحَرَّك عَلى عِلاقَة هِيَ عَلامَة ٓأَة </s> |
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528 <s id="A18-2|07|08">وَ۪ذٰلِكَ قَد بَيَّنَهُ ٓأَرشِميدِس في كِتابِهِ في مُساوات اَل۪مَيل</s> |
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529 <s id="A18-2|07|09">فَ۪يَظهَر مِن هاهُنا أَنَّهُ مُمكِن اَن يُحَرَّك عُظم كَبير بِ۪قُوَّة يَسيرَة </s> |
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530 <s id="A18-2|07|10">لِ۪أَنَّهُ إِذا كانَت دائِرَتان عَلى مَركَز واحِد وَ۪كانَ اَل۪ثِقل اَل۪كَبير عَلى قَوس ما مِن اَل۪دائِرَة اَل۪صَغيرَة وَ۪اَل۪قُوَّة اَل۪يَسيرَة عَلى قَوس ما مِن اَل۪دائِرَة اَل۪عَظيمَة وَ۪كانَت نِسبَة اَل۪خَطّ اَل۪خارِج مِن مَركَز اَل۪كَبيرَة إِلى اَل۪خَطّ اَل۪خارِج مِن مَركَز اَل۪صَغيرَة أَعظَم مِن نِسبَة اَل۪ثِقل اَل۪كَبير إِلى اَل۪قُوَّة اَل۪يَسيرَة اَلَّتي تُحَرِّكُهُ فَ۪إِنَّ اَل۪قُوَّة اَل۪يَسيرَة تَقوى عَلى اَل۪ثِقل اَل۪كَبير</s> |
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531 </p> |
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532 <p n="8"> |
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533 <s id="A18-2|08|00"></s> |
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534 <s id="A18-2|08|01">فَ۪إِذاً كانَ قَد صَحَّ لَنا هٰذا في تَمثيلِنا في اَل۪دائِرَة فَ۪إِنّا نُريد اَن نُبَيِّن ذٰلِكَ في هٰذِهِ اَل۪خَمس قُوى وَ۪نوضِح <pb n="115"></pb> بُرهانَها بَعدَ هٰذا اَل۪عَمَل</s> |
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535 <s id="A18-2|08|02">فَ۪قَد كانَ اَل۪قُدَماء أَلَّذين كانوا قَبلَنا يُقَدِّمون هٰذِهِ اَل۪مُقَدِّمَة </s> |
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536 <s id="A18-2|08|03">فَ۪ل۪نُبَيِّن اَل۪آن ذٰلِكَ أَوَّلاً في اَل۪آلَة اَلَّتي تُسَمّي اَل۪مُخل </s> |
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537 <s id="A18-2|08|04">وَ۪هٰذا اَل۪مُخل يُحَرِّك اَل۪ثَقيلات عَلى ضَربَتَين إِمّا بِ۪اَن كانَ مَوضوعاً وَضعاً يَكون مُوازِياً لِ۪ل۪أَرض أَو۪بِ۪آن يَكون مُتَعالِياً عَن اَل۪أَرض مائِلاً عَلَيها</s> |
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538 <s id="A18-2|08|05">فَ۪يَكون اَل۪عَمَل بِهِ بِ۪اَن يُكَبَّس طَرَفُهُ اَل۪مُتَعالي عَن اَل۪أَرض إِلى ما يَلي اَل۪أَرض </s> |
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539 <s id="A18-2|08|06">فَ۪ل۪نَفرِضهُ أَوَّلاً مُوازِياً لِ۪ل۪أَرض </s> |
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540 <s id="A18-2|08|07">وَ۪ل۪يَكُن اَل۪مُخل خَطّ ٓآب وَ۪ل۪يَكُن اَل۪ثِقل اَلَّذي يَتَحَرَّك بِ۪اَل۪مُخل عَلى عَلامَة ٓأَة وَ۪هُوَ ثِقل ٓغ وَ۪ل۪تَكُن اَل۪قُوَّة اَل۪مُحَرِّكَة عَلى عَلامَة ٓب وَ۪ل۪يَكُن اَل۪حَجَر اَلَّذي تَحتَ اَل۪مُخل اَلَّذي يَتَحَرَّك اَل۪مُخل عَلَيهِ عَلى عَلامَة ٓد وَ۪ل۪يَكُن ٓبٓد أَعظَم مِن خَطّ ٓدٓا </s> |
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541 <s id="A18-2|08|08">فَ۪إِذانَحنُ رَفَعنا طَرَف اَل۪مُخل اَلَّذي عَلامَة ٓب وَ۪نُعالي اَل۪مُخل عَن اَل۪حَجَر اَلَّذي يَدور عَلَيهِ فَ۪إِنَّ اَل۪ثِقل اَلَّذي هُوَ ٓغ يَتَحَرَّك إِلى اَل۪جِهَة اَل۪أُخرا </s> |
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542 <s id="A18-2|08|09">فَ۪تَرسُم عَلامَة ٓب دائِرَة عَلى مَركَز ٓد وَ۪تَرسُم عَلامَة ٓأَة أَيضاً دائِرَة عَلى هٰذا اَل۪مَركَز أَصغَر مِن اَل۪دائِرَة اَلَّتي تَرسُمُها عَلامَة ٓب</s> |
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543 <s id="A18-2|08|10">فَ۪اِن كانَت نِسبَة خَطّ ٓبٓد إِلى ٓدٓا هِيَ نِسبَة اَل۪ثِقل اَلَّذي هُوَ ٓغ إِلى اَل۪قُوَّة اَلَّتي عِندَ ٓب فَ۪إِنَّ ثِقل ٓغ يُعادِل قُوَّة ٓب</s> |
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544 <s id="A18-2|08|11">وَ۪اِن كانَت نِسبَة ٓبٓد إِلى ٓدٓا أَعظَم مِن نِسبَة اَل۪ثِقل إِلى اَل۪قُوَّة فَ۪إِنَّ <pb n="117"></pb> اَل۪قُوَّة تَقوى عَلى اَل۪ثِقل لِ۪أَنَّهُما دائِرَتان عَلى مَركَز واحِد وَ۪اَل۪ثِقل هُوَ عَلى قَوس مِن اَل۪دائِرَة اَل۪صُغرى وَ۪اَل۪قُوَّة اَل۪مُحَرِّكَة عَلى قَوس مِن اَل۪دائِرَة اَل۪عُظمى </s> |
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545 <s id="A18-2|08|12">فَ۪قَد يَظهَر لَنا أَنَّهُ يَعرِض في اَل۪مُخل اَل۪عارِض اَلَّذي عَرَضَ لِ۪ل۪دائِرَتَين أَلَّتَين عَلى مَركَز واحِد </s> |
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546 <s id="A18-2|08|13">فَ۪إِذاً اَل۪مُخل اَل۪مُحَرِّك لِ۪ل۪ثَقيلات اَل۪عِلَّة فيهِ هِيَ اَل۪عِلَّة اَلَّتي عُرِضَت لِ۪ل۪دائِرَتَين</s> |
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547 </p> |
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548 <p n="9"> |
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549 <s id="A18-2|09|00"></s> |
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550 <s id="A18-2|09|01">فَ۪ل۪نَفرِض أَيضاً مُخلاً يَكون خَطّ ٓآب يَتَحَرَّك عَلى حَجَر تَحتَ اَل۪مُخل وَ۪هُوَ ٓد </s> |
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551 <s id="A18-2|09|02">وَ۪ل۪يَكُن أَحَد طَرَفَي اَل۪مُخل اَلَّذي هُوَ عَلامَة ٓأَة يَكون تَحتَ حَمل ٓغ وَ۪اَل۪طَرَف اَل۪آخَر يَكون مُتَعالِياً عَن اَل۪أَرض وَ۪هُوَ عَلى عَلامَة ٓب </s> |
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552 <s id="A18-2|09|03">فَ۪اِن نَحنُ كَبَّسنا طَرَف اَل۪مُخل اَلَّذي هُوَ عَلى عَلامَة ٓب إِلى ما يَلي اَل۪أَرض كُنّا قَد حَرَّكنا ثِقل ٓغ </s> |
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553 <s id="A18-2|09|04">فَ۪أَقول إِنَّهُ لا يَتَحَرَّك بِ۪هٰذا اَل۪عَمَل مِثلَ ما تَحَرَّكَ في اَل۪عَمَل اَل۪آخَر </s> |
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554 <s id="A18-2|09|05">لِ۪أَنَّ في هٰذا اَل۪عَمَل بَعض اَل۪ثِقل يَتَحَرَّك وَ۪بَعضُهُ يَبقى ثابِتاً عَلى اَل۪أَرض </s> |
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555 <s id="A18-2|09|06">فَ۪ل۪نَتَوَهَّم سَطحاً ما خارِجاً عَلى عَلامَة ٓe قائِماً عَلى اَل۪أُفُق وَ۪ل۪يَكُن فاضِل مِن اَل۪ثِقل وَ۪هُوَ ٓeٓزٓت </s> |
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556 <s id="A18-2|09|07">وَ۪ل۪يَكُن هٰذا اَل۪ثِقل اَلَّذي هُوَ ٓeٓزٓت مُعادِلاً لِ۪ل۪ثِقل اَلَّذي هُوَ ٓeٓزٓه </s> |
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557 <s id="A18-2|09|08">فَ۪اِن تَوَهَّمنا هٰذا اَل۪ثِقل اَلَّذي هُوَ جَميع ٓeٓهٓت مَفصولاً مِن اَل۪حَمل مَوضوعاً في اَل۪مَوضِع اَلَّذي هُوَ فيهِ فَ۪إِنَّهُ لا يَميل إِلى جِهَة <pb n="119"></pb> مِن اَل۪جِهات لا إِلى جِهَة ٓت وَ۪لا إِلى جِهَة ٓه لِ۪مُعادَلَة ثِقلَي ٓeٓتٓز ٓeٓهٓز أَحَدِهِما اَل۪آخَر</s> |
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558 <s id="A18-2|09|09">فَ۪إِذاً جُزء اَل۪حَمل اَلَّذي هُوَ ٓeٓهٓت لَيسَ يَحتاج إِلىقُوَّة بَتَّة فَ۪إِذاً جُزء اَل۪حَمل اَلَّذي هُوَ ٓeٓهٓكٓل هُوَ اَلَّذي يُحَرِّكُهُ اَل۪مُخل </s> |
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559 <s id="A18-2|09|10">فَ۪لَو كانَ مُخل ٓآب يُحَرِّك جَميع ثِقل ٓeٓتٓكٓل كانَت نِسبَة ٓبٓد إِلى ٓدٓا كَ۪نِسبَة ثِقل ٓeٓتٓكٓل إِلى اَل۪قُوَّة اَلَّتي عِندَ ٓب</s> |
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560 <s id="A18-2|09|11">وَ۪لَكِنَهُ لَيسَ يَتَحَرَّك كُلُّهُ وَ۪ذٰلِكَ أَنَّ جُزأاً مِنهُ يَضبُطُهُ اَل۪سَطح اَل۪مَفروض وَ۪ذٰلِكَ اَل۪جُزء هُوَ نِصفُهُ </s> |
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561 <s id="A18-2|09|12">لِ۪أَنَّ ذٰلِكَ اَل۪سَطح لَو لَم نَتَوَهَّمهُ وَ۪زَدنا في اَل۪قُوَّة اَل۪مُحَرِّكَة قَدراً مُساوِياً لِ۪ذٰلِكَ اَل۪فَضل كانَت اَل۪قُوَّة تَندَفِع إِلى أَسفَل وَ۪يَرتَفِع طَرَف اَل۪مُخل اَلَّذي عِندَ ٓأَة لِ۪أَنَّ اَل۪أَثقال تَنقَسِم عَلى اَل۪قُوى اَل۪مُحَرِّكَة لَها قِسمَة اَل۪مُساوات </s> |
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562 <s id="A18-2|09|13">فَ۪إِذاً اَل۪سَطح اَل۪مَفروض هُوَ يَأخُذ نِصف اَل۪ثِقل </s> |
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563 <s id="A18-2|09|14">فَ۪إِذاً اِن كانَت اَل۪قُوَّة أَلّلَتي عِندَ ٓب مُعادِلَة لِ۪ثِقل ٓeٓهٓكٓل تَكون نِسبَة ٓبٓد إِلى ٓدٓا كَ۪نِسبَة ثِقل ٓeٓهٓكٓل إِلى قُوَّة ٓب </s> |
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564 <s id="A18-2|09|15">وَ۪اَل۪قَدر اَلَّذي يَرتَفِع اَل۪حَمل عَن اَل۪أَرض بِ۪ذٰلِكَ اَل۪قَدر يَحتاج مِن اَل۪قُوَّة إِلى اَل۪أَقَلّ </s> |
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565 <s id="A18-2|09|16">فَ۪يَكون مَوضوعاً وَضعاً لا يَحتاج إِلى قُوَّة إِذا كانَ اَل۪سَطح اَل۪مُخرَج عَلى عَلامَة ٓe اَل۪قائِم عَلى اَل۪أُفُق يُقَسِّم اَل۪حَمل بِ۪نِصفَين</s> |
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566 <s id="A18-2|09|17">وَ۪هٰذا اَل۪عَمَل بِ۪اَل۪مُخل مَنسوب إِلى اَل۪دائِرَة وَ۪لَكِنَهُ لَيسَ عَلى اَل۪عَمَل اَل۪أَوَّل</s> |
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567 <s id="A18-2|09|18">وَ۪أَمّا اَن يَكون اَل۪ميزان أَيضاً مَنسوباً إِلى اَل۪دائِرَة فَ۪ذٰلِكَ ظاهِر لِ۪أَنَّ اَل۪ضائِرَة ميزان ما</s> |
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568 </p> |
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569 <p n="10"> |
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570 <s id="A18-2|10|00"></s> |
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571 <s id="A18-2|10|01"><pb n="121"></pb> وَ۪أَمّا اَل۪مِحوَر اَل۪مُرَكَّب في اَل۪فَلكَة فَ۪إِنَّهُ لَيسَ شَيء آخَر إِلّا دائِرَتَين عَلى مِحوَر واحِد أَحَدُهُما صَغيرَة وَ۪هِيَ دائِرَة اَل۪مِحوَر وَ۪اَل۪أُخرا كَبيرَة وَ۪هِيَ دائِرَة اَل۪فَلكَة </s> |
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572 <s id="A18-2|10|02">فَ۪ل۪ذٰلِكَ بِ۪إِستِحقاق صارَ تَعليق اَل۪ثِقل عَلى اَل۪مِحوَر وَ۪صارَت اَل۪قُوَّة اَل۪مُحَرِّكَة عَلى اَل۪فَلكَة لِ۪أَنَّ بِ۪هٰذا اَل۪عَمَل تَقوى اَل۪قُوَّة اَل۪يَسيرَة عَلى ثِقل عَظيم </s> |
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573 <s id="A18-2|10|03">وَ۪هٰذا اَل۪قَول قَد قالَهُ أَلَّذين كانوا قَبلَنا إِلّا أَنّا وَضَعناهُ هاهُنا لِ۪يَكون كِتابُنا مُتَمَّماً وَ۪ل۪يَكون لَهُ تَرتيب مُؤَلَّف</s> |
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574 </p> |
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575 <p n="11"> |
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576 <s id="A18-2|11|00"></s> |
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577 <s id="A18-2|11|01">فَ۪ل۪نَقُل اَل۪آن في عِلَّة اَل۪آلَة اَلَّتي تُدعي كَثيرَة اَل۪رَفع </s> |
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578 <s id="A18-2|11|02">نَفرِض فَلكَة مُتَعالِيَة عَلى عَلامَة ٓأَة وَ۪عَلَيها قَلس سِلاح وَ۪هُوَ ٓبٓغ </s> |
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579 <s id="A18-2|11|03">وَ۪نَشُدّ في طَرَفَي اَل۪حَبل اَل۪مَمدودَين ثِقلاً وَ۪هُوَ ٓد وَ۪ل۪يَكُن هٰذا اَل۪ثِقل مُتَعالِياً عَن اَل۪أَرض </s> |
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580 <s id="A18-2|11|04">فَ۪يَظهَر أَنَّ اَل۪جُزأَين اَل۪مُمتَدَّين مِن اَل۪قَلس إِمتِدادُهُما مُتَساوٍ وَ۪كُلّ واحِد مِنهُما ثِقل نِصف ثِقل ٓد لِ۪أَنَّ اَل۪جُزأَين اَل۪مُمتَدَّين اِن لَم يَكُن اَل۪مَمدود مِنهُما مُتَساوِياً فَ۪إِنَّ اَلَّذي هُوَ مِنهُما أَكثَر إِمتِداداً يُشيلُهُ أَكثَرُهُما إِرتِفاعاً</s> |
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581 <s id="A18-2|11|05">وَ۪لَكِنَنا لَيسَ نَرى شَيئاً مِن هٰذا لِ۪أَنَّ كُلّ واحِد مِن اَل۪جُزأَين اَل۪مُمتَدَّين مِن اَل۪قَلس ساكِن </s> |
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582 <s id="A18-2|11|06">فَ۪اِن نَحنُ قَسَّمنا ثِقل ٓد بِ۪نِصفَين أَعني بِ۪جُزأَين مُتَساوِيَين يَظهَر لَنا أَنَّ اَل۪جُزأَين مِن اَل۪قَلس اَل۪مَمدودَين <pb n="123"></pb> يَكونان ساكِنَين لِ۪أَنَّ اَل۪ثِقل اَلَّذي يَمُدُّهُما ثِقل واحِد وَ۪هُوَ اَلَّذي كانَ يَمُدُّهُما أَوَّلاً </s> |
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583 <s id="A18-2|11|07">فَ۪يَكون نِصف اَل۪ثِقل مُعادِلاً لِ۪ل۪ثِقل اَل۪مُساوي لَهُ </s> |
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584 <s id="A18-2|11|08">وَ۪يَكون أَيضاً اَل۪جُزآن اَل۪مَمدودان مِن اَل۪قَلس مُتَساوِيَين مِن جِهَة أُخرا لِ۪أَنَّهُ قَد عُلِّقَ أَثقال مُتَساوِيَة في خُطوط مُتَساوِيَة وَ۪ذٰلِكَ أَنَّ اَل۪قَلس اَل۪مَمدود يُماسّ مِن قَوس اَل۪فَلكَة نُقطَتَين هُما نَظائِر بَعضُها بَعضاً وَ۪بُعدُهُما مِن اَل۪مَركَز مُتَساوٍ وَ۪اَل۪أَثقال كَ۪أَنَّها مُعَلَّقَة بِ۪هاتَين اَل۪نُقطَتَين </s> |
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585 <s id="A18-2|11|09">فَ۪عَلى هٰذا اَل۪عَمَل وَ۪بِ۪هٰذِهِ اَل۪جِهَة لَيسَ يُعادِل حَمل ثَقيل أَو ثِقل عَظيم قُوَّة يَسيرَة وَ۪ل۪ذٰلِكَ يُسَمّي هٰذا اَل۪باب مِن اَل۪آلَة اَلَّتي تُسَمّي كَثيرَة اَل۪رَفع ذا رَفع واحِد </s> |
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586 <s id="A18-2|11|10">وَ۪هٰذا اَلَّذي يُسَمّي ذا اَل۪رَفع اَل۪واحِد هُوَ اَلَّذي اَل۪قَلس فيهِ مَمدود مُدَّتَين</s> |
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587 </p> |
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588 <p n="12"> |
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589 <s id="A18-2|12|00"></s> |
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590 <s id="A18-2|12|01">وَ۪ل۪نُبَيِّن اَل۪آن اَلَّذي هُوَ ذو رَفعَين وَ۪هُوَ اَلَّذي فيهِ مِن اَل۪قَلس ثَلاثَة أَجزاء مَمدودَة </s> |
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591 <s id="A18-2|12|02">وَ۪عَلى هٰذِهِ اَل۪جِهَة كُلَّما تَكاثَرَ إِمتِداد اَل۪قَلس وَ۪تَكَرَّرَ إِنبِساطُهُ بِ۪عِدَّة ذٰلِكَ اَل۪تَكرير تُسَمّي اَل۪آلَة ذا رَفع بَعدَ نُقصان واحِد مِن عَدَد تَكرير إِنبِساط اَل۪قَلس لِ۪يَكون اَل۪اِسم سَمِياً لِ۪ل۪عَدَد اَلَّذي هُوَ أَقَلّ مِن ذٰلِكَ اَل۪عَدَد أَعني عَدَد تَكرير اَل۪قَلس بِ۪واحِد </s> |
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592 <s id="A18-2|12|03">فَ۪ل۪نَتَوَهَّم طَرَف اَل۪قَلس اَلَّذي عِندَ ٓد داخِلاً في بَكرَة نافِذاً مِنها إِلى <pb n="125"></pb> رُكن ثابِت يَكون عِندَ بَكرَة ٓأَة عَلى عَلامَة ٓه فَ۪يَكون إِمتِداد اَل۪قُلوس مُتَساوِياً لِ۪ل۪عِلَّة اَلَّتي وَصَفنا لِ۪أَنَّ كُلّ واحِد مِنهُما يَمُدّ ثُلث اَل۪ثِقل</s> |
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593 <s id="A18-2|12|04">فَ۪اِن قُسِمَ ثِقل ٓز بِ۪ثَلاثَة أَقسام مُتَساوِيَة حَتّى يَكون ما يَلي مِنهُ جإِهَة ٓتٓب ضِعف ٓغ فَ۪إِنَّ اَل۪ثِقل يَسكٌ وَ۪لا يَميل مِنهُ شَيء إِلى جِهَة مِن اَل۪جِهات فَ۪يَكون اَل۪ثِقل اَل۪مُعَلَّق في قَلس ٓغ مُعادِلاً لِ۪ل۪ثِقل اَل۪مُعَلَّق في قَلس ٓد وَ۪هُوَ ضِعف اَل۪جِهَة اَل۪أُخرا </s> |
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594 <s id="A18-2|12|05">فَ۪اِن نَحنُ صَيَّرنا مَكان ٓغ اَلَّتي هِيَ ثُلث اَل۪ثِقل قُوَّة مُعادِلَة لِ۪ل۪ثِقل تَمسُكُ اَل۪قَلس فَ۪إِنَّ اَل۪ثِقل اَل۪باقي لا يَقوا عَلَيها وَ۪هِيَ أَقَلّ مِنهُ </s> |
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595 <s id="A18-2|12|06">وَ۪ذٰلِكَ أَيضاً اِن نَحنُ أَدخَلنا طَرَف اَل۪قَلس اَلَّذي عِندَ ٓه في بَكرَة تَكون مَشدودَة عِندَ ٓه وَ۪مَدَّدنا حَتّى نَشُدّ طَرَفَهُ في ثِقل ٓز عَلى عَلامَة ٓك فَ۪إِنَّ كُلّ واحِد مِن اَل۪قُلوس اَل۪مَمدودَة يُقِلّ رُبع اَل۪ثِقل </s> |
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596 <s id="A18-2|12|07">فَ۪اِن قُسِمَ اَل۪حَمل أَيضاً قِسمَة أُخرا حَتّى يَكون ما يَلي مِنهُ عَلامات ٓرٓبٓغ ثَلاثَة أَمثال ما يَلي عَلامَة ٓك فَ۪إِنَّ اَل۪ثِقل اَلَّذي عِندَ عَلامَة ٓك يُعادِل باقي اَل۪ثِقل وَ۪تَكون نِسبَة عَدَد اَل۪قُلوس اَل۪مَمدودَة اَلَّتي تُقِلّ اَل۪ثِقل إِلى اَل۪قَلس اَلَّذي يَجُرُّهُ كَ۪نِسبَة اَل۪ثِقل إِلى اَل۪ثِقل </s> |
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597 <s id="A18-2|12|08">فَ۪يَنبَغي في كُلِّيَّة هٰذِهِ اَل۪أَثقال اَن تَكون نِسبَة اَل۪ثِقل اَل۪مَعلوم إِلى اَل۪قُوَّة اَلَّتي تُحَرِّكُهُ اَل۪قُوَّة كَ۪نِسبَة اَل۪قُلوس اَل۪مَمدودَة اَلَّتي تُقِلّ اَل۪ثِقل إِلى <pb n="127"></pb> اَل۪قُلوس اَلَّتي تُحَرِّكُها اَل۪قُوَّة اَل۪مُحَرِّكَة </s> |
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598 <s id="A18-2|12|09">فَ۪يَكون ذٰلِكَ مَثَلنا اِن كانَ اَل۪ثِقل خَمسين قِنطاراً وَ۪كانَت اَل۪قُوَّة اَل۪مُحَرِّكَة خَمسَة قَناطير يَحتاج اَن تَكون اَل۪قُلوس اَل۪مَمدودَة اَلَّتي تَحمِل اَل۪ثِقل عَشَرَة أَمثال اَل۪قُلوس اَلَّتي تَمُدُّها قُوَّة خَمسَة قَناطير لَة۪تَكون اَل۪قُلوس اَل۪مَمدودَة اَلَّتي تَحمِل اَل۪ثِقل عَشَرَة وَ۪اَل۪قَلس اَلَّذي عِندَ اَل۪قُوَّة اَل۪مُحَرِّكَة واحِد </s> |
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599 <s id="A18-2|12|10">فَ۪اِن كانَت اَل۪قُلوس اَلَّتي تَحمِل اَل۪ثِقل عِشرين قَلساً كانَت اَل۪قُلوس اَلَّتي عِندَ اَل۪قُوَّة اَل۪مُحَرِّكَة قَلسَين </s> |
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600 <s id="A18-2|12|11">فَ۪عَلى هٰذا تُعادِل اَل۪قُوَّة اَل۪ثِقل </s> |
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601 <s id="A18-2|12|12">فَ۪اِن أَرَدنا اَن تَقوى اَل۪قُوَّة عَلى اَل۪ثِقل إِمّا اَن نَزيد في اَل۪قُوَّة وَ۪إِمّا اَن نَزيد في اَل۪قُلوس اَلَّتي تَحمِل اَل۪ثِقل </s> |
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602 <s id="A18-2|12|13">فَ۪قَد بُيِّنَ بُرهان اَل۪بِكَر اَلَّتي تُسَمّي اَل۪كَثيرَة اَل۪رَفع وَ۪مِن هُنالِكَ ظَهَرَ لَنا أَنَّهُ مُمكِن اَن يُحَرَّك اَل۪ثِقل اَل۪مَعلوم بِ۪اَل۪قُوَّة اَل۪مَعلومَة</s> |
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603 </p> |
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604 <p n="13"> |
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605 <s id="A18-2|13|00"></s> |
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606 <s id="A18-2|13|01">وَ۪قَد يَعرِض في عَمَل ما اَن يُسَمّي اَل۪قَلس اَل۪مُثَنّى اَل۪مَمدود مُدَّتَين فَقَط مَرَّة ذا رَفع واحِد وَ۪مَرَّة ذا رَفعَين عَلى قَدر اَل۪قُوَّة اَلَّتي نَستَعمِلُها فيهِ </s> |
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607 <s id="A18-2|13|02">وَ۪مِثال ذٰلِكَ اَن نَفرِض بَكرَة عَلى عَلامَة ٓأَة عَلَيها حَبل وَ۪ل۪يَكُن جُزآ اَل۪حَبل اَل۪مَمدودان عَلى عَلامَتَي ٓبٓغ وَ۪ل۪يَكُن ٓبٓغ مُرتَبِطَين بِ۪ثِقل ما وَ۪هُوَ ثِقل ٓe </s> |
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608 <s id="A18-2|13|03">فَ۪اِن قَسَّمنا هٰذا اَل۪ثِقل بِ۪نِصفَين يَكون اَل۪جُزآن اَلَّذان في اَل۪جِهَتَين مُتَعادِلَين وَ۪تُسَمّي هٰذِهِ اَل۪بَكرَة ذا رَفع واحِد <pb n="129"></pb> لِ۪أَنَّ اَل۪قُوَّة في هٰذا تَكون مُعادِلَة لِ۪ل۪ثِقل اَل۪مُساوي لَها </s> |
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609 <s id="A18-2|13|04">وَ۪ل۪نَتَوَهَّم أَيضاً ثِقلاً آخَر عَلى عَلامَة ٓز وَ۪ل۪نَربُط عَلَيها بَكرَة وَ۪هِيَ بَكرَة ٓه وَ۪نُدخِل في هٰذِهِ اَل۪بَكرَة قَلساً وَ۪نَشُدّ طَرَفَيهِ في عارِضَة ثابِتَة حَتّى يَتَعَلَّق ثِقل ٓز فَ۪يَكون كُلّ واحِد مِن جُزأَي اَل۪حَبل اَل۪مَمدودَين يُقِلّ نِصف اَل۪ثِقل </s> |
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610 <s id="A18-2|13|05">فَ۪اِن حَلَّ أَحَد طَرَف اَل۪قَلس اَل۪مَشدود عَلى عَلامَة ٓك وَ۪قامَ هُوَ هُناكَ يَمسُك اَل۪قَلس فَ۪إِنَّهُ يَكون يَحمِل نِصف ذٰلِكَ اَل۪ثِقل فَ۪يَكون جَميع اَل۪ثِقل ضِعف اَل۪قُوَّة اَلَّتي تَضبُطُهُ </s> |
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611 <s id="A18-2|13|06">فَ۪يَظهَر مِن هاهُنا أَنَّ قُوَّة أُخرا مِن اَل۪عارِضَة اَل۪ثابِتَة في طَرَف اَل۪حَبل اَل۪مَشدود مُعادِلَة لِ۪ل۪قُوَّة اَل۪ماسِكَة لِ۪ل۪طَرَف اَل۪آخَر تَجتَبِذ اَل۪ثِقل أَيضاً</s> |
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612 <s id="A18-2|13|07">فَ۪ل۪ذٰلِكَ بِ۪إِستِحقاق سُمِّيَت هٰذِهِ اَل۪بَكرَة ذا رَفعَين</s> |
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613 <s id="A18-2|13|08">فَ۪إِذاً اَل۪قَلس اَل۪مُثَنّى اَل۪مَقسوم بِ۪قِسمَين مَمدودَين قَد يُمكِن اَن يُسَمّي ذا رَفع واحِد وَ۪ذا رَفعَين </s> |
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614 <s id="A18-2|13|09">فَ۪مِن هاهُنا ظَهَرَ لَنا أَنَّهُ يَنبَغي اَن يَكون طَرَف اَل۪قَلس اَل۪آخَر مُرتَبِطاً في عارِضَة ثابِتَة لا في اَل۪ثِقل اَل۪مَوضوع لِ۪ل۪رَفع لِ۪أَنَّ قُوَّة ما مِن ذٰلِكَ اَل۪رُكن اَل۪ثابِت تُعادِل اَل۪قُوَّة اَل۪مُحَرِّكَة وَ۪تُعيينها عَلى حَرَكَة اَل۪ثِقل </s> |
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615 <s id="A18-2|13|10">فَ۪قَد ظَهَرَ أَنَّهُ إِذا كانَ طَرَف اَل۪قَلس اَل۪واحِد مُرتَبِطاً في اَل۪حَمل فَ۪إِنَّ اَل۪حَمل يُعادِل قُوَّة مُساوِيَة لَهُ وَ۪إِذا كانَ طَرَفُهُ اَل۪آخَر مُرتَبِطاً في عارِضَة ثابِتَة فَ۪إِنَّ اَل۪قُوَّة تُعادِل ضِعفَها مِن اَل۪ثِقل فَ۪يَتَحَرَّك اَل۪ثِقل بِ۪قُوَّة أَقَلّ مِن اَل۪قُوَّة اَلَّتي كانَت تُحَرِّكُهُ أَوَّلاً</s> |
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616 </p> |
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617 <p n="14"> |
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618 <s id="A18-2|14|00"></s> |
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619 <s id="A18-2|14|01"><pb n="131"></pb> أَمّا اَل۪إِسفين فَ۪إِنَّ اَل۪ضَربَة تُحَرِّكُهُ في زَمان ما لِ۪أَنَّهُ لا تَكون حَرَكَة بِلا زَمان وَ۪هٰذِهِ اَل۪ضَربَة إِنَّما تَفعَل بِ۪اَل۪مُماسَّة فَقَط اَلَّتي لا تَثبُت عَلى اَل۪إِسفين وَ۪لا أَقَلّ زَمان </s> |
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620 <s id="A18-2|14|02">فَ۪يَظهَر لَنا مِن هاهُنا أَنَّهُ بَعدَ اَن تُفارِق اَل۪ضَربَة اَل۪إِسفين يَتَحَرَّك </s> |
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621 <s id="A18-2|14|03">وَ۪قَد نَعلَم ذٰلِكَ أَيضاً مِن جِهَة أُخرا </s> |
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622 <s id="A18-2|14|04">إِنَّهُ بَعدَ اَل۪ضَربَة بِ۪زَمان ما تَكون مِن اَل۪إِسفين وَحَيات وَ۪قِلع مِن قِلعَة عَلى حِدَّتِهِ </s> |
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623 <s id="A18-2|14|05">فَ۪أَمّا اِن تَكون اَل۪ضَربَة وَ۪اِن كانَت لا تُقيم عَلى اَل۪إِسفين وَ۪لا أَقَلّ زَمان تَفعَل فيهِ فَ۪إِنَّ ذٰلِكَ ظاهِر لَنا مِن اَل۪حِجارَة اَلَّتي يُرمي بِها وَ۪اَل۪سِهام كانَ رَميُها مِن يَد فَقَط أَو مِن آلَة أُخرا </s> |
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624 <s id="A18-2|14|06">لِ۪أَنَّهُ بَعدَ اَن يُفارِق اَل۪حَجَر اَل۪يَد نَراهُ يَنفُذ إِلى مَوضِع بَعيد بِ۪قُوَّة بِ۪لا اَن تَكون اَل۪يَد تَدفَعُهُ </s> |
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625 <s id="A18-2|14|07">فَ۪مِن هاهُنا يَظهَر لَنا أَنَّ اَل۪ضَربَة لا تُقيم عَلى اَل۪إِسفين وَ۪لا أَقَلّ زَمان وَ۪لَكِنَ اَل۪إِسفين بَعدَ اَل۪ضَربَة يَأخُذ بِ۪حَرَكَة</s> |
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626 </p> |
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627 <p n="15"> |
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628 <s id="A18-2|15|00"></s> |
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629 <s id="A18-2|15|01">فَ۪أَقول إِنَّ كُلّ ضَربَة وَ۪اِن كانَت يَسيرَة فَ۪إِنَّها تُحَرِّك كُلّ إِسفين </s> |
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630 <s id="A18-2|15|02">فَ۪ل۪نَفرِض إِسفيناً ما يَكون زاوِيَتُهُ عَلى عَلامَة ٓأَة وَ۪يَكون رَأسُهُ خَطّ ٓدٓم </s> |
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631 <s id="A18-2|15|03">وَ۪ل۪تَكُن تُحَرِّكُهُ ضَربَة ٓبٓغ وَ۪ل۪يَكُن بُعدُهُ ٓآد </s> |
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632 <s id="A18-2|15|04">وَ۪ل۪يَكُن يُمكِن اَن يُحَرَّك بِ۪ضَربَة يَسيرَة </s> |
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633 <s id="A18-2|15|05">وَ۪ل۪نَفصِل مِن ضَربَة ٓبٓغ ضَربَة تَكون ضَربَة ٓبٓe وَ۪هِيَ أَقَلّ مِن جَميع اَل۪ضَرَبات اَل۪مَعلومَة فَ۪أَقول إِنَّ ضَربَة ٓبٓe هِيَ في ذات نَفسِهِ تَدفَع جُزأاً ما مِن اَل۪إِسفين </s> |
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634 <s id="A18-2|15|06">بُرهان ذٰلِكَ مِن أَجل أَنَّ <pb n="1 33"></pb> ضَربَة ٓبٓغ تُحَرِّك بُعد ٓآد فَ۪إِنَّ ٓeٓغ تُحَرِّك بُعداً أَقَلّ مِن ٓآد فَ۪ل۪تُحَرِّك بُعد ٓآز </s> |
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635 <s id="A18-2|15|07">وَ۪أَيضاً إِذا زيدَت ضَربَة ٓبٓe فَ۪اِن كانَ بُعد ٓآد يَتَحَرَّك بِ۪ضَربَة ٓبٓغ فَ۪إِذاً ضَربَة ٓبٓe في ذات نَفسِها تُحَرِّك بُعد ٓدٓز </s> |
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636 <s id="A18-2|15|08">تَوَهَّمنا ضَربَة ٓبٓغ مَقسومَة بِ۪ضَرَبات مُساوِيَة لِ۪ٓبٓe وَ۪هِيَ ٓبٓe ٓeٓه ٓهٓغ فَ۪إِنَّ بُعد ٓآد يَنقَسِم بِ۪أَقسام مُساوِيَة لِ۪ٓدٓز وَ۪هِيَ ٓآك ٓكٓل ٓلٓز ٓزٓد فَ۪تَكون كُلّ واحِدَة مِن ضَرَبات ٓبٓe ٓeٓه ٓهٓت ٓتٓغ تُحَرِّك كُلّ واحِد مِن أَبعاد ٓدٓز ٓزٓل ٓلٓك ٓكٓا </s> |
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637 <s id="A18-2|15|09">فَ۪ل۪نَتَوَهَّم خُطوطاً مُوازِيَة لِ۪خَطّ ٓدٓم اَلَّذي هُوَ رَأس اَل۪إِسفين وَ۪هِيَ خُطوط ٓزٓن ٓلٓس ٓكْٓ وَ۪خُطوطاً أَيضاً مُوازِيَة لِ۪خَطّ ٓآد وَ۪هِيَ خُطوط ٓفٓن ٓقٓس ٓرْٓ فَ۪تَكون خُطوط ٓدٓر ٓرٓق ٓقٓف ٓفٓم مُتَساوِيَة </s> |
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638 <s id="A18-2|15|10">فَ۪اِن وَصَلنا عَلامات ٓف ٓق ٓر بِ۪عَلامَة ٓأَة تَحصُل أَربَعَة إِسفينات تَكون زَواياها عِندَ عَلامَة ٓأَة وَ۪تَكون رُؤوسُها خُطوط ٓمٓف ٓفٓق ٓقٓر ٓرٓد </s> |
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639 <s id="A18-2|15|11">وَ۪يَكون كُلّ واحِد مِنها يَتَحَرَّك بِ۪ضَربَة مُساوِيَة لِ۪ضَربَة ٓبٓe بُعداً مُساوِياً لِ۪خَطّ ٓآد فَ۪سَواء اَن يُقال إِنَّ ضَربَة ٓبٓe تَنفُذ مِن اَل۪إِسفين كُلِّهِ بُعد ٓدٓز أَعني بُعد ٓكٓا وَ۪إِنَّ ضَربَة ٓبٓe تَنفُذ اَل۪إِسفين اَلَّذي رَأسُهُ ٓرٓد بِ۪بُعد ٓآد لِ۪أَنَّ بِ۪حَرَكَة كُلّ اَل۪إِسفين يَتَحَرَّك خَطّ ٓكْٓ بِ۪بُعد ٓآك وَ۪بِ۪حَرَكَة اَل۪إِسفين اَلَّذي رَأسُهُ ٓدٓر يَتَحَرَّك اَل۪بُعد اَل۪مُساوي لِ۪خَطّ ٓكْٓ وَ۪هُوَ بُعد ٓرٓد بِ۪بُعد ٓآد فَ۪إِذاً ٓرٓد يَتَحَرَّك بِ۪ضَربَة ٓبٓe بُعد ٓآد </s> |
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640 <s id="A18-2|15|12">وَ۪مِن هاهُنا ظَهَرَ لَنا أَنَّ قَدر ضَربَة ٓبٓe مِن ٓبٓغ هُوَ قَدر اَل۪إِسفين اَلَّذي <pb n="135"></pb> رَأسُهُ ٓرٓد مِن جَميع اَل۪إِسفين </s> |
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641 <s id="A18-2|15|13">وَ۪كَ۪ذٰلِكَ أَيضاً قَدر اَل۪زَمان اَلَّذي يَتَحَرَّك فيهِ اَل۪إِسفين اَلَّذي رَأسُهُ خَطّ ٓرٓد وَ۪قَدر حَرَكَة اَل۪بُعد اَلَّذي يُحَرَّكُهُ اَل۪إِسفين كُلُّهُ بِ۪ضَربَة ٓبٓغ وَ۪نِسبَة ذٰلِكَ أَيضاً كَ۪نِسبَة ضَربَة ٓبٓe إِلى اَل۪ضَربَة كُلِّها </s> |
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642 <s id="A18-2|15|14">وَ۪عَلى وَجه آخَر أَيضاً لا نُصيب إِختِلافاً بَينَ حَرَكَة ضَربَة ٓبٓغ رَأس ٓدٓم أَعني اَل۪إِسفين كُلِّهِ وَ۪بَينَ حَرَكَة كُلّ واحِدَة مِن ضَرَبات ٓبٓe ٓeٓه ٓهٓت ٓتٓغ ٓتٓغ كُلّ واحِد مِن اَل۪إِسفينات اَلَّتي رُؤوسُها ٓمٓف ٓفٓق ٓقٓر ٓرٓد لِ۪أَنَّ اَل۪ضَرَبات اَل۪جُزئِيَّة تُساوي اَل۪ضَربَة اَل۪كُلِّيَّة </s> |
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643 <s id="A18-2|15|15">فَ۪ضَربَة ٓبٓe تَنفُذ مِن اَل۪إِسفين اَلَّذي رَأسُهُ ٓمٓف بِ۪قَدر ما يَنفُضُهُ كُلّ اَل۪ضَربَة مِن كُلّ اَل۪إِسفين وَ۪كُلّ ضَربَة مِن اَل۪ضَرَبات اَل۪باقِيَة كُلّ واحِد مِن اَل۪أَسافين اَل۪باقِيَة </s> |
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644 <s id="A18-2|15|16">فَ۪اِن كانَ اَل۪مَدفوع إِسفيناً واحِداً مِن اَل۪أَسافين اَل۪صِغار إِذا ضُرِبَ ضَرباً كَثيراً وَ۪دُفِعَ فَ۪إِنَّهُ يُدفَع اَل۪قَدر اَلَّذي يُدفَعُهُ كُلّ اَل۪إِسفين بِ۪كُلِّيَّة اَل۪ضَربَة اَل۪واحِدَة </s> |
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645 <s id="A18-2|15|17">وَ۪ذٰلِكَ بِ۪حَرَكَة هٰذا اَل۪قَدر مِن اَل۪ضَرَبات أَعني بِ۪قَدر ضَرَبات ٓبٓe ٓeٓه ٓهٓت ٓتٓغ وَ۪عَلى هٰذا تَكون نِسبَة اَل۪زَمان إِلى اَل۪زَمان كَ۪نِسبَة اَل۪ضَربَة إِلى اَل۪ضَربَة وَ۪رَأس اَل۪إِسفين كُلِّهِ إِلى رَأس أَحَد اَل۪أَسافين اَل۪صِغار </s> |
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646 <s id="A18-2|15|18">فَ۪بِ۪اَل۪قَدر اَلَّذي بِهِ تَكون زاوِيَة اَل۪إِسفين أَصغَر بِ۪ذٰلِكَ اَل۪قَدر يَنفُذ اَل۪إِسفين بِ۪قُوَّة أَصغَر مِن اَل۪قُوَّة اَلَّتي تَنفُذ اَل۪إِسفين كُلُّهُ</s> |
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647 </p> |
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648 <p n="16"> |
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649 <s id="A18-2|16|00"></s> |
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650 <s id="A18-2|16|01">وَ۪قَد بَقِيَة بَعدَ هٰذا اَن نَشرَح اَل۪سَبَب في اَل۪لَولَب </s> |
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651 <s id="A18-2|16|02">فَ۪ل۪نَبدَأ أَوَّلاً بِ۪وَضع ما يَعرِض لِ۪ل۪دَوائِر اَل۪لَولَبِيَّة </s> |
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652 <s id="A18-2|16|03">فَ۪نَقول إِنّا إِذا <pb n="137"></pb> أَرَدنا اَن نَرسُم لَولَباً نَأخُذ عوداً صُلباً قَوِياً يَكون طولُهُ عَلى اَل۪قَدر اَلَّذي نُريد وَ۪ل۪يَكُن ما نُريد اَن نُلَولِبَهُ مِنهُ مَخروطاً وَ۪ل۪يَكُن غِلَظُهُ مُتَساوي اَل۪أَجزاء لِ۪يَكون بَسيطُهُ أُسطُوانَة وَ۪نَرسُم عَلى بَسيطِهِ ضِلع أُسطُوانَة </s> |
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653 <s id="A18-2|16|04">وَ۪نُقَسِّم هٰذا اَل۪ضِلع بِ۪أَجزاء مُتَساوِيَة تَكون عَلى قَدر عَرض اَل۪دائِرَة اَل۪لَولَبِيَّة وَ۪نَفرِض عَلى سَطح خَطَّين مُستَقيمَين أَحَدُهُما قائِم عَلى اَل۪آخَر وَ۪ل۪نُصير أَحَد اَل۪خَطَّين مُساوِياً لِ۪مُحيط اَل۪أُسطُوانَة وَ۪اَل۪آخَر عَلى قَدر عَرض مَوضِع اَل۪دائِرَة اَل۪لَولَبِيَّة وَ۪ل۪نَصِل طَرَفَي اَل۪خَطَّين بِ۪خَطّ يُوَتِّر اَل۪زاوِيَة اَل۪قائِمَة وَ۪نَعمَل مُثَلَّثاً مِن صُفر رَقيق مُساوِياً لِ۪هٰذا اَل۪مُثَلَّث وَ۪ل۪يَكُن في رِقَّتِهِ عَلى اَل۪قَدر اَلَّذي يُمكِنُنا تَعويجُهُ كَيفَ أَرَدنا</s> |
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654 <s id="A18-2|16|05">فَ۪إِذا فَعَلناذٰلِكَ رَكَّبنا اَل۪ضِلع اَل۪مُساوي لِ۪عَرض مَوضِع اَل۪دائِرَة اَل۪لَولَبِيَّة عَلى أَوَّل اَل۪أَبعاد اَل۪مُتَساوِيَة اَلَّتي قَسَّمناها مِن ضِلع اَل۪أُسطُوانَة ثُمَّ نَلُفّ اَل۪مُثَلَّث اَل۪صُفر اَل۪رَقيق عَلى اَل۪خَشَبَة اَل۪أُسطُوانِيَّة فَ۪نُصَيِّر اَل۪زاوِيَة اَل۪حادَّة اَل۪باقِيَة مِن اَل۪مُثَلَّث إِلى اَل۪زاوِيَة اَل۪قائِمَة مِن اَل۪شَكل اَل۪صُفر لِ۪أَنَّ قاعِدَة اَل۪مُثَلَّث مُساوِيَة لِ۪مُحيط اَل۪أُسطُوانَة</s> |
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655 <s id="A18-2|16|06">ثُمَّ نَلزَق كِلتَي اَل۪زاوِيَتَين وَ۪نَرسُم اَل۪دائِرَة اَل۪لَولَبِيَّة عَلى وَتَر اَل۪زاوِيَة اَل۪قائِمَة </s> |
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656 <s id="A18-2|16|07">ثُمَّ نُدير اَل۪مُثَلَّث إِلى اَل۪بُعد اَل۪ثاني وَ۪نُرَكِّب ضِلع اَل۪مُثَلَّث اَل۪رَقيق عَلى اَل۪قِسم اَل۪ثاني </s> |
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657 <s id="A18-2|16|08">وَ۪بِ۪مِثل ذٰلِكَ اَل۪عَمَل اَل۪أَوَّل أَيضاً نَرسُم اَل۪دائِرَة اَل۪لَولَبِيَّة اَل۪ثانِيَة مُلاصِقَ لِ۪ل۪دائِرَة اَل۪ولا </s> |
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658 <s id="A18-2|16|09">وَ۪كَ۪ذٰلِكَ نَفعَل حَتّى نَرسُم جَميع أَبعاد اَل۪خَشَبَة اَل۪أُسطُوانِيَّة </s> |
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659 <s id="A18-2|16|10"><pb n="139"></pb> وَ۪مِن أَجل أَنّا عِندَ إِستِعمالِنا اَل۪لَولَب إِحتَجنا اَن نَضَع في اَل۪حَفر اَل۪أَوَّل اَلَّذي لِ۪ل۪دائِرَة اَل۪لَولَبِيَّة اَل۪خَشَبَة اَلَّتي تُسَمّي طولُس وَ۪هِيَ اَلَّتي تُقِلّ اَل۪ثِقل فَ۪إِنَّهُ عِندَ تَدوير اَل۪لَولَب يَرتَفِع هٰذا اَل۪عود وَ۪يَرتَفِع بِ۪إِرتِفاعِهِ اَل۪ثِقل</s> |
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660 </p> |
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661 <p n="17"> |
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662 <s id="A18-2|17|00"></s> |
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663 <s id="A18-2|17|01">فَ۪يَنبَغي اَن لا نَتَوَهَّم اَل۪لَولَب إِلّا إِسفيناً مُلتَفّاً لِ۪أَنَّ اَل۪مُثَلَّث اَلَّذي يَرسُم اَل۪دائِرَة اَل۪لَولَبِيَّة هُوَ في هَيئَة اَل۪إِسفين وَ۪رَأسُهُ هُوَ اَل۪ضِلع اَلَّذي هُوَ بُعد اَل۪دائِرَة اَل۪لَولَبِيَّة وَ۪زاوِيَة اَل۪إِسفين اَل۪حادَّة هِيَ زاوِيَة اَل۪مُثَلَّث اَل۪باقِيَة اَلَّتي يَكون عِندَها اَل۪عود اَل۪مُسَمّي طولُس فَ۪ل۪هٰذا صارَ اَل۪لَولَب إِسفيناً مُلتَوِياً مُلتَفّاً يَفعَل بِلا ضَربَة لَكِنَ بِ۪إِستِدارَتِهِ وَ۪تَدويرِهِ يَقوم فيهِ مَقام اَل۪ضَرب في اَل۪إِسفين فَ۪يُقِلّ اَل۪ثِقل وَ۪إِقلالُهُ اَل۪حَمل هُوَ بِ۪ضِدّ اَل۪فِعل اَلَّذي يَفعَلُهُ اَل۪إِسفين لِ۪أَنَّ اَل۪إِسفين إِنَّما يَفعَل بِ۪نُفوذِهِ إِلى داخِل فَ۪هُوَ يُحَرِّك اَل۪ثِقل وَ۪اَل۪ثِقل ثابِت في مَكانِهِ وَ۪أَمّا اَل۪لَولَب فَ۪إِنَّهُ إِسفين مُلتَوٍ وَ۪هُوَ ثابِتاً في مَكانِهِ يُقِلّ اَل۪ثِقل إِلَيهِ </s> |
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664 <s id="A18-2|17|02">وَ۪كَما أَنَّهُ قَد تَبَيَّنَ في اَل۪إِسفين أَنَّ اَلَّذي تَكون زاوِيَتُهُ أَصغَر يُحَرِّك اَل۪ثِقل بِ۪قُوَّة أَقَلّ مِن اَل۪قُوَّة اَلَّتي تُحَرِّك اَل۪ثِقل بِ۪اَل۪إِسفين اَلَّذي زاوِيَتُهُ أَعظَم كَ۪ذٰلِكَ يَلزَم اَن نَقول في هٰذا إِنَّ اَل۪لَولَب اَلَّذي اَل۪أَبعاد اَلَّتي بَينَ دَوائِرِهِ اَل۪لَولَبِيَّة أَقَلّ فَ۪إِنَّ حَرَكَتَهُ لِ۪ل۪ثِقل أَكثَر سُهولَة مِن حَرَكَة اَل۪لَولَب اَلَّذي تَكون اَل۪أَبعاد اَلَّتي بَينَ دَوائِرِهِ اَل۪لَولَبِيَّة أَكثَر لِ۪أَنَّ قِلَّة اَل۪بُعد تُصَيِّر اَل۪زَوايا أَصغَر فَ۪يَكون اَل۪لَولَب <pb n="141"></pb> اَلَّذي دَوائِرُهُ أَكثَر إِنتِصاباً يُحَرِّك اَل۪ثِقل بِ۪قُوَّة أَعظَم وَ۪اَلَّذي يَكون أَكثَر إِنخِفاضاً يُحَرِّك اَل۪ثِقل بِ۪قُوَّة أَقَلّ </s> |
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665 </p> |
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666 <p n="18"> |
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667 <s id="A18-2|18|00"></s> |
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668 <s id="A18-2|18|01">فَ۪أَمّا إِنَّهُ إِذا كانَت فَلكَة ذات أَوتاد مُرَكَّبَة في حَفر اَل۪لَولَب فَ۪إِنَّهُ بِ۪دَورَة واحِدَة يَدورُها اَل۪لَولَب يُحَرِّك مِن اَل۪فَلكَة وَتَداً واحِداً فَ۪إِنّا نُبَيِّن ذٰلِكَ بِ۪هٰذِهِ اَل۪جِهَة </s> |
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669 <s id="A18-2|18|02">نَتَوَهَّم لَولَباً يَكون لَولَب ٓآب وَ۪ل۪تَكُن اَل۪دَوائِر اَل۪لَولَبِيَّة اَلَّتي فيهِ ٓآغ ٓدٓe ٓزٓه وَ۪ل۪تَكُن هٰذِهِ اَل۪دَوائِر اَل۪لَولَبِيَّة كُلّ واحِدَة مِنها دائِرَة واحِدَة </s> |
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670 <s id="A18-2|18|03">وَ۪ل۪نَفرِض فَلكَة مَوضوعَة ذات أَوتاد تَكون ٓهٓغٓeٓت وَ۪ل۪تَكُن أَوتادُها ٓهٓغ ٓغٓe ٓeٓت وَ۪ل۪تَكُن مُرَكَّبَة في اَل۪دَوائِر اَل۪لَولَبِيَّة </s> |
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671 <s id="A18-2|18|04">وَ۪ل۪يَكُن وَتَد ٓغٓe مُرَكَّباً في دائِرَة لَولَبِيَّة تَركيباً مُستَقصاً فَ۪تَكون اَل۪أَوتاد اَل۪اُخَر غَير مُرَكَّبَة في اَل۪دَوائِر اَل۪لَولَبِيَّة اَل۪اُخَر </s> |
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672 <s id="A18-2|18|05">فَ۪اِن أَدَرنا اَل۪لَولَب حَتّى تَندَفِع عَلامَة ٓe إِلى ما يَلي ٓغ تَصير ٓe عِندَ ٓغ </s> |
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673 <s id="A18-2|18|06">فَ۪إِذا دارَ اَل۪لَولَب دَورَة واحِدَة وَ۪صارَ وَتَد ٓغٓe في مَوضِع وَتَد ٓغٓه وَ۪وَتَد ٓeٓت في مَوضِع وَتَد ٓغٓe وَ۪وَتَد ٓeٓت أَيضاً في مَوضِع وَتَد ٓغٓe فَ۪إِنَّهُ في دَورَة واحِدَة يَدورُها اَل۪لَولَب يَدور اَل۪بُعد اَلَّذي لِ۪ل۪وَتَد كُلُّهُ </s> |
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674 <s id="A18-2|18|07">وَ۪كَ۪ذٰلِكَ يَنبَغي اَن نَتَوَهَّم في اَل۪أَوتاد اَل۪اُخَر </s> |
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675 <s id="A18-2|18|08">فَ۪يَكون عَلى قَدر ما في اَل۪فَلكَة مِن اَل۪أَوتاد بِ۪ذٰلِكَ اَل۪قَدر يَدور اَل۪لَولَب مِن اَل۪دَورات إِلى اَن تَدور دَورَة واحِدَة</s> |
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676 </p> |
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677 <p n="19"> |
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678 <s id="A18-2|19|00"></s> |
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679 <s id="A18-2|19|01">فَ۪اَل۪لَولَب إِذا دارَ يُحَرِّك اَل۪خَشَبَة اَلَّتي تُسَمّي طولُس عَلى ما تَقَدَّمَ في قَولِنا وَ۪يُشيل اَل۪ثِقل عَلى إِستِقامَة</s> |
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680 <s id="A18-2|19|02"><pb n="143"></pb> وَ۪قَد يَجِب اَن يَكون هٰذا اَل۪طولُس إِذا لَم يَتَحَرَّك اَل۪لَولَب هادِياً ثابِتاً في مَوضِعِهِ بِ۪قُوَّة ما تَكون لَهُ وَ۪لا يَكون عِندَ هُدوء اَل۪لَولَب مِن اَل۪تَدوير يَقوا اَل۪ثِقل عَلَيهِ أَعني اَن يَكون إِذا رُكِّبَ هٰذا اَل۪عود في اَل۪حَفر اَل۪لَولَبي وَ۪كانَ شَبيهاً بِ۪اَل۪سَنَد لَهُ اَن لا يَزلَفَ مِن اَل۪حَفر اَل۪لَولَبي لِ۪أَنَّهُ اِن زَلَفَ إِنحَطَّ جَميع اَل۪ثِقل إِلى اَل۪مَوضِع اَلَّذي مِنهُ شيلَ </s> |
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681 <s id="A18-2|19|03">وَ۪هٰذا اَل۪عود لا يَزلَف مِن اَل۪حَفر اَل۪لَولَبي إِذا كانَ طَرَف اَل۪عود مُهَندَماً عَلى اَل۪حَفر وَ۪كانَ اَل۪حَفر شَبيهاً بِ۪اَل۪مِسمات لَهُ </s> |
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682 <s id="A18-2|19|04">فَ۪ل۪ذٰلِكَ نَحتاج اَن نُصَيِّر دَوائِر اَل۪لَولَب مُتَقارِبَة لِ۪تَكون شَبيهَ بِ۪اَل۪مُوازِيَة لِ۪قاعِدَة اَل۪أُسطُوانَة اَلَّتي اَل۪لَولَب مَرسوم عَلَيها </s> |
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683 <s id="A18-2|19|05">فَ۪إِنَّ اَل۪دَوائِر إِذا كانَت عَلى هٰذا كانَت شَبيهَ بِ۪اَل۪مِسمات لِ۪ل۪عود اَلَّذي يُقِلّ اَل۪ثِقل </s> |
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684 <s id="A18-2|19|06">فَ۪أَمّا اِن كانَت اَل۪دَوائِر اَل۪لَولَبِيَّة اَلَّتي في اَل۪حَفر اَل۪لَولَبي شَديدَة اَل۪إِنتِصاب حَتّى تَكون شَبيهَ بِ۪اَل۪مُوازِيَة لِ۪ضِلع اَل۪أُسطُوانَة فَ۪إِنَّ اَل۪عود اَلَّذي يُقال لَهُ طولُس إِذا تُعَلَّق عَلَيهِ حَمل ثَقيل أَو أَثقَلَتهُ قُوَّة عَظيمَة فَ۪إِنَّهُ يَرُدّ تَدوير اَل۪لَولَب وَ۪يُصَيِّرُهُ يَدور تَدويراً ضِدَّ ذٰلِكَ اَل۪تَدوير اَل۪أَوَّل فَ۪مِن هاهُنا يَظهَر لَنا أَنَّ اَل۪لَولَب قَد يُمكِنُهُ اَن يُحَرِّك اَل۪عود اَلَّذي يُقال لَهُ طولُس وَ۪قَد يُمكِنُهُ اَن يَتَحَرَّك بِ۪هٰذا اَل۪عود أَيضاً فَ۪هُوَ يُحَرِّك اَل۪عود إِذا كانَ حَفرُهُ اَل۪لَولَبي مُتَقارِب اَل۪دَوائِر وَ۪إِذا كانَ عِندَ بُطلان تَدوير اَل۪لَولَب يَثبُت في مَكانِهِ وَ۪يَبقى اَل۪حَمل مُعَلَّقاً عَلَيهِ </s> |
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685 <s id="A18-2|19|07">وَ۪أَمّا إِذا كانَ اَل۪حَفر <pb n="145"></pb> اَل۪لَولَبي شَديد اَل۪إِنتِصاب وَ۪كانَ عِندَ بُطلان تَدوير اَل۪لَولَب لا يَثبُت فَ۪إِنَّ اَل۪عود يَكون اَلَّذي يُحَرِّك اَل۪لَولَب لِ۪أَنَّهُ إِذا كانَ في اَل۪مَوضِع غَير اَل۪مَحفور مِن اَل۪لَولَب حَبل ما مَشدوداً وَ۪شِدَّة في طَرَف ذٰلِكَ اَل۪حَبل ثِقل ما وَ۪كانَ اَل۪حَفر اَل۪لَولَبي شَديد اَل۪إِنتِصاب فَ۪إِنّا إِذا رَفَعنا اَل۪عود اَلَّذي يُقالُ لَهُ طولُس نَرفَع أَيضاً اَل۪ثِقل فَ۪إِذا بَطَلنا مِن رَفع اَل۪عود يَسكٌ اَل۪ثِقل وَ۪يَكون مُتَعَلِّقاً لِ۪أَنَّ هٰذا اَل۪عود قَد يُضادّ حَفر اَل۪لَولَب إِذا كانَ حَفرُهُ شَبيهاً بِ۪اَل۪مُوازي لِ۪ضِلع اَل۪أُسطُوانَة </s> |
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686 <s id="A18-2|19|08">وَ۪اِن لَم يَكُن عَلى اَل۪أُسطُوانَة حَفر لَولَبي وَ۪كانَ عَلَيها حَفر ميزابي عَلى أَحَد أَضلاع اَل۪أُسطُوانَة فَ۪إِنَّ اَل۪عود اَلَّذي يُقال لَهُ طولُس يَكون شَديد اَل۪مُضادَّة لِ۪هٰذا اَل۪حَفر اَل۪ميزابي </s> |
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687 <s id="A18-2|19|09">وَ۪إِذا كانَت اَل۪دَوائِر اَل۪لَولَبِيَّة مُتَقارِبَة وَ۪رَفَعنا اَل۪خَشَبَة اَلَّتي يُقال لَها طولُس فَ۪إِنّا لا نُحَرِّك اَل۪ثِقل إِلّا اِن تَكون قُوَّة عَظيمَة تُقِلّ اَل۪طولُس </s> |
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688 <s id="A18-2|19|10">فَ۪أَمّا إِذا كانَ اَل۪ثِقل مُعَلَّقاً في اَل۪طولُس فَ۪إِنَّهُ إِذا كانَت اَل۪دَوائِر اَل۪لَولَبِيَّة مُتَقارِبَة وَ۪أَدَرنا اَل۪لَولَب يَرتَفِع اَل۪ثِقل وَ۪إِذا بَطَلنا مِن تَدوير اَل۪لَولَب يَسكٌ اَل۪ثِقل وَ۪يَبقى مُتَعَلِّقاً </s> |
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689 <s id="A18-2|19|11">وَ۪إِذا كانَت اَل۪دَوائِر اَل۪لَولَبِيَّة مُنتَصِبَة فَ۪إِنّا لا نُحَرِّك اَل۪ثِقل إِلّا اِن تَكون قُوَّة عَظيمَة تَقهَر اَل۪لَولَب </s> |
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690 <s id="A18-2|19|12">فَ۪قَد قُلنا في طَبيعَة اَل۪لَولَب وَ۪عَمَلِهِ ما يَكتَفي بِهِ</s> |
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691 </p> |
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692 <p n="20"> |
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693 <s id="A18-2|20|00"></s> |
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694 <s id="A18-2|20|01">أَمّا اَن تَكون اَل۪خَمس اَل۪قُوى اَلَّتي تُحَرِّك اَل۪ثِقل مُشاكِلَة لِ۪ل۪دَوائِر اَلَّتي عَلى مَركَز واحِد فَ۪قَد تَبَيَّنَ <pb n="147"></pb> ذٰلِكَ فيما تَقَدَّمَ مِن اَل۪أَشكال اَلَّتي رَسَمناها وَ۪إِنّا أَرى أَنَّها إِلى مُشاكَلَت اَل۪ميزان أَقرَب مِنها إِلى مُشاكَلَت اَل۪دَوائِر لِ۪ما تَقَدَّمَ مِن أَنَّ أَوائِل بُرهان اَل۪دَوائِر إِنَّما خُرِجَ لَنا بِ۪اَل۪ميزان </s> |
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695 <s id="A18-2|20|02">فَ۪إِنَّهُ قَد تَبَيَّنَ أَنَّ نِسبَة اَل۪ثِقل اَل۪مُتَعَلِّق في اَل۪جِهَة اَل۪صُغرى إِلى اَل۪مُعَلَّق في اَل۪جِهَة اَل۪كُبرى كَ۪نِسبَة اَل۪أَعظَم مِن جُزأَي اَل۪ميزان إِلى اَل۪أَصغَر </s> |
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696 <s id="A18-2|20|03">وَ۪هٰذِهِ اَل۪خَمس اَل۪قُوى كُلُّها قَد يَلحَقُها إِمتِناع ما مِن اَل۪فِعل إِذا أَرَدنا اَن نُحَرِّك بِها أَثقالاً عِظاماً بِ۪قُوَّة يَسيرَة </s> |
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697 <s id="A18-2|20|04">أَمّا اَل۪ثَلاث اَل۪ولا فَ۪إِنَّهُ يَعرِض لَها اَن نَزيد في عُظمِها عَلى قَدر زِيادَة اَل۪ثِقل اَلَّذي نُريد اَن نَرفَعُهُ أَعني اَل۪فَلكَة اَلَّتي عَلى اَل۪مِحوَر وَ۪اَل۪مُخل وَ۪اَل۪آلَة اَلَّتي تُسَمّي كَثيرَة اَل۪رَفع فَ۪أَمّا اَل۪اِثنَتان أَعني اَلَّتي تَكون بِ۪اَل۪إِسفين وَ۪اَلَّتي تَكون بِ۪اَل۪لَولَب فَ۪إِنَّهُ يَعرِض لَها اَن نَنقُص مِن عُظمِها عَلى ذٰلِكَ اَل۪قَدر </s> |
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698 <s id="A18-2|20|05">وَ۪مِثال ذٰلِكَ اِن أَرَدنا اَن نُحَرِّك ثِقلاً يَكون أَلف قِنطار بِ۪قُوَّة تَعادَلَ خَمسَة قَناطير وَ۪إِستَعمَلنا هٰذِهِ اَل۪حَرَكَة بِ۪اَل۪مِحوَر اَلَّذي عَلَيهِ فَلكَة يَحتاج اَن يَكون اَل۪خَطّ اَل۪خارِج مِن مَركَز اَل۪فَلكَة إِلى مُحيطِها مِئَتَي مَرَّة مِثل اَل۪خَطّ اَل۪خارِج مِن مَركَز اَل۪مِحوَر إِلى مُحيطِها وَ۪أَكثَر مِن ذٰلِكَ قَليلاً </s> |
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699 <s id="A18-2|20|06">فَ۪اِن إِستَعمَلنا ذٰلِكَ في اَل۪مُخل إِحتَجنا اَن يَكون جُزؤُهُ اَل۪أَعظَم اَلَّذي مِمّا يَلي اَل۪قُوَّة اَل۪مُحَرِّكَة لِ۪ل۪ثِقل عَلى هٰذِهِ اَل۪نِسبَة أَو أَكثَر قَليلاً </s> |
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700 <s id="A18-2|20|07">وَ۪إِستِعمال ذٰلِكَ في مِثل هٰذِهِ اَل۪آلات يَصعُب أَو يَكاد اَن يَكون غَير <pb n="149"></pb> مُمكِن لِ۪أَنّا اِن صَيَّرنا قُطر اَل۪مِحوَر نِصف ذِراع لِ۪كَي يَقوا اَن يَتَعَلَّق اَل۪حَمل عَلَيهِ إِحتَجنا اَن نُصَيِّر قُطر اَل۪فَلكَة مِئَة ذِراع أَو أَكثَر مِن ذٰلِكَ قَليلاً </s> |
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701 <s id="A18-2|20|08">وَ۪عَمَل ذٰلِكَ يَصعُب </s> |
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702 <s id="A18-2|20|09">وَ۪كَ۪ذٰلِكَ يَعرِض في اَل۪مُخل وَ۪في اَل۪آلَة اَل۪كَثيرَة اَل۪رَفع لِ۪أَنَّهُ لا يُمكِنُنا اَن نَعمَل قِسمَة اَل۪مُخل عَلى هٰذا وَ۪لا نَعمَل كَثرَة اَل۪بِكَر عَلى هٰذا اَل۪قَدر </s> |
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703 <s id="A18-2|20|10">فَ۪ل۪نَحتال اَل۪آن في تَسهيل اَل۪إِمتِناع اَلَّذي يَعرِض لِ۪هٰذِهِ اَل۪ثَلاث اَل۪قُوى</s> |
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704 </p> |
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705 <p n="21"> |
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706 <s id="A18-2|21|00"></s> |
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707 <s id="A18-2|21|01">وَ۪نَقول إِنَّ اَل۪دائِرَة هِيَ أَكثَر اَل۪أَشكال كُلِّها حَرَكَة وَ۪أَسهَلُها كانَت اَل۪دائِرَة مُتَحَرِّكَة عَلى مَركَز واحِد أَو كانَت مُتَحَرِّكَة عَلى سَطح قائِمَة عَلَيهِ </s> |
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708 <s id="A18-2|21|02">وَ۪كَ۪ذٰلِكَ اَل۪أَشكال اَل۪قَريبَة مِنها أَعني اَل۪أَكَرّ وَ۪اَل۪أَساطين فَ۪إِنَّ حَرَكَتَها إِستِدارِيَّة كَما قَد بَيَّنّا في اَل۪مَقالَة اَلَّتي قَبلَ هٰذِهِ </s> |
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709 <s id="A18-2|21|03">فَ۪هَبنا نُريد اَن نُحَرِّك أَوَّلاً ثِقلاً عَظيماً بِ۪اَل۪مِحوَر اَل۪داخِل في اَل۪فَلكَة بِ۪قُوَّة يَسيرَة وَ۪لا يَعرِض فيهِ ذٰلِكَ اَل۪إِمتِناع </s> |
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710 <s id="A18-2|21|04">وَ۪ل۪يَكُن اَل۪ثِقل اَلَّذي نُريد تَحريكَهُ أَلف قِنطار مَثَلاً وَ۪اَل۪قُوَّة اَلَّتي نُريد اَن نُحَرِّكَهُ بِها خَمسَة قَناطير </s> |
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711 <s id="A18-2|21|05">فَ۪نَحتاج أَوَّلاً اَن نُصَيِّر اَل۪قُوَّة مُعادِلَة لِ۪ل۪ثِقل لِ۪أَنَّ ذٰلِكَ إِذاظَهَرَ أَمكَنَنا اَن نُصَيِّر تِلكَ اَل۪قُوَّة تَقوى عَلى اَل۪ثِقل بِ۪زِيادَة ما يَسيرَة نَزيدُها في اَل۪آلَة</s> |
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712 <s id="A18-2|21|06">فَ۪ل۪نُصَيِّر اَل۪مِحوَر اَلَّذي يَلتِفّ عَلَيهِ اَل۪قَلس اَل۪مَشدود في اَل۪ثِقل </s> |
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713 <s id="A18-2|21|07">عَلى عَلامَة ٓأَة وَ۪ل۪تَكُن اَل۪فَلكَة اَل۪مُرَكَّبَة عَلى عَلامَة ٓب </s> |
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714 <s id="A18-2|21|08">وَ۪ل۪يَسهُل عَلَينا صَنعَة <pb n="151"></pb> اَل۪آلَة نُصَيِّر قُطر اَل۪فَلكَة خَمسَة أَمثال قُطر اَل۪مِحوَر </s> |
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715 <s id="A18-2|21|09">فَ۪يُحتاج في هٰذا اَن تَكون اَل۪قُوَّة اَل۪مُحَرِّكَة لِ۪فَلكَة ٓب اَل۪مُعادِلَة لِ۪ثِقل أَلف قِنطار مِئَتَي قِنطار وَ۪اَل۪قُوَّة اَل۪مَفروضَة اَلَّتي لَنا إِنَّما هِيَ خَمسَة قَناطير </s> |
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716 <s id="A18-2|21|10">فَ۪لَيسَ يُمكِنُنا اَن نُحَرِّك بِ۪فَلكَة ٓب اَل۪ثِقل اَل۪مَفروض بِ۪هٰذِهِ اَل۪قُوَّة </s> |
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717 <s id="A18-2|21|11">فَ۪ل۪نُصَيِّر مِحوَراً ما مُضَرَّساً وَ۪هُوَ مِحوَر ٓغ مُرَكَّباً في أَضراس فَلكَة ٓب لِ۪تَكون إِذا تَحَرَّكَ مِحوَر ٓغ تَتَحَرَّك بِ۪حَرَكَتِهِ فَلكَة ٓب مَعَ اَل۪مِحوَر اَل۪مَفروض أَوَّلاً فَ۪يَكون إِذا حُرِّكَ مِحوَر ٓغ يَتَحَرَّك اَل۪ثِقل اَل۪مَفروض </s> |
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718 <s id="A18-2|21|12">وَ۪يَكون هٰذا اَل۪مِحوَر يَتَحَرَّك بِ۪اَل۪قُوَّة اَلَّتي تُحَرِّك فَلكَة ٓب لِ۪أَنّا قَد بَرهَنّا أَنَّ كُلّ اَل۪مُتَحَرِّكات عَلى مَراكِز خاصَّة فَ۪إِنَّها تَتَحَرَّك بِ۪قُوَّة يَسيرَة </s> |
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719 <s id="A18-2|21|13">فَ۪ل۪ذٰلِكَ لا يَكون فَصل بَينَ حَرَكَة اَل۪ثِقل بِ۪فَلكَة ٓب وَ۪بَينَ حَرَكَتِهِ بِ۪مِحوَر ٓغ</s> |
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720 <s id="A18-2|21|14">فَ۪ل۪يَكُن أَيضاً عَلى مِحوَر ٓغ فَلكَة ثابِتَة عَلَيهِ وَ۪هِيَ فَلكَة ٓد وَ۪ل۪يَكُن قُطرُها مَثَلاً خَمسَة أَمثال قُطر مِحوَر ٓغ فَ۪يُحتاج اَن تَكون اَل۪قُوَّة اَلَّتي عِندَ فَلكَة ٓد اَل۪مُعادِلَة لِ۪ل۪ثِقل أَربَعين قِنطاراً </s> |
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721 <s id="A18-2|21|15">وَ۪أَيضاً نَفرِض مِحوَراً آخَر وَ۪هُوَ مِحوَر ٓe مُرَكَّباً في هٰذِهِ اَل۪فَلكَة فَ۪تَكون اَل۪قُوَّة اَل۪مُحَرِّكَة اَلَّتي عِندَ ٓe أَيضاً أَربَعين قِنطاراً </s> |
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722 <s id="A18-2|21|16">وَ۪ل۪تَكُن فَلكَة ما ثابِتَة عَلى مِحوَر ٓe وَ۪هِيَ فَلكَة ٓز وَ۪ل۪يَكُن قُطرُها ثَمانِيَة أَمثال قُطر مِحوَر ٓe لِ۪أَنَّ قُوَّة أَربَعين قِنطاراً ثَمانِيَة أَمثال قُوَّة خَمس قَناطير فَ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ فَلكَة ٓز اَل۪مُعادِلَة لِ۪ثِقل أَلف قِنطار خَمسَة قَناطير </s> |
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723 <s id="A18-2|21|17">وَ۪هٰذا كانَ مَفروضاً </s> |
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724 <s id="A18-2|21|18">فَ۪ل۪اَن تَقوى اَل۪قُوَّة عَلى اَل۪ <pb n="153"></pb> ثِقل نَحتاج اَن نُصَيِّر فَلكَة ٓز أَعظَم قَليلاً أَو نُصَيِّر مِحوَر ٓe أَصغَر قَليلاً </s> |
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725 <s id="A18-2|21|19">فَ۪إِذا فَعَلنا ذٰلِكَ قَوِيَت اَل۪قُوَّة عَلى اَل۪ثِقل </s> |
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726 <s id="A18-2|21|20">فَ۪اِن أَرَدنا اَن نَستَعمِل مِحوَراً وَ۪فِلَكاً كَثيرَة في هٰذا اَل۪عَمَل فَ۪إِنّا نَحتاج فيهِ إِلى هٰذِهِ اَل۪نِسبَة لِ۪أَنّا نَحتاج اِن نَحنُ أَرَدنا اَن نُصَيِّر اَل۪قُوَّة مُعادِلَة لِ۪ل۪ثِقل اَن يَكون جَميع اَل۪نِسَب مُعادِلَة لِ۪ل۪ثِقل </s> |
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727 <s id="A18-2|21|21">وَ۪اِن أَرَدنا اَن نَقوى عَلى اَل۪ثِقل إِحتَجنا اَن نُصَيِّر في جُملَة اَل۪نِسَب زِيادَة عَلى مُعادَلَة اَل۪ثِقل </s> |
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728 <s id="A18-2|21|22">أَمّا اَل۪مِحوَر اَلَّذي في داخِل اَل۪فَلكَة فَ۪عَلى هٰذِهِ اَل۪جِهَة تَحَرَّكَ بِهِ اَل۪ثِقل اَل۪مَعلوم </s> |
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729 <s id="A18-2|21|23">فَ۪اِن أَرَدنا اَن لا نُصَيِّر اَل۪فِلَك ذات أَوتاد نَلُفّ عَلى اَل۪مَحاوِر وَ۪اَل۪فِلَك قُلوساً فَ۪يَخرُج لَنا ذٰلِكَ اَل۪عَمَل لِ۪أَنَّ اَل۪فَلكَة اَلَّتي تُحَرَّك أَخيراً يَتَحَرَّك بِها اَل۪مِحوَر اَل۪أَوَّل اَلَّذي يُشيل اَل۪ثِقل </s> |
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730 <s id="A18-2|21|24">وَ۪هٰذِهِ اَل۪صيغَة اَلَّتي لِ۪ل۪مَحاوِر وَ۪اَل۪فِلَك إِنَّما تَكون في أَركان ثابِتَة تَكون فيها ثُقَب تَنفُذ فيها أَطراف اَل۪مَحاوِر </s> |
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731 <s id="A18-2|21|25">وَ۪هٰذِهِ اَل۪أَركان إِذا كانَ اَل۪ثِقل يَرتَفِع يَنبَغي اَن تَكون في مَوضِع ثابِت وَثيق</s> |
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732 </p> |
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733 <p n="22"> |
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734 <s id="A18-2|22|00"></s> |
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735 <s id="A18-2|22|01">وَ۪قَد يَعرِض لِ۪هٰذِهِ اَل۪آلَة وَ۪ما أَشبَهُها مِن اَل۪آلات ذَوات اَل۪قُوَّة اَل۪كَبيرَة إِبطاء لِ۪أَنَّ بِ۪قَدر ضِعف اَل۪قُوَّة اَل۪مُحَرِّكَة عِندَ عُظم اَل۪ثِقل اَل۪مُتَحَرِّك بِ۪ذٰلِكَ اَل۪قَدر نَزيد في اَل۪زَمان فَ۪تَكون بِ۪نِسبَة واحِدَة اَل۪قُوَّة إِلى اَل۪قُوَّة وَ۪اَل۪زَمان إِلى اَل۪زَمان </s> |
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736 <s id="A18-2|22|02"><pb n="155"></pb> مِثال ذٰلِكَ أَنَّهُ لَمّا كانَت اَل۪قُوَّة عِندَ فَلكَة ٓب مِئَتَي قِنطار وَ۪كانَت تُحَرِّك اَل۪ثِقل يُحتاج إِلى دَورَة واحِدَة في اَن يَلتِفّ اَل۪قَلس اَلَّذي لِفَّ عَلى ٓأَة لِ۪يَتَحَرَّك اَل۪قَلس اَلَّذي لِفَّ عَلى ٓأَة لِ۪يَتَحَرَّك اَل۪ثِقل بِ۪حَرَكَة فَلكَة ٓب بِ۪قَدر مُحيط ٓأَة </s> |
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737 <s id="A18-2|22|03">وَ۪اِن كانَ مُتَحَرِّك بِ۪حَرَكَة فَلكَة ٓد يُحتاج اَن تَتَحَرَّك فَلكَة ٓغ خَمس مَرّات لِ۪يَتَحَرَّك مِحوَر ٓأَة مَرَّة واحِدَة لِ۪أَنَّ قُطر فَلكَة ٓب خَمسَة أَمثال قُطر مِحوَر </s> |
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738 <s id="A18-2|22|04">فَ۪خَمسَة أَمثال ٓغ مُساوِيَة لِ۪واحِد مِثل ٓب إِذا نَحنُ صَيَّرنا اَل۪مَحاوِر مُتَساوِيَة وَ۪اَل۪فِلَك </s> |
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739 <s id="A18-2|22|05">وَ۪إِلّا فَ۪إِنّا نَجِد تَناسُباً مُشابِهاً لِ۪هٰذا </s> |
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740 <s id="A18-2|22|06">إِنَّ فَلكَة ٓد تَتَحَرَّك عِندَ ٓب وَ۪اَل۪خَمس مُحيطات اَلَّتي لِ۪ٓد لَها خَمسَة أَزمان مُحيط واحِد وَ۪اَل۪مِئَتا قِنطار خَمسَة أَمثال أَربَعين قِنطاراً </s> |
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741 <s id="A18-2|22|07">فَ۪إِذاً نِسبَة اَل۪قُوَّة اَل۪مُحَرِّكَة إِلى اَل۪قُوَّة اَل۪مُحَرِّكَة بِ۪اَل۪مُبادَلَة </s> |
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742 <s id="A18-2|22|08">وَ۪كَ۪ذٰلِكَ يَعرِض في اَل۪مَحاوِر اَل۪كَثيرَة وَ۪اَل۪فِلَك اَل۪كَثيرَة وَ۪بِ۪هٰذا يَتَبَيّاً</s> |
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743 </p> |
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744 <p n="23"> |
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745 <s id="A18-2|23|00"></s> |
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746 <s id="A18-2|23|01">وَ۪لَزِمَ اَن نُحَرِّك هٰذا اَل۪ثِقل بِ۪هٰذِهِ اَل۪قُوَّة بِ۪اَل۪آلَة اَلَّتي تُسَمّي كَثيرَة اَل۪رَفع </s> |
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747 <s id="A18-2|23|02">وَ۪ل۪يَكُن اَل۪ثِقل اَلَّذي عَلَيهِ عَلامَة ٓأَة وَ۪ل۪يَكُن اَل۪مَوضِع اَلَّذي يُجبَذ مِنهُ عَلَيهِ عَلامَة ٓب وَ۪اَل۪مَوضِع اَلَّذي يُحاذيهِ عَلَيهِ عَلامَة ٓغ وَ۪هُوَ اَل۪رُكن اَل۪ثابِت اَلَّذي نُريد اَن <pb n="157"></pb> نُقِلّ اَل۪ثِقل إِلَيهِ </s> |
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748 <s id="A18-2|23|03">وَ۪ل۪يَكُن مَثَلاً ذا خَمس بِكَر وَ۪ل۪تَكُن اَل۪بَكرَة اَلَّتي يُمَدّ مِنها اَل۪ثِقل عَلى عَلامَة ٓد فَ۪يُحتاج اَن تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓد اَل۪مُعادِلَة لِ۪ل۪أَلف قِنطار مِئَتَي قِنطار وَ۪اَل۪قُوَّة اَل۪مَفروضَة لَنا إِنَّما هِيَ قُوَّة خَمسَة قَناطير </s> |
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749 <s id="A18-2|23|04">فَ۪ل۪نُخرِج مِن بَكرَة ٓد قَلساً إِلى آلَة كَثيرَة اَل۪رَفع تَكون عِندَ ٓe وَ۪ل۪يَكُن رُكن ثابِت مُحاذِياً لَها عِندَ ٓز وَ۪ل۪يَكُن ذٰلِكَ اَل۪رُكن اَل۪ثابِت وَ۪ما يَليهِ عِندَ عَلامَة ٓe مَثَلاً ذاخَمس بِكَر وَ۪ل۪يَكُن اَل۪مَمدود مِنهُ عِندَ ٓه فَ۪يُحتاج اَن تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓه قُوَّة أَربَعين قِنطاراً </s> |
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750 <s id="A18-2|23|05">وَ۪نُخرِج أَيضاً طَرَف اَل۪قَلس اَلَّذي عِندَ ٓه إِلى بَكرَة أُخرا تَكون عِندَ ٓت وَ۪ل۪يَكُن اَل۪رُكن اَل۪ثابِت عِندَ ٓك وَ۪ل۪يَكُن يُمَدّ مِن عَلامَة ٓك وَ۪مِن أَجل أَنَّ اَل۪أَربَعين قِنطاراً هِيَ ثَمانِيَة أَمثال اَل۪خَمسَة قَناطير يُحتاج اَن تَكون اَل۪كَثيرَة اَل۪رَفع ذا ثَمانٍ بِكَر فَ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓك اَل۪مُعادِلَة لِ۪ل۪أَلاف قِنطار خَمسَة قَناطير </s> |
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751 <s id="A18-2|23|06">فَ۪ل۪اَن تَقوى اَل۪قُوَّة اَلَّتي عِندَ ٓك عَلى اَل۪ثِقل يَنبَغي اَن تَكون اَل۪بِكَر أَكثَر مِن ثَمانِيَة </s> |
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752 <s id="A18-2|23|07">فَ۪تَقوى اَل۪قُوَّة عَلى اَل۪ثِقل</s> |
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753 </p> |
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754 <p n="24"> |
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755 <s id="A18-2|24|00"></s> |
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756 <s id="A18-2|24|01">فَ۪أَمَّ اَن يَكون اَل۪إِبطاء قَد يَعرِض في هٰذِهِ اَل۪آلَة أَيضاً فَ۪إِنَّ ذٰلِكَ ظاهِر لِ۪أَنَّ هٰذا في مِثل تِلكَ اَل۪نِسبَة </s> |
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757 <s id="A18-2|24|02">فَ۪إِنَّ اَل۪قُوَّة اَلَّتي عِندَ ٓد اَلَّتي هِيَ مِئَتا قِنطار إِذا رَفَعَت <pb n="159"></pb> اَل۪ثِقل مِن عِندَ ٓب إِلى ٓغ فَ۪إِنَّهُ تُريد اَن تَلُفّ خَمسَة أَحبُل مَمدودَة إِلى اَل۪خَمس بِكَر بِ۪قَدر اَل۪بُعد اَلَّذي بَينَ عَلامَتَي ٓبٓغ وَ۪اَل۪قُوَّة اَلَّتي عِندَ ٓه تُريد اَن تَلُفّ اَل۪خَمسَة أَحبُل خَمس مَرّات </s> |
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758 <s id="A18-2|24|03">فَ۪اِن نَحنُ صَيَّرنا بُعدَي ٓبٓغ ٓeٓز مُتَساوِيَين تَكون بِ۪لَفّ حَبل واحِد مِن اَل۪حِبال اَلَّتي في بُعد ٓبٓغ تَلتِفّ خَمسَة أَحبُل مِن اَل۪حِبال اَلَّتي في بُعد ٓeٓز لِ۪أَنَّ اَل۪ثِقل إِذا تَحَرَّكَ في اَل۪بُعد اَلَّذي بَينَ ٓبٓغ يَحتاج إِلى اَن تَلتِفّ لَهُ خَمس أَحبُل بِ۪قَدر بُعد ٓبٓغ فَ۪تَكون نِسبَة اَل۪زَمان إِلى اَل۪زَمان كَ۪نِسبَة اَل۪قُوَّة اَل۪مُحَرِّكَة إِلى اَل۪قُوَّة اَل۪مُحَرِّكَة </s> |
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759 <s id="A18-2|24|04">وَ۪ل۪أَنَّ لا يَكون إِزدِياد اَل۪حِبال كَثيراً يُحتاج إِلى اَن يَكون بُعد ٓeٓز خَمسَة أَمثال بُعد ٓبٓغ وَ۪ٓتٓك ثَمانِيَة أَمثال ٓeٓز </s> |
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760 <s id="A18-2|24|05">فَ۪عَلى هٰذا اَل۪عَمَل تَرفَع اَل۪بِكَر اَل۪كَثيرَة اَل۪رَفع مَعاً </s> |
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761 </p> |
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762 <p n="25"> |
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763 <s id="A18-2|25|00"></s> |
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764 <s id="A18-2|25|01">فَ۪أَمّا اَل۪مُخل فَ۪إِنَّ هٰذا اَل۪ثِقل يَتَحَرَّك بِ۪هٰذِهِ اَل۪قُوَّة بِ۪هٰذا اَل۪عَمَل </s> |
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765 <s id="A18-2|25|02">فَ۪ل۪يَكُن اَل۪ثِقل عَلى عَلامَة ٓأَة وَ۪ل۪يَكُن اَل۪مُخل ٓبٓغ وَ۪ل۪يَكُن اَل۪حَجَر اَلَّذي تَحت اَل۪مُخل عَلى عَلامَة ٓد </s> |
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766 <s id="A18-2|25|03">وَ۪ل۪تَكُن حَرَكَتُنا لِ۪ل۪ثِقل بِ۪اَل۪مُخل وَ۪هُوَ مُوازٍ لِ۪ل۪أَرض وَ۪ل۪يَكُن ٓغٓد خَمسَة أَمثال ٓدٓب </s> |
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767 <s id="A18-2|25|04">فَ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓغ اَل۪مُعادِلَة لِ۪ل۪أَلف قِنطار مِئَتَي قِنطار </s> |
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768 <s id="A18-2|25|05">وَ۪ل۪يَكُن مُخل آخَر وَ۪هُوَ ٓeٓز وَ۪ل۪تَكُن عَلامَة <pb n="161"></pb> ٓe اَلَّتي هِيَ رَأس اَل۪مُخل مُرَكَّبَة عَلى عَلامَة ٓغ لِ۪يَكُن بِ۪حَرَكَة ٓe يَتَحَرَّك ٓغ وَ۪ل۪يَكُن اَل۪حَجَر اَلَّذي تَحت اَل۪مُخل عَلى عَلامَة ٓه وَ۪ل۪يَكُن مُتَحَرِّكاً إِلى ٓد وَ۪ل۪يَكُن ٓزٓه خَمسَة أَمثال ٓهٓe فَ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓز أَربَعين قِنطاراً </s> |
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769 <s id="A18-2|25|06">وَ۪ل۪يَكُن مُخل آخَر وَ۪هُوَ ٓتٓك وَ۪ل۪نُرَكِّب عَلامَة ٓت عَلى عَلامَة ٓز وَ۪ل۪تَكُن مُتَحَرِّكَة حَرَكَة ضِدّ حَرَكَة ٓزٓe وَ۪ل۪يَكُن اَل۪حَجَر اَلَّذي تَحت اَل۪مُخل عَلى عَلامَة ٓل وَ۪ل۪يَكُن مُتَحَرِّكاً حَرَكَة في اَل۪جِهَة اَلَّتي لَيسَ تَتَحَرَّك إِلَيها عَلامَة ٓe وَ۪ل۪يَكُن ٓكٓل ثَمانِيَة أَمثال ٓلٓت فَ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓك خَمسَة قَناطير فَ۪تُعادِل اَل۪ثِقل </s> |
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770 <s id="A18-2|25|07">فَ۪اِن أَرَدنا اَن تَقوى اَل۪قُوَّة عَلى اَل۪ثِقل نَحتاج اَن نُصَيِّر ٓكٓل أَعظَم مِن ثَمانِيَة أَمثال ٓلٓت </s> |
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771 <s id="A18-2|25|08">فَ۪اِن كانَ ٓكٓل ثَمانِيَة أَمثال ٓلٓت وَ۪ٓزٓه خَمسَة أَمثال ٓهٓe وَ۪ٓغٓد أَكثَر مِن خَمسَة أَمثال ٓدٓب فَ۪إِنَّ اَل۪قُوَّة تَقوى عَلى اَل۪ثِقل</s> |
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772 </p> |
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773 <p n="26"> |
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774 <s id="A18-2|26|00"></s> |
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775 <s id="A18-2|26|01">وَ۪قَد يَعرِض في هٰذا اَل۪إِبطاء عَلى تِلكَ اَل۪نِسبَة لِ۪أَنَّهُ لَيسَ بَينَ هٰذِهِ اَل۪أَمخال وَ۪بَينَ اَل۪مَحاوِر اَلَّتي في داخِل اَل۪فِلَك اَل۪مُتَحَرِّكَة عَلى مَراكِز فَصل </s> |
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776 <s id="A18-2|26|02">لِ۪أَنَّ هٰذِهِ اَل۪أَمخال هِيَ كَ۪اَل۪مَحاوِر تَتَحَرَّك عَلى عَلامات ٓدٓهٓل اَلَّتي هِيَ اَل۪حِجارَة اَلَّتي تَدور عَلَيها اَل۪أَمخال </s> |
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777 <s id="A18-2|26|03">فَ۪تَكون دَوائِر اَل۪مَحاوِر اَل۪دَوائِر اَلَّتي تَرسُمُها عَلامات ٓبٓeٓت وَ۪اَل۪فِلَك اَل۪دَوائِر اَلَّتي تَرسُمُها عَلامات ٓغٓزٓك </s> |
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778 <s id="A18-2|26|04">فَ۪كَما أَنّا قَد بَيَّنّا في تِلكَ اَل۪مَحاوِر أَنَّ نِسبَة <pb n="163"></pb> اَل۪قُوَّة إِلى اَل۪قُوَّة كَ۪نِسبَة اَل۪زَمان إِلى اَل۪زَمان كَ۪ذٰلِكَ نُبَيِّن في هٰذا أَيضاً </s> |
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779 </p> |
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780 <p n="27"> |
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781 <s id="A18-2|27|00"></s> |
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782 <s id="A18-2|27|01">فَ۪أَمّا في اَل۪إِسفين وَ۪اَل۪لَولَب فَ۪إِنَّهُ لا يُمكِنُنا اَن نَقول هٰذا لِ۪أَنَّهُ كَما قَد بَيَّنّا فيما قَبلَ هٰذا أَنَّهُ لَيسَ يَعرِض لِ۪شَيء مِنها إِمتِناع لَكِنَ يَعرِض ضِدّ ذٰلِكَ وَ۪كُلَّما زادَت اَل۪قُوَّة اَلَّتي فيهِما صَغُرَ كُلّ واحِد مِنهُما </s> |
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783 <s id="A18-2|27|02">وَ۪إِنَّما كانَ غَرَضُنا اَن نَحتال فيما يَزداد عُظمُهُ كَ۪زِيادَة اَل۪ثِقل حَتّى يُمكِنَنا اَل۪عَمَل فيهِ بِ۪آلات صِغار فَ۪يَسهُل ذٰلِكَ </s> |
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784 <s id="A18-2|27|03">فَ۪إِذاً لَيسَ نَحتاج في اَل۪إِسفين وَ۪اَل۪لَولَب اَن نَحتال في تَصغيرِهِما لِ۪يَسهُل اَل۪عَمَل </s> |
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785 </p> |
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786 <p n="28"> |
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787 <s id="A18-2|28|00"></s> |
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788 <s id="A18-2|28|01">فَ۪أَمّا اَن يَكون اَل۪إِبطاء أَيضاً قَد يَعرِض لِ۪هٰذَين فَ۪إِنَّ ذٰلِكَ ظاهِر لِ۪أَنَّ اَل۪ضَرَبات اَل۪كَثيرَة لَها مِن اَل۪زَمان أَكثَر مِمّا لِ۪ل۪ضَربَة اَل۪واحِدَة وَ۪تَدوير اَل۪لَولَب دَورات كَثيرَة لَهُ مِن اَل۪زَمان أَكثَر مِمّا لِ۪ل۪دَورَة اَل۪واحِدَة </s> |
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789 <s id="A18-2|28|02">وَ۪قَد بَيَّنّا أَنَّ نِسبَة زاوِيَة اَل۪إِسفين إِلى اَل۪زاوِيَة كَ۪نِسبَة اَل۪ضَربَة اَل۪مُحَرِّكَة إِلى اَل۪ضَربَة اَل۪مُحَرِّكَة</s> |
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790 <s id="A18-2|28|03">فَ۪إِذاً نِسبَة اَل۪زَمان إِلى اَل۪زَمان كَ۪نِسبَة اَل۪قُوَّة إِلى اَل۪قُوَّة</s> |
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791 </p> |
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792 <p n="29"> |
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793 <s id="A18-2|29|00"></s> |
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794 <s id="A18-2|29|01">أَمّا فيما تَقَدَّمَ فَ۪إِنّا حَرَّكنا اَل۪ثِقل اَل۪مَعلوم بِ۪مَحاوِر كَثيرَة في فِلَك وَ۪بِ۪أَمخال كَثيرَة مُرَكَّبَة وَ۪بِ۪بِكَر كَثيرَة </s> |
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795 <s id="A18-2|29|02">وَ۪قَد يُمكِنُنا اَن نُحَرِّك اَل۪ثِقل اَل۪مَعلوم بِ۪إِجتِماع هٰذِهِ وَ۪تَراكُب بَعضِها بِ۪بَعض خَلا اَل۪إِسفين لِ۪أَنَّهُ وَحدَهُ لا يُحَرِّك إِلّا بِ۪اَل۪ضَربَة</s> |
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796 <s id="A18-2|29|03">فَ۪ل۪نُبَيِّن اَل۪آن أَنَّهُ قَد يُمكِنُنا اَن نُراكِب اَل۪أَربَع قُوى وَ۪نُحَرِّك بِ۪إِجتِماعِها <pb n="165"></pb> اَل۪ثِقل اَل۪مَعلوم</s> |
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797 <s id="A18-2|29|04">فَ۪ل۪يَكُن اَل۪ثِقل اَل۪مَعلوم عَلى عَلامَة ٓأَة وَ۪ل۪يَكُن مُخل عَلى عَلامَتَي ٓبٓغ وَ۪ل۪تَكُن عَلامَة ٓب اَلَّتي هِيَ طَرَف اَل۪مُخل تَحت اَل۪حَمل وَ۪عَلامَة ٓغ مُتَعالِيَة وَ۪ل۪يَكُن اَل۪حَجَر اَلَّذي يَتَحَرَّك عَلَيهِ اَل۪مُخل عَلامَة ٓد وَ۪ل۪يَكُن ٓغٓد خَمسَة أَمثال ٓدٓب فَ۪إِذاً اَل۪قُوَّة اَلَّتي عِندَ ٓغ تَكون مِئَتَي قِنطار حَتّى تُعادِل ثِقل ٓأَة </s> |
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798 <s id="A18-2|29|05">وَ۪ل۪نَشُدّ في طَرَف اَل۪مُخل اَلَّذي هُوَ عَلامَة ٓغ آلَة كَثيرَة اَل۪رَفع تَكون عَلى عَلامَة ٓe وَ۪ل۪تَكُن اَل۪آلَة اَل۪أُخرا مُوازِيَة لَها في رُكن ثابِت وَ۪هُوَ عِندَ عَلامَة ٓز </s> |
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799 <s id="A18-2|29|06">وَ۪ل۪يَكُن اَل۪شَيء اَلَّذي يَجذِب هٰذِهِ اَل۪آلَة عَلى عَلامَة ٓغ وَ۪ل۪يَكُن ذا خَمس بِكَر فَ۪تَكون اَل۪قُوَّة اَل۪جاذِبَة أَربَعين قِنطاراً </s> |
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800 <s id="A18-2|29|07">وَ۪ل۪يَكُن مِحوَر عَلى فَلكَة وَ۪هُوَ ٓتٓك فَ۪أَمّا اَل۪مِحوَر فَ۪عَلَيهِ عَلامَة ٓت وَ۪أَمّا اَل۪فَلكَة فَ۪عَلَيها عَلامَة ٓك وَ۪ل۪يَكُن اَل۪حَبل اَلَّذي يَجري عَلى اَل۪بَكرَة مَلفوفاً عَلى اَل۪مِحوَر</s> |
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801 <s id="A18-2|29|08">وَ۪ل۪تَكُن اَل۪فَلكَة ذات أَسنان قائِمَة عَلى اَل۪سَطح اَل۪مَوضوع </s> |
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802 <s id="A18-2|29|09">وَ۪ل۪يُرَكِّب في أَسنانِها لَولَب وَ۪هُوَ لَولَب ٓل وَ۪ل۪يَكُن لَهُ مَقبِض يُدَوِّرُهُ عَلى عَلامَة ٓم وَ۪ل۪يَكُن تَرتيب اَل۪أَسنان في اَل۪حَفر اَل۪لَولَبي</s> |
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803 <s id="A18-2|29|10">فَ۪إِذا أَدَرنا مَقبِض ٓم يَدور لَولَب ٓل وَ۪يَدور بِ۪تَدوير اَل۪لَولَب فَلكَة ٓك فَ۪يَدور بِ۪هٰذا اَل۪تَدوير مِحوَر ٓت وَ۪يَلتِفّ عَلَيهِ اَل۪حَبل اَلَّذي لِ۪ل۪بِكَر فَ۪يُكَبِّس طَرَف اَل۪مُخل اَلَّذي عِندَ ٓغ وَ۪يَرتَفِع اَل۪ثِقل </s> |
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804 <s id="A18-2|29|11">فَ۪ل۪يَكُن قُطر فَلكَة ٓك أَربَعَة أَمثال قُطر مِحوَر ٓت لِ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓك عَشَرَة قَناطير وَ۪ل۪يَكُن وَتَد ٓم ضِعف قُطر <pb n="167"></pb> أُسطُوانَة اَل۪لَولَب فَ۪تَكون اَل۪قُوَّة اَلَّتي عِندَ ٓم اَل۪مُعادِلَة لِ۪ل۪أَلف قِنطار خَمسَة قَناطير </s> |
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805 <s id="A18-2|29|12">فَ۪اِن زَدنا في اَل۪وَتَد اَلَّذي هُوَ عَلامَة ٓم زِيادَة ما قَوِيَت اَل۪قُوَّة اَلَّتي هِيَ خَمسَة قَناطير </s> |
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806 <s id="A18-2|29|13">وَ۪أَمّا اَل۪مِحوَر اَلَّذي في اَل۪فَلكَة وَ۪اَل۪لَولَب فَ۪ل۪يُرَكَّبا في رُكن ثابِت يَكون في هَيئَة اَل۪تابوت لِ۪تَكون أَطراف اَل۪مِحوَر في حائِطَي اَل۪رُكنَين اَل۪قائِمَين وَ۪يَكون طَرَف اَل۪لَولَب اَل۪سُفلاني في أَسفَل اَل۪رُكن اَل۪ثابِت يَدور وَ۪طَرَفُهُ اَل۪أَعلا في وَسَط اَل۪سَطح اَل۪أَعلا </s> |
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807 <s id="A18-2|29|14">وَ۪ل۪نُرَبِّع طَرَفَهُ وَ۪نُصَيِّر فيهِ فَلكَة يَكون اَل۪وَتَد فيها</s> |
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808 <s id="A18-2|29|15">وَ۪ل۪يَكُن هٰذا اَل۪رُكن اَل۪شَبيه بِ۪اَل۪تابوت في مَوضِع ثابِت في مَوضِع جَيِّد اَل۪أَساس مُحكَم اَل۪وَثاقَة </s> |
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809 <s id="A18-2|29|16">إِذا دُوِّرَ اَل۪وَتَد إِرتَفَعَ اَل۪ثِقل</s> |
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810 </p> |
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811 <p n="30"> |
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812 <s id="A18-2|30|00"></s> |
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813 <s id="A18-2|30|01">فَ۪أَمّا في اَل۪إِسفين وَ۪اَل۪لَولَب فَ۪إِنّا نَعمَل هٰذا اَل۪عَمَل </s> |
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814 <s id="A18-2|30|02">تَكون زاوِيَة اَل۪إِسفين اَلَّذي نُريد اَن نَعمَلَهُ زاوِيَة ٓآبٓغ وَ۪هِيَ حادَّة </s> |
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815 <s id="A18-2|30|03">فَ۪أَقولُ إِنَّ اَل۪أَسافين اَلَّتي تَكون زَواياها أَكثَر حِدَّة تُحَرِّك اَل۪ثِقل بِ۪أَقَلّ ضَربَة أَعني بِ۪أَصغَر قُوَّة وَ۪ل۪تَبلُغ مِن صِغَرِها اَن لا تُستَعمَل لِ۪حِدَّتِها </s> |
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816 <s id="A18-2|30|04">وَ۪ل۪يُخرَج خَطّ قائِم عَلى خَطّ ٓغٓب وَ۪هُوَ خَطّ ٓبٓد لِ۪يَقوا اَل۪إِسفين </s> |
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817 <s id="A18-2|30|05">وَ۪ل۪يُخرَج خَطّ مُوازٍ لِ۪خَطّ ٓبٓغ وَ۪هُوَ خَطّ ٓدٓe وَ۪ل۪نُخرِج مِن عَلامَة ٓe خَطّاً عَلى زاوِيَة قائِمَة وَ۪هُوَ خَطّ ٓeٓغ وَ۪ل۪يُعمَل إِسفين كَ۪اَل۪مُعَيّاً وَ۪هُوَ ٓآبٓدٓe </s> |
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818 <s id="A18-2|30|06">وَ۪ل۪يُدخَل ضِلعُهُ اَلَّذي هُوَ ٓبٓد لِ۪يَكون مِنهُ شَيء يَسير تَحت اَل۪حَمل وَ۪ل۪يَكُن رَأسُهُ ٓآe فَ۪يَظهَر لَنا أَنَّ إِسفين ٓآبٓغ إِذا ضُرِبَ يَنفُذ ٓآبٓدٓe </s> |
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819 <s id="A18-2|30|07">بُرهان ذٰلِكَ </s> |
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820 <s id="A18-2|30|08">اَن نُخرِج خَطَّي ٓآب ٓدٓe إِلى ٓز فَ۪تَكون زاوِيَة ٓآزٓe مُساوِيَة لِ۪زاوِيَة ٓآبٓغ فَ۪يَكون ٓآزٓe إِسفيناً أَيضاً يُمكِن اَن يُحَرَّك بِ۪تِلكَ اَل۪قُوَّة </s> |
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821 <s id="A18-2|30|09">وَ۪ل۪نَتَوَهَّم ما يَلي مِنهُ عَلامات ٓبٓزٓد تَحت اَل۪حَمل فَ۪يَكون قَد نَفَذَ اَل۪إِسفين </s> |
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822 <s id="A18-2|30|10">فَ۪أَمّا اَل۪إِسفين فَ۪هٰذا بَيانُهُ </s> |
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823 <s id="A18-2|30|11">وَ۪لَيسَ يَجِب بِ۪إِضطِرار اَن نَستَعمِل لِ۪ل۪إِسفين زاوِيَة حادَّة لِ۪أَنّا قَد بَرهَنّا أَنَّ كُلّ ضَربَة يَسيرَة تُمكٍ اَن تُحَرِّك كُلّ إِسفين إِذا ضُرِبَ ضَرَبات كَثيرَة </s> |
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824 <s id="A18-2|30|12">وَ۪إِستِعمالُنا اَل۪زَوايا اَل۪صِغار إِنَّما هُوَ لِ۪ل۪ضَرَبات اَل۪صِغار </s> |
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825 <s id="A18-2|30|13">فَ۪إِذاً لَيسَ يَجِب بِ۪إِضطِرار اَن نَستَعمِل في اَل۪إِسفين اَل۪زَوايا اَل۪صِغار</s> |
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826 </p> |
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827 <p n="31"> |
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828 <s id="A18-2|31|00"></s> |
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829 <s id="A18-2|31|01">فَ۪أَمّا في اَل۪لَولَب فَ۪إِنَّهُ لَيسَ يُمكِن اَن نَستَعمِل مِثلَ هٰذا اَل۪عَمَل </s> |
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830 <s id="A18-2|31|02">وَ۪ل۪ذٰلِكَ يُحتاج اَن نُرَكِّب في زاوِيَة اَل۪دائِرَة اَل۪لَولَبِيَّة اَلَّتي هِيَ زاوِيَة ٓآبٓغ عَمود ٓآغ قائِماً عَلى ٓبٓغ مُساوِياً لِ۪غِلَظ اَل۪طولُس اَلَّذي نُريد اَن نُرَكِّبَهُ في اَل۪حَفر اَل۪لَولَبي وَ۪نَعمَل أُسطُوانَة يَكون مُحيطُها مُساوِياً لِ۪خَطّ ٓبٓغ </s> |
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831 <s id="A18-2|31|03">وَ۪نَرسُم دائِرَة لَولَبِيَّة مِن هٰذِهِ اَل۪خُطوط في بُعد ٓآغ وَ۪نَحفِر اَل۪دائِرَة اَل۪لَولَبِيَّة وَ۪يَكون بُعدُها مُساوِياً لِ۪خَطّ ٓآغ فَ۪بِ۪هٰذا اَل۪عَمَل يُمكِنُنا اَن نُرَكِّب تِلكَ اَل۪خَشَبَة في اَل۪حَفر اَل۪لَولَبي</s> |
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832 </p> |
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833 <p n="32"> |
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834 <s id="A18-2|32|00"></s> |
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835 <s id="A18-2|32|01"><pb n="171"></pb> وَ۪مِن أَجل أَنّا قَد بَيَّنّا في كُلّ واحِدَة مِن هٰذِهِ اَل۪قُوى أَنَّهُ يُمكِن بِ۪اَل۪قُوَّة اَل۪مَعلومَة اَن يُحَرَّك اَل۪ثِقل اَل۪مَعلوم يَنبَغي اَن نَعلَم هٰذا أَيضاً أَنَّهُ لَو أَمكَنَ اَن تَكون اَل۪مَعمولات كُلُّها مَخروطَ بِ۪اَل۪مِبرَد مُتَساوِيَة اَل۪ثِقل مُتَشابِهَة اَل۪أَجزاء مَلِسَة كانَ يُمكِن في كُلّ واحِدَة مِن هٰذِهِ اَل۪آلات اَن نَستَعمِل اَل۪أَعمال اَلَّتي ذَكَرنا عَلى تِلكَ اَل۪نِسبَة</s> |
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836 <s id="A18-2|32|02">وَ۪لَكِنَ مِن أَجل أَنَّهُ لا يُمكِن اَل۪ناس يَعمَلون ذٰلِكَ بِ۪اَل۪إِستِقصاء في اَل۪مَلاسَة وَ۪اَل۪إِستِواء يَنبَغي اَن يُزاد في اَل۪قُوى لِ۪ما يَعرِض مِن خُشونَة اَل۪آلات وَ۪نَزيد في ذٰلِكَ فَ۪نَعمَلُها أَكثَر قَدراً مِن اَل۪نِسَب اَلَّتي قَدَّمنا لِ۪أَلّا يَعرِض لَنا إِمتِناع في ذٰلِكَ وَ۪نَظَرُنا إِلى اَل۪إِستِعمال بِ۪اَل۪آلات يُكَذِّب بِ۪ما قَد صَحَّ بُرهانُهُ</s> |
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837 </p> |
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838 <p n="33"> |
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839 <s id="A18-2|33|00"></s> |
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840 <s id="A18-2|33|01">وَ۪قَد يَجِب بِ۪اَل۪إِضطِرار لِ۪أَلَّذين يُريدون مَعرِفَة صِناعَة اَل۪حِيَل اَن يَعرِفوا اَل۪عِلَل اَلَّتي تَعرِض في إِستِعمال كُلّ حَرَكَة كَما قَد بَيَّنّا في رَفع اَل۪أَشياء اَل۪ثَقيلَة بِ۪اَل۪بَراهين اَل۪طَبيعِيَّة وَ۪أَخبَرنا بِ۪كُلّ ما يَعرِض لِ۪كُلّ واحِدَة مِن اَل۪قُوى اَلَّتي ذَكَرنا لِ۪أَلّا يَقَع لَهُم شَيء بِ۪لا بُرهان أَو شَيء يَشُكّون فيهِ لَكِنَ إِذا فَحَصوا في كُلّ واحِد مِمّا يَطلُبونَهُ يَخرُج لَهُم صِدق ذٰلِكَ في كُلّ واحِد مِمّا ذَكَرنا </s> |
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841 <s id="A18-2|33|02">فَ۪ل۪نَذكُر أَشياء قَد ذَكَرَها اَل۪قُدَماء لِ۪ما يَصلُح في هٰذا اَل۪نَوع وَ۪قَد نَتَعَجَّب مِن هٰذا ما إِذا بَيَّنّاهُ كانَ ضِدّ ما تَقَدَّمَ في مَعرِفَتِنا </s> |
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842 <s id="A18-2|33|03">وَ۪يَكون إِبتِداء ما نَسأَل عَنهُ مِمّا يَظهَر لَنا </s> |
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843 <s id="A18-2|33|04">وَ۪ما لا يُمكِنُنا اَن نُخَبِّر <pb n="173"></pb> بِ۪أَسبابِهِ إِلّا بَعدَ اَل۪أَشياء اَل۪زاهِرَة فَ۪يَكثُر تَعَجُّبُنا لِ۪ذٰلِكَ إِذ كُنّا نَرى اَل۪أَشياء اَلَّتي نَستَعمِل ضِدّ ما إِعتَدناهُ وَ۪ما كانَ عِندَنا </s> |
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844 <s id="A18-2|33|05">فَ۪ظاهِر لَنا أَنَّهُ يَجِب بِ۪إِضطِرار لِ۪مَن أَرادَ اَل۪إِستِقصاء في وُجود اَل۪عِلَل اَن يَستَعمِل إِبتِداءات طَبيعِيَّة إِمّا واحِدَة وَ۪إِمّا كَثيرَة فَ۪يُضيف كُلّ ما يَسأَل عَنهُ إِلَيهِ وَ۪يَخرُج حَلّ كُلّ واحِدَة مِن اَل۪مَسائِل بِ۪اَل۪إِستِقصاء إِذا ظَهَرَت عِلَّتُها وَ۪كانَت هِيَ اَل۪شَيء اَلَّذي قَد عَرَفناهُ </s> |
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845 <s id="A18-2|33|06">وَ۪ل۪يَكُن لَنا مَوضوعاً أَنَّ اَل۪خَفيف سَهل اَل۪حَرَكَة وَ۪اَل۪ثَقيل عَسِر اَل۪حَرَكَة وَ۪أَنَّ اَل۪ثِقل اَل۪واحِد حَرَكَتُهُ بِ۪اَل۪قُوَّة اَل۪أَكبَر أَسهَل مِنهُ بِ۪اَل۪قُوَّة اَل۪أَقَلّ فَ۪إِنَّ هٰذا قَد نَراهُ عَلى هٰذا وَ۪هُوَ بَيِّن ظاهِر لَنا </s> |
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846 <s id="A18-2|33|07">وَ۪قَد يَجِب اَن نَعلَم أَنَّ كُلّ ما يُسأَل عَنهُ قَد يَعرِض فيهِ شَيء خَفي لَيسَ بِ۪ظاهِر لِ۪أَنَّهُ لا يَكاد يُسأَل عَن شَيء اَل۪عِلَّة فيهِ ظاهِرَة بَيِّنَ </s> |
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847 <s id="A18-2|33|08">وَ۪لَكِنَ يَجِب اَن نَعلَم أَنَّ إِبتِداء كُلّ اَل۪مَسائِل اَلَّتي تَعرِض في صِناعَة اَل۪حِيَل وَ۪خَفِيَة اَل۪عِلَّة في ذٰلِكَ أَنَّهُ لا يُمكِنُنا اَن نَرى اَل۪أَجسام اَل۪ثَقيلَة مُنقَسِمَة عَلى اَل۪قُوى اَل۪مُحَرِّكَة لَها وَ۪هٰذِهِ اَل۪عِلَّة تَكون ظاهِرَة بِ۪أَشياء كَثيرَة وَ۪بِ۪خاصَّة بِ۪حَرَكات هٰذِهِ اَل۪أَجسام </s> |
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848 <s id="A18-2|33|09">لِ۪أَنَّ اَل۪جِسم اَلَّذي لا يُحَرِّكُهُ رَجُل واحِد أَو اَلَّذي إِذا حَرَّكَهُ رَجُل واحِد كانَ ذٰلِكَ عَلَيهِ عَسِراً جِدّاً فَ۪إِنَّ جَماعَة مِن اَل۪رِجال يُحَرِّكونَهُ وَ۪تَكون حَرَكَتُهُ عَلَيهِم سَهلَة</s> |
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849 <s id="A18-2|33|10">فَ۪لَو كانَ يَعرِض اَن يَكون عَلى كُلّ واحِد مِن اَل۪مُحَرِّكين ثِقل اَل۪مُحَرَّك كُلِّهِ كانَ لا يوجَد إِختِلاف حَرَكَة <pb n="175"></pb> بَينَ حَرَكَة اَل۪واحِد وَ۪بَينَ حَرَكَة اَل۪جَماعَة</s> |
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850 <s id="A18-2|33|11">وَ۪لَكِنَهُ قَد نَرى اَل۪حَرَكَة عَلى اَل۪جَماعَة أَسهَل وَ۪مِن أَجل أَنَّ اَل۪جَماعَة قَد يَنال كُلّ واحِد مِنهُم شَيء ما مِن اَل۪حَمل وَ۪قَد يَسهُل عَلَيهِم حَرَكَتُهُ فَ۪ظاهِر لَنا أَنَّ اَل۪حَمل يَنقَسِم عَلى أَلَّذين يُحَرِّكونَهُ </s> |
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851 </p> |
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852 <p n="34"> |
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853 <s id="A18-2|34|00"></s> |
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854 <s id="A18-2|34|01">اَل۪مَسائِل</s> |
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855 <s id="A18-2|34|02">أَة</s> |
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856 <s id="A18-2|34|03">لِ۪ماذا صارَت اَل۪عَجَل اَلَّتي هِيَ ذات فَلكَتَين </s> |
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857 <s id="A18-2|34|04">تَحمِل اَل۪أَثقال أَسهَل مِن اَل۪عَجَل إِذا كانَت ذات أَربَع فِلَك </s> |
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858 <s id="A18-2|34|05">لِ۪أَنَّ اَل۪ثِقل في اَل۪عَجَل اَلَّتي هِيَ ذات فَلكَتَين نَقلُهُ يَنقَسِم بِ۪قِسمَين مُتَساوِيَين عَن جَنبَي اَل۪مِحوَر </s> |
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859 <s id="A18-2|34|06">فَ۪أَمّا في اَل۪عَجَل اَلَّتي هِيَ ذات أَربَع فِلَك فَ۪إِنَّ ذٰلِكَ لا يَتَهَيَّأ وَ۪لا يَنقَسِم اَل۪ثِقل فَ۪يَكون جُزآهُ اَلَّذان في اَل۪جِهَتَين مُتَساوِيَين لَكِنَ يَكون اَل۪حَمل كُلُّهُ أَمام اَل۪فَلكَتَين اَل۪مُؤَخَّرَتَين وَ۪خَلف اَل۪فَلكَتَين اَل۪مُقَدَّمَتَين فَ۪يَذهَب بِ۪سُرعَة حَرَكَة اَل۪فِلَك إِختِلاف وَضع اَل۪ثِقل فَ۪إِنَّ اَل۪فَلكَة إِنَّما صارَت سَريعَة اَل۪حَرَكَة لِ۪أَنَّ ثِقلَها في أَجزائِها كُلِّها مُتَساوٍ</s> |
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860 <s id="A18-2|34|07">ب</s> |
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861 <s id="A18-2|34|08">لِ۪ماذا صارَ جَرّ اَل۪عَجَل يَصعُب عَلى اَل۪دَوابّ في اَل۪رَمل </s> |
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862 <s id="A18-2|34|09">لِ۪أَنَّ بَعض تَقويس اَل۪فِلَك في قَعر اَل۪رَمل فَ۪إِذا جِرَّت اَل۪عَجَلَة تَدعَم اَل۪فَلكَة اَل۪رَمل اَلَّذي هُوَ أَمامَهُ </s> |
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863 <s id="A18-2|34|10">وَ۪أَيضاً قَد يَصعُب ذٰلِكَ مِن أَجل أَنَّ أَرجُل اَل۪دَوابّ تَنفَد في اَل۪رَمل فَ۪يَكون قَلعُها صَعباً </s> |
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864 <s id="A18-2|34|11">فَ۪أَمّا في اَل۪أَرض اَل۪صُلبَة فَ۪إِنَّ ذٰلِكَ لا يَعرِض </s> |
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865 <s id="A18-2|34|12">غ</s> |
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866 <s id="A18-2|34|13">لِ۪ماذا صارَ اَل۪ثِقل اَل۪واحِد في اَل۪مَوازين اَل۪مُتَعادِلَة <pb n="177"></pb> يَفعَل مَيلاً مُختَلِفاً فَ۪يَكون فِعلُهُ اَل۪مَيل اَل۪أَكثَر في اَل۪ثِقل اَل۪أَصغَر </s> |
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867 <s id="A18-2|34|14">فَ۪إِنَّهُ إِذا كانَت كَفَّتان في كُلّ واحِدَة مِنهُما ثَلاثَة أَمناء وَ۪صَيَّرنا في إِحدا اَل۪كَفَّتَين نِصف مَنّاً مالَت تِلكَ اَل۪كَفَّة مَيلاً كَثيراً </s> |
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868 <s id="A18-2|34|15">فَ۪اِن كانَ في كُلّ كَفَّة عَشَرَة أَمناء وَ۪زَدنا في إِحدا اَل۪كَفَّتَين نِصف مَنّاً كانَ مَيل اَل۪عَمود في ذٰلِكَ يَسيراً جِدّاً </s> |
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869 <s id="A18-2|34|16">لِ۪أَنَّهُ يَعرِض في ذٰلِكَ اَن يَتَحَرَّك اَل۪ثِقل بِ۪قُوَّة كَبيرَة فَ۪إِنَّ اَل۪ثَلاثَة اَل۪أَمناء يُحَرِّكُها مِثل وَ۪سُدس مِثل فَ۪أَمّا اَل۪عَشَرَة أَمناء فَ۪إِنَّهُ يُحَرِّكُها مِثل وَ۪نِصف عُشر مِثل </s> |
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870 <s id="A18-2|34|17">لِ۪أَنَّ نِصف اَل۪مَنّ هُوَ نِصف عُشر اَل۪عَشَرَة أَمناء وَ۪هُوَ سُدس اَل۪ثَلاثَة اَل۪أَمناء وَ۪اَل۪ثِقل اَلَّذي تُحَرِّكُهُ اَل۪قُوَّة اَل۪عُظمى تَكون حَرَكَتُهُ أَسهَل</s> |
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871 <s id="A18-2|34|18">د</s> |
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872 <s id="A18-2|34|19">لِ۪ماذا صارَت اَل۪أَثقال اَل۪عِظام يَهبُط إِلى اَل۪أَرض في زَمان أَقَلّ مِن زَمان اَلَّتي هِيَ أَخَفّ </s> |
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873 <s id="A18-2|34|20">لِ۪أَنَّهُ كَما يَعرِض فيها إِذا كانَت اَل۪قُوَّة اَل۪مُحَرِّكَة لَها مِن خارِج أَكبَر فَ۪إِنَّها تَتَحَرَّك أَسهَل كَ۪ذٰلِكَ إِذا كانَت قُوَّتُها في أَنفُسِها أَكبَر تَحَرَّكَت أَسهَل </s> |
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874 <s id="A18-2|34|21">وَ۪اَل۪قُوَّة وَ۪اَل۪جَذب في اَل۪ثِقل اَل۪أَعظَم في اَل۪حَرَكات اَل۪طَبيعِيَّة أَكبَر مِنهُ في اَل۪ثِقل اَل۪أَصغَر</s> |
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875 <s id="A18-2|34|22">e</s> |
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876 <s id="A18-2|34|23">لِ۪ماذا صارَ اَل۪ثِقل اَل۪واحِد إِذا كانَ لَهُ عَرض يَكون هُبوطُهُ إِلى اَل۪أَرض أَبطَأ مِنهُ إِذا كانَ مُستَديراً </s> |
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877 <s id="A18-2|34|24">لِ۪أَنَّهُ لَيسَ كَما ظَنَّ قَوم أَنَّهُ يَنال اَل۪مُعتَرَض بِ۪عَرضِهِ هَواء كَثيراً وَ۪أَمّا اَل۪مُستَدير فَ۪ل۪أَنَّ أَجزاءَهُ بَعضَها مُداخِل في بَعض لا يَنال مِن اَل۪هَواء إِلّا يَسيراً لَكِنَ اَل۪ثِقل اَلَّذي يَنحِطّ مُعتَرَضاً تَكون <pb n="179"></pb> لَهُ أَجزاء كَثيرَة وَ۪ل۪كُلّ واحِد مِنها مِن اَل۪قُوَّة عَلى قَدر عَرضِهِ فَ۪في حَرَكَة هٰذا اَل۪ثِقل يَأخُذ كُلّ واحِد مِن أَجزائِهِ مِن اَل۪قُوَّة اَلَّتي تُحَرِّكُهُ عَلى قَدر ثِقلِهِ وَ۪لا يَنالُهُ كُلَّهُ قُوَّة واحِدَة</s> |
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878 <s id="A18-2|34|25">و</s> |
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879 <s id="A18-2|34|26">لِ۪ماذا صارَ اَل۪رَمي مِن وَسَط اَل۪وَتَر يُنَفِّذ اَل۪سَهم بُعداً كَثيراً </s> |
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880 <s id="A18-2|34|27">لِ۪أَنَّ اَل۪تَوَتُّر يَكون فيهِ أَكثَر وَ۪تَكون اَل۪قُوَّة اَل۪باعِثَة أَعظَم </s> |
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881 <s id="A18-2|34|28">وَ۪ل۪ذٰلِكَ صَيَّروا اَل۪قِسي مِن قُرون لِ۪يُمكِن فيها اَل۪ثَني </s> |
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882 <s id="A18-2|34|29">فَ۪إِذا ثُنِيَت كَثيراً تَوَتَّرَ اَل۪وَتَر بِ۪اَل۪سَهم أَكثَر وَ۪صارَت فيهِ قُوَّة أَعظَم فَ۪نَفَذَ بُعداً أَطوَل </s> |
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883 <s id="A18-2|34|30">وَ۪ل۪ذٰلِكَ صارَت اَل۪قِسي اَل۪صُلبَة اَلَّتي لا تُجيب أَطرافُها إِلى اَل۪ثَني تُنَفِّذ اَل۪سَهم بُعداً أَقَلّ</s> |
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884 <s id="A18-2|34|31">ز</s> |
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885 <s id="A18-2|34|32">لِ۪ماذا صارَ اَل۪خَشَب يَندِقّ أَسرَع إِذا صُيِّرَت اَل۪رُكبَة مِنهُ عَلى اَل۪نِصف</s> |
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886 <s id="A18-2|34|33">لِ۪أَنَّهُ إِذا صُيِّرَت اَل۪رُكبَة مِنهُ عَلى أَقَلّ مِن اَل۪نِصف فَ۪كانَ أَحَد جُزأَيهِ أَطوَل مِن اَل۪آخَر يَكون ميزاناً مُنقَسِماً بِ۪قِسمَين مُختَلِفَين فَ۪تَقوى اَل۪يَد اَل۪بَعيدَة مِن اَل۪رُكبَة عَلى اَل۪يَد اَل۪قَريبَة مِنها </s> |
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887 <s id="A18-2|34|34">وَ۪لَيسَ يَنال إِحداهُما قُوَّة اَل۪أُخرا إِلّا اِن يَكون جَميعُهُما في طَرَف اَل۪عود</s> |
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888 <s id="A18-2|34|35">ه</s> |
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889 <s id="A18-2|34|36">لِ۪ماذا صارَ اَل۪خَشَبَة كُلَّما زادَت في طولِها أَكثَر ضُعفاً وَ۪كَثُرَ إِنثِناؤُها إِذا أُقِلَّت في أَحَد طَرَفَيهِ </s> |
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890 <s id="A18-2|34|37">لِ۪أَنَّ اَل۪خَشَب اَل۪طَويلَة فيها قُوَّة كَبيرَة مُتَفَرِّقَ في أَجزائِها فَ۪تَكون كُلُّها تَقوى عَلى اَل۪ثابِت مِنها اَلَّذي بِهِ تُقَلّ</s> |
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891 <s id="A18-2|34|38">فَ۪يَعرِض لَها ما يَعرِض في اَل۪خَشَب اَل۪قِصار إِذا عُلِّقَ في أَطرافِها شَيء يُكَبِّسُها </s> |
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892 <s id="A18-2|34|39">فَ۪تَكون اَل۪زِيادَة في طول اَل۪خَشَبَة بِ۪قَدر ذٰلِكَ اَل۪ثِقل <pb n="181"></pb> اَلَّذي يَجتَبِذ اَل۪خَشَبَة اَل۪قَصيرَة </s> |
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893 <s id="A18-2|34|40">فَ۪يَنال اَل۪خَشَبَة اَل۪طَويلَة بِ۪ذاتِها مِن طولِها مِثلَ اَلَّذي يَنال اَل۪قَصيرَة إِذا شِدَّة في طَرَفِها شَيء ثَقيل</s> |
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894 <s id="A18-2|34|41">ت</s> |
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895 <s id="A18-2|34|42">لِ۪ماذا صارَ قَلع اَل۪أَضراس يُستَعمَل بِ۪اَل۪كَلبَتَين دونَ اَل۪يَد </s> |
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896 <s id="A18-2|34|43">لِ۪أَنَّهُ لا يُمكِنُنا اَن نَضبُط اَل۪ضِرس بِ۪اَل۪يَد كُلِّها لَكِنَ بِ۪جُزء مِنها وَ۪كَما أَنَّهُ قَد يَصعُب عَلَينا اَن نُشيل ثِقلاً ما بِ۪إِصبَعَين فَقَط أَكثَر مِن صُعوبَتِهِ بِ۪اَل۪يَد كُلِّها كَ۪ذٰلِكَ أَيضاً يَصعُب عَلَينا ضَبط اَل۪ضِرس وَ۪كَبسُهُ بِ۪إِصبَعَين أَكثَر مِنهُ بِ۪اَل۪يَد كُلِّها </s> |
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897 <s id="A18-2|34|44">لِ۪أَنَّ في جَميع اَل۪مَعنَيَين اَل۪قُوَّة واحِدَة وَ۪قِسمَة اَل۪كَلبَتَين عَلى مِسمارِها هِيَ أَيضاً تُصَيِّر اَل۪يَد تَقوى عَلى اَل۪ضِرس لِ۪أَنَّها مُخل تَكون اَل۪يَد مِنهُ عَلى اَل۪جُزء اَل۪أَعظَم وَ۪بُعد اَل۪كَلبَتَين هُوَ يُعَيٍّ عَلى حَرَكَة اَل۪ضِرس </s> |
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898 <s id="A18-2|34|45">وَ۪ذٰلِكَ أَنَّ أَصل اَل۪ضِرس هُوَ اَل۪شَيء اَلَّذي يَتَحَرَّك عَلَيهِ اَل۪مُخل </s> |
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899 <s id="A18-2|34|46">فَ۪ل۪أَنَّ بُعد اَل۪كَلبَتَين يَكون أَكثَر مِن أَصل اَل۪ضِرس اَلَّذي يَتَحَرَّك عَلَيهِ شَيء كَبير تَقوى اَل۪يَد عَلى اَل۪قُوَّة اَلَّتي في أَصل اَل۪ضِرس </s> |
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900 <s id="A18-2|34|47">لِ۪أَنَّهُ لا يَكون فَصل بَينَ حَرَكَة ثِقل وَ۪حَرَكَة قُوَّة تُعادِل ذٰلِكَ اَل۪ثِقل </s> |
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901 <s id="A18-2|34|48">فَ۪اِن رَدَّدنا اَل۪يَد إِذا كانَت مَمدودَة يَكون صَعب لَيسَ لِ۪ثِقل اَل۪يَد لَكِنَ لِ۪قُوَّة إِرتِباط اَل۪عَصَب بَعضِها بِ۪بَعض </s> |
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902 <s id="A18-2|34|49">ي</s> |
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903 <s id="A18-2|34|50">لِ۪ماذا صارَ اَل۪مَوازين إِذا دُوِّرَت تَدويراً كانَت مُثَقَّلَة أَو خَفيفَة تَحَرَّكَت أَسرَع مِن حَرَكَتِها إِلى إِحدا اَل۪جِهات اَلَّتي تَميلُها</s> |
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904 <s id="A18-2|34|51">لِ۪أَنَّهُ إِذا دُوِّرَت كُلُّها كانَ ثِقلُها <pb n="183"></pb> مُتَشابِهاً مُتَساوِياً مِن اَل۪جِهات كُلِّها فَ۪يَكون لِ۪ذٰلِكَ مُتَحَرِّكاً عَلى مَركَز وَ۪مَركَزُهُ عِلاقَتُهُ </s> |
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905 <s id="A18-2|34|52">فَ۪أَمّا إِذا جَذَبنا اَل۪ميزان إِلى إِحدا اَل۪جِهَتَين فَ۪إِنّا نَرفَع ثِقلاً ما لِ۪أَنَّ مَيل اَل۪كَفَّة إِلى أَسفَل يُقِلّ اَل۪أُخرا فَ۪تَكون حَرَكَة غَير طَبيعِيَّة أَعني حَرَكَة ثِقل إِلى ما يَلي اَل۪عُلُوّ فَ۪أَمّا اَل۪حَرَكَة اَل۪طَبيعِيَّة فَ۪إِنَّها سَهلَة وَ۪هِيَ جَذب اَل۪ثِقل إِلى أَسفَل </s> |
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906 <s id="A18-2|34|53">فَ۪ل۪ذٰلِكَ صارَ جَذب اَل۪أَثقال إِلى أَسفَل أَسهَل مِن شَيلِها إِلى فَوقَ</s> |
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907 <s id="A18-2|34|54">يَ</s> |
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908 <s id="A18-2|34|55">لِ۪ماذا صارَت حَرَكَة اَل۪أَثقال اَل۪مُتَعَلِّقَة سَهلَة</s> |
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909 <s id="A18-2|34|56">لِ۪أَنَّ جَميع قُوَّة اَل۪أَثقال قَد قَوِيَت عَلَيها اَل۪قُوَّة اَلَّتي هِيَ مُتَعَلِّقَة بِها </s> |
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910 <s id="A18-2|34|57">فَ۪ل۪أَنَّهُ لَم يَبقَ لَها كَثير قُوَّة صارَ دَفعُها سَهلاً </s> |
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911 <s id="A18-2|34|58">وَ۪كَ۪ذٰلِكَ أَيضاً يَعرِض في اَل۪ميزان إِذا كانَ مُتَعَلِّقاً وَ۪جَذَبناهُ تَحَرَّكَ أَسهَل</s> |
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912 <s id="A18-2|34|59">يب</s> |
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913 <s id="A18-2|34|60">لِ۪ماذا صارَت اَل۪حِجارَة اَل۪مُتَقَدِّرَة اَل۪عُظم اَلَّتي عَلى شَطّ اَل۪بَحر تَكون أَكثَر ذٰلِكَ مُستَديرَة </s> |
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914 <s id="A18-2|34|61">لِ۪أَنَّها تَكون أَوَّلاً ذات زَوايا حادَّة فَ۪بِ۪حَرَكَة اَل۪بَحر يَضرِب بَعضُها بَعضاً فَ۪تُكسَر زَواياها لِ۪ضَعفِها </s> |
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915 <s id="A18-2|34|62">يغ</s> |
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916 <s id="A18-2|34|63">لِ۪ماذا صارَت اَل۪أَثقال اَل۪مُتَعَلِّقَة اَلَّتي نُريد اَن نُحَرِّكَها كُلَّما بَعُدَت اَل۪يَد عَنها حَتّى تَصير إِلى اَل۪رُكن اَل۪ثابِت اَلَّذي هِيَ مُعَلَّقَة عَلَيهِ أَو قَرَبَت مِنهُ صَعُبَت حَرَكَتُها </s> |
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917 <s id="A18-2|34|64">لِ۪أَنّا اِن إِلتَمَسنا اَن نُحَرِّكَها مِن اَل۪مَوضِع اَل۪ثابِت اَلَّذي هِيَ <pb n="185"></pb> مُعَلَّقَة عَلَيهِ صَعُبَ ذٰلِكَ وَ۪كانَ غَير مُمكِن بَتَّة</s> |
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918 <s id="A18-2|34|65">فَ۪إِذا تَباعَدَت اَل۪يَد عَن اَل۪رُكن اَل۪ثابِت حَرَّكَت اَل۪ثِقل لَكِنَ بِ۪صُعوبَ وَ۪ذٰلِكَ لِ۪ل۪قُرب مِن بُطلان اَل۪حَرَكَة بَتَّة </s> |
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919 <s id="A18-2|34|66">وَ۪كُلَّما تَباعَدَ اَل۪مُحَرِّك مِن اَل۪رُكن اَل۪ثابِت كانَت اَل۪حَرَكَة عَلَيهِ أَسهَل </s> |
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920 <s id="A18-2|34|67">مِثال ذٰلِكَ اَن نَفرِض اَل۪رُكن اَل۪ثابِت اَلَّذي اَل۪ثِقل مُعَلَّق عَلَيهِ عَلى عَلامَة ٓأَة وَ۪ل۪يَكُن اَل۪حَبل خَطّ ٓآب </s> |
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921 <s id="A18-2|34|68">وَ۪ل۪نُخرِج خَطّ ٓآغ قائِماً عَلى خَطّ ٓآب وَ۪ل۪نُعَلِّم عَلى خَطّ ٓآب عَلامَتَين كَيفَ ما وَقَعَتا وَ۪هُما عَلامَتا ٓدٓe وَ۪ل۪نَجذِب اَل۪حَبل مِن عَلامَة ٓد وَ۪نَكسِرهُ حَتّى يَكون كَ۪هَيئَة ٓآزٓه </s> |
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922 <s id="A18-2|34|69">فَ۪يَكون اَل۪ثِقل عِندَ ٓه </s> |
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923 <s id="A18-2|34|70">فَ۪أَقول إِنَّ ٓه أَكثَر إِرتِفاعاً مِن ٓب بُرهان ذٰلِكَ </s> |
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924 <s id="A18-2|34|71">أَنّا نُخرِج خَطّ ٓهٓز إِلى ٓغ وَ۪مِن أَجل أَنَّ ٓآزٓه أَعظَم مِن ٓغٓزٓه فَ۪إِنَّ عَلامَة ٓه أَعلا مِن عَلامَة ٓب </s> |
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925 <s id="A18-2|34|72">وَ۪أَيضاً فَ۪ل۪يَكُن اَل۪حَبل اَل۪مُمتَدّ مِن عَلامَة ٓe لَهُ وَضع قائِم عَلى ٓغٓه فَ۪يَكون اَل۪ثِقل في مَوضِع واحِد أَعني يَكون مِثلَ ٓآب </s> |
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926 <s id="A18-2|34|73">وَ۪ل۪يَكُن مِن أَجل أَنَّ ٓآe أَعظَم مِن ٓآز يَكون ٓe أَكثَر إِنحِطاطاً مِن ٓز كَ۪عَلامَة ٓت </s> |
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927 <s id="A18-2|34|74">وَ۪نَصِل ٓآت فَ۪يَكون ٓآت قَد كَسَرَ كِسرَة ٓآتٓه </s> |
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928 <s id="A18-2|34|75">فَ۪أَقول إِنَّ اَل۪ثِقل اَل۪مُعَلَّق هُوَ أَكثَر إِنحِطاطاً مِن ٓه</s> |
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929 <s id="A18-2|34|76">بَيان ذٰلِكَ </s> |
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930 <s id="A18-2|34|77">مِن أَجل أَنَّ ٓآز ٓزٓت أَعظَم مِن ٓآت وَ۪خَطّ ٓهٓت مُشتَرَك فَ۪إِنَّ ٓآز ٓزٓه أَعني ٓآب أَعظَم مِن ٓآت ٓتٓه </s> |
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931 <s id="A18-2|34|78">فَ۪ل۪يَكُن جَميع ٓآت ٓتٓك مُساوِياً لِ۪خَطّ ٓآب فَ۪يَكون اَل۪ثِقل عِندَ ٓك وَ۪ٓك أَكثَر إِنحِطاطاً مِن ٓه </s> |
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932 <s id="A18-2|34|79">فَ۪يَكون إِذا جَذَبنا اَل۪ثِقل مِن عِندَ عَلامَة ٓe عِندَ ٓك وَ۪إِذا جَذَبناهُ مِن عَلامَة ٓد يَكون عِندَ ٓه <pb n="187"></pb> فَ۪يَكون اَل۪ثِقل يَرتَفِع مِن عَلامَة ٓد أَكثَر مِن إِرتِفاعِهِ مِن عَلامَة ٓe </s> |
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933 <s id="A18-2|34|80">وَ۪اَل۪ثِقل اَلَّذي يَرتَفِع إِلى مَكان أَكثَر إِرتِفاعاً يُتعِب اَل۪قُوَّة أَكثَر مِن اَلَّذي يَرتَفِع إِلى مَكان أَقَلّ إِرتِفاعاً لِ۪أَنَّ اَلَّذي يَرتَفِع إِلى مَكان كَثير اَل۪إِرتِفاع يَحتاج إِلى زَمان أَطوَل</s> |
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934 <s id="A18-2|34|81">يد</s> |
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935 <s id="A18-2|34|82">لِ۪ما صارَت اَل۪أَشياء اَلَّتي تَسير في اَل۪ماء إِذا كانَت عَلى حائِط واحِد تَكثُر سُرعَة حَرَكَتِها </s> |
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936 <s id="A18-2|34|83">لِ۪أَنَّ اَلَّذي يَكون مِنها عَلى اَل۪ماء يَكون يَسيراً جِدّاً فَ۪يَكون اَلَّذي يَدعَمُهُ اَل۪ماء أَيضاً يَسيراً وَ۪اَلَّذي يَنالُهُ مِن اَل۪ريح يَقوا عَلى ذٰلِكَ اَل۪ماء اَلَّذي يُضادُّهُ عِندَ حَرَكَتِهِ </s> |
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937 <s id="A18-2|34|84">يe</s> |
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938 <s id="A18-2|34|85">لِ۪ماذا صارَ اَل۪سُكّان وَ۪هُوَ صَغير جِدّاً يَرُدّ سُفُناً عِظاماً </s> |
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939 <s id="A18-2|34|86">لِ۪أَنَّهُ إِذا كانَ إِنسان يَعدوا فَ۪إِجتَذَبَهُ أَحَد إِلى أَيّ جِهَة كانَت فَ۪إِنَّهُ يَميل إِلى تِلكَ اَل۪جِهَة سَريعاً </s> |
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940 <s id="A18-2|34|87">وَ۪اَل۪سُكّان يَدعَمُهُ اَل۪ماء فَ۪يَقوا عَلى اَل۪سَفينَة</s> |
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941 <s id="A18-2|34|88">يو</s> |
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942 <s id="A18-2|34|89">لِ۪ماذا صارَت اَل۪أَسهُم تَتَغَرَّس في اَل۪دُروع وَ۪اَل۪جَواشٍ وَ۪لا تَتَغَرَّس في اَل۪شِراعات اَل۪مَنشورَة </s> |
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943 <s id="A18-2|34|90">لِ۪أَنَّ اَل۪حَمِيَة إِذا صارَت إِلى اَل۪شَيء اَلَّذي يُجيبُها وَ۪لا يُمانِعُها لَم يَفعَل فِعلاً شَديداً لِ۪أَنَّ سُرعَة اَل۪حَرَكَة وَ۪عُظم اَل۪قُوَّة تَتَفَرَّق عِندَ مُلاقات اَل۪شَيء اَل۪مُجيب غَير اَل۪مانِع </s> |
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944 <s id="A18-2|34|91">فَ۪أَمّا اَل۪شَيء اَل۪صُلب إِذا لاقا اَل۪صُلب مِثلَهُ فَ۪ضَرَبَهُ لَم يُجِبهُ اَل۪شَيء اَل۪صُلب وَ۪قاوَمَهُ فَ۪لَم يَتَفَرَّق مِن قُوَّتِهِ شَيء فَ۪تَكون ضَربَتُهُ عَلَيهِ جِدّاً </s> |
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945 <s id="A18-2|34|92">وَ۪ل۪هٰذِهِ اَل۪عِلَّة صارَ أَلَّذين يَلقون أَنفُسَهُم مِن بُعد طَويل في اَل۪ماء لا يَنالُها ضَرَر</s> |
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946 <s id="A18-2|34|93"><pb n="189"></pb> يز </s> |
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947 <s id="A18-2|34|94">لِ۪ماذا صارَت اَل۪رُطوبات وَ۪هِيَ في طَبائِعِها ثَقيلَة تَتَحَرَّك سَريعاً بِ۪سُهولَة </s> |
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948 <s id="A18-2|34|95">فَ۪إِنّا قَد نَرى اَل۪رَجُل اَل۪واحِد يُحَرِّك أَلف قِسط مِن ماء في مَرَّة واحِدَة </s> |
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949 <s id="A18-2|34|96">لِ۪أَنَّ اَل۪ماء مُتَّصِلَة وَ۪أَجزاؤُهُ سَريعَة اَل۪تَفَرُّق </s> |
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950 <s id="A18-2|34|97">فَ۪إِنَّهُ لَيسَ كَ۪مِثل اَل۪حِجارَة وَ۪اَل۪خَشَب مُكتَنِزاً تَصعُب تَجزيئَتُهُ لَكِنَهُ سَهُلَ اَل۪تَفريق وَ۪ل۪ذٰلِكَ صارَ لَيسَ لَهُ ثَبات في نَفسِهِ بَل هُوَ سَيّال إِلى أَسفَل </s> |
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951 <s id="A18-2|34|98">فَ۪يَعرِض مِن ذٰلِكَ أَنّا نُحَرِّك مِنهُ اَل۪جُزء اَل۪يَسير فَ۪تَميل سائِر أَجزائِهِ إِلى ذٰلِكَ اَل۪مَوضِع اَلَّذي إِنتَقَلَ مِنهُ جُزؤُهُ اَل۪يَسير</s> |
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952 </p> |
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953 <p n="35"> |
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954 <s id="A18-2|35|00"></s> |
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955 <s id="A18-2|35|01">وَ۪قَد يَجِب اَن نُبَيِّن أَيضاً أَشياء نَحتاج إِلَيها في اَل۪جَذب وَ۪اَل۪كَبس لَيسَت كَ۪اَلَّتي ذَكَرنا في اَل۪مَقالَة اَلَّتي قَبلَ هٰذِهِ وَ۪لَكِنَ أَشياء اُخَر أَشَدّ أَحكاماً مِن تِلكَ قَد أَوضَحَها ٓأَرشِميدِس وَ۪غَيرُهُ</s> |
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956 <s id="A18-2|35|02">وَ۪أَوَّل ذٰلِكَ نُخَبِّر كَيفَ نَستَخرِج مَركَز ثِقل مُثَلَّث مُتَساوي اَل۪ثُخن وَ۪اَل۪ثِقل </s> |
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957 <s id="A18-2|35|03">فَ۪ل۪يَكُن اَل۪مُثَلَّث اَل۪مَعلوم مُثَلَّث ٓآبٓغ وَ۪نُقَسِّم خَطّ ٓبٓغ بِ۪نِصفَين عَلى عَلامَة ٓد وَ۪ل۪نَصِل عَلامَتَي ٓآد </s> |
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958 <s id="A18-2|35|04">فَ۪اِن أَقَمنا اَل۪مُثَلَّث عَلى خَطّ ٓآد لَم يَمِل إِلى جِهَة مِن اَل۪جِهات لِ۪أَنَّ مُثَلَّثَي ٓآبٓد ٓآدٓغ مُتَساوِيان </s> |
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959 <s id="A18-2|35|05">وَ۪أَيضاً اِن قَسَّمنا خَطّ ٓآغ عَلى عَلامَة ٓe وَ۪وَصَلنا عَلامَتَي ٓبٓe فَ۪اِن أَقَمنا اَل۪مُثَلَّث أَيضاً عَلى خَطّ ٓبٓe لَم يَمِل إِلى جِهَة مِن اَل۪جِهات </s> |
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960 <s id="A18-2|35|06">فَ۪إِذ كانَ اَل۪مُثَلَّث إِذا أُقيمَ عَلى كُلّ واحِد مِن خَطَّي ٓآد ٓبٓe يَعتَدِل أَجزاؤُهُ وَ۪لا يَميل إِلى جِهَة مِن اَل۪جِهات <pb n="191"></pb> فَ۪إِنَّ عَلامَة تَقاطُعِهِما اَل۪مُشتَرَكَة لَهُما هِيَ مَركَز ذٰلِكَ اَل۪ثِقل وَ۪هِيَ عَلامَة ٓز</s> |
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961 <s id="A18-2|35|07">وَ۪قَد يَنبَغي اَن نَتَوَهَّم عَلامَة ٓز في وَسَط ثُخن مُثَلَّث ٓآبٓغ</s> |
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962 <s id="A18-2|35|08">فَ۪يَظهَر لَنا أَنّا إِذا وَصَلنا عَلامَتَي ٓآد وَ۪قَسَّمنا خَطّ ٓآد عَلى عَلامَة ٓز بِ۪قِسمَين يَكون أَحَدُهُما اَلَّذي هُوَ ٓآز ضِعف ٓزٓد فَ۪إِنَّ عَلامَة ٓز تَكون مَركَز اَل۪ثِقل لِ۪أَنّا اِن وَصَلنا عَلامَتَي ٓدٓe يَكون خَطّ ٓآب مُوازِياً لِ۪خَطّ ٓدٓe لِ۪أَنَّ خَطَّي ٓآغ ٓبٓغ قَد قُسِما عَلى عَلامَتَي ٓدٓe</s> |
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963 <s id="A18-2|35|09">فَ۪إِذاً خَطّ ٓآغ عِندَ ٓغٓe مِثلَ ٓآب عِندَ ٓeٓد وَ۪خَطّ ٓآغ ضِعف خَطّ ٓغٓe فَ۪إِذاً خَطّ ٓآب ضِعف ٓeٓد </s> |
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964 <s id="A18-2|35|10">وَ۪خَطّ ٓآب عِندَ ٓeٓد كَ۪خَطّ ٓآز عِندَ ٓدٓز فَ۪إِذاً خَطّ ٓآز ضِعف ٓزٓد مِن أَجل أَنَّ شَكلَي ٓآبٓز وَ۪ٓدٓزٓe مُتَساوِيَي اَل۪زَوايا</s> |
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965 </p> |
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966 <p n="36"> |
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967 <s id="A18-2|36|00"></s> |
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968 <s id="A18-2|36|01">نُريد اَن نَستَخرِج ذٰلِكَ أَيضاً في اَل۪مُرَبَّع </s> |
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969 <s id="A18-2|36|02">فَ۪ل۪يَكُن اَل۪مُرَبَّع اَل۪مَعلوم مُرَبَّع ٓآبٓغٓد </s> |
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970 <s id="A18-2|36|03">وَ۪ل۪نَصِل ٓبٓد وَ۪نَفصِل ٓبٓد وَ۪نَفصِلُهُ بِ۪نِصفَين عَلى عَلامَة ٓe وَ۪ل۪نَصِل خَطَّي ٓآe ٓeٓغ وَ۪نُقَسِّمُهُما عَلى عَلامَتَي ٓزٓه قِسمَة يَكون ٓآز ضِعف ٓزٓe وَ۪ٓهٓغ ضِعف ٓهٓe فَ۪يَكون مَركَز مُثَلَّث ٓآبٓد عَلى عَلامَة ٓز وَ۪مَركَز مُثَلَّث ٓبٓدٓغ عَلى عَلامَة ٓه فَ۪لَيسَ نَجِد إِختِلافاً في تَوَهُّمِنا أَنَّ ثِقل مُثَلَّث ٓآبٓد كُلِّهِ عِندَ عَلامَة ٓز وَ۪أَيضاً ثِقل مُثَلَّث ٓبٓغٓد عِندَ عَلامَة ٓه </s> |
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971 <s id="A18-2|36|04">فَ۪قَد صارَ خَطّ ٓزٓه ميزاناً في طَرَفَيهِ هاذان اَل۪عُظمان</s> |
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972 <s id="A18-2|36|05">فَ۪اِن فَصَلنا <pb n="193"></pb> خَطّ ٓزٓه عَلى عَلامَة ٓت فَصلاً يَكون ٓتٓه عِندَ ٓزٓت كَ۪ثِقل ٓز اَلَّذي هُوَ ثِقل مُثَلَّث ٓآبٓد عِندَ ثِقل ٓه اَلَّذي هُوَ ثِقل مُثَلَّث ٓبٓدٓغ تَكون عَلامَة ٓت اَلَّتي يَتَعادِل عَلَيها اَل۪ثِقلان مَركَز ذٰلِكَ اَل۪مُرَبَّع</s> |
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973 </p> |
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974 <p n="37"> |
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975 <s id="A18-2|37|00"></s> |
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976 <s id="A18-2|37|01">نُريد اَن نُبَيِّن ذٰلِكَ في مُخَمَّس ٓآبٓغٓدٓe </s> |
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977 <s id="A18-2|37|02">فَ۪ل۪نَصِل ٓبٓe وَ۪نُخرِج مَركَز ثِقل مُثَلَّث ٓآبٓe وَ۪ل۪يَقَع عَلى عَلامَة ٓز وَ۪ل۪يَكُن مَركَز ثِقل مُرَبَّع ٓبٓغٓدٓe عَلى عَلامَة ٓه </s> |
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978 <s id="A18-2|37|03">وَ۪ل۪نَصِل عَلامَتَي ٓزٓه وَ۪نُقَسِّم خَطّ ٓزٓه بِ۪قِسمَين يَكون قِسم ٓهٓت عِندَ ٓتٓز كَ۪ثِقل مُثَلَّث ٓآبٓe عِندَ ثِقل مُرَبَّع ٓبٓغٓدٓe فَ۪تَكون عَلامَة ٓت مَركَز ثِقل شَكل ٓآبٓغٓدٓe </s> |
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979 <s id="A18-2|37|04">وَ۪كَ۪ذٰلِكَ يَنبَغي اَن نَتَوَهَّم في كُلّ شَكل كَثير اَل۪أَضلاع</s> |
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980 </p> |
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981 <p n="38"> |
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982 <s id="A18-2|38|00"></s> |
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983 <s id="A18-2|38|01">نُريد اَن نُبَيِّن إِذا كانَ مُثَلَّث ٓآبٓغ مُتَساوي اَل۪ثُخن وَ۪اَل۪ثِقل وَ۪كانَت قَوائِم تَحت عَلامات ٓآبٓغ مُتَساوِيَة اَل۪وَضع كَيفَ نَستَخرِج كَمِّيَّة اَل۪ثِقل اَلَّذي تَحتَمِل كُلّ واحِدَة مِنها مِن مُثَلَّث ٓآبٓغ </s> |
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984 <s id="A18-2|38|02">فَ۪نَفصِل خَطّ ٓبٓغ بِ۪نِصفَين عَلى عَلامَة ٓد وَ۪نَصِل عَلامَتَي ٓآد وَ۪نُقَسِّم خَطّ ٓآد بِ۪قِسمَين عَلى عَلامَة ٓe قِسمَة يَكون قِسم ٓآe ضِعف ٓeٓد فَ۪تَكون عَلامَة ٓe مَركَز جَميع ثِقل اَل۪مُثَلَّث </s> |
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985 <s id="A18-2|38|03">فَ۪يَنبَغي اَن نُقَسِّمَهُ عَلى اَل۪قَوائِم </s> |
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986 <s id="A18-2|38|04"><pb n="195"></pb> وَ۪لَكِنَنا اِن تَوَهَّمنا خَطّ ٓآد مُعتَدِل اَل۪مَيل عِندَ تَعَلُّقِهِ عَلى عَلامَة ٓe يَكون اَل۪ثِقل اَلَّذي عِندَ ٓد ضِعف اَل۪ثِقل اَلَّذي عِندَ ٓأَة لِ۪أَنَّ خَطّ ٓآe ضِعف خَطّ ٓeٓد </s> |
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987 <s id="A18-2|38|05">فَ۪اِن تَوَهَّمنا اَل۪ثِقل اَلَّذي عِندَ ٓد مُنقَسِماً عَلى عَلامَتَي ٓبٓغ وَ۪كانَ خَطّ ٓبٓغ مُعتَدِلاً يَكون عِندَ كُلّ واحِدَة مِن عَلامَتَي ٓبٓغ نِصف اَل۪ثِقل اَلَّذي عِندَ ٓد لِ۪أَنَّ خَطَّي ٓبٓد ٓدٓغ مُتَساوِيان </s> |
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988 <s id="A18-2|38|06">وَ۪قَد كانَ اَل۪ثِقل اَلَّذي عِندَ ٓد ضِعف اَل۪ثِقل اَلَّذي عِندَ ٓأَة فَ۪إِذاً اَل۪أَثقال اَلَّتي عِندَ عَلامات ٓآبٓغ مُتَساوِيَة فَ۪إِذاً اَل۪قَوائِم تَحمِل أَثقالاً مُتَساوِيَة</s> |
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989 </p> |
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990 <p n="39"> |
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991 <s id="A18-2|39|00"></s> |
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992 <s id="A18-2|39|01">وَ۪أَيضاً فَ۪ل۪يَكُن مُثَلَّث ٓآبٓغ مُتَساوي اَل۪ثِقل وَ۪اَل۪ثُخن عَلى قَوائِم مُتَساوِيَة اَل۪وَضع وَ۪ل۪يَكُن عَلى عَلامَة ٓe ثِقل ما مَوضوعاً أَو مُعَلَّقاً وَ۪ل۪يَكُن عَلامَة ٓe واقِعَة حَيثُما وَقَعَت فَ۪نُريد اَن نَستَخرِج كَم تَحتَمِل كُلّ واحِدَة مِن اَل۪قَوائِم مِن ثِقل ٓe</s> |
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993 <s id="A18-2|39|02">فَ۪ل۪نَصِل ٓeٓا وَ۪نُخرِجهُ إِلى ٓد وَ۪نُقَسِّم اَل۪ثِقل اَلَّذي عِندَ ٓe بِ۪قِسمَين يَكون إِذا قُوِّمَ اَل۪مُثَلَّث عَلى خَطّ ٓآد يَعتَدِل فَ۪يَكون اَل۪ثِقل اَلَّذي عِندَ ٓد عِندَ اَل۪ثِقل اَلَّذي عِندَ ٓأَة مِثلَ خَطّ ٓآe عِندَ خَطّ ٓeٓد وَ۪ل۪نُقَسِّم اَل۪ثِقل اَلَّذي عِندَ ٓد قِسمَة يَكون إِذا عُلِّقَ ٓبٓغ يَعتَدِل فَ۪يَكون ثِقل ٓغ عِندَ ثِقل ٓب مِثلَ خَطّ ٓبٓد عِندَ خَطّ ٓدٓغ </s> |
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994 <s id="A18-2|39|03">وَ۪اَل۪ثِقل اَلَّذي عِندَ <pb n="197"></pb> ٓد مَلفوظ فَ۪إِذاً اَل۪ثِقلان اَلَّذان عِندَ ٓبٓغ مَلفوظان </s> |
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995 <s id="A18-2|39|04">وَ۪لَكِنَ اَل۪ثِقل اَلَّذي عِندَ ٓأَة مَلفوظ فَ۪إِذاً اَل۪أَثقال اَلَّتي عَلى اَل۪قَوائِم مَلفوظَة</s> |
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996 </p> |
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997 <p n="40"> |
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998 <s id="A18-2|40|00"></s> |
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999 <s id="A18-2|40|01">نُريد اَن نَستَخرِج إِذاكانَ مُثَلَّث ٓآبٓغ وَ۪كانَت أَثقال ما مَعلومَة مُعَلَّقَة عَلى عَلامات ٓآبٓغ عَلامَة في داخِل اَل۪مُثَلَّث إِذا عُلِّقَ بِها اَل۪مُثَلَّث يَعتَدِل </s> |
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1000 <s id="A18-2|40|02">نُقَسِّم خَطّ ٓآب عَلى عَلامَة ٓد قِسمَة يَكون خَطّ ٓبٓد عِندَ ٓدٓا كَ۪اَل۪ثِقل اَلَّذي عِندَ ٓأَة إِلى اَل۪ثِقل اَلَّذي عِندَ ٓب </s> |
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1001 <s id="A18-2|40|03">فَ۪يَكون مَركَز اَل۪ثِقل اَل۪مُجتَمِع مِن اَل۪ثِقلَين عَلى عَلامَة ٓد </s> |
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1002 <s id="A18-2|40|04">فَ۪ل۪نَصِل عَلامَتَي ٓدٓغ بِ۪خَطّ ٓدٓغ وَ۪نُقَسِّمهُ عَلى عَلامَة ٓe قِسمَة يَكون خَطّ ٓغٓe عِندَ ٓeٓد مِثلَ ثِقل ٓد عِندَ ثِقل ٓغ فَ۪تَكون عَلامَة ٓe مَركَز اَل۪ثِقل اَل۪مُجتَمِع مِن اَل۪جَميع فَ۪إِذاً هِيَ عَلامَة اَل۪عِلاقَة</s> |
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1003 </p> |
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1004 <p n="41"> |
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1005 <s id="A18-2|41|00"></s> |
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1006 <s id="A18-2|41|01">نُريد اَن نُبَيِّن ذٰلِكَ في شَكل كَثير اَل۪أَضلاع </s> |
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1007 <s id="A18-2|41|02">فَ۪ل۪يَكُن شَكل ٓآبٓغٓدٓe كَثير اَل۪أَضلاع </s> |
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1008 <s id="A18-2|41|03">وَ۪ل۪نُعَلِّق عَلى عَلامات ٓآبٓغٓدٓe أَثقالاً مَعلومَة وَ۪نُقَسِّم خَطّ ٓآب عَلى عَلامَة ٓز قِسمَة يَكون خَطّ ٓبٓز عِندَ ٓزٓا مِثل ثِقل ٓأَة عِندَ ثِقل ٓب فَ۪تَكون عَلامَة ٓز مَركَز اَل۪ثِقلَين أَلَّذَين عِندَ ٓآب </s> |
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1009 <s id="A18-2|41|04">وَ۪ل۪نُقَسِّم أَيضاً خَطّ ٓدٓe عَلى عَلامَة ٓه قِسمَة يَكون خَطّ ٓدٓه عِندَ خَطّ ٓهٓe مِثل ثِقل ٓe عِندَ ثِقل ٓد فَ۪تَكون عَلامَة ٓه مَركَز اَل۪ثِقل اَل۪مُجتَمِع <pb n="199"></pb> مِن عَلامَتَي ٓeٓد</s> |
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1010 <s id="A18-2|41|05">وَ۪نَصِل ٓزٓه وَ۪نُقَسِّمُهُ عَلى عَلامَة ٓت قِسمَة يَكون جَميع ٓآب عِندَ جَميع ٓدٓe مِثل ٓهٓت عِندَ ٓتٓز فَ۪تَكون عَلامَة ٓت مَركَز اَل۪ثِقل اَل۪مُجتَمِع مِن عَلامات ٓآبٓدٓe </s> |
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1011 <s id="A18-2|41|06">وَ۪ل۪نَصِل عَلامَتَي ٓغٓت بِ۪خَطّ ٓغٓت وَ۪نُقَسِّمُهُ عَلى عَلامَة ٓك قِسمَة يَكون خَطّ ٓغٓك عِندَ ٓكٓت كَ۪ثِقل ٓآبٓدٓe عِندَ ثِقل ٓغ فَ۪إِذاً عَلامَة ٓك مَركَز اَل۪ثِقل اَل۪مُؤَلَّف مِن اَل۪جَميع</s> |
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1012 </p> |
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1013 <p n="42"> |
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1014 <s id="A18-2|42|00"></s> |
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1015 <s id="A18-2|42|01">تَمَّت اَل۪مَقالَة اَل۪ثانِيَة مِن كِتاب ٓايرُن في رَفع</s> |
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1016 <s id="A18-2|42|02">اَل۪أَشياء اَل۪ثَقيلَة</s> |
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1017 </p> |
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1018 </chap> |
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1019 <chap n="3"> |
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1020 <p n="0"> |
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1021 <s id="A18-3|00|00"></s> |
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1022 <s id="A18-3|00|01">اَل۪مَقالَة اَل۪ثالِثَة مِن كِتاب ٓايرُن في رَفع اَل۪أَشياء اَل۪ثَقيلَة</s> |
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1023 </p> |
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1024 <p n="1"> |
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1025 <s id="A18-3|01|00"></s> |
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1026 <s id="A18-3|01|01">أَمّا في اَل۪مَقالَة اَلَّتي قَبلَ هٰذِهِ فَ۪قَد قُلنا في اَل۪خَمس قُوى وَ۪بَيَّنّا اَل۪عِلَل اَلَّتي تُحَرَّك بِها اَل۪أَثقال اَل۪عَظيمَة بِ۪قُوَّة يَسيرَة وَ۪أَثبَتنا في ذٰلِكَ فيما نَظُنّ أَكثَر مِمَّن كانَ قَبلَنا </s> |
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1027 <s id="A18-3|01|02">وَ۪بَيَّنّا اَل۪عِلَّة لِمَ صارَ يَتبَع اَل۪آلات اَل۪عَظيمَة اَل۪قُوَّة اَل۪إِبطاء وَ۪بَيَّنّا أَشياء اُخَر يَنتَفِع بِها اَل۪مُتَعَلِّمون في اَل۪مَيل وَ۪اَل۪كَبس فيها كِفايَة لِ۪ل۪مُتَعَلِّمين </s> |
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1028 <s id="A18-3|01|03">فَ۪أَمّا في هٰذِهِ اَل۪مَقالَة فَ۪إِنّا نَكتُب حِيَلاً نَنتَفِع بِها في تَسهيل ما تَقَدَّمَ وُجودُهُ وَ۪إِستِعمالُهُ تُعين أَيضاً عَلى حَرَكَة اَل۪أَجسام اَل۪ثَقيلَة </s> |
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1029 <s id="A18-3|01|04">وَ۪أَيضاً نَعمَل آلات نَنتَفِع بِها في اَل۪عَصر لِ۪أَنَّ هٰذِهِ أَيضاً تَحتاج إِلى قُوَّة عَظيمَة في إِستِعمالِها </s> |
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1030 <s id="A18-3|01|05">أَمّا اَل۪أَشياء اَلَّتي تُجَرّ عَلى اَل۪أَرض فَ۪إِنَّها تُجَرّ عَلى اَل۪لَجآت </s> |
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1031 <s id="A18-3|01|06">وَ۪اَل۪لَجأَت هِيَ جِسم ثابِت مَعمول مِن خَشَب مُرَبَّع أَطرافُهُ مَفروضَة </s> |
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1032 <s id="A18-3|01|07">فَ۪هٰذِهِ اَل۪لَجآت تُصَيَّر عَلَيها اَل۪أَثقال وَ۪تُشَدّ في أَطرافِها حِبال أَو شَيء آخَر مَمدود تُجَرّ اَل۪لَجآت بِهِ</s> |
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1033 <s id="A18-3|01|08">وَ۪هٰذِهِ اَل۪قُلوس إِمّا اَن تُمَدّ بِ۪اَل۪أَيدي وَ۪إِمّا بِ۪أَجسام اُخَر </s> |
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1034 <s id="A18-3|01|09">وَ۪إِذا مِدَّت اَل۪قُلوس سارَت اَل۪لَجآت عَلى اَل۪أَرض وَ۪قَد يُصَيَّر تَحت اَل۪لَجآت خَشَب مُستَدير دَقيق أَو أَلاواح لِ۪تَتَحَرَّك اَل۪لَجآت عَلَيها </s> |
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1035 <s id="A18-3|01|10">فَ۪اِن كانَ اَل۪حَمل صَغيراً فَ۪إِنَّهُ يَنبَغي اَن نَستَعمِل اَل۪خَشَب اَل۪مُستَدير وَ۪اِن كانَ اَل۪ثِقل عَظيماً فَ۪يَنبَغي اَن نَستَعمِل اَل۪أَلواح لِ۪أَنَّها لا تَتَحَرَّك سَريعاً </s> |
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1036 <s id="A18-3|01|11">وَ۪ذٰلِكَ أَنَّ اَل۪خَشَب اَل۪مُستَدير إِذا تَدَحرَجَ تَحت اَل۪حَمل يَندِقّ تَحت اَل۪حَمل لِ۪شِدَّة سُرعَة حَرَكَتِهِ </s> |
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1037 <s id="A18-3|01|12">وَ۪قَوم لا يَستَعمِلون أَلواحاً وَ۪لا خَشَباً مُستَديراً وَ۪لَكِنَهُم صَيَّروا في أَطراف اَل۪لَجآت فِلَكاً صُلبَة تَتَحَرَّك عَلَيها</s> |
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1038 </p> |
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1039 <p n="2"> |
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1040 <s id="A18-3|02|00"></s> |
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1041 <s id="A18-3|02|01">وَ۪قَد نَحتاج في رَفع اَل۪أَشياء اَل۪ثَقيلَة إِلى اَل۪عُلُوّ إِلى حِيَل ما فَ۪مِنها ما هُوَ ذو قائِمَة واحِدَة وَ۪مِنها ما هُوَ ذو قائِمَتَين وَ۪مِنها ما هُوَ ذو ثَلاث وَ۪مِنها ما هُوَ ذو أَربَع قَوائِم </s> |
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1042 <s id="A18-3|02|02">أَمّا اَلَّتي هِيَ ذات قائِمَة واحِدَة فَ۪إِنَّها تَكون عَلى هٰذِهِ اَل۪جِهَة</s> |
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1043 <s id="A18-3|02|03">نَأخُذ خَشَبَة طَويلَة لَها إِرتِفاع أَعظَم مِن اَل۪بُعد اَلَّذي نُريد اَن نَرفَع اَل۪ثِقل إِلَيهِ</s> |
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1044 <s id="A18-3|02|04">فَ۪اِن كانَ هٰذا اَل۪عود في نَفسِهِ صُلباً نَأخُذ قَلساً فَ۪نَشُدُّهُ عَلَيهِ وَ۪نَلُفُّهُ عَلى بُعد مُتَساوٍ وَ۪ل۪يَكُن اَل۪خَطّ اَل۪قائِم اَلَّذي بَينَ كُلّ لَفَّة قَدر أَربَعَة أَشبار </s> |
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1045 <s id="A18-3|02|05">فَ۪قَد تَزداد قُوَّة اَل۪عود وَ۪يَكون إِلتِفاف اَل۪قَلس عَلَيهِ كَ۪دَرَج لِ۪مَن يُريد يَعمَل شَيئاً ما في أَعلا اَل۪عود وَ۪تَكثُر بِهِ سُهولَة اَل۪عَمَل</s> |
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1046 <s id="A18-3|02|06">فَ۪اِن <pb n="205"></pb> لَم يَكُن ذٰلِكَ اَل۪عود في نَفسِهِ صُلباً فَ۪يَنبَغي اَن نَنظُر في قَدر اَل۪ثِقل اَلَّذي نُريد اَن نَرفَعَهُ لِ۪اَن لا تَكون قُوَّة اَل۪ثِقل أَعظَم مِن قُوَّة تِلكَ اَل۪قائِمَة </s> |
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1047 <s id="A18-3|02|07">فَ۪نُقيم تِلكَ اَل۪قائِمَة مُستَوِيَة عَلى خَشَبَة تَكون مُضطَرِبَة فيها وَ۪نَربُط في أَعلا ذٰلِكَ اَل۪رُكن ثَلاثَة حِبال أَو أَربَعَة وَ۪نَشُدُّها إِلى أَركان ثابِتَة شَديدَة اَل۪ثَبات فَ۪نَشُدّ اَل۪حِبال عَلَيها</s> |
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1048 <s id="A18-3|02|08">ثُمَّ نُصَيِّر في طَرَف هٰذا اَل۪رُكن بِكَراً تُشَدّ إِلَيهِ بِ۪حَبل وَ۪نَربُط اَل۪قُلوس اَلَّتي في اَل۪بِكَر بِ۪اَل۪حَمل اَلَّذي نُريد اَن نُقِلَّهُ </s> |
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1049 <s id="A18-3|02|09">ثُمَّ نَمُدّ اَل۪قُلوس إِمّا بِ۪اَل۪أَيدي وَ۪إِمّا بِ۪آلَة أُخرا فَ۪إِذاً تَعالى اَل۪حَمل</s> |
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1050 <s id="A18-3|02|10">وَ۪اِن إِحتَجتَ اَن تُصَيِّر اَل۪حَجَر عَلى حائِط أَو عَلى أَيّ مَوضِع أَرَدتَ تَحُلّ اَل۪حَبل اَلَّذي في أَحَد اَل۪أَركان اَل۪ثابِتَة اَلَّتي تَمُدّ اَل۪رُكن اَلَّذي اَل۪بَكرَة مَشدودَة فيهِ إِلى ضِدّ اَل۪جِهَة اَلَّتي تُريد اَن تَضَع اَل۪حَجَر فيها فَ۪يَميل ذٰلِكَ اَل۪رُكن إِلى تِلكَ اَل۪جِهَة وَ۪تَدفَع اَل۪حَبل اَلَّذي في اَل۪بَكرَة قَليلاً قَليلاً إِلى اَل۪مَوضِع اَلَّذي تُريد اَن تُجلِسَهُ فيهِ </s> |
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1051 <s id="A18-3|02|11">فَ۪اِن لَم تَكُن تَبلُغ مِن مَيل اَل۪رُكن اَلَّذي اَل۪بَكرَة عَلَيهِ مَشدودَة ما يُؤَدّي اَل۪ثِقل اَل۪مَرفوع إِلى اَل۪مَوضِع اَلَّذي نُريد صَيَّرنا تَحتَهُ خَشَباً مُستَديراً نُمشيهِ عَلَيهِ أَو نَدفَعُهُ بِ۪اَل۪مُخل حَتّى نُصَيِّرَهُ في اَل۪مَوضِع اَلَّذي <pb n="207"></pb> نُريد</s> |
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1052 <s id="A18-3|02|12">فَ۪إِذا فَعَلنا ذٰلِكَ وَ۪رَدَدنا اَل۪رُكن إِلى مَوضِعِهِ مِن اَل۪جِهَة اَل۪أُخرا اَلَّتي تَلي إِلَينا ثُمَّ نَشُدُّهُ أَيضاً وَ۪نَستَعمِل فيهِ مِثلَ اَل۪عَمَل اَل۪أَوَّل</s> |
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1053 </p> |
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1054 <p n="3"> |
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1055 <s id="A18-3|03|00"></s> |
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1056 <s id="A18-3|03|01">فَ۪أَمّا اَل۪حيلَة اَلَّتي هِيَ ذات رُكنَين فَ۪إِنَّها تُعمَل بِ۪هٰذا اَل۪عَمَل </s> |
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1057 <s id="A18-3|03|02">نَستَعمِل اَل۪آلَة اَلَّتي تُسَمّي ودوس وَ۪نُرَكِّب عَلَيها اَل۪أَركان </s> |
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1058 <s id="A18-3|03|03">وَ۪ل۪تَكُن تَميل إِلى اَل۪جِهَة اَل۪عُليا مَيلاً يَسيراً يَكون قَدر خُمس مِن اَل۪بُعد اَل۪سُفلاني </s> |
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1059 <s id="A18-3|03|04">ثُمَّ نَشُدّ اَل۪رُكنَين عَلى هٰذا اَل۪ودوس لِ۪يَجتَمِع طَرَفَيهِما بَعضَها إِلى بُعد وَ۪نُصَيِّر في أَطراف اَل۪أَركان عارِضَة أُخرا تُشَدّ عَلَيها بَكرَة كَثيرَة اَل۪رَفع </s> |
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1060 <s id="A18-3|03|05">وَ۪ل۪تَكُن بِكَر اُخَر مَشدودَة في اَل۪حَجَر </s> |
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1061 <s id="A18-3|03|06">ثُمَّ نَمُدّ ذٰلِكَ اَل۪حَبل مِثلَ اَل۪عَمَل اَل۪أَوَّل إِمّا بِ۪اَل۪أَيدي وَ۪إِمّا بِ۪دَوابّ فَ۪يَرتَفِع اَل۪ثِقل </s> |
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1062 <s id="A18-3|03|07">فَ۪ل۪تُعالي هٰذِهِ اَل۪أَركان يَنبَغي اَن تَكون مُرتَبِطَة بِ۪اَل۪حِبال كَ۪اَل۪رَبط اَلَّذي وَصَفنا أَوَّلاً </s> |
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1063 <s id="A18-3|03|08">ثُمَّ نَضَع اَل۪حَجَر وَ۪نَنقُل ذٰلِكَ اَل۪ودوس إِلى اَل۪جِهَة اَل۪أُخرا مِن اَل۪بِناء عَلى قَدر ما تَدعوا اَل۪حاجَة إِلَيهِ</s> |
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1064 </p> |
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1065 <p n="4"> |
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1066 <s id="A18-3|04|00"></s> |
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1067 <s id="A18-3|04|01">فَ۪أَمّا اَل۪حيلَة اَلَّتي هِيَ ذات ثَلاثَة أَركان فَ۪إِنَّها <pb n="209"></pb> تُعمَل عَلى هٰذِهِ اَل۪جِهَة</s> |
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1068 <s id="A18-3|04|02">نَعمَل ثَلاثَة أَركان بَعضُها مائِل إِلى بَعض تَجتَمِع أَطرافُها عَلى عَلامَة واحِدَة وَ۪نَشُدّ عَلى تِلكَ اَل۪عَلامَة اَلَّتي إِجتَمَعَت اَل۪ثَلاثَة اَل۪أَركان عَلَيها بَكرَة كَثيرَة اَل۪رَفع وَ۪يَكون بَعضُها مَشدوداً عَلى اَل۪حَبل </s> |
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1069 <s id="A18-3|04|03">فَ۪إِذا جُذِبَت قُلوس اَل۪بِكَر إِرتَفَعَ اَل۪حَمل</s> |
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1070 <s id="A18-3|04|04">وَ۪هٰذِهِ اَل۪آلَة قاعِدَتُها أَوثَق وَ۪أَأماً مِن غَيرِها وَ۪لَكِنَ لَيسَ يَصلُح اَن تُستَعمَل في كُلّ مَوضِع نُريد لَكِنَ في اَل۪مَوضِع اَلَّذي نُريد اَن نَرفَع اَل۪حَمل في وَسَط هٰذِهِ اَل۪آلَة </s> |
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1071 <s id="A18-3|04|05">فَ۪إِذا إِحتَجنا اَن نُقِلّ حَملاً إِلى مَوضِع يُمكِن اَن نُصَيِّر هٰذِهِ اَل۪آلَة تُحيط بِ۪وَسَطِهِ إِستَعمَلناها عِندَ ذٰلِكَ </s> |
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1072 </p> |
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1073 <p n="5"> |
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1074 <s id="A18-3|05|00"></s> |
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1075 <s id="A18-3|05|01">وَ۪أَمّا اَل۪حيلَة اَلَّتي هِيَ ذات أَربَع قَوائِم فَ۪إِنَّها تُستَعمَل في اَل۪أَثقال اَل۪مُفرِطَة في اَل۪عُظم </s> |
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1076 <s id="A18-3|05|02">وَ۪هِيَ اَن يُقام أَربَعَة أَركان مِن خَشَب تَكون حَلقَتُها كَ۪حَلقَة مُرَبَّع مُتَوازي اَل۪أَضلاع وَ۪ل۪يَكُن في سَعَتِهِ عَلى اَل۪مِقدار اَلَّذي يُمكِن اَل۪حَجَر اَن يَضطَرِب فيهِ وَ۪يَتَعالي بِ۪سُهولَة</s> |
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1077 <s id="A18-3|05|03">ثُمَّ نَشُدّ عَلى أَطراف هٰذِهِ اَل۪أَركان خَشَباً نَصِل بَعضَها بِ۪بَعض وَ۪ل۪يَكُن ذٰلِكَ بِ۪إِحكام وَ۪وَثاقَة </s> |
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1078 <s id="A18-3|05|04">ثُمَّ نُصَيِّر أَيضاً عَلى هٰذِهِ اَل۪خَشَب خَشَباً اُخَر نَشُدّ <pb n="211"></pb> بَعضَها بِ۪بَعض شَدّاً مُخالِف اَل۪تَرتيب لِ۪يُربَط جَميع اَل۪أَركان بَعضُها بِ۪بَعض </s> |
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1079 <s id="A18-3|05|05">ثُمَّ نَشُدّ اَل۪بِكَر في وَسَط هٰذِهِ اَل۪خَشَب عَلى اَل۪عَلامَة اَلَّتي تُلاقي اَل۪أَعواد بَعضُها بَعضاً عَلَيها </s> |
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1080 <s id="A18-3|05|06">ثُمَّ نَشُدّ اَل۪حَجَر في تِلكَ اَل۪حِبال اَلَّتي في اَل۪بِكَر وَ۪نَجبِذُها فَ۪يَرتَفِع اَل۪حَمل</s> |
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1081 <s id="A18-3|05|07">فَ۪قَد يَنبَغي اَن نَتَوَقّا في جَميع آلات اَل۪حِيَل مِن اَن نَستَعمِل مَسامير وَ۪أَوتاداً وَ۪بِ۪اَل۪جُملَة كُلّ۪ما يَكون في ثِقل وَ۪لا سِيَّما في اَل۪أَثقال اَل۪عِظام لَكِنَنا نَستَعمِل اَل۪حِبال وَ۪اَل۪قُلوس فَ۪نَشُدّ بِها ما نُريد مَكان اَل۪شَيء اَلَّذي نُريد اَن نُسَمِّرَهُ</s> |
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1082 </p> |
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1083 <p n="6"> |
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1084 <s id="A18-3|06|00"></s> |
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1085 <s id="A18-3|06|01">وَ۪مِن أَجل أَنَّهُ قَد يَعرِض لِ۪ل۪آلَة اَلَّتي كَ۪هَيئَة اَل۪مِقلاع اَلَّتي بِها يَرتَفِع اَل۪حَجَر اَن تُمنَع مِن تَركيب اَل۪حَجَر في اَل۪مَوضِع اَلَّذي نَحتاج اَن يُرَكَّب فيهِ فَ۪إِنّا نَستَعمِل هٰذِهِ اَل۪حيلَة وَ۪هِيَ اَلَّتي تُسَمّي عَلَقاً </s> |
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1086 <s id="A18-3|06|02">نَرسُم عَلى قائِدَت اَل۪حَجَر اَلَّتي هِيَ سَطح ٓآبٓغٓد شَكلاً مُشابِهاً لِ۪ل۪شَكل اَل۪مَرسوم </s> |
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1087 <s id="A18-3|06|03">وَ۪هُوَ اَن يَكون كُلّ واحِد مِن سَطحَي ٓeٓزٓهٓت ٓكٓلٓمٓن مُتَوازي اَل۪أَضلاع وَ۪ل۪يَكُن ٓeٓزٓهٓت أَعظَم عَرضاً مِن ٓكٓلٓمٓن فَ۪أَمّا في اَل۪طول فَ۪ل۪يَكونا مُتَساوِيَين أَعني اَن يَكون خَطّ ٓكٓم مُساوِياً لِ۪خَطّ ٓeٓه </s> |
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1088 <s id="A18-3|06|04">ثُمَّ نَحفِر هٰذا اَل۪شَكل في عَمق اَل۪حَجَر وَ۪ل۪يَكُن عَمق اَل۪حَفر عَلى قَدر ثِقل اَل۪حَجَر </s> |
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1089 <s id="A18-3|06|05">وَ۪ل۪يَكُن <pb n="313"></pb> حَفر سَطح ٓeٓزٓهٓت قائِم اَل۪زَوايا مُستَقصي قِيامُها وَ۪أَمّا سَطح ٓكٓلٓمٓن فَ۪مُوَرَّب اَل۪حَفر أَعني اَن يَكون أَسفَلُهُ أَوسَع مِن أَعلاهُ فَ۪يَكون حَفراً كَ۪هَيئَة اَل۪قُفل اَل۪خَشَب </s> |
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1090 <s id="A18-3|06|06">يَكون اَل۪ضَيِّق مِنهُ مُساوِياً ٓكٓلٓمٓن وَ۪اَل۪عَريض مِنهُ مُساوِياً ٓeٓزٓهٓت </s> |
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1091 <s id="A18-3|06|07">وَ۪نَعمَل جِسماً كَ۪هَيئَة اَل۪قُفل اَل۪خَشَب أَيضاً مِن حَديد يَتَراكِب عَلى هٰذا اَل۪حَفر يَكون في أَعلاهِ حَلقَة مُتَّصِلَة بِهِ فَ۪يُصَيَّر في حَفر ٓeٓزٓهٓت حَتّى يُعَبِّر فيهِ ثُمَّ يُدفَع وَ۪يُدار حَتّى يَصير في اَل۪حَفر اَل۪أُنثا حَتّى لا يَنقَلِع </s> |
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1092 <s id="A18-3|06|08">ثُمَّ يُرَكَّب عَلى حَفر ٓeٓزٓهٓت خَشَب لِ۪أَة۪لا تَندَفِع اَل۪حَديدَة </s> |
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1093 <s id="A18-3|06|09">ثُمَّ نُصَيِّر اَل۪حَلقَة اَل۪مُتَّصِلَة بِ۪اَل۪وَتَد اَل۪حَديد اَل۪حِبال اَلَّتي كانَت تَحمِل اَل۪مِقلاع اَلَّذي كانَ يَكون اَل۪حَجَر فيهِ فَ۪يُقَلّ بِ۪هٰذا اَل۪عَمَل حَتّى يَصير في لِ۪مَوضِع اَلَّذي نُريد بِلا اَن يَكون يَمنَعُهُ شَيء </s> |
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1094 <s id="A18-3|06|10">فَ۪إِذا رُكِّبَ اَل۪حَجَر في مَوضِعِهِ خُلِعَت تِلكَ اَل۪أَوتاد وَ۪نُزِعَت اَل۪حَديدَة ثُمَّ رُكِّبَت في حَجَر آخَر وَ۪يَرتَفِع أَيضاً </s> |
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1095 </p> |
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1096 <p n="7"> |
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1097 <s id="A18-3|07|00"></s> |
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1098 <s id="A18-3|07|01">وَ۪قَد تَتَعالي اَل۪حِجارَة أَيضاً بِ۪اَل۪آلات اَلَّتي تُسَمّي اَل۪سَراطين إِذا كانَت ذات ثَلاث قَوائِم أَو أَربَع وَ۪عُوِّجَت أَطرافُها حَتّى تَصير كَ۪هَيئَة اَل۪شَصاص وَ۪رُكِّبَت هٰذِهِ اَل۪شَصاص في جانِب اَل۪حَمل </s> |
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1099 <s id="A18-3|07|02">وَ۪صيرَ في أَطرافِها عَوارِض <pb n="215"></pb> أَعني في أَطراف اَل۪قَوائِم وَ۪شِدَّة بِ۪حِبال وَ۪رُفِعَت فَ۪إِنَّها تُقِلّ اَل۪حَمل</s> |
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1100 <s id="A18-3|07|03">وَ۪قَد يَنبَغي اَن يُصَيَّر في أَطراف هٰذِهِ اَل۪قَوائِم عَوارِض يُجمَع بَعضُها إِلى بَعض خارِج اَل۪حَجَر في أَطرافِها لِكَي لا تَكون إِذا تُعَلَّق اَل۪حَجَر عَلَيها فَ۪قِلَّة فَ۪يَقَع اَل۪حَجَر لَكِنَ تَكون هٰذِهِ اَل۪عارِضَة تُشَدّ بَعضُها إِلى بَعض وَ۪تَكون اَل۪حِبال مَشدودَة عَلَيها خارِجَة مِنها إِلى اَل۪بِكَر فَ۪إِذا مِدَّت رُفِعَت اَل۪حَجَر</s> |
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1101 </p> |
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1102 <p n="8"> |
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1103 <s id="A18-3|08|00"></s> |
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1104 <s id="A18-3|08|01">وَ۪قَد نَستَعمِل في هٰذا عَمَلاً آخَر أَسهَل مِن ذٰلِكَ وَ۪أَكثَر وَثاقَة مِنهُ </s> |
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1105 <s id="A18-3|08|02">فَ۪ل۪تَكُن قاعِدَة اَل۪حَجَر اَلَّتي عَلَيها ٓآبٓغٓد وَ۪ل۪نَحفِر فيها حَفراً شَبيهاً بِ۪اَل۪مُتَوازي اَل۪أَضلاع وَ۪هُوَ ٓeٓزٓهٓت وَ۪ل۪يَكُن مُعتَدِل اَل۪عَمق </s> |
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1106 <s id="A18-3|08|03">وَ۪ل۪يَكُن حَفرُهُ مُوَرَّب اَل۪جَوانِب أَعني اَن يَكون لَهُ في أَسفَلِهِ مِن اَل۪جانِبَين غَور مُقتَدِر </s> |
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1107 <s id="A18-3|08|04">وَ۪يَكون عَلى ذٰلِكَ اَل۪غَور صُلباً لِ۪يَجُرّ اَل۪حَجَر اَلَّذي عَلَيهِ </s> |
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1108 <s id="A18-3|08|05">وَ۪نَستَعمِل وَتَدَين مِن حَديد تَكون أَطرافُهُما مُعَوَّجَة كَ۪هَيئَة حَرف غَمّا </s> |
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1109 <s id="A18-3|08|06">وَ۪ل۪يَكُن في أَعلاها حَلَق أَو ثُقَب ثُمَّ نُرَكِّب كُلّ واحِد مِنهُما في جانِب مِن اَل۪حَفر وَ۪نُدخِل اَل۪مُعَوَّج مِنهُ في اَل۪حَفر اَل۪مُوَرَّب وَ۪نَعمَل أَيضاً وَتَداً آخَر <pb n="217"></pb> ثالِثاً حَديداً نُرَكِّبُهُ بَينَ هٰذَين اَل۪وَتَدَين لِ۪يَمنَع هٰذَين اَل۪وَتَدَين مِن اَن يَضطَرِبا </s> |
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1110 <s id="A18-3|08|07">وَ۪ل۪يَكُن اَل۪وَتَد اَل۪ثالِث أَيضاً مَثقوباً في أَعلاهِ ثُقباً مُوازِياً لِ۪ثُقبَي اَل۪وَتَدَين اَل۪آخَرَين </s> |
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1111 <s id="A18-3|08|08">وَ۪نُرَكِّب في اَل۪ثَلاث اَل۪ثُقَب مِحوَراً يَكون أَحَد طَرَفَيهِ غَليظاً </s> |
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1112 <s id="A18-3|08|09">فَ۪تَكون اَل۪ثَلاثَة اَل۪أَوتاد قَد مَلَأَت حَفر ٓeٓزٓهٓت وَ۪يَكون اَل۪مُعَوَّج مِن <pb n="219"></pb> اَل۪وَتَدَين قَد دَخَلَ في اَل۪حَفر اَلَّذي عَن جَنبَتَي سَطح اَل۪حَفر وَ۪يَكون اَل۪وَتَد اَل۪ثالِث قَد مَلَأَ ما بَينَ اَل۪وَتَدَين فَ۪صارَت اَل۪ثَلاثَة اَل۪أَوتاد كَ۪هَيئَة جِسم واحِد </s> |
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1113 <s id="A18-3|08|10">ثُمَّ يُشَدّ عَلى ذٰلِكَ اَل۪مِحوَر اَل۪نافِذ في اَل۪ثَلاثَة اَل۪أَوتاد قُلوس تَكون فيها بِكَر </s> |
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1114 <s id="A18-3|08|11">وَ۪تَكون في أَعلا اَل۪آلَة اَلَّتي بِها نَرفَع اَل۪ثِقل بِكَر اُخَر مُحاذِيَ لِ۪اَلَّتي في اَل۪حَجَر فَ۪تُنفَذ اَل۪قُلوس فيها وَ۪تُجبَذ فَ۪إِنَّ اَل۪حَجَر يَرتَفِع لِ۪أَنَّ اَل۪وَتَد اَل۪أَوسَط لا يَدَع اَل۪وَتَدَين أَلَّذَين أَطرافُهُما اَل۪مُعَوَّجَة في داخِل اَل۪حَجَر تُوَكَّد </s> |
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1115 <s id="A18-3|08|12">ثُمَّ يُرفَع إِلى اَن يُحاذي اَل۪مَوضِع اَلَّذي نُريد اَن يُرَكَّب فيهِ فَ۪يُجلَس عَلى ذٰلِكَ اَل۪مَوضِع </s> |
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1116 <s id="A18-3|08|13">فَ۪إِذا جَلَسَ اَل۪حَجَر في مَوضِعِهِ أُخرِجَ اَل۪مِحوَر وَ۪قُلِعَ اَل۪وَتَد اَل۪أَوسَط وَ۪أُخرِجَ كُلّ واحِد مِن اَل۪وَتَدَين اَل۪مُعَوَّجَة اَل۪أَطراف ثُمَّ نُرَكِّب حَجَراً آخَر وَ۪نَعمَل بِهِ اَل۪عَمَل اَل۪أَوَّل</s> |
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1117 <s id="A18-3|08|14">وَ۪قَد يَنبَغي اَن نَتَوَقّا في هٰذا اَل۪عَمَل إِستِعمال ما صُلب مِن اَل۪حَديد لِ۪أَة۪لا يَنقَصِف وَ۪نَتَوَقّا أَيضاً اَل۪لين مِنهُ لِ۪أَة۪لا يَتَعَوَّج وَ۪يَنقَلِب لِ۪ثِقل اَل۪حَجَر بَل نَستَعمِل مِنهُ ما كانَ مُتَوَسِّطاً لَيسَ شَديد اَل۪صَلابَة وَ۪لا شَديد اَل۪لين </s> |
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1118 <s id="A18-3|08|15">وَ۪يَنبَغي أَيضاً اَن يَتَوَقّا عَطَف شَيء مِن اَل۪حَديد وَ۪تَثَنّيهِ أَو شَقّ يَنالُهُ في صَنعَتِهِ فَ۪إِنَّ اَل۪خَطاء فيهِ يَعظُم جِدّاً لَيسَ لِ۪وُقوع اَل۪حَجَر فَقَط لَكِنَ لِ۪أَنَّهُ يَنال اَل۪صُنّاع أَيضاً إِذا وَقَعَ</s> |
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1119 </p> |
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1120 <p n="9"> |
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1121 <s id="A18-3|09|00"></s> |
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1122 <s id="A18-3|09|01">أَمّا اَل۪أَنواع اَلَّتي نَرفَع بِها أَو نُعلي اَل۪شَيء اَل۪ثَقيل فَ۪إِنَّها هٰذِهِ اَلَّتي ذَكَرنا </s> |
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1123 <s id="A18-3|09|02">وَ۪قَد يَنبَغي اَن نَحتال في <pb n="221"></pb> اَل۪مَكان وَ۪اَل۪زَمان وَ۪ما يُحتاج إِلَيهِ مِن غَير هٰذا أَيضاً وَ۪نُبَيِّن كَيفَ يَنبَغي اَن نَستَعمِل في كُلّ واحِد مِن هٰذِهِ </s> |
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1124 <s id="A18-3|09|03">فَ۪قَد إِستَعمَلَ قَوم في إِحدار اَل۪حِجارَة اَل۪كِبار مِن رُؤُس اَل۪جِبال اَل۪شاهِقَة حيلَة لِ۪أَة۪لا يَكون اَل۪إِنصِباب يَتَحَدَّر اَل۪حَجَر لِ۪حَيدَت نَفسِهِ فَ۪يَقَع عَلى اَل۪دَوابّ اَلَّتي تَجُرُّهُ وَ۪اَل۪عَجَل فَ۪يَتلَفُها </s> |
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1125 <s id="A18-3|09|04">فَ۪إِستَعمَلوا طَريقَين في اَل۪جَبَل في اَل۪مَوضِع اَلَّذي أَرادوا اَن يُحدِروا اَل۪حَجَر فيهِ مِن أَعلاهِ إِلى أَسفَلِهِ وَ۪سَهَّلوها بِ۪غايَة ما يُمكِنُهُم وَ۪إِتَّخَذوا عَجَلَتَين ذات أَربَع فِلَك وَ۪صَيَّروا إِخداهُما في أَعلا اَل۪طَريق اَلَّذي أَرادوا إِحدار اَل۪حَجَر فيها وَ۪اَل۪أُخرا في أَسفَل اَل۪طَريق اَل۪آخَر </s> |
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1126 <s id="A18-3|09|05">ثُمَّ شَدّوا عَلى رُكن ثابِت بَينَ اَل۪طَريقَين بِكَراً وَ۪أَجازوا مِن اَل۪عَجَلَة اَلَّتي تَجُرّ اَل۪حَجَر إِلى اَل۪بِكَر حِبالاً وَ۪أَنفَذوها إِلى اَل۪عَجَلَة اَل۪أُخرا اَلَّتي أَسفَل </s> |
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1127 <s id="A18-3|09|06">وَ۪صَيَّروا عَلى تِلكَ اَل۪عَجَلَة اَلَّتي أَسفَل حِجارَة صِغاراً مِمّا وَقَعَ لَهُم مِن نِجارَت اَل۪حَجَر اَل۪أَعظَم حَتّى ثَقَّلوها ثِقلاً ما أَقَلّ مِن اَل۪حَجَر اَلَّذي أَرادوا إِحدارَهُ </s> |
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1128 <s id="A18-3|09|07">ثُمَّ شَدّوا إِلى تِلكَ اَل۪عَجَلَة دَوابّ تَجُرُّها مُصعِداً فَ۪كانَ بِ۪صُعود تِلكَ اَل۪عَجَلَة قَليلاً قَليلاً يَنحَدِر اَل۪حَجَر اَل۪أَعزَم إِلى أَسفَل إِنحِداراً سَهلاً قَليلاً قَليلاً أَيضاً </s> |
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1129 </p> |
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1130 <p n="10"> |
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1131 <s id="A18-3|10|00"></s> |
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1132 <s id="A18-3|10|01"><pb n="223"></pb> وَ۪قَد رامَ قَوم اَن يَرفَعوا بِ۪هٰذا اَل۪عَمَل أَيضاً أَساطين عِظاماً فَ۪يُجلِسوها عَلى قَواعِدِها في اَل۪مَوضِع اَلَّذي يُريدون </s> |
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1133 <s id="A18-3|10|02">وَ۪بِ۪هٰذِهِ اَل۪حيلَة رَبَطوا في رَأس اَل۪أُسطُوانَة اَلَّتي أَرادوا رَفعَها حِبالاً وَ۪أَجَرّوها إِلى بِكَر مَشدودَة في بُرج ثابِت وَ۪أَنفَذوها حَتّى خَرَجَت إِلى اَل۪جِهَة اَل۪أُخرا عَن اَل۪بِكَر </s> |
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1134 <s id="A18-3|10|03">ثُمَّ شَدّوا في أَطرافِها اَلَّتي أُنفِذَت في اَل۪بِكَر أَوعِيَة تَحتَمِل اَن توضَع فيها اَل۪حِجارَة وَ۪أَشياء ثَقيلَة أَعني كَ۪اَل۪صَناديق أَو غَير ذٰلِكَ مِمّا يُشبِهُهُ </s> |
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1135 <s id="A18-3|10|04">ثُمَّ صَيَّروا في تِلكَ اَل۪أَوعِيَة حِجارَة مُقتَدِرَة وَ۪أَثقالاً حَتّى تُوازٍ ثِقل اَل۪عَمود وَ۪تَقوى عَلَيهِ فَ۪إِنَّها عِندَ ذٰلِكَ تَرفَعُهُ فَ۪يَقوم قائِماً عَلى قاعِدَتِهِ </s> |
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1136 <s id="A18-3|10|05">وَ۪قَد يَنبَغي اَن يُشَدّ أَسفَل اَل۪أُسطُوانَة إِلى قاعِدَتِها لِ۪أَة۪لا يَخرُج عَنها إِذا رُفِعَت أَو يَزول عَنها أَو يُلَفّ عَلى قاعِدَة اَل۪أُسطُوانَة قُلوس تُصير لَها مِثلَ اَل۪إِكليل لِ۪يَكون إِذا رُفِعَت اَل۪أُسطُوانَة ثَبَتَ أَسفَلُها في تِلكَ اَل۪قُلوس اَلَّتي قَد أُديرَت عَلَيها</s> |
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1137 </p> |
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1138 <p n="11"> |
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1139 <s id="A18-3|11|00"></s> |
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1140 <s id="A18-3|11|01">وَ۪قَد رامَ قَوم اَن يَجُرّوا أَحمالاً عِظاماً في اَل۪بَحر بِ۪هٰذِهِ اَل۪حيلَة </s> |
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1141 <s id="A18-3|11|02">فَ۪إِنَّهُم عَمَلوا طَوفاً مِن خَشَب مُرَبَّعاً يُشَدّ بَعضُهُ إِلى بَعض بِ۪مَسامير وَ۪أَوتاد </s> |
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1142 <s id="A18-3|11|03">وَ۪صَيَّروا لَهُ حيطاناً وَثيقَة وَ۪أَلقوهُ في اَل۪ماء حَيثُ أَرادوا اَن يَحمِلوا اَل۪ثِقل </s> |
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1143 <s id="A18-3|11|04"><pb n="225"></pb> وَ۪صَيَّروا تَحت اَل۪طَوف تَلاليس مَملُوَّ رَملاً مَشدودَة اَل۪أَكفال فَ۪رَكَّبوا اَل۪طَوف عَلى اَل۪تَلاليس </s> |
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1144 <s id="A18-3|11|05">ثُمَّ أَخَذوا سَفينَتَين فَ۪شَدّوهُما بِ۪اَل۪قُلوس عَن جَنبَتَي اَل۪طَوف في حائِطَيهِ </s> |
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1145 <s id="A18-3|11|06">ثُمَّ صَيَّروا اَل۪حَمل عَلى اَل۪طَوف وَ۪حَلّوا اَل۪تَلاليس وَ۪سَيَّلوا اَل۪رَمل </s> |
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1146 <s id="A18-3|11|07">ثُمَّ سَيَّروا اَل۪سَفينَتَين في اَل۪بَحر فَ۪نَفَذَت تَحمِل اَل۪طَوف</s> |
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1147 </p> |
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1148 <p n="12"> |
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1149 <s id="A18-3|12|00"></s> |
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1150 <s id="A18-3|12|01">وَ۪قَوم إِحتالوا أَيضاً بِ۪اَن يُسَبِّحوا اَل۪حِجارَة اَل۪عِظام في اَل۪بَحر بِ۪هٰذِهِ اَل۪جِهَة </s> |
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1151 <s id="A18-3|12|02">وَ۪قَوم إِحتالوا في رَفع اَل۪حيطان اَلَّتي قَد مالَت في اَل۪زَلازِل بِ۪هٰذِهِ اَل۪جِهَة </s> |
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1152 <s id="A18-3|12|03">حَفَروا في اَل۪أَرض في اَل۪جِهَة اَلَّتي مالَ إِلَيها اَل۪حائِط حَفراً بِ۪طول اَل۪حائِط </s> |
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1153 <s id="A18-3|12|04">ثُمَّ وَضَعوا فيهِ خَشَباً مُرَبَّعاً بَعيداً عَن اَل۪حائِط بُعداً يَسيراً وَ۪أَقاموا خَشَباً آخَر قائِماً فيما بَينَ اَل۪حائِط وَ۪اَل۪خَشَب اَل۪مُرَبَّع اَلَّذي صَيَّروا في اَل۪حَفر </s> |
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1154 <s id="A18-3|12|05">ثُمَّ صَيَّروا في أَطراف اَل۪خَشَب اَل۪قائِم بِكَراً وَ۪أَجازوا عَلَيها اَل۪حِبال إِلى آلَة تُسَمّي مِلَفَّة </s> |
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1155 <s id="A18-3|12|06">ثُمَّ أَداروا تِلكَ اَل۪آلَة حَتّى إِنجَذَبَت اَل۪حِبال وَ۪جُذِبَت اَل۪خَشَبَة اَل۪مُعتَرَضَة </s> |
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1156 <s id="A18-3|12|07">وَ۪إِنجَذَبَ بِ۪إِنجِذابِها اَل۪خَشَب اَل۪قائِم فَ۪مَيَّلَ اَل۪حائِط حَتّى رَدَّهُ إِلى مَوضِعِهِ </s> |
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1157 <s id="A18-3|12|08">فَ۪لَمّا رَدَّهُ إِلى مَوضِعِهِ تَرَكوهُ مَشدوداً بِ۪ذٰلِكَ اَل۪خَشَب زَماناً لِ۪تَستَقِرّ <pb n="227"></pb> اَل۪حِجارَة بَعضُها عَلى بَعض </s> |
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1158 <s id="A18-3|12|09">ثُمَّ حَلّوا اَل۪خَشَب فَ۪يَثبُت اَل۪حائِط عَلى حالَتِهِ اَل۪مُستَوِيَة</s> |
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1159 </p> |
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1160 <p n="13"> |
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1161 <s id="A18-3|13|00"></s> |
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1162 <s id="A18-3|13|01">أَمّا ما يُحتاج إِلَيهِ في حَرَكَة اَل۪أَثقال وَ۪ما يَنفَع في ذٰلِكَ فَ۪قَد أَثبَتنا بَيانَهُ بِ۪ما فيهِ كِفايَة </s> |
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1163 <s id="A18-3|13|02">وَ۪اَل۪آن آلات اَل۪فِلاحَة أَعني اَلَّتي تُعصَر بِها اَل۪أَنبِذَة وَ۪اَل۪أَدهان لَيسَ بِ۪بَعيدَة عَمّا ذَكَرنا مِن إِستِعمال اَل۪أَمخال فَ۪إِنَّهُ قَد يَجِب <pb n="229"></pb> اَن نُبَيِّن ذٰلِكَ وَ۪نَشرَح مِنهُ قَدر يَكتَفي بِ۪مَعرِفَتِهِ</s> |
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1164 <s id="A18-3|13|03">فَ۪أَمّا اَل۪خَشَبَة اَلَّتي تُسَمّي جَبَلاً اَلَّذي يُسَمّيهِ قَوم آخَرون عِصاراً فَ۪لَيسَ شَيئاً آخَر غَير مُخل ما وَ۪حَجَرُهُ اَلَّذي تَحتَ اَل۪مُخل </s> |
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1165 <s id="A18-3|13|04">وَ۪هُوَ حائِط اَل۪مِعصَرَة اَلَّذي طَرَف اَل۪خَشَبَة فيهِ </s> |
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1166 <s id="A18-3|13|05">وَ۪اَل۪ثِقل هُوَ اَل۪حَبل اَل۪مَلفوف عَلى اَل۪عِنَب اَل۪مُرَضَّض وَ۪اَل۪قُوَّة اَل۪مُحَرِّكَة هِيَ اَل۪حَجَر اَل۪مُعَلَّق في طَرَف اَل۪خَشَبَة اَلَّذي يُسَمّي لِثُس </s> |
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1167 <s id="A18-3|13|06">وَ۪قَد يَعرِض في اَل۪خَشَب اَل۪عِظام اَن يَكون ثِقل اَل۪حَجَر عَظيماً أَيضاً لِ۪يَقوا عَلى اَل۪عَصر </s> |
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1168 <s id="A18-3|13|07">أَمّا اَل۪خَشَبَة اَل۪عَظيمَة فَ۪إِنَّهُ قَد يَكون طولُها خَمسَة وَ۪عِشرين ذِراعاً وَ۪اَل۪حَجَر اَل۪مُعَلَّق عَلَيهِ اَلَّذي يُسَمّي لِثُس يَكون ثِقلُهُ عِشرين قِنطاراً</s> |
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1169 </p> |
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1170 <p n="14"> |
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1171 <s id="A18-3|14|00"></s> |
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1172 <s id="A18-3|14|01">فَ۪نُريد اَن نَحتال في تَعليق اَل۪حَجَر </s> |
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1173 <s id="A18-3|14|02">فَ۪نَستَعمِل هٰذا اَل۪عَمَل نَتَّخِذ آلَة كَثيرَة اَل۪رَفع وَ۪نَشُدّ عَلى طَرَف اَل۪جَبَل بَكرَة وَ۪عَلى اَل۪حَجرَة بَكرَة أُخرا </s> |
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1174 <s id="A18-3|14|03">وَ۪نَشُدّ عَلى اَل۪حَجَر فَوقَ اَل۪بَكرَة خَشَبَة مُعتَرَضَة نُعَلِّقُها عَلى اَل۪خَشَبَة اَلَّتي تُسَمّي اَل۪جَبَل </s> |
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1175 <s id="A18-3|14|04">وَ۪ل۪نُخرِج ذٰلِكَ اَل۪حَبل إِلى مِحوَر عَلَيهِ فَلَكَة وَ۪نُدير اَل۪فَلكَة فَ۪يَلتِفّ اَل۪حَبل عَلى اَل۪مِحوَر وَ۪يَرتَفِع اَل۪حَجَر </s> |
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1176 </p> |
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1177 <p n="15"> |
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1178 <s id="A18-3|15|00"></s> |
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1179 <s id="A18-3|15|01">وَ۪قَد نَجِد حيلَة أُخرا نَحُطّ بِها اَل۪خَشَبَة اَلَّتي تُسَمّي ورُس وَ۪نَرفَع بِها اَل۪حَجَر اَلَّذي يُسَمّي لِثُس </s> |
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1180 <s id="A18-3|15|02"><pb n="231"></pb> فَ۪إِنَّ صَلابَة اَل۪حَبل تَفعَل إِمتِناعاً ما مِن إِنحِطاط اَل۪خَشَبَة وَ۪إِرتِفاع اَل۪حَجَر لِ۪أَنَّ اَل۪حَبل إِذا كانَ صُلباً فَ۪إِنَّهُ لا يَجري عَلى اَل۪بۦۦۦۦاي رَفع اَل۪حَجَر إِلى اَل۪جِهَة اَل۪عُليا وَ۪في إِنحِطاط اَل۪خَشَبَة إِلى أَسفَل </s> |
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1181 <s id="A18-3|15|03">وَ۪في رَفع اَل۪حَجَر يُحتاج اَن نَستَعمِل أَوتاداً طِوالاً نُدير اَل۪مِحوَر بِها </s> |
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1182 <s id="A18-3|15|04">وَ۪لا تَأَمَّنّا إِذا كانَ اَل۪عِنَب اَل۪مَرضوض اَلَّذي تَحتَ اَل۪خَشَبَة كَثيراً وَ۪كانَ أَلَّذين يُديرون هٰذا اَل۪مِحوَر اَلَّذي اَل۪حَبل عَلَيهِ جَماعَة اَن يَنكَسِر بَعض اَل۪أَوتاد فَ۪يَقَع فَ۪يَنالُهُم ضَرَر أَو يَنقَلِب مِن اَل۪ثُقب فَ۪يَقَع أَيضاً فَ۪يَنالُهُم مِثلَ ذٰلِكَ </s> |
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1183 <s id="A18-3|15|05">فَ۪إِستَخرَجوا حيلَة أُخرا لا يُحتاج فيها إِلى حَبل أَسهَل مِن هٰذِهِ وَ۪أَوثَق مِنها </s> |
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1184 <s id="A18-3|15|06">وَ۪هٰذِهِ صِفَتُها</s> |
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1185 <s id="A18-3|15|07">نَستَعمِل جِسماً مِن خَشَب مُرَبَّع كَ۪هَيئَة اَل۪لَبِنَة فَ۪نُرَكِّبُها تَحتَ اَل۪خَشَبَة اَلَّتي تُدعي اَل۪جَبَل في اَل۪مَوضِع اَلَّذي كانَ يُصَيَّر فيهِ اَل۪حَبل </s> |
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1186 <s id="A18-3|15|08">وَ۪ل۪يَصير أَحَد أَجزائِهِ اَلَّتي تَلي ما فَوقَ مُستَديرَة وَ۪نُصَيِّر مِن كُلّ جِهَة مِن ناحِيَتَي اَل۪رُكن اَل۪ثابِت لَجآت ثابِتَة عَلى اَل۪خَشَبَة اَلَّتي يُقال لَها اَل۪جَبَل لِ۪أَة۪لا تَجري هٰذِهِ اَل۪لَبِنَة أَكثَر مِمّا يُحتاج إِلَيهِ وَ۪يُمكِنُها اَن تَميل إِلى اَل۪جِهَتَين جَميعاً </s> |
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1187 <s id="A18-3|15|09">ثُمَّ نَرفَع اَل۪خَشَبَة أَعظَم رَفعِها اَلَّذي نَرفَعُهُ لِ۪وَضع اَل۪عِنَب تَحتَها وَ۪نُقَدِّر اَل۪بُعد اَلَّذي بَينَ اَل۪لَبِنَة <pb n="233"></pb> وَ۪بَينَ اَل۪حَجَر وَ۪نَأخُذ نِصفَهُ أَو أَكثَر مِن ذٰلِكَ قَليلاً وَ۪نَعمَل بِ۪هٰذا اَل۪طول لَولَباً عَدَسِيّاً مُعتَدِل اَل۪ثُخن</s> |
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1188 <s id="A18-3|15|10">وَ۪ل۪يَكُن اَل۪حَفر اَل۪لَولَبي لا يُخرَج إِلى نِهايَة خَشَبَة اَل۪لَولَب مِن اَل۪جِهَة اَل۪واحِدَة فَ۪أَمّا مِن اَل۪جِهَة اَل۪أُخرا فَ۪إِنَّهُ يَنبَغي اَن يَكون اَل۪حَفر اَل۪لَولَبي يَبلُغ نِهايَة اَل۪خَشَبَة اَل۪لَولَبِيَّة </s> |
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1189 <s id="A18-3|15|11">وَ۪نُصَيِّر اَل۪فاضِل مِن اَل۪خَشَبَة مُرَبَّعاً وَ۪نُفَرِّض في هٰذا اَل۪مُرَبَّع حَفراً يُسَمّي طُرمُس </s> |
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1190 <s id="A18-3|15|12">وَ۪هُوَ دائِرَة تُحفَر في طَرَف اَل۪عود حَتّى يَتَراكِب اَل۪عود بِ۪اَل۪خَشَبَة اَلَّتي يُحتاج اَن يوصَل بِها </s> |
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1191 <s id="A18-3|15|13">ثُمَّ نُرَكِّب هٰذا اَل۪طُرمُس في إِحدا جِهات اَل۪لَبِنَة اَلَّتي تَلي ما تَحتَ اَل۪خَشَبَة ثُمَّ نَستَعمِل مَسامير مِن حَديد مُعتَرَضَة فَ۪نُرَكِّب أَطرافَها في هٰذا اَل۪حَفر وَ۪نُسَمِّر باقيها عَلى اَل۪لَبِنَة </s> |
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1192 <s id="A18-3|15|14">وَ۪نَستَعمِل أَيضاً مِحوَر حَديد نُجيزُهُ في هٰذا اَل۪طُرمُس وَ۪نُخرِجُهُ إِلى اَل۪لَبِنَة فَ۪نَشُدُّهُ فيها لِ۪يَزيدَهُ وَثاقَة وَ۪إِتِّصالاً بِ۪اَل۪لَبِنَة </s> |
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1193 <s id="A18-3|15|15">ثُمَّ نَستَعمِل خَشَبَة أُخرا مُرَبَّعَة مِن عود صُلب قَوي يَكون طولُها مُساوِياً لِ۪طول اَل۪لَولَب وَ۪عَرضُها اَلَّذي يُحيط بِهِ ضِلع مِن أَضلاع مُرَبَّع قاعِدَتُها أَطوَل مِن قُطر اَل۪أُسطُوانَة اَل۪لَولَبِيَّة بِ۪اَل۪قَدر اَلَّذي يُمكِن بِهِ اَن تُرَكَّب تِلكَ اَل۪أُسطُوانَة في داخِل هٰذِهِ اَل۪خَشَبَة اَل۪مُرَبَّعَة</s> |
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1194 <s id="A18-3|15|16">ثُمَّ نَشُقُّها بِ۪نِصفَين طولاً وَ۪نَحفِر مِن كُلّ واحِد مِن جُزأَيها حَفراً ميزابِيّاً مُستَديراً نُصَيِّرُهُ أُنثا اَل۪لَولَب وَ۪نَحفِرُهُ حَفراً لَولَبِيّاً يُمكِن اَن يَتَراكِب فيهِ اَل۪لَولَب اَل۪ذَكَر </s> |
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1195 <s id="A18-3|15|17">ثُمَّ نَلصَق <pb n="235"></pb> اَل۪جُزأَين حَتّى تَصيرا شَيئاً واحِداً</s> |
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1196 <s id="A18-3|15|18">يَنبَغي اَن يَكون اَل۪حَفر اَل۪لَولَبي أَيضاً في اَل۪خَشَبَة اَل۪أُنثا نافِذاً في اَل۪جِهَة اَل۪واحِدَة إِلى غايَة اَل۪خَشَبَة فَ۪أَمّا في اَل۪جِهَة اَل۪أُخرا فَ۪إِنَّهُ يَدَع غَير مَحفور صُلباً</s> |
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1197 <s id="A18-3|15|19">فَ۪إِذا رَكَّبنا طَرَف اَل۪لَولَب في طَرَف اَل۪خَشَبَة اَل۪مُجَوَّفَة اَلَّتي قَد بَلَغَ حَفرُها اَل۪لَولَبي إِلى أَقصاها وَ۪دُوِّرَ ذٰلِكَ يَنفُذ اَل۪لَولَب كُلُّهُ في اَل۪خَشَبَة اَل۪مَحفورَة حَتّى يَستَتِر كُلُّهُ </s> |
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1198 <s id="A18-3|15|20">فَ۪إِذا فَعَلنا ذٰلِكَ حَفَرنا في طَرَف هٰذِهِ اَل۪خَشَبَة اَل۪مَحفورَة اَل۪داخِل دائِرَة في عُنقِها دونَ طَرَفِها بِ۪بُعد يَسير وَ۪رَكَّبنا عَلَيهِ خَواتيم حَديد كَما نَفعَل في مَحاوِر اَل۪عَجَل </s> |
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1199 <s id="A18-3|15|21">ثُمَّ نَحفِر في اَل۪حَجَر حَفراً يَسَع طَرَف هٰذِهِ اَل۪خَشَبَة اَن تَتَراكِب فيهِ وَ۪ل۪يَكُن يُمكِن فيهِ اَن تُدَوَّر اَل۪خَشَبَة تَدويراً سَهلاً </s> |
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1200 <s id="A18-3|15|22">ثُمَّ نُرَكِّب طَرَف اَل۪خَشَبَة في ذٰلِكَ اَل۪حَفر وَ۪نُصَيِّر لَهُ ضِباباً حَديداً تَمنَع اَل۪خَشَبَة مِن اَن تَخرُج مِن اَل۪حَفر اَلَّذي في اَل۪حَجَر </s> |
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1201 <s id="A18-3|15|23">وَ۪نُصَيِّر عَلى اَل۪دائِرَة اَل۪مَفروضَة في طَرَف اَل۪خَشَبَة أَيضاً خاتِماً حَديداً لِ۪يَكون تَدويرُها سَهلاً</s> |
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1202 <s id="A18-3|15|24">وَ۪نُصَيِّر فَوقَ هٰذا اَل۪طَرَف اَل۪مُرَكَّب في اَل۪حَجَر ثُقَباً مُتَخالِفَة تَخرُج مِنها أَربَعَة أَطراف وَتَدَين </s> |
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1203 <s id="A18-3|15|25">فَ۪إِذا فَعَلنا ذٰلِكَ وَ۪أَرَدنا إِستِعمال اَل۪خَشَبَة اَلَّتي تُسَمّي اَل۪جَبَل أَوصَلنا طَرَفَي اَل۪لَولَب وَ۪اَل۪خَشَبَة اَل۪مَحفورَة اَل۪داخِل </s> |
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1204 <s id="A18-3|15|26">ثُمَّ تُدار اَل۪أَربَعَة اَل۪أَوتاد <pb n="237"></pb> فَ۪تَنكَبِس اَل۪خَشَبَة وَ۪يَرتَفِع اَل۪حَجَر فَ۪يَنعَصِر كُلّ شَيء تَحتَ اَل۪خَشَبَة</s> |
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1205 <s id="A18-3|15|27">فَ۪إِذا إِنحَطَّ اَل۪حَجَر إِلى اَن يَقعُد عَلى اَل۪أَرض أَدَرنا تَدويراً ضِدّ ذٰلِكَ حَتّى تَرتَفِع اَل۪خَشَبَة وَ۪يَثبُت اَل۪حَجَر </s> |
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1206 <s id="A18-3|15|28">وَ۪هٰذا اَل۪عَمَل قَوي وَثيق مَأمون اَل۪عاقِبَة لَيسَ فيهِ كَثير تَعب</s> |
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1207 </p> |
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1208 <p n="16"> |
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1209 <s id="A18-3|16|00"></s> |
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1210 <s id="A18-3|16|01">وَ۪قَد إِحتالَ قَوم في إِستِخراج أَجناس اُخَر مِن آلات اَل۪عَصر فَ۪عَمَلوا مَكان اَل۪حَبل اَلَّذي يُلَفّ عَلى اَل۪عِنَب اَل۪مَرضوض وَ۪مَكان اَل۪قُفاف اَلَّتي تُصَيَّر فيها اَل۪زَيتون بَعدَ اَن فُرِضَ وَ۪تُدخَل تَحت اَل۪جَبَل آلَة مِن خَشَب سَمّوها غَلا أَغرا </s> |
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1211 <s id="A18-3|16|02">يَملُؤونَها ما أَرادوا وَ۪يَضَعونَها تَحتَ اَل۪خَشَبَة اَلَّتي تُسَمّي اَل۪جَبَل وَ۪يَحُطّون اَل۪خَشَبَة عَلَيها </s> |
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1212 <s id="A18-3|16|03">فَ۪إِنَّهُ يَجتَمِع لَهُم بِ۪ذٰلِكَ وَسع لِ۪ما يُريدون اَن يَعصِرونَهُ وَ۪سُهولَة اَل۪عَمَل </s> |
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1213 <s id="A18-3|16|04">وَ۪هٰذِهِ اَل۪غَلا أَغرا صَنعَتُها عَلى ضَربَتَين </s> |
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1214 <s id="A18-3|16|05">إِحداهُما تَكون مُرَكَّبَة وَ۪هِيَ عَلى هٰذا اَل۪عَمَل </s> |
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1215 <s id="A18-3|16|06">تُؤخَذ خَشَبَة صُلبَة في طَبيعَتِها مُكتَنِزَ فَ۪نَعمَل مِنها مَساطِر يَكون طولُها بِ۪قَدر اَل۪آلَة اَلَّتي نُريد اَن نَعمَلَها </s> |
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1216 <s id="A18-3|16|07">وَ۪يَكون عَرضُها قَدر شِبرَين وَ۪ثُخنُها قَدر سِتَّة أَصابِع </s> |
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1217 <s id="A18-3|16|08">ثُمَّ نَفرِض في طَرَفَي كُلّ مِسطَرَة مِن اَل۪جِهَتَين جَميعاً بَعدَ اَن نَدَع مِنها سِتَّة أَصابِع فَرضاً في أَعلاها وَ۪نُنفِذ في عَمق اَل۪مَساطِر قَدر رُبع ثُخنِها </s> |
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1218 <s id="A18-3|16|09">وَ۪كَ۪ذٰلِكَ أَيضاً نَفعَل في <pb n="239"></pb> أَسافِلِها حَتّى يَكون اَلَّذي يَبقى مِن ثُخن اَل۪خَشَب قَدر نِصفِهِ </s> |
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1219 <s id="A18-3|16|10">وَ۪قَد يَنبَغي اَن يَكون اَل۪فَرض اَلَّذي في اَل۪مَساطِر مُتَساوِياً لِ۪يَتَراكِب بَعضُها عَلى بَعض </s> |
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1220 <s id="A18-3|16|11">ثُمَّ نُرَكِّب اَل۪مَساطِر حَتّى يَكون بِ۪تَركيب جَميعِها شَكل مُرَبَّع مُتَساوي اَل۪أَضلاع شَبيه بِ۪اَل۪تابوت </s> |
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1221 <s id="A18-3|16|12">وَ۪قَد يَنبَغي اَن تَكون فُرَج اَل۪مَساطِر اَل۪داخِلَة واسِعَ لِ۪تَسيل اَل۪رُطوبات مِنها سَريعاً </s> |
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1222 <s id="A18-3|16|13">أَمّا في هٰذِهِ اَل۪آلَة فَ۪لَيسَ يُحتاج اَن يَكون اَل۪خَشَب عَلى اَل۪عِنَب وَ۪اَل۪أَلواح اَل۪مُرَكَّبَة فَوقَهُ ثَخينَ جِدّاً لِ۪أَنَّهُ إِذا إِنعَصَرَ اَل۪عِنَب فَ۪بِ۪قَدر ما إِنعَصَرَ مِنهُ يَرتَفِع مِن اَل۪مَساطِر لِ۪أَة۪لا يَعرِض مِنها إِمتِناع </s> |
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1223 </p> |
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1224 <p n="17"> |
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1225 <s id="A18-3|17|00"></s> |
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1226 <s id="A18-3|17|01">فَ۪أَمّا اَل۪غَلا أَغرا اَل۪أُخرا فَ۪إِنَّ أَربَعَة حيطانِها تُعمَل مُتَّصِلَة بَأضُها بِ۪بَعض بِ۪ثَلاث عَوارِض في كُلّ واحِد مِنها </s> |
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1227 <s id="A18-3|17|02">وَ۪قَد يَنبَغي اَن يُصَيَّر في هٰذِهِ اَل۪ثَلاث اَل۪عَوارِض فَضل في جَوانِبِها مَفروض فَرضاً يَبلُغ إِلى نِصف ثُخنِها لِ۪اَن تَكون إِذا رُكِّبَ بَعضُها إِلى بَعض تَثبُت اَل۪أَربَعَة اَل۪حيطان مُهَندَمَة </s> |
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1228 <s id="A18-3|17|03">وَ۪قَد يَنبَغي في هٰذِهِ اَل۪آلَة أَيضاً اَن تَكون فُرَجُها واسِعَ وَ۪توضَع عَلى لَوحِها اَل۪أَعلا قَرَمِيَّة يَكون لَها إِرتِفاع عَلى ما ذَكَرنا أَوَّلاً لِ۪أَة۪لا تَنال اَل۪خَشَبَة بَعض اَل۪عِنَب وَ۪تَزول اَل۪قَرَمِيَّة إِلَ أَسفَل اَل۪غَلا أَغرا </s> |
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1229 </p> |
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1230 <p n="18"> |
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1231 <s id="A18-3|18|00"></s> |
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1232 <s id="A18-3|18|01"><pb n="241"></pb> وَ۪اَل۪آن نُخَبِّر بِ۪صَنعَة اَل۪مَعاصِر اَلَّتي تُعصَر بِها بِ۪شِدَّة وَ۪قُوَّة وَ۪نَذكُر اَل۪فَصل اَلَّذي بَينَ اَل۪آلات اَلَّتي تَقَدَّمَ ذِكرُها وَ۪بَينَ هٰذِهِ اَل۪آلات وَ۪هِيَ مِن أَقوا ما يَكون وَ۪أَتقَنُهُ </s> |
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1233 <s id="A18-3|18|02">وَ۪أَوَّلاً نُخَبِّر اَل۪فَصل اَلَّذي بَينَهُما ثُمَّ نَصِف صَنعَتَها </s> |
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1234 <s id="A18-3|18|03">فَ۪نَقول إِنَّ اَل۪خَشَبَة اَلَّتي تُسَمّي اَل۪جَبَل لَيسَ هِيَ إِلّا مُخل ما يُكَبِّسُهُ ثِقل </s> |
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1235 <s id="A18-3|18|04">وَ۪اَل۪ثِقل اَلَّذي يُكَبِّسُهُ هُوَ في طَرَفِهِ اَل۪مُتَعالي عَن اَل۪أَرض </s> |
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1236 <s id="A18-3|18|05">فَ۪إِذا كَبَّسَ لا تَزال اَل۪رُطوبات تَسيل إِلى اَن يَقعُد اَل۪ثِقل عَلى اَل۪أَرض </s> |
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1237 <s id="A18-3|18|06">فَ۪أَمّا هٰذِهِ اَل۪آلات اَلَّتي نُريد صِفَتَها فَ۪إِنَّها قَوِيَ جِدّاً وَ۪لَكِنَ كَبسُها لَيسَ بِ۪مُتَّصِل أَيضاً شَديد </s> |
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1238 <s id="A18-3|18|07">فَ۪ل۪ذٰلِكَ يَجِب اَن نَتَعاهِد وَقتاً بَعدَ وَقت بِ۪اَل۪تَدوير وَ۪اَل۪شَدّ </s> |
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1239 <s id="A18-3|18|08">فَ۪أَمّا في اَل۪خَشَبَة اَلَّتي تُسَمّيها جَبَلاً فَ۪إِنَّكَ إِذا عَلَّقتَ اَل۪حَجَر وَ۪تَرَكتَهُ كانَ هُوَ وَحدَهُ يُكَبِّس وَ۪لَم يَحتَج إِلى اَن تَتَعاهِد بِ۪اَل۪كَبس مَرَّة بَعدَ مَرَّة </s> |
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1240 <s id="A18-3|18|09">فَ۪هٰذا اَل۪إِختِلاف اَلَّذي يَعرِض بَينَ اَل۪آلات</s> |
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1241 </p> |
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1242 <p n="19"> |
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1243 <s id="A18-3|19|00"></s> |
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1244 <s id="A18-3|19|01">وَ۪قَد تَنفَع هٰذِهِ اَل۪آلات اَلَّتي نُخَبِّر اَل۪آن بِ۪صَنعَتِها في عَصر اَل۪زَيت </s> |
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1245 <s id="A18-3|19|02">وَ۪هِيَ سَهلَة اَل۪عَمَل يُمكِن اَن تُنقَل أَو تُصَيَّر في أَيّ اَل۪مَواضِع أَرَدنا </s> |
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1246 <s id="A18-3|19|03">وَ۪لَيسَ نَحتاج فيها إِلى <pb n="243"></pb> خَشَبَة طَويلَة مُستَوِيَة صُلبَة في طَبيعَتِها وَ۪لا إِلى حَجَر ثَقيل عَظيم وَ۪لا حِبال قَوِيَ وَ۪لا يَنالُنا فيها إِمتِناع لِ۪صَلابَة اَل۪حِبال وَ۪لَكِنَها سَليمَة مِن هٰذا كُلِّهِ تُكَبِّس كَبساً شَديداً وَ۪تُخرِج اَل۪رُطوبات بِ۪إِستِقصاء </s> |
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1247 <s id="A18-3|19|04">وَ۪صَنعَتُها هِيَ هٰذِهِ اَلَّتي نَحنُ ذاكِروها</s> |
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1248 <s id="A18-3|19|05">نَستَعمِل خَشَبَة مُرَبَّعَة يَكون طولُها سِتَّة أَشبار وَ۪عَرضُها لَيسَ بِ۪أَقَلّ مِن قَدَمَين وَ۪ثُخنُها لَيسَ بِ۪أَقَلّ مِن قَدَم واحِد </s> |
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1249 <s id="A18-3|19|06">وَ۪ل۪تَكُن هٰذِهِ اَل۪خَشَبَة صُلبَة في جِنسِها لا تَكون شَديدَة اَل۪لين وَ۪لا هَشيمَة لَكِنَها تَكون مُتَوَسِّطَة </s> |
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1250 <s id="A18-3|19|07">وَ۪ل۪نُسَمِّها مائِدَة </s> |
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1251 <s id="A18-3|19|08">فَ۪نَضَع اَل۪مائِدَة مُعتَرَضَة وَ۪نَحفِر في طَرَفَيها عَلى بُعد مُتَقارِب ثُقبَين عَميقَين في داخِلِها مُستَديرَين </s> |
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1252 <s id="A18-3|19|09">وَ۪نُصَيِّر لِ۪كُلّ ثُقب ضَبَّتَين مِن خَشَب نافِذَتَين في عَمق اَل۪مائِدَة </s> |
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1253 <s id="A18-3|19|10">وَ۪ل۪يَكُن طَرَفاهُما قِسيياً تَلتَقي فَ۪تَكون مِنهُما دائِرَة صَغيرَة أَصغَر مِن اَل۪دَوائِر اَل۪مَحفورَة </s> |
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1254 <s id="A18-3|19|11">وَ۪ل۪تَكُن هٰذِهِ اَل۪ضِباب مُوَرَّبَة اَل۪حَفر لِ۪تَكون إِذا رُكِّبَت ثَبَتَت فَ۪لا تَنقَطِع بَتَّة </s> |
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1255 <s id="A18-3|19|12">ثُمَّ نَأخُذ عودَين صُلبَين مُستَوِيَين مُرَبَّعَين عَلى مِسطَرَة يَكون ثُخنُهُما وَ۪عَرضُهُما مُتَساوِيَين وَ۪ل۪نَدَع مِن أَحَد رَأسَيهِما بُعداً مُقتَدِراً مُرَبَّعاً </s> |
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1256 <s id="A18-3|19|13">وَ۪نَأخُذ زَوايا باقي اَل۪عودَين وَ۪نُدَوِّرُها بِ۪اَل۪مِبرَد وَ۪نَرسُم عَلَيهِما لَولَباً مُتَساوي اَل۪ثُخن </s> |
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1257 <s id="A18-3|19|14">وَ۪نُصَيِّر في طَرَف خَشَب اَل۪لَولَب اَلَّذي تَرَكناهُ مُرَبَّعاً فَلكَة مَثقوبَة بِ۪أَربَع ثُقَب وَ۪نُصَيِّر <pb n="245"></pb> في هٰذِهِ اَل۪ثُقَب أَربَعَة أَوتاد </s> |
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1258 <s id="A18-3|19|15">وَ۪باقي اَل۪عودَين تُحيط بِهِ دائِرَة بِ۪فَرض غَليظ تَكون داخِلَة عَن طَرَفِهِما قَدر عَمق اَل۪حَفر اَل۪مُستَدير اَلَّذي حَفَرناهُ في اَل۪مائِدَة</s> |
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1259 <s id="A18-3|19|16">وَ۪ل۪يَكُن قُطر هٰذِهِ اَل۪دائِرَة نِصف قُطر دائِرَة قاعِدَة اَل۪لَولَب </s> |
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1260 <s id="A18-3|19|17">فَ۪إِذا فَعَلنا هٰذا رَكَّبنا طَرَف اَل۪لَولَب اَلَّذي فيهِ هٰذِهِ اَل۪دائِرَة اَل۪مَفروضَة في اَل۪حَفر اَل۪مُستَدير اَلَّذي في اَل۪مائِدَة </s> |
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1261 <s id="A18-3|19|18">ثُمَّ دَفَعنا اَل۪ضِباب اَلَّتي عَمَلناها حَتّى تُداخِل اَل۪دائِرَة اَل۪مَفروضَة فَ۪ثَبَتَت عَلَيها فَ۪لا تَدَع لِ۪ل۪لَولَب مَخرَج </s> |
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1262 <s id="A18-3|19|19">وَ۪كَ۪ذٰلِكَ أَيضاً نَفعَل بِ۪<pb n="l-"></pb>لَولَب اَلَّذي في اَل۪رَأس اَل۪آخَر مِن اَل۪مائِدَة </s> |
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1263 <s id="A18-3|19|20">ثُمَّ نَأخُذ خَشَبَة مُرَبَّعَة طَويلَة يَكون طولُها قَدر اَل۪خَشَبَة اَل۪سُفلانِيَّة اَلَّتي اَل۪لَولَب مُرَكَّب فيها </s> |
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1264 <s id="A18-3|19|21">وَ۪ل۪يَكُن في هٰذِهِ اَل۪خَشَبَة دائِرَتان نافِذَتان في عَمق اَل۪خَشَبَة تَخرُجان إِلى اَل۪جِهَة اَل۪أُخرا مُسامِتَتان لِ۪حَفرَي اَل۪دائِرَتَين أَلَّتَين طَرَفا اَل۪لَولَبَين فيهِما </s> |
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1265 <s id="A18-3|19|22">وَ۪ل۪يَكُن في هاتَين اَل۪دائِرَتَين حَفر لَولَبي في داخِلِهِما لِ۪تَكون اَل۪دائِرَتان أُنثَيَين لِ۪ل۪لَولَبَين حَتّى تَكون إِذا دُوِّرَ اَل۪لَولَبان تَنحِطّ اَل۪خَشَبَة وَ۪كَ۪ذٰلِكَ أَيضاً إِذا دُوِّرَ في اَل۪جِهَة اَل۪أُخرا تَرتَفِع اَل۪خَشَبَة </s> |
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1266 <s id="A18-3|19|23">فَ۪أَمّا كَيفَ نَعمَل حَفر اَل۪لَولَب اَل۪أُنثا فَ۪إِنّا سَنُخَبِّر بِهِ فيما بَعد </s> |
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1267 <s id="A18-3|19|24">وَ۪قَد يَنبَغي اَن يَكون طول هٰذِهِ اَل۪خَشَبَة وَ۪ثُخنُها كَما قُلنا عَلى قَدر طول اَل۪مائِدَة وَ۪ثُخنِها فَ۪أَمّا عَرضُها فَ۪يَنبَغي <pb n="247"></pb> اَن يَكون أَقَلّ مِن عَرض تِلكَ بِ۪رُبع عَرضِها</s> |
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1268 <s id="A18-3|19|25">ثُمَّ نُصَيِّر لِ۪هٰذِهِ اَل۪مائِدَة رِجلاً مُرَبَّعاً عَلى زَوايا قائِمَة يَكون أَسافِلُها كَ۪هَيئَة اَل۪دَرَج وَ۪يَكون طولُها أَكثَر مِن عَرض اَل۪مائِدَة بِ۪شَيء يَسير لِ۪يَقوم عَلَيها جَميع اَل۪آلَة قِياماً جَيِّداً </s> |
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1269 <s id="A18-3|19|26">وَ۪يَنبَغي اَن نَفرِض نِصف اَل۪قائِمَة فَرضاً مُقتَدِراً وَ۪نَفرِض نِصف اَل۪مائِدَة بِ۪قَدر ذٰلِكَ اَل۪فَرض اَلَّذي في اَل۪قائِمَة وَ۪نُرَكِّب أَحَد اَل۪فَرضَين عَلى اَل۪آخَر حَتّى يَثبُت عَلَيهِ ثَباتاً جَيِّداً </s> |
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1270 <s id="A18-3|19|27">ثُمَّ نُصَيِّر عَلى اَل۪مائِدَة بَينَ اَل۪لَولَبَين أَربَعَة حيطان مُتَّصِلَة مِن أَلواح رِقاق يَكون ثُخنُها أَقَلّ مِن إِصبَع وَ۪يَكون طول اَل۪مُرَبَّع وَ۪عَرضُها اَلَّتي تَكون بَينَ هٰذِهِ اَل۪أَلواح بِ۪اَل۪قَدر اَلَّذي إِذا صيرَت في وَسَطِها اَل۪غَلا أَغرا يَكون بَينَهُما وَسع يُحيط بِ۪اَل۪غَلا أَغرا تَسيل فيهِ اَل۪رُطوبات </s> |
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1271 <s id="A18-3|19|28">وَ۪يَنبَغي اَن نَحفِر في وَسَط هٰذِهِ اَل۪مائِدَة حَفراً يَسَع سَطح اَل۪غَلا أَغرا اَلَّذي يُماسّ اَل۪مائِدَة أَيّ تَدخُل فيهِ وَ۪نُرَكِّب اَل۪غَلا أَغرا في هٰذا اَل۪حَفر </s> |
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1272 <s id="A18-3|19|29">ثُمَّ نُصَيِّر في أَعلاها لَوحاً ثَخيناً يَملَؤُها وَ۪نُرَكِّب عَلَيهِ قَرَمِيَّة أَصغَر مِن اَل۪لَوح طولاً وَ۪عَرضاً يَكون ثُخنُها يَملَؤُ اَل۪غَلا أَغرا </s> |
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1273 <s id="A18-3|19|30">ثُمَّ نُدير اَل۪لَولَبَين بِ۪اَل۪أَوتاد اَلَّتي في اَل۪فِلَك حَتّى تَنحِطّ اَل۪خَشَبَة اَلَّتي فيها اَل۪حَفر اَل۪لَولَبي اَل۪أُنثا عَلى اَل۪قَرَمِيَّة </s> |
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1274 <s id="A18-3|19|31">فَ۪تَنكَبِس اَل۪قَرَمِيَّة وَ۪تُكَبِّس اَل۪قَرَمِيَّة اَل۪لَوح اَلَّذي في داخِل اَل۪غَلا أَغرا فَ۪يُعصَر اَل۪جِسم اَلَّذي في اَل۪غَلا أَغرا وَ۪تَسيل اَل۪رُطوبات </s> |
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1275 <s id="A18-3|19|32">ثُمَّ يُدار <pb n="249"></pb> اَل۪لَولَب أَيضاً في اَل۪جِهَة اَل۪أُخرا فَ۪تَرتَفِع اَل۪خَشَبَة وَ۪تُقلَع اَل۪قَرَمِيَّة وَ۪يُبدَل اَل۪جِسم اَل۪مَعصور حَتّى يَخرُج كُلّ شَيء فيهِ مِن اَل۪رُطوبات</s> |
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1276 </p> |
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1277 <p n="20"> |
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1278 <s id="A18-3|20|00"></s> |
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1279 <s id="A18-3|20|01">وَ۪قَد تَكون آلَة أُخرا بِ۪لَولَب واحِد </s> |
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1280 <s id="A18-3|20|02">وَ۪ذٰلِكَ بِ۪اَن نَعمَل عَلى اَل۪مائِدَة قائِمَتَين تَحمِل اَل۪خَشَبَة اَل۪مُعتَرَضَة اَلَّتي فيها اَل۪حَفر اَل۪لَولَبي اَل۪أُنثا </s> |
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1281 <s id="A18-3|20|03">وَ۪ل۪يَكُن اَل۪حَفر اَل۪لَولَبي في وَسَط هٰذِهِ اَل۪خَشَبَة </s> |
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1282 <s id="A18-3|20|04">ثُمَّ يَدخُل اَل۪لَولَب في هٰذا اَل۪حَفر وَ۪يُدَوَّر بِ۪اَل۪أَوتاد اَلَّتي في اَل۪فَلكَة حَتّى يَنحِطّ اَل۪لَولَب عَلى اَل۪لَوح اَل۪مُرَكَّب عَلى اَل۪غَلا أَغرا فَ۪يُكَبِّسُهُ فَ۪تَسيل اَل۪رُطوبات </s> |
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1283 <s id="A18-3|20|05">وَ۪قَد يَنبَغي اَن نَتَعاهِد بِ۪اَل۪شَدّ مَرَّة بَعدَ مَرَّة حَتّى لا يَبقى في اَل۪جِسم اَل۪مَعصور مِن اَل۪رُطوبات شَيء </s> |
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1284 <s id="A18-3|20|06">وَ۪قَد تَكون مِن اَل۪مَعاصِر أَجناس اُخَر غَير هٰذِهِ كَثيرَة لَم نَرَ اَن نَكتُبَها لِ۪أَنَّها قَد كَثُرَ إِستِعمالُها عِندَ اَل۪عامَّة وَ۪خَلُقَت عِندَهُم وَ۪هِيَ دونَ هٰذِهِ اَلَّتي ذَكَرناها في اَل۪فِعل</s> |
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1285 </p> |
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1286 <p n="21"> |
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1287 <s id="A18-3|21|00"></s> |
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1288 <s id="A18-3|21|01">فَ۪أَمّا اَل۪لَولَب اَل۪أُنثا فَ۪إِنَّهُ يُعمَل عَلى هٰذِهِ اَل۪جِهَة </s> |
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1289 <s id="A18-3|21|02">تُؤخَذ خَشَبَة صُلبَة يَكون طولُها أَكثَر مِن مِثلَي اَل۪لَولَب اَل۪أُنثا وَ۪ثُخنُها مُساوٍ لِ۪ل۪لَولَب اَل۪أُنثا </s> |
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1290 <s id="A18-3|21|03">وَ۪نَعمَل في اَل۪جِهَة اَل۪واحِدَة في نِصف طول اَل۪خَشَبَة لَولَباً عَلى ما قَدَّمنا صِفَتَهُ </s> |
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1291 <s id="A18-3|21|04">وَ۪ل۪يَكُن عَمق اَل۪دَوائِر اَل۪لَولَبِيَّة فيهِ كَ۪عَمق دَوائِر اَل۪لَولَب اَلَّذي نُريد اَن نُديرَهُ في هٰذا اَل۪لَولَب اَل۪أُنثا </s> |
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1292 <s id="A18-3|21|05">وَ۪نَخرِط مِن <pb n="251"></pb> اَل۪جِهَة اَل۪أُخرا قَدر ثُخن اَل۪دَوائِر اَل۪لَولَبِيَّة حَتّى تُصَيِّرَهُ كَ۪وَتَد مُتَساوي اَل۪ثُخن </s> |
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1293 <s id="A18-3|21|06">وَ۪نُخرِج قُطر قاعِدَة اَل۪خَشَبَة وَ۪نُقَسِّمُهُ بِ۪ثَلاثَة أَقسام مُتَساوِيَة </s> |
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1294 <s id="A18-3|21|07">وَ۪نُخرِج عَلى عَلامَة واحِدَة مِن عَلامَتَي اَل۪قِسمَة خَطّاً قائِماً عَلى اَل۪قُطر </s> |
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1295 <s id="A18-3|21|08">ثُمَّ نُخرِج مِن طَرَفَي اَل۪خَطّ اَل۪قائِم عَلى ذٰلِكَ اَل۪قُطر في طول اَل۪وَتَد كُلِّهِ خَطَّين قائِمَين </s> |
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1296 <s id="A18-3|21|09">وَ۪ذٰلِكَ يَتَهَيَّأ لَنا إِذا وَضَعنا هٰذا اَل۪وَتَد عَلى لَوح قائِم وَ۪خَطَّطناهُ بِ۪اَل۪كَلبَتَين إِلى اَن نَنال اَل۪حَفر اَل۪لَولَبي </s> |
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1297 <s id="A18-3|21|10">ثُمَّ نَتَلَطَّف بِ۪مِنشار دَقيق حَتّى نَنشُر ما يَلي اَل۪حَفر اَل۪لَولَبي </s> |
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1298 <s id="A18-3|21|11">ثُمَّ نَفصِل هٰذا اَل۪ثُلث اَل۪مَرسوم مِن اَل۪وَتَد وَ۪نَفرِض في اَل۪جُزأَين اَل۪باقِيَين في وَسَطِهِما حَفراً ميزابِيّاً في كُلّ اَل۪طول يَكون قَدر نِصف اَل۪ثُخن اَل۪باقي </s> |
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1299 <s id="A18-3|21|12">ثُمَّ نَأخُذ قَضيباً مِن حَديد فَ۪نُديرُهُ عَلى اَل۪دَوائِر اَل۪لَولَبِيَّة </s> |
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1300 <s id="A18-3|21|13">ثُمَّ نُرَكِّبُهُ عَلى اَل۪وَتَد اَلَّذي اَل۪حَفر فيهِ ثُمَّ نُصَيِّر طَرَفَهُ في اَل۪دَوائِر اَل۪لَولَبِيَّة بَعدَ اَن نَشُدّ اَل۪قِطعَتَين جَميعاً شَدّاً جَيِّداً حَتّى يَلتَئِم إِحداهُما إِلى اَل۪أُخرا وَ۪لا يَكون بَينَهُما حَلَل بَتَّة </s> |
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1301 <s id="A18-3|21|14">ثُمَّ نَتَّخِذ إِسفيناً صَغيراً فَ۪نُدخِلُهُ في اَل۪حَفر اَل۪ميزابي وَ۪نَضرِبُهُ إِلى اَن يَخرُج اَل۪قَضيب اَل۪حَديد فَ۪يَقَع بَينَ اَل۪قِطعَتَين </s> |
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1302 <s id="A18-3|21|15">فَ۪إِذَ فَعَلنا ذٰلِكَ رَكَّبنا اَل۪لَولَب في خَشَبَة مَحفورَة فيها ثُقب <pb n="253"></pb> مُستَقصي اَل۪إِستِواء بِ۪قَدر ثُخن اَل۪لَولَب </s> |
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1303 <s id="A18-3|21|16">ثُمَّ نَثقُب في جَوانِب هٰذا اَل۪حَفر اَل۪واسِع ثُقَباً صِغاراً مُتَوالِيَ وَ۪نُرَكِّب فيها أَوتاداً صِغاراً مائِلَة مُستَديرَة وَ۪نُنفِذُها إِلى اَن تَقَع في دَوائِر اَل۪لَولَب </s> |
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1304 <s id="A18-3|21|17">ثُمَّ نَأخُذ اَل۪خَشَبَة اَلَّتي نُريد اَن نَحفِر فيها اَل۪لَولَب اَل۪أُنثا فَ۪نَثقُب فيها ثُقباً بِ۪قَدر وَتَد اَل۪لَولَب وَ۪نَصِل بَينَ هٰذِهِ اَل۪خَشَبَة وَ۪اَل۪خَشَبَة اَلَّتي رَكَّبنا فيها اَل۪لَولَب بِ۪قائِمَتَين نَشُدُّهُما شَدّاً مُستَقصي </s> |
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1305 <s id="A18-3|21|18">ثُمَّ نُرَكِّب اَل۪وَتَد اَلَّذي فيهِ اَل۪إِسفين في اَل۪حَفر اَلَّذي في اَل۪خَشَبَة اَلَّتي نُريد اَن نَحفِر فيها اَل۪لَولَب اَل۪أُنثا وَ۪نَثقُب في طَرَف اَل۪لَولَب اَل۪أَعلا ثُقَباً نُصَيِّر فيها أَوتاداً فَ۪نُديرُها إِلى اَن تَنفُذ في اَل۪خَشَبَة</s> |
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1306 <s id="A18-3|21|19">فَ۪لا نَزال نُديرُها صاعِداً وَ۪نازِلاً وَ۪نَتَعاهِد هٰذا اَل۪إِسفين بِ۪اَل۪ضَرب مَرَّة بَعدَ مَرَّة حَتّى يُحفَر اَل۪لَولَب اَل۪أُنثا اَل۪حَفر اَلَّذي نُريد</s> |
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1307 <s id="A18-3|21|20">فَ۪نَكون قَد حَفَرنا اَل۪لَولَب اَل۪أُنثا</s> |
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1308 <s id="A18-3|21|21">وَ۪هٰذا اَل۪شَكل وَ۪بِ۪تَمامِهِ تَمَّ اَل۪كِتاب</s> |
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1309 </p></chap> |
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1310 </body> |
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1311 </text> |
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1312 </archimedes> |