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annotate texts/XML/echo/fr/Varignon_1687_TP04WPNS.xml @ 31:edf6e8fcf323 default tip
Removing DESpecs directory which deserted to git
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
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| date | Wed, 29 Nov 2017 16:55:37 +0100 |
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1 <?xml version="1.0" encoding="utf-8"?><echo xmlns="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:de="http://www.mpiwg-berlin.mpg.de/ns/de/1.0/" xmlns:dcterms="http://purl.org/dc/terms" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:echo="http://www.mpiwg-berlin.mpg.de/ns/echo/1.0/" xmlns:xhtml="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" version="1.0RC"> |
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2 <metadata> |
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3 <dcterms:identifier>ECHO:TP04WPNS.xml</dcterms:identifier> |
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4 <dcterms:creator identifier="GND:119062372">Varignon, Pierre</dcterms:creator> |
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5 <dcterms:title xml:lang="fr">Projet d' une nouvelle mechanique : avec un examen de l' opinion de M. Borelli sur les propriétez des poids suspendus par des cordes</dcterms:title> |
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6 <dcterms:alternative xml:lang="fr">Projet d' une nouvelle mechanique : avec un examen de l' opinion de M. Borelli sur les propriétés des poids suspendus par des cordes</dcterms:alternative> |
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7 <dcterms:date xsi:type="dcterms:W3CDTF">1687</dcterms:date> |
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8 <dcterms:language xsi:type="dcterms:ISO639-3">fra</dcterms:language> |
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9 <dcterms:rights>CC-BY-SA</dcterms:rights> |
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10 <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license> |
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11 <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder> |
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12 <log>escape sequence { not only in fractions but also for two-line text</log> |
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13 </metadata> |
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14 <text xml:lang="fr" type="free"> |
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15 <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="0001" n="1"/> |
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16 <pb file="0002" n="2"/> |
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17 <pb file="0003" n="3"/> |
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18 <pb file="0004" n="4"/> |
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19 <pb file="0005" n="5"/> |
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20 <pb file="0006" n="6"/> |
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21 <pb file="0007" n="7"/> |
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22 <pb file="0008" n="8"/> |
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23 <handwritten/> |
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24 <handwritten/> |
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25 <handwritten/> |
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26 <pb file="0009" n="9"/> |
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27 </div> |
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28 <div xml:id="echoid-div2" type="section" level="1" n="2"> |
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29 <head xml:id="echoid-head1" xml:space="preserve">PROJET <lb/>D’UNE NOUVELLE <lb/>MECHANIQUE</head> |
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30 <head xml:id="echoid-head2" style="it" xml:space="preserve">AVEC</head> |
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31 <p> |
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32 <s xml:id="echoid-s1" xml:space="preserve">Un Examen de l’opinion de M. </s> |
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33 <s xml:id="echoid-s2" xml:space="preserve">BORELLI, <lb/>ſur les propriétez des Poids ſuſpendus <lb/>par des Cordes.</s> |
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34 <s xml:id="echoid-s3" xml:space="preserve"/> |
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35 </p> |
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36 <figure> |
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37 <image file="0009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0009-01"/> |
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38 </figure> |
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39 </div> |
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40 <div xml:id="echoid-div3" type="section" level="1" n="3"> |
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41 <head xml:id="echoid-head3" xml:space="preserve">A PARIS,</head> |
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42 <p> |
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43 <s xml:id="echoid-s4" xml:space="preserve">Chez {la Vcuve d’<emph style="sc">Edme</emph> <emph style="sc">Martin</emph>, \\ <emph style="sc">Jean</emph> <emph style="sc">Boudot</emph>, \\ & </s> |
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44 <s xml:id="echoid-s5" xml:space="preserve"><emph style="sc">Estienne</emph> <emph style="sc">Martin</emph>,} ruë S. </s> |
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45 <s xml:id="echoid-s6" xml:space="preserve">Jaques, \\ au Soleil d’or.</s> |
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46 <s xml:id="echoid-s7" xml:space="preserve"/> |
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47 </p> |
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48 </div> |
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49 <div xml:id="echoid-div4" type="section" level="1" n="4"> |
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50 <head xml:id="echoid-head4" xml:space="preserve">M. DC. LXXXVII. <lb/>AVEC PRIVILEGE DU ROI.</head> |
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51 <pb file="0010" n="10"/> |
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52 <pb file="0011" n="11"/> |
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53 <figure> |
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54 <image file="0011-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0011-01"/> |
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55 </figure> |
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56 </div> |
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57 <div xml:id="echoid-div5" type="section" level="1" n="5"> |
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58 <head xml:id="echoid-head5" xml:space="preserve">A MESSIEURS <lb/>DE <lb/>L’ACADEMIE <lb/>ROYALE <lb/>DES SCIENCES@</head> |
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59 <p style="it"> |
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60 <s xml:id="echoid-s8" xml:space="preserve">MESSIEVRS, <lb/>Fe n’ay pas crû devoir expoſer au <lb/>jugement du public ce Projet d’une |
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61 <pb file="0012" n="12" rhead="EPITRE."/> |
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62 Nouvelle Mècbanique, ſans m’ap-<lb/>puyer d’une auſſi grande autboritè <lb/>que la vôtre, moy qui n’ay encore au-<lb/>cun nom dans les Lettres, & </s> |
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63 <s xml:id="echoid-s9" xml:space="preserve">qui dois <lb/>par conſèquent me dèfier de ces pre-<lb/>miers mouvemens que @amour des <lb/>Sciences inſpire àceux qui commencent <lb/>à s’y apliquer. </s> |
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64 <s xml:id="echoid-s10" xml:space="preserve">Sans cela on pourroit <lb/>juſtement m’accuſer de quelque tèmèri-<lb/>tè, d’avoir entrepris de dècouvrir dans <lb/>cette matière ce que tant de ſc1;</s> |
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65 <s xml:id="echoid-s11" xml:space="preserve">avans <lb/>Autbeurs n’ont pas dècouvert; </s> |
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66 <s xml:id="echoid-s12" xml:space="preserve">& </s> |
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67 <s xml:id="echoid-s13" xml:space="preserve">je <lb/>craindrois de m’être laiſſè tromper <lb/>par ces illuſions flateuſes de la nou-<lb/>veautè qui abuſent d’ordinaire les <lb/>bommes, lorſqu’ils ſe piquent d’avoir <lb/>des opinions particulières. </s> |
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68 <s xml:id="echoid-s14" xml:space="preserve">Fe puis dire <lb/>neanmoins, <emph style="sc">Messieurs</emph>, que ce <lb/>n’eſt pas l’ambition de me ſignaler par <lb/>des idèes extraordinaires qui m’a |
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69 <pb file="0013" n="13" rhead="EPITRE."/> |
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70 pouſſè à ècrire ce petit traitè; </s> |
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71 <s xml:id="echoid-s15" xml:space="preserve">c’eſt un <lb/>Eſſay que j’ay voulu faire de mes for-<lb/>ces pour être connu de vous, & </s> |
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72 <s xml:id="echoid-s16" xml:space="preserve">pour <lb/>vous donner occaſion de m’encourager <lb/>dans l’ètude que j’ay embraſsèe. </s> |
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73 <s xml:id="echoid-s17" xml:space="preserve">Si je <lb/>n’ay pas tout ce qui eſt nècèſſaire pour <lb/>inſtruire les autres, j’ay du moins <lb/>toute la docilitè qu’il faut pour être <lb/>inſtruit: </s> |
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74 <s xml:id="echoid-s18" xml:space="preserve">je ne me flatte point auſſi <lb/>d’avoir ètabli des principes certains <lb/>dans ce Projet, n’y d’en pouvoir <lb/>tirer des conſèquences infaillibles: <lb/></s> |
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75 <s xml:id="echoid-s19" xml:space="preserve">Vous enjugerez mieux que perſonne, <lb/><emph style="sc">Messieurs</emph>, Vous qui pènètrez ſi <lb/>avant dans les Sciences les plus rele-<lb/>vèes. </s> |
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76 <s xml:id="echoid-s20" xml:space="preserve">On ſçait que rien n’ècbape à <lb/>vos ſoins & </s> |
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77 <s xml:id="echoid-s21" xml:space="preserve">à vôtre èxactitude; </s> |
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78 <s xml:id="echoid-s22" xml:space="preserve">La <lb/>Nature ſi avare aux autres de ſes <lb/>treſors & </s> |
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79 <s xml:id="echoid-s23" xml:space="preserve">ſi obſtinèe à ſe cacber, n’a <lb/>pû ſe dèfendre contre la pènètration <lb/>de vôtre eſprit & </s> |
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80 <s xml:id="echoid-s24" xml:space="preserve">contre la ſubtilitè |
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81 <pb file="0014" n="14" rhead="EPITRE."/> |
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82 de vos recbercbes; </s> |
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83 <s xml:id="echoid-s25" xml:space="preserve">vous en avez plus <lb/>dècouvert en vingt ans, qu’on n’a-<lb/>voit fait en pluſieurs Siècles. </s> |
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84 <s xml:id="echoid-s26" xml:space="preserve">Vos <lb/>Obſervations Aſtronomiques ont dè-<lb/>voilè (pour ainſi dire) des Planettes <lb/>qui ſe dèroboient à nos yeux; </s> |
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85 <s xml:id="echoid-s27" xml:space="preserve">vos <lb/>meſures ſi prèciſes ſur la terre, par <lb/>raport à celles que vous preniez en <lb/>même tems dans le Ciel, ont rècti-<lb/>fiè mille erreurs de nos anciens Geo-<lb/>grapbes. </s> |
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86 <s xml:id="echoid-s28" xml:space="preserve">La Pbyſique vous doit <lb/>ce qu’elle a de plus curieux, ſoit <lb/>dans la diſſection du Corps bumain <lb/>& </s> |
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87 <s xml:id="echoid-s29" xml:space="preserve">des Animaux, ſoit dans la deſ-<lb/>cription & </s> |
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88 <s xml:id="echoid-s30" xml:space="preserve">dans l’analyſe des Plan-<lb/>tes, des Eaux & </s> |
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89 <s xml:id="echoid-s31" xml:space="preserve">des Mineraux. <lb/></s> |
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90 <s xml:id="echoid-s32" xml:space="preserve">Lue ne vous doivent point auſſi les <lb/>Matbematiques en gènèral pour <lb/>tant d’ouvrages celebres que vous <lb/>avez mis au jour? </s> |
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91 <s xml:id="echoid-s33" xml:space="preserve">Enfin, il n’y a |
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92 <pb file="0015" n="15" rhead="EPITRE."/> |
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93 point de Science que vous n’ayez <lb/>perfectionnèe & </s> |
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94 <s xml:id="echoid-s34" xml:space="preserve">que vous n’enri-<lb/>cbiſſiez de tems en tems par vos <lb/>travaux. </s> |
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95 <s xml:id="echoid-s35" xml:space="preserve">Lue n’attend on pas en-<lb/>core de vous, animez comme vous <lb/>êtes par les bienfaits d’un Grand <lb/>Roy, qui veut renàre ſon Regne <lb/>auſſi glorieux par les Sciences & </s> |
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96 <s xml:id="echoid-s36" xml:space="preserve">par <lb/>les Arts, qu’il l’eſt dèja par ſes <lb/>prodigieuſes Conqueſtes, & </s> |
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97 <s xml:id="echoid-s37" xml:space="preserve">par tou-<lb/>tes ſes Hèroϊques actions? </s> |
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98 <s xml:id="echoid-s38" xml:space="preserve">A quoy <lb/>ne devez vous pas aſpirer vous-<lb/>meſmes aujourd’buy ſous la protè-<lb/>ction d’un Miniſtre ſi ſage & </s> |
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99 <s xml:id="echoid-s39" xml:space="preserve">ſi vi-<lb/>gilant, qui excite tout le monde par <lb/>ſes ordres & </s> |
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100 <s xml:id="echoid-s40" xml:space="preserve">par ſon exemple à <lb/>illuſtrer & </s> |
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101 <s xml:id="echoid-s41" xml:space="preserve">à cèlèbrer un Regne ſi <lb/>plein de merveilles ? </s> |
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102 <s xml:id="echoid-s42" xml:space="preserve">Souffrez donc, <lb/><emph style="sc">Messieurs</emph>, s’il vous plaît, <lb/>vous qui êtes comme à la ſource de |
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103 <pb file="0016" n="16" rhead="EPITRE."/> |
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104 toutes les Sciences bumaines, & </s> |
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105 <s xml:id="echoid-s43" xml:space="preserve">à qui <lb/>rien ne manque pour continuer vos <lb/>recbercbes, & </s> |
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106 <s xml:id="echoid-s44" xml:space="preserve">pour augmenter vos <lb/>connoiſſances, que j’oſe vous offrir <lb/>& </s> |
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107 <s xml:id="echoid-s45" xml:space="preserve">mettre au jour ce que j’ay puisè <lb/>dans cette ſource, & </s> |
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108 <s xml:id="echoid-s46" xml:space="preserve">qu’en eſſayant <lb/>de vous ſuivre & </s> |
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109 <s xml:id="echoid-s47" xml:space="preserve">de vous imiter, je <lb/>puiſſe quelquefois profiter de vos <lb/>lumières, & </s> |
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110 <s xml:id="echoid-s48" xml:space="preserve">vous aſſeurer que je ſuis <lb/>avec une parfaite vènèration,</s> |
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111 </p> |
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112 <p> |
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113 <s xml:id="echoid-s49" xml:space="preserve">MESSIEVRS,</s> |
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114 </p> |
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115 <p> |
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116 <s xml:id="echoid-s50" xml:space="preserve">Vôtre tres-humble & </s> |
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117 <s xml:id="echoid-s51" xml:space="preserve">tres-<lb/>obéϊſſant ſerviteur</s> |
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118 </p> |
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119 <p> |
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120 <s xml:id="echoid-s52" xml:space="preserve">V<emph style="sc">ARIGNON.</emph></s> |
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121 </p> |
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122 <pb file="0017" n="17"/> |
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123 <figure> |
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124 <image file="0017-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0017-01"/> |
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125 </figure> |
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126 </div> |
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127 <div xml:id="echoid-div6" type="section" level="1" n="6"> |
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128 <head xml:id="echoid-head6" xml:space="preserve">PREFACE.</head> |
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129 <p> |
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130 <s xml:id="echoid-s53" xml:space="preserve">A L’ouverture du ſecond Tome des <lb/>Lettres de Monſieur Deſcartes, je <lb/>tombai ſur un endroit de la 24. </s> |
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131 <s xml:id="echoid-s54" xml:space="preserve">où <lb/>il dit que c’eſt une cboſe ridicule, <lb/>que de vouloir employer la raiſon du Le-<lb/>vier dans la Poulie. </s> |
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132 <s xml:id="echoid-s55" xml:space="preserve">Cette réfléxion m’en <lb/>fit faire une autre@<unsure/>: </s> |
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133 <s xml:id="echoid-s56" xml:space="preserve">Sçavoir s’il eſt plus rai-<lb/>ſonnable de s’imaginer un levier dans un <lb/>poids qui eſt ſur un plan incliné, que dans <lb/>une poulie. </s> |
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134 <s xml:id="echoid-s57" xml:space="preserve">Aprés y avoir penſé, il me <lb/>ſembla que ces deux machines étant pour le <lb/>moins auſſi ſimples que le levier, elles n’en <lb/>devoient avoir aucune dépendance, & </s> |
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135 <s xml:id="echoid-s58" xml:space="preserve">que <lb/>ceux qui les y rapportoient, n’y étoient forcez <lb/>que parce que leurs principes n’avoient pas aſſez <lb/>d’étenduë pour en pouvoir démontrer les pro-<lb/>priétez indépendamment les unes des autres.</s> |
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136 <s xml:id="echoid-s59" xml:space="preserve"/> |
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137 </p> |
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138 <p> |
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139 <s xml:id="echoid-s60" xml:space="preserve">En effet en éxaminant ces principes un peu |
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140 <pb file="0018" n="18" rhead="PREFACE."/> |
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141 de prês, il me parut qu’ils ne pouvoient ſervir, <lb/>tout au plus, qu’à démontrer que l’equilibre <lb/>ſe trouve toujours dans un levier auquel ſont <lb/>appliquez deux poids qui ſont entr’ eux en <lb/>raiſon rèciproque des diſtances de leurs lignes <lb/>de direction à ſon point d’appui; </s> |
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142 <s xml:id="echoid-s61" xml:space="preserve">encore n’é-<lb/>toit-ce qu’en ce cas: </s> |
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143 <s xml:id="echoid-s62" xml:space="preserve">1°. </s> |
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144 <s xml:id="echoid-s63" xml:space="preserve">Que ce levier fût <lb/>droit. </s> |
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145 <s xml:id="echoid-s64" xml:space="preserve">2°. </s> |
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146 <s xml:id="echoid-s65" xml:space="preserve">Que ſon point d’appui fût entre les <lb/>lignes de direction des poids qui y ſont appli-<lb/>quez. </s> |
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147 <s xml:id="echoid-s66" xml:space="preserve">3°. </s> |
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148 <s xml:id="echoid-s67" xml:space="preserve">Lue ces mêmes lignes fuſſent pa-<lb/>ralleles entr’elles, & </s> |
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149 <s xml:id="echoid-s68" xml:space="preserve">perpendiculaιres à ce <lb/>levier. </s> |
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150 <s xml:id="echoid-s69" xml:space="preserve">Auſſi Guid-Ubalde, & </s> |
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151 <s xml:id="echoid-s70" xml:space="preserve">les autres qui <lb/>s’en tiennent à la démonſtration d’Archimede, <lb/>ont-ils été obligez de faire@<unsure/>revenir de gré ou <lb/>de force toutes ſortes de machines à cette <lb/>eſpece de levier, & </s> |
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152 <s xml:id="echoid-s71" xml:space="preserve">de réduire de même tous <lb/>les autres cas à celui-ci.</s> |
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153 <s xml:id="echoid-s72" xml:space="preserve"/> |
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154 </p> |
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155 <p> |
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156 <s xml:id="echoid-s73" xml:space="preserve">C’eſt peut-être ce qui a porté M. </s> |
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157 <s xml:id="echoid-s74" xml:space="preserve">Deſcartes, <lb/>& </s> |
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158 <s xml:id="echoid-s75" xml:space="preserve">M. </s> |
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159 <s xml:id="echoid-s76" xml:space="preserve">Vvallis a prendre une autre route; <lb/></s> |
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160 <s xml:id="echoid-s77" xml:space="preserve">quoi qu’il en ſoit, ce n’a pas été ſans ſuccez: </s> |
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161 <s xml:id="echoid-s78" xml:space="preserve"><lb/>puiſque celle qu’ils ont ſuivie, conduit éga-<lb/>lement à la connoiſſance des uſages de chacune <lb/>de ces machines, ſans être obligé de les faire <lb/>dépendre l’une de l’autre; </s> |
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162 <s xml:id="echoid-s79" xml:space="preserve">outre qu’elle à mené <lb/>M. </s> |
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163 <s xml:id="echoid-s80" xml:space="preserve">Vvallis beaucoup plus loin qu’aucun |
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164 <pb file="0019" n="19" rhead="PREFACE."/> |
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165 Autheur, que je ſçache, n’eût encore été de <lb/>ce côté-là.</s> |
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166 <s xml:id="echoid-s81" xml:space="preserve"/> |
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167 </p> |
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168 <p> |
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169 <s xml:id="echoid-s82" xml:space="preserve">La comparaiſon que je fis de ces deux <lb/>fortes de principes, me fit ſentir que ceux d’Ar-<lb/>chimede n’étoient ny ſi étendus, ny ſi con-<lb/>vainquants que ceux de M. </s> |
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170 <s xml:id="echoid-s83" xml:space="preserve">Deſcartes, & </s> |
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171 <s xml:id="echoid-s84" xml:space="preserve">de <lb/>M. </s> |
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172 <s xml:id="echoid-s85" xml:space="preserve">Vvallis; </s> |
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173 <s xml:id="echoid-s86" xml:space="preserve">mais je ne ſentis point que les uns <lb/>ny les autres m’éclairaſſent beaucoup: </s> |
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174 <s xml:id="echoid-s87" xml:space="preserve">J’en <lb/>cherchai la raiſon, & </s> |
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175 <s xml:id="echoid-s88" xml:space="preserve">ce défaut me parut venir <lb/>de ce que ces Autheurs ſe ſont tous plus atta-<lb/>chez à prouver la néceſſité de l’équilibre, qu’à <lb/>montrer la maniére dont il ſe fait.</s> |
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176 <s xml:id="echoid-s89" xml:space="preserve"/> |
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177 </p> |
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178 <p> |
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179 <s xml:id="echoid-s90" xml:space="preserve">Ce fut ce qui me fit réſoudre à prendre le <lb/>parti d’épier moi-même la nature, & </s> |
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180 <s xml:id="echoid-s91" xml:space="preserve">d’eſſayer <lb/>ſi en la ſuivant pas à pas, je ne pourrois point <lb/>apercevoir comment elle s’y prend pour faire <lb/>que deux puiſſances, ſoit égales, ſoit inégales, <lb/>demeurent en équilibre. </s> |
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181 <s xml:id="echoid-s92" xml:space="preserve">Enfin je m’appliquai <lb/>à chercher l’équilibre lui-même dans ſa ſource, <lb/>ou pour mieux dire, dans ſa génération.</s> |
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182 <s xml:id="echoid-s93" xml:space="preserve"/> |
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183 </p> |
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184 <p> |
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185 <s xml:id="echoid-s94" xml:space="preserve">Le premier objet qui me vint à l’eſprit, ce <lb/>fut un poids qu’une puiſſance ſoutient ſur <lb/>un plan incliné; </s> |
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186 <s xml:id="echoid-s95" xml:space="preserve">D’abord je me le repréſentai |
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187 <pb file="0020" n="20" rhead="PREFACE."/> |
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188 de telle figure que le concours de ſa ligne de <lb/>direction avec celle de cette puiſſance, ſe fit <lb/>dans quelqu’un de ſes points: </s> |
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189 <s xml:id="echoid-s96" xml:space="preserve">De-là je vis que <lb/>leur concours d’action ſe faiſant auſſi par ce <lb/>moyen dans ce ſeul point, il devenoit alors <lb/>ſon centre de direction: </s> |
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190 <s xml:id="echoid-s97" xml:space="preserve">De ſorte que ſi ce <lb/>plan eut manqué tout d’un coup, ce corps au-<lb/>roit néceſſairement ſuivi l’impreſſion de ce <lb/>point. </s> |
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191 <s xml:id="echoid-s98" xml:space="preserve">Je cherchai enſuite quelle devoit être <lb/>cette impreſſion, & </s> |
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192 <s xml:id="echoid-s99" xml:space="preserve">j’aperçus que celles que <lb/>faiſoient ſur ce point, & </s> |
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193 <s xml:id="echoid-s100" xml:space="preserve">la peſanteur de ce <lb/>poids, & </s> |
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194 <s xml:id="echoid-s101" xml:space="preserve">la puiſſance qui le retenoit, étant <lb/>les mêmes que s’il eut été pouſſé en même-<lb/>tems par deux forces qui leur euſſent été éga-<lb/>les, & </s> |
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195 <s xml:id="echoid-s102" xml:space="preserve">qui euſſent agi ſuivant leurs lignes de <lb/>direction: </s> |
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196 <s xml:id="echoid-s103" xml:space="preserve">J’aperçus, dî-je, qu’il lui en réſultoit <lb/>une impreſſion compoſée ſuivant une ligne <lb/>qui étoit la diagonale d’un parallelogramme <lb/>fait ſous des parties de ces lignes de direction, <lb/>qui étoient entr’elles, comme ce poids & </s> |
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197 <s xml:id="echoid-s104" xml:space="preserve"><lb/>cette puiſſance: </s> |
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198 <s xml:id="echoid-s105" xml:space="preserve">D’où je vis que l’impreſſion <lb/>de ce corps ſe faiſoit alors ſuivant cette diago-<lb/>nale, qui devenoit en ce cas ſa ligne de di-<lb/>rection; </s> |
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199 <s xml:id="echoid-s106" xml:space="preserve">mais que ce plan lui étant perpendi-<lb/>culairement oppoſé, il la ſoutenoit toute en-<lb/>tiére; </s> |
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200 <s xml:id="echoid-s107" xml:space="preserve">ce qui faiſoit que ce poids ainſi pouſſé |
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201 <pb file="0021" n="21" rhead="PREF ACE."/> |
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202 par le concours d’action de ſa peſanteur & </s> |
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203 <s xml:id="echoid-s108" xml:space="preserve">de <lb/>la puiſſance qui lui étoit appliquée, demeuroit <lb/>ſur ce plan incliné de même que s’il eut été <lb/>horizontal, & </s> |
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204 <s xml:id="echoid-s109" xml:space="preserve">que cette impreſſion compoſée <lb/>n’eut été qu’un effet de ſa ſeule peſanteur.</s> |
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205 <s xml:id="echoid-s110" xml:space="preserve"/> |
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206 </p> |
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207 <p> |
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208 <s xml:id="echoid-s111" xml:space="preserve">De cette penſée j’en vis naître pluſieurs <lb/>autres, & </s> |
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209 <s xml:id="echoid-s112" xml:space="preserve">jem’aperçus 1°. </s> |
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210 <s xml:id="echoid-s113" xml:space="preserve">Que toute l’impreſ-<lb/>ſion que ce plan recevoit alors de ce poids <lb/>ainſi ſoutenu par cette puiſſance, ſe faiſoit <lb/>ſuivant cette diagonale. </s> |
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211 <s xml:id="echoid-s114" xml:space="preserve">2°. </s> |
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212 <s xml:id="echoid-s115" xml:space="preserve">Que ſa charge, <lb/>c’eſt-à-dire, la force de cette même impreſ-<lb/>ſion, étoit à ce poids & </s> |
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213 <s xml:id="echoid-s116" xml:space="preserve">à cette puiſſance, <lb/>comme cette même diagonale à chacun des <lb/>côtez qui les répréſentent dans ſon parallelo-<lb/>gramme. </s> |
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214 <s xml:id="echoid-s117" xml:space="preserve">3°. </s> |
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215 <s xml:id="echoid-s118" xml:space="preserve">Que ce poids, & </s> |
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216 <s xml:id="echoid-s119" xml:space="preserve">cette puiſſance <lb/>étoient toujours entr’eux comme ces mêmes <lb/>côtez, c’eſt-à-dire, en raiſon réciproque des <lb/>ſinus des angles que font leurs lignes de direc-<lb/>tion avec cette diagonale, ou (ce qui revient <lb/>au même ) en raiſon réciproque des diſtances <lb/>de quelque point que ce ſoit de cette diago-<lb/>nale à leur lignes de direction. </s> |
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217 <s xml:id="echoid-s120" xml:space="preserve">Je vis enfin <lb/>preſque tout à la fois quantité de choſes tou-<lb/>tes nouvelles qu’on verra dans les Corollaires <lb/>de la propoſition des ſurfaces.</s> |
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218 <s xml:id="echoid-s121" xml:space="preserve"/> |
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219 </p> |
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220 <pb file="0022" n="22" rhead="PREF ACE."/> |
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221 <p> |
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222 <s xml:id="echoid-s122" xml:space="preserve">Aprés avoir ainſi trouvé la maniére dont <lb/>l’équilibre ſefait ſur des plans inclinez, je cher-<lb/>chai par le même chemin comment des poids <lb/>ſoutenus avec des cordes ſeulement, ou appli-<lb/>quez à des poulies, ou bien à des leviers, font <lb/>équilibre entr’eux, ou avec les puiſſances qui <lb/>les ſoutiennent; </s> |
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223 <s xml:id="echoid-s123" xml:space="preserve">& </s> |
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224 <s xml:id="echoid-s124" xml:space="preserve">j’aperçus de même que tout <lb/>cela ſe faiſoit encore par la voye des mouve-<lb/>mens compoſez, & </s> |
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225 <s xml:id="echoid-s125" xml:space="preserve">avec tant d’uniformité <lb/>que je ne pûs m’empêcher de croire que cette <lb/>voye ne fût véritablement celle que ſuit la <lb/>nature dans le concours d’action de deux <lb/>poids, ou de deux puiſſances, en faiſant que <lb/>leurs impreſſions particulieres, quelque pro-<lb/>portion qu’elles ayent, ſe confondent en un@ <lb/>ſeule qui ſe décharge toute entiére ſur le point <lb/>ou ſe fait cét équilibre: </s> |
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226 <s xml:id="echoid-s126" xml:space="preserve">De ſorte que la <lb/>raiſon Phyſique des effets qu’on admire le <lb/>plus dans les machines me parut être juſte-<lb/>ment celle des mouvemens compoſez.</s> |
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227 <s xml:id="echoid-s127" xml:space="preserve"/> |
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228 </p> |
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229 <p> |
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230 <s xml:id="echoid-s128" xml:space="preserve">Je me démontrai d’abord par cett@ mé-<lb/>thode, & </s> |
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231 <s xml:id="echoid-s129" xml:space="preserve">ſans le ſecours d’aucune machine, <lb/>les propriétez des poids ſuſpendus avec des <lb/>cordes, en quelque nombre qu’elles ſoient, &</s> |
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232 <s xml:id="echoid-s130" xml:space="preserve"> |
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233 <pb file="0023" n="23" rhead="PREF ACE."/> |
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234 pour tous les angles poſſibles qu’elles peuvent <lb/>faire entr’elles. </s> |
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235 <s xml:id="echoid-s131" xml:space="preserve">De-là je paſſai à une démonſ-<lb/>tration des poulies qui comprend toutes les <lb/>directions poſſibles des puiſſances, ou des <lb/>poids qui y ſont appliquez, ſoit que le centre <lb/>de ces poulies demeure fixe, ſoit qu’on le ſup-<lb/>poſe mobile. </s> |
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236 <s xml:id="echoid-s132" xml:space="preserve">Enſuite au lieu de la démonſtra-<lb/>tion qu’on ne fait ordinairement que pour les <lb/>plans inclinez, j’en trouvai une qui s’étend <lb/>généralement à toutes ſortes de ſurfaces, & </s> |
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237 <s xml:id="echoid-s133" xml:space="preserve">à <lb/>toutes les directions poſſibles des puiſſances, <lb/>ou des poids qui y ſont appliquez. </s> |
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238 <s xml:id="echoid-s134" xml:space="preserve">Enfin d’une <lb/>ſeule démonſtration je découvris les proprié-<lb/>tez de toutes les eſpeces de leviers, de quel-<lb/>que figure, & </s> |
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239 <s xml:id="echoid-s135" xml:space="preserve">dans quelque ſituation qu’ils <lb/>ſoient, & </s> |
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240 <s xml:id="echoid-s136" xml:space="preserve">pour toutes les directions poſſibles <lb/>des puiſſances, ou des poids qui y ſont appli-<lb/>quez.</s> |
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241 <s xml:id="echoid-s137" xml:space="preserve"/> |
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242 </p> |
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243 <p> |
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244 <s xml:id="echoid-s138" xml:space="preserve">Des vuës ſi étenduës me ſurprirent, & </s> |
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245 <s xml:id="echoid-s139" xml:space="preserve">l’é-<lb/>vidence avec laquelle le détail de tout cela <lb/>me paroiſſoit, indépendamment même du <lb/>général, me confirma encore dans l’opinion <lb/>ou j’étois, qu’il faut entrer dans la génération <lb/>d e l’équilibre pour y voir en ſoi, & </s> |
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246 <s xml:id="echoid-s140" xml:space="preserve">pour y <lb/>reconnoître les propriétez que tous les autres |
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247 <pb file="0024" n="24" rhead="PREF ACE."/> |
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248 principes ne prouvent, tout au plus, que par <lb/>néceſſité de conſéquence.</s> |
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249 <s xml:id="echoid-s141" xml:space="preserve"/> |
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250 </p> |
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251 <p> |
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252 <s xml:id="echoid-s142" xml:space="preserve">Il y a encore un avantage dans la route <lb/>que je tiens, c’eſt qu’elle facilite extrémement <lb/>le calcul des forces, tant des poids, que des <lb/>puiſſances, en ce que leurs raports y ſont tou-<lb/>jours déterminez immédiatement par les ſinus <lb/>des angles que font leurs lignes de direction <lb/>avec celle de l’impreſſion qui réſulte de <lb/>leur concours d’action, & </s> |
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253 <s xml:id="echoid-s143" xml:space="preserve">que cette méthode <lb/>détermine pour le point ou elles concourent. <lb/></s> |
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254 <s xml:id="echoid-s144" xml:space="preserve">On y voit, que lors que deux puiſſances, <lb/>ou deux poids, ou bien une puiſſance & </s> |
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255 <s xml:id="echoid-s145" xml:space="preserve">un <lb/>poids font équilibre, ſoit avec des cordes <lb/>ſeulement, ſoit à l’aide de quelque poulie, de <lb/>quelque ſurface, ou de quelque levier que ce <lb/>ſoit; </s> |
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256 <s xml:id="echoid-s146" xml:space="preserve">ils ſont toujours entr’ eux en raiſon réci-<lb/>proque des ſinus de ces mêmes angles.</s> |
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257 <s xml:id="echoid-s147" xml:space="preserve"/> |
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258 </p> |
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259 <p> |
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260 <s xml:id="echoid-s148" xml:space="preserve">J’avois deſſein d’expliquer avec cette mé-<lb/>thode les effets les plus ſurprenans, & </s> |
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261 <s xml:id="echoid-s149" xml:space="preserve">les plus <lb/>difficiles des machines compoſées que l’on ren-<lb/>contre dans les arts, & </s> |
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262 <s xml:id="echoid-s150" xml:space="preserve">dans la nature; </s> |
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263 <s xml:id="echoid-s151" xml:space="preserve">mais cela <lb/>demandoit plus de loiſir, & </s> |
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264 <s xml:id="echoid-s152" xml:space="preserve">même un plus <lb/>grand nombre d’expériences que l’état de ma |
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265 <pb file="0025" n="25" rhead="PREF ACE."/> |
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266 fortune ne me peut permetre: </s> |
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267 <s xml:id="echoid-s153" xml:space="preserve">c’eſt pour cela <lb/>que je me ſuis déterminé à ne donner préſente-<lb/>ment que les Propoſitions fondamentales de <lb/>la Méchanique: </s> |
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268 <s xml:id="echoid-s154" xml:space="preserve">peut-être que de plus habiles <lb/>gens que moy, & </s> |
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269 <s xml:id="echoid-s155" xml:space="preserve">qui ſeront plus en état de <lb/>faire cette entrepriſe, voudront bien ſe donner <lb/>la peine d’en faire l’application à la Phyſique.</s> |
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270 <s xml:id="echoid-s156" xml:space="preserve"/> |
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271 </p> |
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272 <p> |
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273 <s xml:id="echoid-s157" xml:space="preserve">Mais en attendant, je ne laiſſeray pas d’a-<lb/>maſſer tout ce que je pouray d’expériences <lb/>pour ce deſſein; </s> |
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274 <s xml:id="echoid-s158" xml:space="preserve">c’eſt pourquoy je prie ceux <lb/>qui n’auront pas en vuë d’y travailler, de vou-<lb/>loir bien me communiquer celles qu’ils croi-<lb/>ront s’y pouvoir rapporter: </s> |
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275 <s xml:id="echoid-s159" xml:space="preserve">& </s> |
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276 <s xml:id="echoid-s160" xml:space="preserve">ſur tout de <lb/>me faire part de tout ce qui leur viendra de <lb/>difficultez ou de lumieres ſur les principes <lb/>qu’on propoſe icy, leur promettant d’en uſer <lb/>avec toute la docilité d’un homme qui ne <lb/>cherche que la vérité.</s> |
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277 <s xml:id="echoid-s161" xml:space="preserve"/> |
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278 </p> |
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279 <pb file="0026" n="26"/> |
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280 <figure> |
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281 <image file="0026-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0026-01"/> |
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282 </figure> |
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283 </div> |
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284 <div xml:id="echoid-div7" type="section" level="1" n="7"> |
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285 <head xml:id="echoid-head7" xml:space="preserve">AVER TISSE MENT.</head> |
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286 <p style="it"> |
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287 <s xml:id="echoid-s162" xml:space="preserve">LES corollaires qu’on verra <lb/>citez dans la Solution de cba-<lb/>que Problême ſuivant, ſeront de la <lb/>Propoſition fondamentale qui le pré-<lb/>cède. </s> |
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288 <s xml:id="echoid-s163" xml:space="preserve">C’eſt de peur d’ennuyer par <lb/>des rèpètitions trop frèquentes qu’on <lb/>ne la citera point.</s> |
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289 <s xml:id="echoid-s164" xml:space="preserve"/> |
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290 </p> |
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291 <pb o="1" file="0027" n="27"/> |
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292 <figure> |
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293 <image file="0027-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0027-01"/> |
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294 </figure> |
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295 </div> |
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296 <div xml:id="echoid-div8" type="section" level="1" n="8"> |
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297 <head xml:id="echoid-head8" xml:space="preserve">PROJET <lb/>D’UNE <lb/>NOUVELLE MECHANIQUE.</head> |
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298 <figure> |
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299 <image file="0027-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0027-02"/> |
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300 </figure> |
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301 <p style="it"> |
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302 <s xml:id="echoid-s165" xml:space="preserve">CE C 1<unsure/> n’ètant que pour ceux qui entendent aſſez <lb/>ces matières pour en pouvoir juger, on ne s’arrê-<lb/>tera point à répéter des Définitions, ny des Axio-<lb/>mes qui ſe trouvent par tout; </s> |
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303 <s xml:id="echoid-s166" xml:space="preserve">en voici ſeulcment <lb/>un, avec une demande, & </s> |
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304 <s xml:id="echoid-s167" xml:space="preserve">quelques Lemmes <lb/>particuliérement néceſſaires pour l’intelligence de ce Projet.</s> |
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305 <s xml:id="echoid-s168" xml:space="preserve"/> |
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306 </p> |
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307 </div> |
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308 <div xml:id="echoid-div9" type="section" level="1" n="9"> |
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309 <head xml:id="echoid-head9" xml:space="preserve"><emph style="sc">Axiome</emph>.</head> |
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310 <p> |
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311 <s xml:id="echoid-s169" xml:space="preserve">Les eſpaces que parcourt un même corps, ou des <lb/>corps égaux dans des tems égaux, ſont entre-eux <lb/>comme les forces qui les meuvent; </s> |
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312 <s xml:id="echoid-s170" xml:space="preserve">& </s> |
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313 <s xml:id="echoid-s171" xml:space="preserve">réciproque-<lb/>ment lorſque ces Eſpaces ſont entre-eux comme ces |
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314 <pb o="2" file="0028" n="28" rhead="NOUVELLE"/> |
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315 forces, elles les font parcourir au même corps, ou à <lb/> |
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316 <anchor type="note" xlink:label="note-0028-01a" xlink:href="note-0028-01"/> |
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317 des corps égaux en tems égaux.</s> |
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318 <s xml:id="echoid-s172" xml:space="preserve"/> |
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319 </p> |
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320 <div xml:id="echoid-div9" type="float" level="2" n="1"> |
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321 <note position="left" xlink:label="note-0028-01" xlink:href="note-0028-01a" xml:space="preserve">LEMMES.</note> |
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322 </div> |
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323 </div> |
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324 <div xml:id="echoid-div11" type="section" level="1" n="10"> |
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325 <head xml:id="echoid-head10" xml:space="preserve"><emph style="sc">Demande</emph>.</head> |
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326 <p> |
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327 <s xml:id="echoid-s173" xml:space="preserve">On ſuppoſe ici que dans tout corps qui ſe meut, <lb/>ou qui fait effort pour ſe mouvoir, il y a toûjours <lb/>un certain point qui ſurchargé de l’impreſſion de <lb/>tous les autres, détermine ce corps à ſuivre celle <lb/>qu’il a pour lors vers l’endroit où il tend. </s> |
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328 <s xml:id="echoid-s174" xml:space="preserve">On ne ſe <lb/>met point en peine que ce point ſoit le même dans <lb/>toutes les ſituations poſſibles de ce corps: </s> |
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329 <s xml:id="echoid-s175" xml:space="preserve">c’eſt aſſez <lb/>que dans chaque ſituation il y en ait un que l’on <lb/>appelle ici ſon Centre de gravité, ou, plus générale-<lb/>ment ſon Centre de direction, ou, d’équilibre, du moins <lb/>pour le tems qu’il détermine ainſi ce corps à ſuivre <lb/>ſon impreſſion; </s> |
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330 <s xml:id="echoid-s176" xml:space="preserve">& </s> |
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331 <s xml:id="echoid-s177" xml:space="preserve">la ligne qui joint ce point avec <lb/>celui où il tend, s’appelle ſa Ligne de direction.</s> |
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332 <s xml:id="echoid-s178" xml:space="preserve"/> |
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333 </p> |
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334 <p style="it"> |
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335 <s xml:id="echoid-s179" xml:space="preserve">On ne met ceci en ſuppoſition que pour abréger; </s> |
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336 <s xml:id="echoid-s180" xml:space="preserve">autrement <lb/>on le pourroit dèmontrer: </s> |
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337 <s xml:id="echoid-s181" xml:space="preserve">car il n’y arien de plus évident que <lb/>de tous les points d’un corps, il y en a toûjours, & </s> |
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338 <s xml:id="echoid-s182" xml:space="preserve">même <lb/>néceſſairement, quelqu’un autour duquel l’impreſſion qu’ils <lb/>ont tous vers le côtè ou ce corps tend, ſe trouve ſi ègalement <lb/>partagèe qu’ils demeureroient en èquilibre deſſus, ſi ſans cban-<lb/>ger la ſituation de ce corps par raport à l’endroit où il tend, <lb/>on le rendoit fixe; </s> |
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339 <s xml:id="echoid-s183" xml:space="preserve">& </s> |
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340 <s xml:id="echoid-s184" xml:space="preserve">par conſèquent l’impreſſion d’un tel <lb/>point ainſi ſurcbargè de celle de tous les autres, étant l<unsure/>a <lb/>même que s’il ètoit le ſeul qui en eût, il doit déterminer ce <lb/>corps à la ſuivre.</s> |
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341 <s xml:id="echoid-s185" xml:space="preserve"/> |
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342 </p> |
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343 <p style="it"> |
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344 <s xml:id="echoid-s186" xml:space="preserve">Il n’y a rien-là, ce me ſemble, que de clair; </s> |
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345 <s xml:id="echoid-s187" xml:space="preserve">cependant <lb/>s’il ſe trouvoit quelqu’un qui faute de le voir de même, fit <lb/>difficultè de l’accorder, il peut prendre dans la ſuite les corps <lb/>dont on parlera, pou@ des points qui ayent la peſanteur, ou <lb/>l’impreſſion qu’on y ſuppoſe; </s> |
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346 <s xml:id="echoid-s188" xml:space="preserve">ou bien pour des puiſſances appli-<lb/>quées de même, & </s> |
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347 <s xml:id="echoid-s189" xml:space="preserve">qui leur ſoient ègales: </s> |
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348 <s xml:id="echoid-s190" xml:space="preserve">parce que les démonſ- |
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349 <pb o="3" file="0029" n="29" rhead="ME’CHANIQUE."/> |
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350 trations ſuivantes ſe peuvent également appliquor aux uns <lb/> |
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351 <anchor type="note" xlink:label="note-0029-01a" xlink:href="note-0029-01"/> |
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352 & </s> |
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353 <s xml:id="echoid-s191" xml:space="preserve">aux autres.</s> |
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354 <s xml:id="echoid-s192" xml:space="preserve"/> |
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355 </p> |
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356 <div xml:id="echoid-div11" type="float" level="2" n="1"> |
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357 <note position="right" xlink:label="note-0029-01" xlink:href="note-0029-01a" xml:space="preserve">LEMMES.</note> |
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358 </div> |
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359 <figure> |
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360 <image file="0029-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0029-01"/> |
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361 </figure> |
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362 </div> |
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363 <div xml:id="echoid-div13" type="section" level="1" n="11"> |
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364 <head xml:id="echoid-head11" xml:space="preserve">LEMME I.</head> |
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365 <p style="it"> |
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366 <s xml:id="echoid-s193" xml:space="preserve">LE poids A ètant ſuſpendu à une corde EH, ou à deux <lb/> |
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367 <anchor type="note" xlink:label="note-0029-02a" xlink:href="note-0029-02"/> |
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368 MH & </s> |
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369 <s xml:id="echoid-s194" xml:space="preserve">NH attacbèes à un même point fixe H; <lb/></s> |
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370 <s xml:id="echoid-s195" xml:space="preserve">ou bien ſoutenu ſur un pieu EH, ou ſur deux MH & </s> |
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371 <s xml:id="echoid-s196" xml:space="preserve">NH <lb/>appuyez auſſi ſur un même point H: </s> |
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372 <s xml:id="echoid-s197" xml:space="preserve">en ſorte que la li-<lb/>gne A H, qui joint ſon Centre de gravitè A avec ſon <lb/>point de ſuſpenſion, ou d’apuy, faſſe quelque angle que c@ <lb/>ſoit avec ſa ligne de direction AK: </s> |
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373 <s xml:id="echoid-s198" xml:space="preserve">Ce poids tombera de A <lb/>vers B le long de l’arc A B dont H eſt le centre, juſqu’à <lb/>ce que la ligne AH ſoit dans la perpendiculaire, ou dans <lb/>le plan borizontal H B, & </s> |
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374 <s xml:id="echoid-s199" xml:space="preserve">étant arrivé en B, ily demeu-<lb/>rera, ſi l’on n’y ſuppoſe à’autre cauſe que ſa peſanteur.</s> |
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375 <s xml:id="echoid-s200" xml:space="preserve"/> |
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376 </p> |
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377 <div xml:id="echoid-div13" type="float" level="2" n="1"> |
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378 <note position="right" xlink:label="note-0029-02" xlink:href="note-0029-02a" xml:space="preserve">fig. 1. <lb/>2. <lb/>3. <lb/>4.</note> |
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379 </div> |
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380 </div> |
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381 <div xml:id="echoid-div15" type="section" level="1" n="12"> |
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382 <head xml:id="echoid-head12" xml:space="preserve"><emph style="sc">Demonstr ation</emph>.</head> |
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383 <p> |
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384 <s xml:id="echoid-s201" xml:space="preserve">L’effet de la peſanteur du poids A, c’eſt de l’ap-<lb/>procher ( byp. </s> |
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385 <s xml:id="echoid-s202" xml:space="preserve">) du centre de la terre, c’eſt-à-dire, <lb/>( dem. </s> |
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386 <s xml:id="echoid-s203" xml:space="preserve">) d’en approcher ſon centre de gravité A, <lb/>tant que rien ne l’en empêche. </s> |
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387 <s xml:id="echoid-s204" xml:space="preserve">Or dans la ſituation <lb/>preſente rien ne l’empêche de s’en approcher de la <lb/>longueur de A K, en tombant le long de l’arc A B <lb/>juſqu’en B; </s> |
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388 <s xml:id="echoid-s205" xml:space="preserve">au contraire étant arrivé en B, la cor-<lb/>de E H, ou les cordes M H & </s> |
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389 <s xml:id="echoid-s206" xml:space="preserve">N H; </s> |
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390 <s xml:id="echoid-s207" xml:space="preserve">ou bien le plan <lb/>horizontal H B, le retiennent & </s> |
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391 <s xml:id="echoid-s208" xml:space="preserve">l’empêchent de <lb/>deſcendre davantage; </s> |
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392 <s xml:id="echoid-s209" xml:space="preserve">& </s> |
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393 <s xml:id="echoid-s210" xml:space="preserve">par conſéquent ce poids <lb/>dans la ſituation preſente tombera le long de l’arc A B <lb/>juſqu’en B, & </s> |
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394 <s xml:id="echoid-s211" xml:space="preserve">y étant arrivé, il y demeurera. </s> |
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395 <s xml:id="echoid-s212" xml:space="preserve">Ce <lb/>qu’il faloit demontrer.</s> |
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396 <s xml:id="echoid-s213" xml:space="preserve"/> |
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397 </p> |
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398 </div> |
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399 <div xml:id="echoid-div16" type="section" level="1" n="13"> |
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400 <head xml:id="echoid-head13" xml:space="preserve"><emph style="sc">Corollaire</emph>.</head> |
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401 <p> |
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402 <s xml:id="echoid-s214" xml:space="preserve">On prouvera de même que tout autre corps, de |
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403 <pb o="4" file="0030" n="30" rhead="NOUVELLE"/> |
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404 quelque côté qu’il tende, appuyé ſeulement ſur un <lb/> |
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405 <anchor type="note" xlink:label="note-0030-01a" xlink:href="note-0030-01"/> |
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406 de ſes points, ou même ſur une de ſes faces, de quel-<lb/>que largeur qu’elle ſoit, doit neceſſairement avancer <lb/>du côté ou il eſt pouſſé par ſa peſanteur, ou par <lb/>quelqu’autre force que ce ſoit, non-ſeulement tant <lb/>que ſa ligne de direction ne paſſe point par ce point <lb/>d’apuy, ny par aucun de la partie de cette face ſur <lb/>laquelle il s’appuye; </s> |
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407 <s xml:id="echoid-s215" xml:space="preserve">mais encore tant qu’elle n’eſt <lb/>point perpendiculaire au plan, ou à la ſurface qui ſe <lb/>trouve à ſon paſſage; </s> |
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408 <s xml:id="echoid-s216" xml:space="preserve">c’eſt-à-dire, tant que ſon centre <lb/>de direction n’eſt point appuyé: </s> |
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409 <s xml:id="echoid-s217" xml:space="preserve">Car ce centre pou-<lb/>vant encore avancer du côté où il tend, la force qui <lb/>le pouſſe, ne manquera pas de l’y obliger; </s> |
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410 <s xml:id="echoid-s218" xml:space="preserve">Mais auſſi <lb/>par une raiſon toute contraire, ſi-tôt que l’un, & </s> |
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411 <s xml:id="echoid-s219" xml:space="preserve"><lb/>l’autre arrivera, ce corps demeurera néceſſairement <lb/>en cet état.</s> |
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412 <s xml:id="echoid-s220" xml:space="preserve"/> |
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413 </p> |
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414 <div xml:id="echoid-div16" type="float" level="2" n="1"> |
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415 <note position="left" xlink:label="note-0030-01" xlink:href="note-0030-01a" xml:space="preserve">LEMMES.</note> |
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416 </div> |
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417 <figure> |
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418 <image file="0030-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0030-01"/> |
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419 </figure> |
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420 </div> |
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421 <div xml:id="echoid-div18" type="section" level="1" n="14"> |
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422 <head xml:id="echoid-head14" xml:space="preserve">LEMME II.</head> |
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423 <p style="it"> |
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424 <s xml:id="echoid-s221" xml:space="preserve">LE poids MN étant ſuſpendu par deux cordes P M & </s> |
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425 <s xml:id="echoid-s222" xml:space="preserve"><lb/> |
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426 <anchor type="note" xlink:label="note-0030-02a" xlink:href="note-0030-02"/> |
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427 RN, attacbées aux clous P & </s> |
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428 <s xml:id="echoid-s223" xml:space="preserve">R, & </s> |
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429 <s xml:id="echoid-s224" xml:space="preserve">qui prolon-<lb/>gées concourent en H, ſa ligne de diréction A H paſſera <lb/>par ce point de concours.</s> |
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430 <s xml:id="echoid-s225" xml:space="preserve"/> |
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431 </p> |
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432 <div xml:id="echoid-div18" type="float" level="2" n="1"> |
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433 <note position="left" xlink:label="note-0030-02" xlink:href="note-0030-02a" xml:space="preserve">fig. 5. <lb/>6.</note> |
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434 </div> |
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435 </div> |
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436 <div xml:id="echoid-div20" type="section" level="1" n="15"> |
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437 <head xml:id="echoid-head15" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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438 <p> |
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439 <s xml:id="echoid-s226" xml:space="preserve">Premiérement ( fig. </s> |
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440 <s xml:id="echoid-s227" xml:space="preserve">5. </s> |
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441 <s xml:id="echoid-s228" xml:space="preserve">) l’effort que le poids M N <lb/>fait pour attirer le point P de la corde P M vers M, <lb/>étant le même qu’il feroit contre le point H, ſi cette <lb/>corde prolongée y étoit attachée, & </s> |
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442 <s xml:id="echoid-s229" xml:space="preserve">non plus en P; <lb/></s> |
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443 <s xml:id="echoid-s230" xml:space="preserve">ce corps, ou ce poids eſt ſoutenu par cette corde, <lb/>comme ſi elle n’étoit attachée qu’en H. </s> |
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444 <s xml:id="echoid-s231" xml:space="preserve">Pour la <lb/>même raiſon il eſt auſſi ſoutenu par la corde R N, <lb/>comme ſi étant prolongée, elle n’étoit attachée qu’en <lb/>H: </s> |
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445 <s xml:id="echoid-s232" xml:space="preserve">Il eſt donc ſoutenu par ces deux cordes enſem- |
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446 <pb o="5" file="0031" n="31" rhead="ME’CHANIQUE."/> |
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447 ble, comme ſi l’une, & </s> |
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448 <s xml:id="echoid-s233" xml:space="preserve">l’autre étant prolongée, elles <lb/> |
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449 <anchor type="note" xlink:label="note-0031-01a" xlink:href="note-0031-01"/> |
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450 n’étoient attachées qu’en ce ſeul point: </s> |
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451 <s xml:id="echoid-s234" xml:space="preserve">& </s> |
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452 <s xml:id="echoid-s235" xml:space="preserve">par con-<lb/>ſéquent ( Lemm. </s> |
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453 <s xml:id="echoid-s236" xml:space="preserve">1. </s> |
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454 <s xml:id="echoid-s237" xml:space="preserve">) la ligne de direction A K de ce <lb/>poids ainſi ſuſpendu, paſſera par le point H où les <lb/>cordes P M & </s> |
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455 <s xml:id="echoid-s238" xml:space="preserve">R N concourent. </s> |
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456 <s xml:id="echoid-s239" xml:space="preserve">Ce qu’il F.</s> |
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457 <s xml:id="echoid-s240" xml:space="preserve">D.</s> |
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458 <s xml:id="echoid-s241" xml:space="preserve"/> |
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459 </p> |
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460 <div xml:id="echoid-div20" type="float" level="2" n="1"> |
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461 <note position="right" xlink:label="note-0031-01" xlink:href="note-0031-01a" xml:space="preserve">LEMMES.</note> |
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462 </div> |
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463 <p> |
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464 <s xml:id="echoid-s242" xml:space="preserve">Secondement ( fig. </s> |
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465 <s xml:id="echoid-s243" xml:space="preserve">6. </s> |
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466 <s xml:id="echoid-s244" xml:space="preserve">) l’effort que le poids M N fait <lb/>pour attirer le point P de ſa corde P M vers M, étant <lb/>le même que celui dont il preſſe ſon point C vers H, <lb/>il eſt encore ſoutenu par cette corde, comme il le <lb/>ſeroit par le pieu C H. </s> |
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467 <s xml:id="echoid-s245" xml:space="preserve">Et pour la même raiſon il <lb/>eſt ſoutenu par la corde R N, comme il le ſeroit par <lb/>le pieu D H: </s> |
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468 <s xml:id="echoid-s246" xml:space="preserve">Donc il eſt ſoutenu par ces deux cor-<lb/>des, comme il le ſeroit par ces deux pieux enſemble: <lb/></s> |
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469 <s xml:id="echoid-s247" xml:space="preserve">& </s> |
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470 <s xml:id="echoid-s248" xml:space="preserve">par conſéquent ( Lemm. </s> |
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471 <s xml:id="echoid-s249" xml:space="preserve">1. </s> |
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472 <s xml:id="echoid-s250" xml:space="preserve">) la ligne de direction <lb/>A K de ce poids ainſi ſuſpendu, paſſera encore par le <lb/>point H. </s> |
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473 <s xml:id="echoid-s251" xml:space="preserve">Ce qu’il F. </s> |
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474 <s xml:id="echoid-s252" xml:space="preserve">D.</s> |
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475 <s xml:id="echoid-s253" xml:space="preserve"/> |
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476 </p> |
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477 </div> |
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478 <div xml:id="echoid-div22" type="section" level="1" n="16"> |
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479 <head xml:id="echoid-head16" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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480 <p> |
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481 <s xml:id="echoid-s254" xml:space="preserve">De-là il eſt clair que de quelque côté que tende <lb/>le corps M N, & </s> |
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482 <s xml:id="echoid-s255" xml:space="preserve">que ſa ligne de direction ſoit tour-<lb/>née, ſoit que cette impreſſion lui vienne de ſa pe-<lb/>ſanteur, ou de quelque autre force, cette ligne de <lb/>direction paſſera toûjours par le point H, ou les cor-<lb/>des qui le retiennent, doivent concourir, ou con-<lb/>courent en effet.</s> |
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483 <s xml:id="echoid-s256" xml:space="preserve"/> |
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484 </p> |
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485 </div> |
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486 <div xml:id="echoid-div23" type="section" level="1" n="17"> |
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487 <head xml:id="echoid-head17" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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488 <p> |
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489 <s xml:id="echoid-s257" xml:space="preserve">De ſorte que ſi ces cordes ne concourent qu’à une <lb/>diſtance infinie, c’eſt-à-dire qu’elles ſoient paralleles <lb/>entre-elles, cette ligne de direction ſera auſſi parallele <lb/>à l’une & </s> |
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490 <s xml:id="echoid-s258" xml:space="preserve">à l’autre.</s> |
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491 <s xml:id="echoid-s259" xml:space="preserve"/> |
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492 </p> |
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493 <figure> |
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494 <image file="0031-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0031-01"/> |
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495 </figure> |
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496 <pb o="6" file="0032" n="32" rhead="NOUVELLE"/> |
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497 <note position="left" xml:space="preserve">LEMMES.</note> |
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498 <figure> |
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499 <image file="0032-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0032-01"/> |
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500 </figure> |
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501 </div> |
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502 <div xml:id="echoid-div24" type="section" level="1" n="18"> |
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503 <head xml:id="echoid-head18" xml:space="preserve">LEMME III.</head> |
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504 <p style="it"> |
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505 <s xml:id="echoid-s260" xml:space="preserve">SI le point A ſans peſanteur eſt pouſſé en même tems, <lb/> |
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506 <anchor type="note" xlink:label="note-0032-02a" xlink:href="note-0032-02"/> |
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507 & </s> |
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508 <s xml:id="echoid-s261" xml:space="preserve">uniformément par deux puiſſances E & </s> |
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509 <s xml:id="echoid-s262" xml:space="preserve">F ſuivant <lb/>les lignes A C & </s> |
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510 <s xml:id="echoid-s263" xml:space="preserve">A B, qui faſſent entre-elles quelque an-<lb/>gle C A B que ce ſoit, & </s> |
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511 <s xml:id="echoid-s264" xml:space="preserve">que la force dont agit la puiſ-<lb/>ſance E, ſoit à celle dont agit la puiſſance F, comme A C <lb/>à A B. </s> |
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512 <s xml:id="echoid-s265" xml:space="preserve">Ce point A ſuivra la Diagonale A D du paral-<lb/>lelogramme B C fait ſous ces deux lignes.</s> |
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513 <s xml:id="echoid-s266" xml:space="preserve"/> |
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514 </p> |
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515 <div xml:id="echoid-div24" type="float" level="2" n="1"> |
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516 <note position="left" xlink:label="note-0032-02" xlink:href="note-0032-02a" xml:space="preserve">fig. 7.</note> |
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517 </div> |
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518 </div> |
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519 <div xml:id="echoid-div26" type="section" level="1" n="19"> |
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520 <head xml:id="echoid-head19" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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521 <p> |
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522 <s xml:id="echoid-s267" xml:space="preserve">Le point A pouſſé par la puiſſance E vers C D, <lb/>l’eſt de même que s’il y étoit porté avec la ligne A B <lb/>toûjours parallele à elle-même, de la même viteſſe <lb/>qu’il y eſt pouſſé; </s> |
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523 <s xml:id="echoid-s268" xml:space="preserve">Nous pouvons donc le regarder <lb/>comme pouſſé de cette maniére vers C D avec la <lb/>ligne A B toûjours parallelle à elle-même, ou à C D, <lb/>au même tems qu’il eſt pouſſé par la puiſſance F <lb/>le long de la même ligne A B. </s> |
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524 <s xml:id="echoid-s269" xml:space="preserve">Or cela bien conçu, <lb/>il eſt clair qu’en quelque point, par exemple G, que <lb/>la ligne A B rencontre A D, le point A s’y trouvera <lb/>toûjours: </s> |
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525 <s xml:id="echoid-s270" xml:space="preserve">parce que la force qui le porte avec A B <lb/>vers C D, eſt à celle qui le porte le long de la mê-<lb/>me A B, comme ( byp. </s> |
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526 <s xml:id="echoid-s271" xml:space="preserve">) A C à A B; </s> |
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527 <s xml:id="echoid-s272" xml:space="preserve">c’eſt-à-dire, en <lb/>tirant H K par le point G parallele à A B, comme <lb/>A K à K G: </s> |
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528 <s xml:id="echoid-s273" xml:space="preserve">Donc ( ax. </s> |
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529 <s xml:id="echoid-s274" xml:space="preserve">) au même tems que A B <lb/>parcourt A K, & </s> |
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530 <s xml:id="echoid-s275" xml:space="preserve">qu’elle arrive avec le point A en <lb/>H K, ce même point parcourt une partie de A B <lb/>égale à K G; </s> |
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531 <s xml:id="echoid-s276" xml:space="preserve">& </s> |
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532 <s xml:id="echoid-s277" xml:space="preserve">par conſéquent il ſe trouve alors <lb/>en G. </s> |
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533 <s xml:id="echoid-s278" xml:space="preserve">On démontrera de même qu’au même tems <lb/>que A B arrive en C D, le point A ſe trouve en D; <lb/></s> |
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534 <s xml:id="echoid-s279" xml:space="preserve">& </s> |
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535 <s xml:id="echoid-s280" xml:space="preserve">ainſi dans tous les autres points de la Diagona-<lb/>le A D: </s> |
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536 <s xml:id="echoid-s281" xml:space="preserve">& </s> |
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537 <s xml:id="echoid-s282" xml:space="preserve">par conſéquent ce point ainſi pouſſé ſe |
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538 <pb o="7" file="0033" n="33" rhead="ME’CHANIQUE."/> |
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539 meuvra exactement le long de cette ligne. </s> |
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540 <s xml:id="echoid-s283" xml:space="preserve">Ce qu’il <lb/> |
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541 <anchor type="note" xlink:label="note-0033-01a" xlink:href="note-0033-01"/> |
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542 F. </s> |
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543 <s xml:id="echoid-s284" xml:space="preserve">D.</s> |
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544 <s xml:id="echoid-s285" xml:space="preserve"/> |
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545 </p> |
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546 <div xml:id="echoid-div26" type="float" level="2" n="1"> |
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547 <note position="right" xlink:label="note-0033-01" xlink:href="note-0033-01a" xml:space="preserve">LEMMES.</note> |
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548 </div> |
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549 </div> |
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550 <div xml:id="echoid-div28" type="section" level="1" n="20"> |
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551 <head xml:id="echoid-head20" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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552 <p> |
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553 <s xml:id="echoid-s286" xml:space="preserve">Quand bien même les forces dont agiſſent les puiſ-<lb/>ſances E & </s> |
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554 <s xml:id="echoid-s287" xml:space="preserve">F augmenteroient ou diminuëroient, <lb/>pourvu que ce fut ſuivant la même proportion de <lb/>part & </s> |
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555 <s xml:id="echoid-s288" xml:space="preserve">d’autre; </s> |
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556 <s xml:id="echoid-s289" xml:space="preserve">ce même point ſe meuvroit encore <lb/>exactement le long de A D: </s> |
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557 <s xml:id="echoid-s290" xml:space="preserve">parce que ces forces <lb/>ſeroient encore entre-elles comme A C à A B, ou <lb/>comme A K à K G.</s> |
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558 <s xml:id="echoid-s291" xml:space="preserve"/> |
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559 </p> |
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560 </div> |
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561 <div xml:id="echoid-div29" type="section" level="1" n="21"> |
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562 <head xml:id="echoid-head21" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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563 <p> |
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564 <s xml:id="echoid-s292" xml:space="preserve">C’eſt la même choſe que le point A ſoit pouſſé le <lb/>long de A D par le concours d’action des puiſſances <lb/>E & </s> |
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565 <s xml:id="echoid-s293" xml:space="preserve">F, ou qu’il y ſoit pouſſé par une ſeule puiſſance <lb/>d’une viteſſe égale à celle que lui cauſent ces deux <lb/>enſemble.</s> |
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566 <s xml:id="echoid-s294" xml:space="preserve"/> |
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567 </p> |
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568 </div> |
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569 <div xml:id="echoid-div30" type="section" level="1" n="22"> |
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570 <head xml:id="echoid-head22" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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571 <p> |
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572 <s xml:id="echoid-s295" xml:space="preserve">Puiſque le point A parcourt A D & </s> |
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573 <s xml:id="echoid-s296" xml:space="preserve">A B en même <lb/>tems, la force, ou le compoſé de forces, qui le pouſ-<lb/>ſe le long de A D, eſt à celle qui le pouſſe le long <lb/>de A B, ( ax. </s> |
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574 <s xml:id="echoid-s297" xml:space="preserve">) comme A D à A B. </s> |
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575 <s xml:id="echoid-s298" xml:space="preserve">Et pour la même <lb/>raiſon, elle eſt à celle dont il eſt pouſſé le long de <lb/>A C, comme A D à A C.</s> |
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576 <s xml:id="echoid-s299" xml:space="preserve"/> |
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577 </p> |
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578 <figure> |
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579 <image file="0033-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0033-01"/> |
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580 </figure> |
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581 </div> |
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582 <div xml:id="echoid-div31" type="section" level="1" n="23"> |
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583 <head xml:id="echoid-head23" xml:space="preserve">LEMME IV.</head> |
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584 <p style="it"> |
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585 <s xml:id="echoid-s300" xml:space="preserve">PRèſentement que le point A ſoit le centre de diréction <lb/> |
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586 <anchor type="note" xlink:label="note-0033-02a" xlink:href="note-0033-02"/> |
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587 du corps E F, & </s> |
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588 <s xml:id="echoid-s301" xml:space="preserve">que ce corps ſoit pouſſè en même tems <lb/>& </s> |
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589 <s xml:id="echoid-s302" xml:space="preserve">uniformèment par deux puiſſances appliquées en E & </s> |
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590 <s xml:id="echoid-s303" xml:space="preserve"><lb/>en F, ſuivant les lignes E C & </s> |
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591 <s xml:id="echoid-s304" xml:space="preserve">F B, qui paſſent par le <lb/>point A, avec des forces qui ſoient entr’elles comme A C |
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592 <pb o="8" file="0034" n="34" rhead="NOUVELLE"/> |
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593 & </s> |
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594 <s xml:id="echoid-s305" xml:space="preserve">A B: </s> |
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595 <s xml:id="echoid-s306" xml:space="preserve">que l’on acbeve le parallelogramme B C, & </s> |
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596 <s xml:id="echoid-s307" xml:space="preserve">que <lb/> |
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597 <anchor type="note" xlink:label="note-0034-01a" xlink:href="note-0034-01"/> |
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598 l’on regarde pour un moment ce corps comme s’il n’avoit au-<lb/>cune peſanteur. </s> |
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599 <s xml:id="echoid-s308" xml:space="preserve">Quelque angle BAC que ces lignes faſſe<unsure/>nt <lb/>entr’elles, ce corps ainſi pouſſè ſuivra la diagonale A D.</s> |
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600 <s xml:id="echoid-s309" xml:space="preserve"/> |
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601 </p> |
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602 <div xml:id="echoid-div31" type="float" level="2" n="1"> |
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603 <note position="right" xlink:label="note-0033-02" xlink:href="note-0033-02a" xml:space="preserve">fig. 8.</note> |
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604 <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">LEMMES.</note> |
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605 </div> |
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606 </div> |
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607 <div xml:id="echoid-div33" type="section" level="1" n="24"> |
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608 <head xml:id="echoid-head24" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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609 <p> |
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610 <s xml:id="echoid-s310" xml:space="preserve">Les lignes EC & </s> |
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611 <s xml:id="echoid-s311" xml:space="preserve">FB, ſuivant leſquelles les puiſ-<lb/>ſances E & </s> |
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612 <s xml:id="echoid-s312" xml:space="preserve">F agiſſent, paſſant ( byp. </s> |
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613 <s xml:id="echoid-s313" xml:space="preserve">) par le point A, <lb/>il eſt pouſſé en même-tems, & </s> |
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614 <s xml:id="echoid-s314" xml:space="preserve">uniformement ſuivant <lb/>ces mêmes lignes vers CD & </s> |
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615 <s xml:id="echoid-s315" xml:space="preserve">BD, par des forces <lb/>qui ſont entr’elles, ( byp. </s> |
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616 <s xml:id="echoid-s316" xml:space="preserve">) comme A C à A B: </s> |
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617 <s xml:id="echoid-s317" xml:space="preserve">Donc <lb/>( Lem. </s> |
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618 <s xml:id="echoid-s318" xml:space="preserve">3. </s> |
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619 <s xml:id="echoid-s319" xml:space="preserve">) le point A, & </s> |
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620 <s xml:id="echoid-s320" xml:space="preserve">par conſéquent auſſi <lb/>( Dem. </s> |
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621 <s xml:id="echoid-s321" xml:space="preserve">) le corps EF ſuivra la diagonale AD. </s> |
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622 <s xml:id="echoid-s322" xml:space="preserve">Ce <lb/>qu’il F. </s> |
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623 <s xml:id="echoid-s323" xml:space="preserve">D.</s> |
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624 <s xml:id="echoid-s324" xml:space="preserve"/> |
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625 </p> |
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626 </div> |
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627 <div xml:id="echoid-div34" type="section" level="1" n="25"> |
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628 <head xml:id="echoid-head25" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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629 <p> |
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630 <s xml:id="echoid-s325" xml:space="preserve">On voit que c’eſt la même choſe que le corps EF <lb/>ſoit pouſſé ſuivant AD par le concours d’action de <lb/>deux puiſſances appliquées en E, & </s> |
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631 <s xml:id="echoid-s326" xml:space="preserve">en F, ſuivant <lb/>des lignes EC & </s> |
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632 <s xml:id="echoid-s327" xml:space="preserve">FB qui paſſent par ſon centre de <lb/>gravité A, ou qu’il y ſoit pouſſé par une ſimple <lb/>puiſſance d’une viteſſe égale à celle que lui cauſent <lb/>ces deux enſemble: </s> |
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633 <s xml:id="echoid-s328" xml:space="preserve">de ſorte que ſi AD étoit perpen-<lb/>diculaire à l’horizon, & </s> |
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634 <s xml:id="echoid-s329" xml:space="preserve">que la peſanteur, que nous <lb/>concevons préſentement être dans ce corps, l’em-<lb/>portât le long de cette ligne avec une ſemblable vi-<lb/>teſſe, il la ſuivroit de même que s’il n’avoit en effet <lb/>aucune peſanteur, & </s> |
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635 <s xml:id="echoid-s330" xml:space="preserve">qu’il fût pouſſé de la maniére <lb/>que nous venons de dire, par les deux puiſſances <lb/>E & </s> |
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636 <s xml:id="echoid-s331" xml:space="preserve">F.</s> |
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637 <s xml:id="echoid-s332" xml:space="preserve"/> |
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638 </p> |
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639 </div> |
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640 <div xml:id="echoid-div35" type="section" level="1" n="26"> |
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641 <head xml:id="echoid-head26" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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642 <p> |
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643 <s xml:id="echoid-s333" xml:space="preserve">C’eſt pour cela auſſi que ce corps étant pouſſé par <lb/>ſa peſanteur ſuivant A D perpendiculaire à l’hori-<lb/>zon, s’il lui ſurvenoit quelqu’autre force qui le |
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644 <pb o="9" file="0035" n="35" rhead="ME’CHANIQUE."/> |
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645 pouſſât de même ſuivant quelqu’autre ligne qui ren-<lb/> |
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646 <anchor type="note" xlink:label="note-0035-01a" xlink:href="note-0035-01"/> |
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647 contrât celle-cy; </s> |
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648 <s xml:id="echoid-s334" xml:space="preserve">Quelque angle que ces deux lignes <lb/>fiſſent entr’elles, ce corps ſuivroit la diagonale d’un <lb/>parallelogramme fait ſous des parties de ces lignes, <lb/>qui depuis le point de leur rencontre, fuſſent entre-<lb/>elles, comme la peſanteur de ce poids & </s> |
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649 <s xml:id="echoid-s335" xml:space="preserve">cette nou-<lb/>velle force: </s> |
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650 <s xml:id="echoid-s336" xml:space="preserve">Il la ſuivroit, dis-je, de la même <lb/>maniére que s’il n’étoit pouſſé que par une ſeule <lb/>puiſſance ſuivant cette diréction, & </s> |
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651 <s xml:id="echoid-s337" xml:space="preserve">d’une viteſſe <lb/>égale à celle que lui pouroient cauſer ces deux en-<lb/>ſemble.</s> |
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652 <s xml:id="echoid-s338" xml:space="preserve"/> |
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653 </p> |
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654 <div xml:id="echoid-div35" type="float" level="2" n="1"> |
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655 <note position="right" xlink:label="note-0035-01" xlink:href="note-0035-01a" xml:space="preserve">LEMMES.</note> |
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656 </div> |
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657 </div> |
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658 <div xml:id="echoid-div37" type="section" level="1" n="27"> |
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659 <head xml:id="echoid-head27" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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660 <p> |
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661 <s xml:id="echoid-s339" xml:space="preserve">Il ſuit encore de cette propoſition, & </s> |
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662 <s xml:id="echoid-s340" xml:space="preserve">du Corol-<lb/>laire 3. </s> |
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663 <s xml:id="echoid-s341" xml:space="preserve">du Lemme 3.</s> |
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664 <s xml:id="echoid-s342" xml:space="preserve">, que la force dont le corps E F <lb/>eſt pouſſé le long de A D, eſt à celle dont la puiſ-<lb/>ſance F le pouſſe le long de A B, comme A D à A B; <lb/></s> |
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665 <s xml:id="echoid-s343" xml:space="preserve">& </s> |
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666 <s xml:id="echoid-s344" xml:space="preserve">à celle dont la puiſſance E le pouſſe le long de A C, <lb/>comme A D à A C.</s> |
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667 <s xml:id="echoid-s345" xml:space="preserve"/> |
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668 </p> |
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669 <figure> |
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670 <image file="0035-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0035-01"/> |
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671 </figure> |
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672 </div> |
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673 <div xml:id="echoid-div38" type="section" level="1" n="28"> |
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674 <head xml:id="echoid-head28" xml:space="preserve">LEMME V.</head> |
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675 <p style="it"> |
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676 <s xml:id="echoid-s346" xml:space="preserve">L E S trois côtez d’un triangle réctiligne, quel qu’il ſoit, <lb/> |
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677 <anchor type="note" xlink:label="note-0035-02a" xlink:href="note-0035-02"/> |
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678 ſont entr’eux, comme les ſinus des angles auſquels ils <lb/>ſont ooppoſez.</s> |
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679 <s xml:id="echoid-s347" xml:space="preserve"/> |
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680 </p> |
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681 <div xml:id="echoid-div38" type="float" level="2" n="1"> |
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682 <note position="right" xlink:label="note-0035-02" xlink:href="note-0035-02a" xml:space="preserve">fig 9.</note> |
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683 </div> |
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684 </div> |
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685 <div xml:id="echoid-div40" type="section" level="1" n="29"> |
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686 <head xml:id="echoid-head29" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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687 <p> |
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688 <s xml:id="echoid-s348" xml:space="preserve">Soit ABD tel triangle réctiligne qu’on voudra, <lb/>inſcrit dans un cercle, dont C ſoit le centre; </s> |
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689 <s xml:id="echoid-s349" xml:space="preserve">ſur <lb/>quelqu’un de ſes côtez, comme A B, ſoit menée du <lb/>centre C la perpendiculaire C E avec la ligne C A. <lb/></s> |
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690 <s xml:id="echoid-s350" xml:space="preserve">Il eſt clair que A E eſt le ſinus de l’angle A C E, <lb/>qui eſt égal à l’angle D; </s> |
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691 <s xml:id="echoid-s351" xml:space="preserve">Donc A B eſt le double du |
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692 <pb o="10" file="0036" n="36" rhead="NOUVELLE"/> |
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693 ſinus de l’angle D. </s> |
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694 <s xml:id="echoid-s352" xml:space="preserve">Et pour la même raiſon, BD eſt <lb/> |
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695 <anchor type="note" xlink:label="note-0036-01a" xlink:href="note-0036-01"/> |
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696 le double du ſinus de l’angle BAD; </s> |
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697 <s xml:id="echoid-s353" xml:space="preserve">& </s> |
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698 <s xml:id="echoid-s354" xml:space="preserve">AD le dou-<lb/>ble auſſi de celui de l’angle B: </s> |
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699 <s xml:id="echoid-s355" xml:space="preserve">Donc les trois côtez <lb/>de cetriangle ſont entr’eux, comme le double du ſinus <lb/>de chacun des angles auſquels ils ſont oppoſez: </s> |
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700 <s xml:id="echoid-s356" xml:space="preserve">Donc <lb/>ils ſont auſſi entr’eux, comme ces mêmes ſinus. </s> |
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701 <s xml:id="echoid-s357" xml:space="preserve">Ce <lb/>qu’il F. </s> |
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702 <s xml:id="echoid-s358" xml:space="preserve">D.</s> |
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703 <s xml:id="echoid-s359" xml:space="preserve"/> |
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704 </p> |
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705 <div xml:id="echoid-div40" type="float" level="2" n="1"> |
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706 <note position="left" xlink:label="note-0036-01" xlink:href="note-0036-01a" xml:space="preserve">LEMMES.</note> |
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707 </div> |
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708 <figure> |
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709 <image file="0036-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0036-01"/> |
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710 </figure> |
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711 <pb o="11" file="0037" n="37" rhead="MECHANIQUE."/> |
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712 <figure> |
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713 <image file="0037-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0037-01"/> |
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714 </figure> |
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715 </div> |
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716 <div xml:id="echoid-div42" type="section" level="1" n="30"> |
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717 <head xml:id="echoid-head30" xml:space="preserve">PROPOSITION <lb/>FONDAMENTALE <lb/>DES POIDS SUSPENDUS <lb/>AVEC DES CORDES</head> |
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718 <p> |
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719 <s xml:id="echoid-s360" xml:space="preserve">En quelque nombre qu’elles ſoient; </s> |
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720 <s xml:id="echoid-s361" xml:space="preserve">& </s> |
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721 <s xml:id="echoid-s362" xml:space="preserve">pour <lb/>tousles angles poſſibles qu’elles peuvent faire <lb/>entre-elles.</s> |
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722 <s xml:id="echoid-s363" xml:space="preserve"/> |
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723 </p> |
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724 <p style="it"> |
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725 <s xml:id="echoid-s364" xml:space="preserve">LE Poids K ſoutenu avec les cordes P B & </s> |
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726 <s xml:id="echoid-s365" xml:space="preserve">C R par <lb/> |
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727 <anchor type="note" xlink:label="note-0037-01a" xlink:href="note-0037-01"/> |
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728 les puiſſances P & </s> |
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729 <s xml:id="echoid-s366" xml:space="preserve">R, & </s> |
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730 <s xml:id="echoid-s367" xml:space="preserve">en équilibre avec elles, eſt <lb/>toujours à cbacune d’elles, comme le ſinus de l’angle P A R que <lb/>leurs cordes font entre-elles, à chacun des ſinus des angles <lb/>RAK & </s> |
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731 <s xml:id="echoid-s368" xml:space="preserve">PAK que font avec la ligne de direction AK <lb/>de ce poids, chacune de ces cordes réciproquement priſes. </s> |
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732 <s xml:id="echoid-s369" xml:space="preserve">Par <lb/>exemple, il eſt à la puiſſance P, comme le ſinus de R A P <lb/>au ſinus de R A K; </s> |
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733 <s xml:id="echoid-s370" xml:space="preserve">& </s> |
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734 <s xml:id="echoid-s371" xml:space="preserve">à la puiſſance R, comme le mème <lb/>ſinus de R A P au ſinus de P A K.</s> |
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735 <s xml:id="echoid-s372" xml:space="preserve"/> |
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736 </p> |
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737 <div xml:id="echoid-div42" type="float" level="2" n="1"> |
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738 <note position="right" xlink:label="note-0037-01" xlink:href="note-0037-01a" xml:space="preserve">fig. 10. <lb/>11. <lb/>12. <lb/>13. <lb/>14. <lb/>15. <lb/>16. <lb/>17.</note> |
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739 </div> |
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740 </div> |
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741 <div xml:id="echoid-div44" type="section" level="1" n="31"> |
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742 <head xml:id="echoid-head31" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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743 <p> |
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744 <s xml:id="echoid-s373" xml:space="preserve">Les impreſſions particuliéres que font les puiſſances <lb/>P & </s> |
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745 <s xml:id="echoid-s374" xml:space="preserve">R, ſur le point A de ce corps, (fig. </s> |
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746 <s xml:id="echoid-s375" xml:space="preserve">10. </s> |
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747 <s xml:id="echoid-s376" xml:space="preserve">11. </s> |
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748 <s xml:id="echoid-s377" xml:space="preserve">12. <lb/></s> |
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749 <s xml:id="echoid-s378" xml:space="preserve">13. </s> |
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750 <s xml:id="echoid-s379" xml:space="preserve">& </s> |
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751 <s xml:id="echoid-s380" xml:space="preserve">14.) </s> |
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752 <s xml:id="echoid-s381" xml:space="preserve">ou de ſa corde, (fig. </s> |
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753 <s xml:id="echoid-s382" xml:space="preserve">15.) </s> |
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754 <s xml:id="echoid-s383" xml:space="preserve">étant les mê-<lb/>mes qu’elles feroient, ſi elles le pouſſoient chacune <lb/>ſuivant ſa ligne de direction AP & </s> |
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755 <s xml:id="echoid-s384" xml:space="preserve">AR: </s> |
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756 <s xml:id="echoid-s385" xml:space="preserve">1°. </s> |
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757 <s xml:id="echoid-s386" xml:space="preserve">Ce |
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758 <pb o="12" file="0038" n="38" rhead="NOUVELLE"/> |
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759 point regardé comme tiré ſeulement par ces deux <lb/> |
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760 <anchor type="note" xlink:label="note-0038-01a" xlink:href="note-0038-01"/> |
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761 puiſſances, doit tendre (Lemm. </s> |
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762 <s xml:id="echoid-s387" xml:space="preserve">3.) </s> |
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763 <s xml:id="echoid-s388" xml:space="preserve">le long de quelque <lb/>ligne AD, quiſoit la diagonale d’un parallelogramme <lb/>fait ſous des parties AB & </s> |
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764 <s xml:id="echoid-s389" xml:space="preserve">AC des lignes de direction <lb/>des puiſſances P & </s> |
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765 <s xml:id="echoid-s390" xml:space="preserve">R, qui ſoient entre-elles, comme <lb/>ces mêmes puiſſances. </s> |
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766 <s xml:id="echoid-s391" xml:space="preserve">2°. </s> |
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767 <s xml:id="echoid-s392" xml:space="preserve">Cette ligne AD doit être <lb/>la même que la ligne de direction A K de ce poids <lb/>prolongée du côté de D: </s> |
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768 <s xml:id="echoid-s393" xml:space="preserve">autrement ces lignes A K <lb/>& </s> |
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769 <s xml:id="echoid-s394" xml:space="preserve">AD faiſant en A quelque angle entre-elles, ce <lb/>point ainſi pouſſé, ou tiré ſuivant la ligne AD par <lb/>le concours d’action de ces puiſſances, & </s> |
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770 <s xml:id="echoid-s395" xml:space="preserve">à même <lb/>tems ſuivant ſa ligne de direction A K par la peſan-<lb/>teur du poids K, devroit (Lemm. </s> |
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771 <s xml:id="echoid-s396" xml:space="preserve">3.) </s> |
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772 <s xml:id="echoid-s397" xml:space="preserve">ſuivre une <lb/>troiſiéme ligne qui fût la Diagonale d’un parallelo-<lb/>gramme fait ſous des parties de ces lignes priſes de-<lb/>puis A, & </s> |
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773 <s xml:id="echoid-s398" xml:space="preserve">qui fuſſent entre-elles, comme la force <lb/>dont ce point eſt tiré par ces puiſſances ſuivant AD, <lb/>eſt à la peſanteur du poids K; </s> |
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774 <s xml:id="echoid-s399" xml:space="preserve">ainſi ce poids ne ſeroit <lb/>plus en équilibre avec ces puiſſances, ce qui eſt contre <lb/>l’hypothêſe. </s> |
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775 <s xml:id="echoid-s400" xml:space="preserve">3°. </s> |
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776 <s xml:id="echoid-s401" xml:space="preserve">La force dont ce point eſt tiré ſuivant <lb/>AD, eſt auſſi égale à la peſanteur de ce poids; </s> |
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777 <s xml:id="echoid-s402" xml:space="preserve">au-<lb/>trement cette ligne étant la même que la ligne de di-<lb/>rection de ce poids, il ſe meuvroit encore en haut, ou <lb/>en bas ſelon la différence de ces forces, ce qui eſt <lb/>encore contre l’hypothêſe: </s> |
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778 <s xml:id="echoid-s403" xml:space="preserve">Donc ce point eſt tiré <lb/>de A vers D par le concours d’action des puiſſances <lb/>P & </s> |
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779 <s xml:id="echoid-s404" xml:space="preserve">R ſuivant la ligne de direction de ce poids, & </s> |
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780 <s xml:id="echoid-s405" xml:space="preserve"><lb/>d’une force êgale à ſa peſanteur. </s> |
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781 <s xml:id="echoid-s406" xml:space="preserve">Or la force dont il <lb/>eſt ainſi tiré de A vers D, eſt à celle dont la puiſ-<lb/>ſance P le tire à elle, comme (Lemm. </s> |
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782 <s xml:id="echoid-s407" xml:space="preserve">3. </s> |
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783 <s xml:id="echoid-s408" xml:space="preserve">Cor. </s> |
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784 <s xml:id="echoid-s409" xml:space="preserve">3.) </s> |
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785 <s xml:id="echoid-s410" xml:space="preserve">A D <lb/>à A B; </s> |
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786 <s xml:id="echoid-s411" xml:space="preserve">c’eſt-à-dire, (Lemm. </s> |
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787 <s xml:id="echoid-s412" xml:space="preserve">5.) </s> |
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788 <s xml:id="echoid-s413" xml:space="preserve">comme le ſinus de <lb/>l’angle D B A, ou de ſon complement PAR, (BC <lb/>eſt un parallelogramme) au ſinus de l’angle BDA, <lb/>ou de RAK égal à celui-ci, ou à ſon complement: <lb/></s> |
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789 <s xml:id="echoid-s414" xml:space="preserve">Donc ce poids eſt à la puiſſance P, comme le ſinus |
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790 <pb o="13" file="0039" n="39" rhead="MECHANIQUE."/> |
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791 de l’angle PAR, au ſinus de l’angle RAK. </s> |
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792 <s xml:id="echoid-s415" xml:space="preserve">On dé-<lb/> |
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793 <anchor type="note" xlink:label="note-0039-01a" xlink:href="note-0039-01"/> |
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794 montrera de même que ce même poids eſt à la puiſ-<lb/>ſance R, comme le même ſinus de l’angle PAR, au <lb/>ſinus de l’angle PAK.</s> |
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795 <s xml:id="echoid-s416" xml:space="preserve"/> |
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796 </p> |
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797 <div xml:id="echoid-div44" type="float" level="2" n="1"> |
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798 <note position="left" xlink:label="note-0038-01" xlink:href="note-0038-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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799 <note position="right" xlink:label="note-0039-01" xlink:href="note-0039-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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800 </div> |
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801 <p> |
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802 <s xml:id="echoid-s417" xml:space="preserve">Voilà pour les ſix premiers cas. </s> |
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803 <s xml:id="echoid-s418" xml:space="preserve">(fig. </s> |
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804 <s xml:id="echoid-s419" xml:space="preserve">10. </s> |
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805 <s xml:id="echoid-s420" xml:space="preserve">11. </s> |
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806 <s xml:id="echoid-s421" xml:space="preserve">12. </s> |
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807 <s xml:id="echoid-s422" xml:space="preserve">13. <lb/></s> |
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808 <s xml:id="echoid-s423" xml:space="preserve">14. </s> |
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809 <s xml:id="echoid-s424" xml:space="preserve">& </s> |
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810 <s xml:id="echoid-s425" xml:space="preserve">15.) </s> |
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811 <s xml:id="echoid-s426" xml:space="preserve">Pour les deux autres, (fig. </s> |
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812 <s xml:id="echoid-s427" xml:space="preserve">16. </s> |
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813 <s xml:id="echoid-s428" xml:space="preserve">& </s> |
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814 <s xml:id="echoid-s429" xml:space="preserve">17.) </s> |
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815 <s xml:id="echoid-s430" xml:space="preserve"><lb/>il ne faut que concevoir le poids K de telle figure <lb/>que le point A lui appartienne; </s> |
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816 <s xml:id="echoid-s431" xml:space="preserve">c’eſt-à-dire qu’il lui <lb/>ſoit continu, ſans àugmenter ny diminuër ſa peſan-<lb/>teur, ni ſans changer ſon centre de gravité, non <lb/>plus que les angles RAK & </s> |
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817 <s xml:id="echoid-s432" xml:space="preserve">PAK que font les <lb/>cordes que tiennent les puiſſances P & </s> |
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818 <s xml:id="echoid-s433" xml:space="preserve">R, avec ſa <lb/>ligne de direction A K. </s> |
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819 <s xml:id="echoid-s434" xml:space="preserve">Or cela bien conçu, il eſt <lb/>clair par ce qui vient d’être dit, que la peſanteur <lb/>de tout le poids K eſt égale à la force dont le point A <lb/>en ce cas ſeroit pouſſé, ou tiré de A vers D: </s> |
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820 <s xml:id="echoid-s435" xml:space="preserve">ainſi <lb/>une telle force étant (Lemm. </s> |
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821 <s xml:id="echoid-s436" xml:space="preserve">3. </s> |
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822 <s xml:id="echoid-s437" xml:space="preserve">Cor. </s> |
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823 <s xml:id="echoid-s438" xml:space="preserve">3.) </s> |
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824 <s xml:id="echoid-s439" xml:space="preserve">à celle de la <lb/>puiſſance P, comme AD à AB; </s> |
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825 <s xml:id="echoid-s440" xml:space="preserve">le poids K, qui eſt le <lb/>même (byp.) </s> |
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826 <s xml:id="echoid-s441" xml:space="preserve">que s’il avoit une telle figure, eſt encore <lb/>ici à la puiſſance P, qui eſt encore auſſi (byp) la même, <lb/>comme AD à AB; </s> |
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827 <s xml:id="echoid-s442" xml:space="preserve">c’eſt-à-dire, (Lemm. </s> |
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828 <s xml:id="echoid-s443" xml:space="preserve">5.) </s> |
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829 <s xml:id="echoid-s444" xml:space="preserve">comme <lb/>le ſinus de l’angle DBA, ou de ſon complement PAR, <lb/>au ſinus de l’angle BDA, ou de RAK qui lui eſt <lb/>égal; </s> |
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830 <s xml:id="echoid-s445" xml:space="preserve">& </s> |
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831 <s xml:id="echoid-s446" xml:space="preserve">de même à la puiſſance R, comme le ſinus <lb/>du même angle PAR au ſinus de l’angle PAK.</s> |
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832 <s xml:id="echoid-s447" xml:space="preserve"/> |
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833 </p> |
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834 <p> |
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835 <s xml:id="echoid-s448" xml:space="preserve">Et par conſéquent, quelque ſoit le poids K, & </s> |
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836 <s xml:id="echoid-s449" xml:space="preserve">de <lb/>quelque maniére qu’il ſoit ſoutenu avec les cordes <lb/>BP, & </s> |
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837 <s xml:id="echoid-s450" xml:space="preserve">CR par les puiſſances P & </s> |
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838 <s xml:id="echoid-s451" xml:space="preserve">R, il eſt toujours <lb/>à chacune de ces puiſſances, comme le ſinus de l’an-<lb/>gle que leurs cordes font entre-elles, à chacun des <lb/>ſinus des angles que font chacune de ces cordes ré-<lb/>ciproquement priſes avec ſa ligne de direction. </s> |
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839 <s xml:id="echoid-s452" xml:space="preserve">Ce <lb/>qu’il F. </s> |
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840 <s xml:id="echoid-s453" xml:space="preserve">D.</s> |
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841 <s xml:id="echoid-s454" xml:space="preserve"/> |
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842 </p> |
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843 <p style="it"> |
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844 <s xml:id="echoid-s455" xml:space="preserve">Ce ſeroit ici le lieu de répondre à la digreſſion que Monſieur |
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845 <pb o="14" file="0040" n="40" rhead="MECHANIQUE."/> |
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846 Borelli à faite contre ce ſentiment dans ſon Traité du mo u-<lb/> |
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847 <anchor type="note" xlink:label="note-0040-01a" xlink:href="note-0040-01"/> |
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848 vement des Animaux, tom. </s> |
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849 <s xml:id="echoid-s456" xml:space="preserve">1. </s> |
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850 <s xml:id="echoid-s457" xml:space="preserve">chap. </s> |
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851 <s xml:id="echoid-s458" xml:space="preserve">13. </s> |
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852 <s xml:id="echoid-s459" xml:space="preserve">Mais la bréveté <lb/>qu’on s’eſt propoſée dans cet eſſay, ne permet pas de s’étendre <lb/>ici autant qu’il faudroit pour cela: </s> |
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853 <s xml:id="echoid-s460" xml:space="preserve">On en verra dans peu <lb/>un examen particulier, où l’on fera voir en quoy cet Illuſtre <lb/>Autbeur s’eſt mépris.</s> |
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854 <s xml:id="echoid-s461" xml:space="preserve"/> |
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855 </p> |
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856 <div xml:id="echoid-div45" type="float" level="2" n="2"> |
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857 <note position="left" xlink:label="note-0040-01" xlink:href="note-0040-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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858 </div> |
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859 </div> |
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860 <div xml:id="echoid-div47" type="section" level="1" n="32"> |
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861 <head xml:id="echoid-head32" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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862 <p> |
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863 <s xml:id="echoid-s462" xml:space="preserve">Il ſuit de cette propoſition que les puiſſances P & </s> |
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864 <s xml:id="echoid-s463" xml:space="preserve"><lb/>R ſont entr’elles en raiſon réciproque des ſinus des <lb/>angles que font leurs lignes de direction avec celle <lb/>du poid qu’elles ſoutiennent, c’eſt-à-dire, en raiſon <lb/>réciproque des diſtances de leurs lignes de direction <lb/>à celle de ce poids.</s> |
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865 <s xml:id="echoid-s464" xml:space="preserve"/> |
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866 </p> |
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867 </div> |
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868 <div xml:id="echoid-div48" type="section" level="1" n="33"> |
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869 <head xml:id="echoid-head33" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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870 <p> |
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871 <s xml:id="echoid-s465" xml:space="preserve">D’où l’on voit qu’en mettant une troiſiéme puiſ-<lb/>ſance, dont le nom ſoit K, à la place de ce poids, <lb/>qui faſſe équilibre, comme lui, avec les deux P & </s> |
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872 <s xml:id="echoid-s466" xml:space="preserve">R <lb/>qui le ſoutiennent: </s> |
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873 <s xml:id="echoid-s467" xml:space="preserve">ces trois puiſſances K, P, & </s> |
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874 <s xml:id="echoid-s468" xml:space="preserve">R <lb/>ſeront entr’elles, comme les ſinus des angles P A R, <lb/>RAK, & </s> |
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875 <s xml:id="echoid-s469" xml:space="preserve">PAK.</s> |
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876 <s xml:id="echoid-s470" xml:space="preserve"/> |
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877 </p> |
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878 </div> |
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879 <div xml:id="echoid-div49" type="section" level="1" n="34"> |
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880 <head xml:id="echoid-head34" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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881 <p> |
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882 <s xml:id="echoid-s471" xml:space="preserve">D’où il ſuit, non ſeulement que chacune de ces <lb/>puiſſances, de quelque maniére qu’on les prenne, <lb/>eſt toûjours plus petite que la ſomme des deux autres, <lb/>de même que chacun de ces ſinus eſt toujours moin-<lb/>dre que la ſomme des deux autres.</s> |
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883 <s xml:id="echoid-s472" xml:space="preserve"/> |
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884 </p> |
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885 </div> |
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886 <div xml:id="echoid-div50" type="section" level="1" n="35"> |
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887 <head xml:id="echoid-head35" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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888 <p> |
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889 <s xml:id="echoid-s473" xml:space="preserve">Mais encore qu’elles ſont toutes trois priſes à <lb/>diſcrétion deux à deux, en raiſon réciproque des ſinus <lb/>des angles que font leurs cordes, ou leurs lignes de <lb/>diréction avec celle de la troiſiéme; </s> |
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890 <s xml:id="echoid-s474" xml:space="preserve">C’eſt-à-dire, |
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891 <pb o="15" file="0041" n="41" rhead="NOUVELLE"/> |
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892 en raiſon réciproque des diſtances de leurs lignes de <lb/> |
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893 <anchor type="note" xlink:label="note-0041-01a" xlink:href="note-0041-01"/> |
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894 diréction à quelque point que ce ſoit de celle de la <lb/>troiſiéme.</s> |
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895 <s xml:id="echoid-s475" xml:space="preserve"/> |
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896 </p> |
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897 <div xml:id="echoid-div50" type="float" level="2" n="1"> |
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898 <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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899 </div> |
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900 </div> |
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901 <div xml:id="echoid-div52" type="section" level="1" n="36"> |
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902 <head xml:id="echoid-head36" xml:space="preserve"><emph style="sc">Crollaire</emph> V.</head> |
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903 <p> |
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904 <s xml:id="echoid-s476" xml:space="preserve">Il ſuit encore de cette propoſition, que de quel-<lb/>que côté que tende le corps K, ſoit que cette impreſ-<lb/>ſion lui vienne de ſa peſanteur, ou de quelqu’autre <lb/>force; </s> |
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905 <s xml:id="echoid-s477" xml:space="preserve">celle de cette impreſſion, tant que ce corps <lb/>ſera en équilibre avec les puiſſances P & </s> |
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906 <s xml:id="echoid-s478" xml:space="preserve">R, ſera <lb/>toujours à celle dont chacune d’elles le retient, com-<lb/>me le ſinus de l’angle P A R que font leurs cordes <lb/>entr’elles, à chacun des ſinus des angles R A K & </s> |
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907 <s xml:id="echoid-s479" xml:space="preserve"><lb/>PAK, que font chacune de ces cordes réciproque-<lb/>ment priſes, avec la ligne de direction A K de ce <lb/>corps, qui paſſe toûjours (Lem. </s> |
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908 <s xml:id="echoid-s480" xml:space="preserve">2. </s> |
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909 <s xml:id="echoid-s481" xml:space="preserve">Cor. </s> |
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910 <s xml:id="echoid-s482" xml:space="preserve">1.) </s> |
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911 <s xml:id="echoid-s483" xml:space="preserve">par le <lb/>point A de leur concours.</s> |
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912 <s xml:id="echoid-s484" xml:space="preserve"/> |
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913 </p> |
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914 </div> |
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915 <div xml:id="echoid-div53" type="section" level="1" n="37"> |
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916 <head xml:id="echoid-head37" xml:space="preserve"><emph style="sc">Corollaire</emph> VI.</head> |
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917 <p> |
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918 <s xml:id="echoid-s485" xml:space="preserve">Ce qui fait voir que ſi l’angle de ces cordes étoit infi-<lb/>niment aigu, c’eſt-à-dire, qu’elles fuſſent paralleles <lb/>entre-elles, la force, quelle qu’elle fût, dont ce corps <lb/>agiroit contre ces puiſſances, ſeroit égale à la ſomme <lb/>de celles dont elles lui reſiſtent: </s> |
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919 <s xml:id="echoid-s486" xml:space="preserve">De ſorte que s’il <lb/>agiſſoit ſeulement comme poids, il ſeroit alors égal <lb/>à la ſomme de ces puiſſances; </s> |
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920 <s xml:id="echoid-s487" xml:space="preserve">& </s> |
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921 <s xml:id="echoid-s488" xml:space="preserve">chacune d’elle ſeroit <lb/>à l’autre en raiſon réciproque des diſtances de leurs <lb/>lignes de direction à celle de ce corps, ou de ce poids, <lb/>qui pour lors leur ſeroit (Lem. </s> |
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922 <s xml:id="echoid-s489" xml:space="preserve">2. </s> |
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923 <s xml:id="echoid-s490" xml:space="preserve">Cor. </s> |
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924 <s xml:id="echoid-s491" xml:space="preserve">2.) </s> |
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925 <s xml:id="echoid-s492" xml:space="preserve">auſſi parallele.</s> |
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926 <s xml:id="echoid-s493" xml:space="preserve"/> |
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927 </p> |
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928 </div> |
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929 <div xml:id="echoid-div54" type="section" level="1" n="38"> |
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930 <head xml:id="echoid-head38" xml:space="preserve"><emph style="sc">Corollaire</emph> VII.</head> |
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931 <p> |
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932 <s xml:id="echoid-s494" xml:space="preserve">Il ſuit de plus, que ſi le poids K eſt à chacune des <lb/>puiſſances P & </s> |
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933 <s xml:id="echoid-s495" xml:space="preserve">R, comme les ſinus de l’angle R A P, <lb/>à chacun des ſinus des angles R A K & </s> |
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934 <s xml:id="echoid-s496" xml:space="preserve">P A K, elles <lb/>le ſoutiendront en cet état, & </s> |
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935 <s xml:id="echoid-s497" xml:space="preserve">feront équilibre avec |
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936 <pb o="16" file="0042" n="42" rhead="MECHANIQUE."/> |
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937 lui: </s> |
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938 <s xml:id="echoid-s498" xml:space="preserve">Car ces deux puiſſances étant alors entr’elles, <lb/> |
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939 <anchor type="note" xlink:label="note-0042-01a" xlink:href="note-0042-01"/> |
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940 comme les ſinus des angles BDA & </s> |
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941 <s xml:id="echoid-s499" xml:space="preserve">BAD, c’eſt-à-<lb/>dire, (Lem. </s> |
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942 <s xml:id="echoid-s500" xml:space="preserve">5.) </s> |
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943 <s xml:id="echoid-s501" xml:space="preserve">comme AB à BD, ou à CA qui lui <lb/>eſt égale; </s> |
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944 <s xml:id="echoid-s502" xml:space="preserve">l’impreſſion compoſée qui réſulte du <lb/>concours d’action de ces deux puiſſances ſur le point <lb/>A, doit (Lem. </s> |
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945 <s xml:id="echoid-s503" xml:space="preserve">3.) </s> |
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946 <s xml:id="echoid-s504" xml:space="preserve">le faire tendre de A vers D ſui-<lb/>vant AD, d’une force qui ſoit à celle de chacune <lb/>de ces puiſſances P & </s> |
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947 <s xml:id="echoid-s505" xml:space="preserve">R, (Lem. </s> |
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948 <s xml:id="echoid-s506" xml:space="preserve">3. </s> |
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949 <s xml:id="echoid-s507" xml:space="preserve">Cor. </s> |
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950 <s xml:id="echoid-s508" xml:space="preserve">3.) </s> |
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951 <s xml:id="echoid-s509" xml:space="preserve">comme <lb/>AD eſt à chacun des côtez AB & </s> |
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952 <s xml:id="echoid-s510" xml:space="preserve">AC, ou BD, du <lb/>parallelogramme BC; </s> |
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953 <s xml:id="echoid-s511" xml:space="preserve">ou bien (Lemm. </s> |
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954 <s xml:id="echoid-s512" xml:space="preserve">5.) </s> |
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955 <s xml:id="echoid-s513" xml:space="preserve">comme <lb/>le ſinus de l’angle DBA, ou de ſon complement <lb/>PAR, à chacun des ſinus des angles BDA & </s> |
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956 <s xml:id="echoid-s514" xml:space="preserve">BAD, <lb/>ou de RAK & </s> |
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957 <s xml:id="echoid-s515" xml:space="preserve">de PAK, quileur ſontégaux, ou qui <lb/>ſont leurs complemens; </s> |
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958 <s xml:id="echoid-s516" xml:space="preserve">c’eſt-à-dire, (byp.) </s> |
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959 <s xml:id="echoid-s517" xml:space="preserve">comme <lb/>le poids K à chacune de ces puiſſances: </s> |
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960 <s xml:id="echoid-s518" xml:space="preserve">& </s> |
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961 <s xml:id="echoid-s519" xml:space="preserve">par conſé-<lb/>quent la force dont ces puiſſances tirent ou pouſſent <lb/>le point A de ce corps, ou de ſa corde vers D, eſt <lb/>égale à celle, dont il eſt tiré vers K ſuivant la même <lb/>ligne DK par la peſanteur de ce poids: </s> |
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962 <s xml:id="echoid-s520" xml:space="preserve">ainſi elles <lb/>le doivent ſoutenir en cet état, & </s> |
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963 <s xml:id="echoid-s521" xml:space="preserve">demeurer en équi-<lb/>libre avec lui.</s> |
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964 <s xml:id="echoid-s522" xml:space="preserve"/> |
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965 </p> |
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966 <div xml:id="echoid-div54" type="float" level="2" n="1"> |
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967 <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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968 </div> |
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969 </div> |
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970 <div xml:id="echoid-div56" type="section" level="1" n="39"> |
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971 <head xml:id="echoid-head39" xml:space="preserve"><emph style="sc">Corollaire</emph> VIII.</head> |
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972 <p> |
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973 <s xml:id="echoid-s523" xml:space="preserve">Ce qui fait voir que l’on peut faire ſoutenir quel-<lb/> |
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974 <anchor type="note" xlink:label="note-0042-02a" xlink:href="note-0042-02"/> |
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975 que grand poids K, que ce ſoit, à quelque puiſſance R <lb/>que ce puiſſe être par le moyen d’une corde ſeulement. <lb/></s> |
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976 <s xml:id="echoid-s524" xml:space="preserve">Il ne faut pour cela que de quelque point D comme <lb/>centre, avec le rayon A D perpendiculaire à l’hori-<lb/>zon, & </s> |
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977 <s xml:id="echoid-s525" xml:space="preserve">pris à diſcrétion, décrire l’arc A C B; </s> |
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978 <s xml:id="echoid-s526" xml:space="preserve">& </s> |
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979 <s xml:id="echoid-s527" xml:space="preserve">y <lb/>ayant inſcrit A C qui ſoit à A D, comme la puiſ-<lb/>ſance R au poids K, joignez D C, & </s> |
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980 <s xml:id="echoid-s528" xml:space="preserve">apres avoir <lb/>dirigé par le point A la corde A P de ce poids pa-<lb/>rallelement à C D, attachez-la au crochet P, & </s> |
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981 <s xml:id="echoid-s529" xml:space="preserve">luy <lb/>appliquez en A la puiſſance R ſuivant A C. </s> |
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982 <s xml:id="echoid-s530" xml:space="preserve">Il eſt <lb/>clair par le Corollaire précédent que cette puiſſance |
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983 <pb o="17" file="0043" n="43" rhead="MECHANIQUE."/> |
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984 étant (byp.) </s> |
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985 <s xml:id="echoid-s531" xml:space="preserve">à ce poids comme A C à A D; </s> |
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986 <s xml:id="echoid-s532" xml:space="preserve">c’eſt-à-<lb/> |
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987 <anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/> |
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988 dire, (Lemm. </s> |
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989 <s xml:id="echoid-s533" xml:space="preserve">5.) </s> |
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990 <s xml:id="echoid-s534" xml:space="preserve">comme le ſinus de l’angle D, ou <lb/>de ſon égal D A P, au ſinus de l’angle D C A, ou deſon <lb/>complement PAC; </s> |
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991 <s xml:id="echoid-s535" xml:space="preserve">elle ſe ſoutiendraen cet état.</s> |
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992 <s xml:id="echoid-s536" xml:space="preserve"/> |
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993 </p> |
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994 <div xml:id="echoid-div56" type="float" level="2" n="1"> |
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995 <note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">fig. 18.</note> |
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996 <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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997 </div> |
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998 </div> |
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999 <div xml:id="echoid-div58" type="section" level="1" n="40"> |
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1000 <head xml:id="echoid-head40" xml:space="preserve"><emph style="sc">Corollaire</emph> IX.</head> |
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1001 <p> |
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1002 <s xml:id="echoid-s537" xml:space="preserve">Ainſi il n’y a point de force R, quelque petite qu’on <lb/>l’imagine, qui ne ſoit capable de mouvoir quelque <lb/>grand poids K que ce ſoit, ſuſpendu à une corde, <lb/>& </s> |
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1003 <s xml:id="echoid-s538" xml:space="preserve">de le faire ſortir de la ligne PF qui tombe à plomb <lb/>de ſon point de ſuſpenſion: </s> |
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1004 <s xml:id="echoid-s539" xml:space="preserve">& </s> |
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1005 <s xml:id="echoid-s540" xml:space="preserve">cela, juſqu’à ce que <lb/>les ſinus des angles que font leurs lignes de direction <lb/>AC & </s> |
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1006 <s xml:id="echoid-s541" xml:space="preserve">AD avec AP, qui va du point où elles <lb/>concourent, à ce point de ſuſpenſion, ſoient en raiſon <lb/>réciproque de ce poids & </s> |
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1007 <s xml:id="echoid-s542" xml:space="preserve">de cette puiſſance.</s> |
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1008 <s xml:id="echoid-s543" xml:space="preserve"/> |
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1009 </p> |
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1010 </div> |
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1011 <div xml:id="echoid-div59" type="section" level="1" n="41"> |
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1012 <head xml:id="echoid-head41" xml:space="preserve"><emph style="sc">Corollaire</emph> X.</head> |
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1013 <p> |
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1014 <s xml:id="echoid-s544" xml:space="preserve">Et parce que ce mouvement eſt impoſſible, à moins <lb/>que ce poids ne monte de même que le point A de ſa <lb/>corde, du moins de la hauteur du ſinus verſe H E <lb/>de l’angle APE fait par la partie AP de ſa corde, <lb/>avec la ligne AF, qui tombe à plomb de ſon point A <lb/>de ſuſpenſion: </s> |
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1015 <s xml:id="echoid-s545" xml:space="preserve">il ſuit évidemment qu’il n’y a point <lb/>de force, quelque petite qu’on l’imagine, qui ne ſoit <lb/>capable de faire monter du moins à cette hauteur <lb/>quelque grand poids que ce ſoit à l’aide ſeulement <lb/>d’une corde attachée à quelque point fixe.</s> |
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1016 <s xml:id="echoid-s546" xml:space="preserve"/> |
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1017 </p> |
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1018 <p style="it"> |
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1019 <s xml:id="echoid-s547" xml:space="preserve">La raiſon pour laquelle on dit ici du moins, c’eſt pour <lb/>s’ accommoder à toute bypothêſe: </s> |
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1020 <s xml:id="echoid-s548" xml:space="preserve">car ſi l’on regarde les lignes <lb/>de direction des poids comme paralleles entre-elles, ce poids <lb/>monte-ici juſtement de cette hauteur; </s> |
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1021 <s xml:id="echoid-s549" xml:space="preserve">mais ſi elles concourent <lb/>en quelque endroit du monde, il doit néceſſairement monter <lb/>plus baut, & </s> |
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1022 <s xml:id="echoid-s550" xml:space="preserve">ce d’autant plus (quoi. </s> |
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1023 <s xml:id="echoid-s551" xml:space="preserve">qu’en proportion diffé-<lb/>rente) que l’angle que fait ſa ligne de direction avec celle qui |
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1024 <pb o="18" file="0044" n="44" rhead="NOUVELLE"/> |
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1025 tombe à plomb de ſon point de ſuſpenſion, lorſque ce poids <lb/> |
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1026 <anchor type="note" xlink:label="note-0044-01a" xlink:href="note-0044-01"/> |
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1027 n’eſt plus dans cette même ligne, eſt plus obtus. </s> |
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1028 <s xml:id="echoid-s552" xml:space="preserve">Tout cela eſt <lb/>clair; </s> |
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1029 <s xml:id="echoid-s553" xml:space="preserve">c’eſt pourquoi on ne s’y arrête pas davantage.</s> |
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1030 <s xml:id="echoid-s554" xml:space="preserve"/> |
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1031 </p> |
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1032 <div xml:id="echoid-div59" type="float" level="2" n="1"> |
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1033 <note position="left" xlink:label="note-0044-01" xlink:href="note-0044-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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1034 </div> |
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1035 </div> |
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1036 <div xml:id="echoid-div61" type="section" level="1" n="42"> |
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1037 <head xml:id="echoid-head42" xml:space="preserve"><emph style="sc">Corollaire</emph> XI.</head> |
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1038 <p> |
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1039 <s xml:id="echoid-s555" xml:space="preserve">Il ſuit encore du Corollaire 7. </s> |
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1040 <s xml:id="echoid-s556" xml:space="preserve">que ſi au lieu du <lb/> |
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1041 <anchor type="note" xlink:label="note-0044-02a" xlink:href="note-0044-02"/> |
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1042 poid K, on mettoit quelque nouvelle puiſſance, (quel-<lb/>le ſoit auſſi appellée K) qui fûtaux deux premiéres P <lb/>& </s> |
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1043 <s xml:id="echoid-s557" xml:space="preserve">R, commele ſinus de l’angle P A R, aux ſinus des <lb/>angles RAK, & </s> |
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1044 <s xml:id="echoid-s558" xml:space="preserve">PAK; </s> |
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1045 <s xml:id="echoid-s559" xml:space="preserve">c’eſt-à-dire, que ces trois <lb/>puiſſances K, P, & </s> |
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1046 <s xml:id="echoid-s560" xml:space="preserve">R fuſſent entr’elles, comme les <lb/>ſinus de ces trois angles PAR, RAK, & </s> |
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1047 <s xml:id="echoid-s561" xml:space="preserve">PAK; <lb/></s> |
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1048 <s xml:id="echoid-s562" xml:space="preserve">elles demeureroient en équilibre entr’elles, de ſorte <lb/>qu’aucune ne l’emporteroit ſur aucune autre.</s> |
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1049 <s xml:id="echoid-s563" xml:space="preserve"/> |
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1050 </p> |
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1051 <div xml:id="echoid-div61" type="float" level="2" n="1"> |
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1052 <note position="left" xlink:label="note-0044-02" xlink:href="note-0044-02a" xml:space="preserve">fig. 10. <lb/>11. <lb/>12. <lb/>13. <lb/>14. <lb/>15. <lb/>16. <lb/>17.</note> |
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1053 </div> |
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1054 </div> |
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1055 <div xml:id="echoid-div63" type="section" level="1" n="43"> |
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1056 <head xml:id="echoid-head43" xml:space="preserve"><emph style="sc">Corollaire</emph> XII.</head> |
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1057 <p> |
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1058 <s xml:id="echoid-s564" xml:space="preserve">Ce qui fait encore voir, que ſans rien changer à <lb/>l’inclinaiſon des cordes B P & </s> |
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1059 <s xml:id="echoid-s565" xml:space="preserve">C R de ces puiſſances, <lb/>une infinité d’autres miſes en leurs places, pouront <lb/>demeurer en équilibre trois à trois, pourvu qu’elles <lb/>ſoient entr’elles, comme ces trois premiéres.</s> |
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1060 <s xml:id="echoid-s566" xml:space="preserve"/> |
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1061 </p> |
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1062 </div> |
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1063 <div xml:id="echoid-div64" type="section" level="1" n="44"> |
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1064 <head xml:id="echoid-head44" xml:space="preserve"><emph style="sc">Corollaire</emph> XIII.</head> |
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1065 <p> |
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1066 <s xml:id="echoid-s567" xml:space="preserve">On peut auſſi en changeant l’inclinaiſon de ces <lb/>cordes conſerver l’équilibre de ces trois premiéres <lb/>puiſſances K, P, & </s> |
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1067 <s xml:id="echoid-s568" xml:space="preserve">R, dans ſix variations différentes <lb/>de leurs angles, pourvu que ces puiſſances faſſent <lb/>échange entr’elles de leurs cordes, juſqu’à ce que <lb/>chacune d’elles ſe trouve appliquée ſucceſſivement <lb/>à chacune de ces cordes pendant deux ſituations dif-<lb/>férentes des deux autres. </s> |
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1068 <s xml:id="echoid-s569" xml:space="preserve">Pour l’appercevoir il ne faut <lb/>que s’imaginer que lorſque deux de ces puiſſances, <lb/>par exemple P & </s> |
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1069 <s xml:id="echoid-s570" xml:space="preserve">R, font échange de leurs cordes, il <lb/>ſe fait en même-tems une échange des angles que <lb/>ces mêmes cordes faiſoient auparavant avec celle de |
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1070 <pb o="19" file="0045" n="45" rhead="MECHANIQUE."/> |
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1071 la puiſſance K, qui n’en change point alors, ſans qu’il <lb/> |
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1072 <anchor type="note" xlink:label="note-0045-01a" xlink:href="note-0045-01"/> |
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1073 arrive encore aucun changement à celui qu’elles font <lb/>entr’elles: </s> |
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1074 <s xml:id="echoid-s571" xml:space="preserve">de cette maniére l’on aura deux des cas <lb/>dont il eſt ici queſtion. </s> |
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1075 <s xml:id="echoid-s572" xml:space="preserve">On en trouvera encore deux <lb/>en concevant de même l’échange des angles qui ſe <lb/>fait dans l’échange des cordes de P & </s> |
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1076 <s xml:id="echoid-s573" xml:space="preserve">de K; </s> |
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1077 <s xml:id="echoid-s574" xml:space="preserve">& </s> |
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1078 <s xml:id="echoid-s575" xml:space="preserve">encore <lb/>deux pour l’échange de celles de K & </s> |
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1079 <s xml:id="echoid-s576" xml:space="preserve">de R: </s> |
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1080 <s xml:id="echoid-s577" xml:space="preserve">c’eſt ainſi <lb/>qu’on les aura tous ſix.</s> |
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1081 <s xml:id="echoid-s578" xml:space="preserve"/> |
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1082 </p> |
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1083 <div xml:id="echoid-div64" type="float" level="2" n="1"> |
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1084 <note position="right" xlink:label="note-0045-01" xlink:href="note-0045-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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1085 </div> |
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1086 </div> |
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1087 <div xml:id="echoid-div66" type="section" level="1" n="45"> |
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1088 <head xml:id="echoid-head45" xml:space="preserve"><emph style="sc">Corollaire</emph> XIV.</head> |
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1089 <p> |
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1090 <s xml:id="echoid-s579" xml:space="preserve">Mais tant que chacune de ces puiſſances demeure <lb/>appliquée à la même corde, l’on ne peut en changer <lb/>la direction, c’eſt-à-dire, l’inclinaiſon de ces cordes, <lb/>ſans en rompre l’équilibre; </s> |
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1091 <s xml:id="echoid-s580" xml:space="preserve">parce qu’il n’eſt pas poſ-<lb/>ſible de trouver ſeulement deux ſituations de cordes, <lb/>ou les ſinus de ces trois angles R A P, R A K, & </s> |
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1092 <s xml:id="echoid-s581" xml:space="preserve">P A K, <lb/>ayent le même raport entr’eux.</s> |
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1093 <s xml:id="echoid-s582" xml:space="preserve"/> |
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1094 </p> |
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1095 </div> |
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1096 <div xml:id="echoid-div67" type="section" level="1" n="46"> |
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1097 <head xml:id="echoid-head46" xml:space="preserve"><emph style="sc">Corollaire</emph> XV.</head> |
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1098 <p> |
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1099 <s xml:id="echoid-s583" xml:space="preserve">C’eſt ce qui fait que tout autant de fois que les <lb/>angles RAP, que font entr’elles les cordes des puiſ-<lb/>ſances P & </s> |
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1100 <s xml:id="echoid-s584" xml:space="preserve">R, ſont différens, les poids qu’elles ſou-<lb/>tiennent ſont différens auſſi. </s> |
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1101 <s xml:id="echoid-s585" xml:space="preserve">En effet plus cet angle <lb/>eſt obtus, plus le poids qu elles ſoutiennent, doit être <lb/>petit, quoi-qu’en proportion différente: </s> |
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1102 <s xml:id="echoid-s586" xml:space="preserve">puiſque plus <lb/>cet angle eſt obtus, moins eſt grande la raiſon de AD <lb/>à AB, & </s> |
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1103 <s xml:id="echoid-s587" xml:space="preserve">à BD; </s> |
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1104 <s xml:id="echoid-s588" xml:space="preserve">c’eſt-à-dire, (Lemm. </s> |
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1105 <s xml:id="echoid-s589" xml:space="preserve">5.) </s> |
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1106 <s xml:id="echoid-s590" xml:space="preserve">celle du <lb/>ſinus de l’angle DBA, ou de ſon complement PAR, <lb/>à chacun des ſinus de l’angle BDA, ou de RAK qui <lb/>lui eſt égal, ou ſon complement; </s> |
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1107 <s xml:id="echoid-s591" xml:space="preserve">& </s> |
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1108 <s xml:id="echoid-s592" xml:space="preserve">de l’angle BAD, <lb/>ou PAK encore égal à celui-ci, ou ſon complement: <lb/></s> |
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1109 <s xml:id="echoid-s593" xml:space="preserve">qui eſt juſtement celle que ce poids doit alors avoir à <lb/>chacune de ces puiſſances pour demeurer en équilibre <lb/>avec elles; </s> |
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1110 <s xml:id="echoid-s594" xml:space="preserve">De ſorte que cet angle peut être ſi obtus <lb/>que ces mêmes puiſſances pourront faire équilibre |
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1111 <pb o="20" file="0046" n="46" rhead="NOUVELLE"/> |
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1112 avec ce poids, quelque petit qu’il ſoit: </s> |
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1113 <s xml:id="echoid-s595" xml:space="preserve">c’eſt ainſi qu’il <lb/> |
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1114 <anchor type="note" xlink:label="note-0046-01a" xlink:href="note-0046-01"/> |
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1115 peut diminuer à l’infini, & </s> |
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1116 <s xml:id="echoid-s596" xml:space="preserve">faire cependant tou-<lb/>jours équilibre avec elles, que@ques grandes qu’on les <lb/>ſuppoſe.</s> |
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1117 <s xml:id="echoid-s597" xml:space="preserve"/> |
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1118 </p> |
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1119 <div xml:id="echoid-div67" type="float" level="2" n="1"> |
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1120 <note position="left" xlink:label="note-0046-01" xlink:href="note-0046-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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1121 </div> |
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1122 </div> |
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1123 <div xml:id="echoid-div69" type="section" level="1" n="47"> |
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1124 <head xml:id="echoid-head47" xml:space="preserve"><emph style="sc">Corollaire</emph> XVI.</head> |
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1125 <p> |
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1126 <s xml:id="echoid-s598" xml:space="preserve">Voilà ce qui peut arriver en changeant la direction <lb/>de l’une, & </s> |
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1127 <s xml:id="echoid-s599" xml:space="preserve">de l’autre de ces deux puiſſances; </s> |
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1128 <s xml:id="echoid-s600" xml:space="preserve">Mais à <lb/>n’en déplacer qu’une: </s> |
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1129 <s xml:id="echoid-s601" xml:space="preserve">1°. </s> |
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1130 <s xml:id="echoid-s602" xml:space="preserve">Si elles ſont égales, ou ſi <lb/>étant inégales, il s’en trouve une qui ait une direc-<lb/>tion horizontale, il eſt clair qu’on changeroit le ra-<lb/>port des ſinus des angles que leurs cordes font avec <lb/>la ligne de direction du poids qu’elles ſoutiennent: <lb/></s> |
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1131 <s xml:id="echoid-s603" xml:space="preserve">ainſi (Cor. </s> |
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1132 <s xml:id="echoid-s604" xml:space="preserve">I.) </s> |
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1133 <s xml:id="echoid-s605" xml:space="preserve">elles ne pouroient plus ſoutenir n’y ce <lb/>poids, ny aucun autre. </s> |
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1134 <s xml:id="echoid-s606" xml:space="preserve">2°. </s> |
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1135 <s xml:id="echoid-s607" xml:space="preserve">Au contraire ſi étant inéga-<lb/>les, elles n’ont aucune de leurs cordes qui ſoit hori-<lb/>zontale; </s> |
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1136 <s xml:id="echoid-s608" xml:space="preserve">au lieu du poids qu’elles ſoutiennent, on <lb/>poura encore leur en faire ſoutenir un autre, pourvu <lb/>qu’on change tellement celle de leurs directions qui <lb/>fait le plus grand angle avec celle du poids qu’elles <lb/>ſoutiennent, qu’on lui en faſſe faire un autre encore <lb/>avec elle, qui ſoit le complement du premier: </s> |
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1137 <s xml:id="echoid-s609" xml:space="preserve">Car <lb/>les ſinus des angles de leurs cordes avec la direction <lb/>du poids appliqué à leur point de concours, étant <lb/>encore les mêmes qu’auparavant, elles en pouront <lb/>encore ſoutenir un (Cor. </s> |
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1138 <s xml:id="echoid-s610" xml:space="preserve">II.) </s> |
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1139 <s xml:id="echoid-s611" xml:space="preserve">à qui elles ſeront com-<lb/>me ces mêmes ſinus réciproquement pris, à celui de <lb/>l’angle que feront alors leurs cordes entr’elles; </s> |
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1140 <s xml:id="echoid-s612" xml:space="preserve">c’eſt-<lb/>à-dire, qui ſera à celui qu’elles ſoutenoient aupara-<lb/>vant, comme ce dernier ſinus à celui de l’angle qu’el-<lb/>les faiſoient alors entr’elles. </s> |
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1141 <s xml:id="echoid-s613" xml:space="preserve">Mais auſſi par une raiſon <lb/>toute contraire en tout autre changement de cette <lb/>lignede direction ces deux puiſſances ne peuvent plus <lb/>rien ſoutenir.</s> |
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1142 <s xml:id="echoid-s614" xml:space="preserve"/> |
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1143 </p> |
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1144 <pb o="21" file="0047" n="47" rhead="MECHANIQUE."/> |
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1145 <p style="it"> |
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1146 <s xml:id="echoid-s615" xml:space="preserve">La raiſon pour laquelle on vient de demander que ce <lb/> |
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1147 <anchor type="note" xlink:label="note-0047-01a" xlink:href="note-0047-01"/> |
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1148 changement ſe fit dans celle des directions de ces puiſſances, qui <lb/>fait le plus grand angle avec celle du poids qu’elles ſoutien-<lb/>nent; </s> |
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1149 <s xml:id="echoid-s616" xml:space="preserve">c’eſt que ſi l’on faiſoit un tel cbangement à l’autre, l’an-<lb/>gle des cordes ſe tourneroit en deſſous, ce qui détermineroit <lb/>l’action de ces deux puiſſances à ſeconder ſa peſanteur, plutôt <lb/>qu’àla ſoutenir.</s> |
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1150 <s xml:id="echoid-s617" xml:space="preserve"/> |
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1151 </p> |
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1152 <div xml:id="echoid-div69" type="float" level="2" n="1"> |
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1153 <note position="right" xlink:label="note-0047-01" xlink:href="note-0047-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>d s cordes ſeu-<lb/>lement.</note> |
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1154 </div> |
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1155 </div> |
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1156 <div xml:id="echoid-div71" type="section" level="1" n="48"> |
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1157 <head xml:id="echoid-head48" xml:space="preserve"><emph style="sc">Corollaire</emph> XVII.</head> |
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1158 <p> |
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1159 <s xml:id="echoid-s618" xml:space="preserve">Puiſque ce poids pour faire équilibre avec les <lb/>puiſſances P & </s> |
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1160 <s xml:id="echoid-s619" xml:space="preserve">R, doit toujours être à chacune d’elles, <lb/>comme le ſinus de l’angle PAR de leurs cordes, à <lb/>chacun des ſinus des angles RAK & </s> |
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1161 <s xml:id="echoid-s620" xml:space="preserve">PAK: </s> |
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1162 <s xml:id="echoid-s621" xml:space="preserve">Il ſuit <lb/>évidemment que ſi enfin cet angle, à force de deve-<lb/>nir obtus, devenoit à rien; </s> |
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1163 <s xml:id="echoid-s622" xml:space="preserve">c’eſt-à-dire, que R A & </s> |
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1164 <s xml:id="echoid-s623" xml:space="preserve"><lb/>AP ne fiſſent plus qu’une même ligne droite, ce poids <lb/>ſeroit auſſi réduit à rien, & </s> |
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1165 <s xml:id="echoid-s624" xml:space="preserve">ces deux puiſſances agi-<lb/>roient ſeulement alors l’une contre l’autre: </s> |
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1166 <s xml:id="echoid-s625" xml:space="preserve">ainſi tant <lb/>qu’il reſte quelque poids attaché à ces cordes entre ces <lb/>puiſſances, elles font toujours quelque angle PAR <lb/>que ce ſoit.</s> |
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1167 <s xml:id="echoid-s626" xml:space="preserve"/> |
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1168 </p> |
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1169 </div> |
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1170 <div xml:id="echoid-div72" type="section" level="1" n="49"> |
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1171 <head xml:id="echoid-head49" xml:space="preserve"><emph style="sc">Corollaire</emph> XVIII.</head> |
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1172 <p> |
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1173 <s xml:id="echoid-s627" xml:space="preserve">De-là on voit qu’il n’y a point de force imaginable, <lb/>n’y de poids, quelques grands qu’on les conçoive, qui <lb/>appliquez aux extrémitez d’une corde parfaitement <lb/>fléxible, la puiſſent tellement bander qu’elle devienne <lb/>parfaitement droite, pour peu de peſanteur qu’on y <lb/>ſuppoſe: </s> |
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1174 <s xml:id="echoid-s628" xml:space="preserve">car quelque prodigieuſe que ſoit cette force, <lb/>& </s> |
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1175 <s xml:id="echoid-s629" xml:space="preserve">quelques grands que ſoient ces poids, ils auront <lb/>toujours quelque raport à la peſanteur de cette corde: <lb/></s> |
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1176 <s xml:id="echoid-s630" xml:space="preserve">& </s> |
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1177 <s xml:id="echoid-s631" xml:space="preserve">par conſéquent elle ſe courbera toujours.</s> |
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1178 <s xml:id="echoid-s632" xml:space="preserve"/> |
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1179 </p> |
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1180 <p style="it"> |
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1181 <s xml:id="echoid-s633" xml:space="preserve">Iuſqu’ici nous n’avons eu aucun égard à cette peſan-<lb/>@eur de cordes, c’eſt pour cela que nous n’y avons conſidéré |
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1182 <pb o="22" file="0048" n="48" rhead="NOUVELLE"/> |
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1183 que l’angle qu’elles font entr’elles à l’endroit ou le poids <lb/> |
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1184 <anchor type="note" xlink:label="note-0048-01a" xlink:href="note-0048-01"/> |
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1185 qu’elles ſoutiennent, leur eſt attacbé: </s> |
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1186 <s xml:id="echoid-s634" xml:space="preserve">ce ſera en les conſidé-<lb/>rant de même que nous prendrons quelque jour leur peſanteur <lb/>pourune infinité de poids, qui leur étant appliquez dans toute <lb/>leur longueur, leur font faire une infinité d’angles quinous ſer-<lb/>viront à en déterminer la courbure pour toutes ſortes d’bypo-<lb/>theſes.</s> |
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1187 <s xml:id="echoid-s635" xml:space="preserve"/> |
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1188 </p> |
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1189 <div xml:id="echoid-div72" type="float" level="2" n="1"> |
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1190 <note position="left" xlink:label="note-0048-01" xlink:href="note-0048-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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1191 </div> |
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1192 </div> |
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1193 <div xml:id="echoid-div74" type="section" level="1" n="50"> |
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1194 <head xml:id="echoid-head50" xml:space="preserve"><emph style="sc">Corollaire</emph> XIX.</head> |
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1195 <p> |
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1196 <s xml:id="echoid-s636" xml:space="preserve">On pourroit encore de même démontrer le raport <lb/>du poids K ſuſpendu partrois cordes, ou par davanta-<lb/>ge, même juſqu’à l’infini, aux puiſſances qui le ſou-<lb/>tiendroient; </s> |
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1197 <s xml:id="echoid-s637" xml:space="preserve">en prenant pour une ſeule, l’impreſſion <lb/>compoſée de chacun des points, ou deux de ces cor-<lb/>des concourent, laquelle réſulte du concours d’action <lb/>des deux puiſſances qui y ſont appliquées; </s> |
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1198 <s xml:id="echoid-s638" xml:space="preserve">& </s> |
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1199 <s xml:id="echoid-s639" xml:space="preserve">ainſi <lb/>toujours de même, juſqu’à ce qu’enfin toutes ces <lb/>puiſſances, en quelque nombre qu’elles ſoient, fuſſent <lb/>réduites à deux ſeulement: </s> |
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1200 <s xml:id="echoid-s640" xml:space="preserve">ce qui réduiroit toujours <lb/>tous ces cas, quclques différens qu’ils fuſſent, à celui <lb/>de la propoſition préſente, qui pour cela a été appel-<lb/>lée Fondamentale.</s> |
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1201 <s xml:id="echoid-s641" xml:space="preserve"/> |
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1202 </p> |
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1203 </div> |
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1204 <div xml:id="echoid-div75" type="section" level="1" n="51"> |
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1205 <head xml:id="echoid-head51" xml:space="preserve"><emph style="sc">Remarque</emph>.</head> |
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1206 <p> |
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1207 <s xml:id="echoid-s642" xml:space="preserve">Lorſque de chacun des nocuds qui lient enſemble les <lb/>cordes avec leſquelles un poids eſt ſoutenu par plu-<lb/>ſieurs puiſſances, ſuivant chacune ſa direction, il <lb/>ne s’en répand point plus de trois dans un même <lb/>plan; </s> |
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1208 <s xml:id="echoid-s643" xml:space="preserve">alors cette réduction ſe peut faire ſans con-<lb/>noître aucun raport entre ces puiſſances, n’y d’au-<lb/>cune d’elles à ce poids. </s> |
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1209 <s xml:id="echoid-s644" xml:space="preserve">Mais lorſque le contraire <lb/>arrive, c’eſt-à-dire, lorſque d’un même næud il ſe <lb/>répand plus de trois cordes dans un même plan; </s> |
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1210 <s xml:id="echoid-s645" xml:space="preserve">alors <lb/>pour chacun de ces plans, il faut connoître entre leſ-<lb/>quelles on voudra des forces qui y ſont appliquées.</s> |
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1211 <s xml:id="echoid-s646" xml:space="preserve"> |
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1212 <pb o="23" file="0049" n="49" rhead="MECHANIQUE."/> |
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1213 autant de raports, moins trois, qu’il y aura de telles <lb/> |
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1214 <anchor type="note" xlink:label="note-0049-01a" xlink:href="note-0049-01"/> |
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1215 forces, ou qu’un même noeud y répandra de cordes. <lb/></s> |
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1216 <s xml:id="echoid-s647" xml:space="preserve">Par exemple, pour 4. </s> |
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1217 <s xml:id="echoid-s648" xml:space="preserve">cordes, il ne faudra connoître <lb/>qu’un tel raport. </s> |
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1218 <s xml:id="echoid-s649" xml:space="preserve">Pour 5. </s> |
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1219 <s xml:id="echoid-s650" xml:space="preserve">il en faudra 2. </s> |
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1220 <s xml:id="echoid-s651" xml:space="preserve">Pour 6. </s> |
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1221 <s xml:id="echoid-s652" xml:space="preserve">3. </s> |
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1222 <s xml:id="echoid-s653" xml:space="preserve"><lb/>Pour 7. </s> |
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1223 <s xml:id="echoid-s654" xml:space="preserve">4. </s> |
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1224 <s xml:id="echoid-s655" xml:space="preserve">& </s> |
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1225 <s xml:id="echoid-s656" xml:space="preserve">ainſi toujours 3. </s> |
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1226 <s xml:id="echoid-s657" xml:space="preserve">moins que le nombre <lb/>de ces cordes.</s> |
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1227 <s xml:id="echoid-s658" xml:space="preserve"/> |
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1228 </p> |
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1229 <div xml:id="echoid-div75" type="float" level="2" n="1"> |
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1230 <note position="right" xlink:label="note-0049-01" xlink:href="note-0049-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſ@u-<lb/>lement.</note> |
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1231 </div> |
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1232 <p style="it"> |
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1233 <s xml:id="echoid-s659" xml:space="preserve">On n’entre point dans le détail de tout ceci, de peur de ſe <lb/>trop éloigner de la breveté qu’on s’eſt propoſée; </s> |
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1234 <s xml:id="echoid-s660" xml:space="preserve">outre qu’en voi-<lb/>la, ce me ſemble, aſſez pour juger de l’étenduë & </s> |
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1235 <s xml:id="echoid-s661" xml:space="preserve">de la fécondité <lb/>de ces principes: </s> |
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1236 <s xml:id="echoid-s662" xml:space="preserve">on le verra démontré dans un autre ouvrage.</s> |
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1237 <s xml:id="echoid-s663" xml:space="preserve"/> |
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1238 </p> |
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1239 <figure> |
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1240 <image file="0049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0049-01"/> |
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1241 </figure> |
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1242 </div> |
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1243 <div xml:id="echoid-div77" type="section" level="1" n="52"> |
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1244 <head xml:id="echoid-head52" xml:space="preserve">PROBLEME.</head> |
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1245 <p style="it"> |
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1246 <s xml:id="echoid-s664" xml:space="preserve">LEs forces de trois bommes K, P, & </s> |
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1247 <s xml:id="echoid-s665" xml:space="preserve">R, étant données, <lb/>ou même ſeulement le raport qu’elles ont entr’elles, les <lb/>appliquer tellement à trois cordes A K, A P, & </s> |
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1248 <s xml:id="echoid-s666" xml:space="preserve">A R, qui <lb/>aboutiſſent à un même næud A, qu’aucun des trois ne l’emporte <lb/>ſur aucun des deux autres.</s> |
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1249 <s xml:id="echoid-s667" xml:space="preserve"/> |
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1250 </p> |
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1251 </div> |
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1252 <div xml:id="echoid-div78" type="section" level="1" n="53"> |
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1253 <head xml:id="echoid-head53" xml:space="preserve"><emph style="sc">Solution</emph>.</head> |
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1254 <p> |
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1255 <s xml:id="echoid-s668" xml:space="preserve">Premièremènt, s’il y a quelqu’une des forces de <lb/>ces trois perſonnes, qui ſoit égale, ou plus grande que <lb/>la ſomme de celles des deux autres, ce Problême par <lb/>le Corollaire 3. </s> |
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1256 <s xml:id="echoid-s669" xml:space="preserve">de la propoſition préſente eſt impoſ-<lb/>ſible.</s> |
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1257 <s xml:id="echoid-s670" xml:space="preserve"/> |
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1258 </p> |
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1259 <p> |
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1260 <s xml:id="echoid-s671" xml:space="preserve">Secondement ſi chacune de ces forces, de quelque <lb/>maniére qu’on les prenne, eſt en effet moindre que <lb/>la ſomme des deux autres; </s> |
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1261 <s xml:id="echoid-s672" xml:space="preserve">placez à diſcretion une de <lb/>ces trois perſonnes, par exemple K, & </s> |
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1262 <s xml:id="echoid-s673" xml:space="preserve">lui donnez la <lb/>direction AK qu’il vous plaira. </s> |
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1263 <s xml:id="echoid-s674" xml:space="preserve">Ayant prolongé à <lb/>diſcretion AK du côté de E, faite ſur AE le triangle <lb/>AEF, tel que ſes trois côtez AE, EF, & </s> |
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1264 <s xml:id="echoid-s675" xml:space="preserve">AF, ſoient <lb/>entr’eux, comme les forces de ces trois perſonnes K, |
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1265 <pb o="24" file="0050" n="50" rhead="NOUVELLE"/> |
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1266 P, & </s> |
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1267 <s xml:id="echoid-s676" xml:space="preserve">R. </s> |
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1268 <s xml:id="echoid-s677" xml:space="preserve">Placez enſuite la perſonne R ſuivant le côté <lb/> |
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1269 <anchor type="note" xlink:label="note-0050-01a" xlink:href="note-0050-01"/> |
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1270 AF de ce triangle, & </s> |
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1271 <s xml:id="echoid-s678" xml:space="preserve">la perſonne P ſuivant AP paral-<lb/>lele à EF. </s> |
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1272 <s xml:id="echoid-s679" xml:space="preserve">Cela fait, ces trois hommes ſeront dans la <lb/>ſituation requiſe pour demeurer en équilibre.</s> |
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1273 <s xml:id="echoid-s680" xml:space="preserve"/> |
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1274 </p> |
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1275 <div xml:id="echoid-div78" type="float" level="2" n="1"> |
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1276 <note position="left" xlink:label="note-0050-01" xlink:href="note-0050-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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1277 </div> |
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1278 </div> |
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1279 <div xml:id="echoid-div80" type="section" level="1" n="54"> |
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1280 <head xml:id="echoid-head54" xml:space="preserve"><emph style="sc">Demonstration</emph></head> |
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1281 <p> |
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1282 <s xml:id="echoid-s681" xml:space="preserve">Leurs forces K, P, & </s> |
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1283 <s xml:id="echoid-s682" xml:space="preserve">R ſont (Hyp.) </s> |
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1284 <s xml:id="echoid-s683" xml:space="preserve">entr’elles, <lb/>comme AE, EF, & </s> |
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1285 <s xml:id="echoid-s684" xml:space="preserve">AF; </s> |
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1286 <s xml:id="echoid-s685" xml:space="preserve">C’eſt-à-dire, (Lemm. </s> |
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1287 <s xml:id="echoid-s686" xml:space="preserve">5.) <lb/></s> |
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1288 <s xml:id="echoid-s687" xml:space="preserve">comme les ſinus des angles AFE, EAF, & </s> |
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1289 <s xml:id="echoid-s688" xml:space="preserve">AEF, <lb/>qui ſont les mêmes que ceux desangles PAR, RAK, <lb/>& </s> |
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1290 <s xml:id="echoid-s689" xml:space="preserve">PAK: </s> |
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1291 <s xml:id="echoid-s690" xml:space="preserve">Donc (Corol. </s> |
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1292 <s xml:id="echoid-s691" xml:space="preserve">II.) </s> |
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1293 <s xml:id="echoid-s692" xml:space="preserve">ces trois hommes demeu-<lb/>reront ainſien équilibre, ſans qu’aucun d’eux le puiſſe <lb/>emporter ſur lequel que ce ſoit de deux autres. </s> |
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1294 <s xml:id="echoid-s693" xml:space="preserve">Ce <lb/>qu’il faloit faire.</s> |
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1295 <s xml:id="echoid-s694" xml:space="preserve"/> |
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1296 </p> |
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1297 <figure> |
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1298 <image file="0050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0050-01"/> |
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1299 </figure> |
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1300 <pb o="25" file="0051" n="51" rhead="MECHANIQUE."/> |
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1301 <figure> |
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1302 <image file="0051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0051-01"/> |
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1303 </figure> |
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1304 </div> |
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1305 <div xml:id="echoid-div81" type="section" level="1" n="55"> |
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1306 <head xml:id="echoid-head55" xml:space="preserve">PROPOSITION <lb/>FONDAMENTALE <lb/>DES POULIES,</head> |
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1307 <p> |
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1308 <s xml:id="echoid-s695" xml:space="preserve">Soit que le centre en demeure fixe, ſoit qu’on <lb/>le ſuppoſe mobile; </s> |
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1309 <s xml:id="echoid-s696" xml:space="preserve">& </s> |
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1310 <s xml:id="echoid-s697" xml:space="preserve">pour toutes les <lb/>directions poſſibles des puiſſances, ou des <lb/>poids qui y ſont appliquez.</s> |
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1311 <s xml:id="echoid-s698" xml:space="preserve"/> |
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1312 </p> |
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1313 <p style="it"> |
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1314 <s xml:id="echoid-s699" xml:space="preserve">SOit la puiſſance, ou le poids D appliquè, ou ſuſpendu <lb/> |
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1315 <anchor type="note" xlink:label="note-0051-01a" xlink:href="note-0051-01"/> |
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1316 au centre mobile d’une poulie A, autour de laquelle paſſe <lb/>la corde PMNR, dont les extremitez ſont retenuës par <lb/>les puiſſances P & </s> |
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1317 <s xml:id="echoid-s700" xml:space="preserve">R: </s> |
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1318 <s xml:id="echoid-s701" xml:space="preserve">quelque angle MHN que faſ-<lb/>ſent entre-elles les parties MP, & </s> |
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1319 <s xml:id="echoid-s702" xml:space="preserve">NR de cette corde, <lb/>prolongées juſqu’àce qu’elles concourent en H; </s> |
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1320 <s xml:id="echoid-s703" xml:space="preserve">le poids, ou la <lb/>puiſſance D, ſera toujours à cbacune des puiſſances P & </s> |
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1321 <s xml:id="echoid-s704" xml:space="preserve">R, <lb/>comme le ſinus de cet angle, au ſinus de ſa moitié.</s> |
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1322 <s xml:id="echoid-s705" xml:space="preserve"/> |
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1323 </p> |
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1324 <div xml:id="echoid-div81" type="float" level="2" n="1"> |
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1325 <note position="right" xlink:label="note-0051-01" xlink:href="note-0051-01a" xml:space="preserve">fig. 20 <lb/>21. <lb/>22. <lb/>23.</note> |
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1326 </div> |
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1327 </div> |
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1328 <div xml:id="echoid-div83" type="section" level="1" n="56"> |
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1329 <head xml:id="echoid-head56" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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1330 <p> |
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1331 <s xml:id="echoid-s706" xml:space="preserve">Il eſt clair que tant quele poids, ou la puiſſance D, <lb/>demeure ainſi en équilibre avec les puiſſances P & </s> |
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1332 <s xml:id="echoid-s707" xml:space="preserve">R <lb/>ſur la poulie A, non-ſeulement cette poulie demeure <lb/>ſans mouvement; </s> |
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1333 <s xml:id="echoid-s708" xml:space="preserve">mais encore la corde PMNR de-<lb/>meure fixe deſſus ſans gliſſer, n’y ſe mouvoir non plus <lb/>que ſi elley étoit colée, ou phyſiquement unie depuis</s> |
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1334 </p> |
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1335 <pb o="26" file="0052" n="52" rhead="NOUVELLE"/> |
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1336 <p> |
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1337 <s xml:id="echoid-s709" xml:space="preserve">M juſqu’à N; </s> |
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1338 <s xml:id="echoid-s710" xml:space="preserve">& </s> |
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1339 <s xml:id="echoid-s711" xml:space="preserve">les points M, & </s> |
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1340 <s xml:id="echoid-s712" xml:space="preserve">N de cette corde <lb/> |
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1341 <anchor type="note" xlink:label="note-0052-01a" xlink:href="note-0052-01"/> |
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1342 ſont auſſi fixes ſur cette poulie, tant que dure cet <lb/>équilibre, que ſi en effet PM, & </s> |
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1343 <s xml:id="echoid-s713" xml:space="preserve">RN étoient deux <lb/>cordes, qui y fuſſent ſéparément attachées: </s> |
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1344 <s xml:id="echoid-s714" xml:space="preserve">Les puiſ-<lb/>ſances P, & </s> |
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1345 <s xml:id="echoid-s715" xml:space="preserve">R reſi ſtent donc au poids, ou à la puiſſan-<lb/>ce D, de même que ſi MP, & </s> |
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1346 <s xml:id="echoid-s716" xml:space="preserve">RN étoient deux cor-<lb/>des différentes & </s> |
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1347 <s xml:id="echoid-s717" xml:space="preserve">attachées aux points M & </s> |
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1348 <s xml:id="echoid-s718" xml:space="preserve">N de la <lb/>poulie A, ſuivant les tangentes en cespoints: </s> |
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1349 <s xml:id="echoid-s719" xml:space="preserve">De ſorte <lb/>que l’on peut regarder cette poulie comme un corps <lb/>qui tend vers D, ſuivant AD, d’une force égale à <lb/>celle du poids, ou de la puiſſance D; </s> |
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1350 <s xml:id="echoid-s720" xml:space="preserve">mais qui eſt re-<lb/>tenu avec les cordes PM & </s> |
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1351 <s xml:id="echoid-s721" xml:space="preserve">RN par les puiſſances <lb/>P & </s> |
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1352 <s xml:id="echoid-s722" xml:space="preserve">R. </s> |
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1353 <s xml:id="echoid-s723" xml:space="preserve">Or en ce cas, non-ſeulement ſa ligne de di-<lb/>rection AD paſſeroit (Lemm. </s> |
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1354 <s xml:id="echoid-s724" xml:space="preserve">2. </s> |
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1355 <s xml:id="echoid-s725" xml:space="preserve">Cor. </s> |
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1356 <s xml:id="echoid-s726" xml:space="preserve">1.) </s> |
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1357 <s xml:id="echoid-s727" xml:space="preserve">par le point H, <lb/>ou concourent ces cordes prolongées; </s> |
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1358 <s xml:id="echoid-s728" xml:space="preserve">mais encore <lb/>cette poulie regardée avec une telle impreſſion, ſeroit <lb/>(prop. </s> |
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1359 <s xml:id="echoid-s729" xml:space="preserve">fond. </s> |
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1360 <s xml:id="echoid-s730" xml:space="preserve">des cordes. </s> |
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1361 <s xml:id="echoid-s731" xml:space="preserve">Cor. </s> |
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1362 <s xml:id="echoid-s732" xml:space="preserve">5.) </s> |
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1363 <s xml:id="echoid-s733" xml:space="preserve">aux puiſſances P, & </s> |
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1364 <s xml:id="echoid-s734" xml:space="preserve">R, <lb/>qui la retiennent, comme le finus de l’angle MHN, <lb/>aux ſinus des angles NHA, & </s> |
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1365 <s xml:id="echoid-s735" xml:space="preserve">MHA: </s> |
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1366 <s xml:id="echoid-s736" xml:space="preserve">Donc en effet <lb/>la ligne de direction AD de la poulie A ainſi tirée <lb/>par le poids, ou la puiſſance D, contre les puiſſances <lb/>P & </s> |
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1367 <s xml:id="echoid-s737" xml:space="preserve">R, paſſe toujours par le point H, ou leurs cordes <lb/>prolongées concourent; </s> |
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1368 <s xml:id="echoid-s738" xml:space="preserve">& </s> |
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1369 <s xml:id="echoid-s739" xml:space="preserve">le poids, ou la puiſſance <lb/>D, eſt auſſi à chacune de ces puiſſances, comme le <lb/>ſinus de l’angle MHN à chacun des ſinus des angles <lb/>NHA, & </s> |
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1370 <s xml:id="echoid-s740" xml:space="preserve">MHA. </s> |
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1371 <s xml:id="echoid-s741" xml:space="preserve">Or à cauſe que HA, paſſe auſſi <lb/>parle centre de cette poulie, & </s> |
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1372 <s xml:id="echoid-s742" xml:space="preserve">que MH, & </s> |
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1373 <s xml:id="echoid-s743" xml:space="preserve">NH ſont <lb/>deux tangentes, les angles NHA, & </s> |
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1374 <s xml:id="echoid-s744" xml:space="preserve">MHA, ſont <lb/>chacun la moitié de l’angle MHN: </s> |
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1375 <s xml:id="echoid-s745" xml:space="preserve">Donc le poids, <lb/>ou la puiſſance D, eſt toujours à chacune de puiſſan-<lb/>ces P & </s> |
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1376 <s xml:id="echoid-s746" xml:space="preserve">R, comme le ſinus de l’angle MHN, que <lb/>ſont leurs cordes entr’elles, au ſinus de ſa moitié. </s> |
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1377 <s xml:id="echoid-s747" xml:space="preserve">Ce <lb/>qu’il faloit démontrer.</s> |
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1378 <s xml:id="echoid-s748" xml:space="preserve"/> |
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1379 </p> |
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1380 <div xml:id="echoid-div83" type="float" level="2" n="1"> |
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1381 <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">DES <lb/>POULIES.</note> |
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1382 </div> |
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1383 <figure> |
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1384 <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0052-01"/> |
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1385 </figure> |
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1386 <pb o="27" file="0053" n="53" rhead="MECHANIQUE."/> |
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1387 </div> |
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1388 <div xml:id="echoid-div85" type="section" level="1" n="57"> |
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1389 <head xml:id="echoid-head57" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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1390 <note position="right" xml:space="preserve">DES <lb/>POULIES.</note> |
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1391 <p> |
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1392 <s xml:id="echoid-s749" xml:space="preserve">Il ſuit de-là que le poids, ou la puiſſance D, tant <lb/>que dure cet équilibre, eſt toujours à chacune des <lb/>puiſſances P, & </s> |
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1393 <s xml:id="echoid-s750" xml:space="preserve">R, en raiſon réciproque des ſinus des <lb/>angles que font les lignes de direction de ce poids, & </s> |
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1394 <s xml:id="echoid-s751" xml:space="preserve"><lb/>de cette puiſſance avec celle de l’autre; </s> |
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1395 <s xml:id="echoid-s752" xml:space="preserve">c’eſt-à-dire, <lb/>en raiſon réciproque des diſtances des lignes de di-<lb/>rection de ce poids & </s> |
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1396 <s xml:id="echoid-s753" xml:space="preserve">de cette puiſſance, à quelque <lb/>point que ce ſoit de celle de l’autre. </s> |
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1397 <s xml:id="echoid-s754" xml:space="preserve">Et pour la même <lb/>raiſon les puiſſances P & </s> |
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1398 <s xml:id="echoid-s755" xml:space="preserve">R ſont auſſi entr’elles en <lb/>raiſon rèciproque des diſtances de leurs lignes de di-<lb/>rection à quelque point que ce ſoit de celle du poids, <lb/>ou de la puiſſance D, qu’elles ſoutiennent.</s> |
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1399 <s xml:id="echoid-s756" xml:space="preserve"/> |
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1400 </p> |
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1401 </div> |
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1402 <div xml:id="echoid-div86" type="section" level="1" n="58"> |
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1403 <head xml:id="echoid-head58" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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1404 <p> |
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1405 <s xml:id="echoid-s757" xml:space="preserve">Si la puiſſance, ou le poids D, (le tout étant <lb/>appliqué à la poulie A comme cy-deſſus) eſt à chacune <lb/>des puiſſances P, & </s> |
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1406 <s xml:id="echoid-s758" xml:space="preserve">R, comme le ſinus de l’angle <lb/>MHN, que font leurs cordes entr’elles, au ſinus de <lb/>ſa moitié; </s> |
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1407 <s xml:id="echoid-s759" xml:space="preserve">elles le ſoutiendront en cet état: </s> |
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1408 <s xml:id="echoid-s760" xml:space="preserve">parce <lb/>que cette raiſon étant la même qu’il doit avoir aux <lb/>puiſſances qui l’y pourroient ſoutenir; </s> |
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1409 <s xml:id="echoid-s761" xml:space="preserve">les puiſſances <lb/>p, & </s> |
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1410 <s xml:id="echoid-s762" xml:space="preserve">R leur ſont néceſſairement égales; </s> |
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1411 <s xml:id="echoid-s763" xml:space="preserve">& </s> |
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1412 <s xml:id="echoid-s764" xml:space="preserve">par conſé-<lb/>quent étant appliquées de même, elles l’y doivent <lb/>auſſi ſoutenir.</s> |
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1413 <s xml:id="echoid-s765" xml:space="preserve"/> |
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1414 </p> |
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1415 </div> |
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1416 <div xml:id="echoid-div87" type="section" level="1" n="59"> |
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1417 <head xml:id="echoid-head59" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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1418 <p> |
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1419 <s xml:id="echoid-s766" xml:space="preserve">Ce qui fait voir que lorſque lepoids D, eſt à cha-<lb/>cune des puiſſances P, & </s> |
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1420 <s xml:id="echoid-s767" xml:space="preserve">R, en raiſon réciproque des <lb/>diſtances des lignes de direction de ce poids, & </s> |
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1421 <s xml:id="echoid-s768" xml:space="preserve">de <lb/>cette puiſſance, à quelque point que ce ſoit de celle <lb/>de l’autre, il demeure en équilibre avec elles. </s> |
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1422 <s xml:id="echoid-s769" xml:space="preserve">Ce <lb/>qu’on dit du poids D ſe doit auſſi de la puiſſance D.</s> |
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1423 <s xml:id="echoid-s770" xml:space="preserve"/> |
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1424 </p> |
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1425 <pb o="28" file="0054" n="54" rhead="NOUVELLE"/> |
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1426 </div> |
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1427 <div xml:id="echoid-div88" type="section" level="1" n="60"> |
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1428 <head xml:id="echoid-head60" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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1429 <note position="left" xml:space="preserve">DES <lb/>POULIES.</note> |
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1430 <p> |
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1431 <s xml:id="echoid-s771" xml:space="preserve">Il ſuit de plus de cette propoſition que les puiſ-<lb/>ſances P, & </s> |
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1432 <s xml:id="echoid-s772" xml:space="preserve">R agiſſent contre la puiſſance, ou le poids <lb/>D; </s> |
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1433 <s xml:id="echoid-s773" xml:space="preserve">& </s> |
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1434 <s xml:id="echoid-s774" xml:space="preserve">ce poids, ou cette puiſſance réciproquement <lb/>auſſi contr’elles, de la même maniére que ſi leurs cor-<lb/>des PM, & </s> |
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1435 <s xml:id="echoid-s775" xml:space="preserve">RN, prolongées juſqu’en H, y etoient <lb/>noiiées avec la corde AD du poids, ou de la puiſſance <lb/>D; </s> |
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1436 <s xml:id="echoid-s776" xml:space="preserve">& </s> |
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1437 <s xml:id="echoid-s777" xml:space="preserve">que la poulie A étant ôtée, elles tiraſſent contre <lb/>ce poids, ou contre cette puiſſance ſuivant les mêmes <lb/>angles MHA, & </s> |
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1438 <s xml:id="echoid-s778" xml:space="preserve">NHA: </s> |
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1439 <s xml:id="echoid-s779" xml:space="preserve">puis qu’alors le poids, ou la <lb/>puiſſance D ſeroit encore (prop. </s> |
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1440 <s xml:id="echoid-s780" xml:space="preserve">fond. </s> |
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1441 <s xml:id="echoid-s781" xml:space="preserve">des cordes. </s> |
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1442 <s xml:id="echoid-s782" xml:space="preserve">Cor. </s> |
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1443 <s xml:id="echoid-s783" xml:space="preserve">2. </s> |
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1444 <s xml:id="echoid-s784" xml:space="preserve">& </s> |
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1445 <s xml:id="echoid-s785" xml:space="preserve"><lb/>5.) </s> |
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1446 <s xml:id="echoid-s786" xml:space="preserve">à chacune d’elles, comme le ſinus de l’angle MHN <lb/>de leurs cordes, au ſinus de la moitié de cet angle. <lb/></s> |
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1447 <s xml:id="echoid-s787" xml:space="preserve">Ainſi que les puiſſances P & </s> |
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1448 <s xml:id="echoid-s788" xml:space="preserve">R ſoutiennent le poids, <lb/>ou la puiſſance D, par le moyen de la poulie A, avec <lb/>la même corde PMNR; </s> |
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1449 <s xml:id="echoid-s789" xml:space="preserve">ou qu’elles ſoutiennent l’un <lb/>ou l’autre ſans poulie, mais avec chacune une corde <lb/>PH, & </s> |
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1450 <s xml:id="echoid-s790" xml:space="preserve">RH, noiiée avec AD en H; </s> |
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1451 <s xml:id="echoid-s791" xml:space="preserve">C’eſt toujours <lb/>la même choſe, pourvu que les angles de ces cordes <lb/>avec la ligne de direction du poids, ou de la puiſſan-<lb/>ce D, ſoient les mêmes dans l’un & </s> |
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1452 <s xml:id="echoid-s792" xml:space="preserve">l’autre cas.</s> |
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1453 <s xml:id="echoid-s793" xml:space="preserve"/> |
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1454 </p> |
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1455 </div> |
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1456 <div xml:id="echoid-div89" type="section" level="1" n="61"> |
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1457 <head xml:id="echoid-head61" xml:space="preserve"><emph style="sc">Corollaire</emph> V.</head> |
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1458 <p> |
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1459 <s xml:id="echoid-s794" xml:space="preserve">On voit encore que ſi au lieu du poids, ou de la <lb/>puiſſance D, on attachoit la corde AD à quelque <lb/>clou, comme en D, ou ailleurs; </s> |
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1460 <s xml:id="echoid-s795" xml:space="preserve">ce clou feroit la même <lb/>réſiſtance contre les puiſſances P, & </s> |
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1461 <s xml:id="echoid-s796" xml:space="preserve">R, que fait pré-<lb/>ſentement le poids, ou la puiſſance D: </s> |
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1462 <s xml:id="echoid-s797" xml:space="preserve">ainſi n’étant <lb/>arrivé aucun changement du côté de ces puiſſances, <lb/>la direction de la corde AD ſeroit non ſeulement en-<lb/>core la même qu’auparavant, c’eſt-à-dire, qu’elle <lb/>diviſeroit encore l’angle MHN en deux parties éga-<lb/>les; </s> |
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1463 <s xml:id="echoid-s798" xml:space="preserve">mais encore la réſiſtance de ce clou ſeroit égale <lb/>à celle du poids, ou de la puiſſance D: </s> |
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1464 <s xml:id="echoid-s799" xml:space="preserve">D’où il ſuit</s> |
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1465 </p> |
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1466 <pb o="29" file="0055" n="55" rhead="MECHANIQUE."/> |
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1467 <p> |
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1468 <s xml:id="echoid-s800" xml:space="preserve">I°. </s> |
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1469 <s xml:id="echoid-s801" xml:space="preserve">Que lors qu’une poulie ſur laquelle deux puiſſan-<lb/> |
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1470 <anchor type="note" xlink:label="note-0055-01a" xlink:href="note-0055-01"/> |
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1471 ces font équilibre, comme ici P & </s> |
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1472 <s xml:id="echoid-s802" xml:space="preserve">R, eſt ſuſpenduë <lb/>ou retenuë par une corde telle qu’eſt ici AD, cette <lb/>corde ſe dirige toujours en ſorte qu’elle diviſe en <lb/>deux également l’angle des tangentes de cette poulie <lb/>aux points ou les cordes de ces puiſſances la touchent. <lb/></s> |
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1473 <s xml:id="echoid-s803" xml:space="preserve">(Il eſt clair que la même choſe arriveroit, ſi au lieu <lb/>de ces puiſſances on appliquoit à leurs cordes des poids <lb/>qui demeuraſſent de même en équilibre ſur cette pou-<lb/>lie) 2°. </s> |
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1474 <s xml:id="echoid-s804" xml:space="preserve">La charge du clou, ou la corde qui retient cette <lb/>poulie, eſt attachée, étant égale à la réſiſtance qu’il fait <lb/>contre chacune de ces puiſſances, ou des poids mis en <lb/>leurs places; </s> |
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1475 <s xml:id="echoid-s805" xml:space="preserve">eſt à chacun d’eux, ou d’elles, comme le <lb/>ſinus de l’angle de ces tangentes, au ſinus de ſa moitié.</s> |
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1476 <s xml:id="echoid-s806" xml:space="preserve"/> |
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1477 </p> |
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1478 <div xml:id="echoid-div89" type="float" level="2" n="1"> |
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1479 <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">DES <lb/>POULIES.</note> |
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1480 </div> |
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1481 </div> |
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1482 <div xml:id="echoid-div91" type="section" level="1" n="62"> |
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1483 <head xml:id="echoid-head62" xml:space="preserve"><emph style="sc">Corollaire</emph> VI.</head> |
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1484 <p> |
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1485 <s xml:id="echoid-s807" xml:space="preserve">Préſentement ſi la poulie A, au lieu d’être arrêtée <lb/>en D, ou en quelqu’autre point de ſa corde AD, <lb/>étoit ſeulement fixe en ſon centre A; </s> |
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1486 <s xml:id="echoid-s808" xml:space="preserve">les puiſſances <lb/>P & </s> |
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1487 <s xml:id="echoid-s809" xml:space="preserve">R agiſſant encore deſſus de la même maniére <lb/>qu’auparavant, & </s> |
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1488 <s xml:id="echoid-s810" xml:space="preserve">cette poulie leur faiſant auſſi en-<lb/>core la même réſiſtance qu’elle leur faiſoit, lors qu’elle <lb/>étoit retenuë parla corde AH; </s> |
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1489 <s xml:id="echoid-s811" xml:space="preserve">elle doit en recevoir <lb/>encore la même impreſſion, & </s> |
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1490 <s xml:id="echoid-s812" xml:space="preserve">ſuivant la même di-<lb/>rection qu’auparavant: </s> |
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1491 <s xml:id="echoid-s813" xml:space="preserve">Ainſi l’effort commun des <lb/>puiſſances P & </s> |
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1492 <s xml:id="echoid-s814" xml:space="preserve">R ſur cette poulie, ne tend encore <lb/>qu’à la mouvoir ſuivant HA avec la même force dont <lb/>elles tiroient auparavant contre le poids, ou la puiſ-<lb/>ſance D, ou contre le clou qu’on vient de ſuſpoſer en <lb/>D: </s> |
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1493 <s xml:id="echoid-s815" xml:space="preserve">de ſorte que la charge de cette poulie, lors qu’elle eſt <lb/>fixe, eſt toujours à chacune des puiſſances P & </s> |
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1494 <s xml:id="echoid-s816" xml:space="preserve">R, ou <lb/>à chacun des poids qui leur étant égaux, ſeroient mis <lb/>en leurs places, comme le ſinus de l’angle de leurs par-<lb/>ties de cordes PM & </s> |
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1495 <s xml:id="echoid-s817" xml:space="preserve">RN prolongées juſqu’à ce <lb/>qu’elles concourent, au ſinus de ſa moitié.</s> |
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1496 <s xml:id="echoid-s818" xml:space="preserve"/> |
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1497 </p> |
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1498 <pb o="30" file="0056" n="56" rhead="NOUVELLE"/> |
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1499 </div> |
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1500 <div xml:id="echoid-div92" type="section" level="1" n="63"> |
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1501 <head xml:id="echoid-head63" xml:space="preserve"><emph style="sc">Corollaire</emph> VII.</head> |
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1502 <note position="left" xml:space="preserve">DES <lb/>POULIES.</note> |
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1503 <p> |
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1504 <s xml:id="echoid-s819" xml:space="preserve">D’où il ſuit que plus l’angle MHN, que ces par-<lb/>ties de corde prolongées du côté de H, font entr’elles, <lb/>ſera obtus, moins ſera grande la charge de la poulie A, <lb/>ſoit que le centre en ſoit fixe, ou qu’il ſoit mobile: <lb/></s> |
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1505 <s xml:id="echoid-s820" xml:space="preserve">parce que plus cet angle ſera obtus, moins ſera grande <lb/>la raiſon de ſon ſinus au ſinus de ſa moitié, quoi qu’en <lb/>proportion difféentes: </s> |
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1506 <s xml:id="echoid-s821" xml:space="preserve">De ſorte que cet angle peut <lb/>être ſi obtus, que la poulie A ne ſera chargée que ſi <lb/>peu qu’on voudra des puiſſances P & </s> |
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1507 <s xml:id="echoid-s822" xml:space="preserve">R: </s> |
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1508 <s xml:id="echoid-s823" xml:space="preserve">juſques-là <lb/>même qu’elle pourroit être ſoutenuë contre elles <lb/>par une puiſſance, ou un poids D indéfiniment petit, <lb/>c’eſt-à-dire, moindre que quelque poids donné, que <lb/>ce ſoit: </s> |
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1509 <s xml:id="echoid-s824" xml:space="preserve">Car il ne faut pour cela qu’ouvrir l’angle <lb/>MHN, que font entr’elles les parties de corde PM <lb/>& </s> |
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1510 <s xml:id="echoid-s825" xml:space="preserve">RN, juſqu’à ce qu’enfin ſon ſinus ſoit au ſinus de <lb/>ſa moitié en moindre raiſon que le poids donné, à <lb/>chacune des puiſſances P & </s> |
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1511 <s xml:id="echoid-s826" xml:space="preserve">R.</s> |
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1512 <s xml:id="echoid-s827" xml:space="preserve"/> |
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1513 </p> |
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1514 </div> |
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1515 <div xml:id="echoid-div93" type="section" level="1" n="64"> |
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1516 <head xml:id="echoid-head64" xml:space="preserve"><emph style="sc">Corollaire</emph> VIII.</head> |
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1517 <p> |
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1518 <s xml:id="echoid-s828" xml:space="preserve">Au contraire on peut rendre cet angle MHN <lb/>ſiaigu que la puiſſance, ou le poids D, ou quel-<lb/>qu’autre en ſa place, devra être plus grand que <lb/>chacune des puiſſances P & </s> |
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1519 <s xml:id="echoid-s829" xml:space="preserve">R pour être en équilibre <lb/>avec elles; </s> |
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1520 <s xml:id="echoid-s830" xml:space="preserve">mais ce poids ne peut pas ainſi augmèn-<lb/>ter à l’infini, de même que nous venons de dire qu’il <lb/>peut diminuer; </s> |
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1521 <s xml:id="echoid-s831" xml:space="preserve">Car ne pouvant jamais être plus <lb/>grand que lors que cet angle eſt infiniment aigu, <lb/>c’eſt-à-dire, lors que les parties de corde MP & </s> |
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1522 <s xml:id="echoid-s832" xml:space="preserve">NR <lb/>ſont paralleles; </s> |
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1523 <s xml:id="echoid-s833" xml:space="preserve">& </s> |
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1524 <s xml:id="echoid-s834" xml:space="preserve">le ſinus de cet angle n’étant encore <lb/>alors que double du ſinus de ſa moitié, ce poids ne <lb/>peut être tout au plus que double de chacune des puiſ-<lb/>ſances P & </s> |
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1525 <s xml:id="echoid-s835" xml:space="preserve">R.</s> |
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1526 <s xml:id="echoid-s836" xml:space="preserve"/> |
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1527 </p> |
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1528 <pb o="31" file="0057" n="57" rhead="MECHANIQUE."/> |
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1529 </div> |
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1530 <div xml:id="echoid-div94" type="section" level="1" n="65"> |
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1531 <head xml:id="echoid-head65" xml:space="preserve"><emph style="sc">Corollaire</emph> IX.</head> |
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1532 <note position="right" xml:space="preserve">DES <lb/>POULIES.</note> |
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1533 <p> |
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1534 <s xml:id="echoid-s837" xml:space="preserve">D’ou l’on voit en général que lors qu’un poids fait <lb/>ainfi équilibre avec deux puiſſances, ou avec deux au-<lb/>tres poids par le moyen de quelque poulie à moufle, <lb/>il ne peut être tout au plus que double de chacune de <lb/>ces puiſſances, ou de ces autres poids; </s> |
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1535 <s xml:id="echoid-s838" xml:space="preserve">mais au con-<lb/>traire il peut diminuer à l’infini, & </s> |
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1536 <s xml:id="echoid-s839" xml:space="preserve">faire cependant <lb/>toujours équilibre avec elles, ou avec ces poids, quoi <lb/>qu’ils demeurent toujours les mêmes.</s> |
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1537 <s xml:id="echoid-s840" xml:space="preserve"/> |
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1538 </p> |
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1539 </div> |
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1540 <div xml:id="echoid-div95" type="section" level="1" n="66"> |
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1541 <head xml:id="echoid-head66" xml:space="preserve"><emph style="sc">Corollaire</emph> X.</head> |
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1542 <p> |
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1543 <s xml:id="echoid-s841" xml:space="preserve">Ce qui fait voir que ſur une infinité de cas diffé-<lb/>rens ou cet équilibre peut arriver, il n’y en a qu’un <lb/>feul ou le poids, ou bien la puiſſance D, puiſſe être <lb/>double de chacune des puiſſances P & </s> |
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1544 <s xml:id="echoid-s842" xml:space="preserve">R; </s> |
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1545 <s xml:id="echoid-s843" xml:space="preserve">& </s> |
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1546 <s xml:id="echoid-s844" xml:space="preserve">que dans <lb/>tousles autres il eſt toujours moindre que double, & </s> |
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1547 <s xml:id="echoid-s845" xml:space="preserve"><lb/>même moindre à l’infini que chacune d’elles.</s> |
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1548 <s xml:id="echoid-s846" xml:space="preserve"/> |
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1549 </p> |
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1550 <p> |
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1551 <s xml:id="echoid-s847" xml:space="preserve">Tous ceux qwi ſe mêlent de Mècbanique, ſcavent aſſez <lb/>que l’on regarde ordinairement comme génèrale & </s> |
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1552 <s xml:id="echoid-s848" xml:space="preserve">comme <lb/>abſolument vraye cette propoſition: </s> |
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1553 <s xml:id="echoid-s849" xml:space="preserve">qu’un poids attaché, <lb/>ou ſuſpendu au centre mobile d’une poulie à moufle, <lb/>& </s> |
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1554 <s xml:id="echoid-s850" xml:space="preserve">en équilibre avec une puiſſance appliquée à l’ex-<lb/>trémitè d’une corde qui embraſſant cette poulie, à <lb/>ſon autre extrémité retenuë par quelque clou, ou <lb/>autrement, eſt double de cette puiſſance. </s> |
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1555 <s xml:id="echoid-s851" xml:space="preserve">Cependant <lb/>on voit par ce dernier Corollaire que ſur une infinité de cas <lb/>diffèrens, ou cet équilibre peut arriver, cette propoſition n’eſt <lb/>vraye que dans un ſeul, qui eſt lors que les parties de corde <lb/>gui touchent cette poulie ſont paralleles; </s> |
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1556 <s xml:id="echoid-s852" xml:space="preserve">& </s> |
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1557 <s xml:id="echoid-s853" xml:space="preserve">fauſſe dans tous <lb/>les autres. </s> |
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1558 <s xml:id="echoid-s854" xml:space="preserve">Il eſt vrai que dans la dèmonſtration que les Au-<lb/>teurs qui l’ont avancèe, en donnent, ils ſuppoſent tous que ces <lb/>parties de corde touchent cette poulie aux extrèmitez d’un <lb/>même diametre, & </s> |
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1559 <s xml:id="echoid-s855" xml:space="preserve">conſèquemment qu’elles ſont paralleles;</s> |
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1560 <s xml:id="echoid-s856" xml:space="preserve"> |
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1561 <pb o="32" file="0058" n="58" rhead="NOUVELLE"/> |
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1562 mais outre qu’il eſt rare qu’elles le ſoient, c’eſt que n’ayant <lb/> |
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1563 <anchor type="note" xlink:label="note-0058-01a" xlink:href="note-0058-01"/> |
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1564 point fait cette reſtriction dans leur propoſition, ils la regar-<lb/>dent dans la ſuite comme générale, & </s> |
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1565 <s xml:id="echoid-s857" xml:space="preserve">l’appliquent indiffé-<lb/>remment à toutes les machines ou l’on ſe ſert de moufles, ſans <lb/>avoir égard à la ſituation de leurs cordes; </s> |
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1566 <s xml:id="echoid-s858" xml:space="preserve">Ce qui les a jettez <lb/>dans des mépriſes conſidérables, comme on le verra dans les <lb/>Corollaires 15. </s> |
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1567 <s xml:id="echoid-s859" xml:space="preserve">& </s> |
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1568 <s xml:id="echoid-s860" xml:space="preserve">17.</s> |
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1569 <s xml:id="echoid-s861" xml:space="preserve"/> |
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1570 </p> |
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1571 <div xml:id="echoid-div95" type="float" level="2" n="1"> |
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1572 <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">DES <lb/>POULIES.</note> |
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1573 </div> |
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1574 </div> |
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1575 <div xml:id="echoid-div97" type="section" level="1" n="67"> |
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1576 <head xml:id="echoid-head67" xml:space="preserve"><emph style="sc">Corollaire</emph> XI.</head> |
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1577 <p> |
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1578 <s xml:id="echoid-s862" xml:space="preserve">Soit que le centre de la poulie A demeure fixe, <lb/>ſoit qu’on le ſuppoſe mobile, tant que ces puiſſances <lb/>demeurent ainſi en équilibre aux extrémitez P & </s> |
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1579 <s xml:id="echoid-s863" xml:space="preserve">R <lb/>d’une même corde paſſée par deſſus, ou par deſſous <lb/>cette poulie, elles ſont toujours égales: </s> |
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1580 <s xml:id="echoid-s864" xml:space="preserve">puiſque quel-<lb/>que ſoit la charge de cette poulie, ſi elle eſt fixe, ou <lb/>bien le poids qui y eſt attaché, ſi elle eſt mobile; </s> |
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1581 <s xml:id="echoid-s865" xml:space="preserve">cette <lb/>charge, ou ce poids, tant que dure cet équilibre, eſt <lb/>toujours à chacune d’elles, comme le ſinus de l’angle <lb/>de leurs parties de corde, au ſinus de ſa moitié.</s> |
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1582 <s xml:id="echoid-s866" xml:space="preserve"/> |
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1583 </p> |
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1584 </div> |
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1585 <div xml:id="echoid-div98" type="section" level="1" n="68"> |
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1586 <head xml:id="echoid-head68" xml:space="preserve"><emph style="sc">Corollaire</emph> XII.</head> |
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1587 <p> |
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1588 <s xml:id="echoid-s867" xml:space="preserve">Si ces parties de corde des puiſſances P, & </s> |
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1589 <s xml:id="echoid-s868" xml:space="preserve">R, <lb/>lorſqu’elles ſoutiennent la puiſſance, ou le poids D, <lb/>ne ſont point paralleles, ces deux mêmes puiſſances <lb/>le pourront ſoutenir dans deux ſituations différentes <lb/>de leurs cordes; </s> |
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1590 <s xml:id="echoid-s869" xml:space="preserve">parce que ces cordes peuvent faire <lb/>des angles égaux en H de part & </s> |
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1591 <s xml:id="echoid-s870" xml:space="preserve">d’autre de la poulie <lb/>A, avec ſa ligne de direction AH, ſoit en s’écartant <lb/>l’une de l’autre, (fig. </s> |
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1592 <s xml:id="echoid-s871" xml:space="preserve">20. </s> |
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1593 <s xml:id="echoid-s872" xml:space="preserve">& </s> |
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1594 <s xml:id="echoid-s873" xml:space="preserve">22.) </s> |
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1595 <s xml:id="echoid-s874" xml:space="preserve">ſoit en s’approchant; <lb/></s> |
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1596 <s xml:id="echoid-s875" xml:space="preserve">(fig. </s> |
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1597 <s xml:id="echoid-s876" xml:space="preserve">21. </s> |
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1598 <s xml:id="echoid-s877" xml:space="preserve">& </s> |
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1599 <s xml:id="echoid-s878" xml:space="preserve">23.) </s> |
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1600 <s xml:id="echoid-s879" xml:space="preserve">& </s> |
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1601 <s xml:id="echoid-s880" xml:space="preserve">par conſéquent les mêmes puiſſan-<lb/>ces P, & </s> |
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1602 <s xml:id="echoid-s881" xml:space="preserve">R, qui dans l’une de ces ſituations de cor-<lb/>des, ſont capables de ſoutenir la puiſſance, ou le <lb/>poids D, le pourront encore ſoutenir dans l’autre.</s> |
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1603 <s xml:id="echoid-s882" xml:space="preserve"/> |
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1604 </p> |
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1605 <pb o="33" file="0059" n="59" rhead="MECHANIQUE."/> |
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1606 </div> |
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1607 <div xml:id="echoid-div99" type="section" level="1" n="69"> |
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1608 <head xml:id="echoid-head69" xml:space="preserve"><emph style="sc">Corollaire</emph> XIII.</head> |
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1609 <note position="right" xml:space="preserve">DES <lb/>POULIES.</note> |
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1610 <p> |
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1611 <s xml:id="echoid-s883" xml:space="preserve">Mais ſi les parties de corde des puiſſances P & </s> |
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1612 <s xml:id="echoid-s884" xml:space="preserve">R <lb/>ſont paralleles, elles ne pourront ſoutenir la puiſſan-<lb/>ce, ou le poids D qu’en cette ſeule ſituation; </s> |
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1613 <s xml:id="echoid-s885" xml:space="preserve">parce <lb/>qu’il n’eſt pas poſſible d’en trouver d’autre, ou cette <lb/>puiſſance, ou bien ce poids, ſoit double de chacune <lb/>des puiſſances P & </s> |
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1614 <s xml:id="echoid-s886" xml:space="preserve">R qui le ſoutiennent.</s> |
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1615 <s xml:id="echoid-s887" xml:space="preserve"/> |
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1616 </p> |
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1617 </div> |
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1618 <div xml:id="echoid-div100" type="section" level="1" n="70"> |
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1619 <head xml:id="echoid-head70" xml:space="preserve"><emph style="sc">Corollaire</emph> XIV.</head> |
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1620 <p> |
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1621 <s xml:id="echoid-s888" xml:space="preserve">On voit encore de cette propoſition que le poids <lb/> |
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1622 <anchor type="note" xlink:label="note-0059-02a" xlink:href="note-0059-02"/> |
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1623 D étant en équilibre avec la puiſſance R, par le <lb/>moyen de pluſieurs moufles A, B, C, &</s> |
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1624 <s xml:id="echoid-s889" xml:space="preserve">c. </s> |
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1625 <s xml:id="echoid-s890" xml:space="preserve">Séparez, <lb/>& </s> |
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1626 <s xml:id="echoid-s891" xml:space="preserve">appliquez le long du poteau EG, ou de quelqu’au-<lb/>tre corps que ce ſoit, de la maniére qu’on les voit <lb/>ici; </s> |
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1627 <s xml:id="echoid-s892" xml:space="preserve">eſt à cette puiſſance, comme le produit des ſinus <lb/>des angles H, K, L, &</s> |
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1628 <s xml:id="echoid-s893" xml:space="preserve">c. </s> |
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1629 <s xml:id="echoid-s894" xml:space="preserve">que font, lors qu’on les pro-<lb/>longe, les parties des cordes EK, FL, GR, &</s> |
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1630 <s xml:id="echoid-s895" xml:space="preserve">c. <lb/></s> |
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1631 <s xml:id="echoid-s896" xml:space="preserve">qui touchent ces poulies; </s> |
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1632 <s xml:id="echoid-s897" xml:space="preserve">au produit des ſinus de <lb/>chacun leur moitié: </s> |
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1633 <s xml:id="echoid-s898" xml:space="preserve">Car ſelon la propoſition préſen-<lb/>te, la réſiſtance de la poulie A, ou bien le poids D eſt <lb/>à la réſiſtance de la poulie B, comme le ſinus de l’angle <lb/>H, au ſinus de ſa moitié. </s> |
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1634 <s xml:id="echoid-s899" xml:space="preserve">La réſiſtance de la poulie <lb/>B eſt auſſi à celle de la poulie C, comme le ſinus de <lb/>l’angle K, au ſinus de ſa moitié. </s> |
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1635 <s xml:id="echoid-s900" xml:space="preserve">Enfin la réſiſtance <lb/>de la poulie C eſt encore à celle de la puiſſance R, <lb/>comme le ſinus de l’angle L, au ſinus de ſa moitié; </s> |
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1636 <s xml:id="echoid-s901" xml:space="preserve">& </s> |
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1637 <s xml:id="echoid-s902" xml:space="preserve"><lb/>ainſi de même à l’infini: </s> |
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1638 <s xml:id="echoid-s903" xml:space="preserve">Donc en multipliant par <lb/>ordre les termes de toutes ces proportions, c’eſt-à-<lb/>dire, les antécédens par les antécédens, & </s> |
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1639 <s xml:id="echoid-s904" xml:space="preserve">les conſé-<lb/>quens par les conſéquens, on aura le poids D à la <lb/>puiſſance R, comme le produit des ſinus des angles <lb/>H, K, L, &</s> |
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1640 <s xml:id="echoid-s905" xml:space="preserve">c. </s> |
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1641 <s xml:id="echoid-s906" xml:space="preserve">au produit des ſinus de chacun leur <lb/>moitié.</s> |
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1642 <s xml:id="echoid-s907" xml:space="preserve"/> |
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1643 </p> |
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1644 <div xml:id="echoid-div100" type="float" level="2" n="1"> |
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1645 <note position="right" xlink:label="note-0059-02" xlink:href="note-0059-02a" xml:space="preserve">fig. 24. <lb/>205.</note> |
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1646 </div> |
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1647 <pb o="34" file="0060" n="60" rhead="NOUVELLE"/> |
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1648 </div> |
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1649 <div xml:id="echoid-div102" type="section" level="1" n="71"> |
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1650 <head xml:id="echoid-head71" xml:space="preserve"><emph style="sc">Corollaire</emph> XV.</head> |
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1651 <note position="left" xml:space="preserve">DES <lb/>POULIES.</note> |
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1652 <p> |
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1653 <s xml:id="echoid-s908" xml:space="preserve">Il ſuit de ce dernier Corollaire que ſur une in-<lb/>finité de cas différens, ou le poids D peut être en <lb/>équilibre avec la puiſſance R, à l’aide de pluſieurs <lb/>moufles, de la maniére qu’ils ſont ici; </s> |
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1654 <s xml:id="echoid-s909" xml:space="preserve">il n’y en a qu’un <lb/>ſeul, ou ce poids ſoit à cette puiſſance comme le der-<lb/>nier terme d’une progreſſion double, qui en a autant <lb/>qu’il y a de moufles, plus un, eſt au premier; </s> |
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1655 <s xml:id="echoid-s910" xml:space="preserve">c’eſt-à-<lb/>dire, ici, comme 8. </s> |
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1656 <s xml:id="echoid-s911" xml:space="preserve">à 1. </s> |
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1657 <s xml:id="echoid-s912" xml:space="preserve">C’eſt lors que les parties de <lb/>corde qui ſont tangentes de ces moufles, ſont paralle-<lb/>les entr’elles: </s> |
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1658 <s xml:id="echoid-s913" xml:space="preserve">parce que les angles H, K, L, &</s> |
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1659 <s xml:id="echoid-s914" xml:space="preserve">c. </s> |
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1660 <s xml:id="echoid-s915" xml:space="preserve">étant <lb/>alors infiniment aigus, leurs ſinus ſont doubles des <lb/>ſinus de leurs moitiez. </s> |
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1661 <s xml:id="echoid-s916" xml:space="preserve">Pour dans tous les autres, il <lb/>eſt toujours à cette puiſſance en moindre raiſon que <lb/>ce dernier terme au premier, & </s> |
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1662 <s xml:id="echoid-s917" xml:space="preserve">même, en moindre à <lb/>l’infini: </s> |
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1663 <s xml:id="echoid-s918" xml:space="preserve">parce que les angles H, K, L, &</s> |
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1664 <s xml:id="echoid-s919" xml:space="preserve">c. </s> |
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1665 <s xml:id="echoid-s920" xml:space="preserve">ne pou-<lb/>vant devenir plus aigus que lorſque ces parties de <lb/>cordes ſont paralleles, les raiſons de leurs ſinus aux <lb/>ſinus de leurs moitiez, ne peuvent auſſi jamais être <lb/>chacune plus grande que celle de 2. </s> |
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1666 <s xml:id="echoid-s921" xml:space="preserve">à I. </s> |
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1667 <s xml:id="echoid-s922" xml:space="preserve">au contraire <lb/>ces angles pouvant devenir toujours plus obtus juſqu’à <lb/>l’infini, les raiſons de leurs ſinus aux ſinus de leurs <lb/>moitiez, peuvent auſſi diminuer à l’infini.</s> |
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1668 <s xml:id="echoid-s923" xml:space="preserve"/> |
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1669 </p> |
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1670 <p> |
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1671 <s xml:id="echoid-s924" xml:space="preserve">On voit aſſez la mépriſe de ceux qui dans cet uſage des <lb/>poulies à moufle, ont avancé comme propoſition générale que le <lb/>poids D eſt à la puiſſance R, comme le dernier terme <lb/>d’une progreſſion double, qui en à autant qu’il y a <lb/>de moufles, plus un, eſt au premier. </s> |
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1672 <s xml:id="echoid-s925" xml:space="preserve">Ce qui les a trom-<lb/>pez c’eſt l’uſage trop étendu qu’ils ont donné à la propoſition <lb/>raportée dans la réfléxion qui ſuit le Corollaire 10. </s> |
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1673 <s xml:id="echoid-s926" xml:space="preserve">de la <lb/>propoſition préſente.</s> |
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1674 <s xml:id="echoid-s927" xml:space="preserve"/> |
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1675 </p> |
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1676 <figure> |
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1677 <image file="0060-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0060-01"/> |
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1678 </figure> |
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1679 <pb o="35" file="0061" n="61" rhead="MECHANIQUE."/> |
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1680 </div> |
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1681 <div xml:id="echoid-div103" type="section" level="1" n="72"> |
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1682 <head xml:id="echoid-head72" xml:space="preserve"><emph style="sc">Corollaire</emph> XVI.</head> |
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1683 <note position="right" xml:space="preserve">DES <lb/>POULIES.</note> |
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1684 <p> |
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1685 <s xml:id="echoid-s928" xml:space="preserve">Préſentement ſi l’on ſe ſert de pluſieurs poulies <lb/>liées enſemble, comme on les voit dans les figures 26. <lb/></s> |
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1686 <s xml:id="echoid-s929" xml:space="preserve"> |
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1687 <anchor type="note" xlink:label="note-0061-02a" xlink:href="note-0061-02"/> |
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1688 & </s> |
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1689 <s xml:id="echoid-s930" xml:space="preserve">27. </s> |
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1690 <s xml:id="echoid-s931" xml:space="preserve">Il ſuit encore de cette propoſition que la puiſ-<lb/>ſance R eſt au poids D qu’elle ſoutient à l’aide de ces <lb/>poulies, comme le produit des ſinus des moitiez de <lb/>chacun des angles que font, ſi on les prolonge, les <lb/>cordes tangentes des poulies mobiles L, K, & </s> |
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1691 <s xml:id="echoid-s932" xml:space="preserve">H, à la <lb/>ſomme des produits de chacun des ſinus de ces mêmes <lb/>angles par les ſinus des moitiez de chacun des autres. <lb/></s> |
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1692 <s xml:id="echoid-s933" xml:space="preserve">Par exemple, ſoit le ſinus de l’angle de ces cordes fait <lb/>en A, appellé a; </s> |
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1693 <s xml:id="echoid-s934" xml:space="preserve">& </s> |
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1694 <s xml:id="echoid-s935" xml:space="preserve">celui de ſa moitié appellé b. </s> |
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1695 <s xml:id="echoid-s936" xml:space="preserve">Celui de <lb/>l’angle C, appellé c; </s> |
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1696 <s xml:id="echoid-s937" xml:space="preserve">& </s> |
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1697 <s xml:id="echoid-s938" xml:space="preserve">celui de ſa moitié appellé d. </s> |
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1698 <s xml:id="echoid-s939" xml:space="preserve"><lb/>Enfin celui de l’angle E, appellé e; </s> |
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1699 <s xml:id="echoid-s940" xml:space="preserve">& </s> |
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1700 <s xml:id="echoid-s941" xml:space="preserve">celui de ſa moi-<lb/>tié appellé f. </s> |
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1701 <s xml:id="echoid-s942" xml:space="preserve">Cela ſuppoſé il ſuit, dî-je, de cette pro-<lb/>poſition que la puiſſance R en ce cas eſt au poids D, <lb/>comme bàf à adf + cbf + ebd. </s> |
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1702 <s xml:id="echoid-s943" xml:space="preserve">Parceque la corde <lb/>RRORNRM étant également bandée dans tou-<lb/>tes ſes parties, & </s> |
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1703 <s xml:id="echoid-s944" xml:space="preserve">d’une force égale à celle de la puiſ-<lb/>ſance R; </s> |
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1704 <s xml:id="echoid-s945" xml:space="preserve">on la peut regarder, tant que dure cet équi-<lb/>libre, comme diviſée en autant de cordes RRO, <lb/>RN, & </s> |
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1705 <s xml:id="echoid-s946" xml:space="preserve">RM, qu’il y a de poulies L, K, & </s> |
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1706 <s xml:id="echoid-s947" xml:space="preserve">H, dans <lb/>l’écharpe LH; </s> |
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1707 <s xml:id="echoid-s948" xml:space="preserve">& </s> |
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1708 <s xml:id="echoid-s949" xml:space="preserve">chacune de ces cordes comme fixe <lb/>en O, N, & </s> |
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1709 <s xml:id="echoid-s950" xml:space="preserve">M, & </s> |
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1710 <s xml:id="echoid-s951" xml:space="preserve">tirée du côté de R, R, & </s> |
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1711 <s xml:id="echoid-s952" xml:space="preserve">R par la <lb/>puiſſance R, ou par d’autres qui lui ſoient égales. </s> |
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1712 <s xml:id="echoid-s953" xml:space="preserve"><lb/>Et parce que les poulies L, K, & </s> |
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1713 <s xml:id="echoid-s954" xml:space="preserve">H, portent chacune <lb/>quelque choſe du poids D, regardons-le auſſi comme <lb/>diviſé en autant de parties x, y, & </s> |
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1714 <s xml:id="echoid-s955" xml:space="preserve">z, dont la partie x <lb/>ſoit portée par la poulie L; </s> |
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1715 <s xml:id="echoid-s956" xml:space="preserve">la partie y, par la poulie <lb/>K; </s> |
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1716 <s xml:id="echoid-s957" xml:space="preserve">& </s> |
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1717 <s xml:id="echoid-s958" xml:space="preserve">la partie z, par la poulie H.</s> |
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1718 <s xml:id="echoid-s959" xml:space="preserve"/> |
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1719 </p> |
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1720 <div xml:id="echoid-div103" type="float" level="2" n="1"> |
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1721 <note position="right" xlink:label="note-0061-02" xlink:href="note-0061-02a" xml:space="preserve">fig. 26.</note> |
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1722 </div> |
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1723 <pb o="36" file="0062" n="62" rhead="NOUVELLE"/> |
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1724 <p> |
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1725 <s xml:id="echoid-s960" xml:space="preserve">Cela conçcû il eſt clair par la propoſition qu’on vient <lb/> |
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1726 <anchor type="note" xlink:label="note-0062-01a" xlink:href="note-0062-01"/> |
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1727 de démontrer</s> |
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1728 </p> |
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1729 <div xml:id="echoid-div104" type="float" level="2" n="2"> |
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1730 <note position="left" xlink:label="note-0062-01" xlink:href="note-0062-01a" xml:space="preserve">DES <lb/>POULIES.</note> |
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1731 </div> |
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1732 <note position="right" xml:space="preserve"> <lb/>que{ # {x. R :: a. b. \\ R. y :: d. c.} # Donc {x. y :: ad. bc. \\ & \\ x. x + y :: ad. ad + bc. # }Donc <lb/># {z. R :: e. f. \\ R. x :: b. a.} # Donc z. x :: eb. fa. <lb/></note> |
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1733 <p> |
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1734 <s xml:id="echoid-s961" xml:space="preserve">z. </s> |
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1735 <s xml:id="echoid-s962" xml:space="preserve">x + y :</s> |
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1736 <s xml:id="echoid-s963" xml:space="preserve">: adeb. </s> |
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1737 <s xml:id="echoid-s964" xml:space="preserve">aadf + abcf. </s> |
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1738 <s xml:id="echoid-s965" xml:space="preserve">Donc z. </s> |
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1739 <s xml:id="echoid-s966" xml:space="preserve">z + x + y :</s> |
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1740 <s xml:id="echoid-s967" xml:space="preserve">: <lb/>adeb. </s> |
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1741 <s xml:id="echoid-s968" xml:space="preserve">adeb + aadf + abcf. </s> |
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1742 <s xml:id="echoid-s969" xml:space="preserve">Or R. </s> |
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1743 <s xml:id="echoid-s970" xml:space="preserve">z :</s> |
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1744 <s xml:id="echoid-s971" xml:space="preserve">: f. </s> |
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1745 <s xml:id="echoid-s972" xml:space="preserve">e. </s> |
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1746 <s xml:id="echoid-s973" xml:space="preserve">Donc R. <lb/></s> |
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1747 <s xml:id="echoid-s974" xml:space="preserve">z + x + y = D :</s> |
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1748 <s xml:id="echoid-s975" xml:space="preserve">: adefb. </s> |
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1749 <s xml:id="echoid-s976" xml:space="preserve">adeeb + aadef + aebcf. </s> |
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1750 <s xml:id="echoid-s977" xml:space="preserve">Et en <lb/>diviſant les deux terniers termes de cette derniére <lb/>proportion, par ae, l’on aura R. </s> |
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1751 <s xml:id="echoid-s978" xml:space="preserve">D :</s> |
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1752 <s xml:id="echoid-s979" xml:space="preserve">: dfb. </s> |
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1753 <s xml:id="echoid-s980" xml:space="preserve">edb + <lb/>adf + bcf. </s> |
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1754 <s xml:id="echoid-s981" xml:space="preserve">Ce qu’il faloit démontrer.</s> |
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1755 <s xml:id="echoid-s982" xml:space="preserve"/> |
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1756 </p> |
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1757 </div> |
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1758 <div xml:id="echoid-div106" type="section" level="1" n="73"> |
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1759 <head xml:id="echoid-head73" xml:space="preserve"><emph style="sc">Corollaire</emph> XVII.</head> |
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1760 <p> |
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1761 <s xml:id="echoid-s983" xml:space="preserve">D’où il ſuit que dans cet uſage des poulies, lors <lb/>que les parties de corde, qui touchent celles de l’é-<lb/>charpe LH, ſont paralleles, la puiſſance R eſt au <lb/>poids D, comme l’unité au double du nombre des <lb/>poulies ſuſpenduës; </s> |
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1762 <s xml:id="echoid-s984" xml:space="preserve">mais que dans tout autre cas, <lb/>elle lui eſt toujours en plus grande raiſon; </s> |
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1763 <s xml:id="echoid-s985" xml:space="preserve">& </s> |
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1764 <s xml:id="echoid-s986" xml:space="preserve">même, <lb/>cette raiſon augmente, quoi qu’en proportion diffé-<lb/>rente, à meſure que les angles A, C & </s> |
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1765 <s xml:id="echoid-s987" xml:space="preserve">E deviennent <lb/>moins aigus, ou plus obtus.</s> |
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1766 <s xml:id="echoid-s988" xml:space="preserve"/> |
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|
1767 </p> |
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|
1768 <p style="it"> |
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1769 <s xml:id="echoid-s989" xml:space="preserve">On voit aſſez que tous ces Corollaires avec une infinité <lb/>d’autres qu’on pourroit encore tirer de cette propoſition, dé-<lb/>pendent abſolument de ſon univerſalité, & </s> |
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1770 <s xml:id="echoid-s990" xml:space="preserve">que ſans cela <lb/>il ſeroit impoſſible de réſoudre une infinité de Problêmes <lb/>qu’on peut faire ſur cette matiére. </s> |
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1771 <s xml:id="echoid-s991" xml:space="preserve">Par exemple celui-ci.</s> |
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1772 <s xml:id="echoid-s992" xml:space="preserve"/> |
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1773 </p> |
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1774 <figure> |
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1775 <image file="0062-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0062-01"/> |
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1776 </figure> |
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1777 <pb o="37" file="0063" n="63" rhead="MECHANIQUE."/> |
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1778 <figure> |
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1779 <image file="0063-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0063-01"/> |
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1780 </figure> |
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1781 <note position="right" xml:space="preserve">DES <lb/>POULIES.</note> |
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1782 </div> |
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1783 <div xml:id="echoid-div107" type="section" level="1" n="74"> |
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1784 <head xml:id="echoid-head74" xml:space="preserve">PROBLEME.</head> |
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1785 <p style="it"> |
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1786 <s xml:id="echoid-s993" xml:space="preserve">F Aire ſoutenir quelque poids D que ce ſoit, à quelque <lb/> |
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1787 <anchor type="note" xlink:label="note-0063-02a" xlink:href="note-0063-02"/> |
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1788 puiſſance R que ce puiſſe être, par le moyen d’une ſeule <lb/>poulie à moufle.</s> |
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1789 <s xml:id="echoid-s994" xml:space="preserve"/> |
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1790 </p> |
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1791 <div xml:id="echoid-div107" type="float" level="2" n="1"> |
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1792 <note position="right" xlink:label="note-0063-02" xlink:href="note-0063-02a" xml:space="preserve">fig. 28.</note> |
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1793 </div> |
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1794 </div> |
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1795 <div xml:id="echoid-div109" type="section" level="1" n="75"> |
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1796 <head xml:id="echoid-head75" xml:space="preserve"><emph style="sc">Solution</emph></head> |
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1797 <p> |
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1798 <s xml:id="echoid-s995" xml:space="preserve">Premiérement ſi cette puiſſance eſt plus grande <lb/>que ce poids, faite ſur EH perpendiculaire à l’hori-<lb/>zon, & </s> |
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1799 <s xml:id="echoid-s996" xml:space="preserve">priſe à diſcretion, le triangle Iſocelle EFH, <lb/>dont chacun des côtez EF, & </s> |
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1800 <s xml:id="echoid-s997" xml:space="preserve">FH, ſoit en même rai-<lb/>ſon à ſa baſe EH, que la puiſſance R, dont il eſt <lb/>queſtion, eſt au poids D. </s> |
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1801 <s xml:id="echoid-s998" xml:space="preserve">Du point H tirez HG per-<lb/>pendiculaire à HF, & </s> |
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1802 <s xml:id="echoid-s999" xml:space="preserve">égale au rayon de la poulie <lb/>A, dont on ſe veut ſervir; </s> |
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1803 <s xml:id="echoid-s1000" xml:space="preserve">du point G faite encore <lb/>GM parallele à HE, & </s> |
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1804 <s xml:id="echoid-s1001" xml:space="preserve">qui rencontre HF en M; </s> |
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1805 <s xml:id="echoid-s1002" xml:space="preserve">& </s> |
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1806 <s xml:id="echoid-s1003" xml:space="preserve"><lb/>de ce même point M faite auſſi MA parallele à HG, <lb/>& </s> |
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1807 <s xml:id="echoid-s1004" xml:space="preserve">qui rencontre auſſi EH en A; </s> |
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1808 <s xml:id="echoid-s1005" xml:space="preserve">placez enſuite en <lb/>ce point le centre de la poulie A, & </s> |
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1809 <s xml:id="echoid-s1006" xml:space="preserve">ſuſpendez le poids <lb/>D à cette poulie ſuivant AH. </s> |
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1810 <s xml:id="echoid-s1007" xml:space="preserve">Enfin aprés avoir di-<lb/>rigé la partie MR dè ſa corde ſuivant HF, & </s> |
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1811 <s xml:id="echoid-s1008" xml:space="preserve">ſon <lb/>autre partie PN parallelement à EF; </s> |
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1812 <s xml:id="echoid-s1009" xml:space="preserve">arrêtez cette <lb/>corde par un bout au clou P, & </s> |
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1813 <s xml:id="echoid-s1010" xml:space="preserve">appliquez à l’autre <lb/>la puiſſance R: </s> |
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1814 <s xml:id="echoid-s1011" xml:space="preserve">cela fait elle ſoutiendra ce poids en <lb/>cet état.</s> |
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1815 <s xml:id="echoid-s1012" xml:space="preserve"/> |
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1816 </p> |
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1817 </div> |
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1818 <div xml:id="echoid-div110" type="section" level="1" n="76"> |
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1819 <head xml:id="echoid-head76" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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1820 <p> |
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1821 <s xml:id="echoid-s1013" xml:space="preserve">Le poids D peut être ſoutenu en cet état (Cor. </s> |
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1822 <s xml:id="echoid-s1014" xml:space="preserve">2.) <lb/></s> |
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1823 <s xml:id="echoid-s1015" xml:space="preserve">par deux puiſſances, à chacune deſquelles il ſoit <lb/>comme le ſinus de l’angle RHP, au ſinus de ſa moitié <lb/>EHR, ou EHP; </s> |
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1824 <s xml:id="echoid-s1016" xml:space="preserve">c’eſt-à-dire, (Lemm. </s> |
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1825 <s xml:id="echoid-s1017" xml:space="preserve">5.) </s> |
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1826 <s xml:id="echoid-s1018" xml:space="preserve">comme <lb/>EH à EF, ou bien (hyp.) </s> |
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1827 <s xml:id="echoid-s1019" xml:space="preserve">comme il eſt à la puiſſance <lb/>R: </s> |
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1828 <s xml:id="echoid-s1020" xml:space="preserve">Donc le clou P faiſant la fonction d’une de ces |
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1829 <pb o="38" file="0064" n="64" rhead="NOUVELLE"/> |
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1830 puiſſances, celle-ci ſoutiendra ce poids en cet état. </s> |
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1831 <s xml:id="echoid-s1021" xml:space="preserve">Ce <lb/> |
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1832 <anchor type="note" xlink:label="note-0064-01a" xlink:href="note-0064-01"/> |
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1833 qu’il faloit faire.</s> |
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1834 <s xml:id="echoid-s1022" xml:space="preserve"/> |
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1835 </p> |
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1836 <div xml:id="echoid-div110" type="float" level="2" n="1"> |
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1837 <note position="left" xlink:label="note-0064-01" xlink:href="note-0064-01a" xml:space="preserve">DES <lb/>POULIES.</note> |
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1838 </div> |
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1839 <p> |
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1840 <s xml:id="echoid-s1023" xml:space="preserve">Secondement, ſi c’eſt le poids D qui ſoit plus <lb/>grand que la puiſſance R, quelque grand qu’il ſoit, <lb/>& </s> |
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1841 <s xml:id="echoid-s1024" xml:space="preserve">quelque petite elle, qu’elle puiſſe être, on le lui <lb/> |
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1842 <anchor type="note" xlink:label="note-0064-02a" xlink:href="note-0064-02"/> |
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1843 pourra encore faire ſoutenir: </s> |
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1844 <s xml:id="echoid-s1025" xml:space="preserve">voici comment. </s> |
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1845 <s xml:id="echoid-s1026" xml:space="preserve">Ayant <lb/>décrit du centre F avec le rayon HF perpendicu-<lb/>laire à l’horizon, & </s> |
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1846 <s xml:id="echoid-s1027" xml:space="preserve">pris à diſcretion, l’arc HEB; </s> |
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1847 <s xml:id="echoid-s1028" xml:space="preserve">& </s> |
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1848 <s xml:id="echoid-s1029" xml:space="preserve"><lb/>y ayant inſcrit une ligne HE, qui ſoit à HF, comme <lb/>la puiſſance R au poids D; </s> |
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1849 <s xml:id="echoid-s1030" xml:space="preserve">joignez FE, & </s> |
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1850 <s xml:id="echoid-s1031" xml:space="preserve">faite en-<lb/>ſuite HG perpendiculaire à HF, & </s> |
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1851 <s xml:id="echoid-s1032" xml:space="preserve">égale au rayon de <lb/>la poulie A, dont on ſe veut ſervir; </s> |
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1852 <s xml:id="echoid-s1033" xml:space="preserve">Du point G faite <lb/>encore GM parallele à HE, & </s> |
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1853 <s xml:id="echoid-s1034" xml:space="preserve">qui rencontre HF en <lb/>M, d’où il faut faire encore MA parallele à HG, & </s> |
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1854 <s xml:id="echoid-s1035" xml:space="preserve">qui <lb/>rencontre HE en A, où vous placerez le centre de <lb/>la poulie A, à laquelle vous appliquerez la puiſſance <lb/>R ſuivant AH, & </s> |
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1855 <s xml:id="echoid-s1036" xml:space="preserve">le poids D ſuivant HF, l’autre <lb/>bout de ſa corde étant attaché en P fuivant NP pa-<lb/>rallele à EF. </s> |
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1856 <s xml:id="echoid-s1037" xml:space="preserve">Cela fait la puiſſance R ſoutiendra en-<lb/>core le poids D en cet état.</s> |
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1857 <s xml:id="echoid-s1038" xml:space="preserve"/> |
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1858 </p> |
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1859 <div xml:id="echoid-div111" type="float" level="2" n="2"> |
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1860 <note position="left" xlink:label="note-0064-02" xlink:href="note-0064-02a" xml:space="preserve">fig. 29.</note> |
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1861 </div> |
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1862 </div> |
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1863 <div xml:id="echoid-div113" type="section" level="1" n="77"> |
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1864 <head xml:id="echoid-head77" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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1865 <p> |
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1866 <s xml:id="echoid-s1039" xml:space="preserve">Cette puiſſance peut faire équilibre en cet état avec <lb/>deux autres, pourvu qu’elle ſoit à chacune d’elles, <lb/>(Cor. </s> |
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1867 <s xml:id="echoid-s1040" xml:space="preserve">2.) </s> |
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1868 <s xml:id="echoid-s1041" xml:space="preserve">comme le ſinus de l’angle PHF, au ſinus <lb/>de ſa moitié PHE, ou à EF; </s> |
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1869 <s xml:id="echoid-s1042" xml:space="preserve">c’eſt-à-dire, (Lemm. </s> |
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1870 <s xml:id="echoid-s1043" xml:space="preserve">5.) <lb/></s> |
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1871 <s xml:id="echoid-s1044" xml:space="preserve">Comme HE à HF, ou EHF; </s> |
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1872 <s xml:id="echoid-s1045" xml:space="preserve">ou bien (hyp.) </s> |
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1873 <s xml:id="echoid-s1046" xml:space="preserve">comme <lb/>elle eſt au poids D: </s> |
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1874 <s xml:id="echoid-s1047" xml:space="preserve">Donc le clou P faiſant la fonc-<lb/>tion d’une de ces puiſſances, & </s> |
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1875 <s xml:id="echoid-s1048" xml:space="preserve">le poids D celle de <lb/>l’autre, la puiſſance R doit le ſoutenir en cet état. </s> |
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1876 <s xml:id="echoid-s1049" xml:space="preserve"><lb/>Ce qu’il F. </s> |
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1877 <s xml:id="echoid-s1050" xml:space="preserve">D.</s> |
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1878 <s xml:id="echoid-s1051" xml:space="preserve"/> |
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1879 </p> |
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1880 </div> |
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1881 <div xml:id="echoid-div114" type="section" level="1" n="78"> |
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1882 <head xml:id="echoid-head78" xml:space="preserve"><emph style="sc">Corollaire.</emph></head> |
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1883 <p> |
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1884 <s xml:id="echoid-s1052" xml:space="preserve">On voit que l’on peut toujours faire ſoutenir quel- |
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1885 <pb o="39" file="0065" n="65" rhead="MECHANIQUE."/> |
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1886 que poids que ce ſoit, à quelque puiſſance que ce <lb/> |
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1887 <anchor type="note" xlink:label="note-0065-01a" xlink:href="note-0065-01"/> |
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1888 puiſſe être, par le moyen d’une ſeule poulie à mouf-<lb/>fle: </s> |
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1889 <s xml:id="echoid-s1053" xml:space="preserve">en appliquant le moindre des deux au centre <lb/>mobile de cette poulie, & </s> |
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1890 <s xml:id="echoid-s1054" xml:space="preserve">le plus grand au bout libre <lb/>de la corde qui l’embraſſe. </s> |
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1891 <s xml:id="echoid-s1055" xml:space="preserve">La raiſon en eſt évidente <lb/>par les Corollaires 7. </s> |
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1892 <s xml:id="echoid-s1056" xml:space="preserve">& </s> |
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1893 <s xml:id="echoid-s1057" xml:space="preserve">8.</s> |
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1894 <s xml:id="echoid-s1058" xml:space="preserve"/> |
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1895 </p> |
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1896 <div xml:id="echoid-div114" type="float" level="2" n="1"> |
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1897 <note position="right" xlink:label="note-0065-01" xlink:href="note-0065-01a" xml:space="preserve">DES <lb/>POULIES.</note> |
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1898 </div> |
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1899 </div> |
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1900 <div xml:id="echoid-div116" type="section" level="1" n="79"> |
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1901 <head xml:id="echoid-head79" xml:space="preserve"><emph style="sc">Remarque.</emph></head> |
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1902 <p> |
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1903 <s xml:id="echoid-s1059" xml:space="preserve">Il n’eſt pas cependant toujours néceſſaire de les <lb/>diſpoſer ainſi: </s> |
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1904 <s xml:id="echoid-s1060" xml:space="preserve">car s’il arrive que le plus grand des <lb/>deux ne ſoit point plus que double de l’autre, on ſera <lb/>libre d’appliquer celuy qu’on voudra au centre mo-<lb/>bile de la poulie A: </s> |
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1905 <s xml:id="echoid-s1061" xml:space="preserve">puiſque, qu’il y ſoit, (Cor. </s> |
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1906 <s xml:id="echoid-s1062" xml:space="preserve">8.) <lb/></s> |
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1907 <s xml:id="echoid-s1063" xml:space="preserve">ou non, (Cor. </s> |
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1908 <s xml:id="echoid-s1064" xml:space="preserve">7.) </s> |
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1909 <s xml:id="echoid-s1065" xml:space="preserve">il peut toujours monter juſqu’à <lb/>être double de l’autre, mais jamais davantage: </s> |
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1910 <s xml:id="echoid-s1066" xml:space="preserve">(Cor. </s> |
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1911 <s xml:id="echoid-s1067" xml:space="preserve">8.) </s> |
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1912 <s xml:id="echoid-s1068" xml:space="preserve"><lb/>ainſi lorſque l’un des deux (la puiſſance ou le poids) <lb/>fera plus que double de l’autre, il faudra néceſſai-<lb/>rement les appliquer ſuivant le Corollaire ci-deſſus; </s> |
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1913 <s xml:id="echoid-s1069" xml:space="preserve"><lb/>c’eſt-à-dire, appliquer le moindre au centre du mouf-<lb/>fle dont on ſe ſert, & </s> |
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1914 <s xml:id="echoid-s1070" xml:space="preserve">le plus grand ou bout libre <lb/>de la corde qui embraſſe cette poulie à moufle.</s> |
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1915 <s xml:id="echoid-s1071" xml:space="preserve"/> |
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1916 </p> |
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1917 <figure> |
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1918 <image file="0065-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0065-01"/> |
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1919 </figure> |
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1920 <pb o="40" file="0066" n="66" rhead="NOUVELLE"/> |
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1921 <figure> |
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1922 <image file="0066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0066-01"/> |
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1923 </figure> |
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1924 </div> |
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1925 <div xml:id="echoid-div117" type="section" level="1" n="80"> |
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1926 <head xml:id="echoid-head80" xml:space="preserve">PROPOSITION <lb/>FONDAMENTALE <lb/>DES POIDS SOUTENUS</head> |
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1927 <p> |
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1928 <s xml:id="echoid-s1072" xml:space="preserve">Sur quelque eſpéce de ſurfaces que ceſoit; <lb/></s> |
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1929 <s xml:id="echoid-s1073" xml:space="preserve">& </s> |
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1930 <s xml:id="echoid-s1074" xml:space="preserve">pour toutes les directions poſſibles <lb/>des puiſſances qui y ſont appliquées.</s> |
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1931 <s xml:id="echoid-s1075" xml:space="preserve"/> |
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1932 </p> |
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1933 <p style="it"> |
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1934 <s xml:id="echoid-s1076" xml:space="preserve">TELLE que ſoit la ſurface GH; </s> |
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1935 <s xml:id="echoid-s1077" xml:space="preserve">le poids EO, & </s> |
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1936 <s xml:id="echoid-s1078" xml:space="preserve"><lb/> |
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1937 <anchor type="note" xlink:label="note-0066-01a" xlink:href="note-0066-01"/> |
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1938 la puiſſance R qui le ſoutient deſſus, ſont toujours en-<lb/>tr’ eux en raiſon réciproque des ſinus des angles que font leurs <lb/>lignes de direction avec AD tirée perpendiculairement du point <lb/>A de leur concours, ſur la ſurface GH.</s> |
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1939 <s xml:id="echoid-s1079" xml:space="preserve"/> |
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1940 </p> |
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1941 <div xml:id="echoid-div117" type="float" level="2" n="1"> |
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1942 <note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">fig. 30. <lb/>31. <lb/>32. <lb/>33. <lb/>34. <lb/>35. <lb/>36.</note> |
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1943 </div> |
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1944 </div> |
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1945 <div xml:id="echoid-div119" type="section" level="1" n="81"> |
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1946 <head xml:id="echoid-head81" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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1947 <p> |
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1948 <s xml:id="echoid-s1080" xml:space="preserve">A fin que ce poids & </s> |
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1949 <s xml:id="echoid-s1081" xml:space="preserve">cette puiſſance demeurent ainſi <lb/>en equilibre ſur la ſurface GH, telle qu’elle ſoit, <lb/>il faut 1°. </s> |
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1950 <s xml:id="echoid-s1082" xml:space="preserve">que leurs lignes de direction EB & </s> |
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1951 <s xml:id="echoid-s1083" xml:space="preserve">FC, <lb/>ſe rencontrent en quelque point A: </s> |
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1952 <s xml:id="echoid-s1084" xml:space="preserve">car ſi elles étoient <lb/>paralleles, il eſt clair que le centre de gravité de ce <lb/>poids pourroit encore deſcendre d’une longueur éga-<lb/>le à la diſtance qu’elles auroient entr’elles; </s> |
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1953 <s xml:id="echoid-s1085" xml:space="preserve">ce qui <lb/>eſt contre l’hypothêſe. </s> |
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1954 <s xml:id="echoid-s1086" xml:space="preserve">2°. </s> |
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1955 <s xml:id="echoid-s1087" xml:space="preserve">Les impreſſions particu-<lb/>liéres que font ſur le point A, & </s> |
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1956 <s xml:id="echoid-s1088" xml:space="preserve">la peſanteur de ce <lb/>poids, & </s> |
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1957 <s xml:id="echoid-s1089" xml:space="preserve">la puiſſance R qui le retient; </s> |
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1958 <s xml:id="echoid-s1090" xml:space="preserve">étant les mê-<lb/>mes que ſi ce point étoit pouſſé en même temps par |
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1959 <pb o="41" file="0067" n="67" rhead="MECHANIQUE."/> |
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1960 deux forces qui leur fuſſent égales, ſuivant leurs lignes <lb/> |
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1961 <anchor type="note" xlink:label="note-0067-01a" xlink:href="note-0067-01"/> |
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1962 de direction AC & </s> |
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1963 <s xml:id="echoid-s1091" xml:space="preserve">AB:</s> |
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1964 <s xml:id="echoid-s1092" xml:space="preserve">le poids EO ainſi ſoutenu ſur <lb/>la ſurface GH par le concours d’action de ſa peſan-<lb/>teur & </s> |
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1965 <s xml:id="echoid-s1093" xml:space="preserve">de la puiſſance R, doittendre (Lem. </s> |
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1966 <s xml:id="echoid-s1094" xml:space="preserve">4. </s> |
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1967 <s xml:id="echoid-s1095" xml:space="preserve">Cor. </s> |
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1968 <s xml:id="echoid-s1096" xml:space="preserve">2.) <lb/></s> |
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1969 <s xml:id="echoid-s1097" xml:space="preserve">ſuivant quelque ligne AD qui ſoit la diagonale d’un <lb/>parallelogramme fait ſous des parties AC & </s> |
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1970 <s xml:id="echoid-s1098" xml:space="preserve">AB de <lb/>leurs lignes de direction, qui ſoient entr’elles, com-<lb/>me ce poids eſt à cette puiſſance. </s> |
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1971 <s xml:id="echoid-s1099" xml:space="preserve">3°. </s> |
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1972 <s xml:id="echoid-s1100" xml:space="preserve">Cette ligne AD <lb/>doit toujours être perpendiculaire à la ſurface GH, <lb/>telle qu’elle ſoit; </s> |
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1973 <s xml:id="echoid-s1101" xml:space="preserve">par exemple, au point O: </s> |
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1974 <s xml:id="echoid-s1102" xml:space="preserve">autrement <lb/>AD devenant alors la ligne dedirection de ce corps, il <lb/>rouleroit ou couleroit (Cor. </s> |
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1975 <s xml:id="echoid-s1103" xml:space="preserve">Lemm. </s> |
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1976 <s xml:id="echoid-s1104" xml:space="preserve">1.) </s> |
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1977 <s xml:id="echoid-s1105" xml:space="preserve">vers H, ou vers <lb/>G, ſelon que cette ligne ſe trouveroit au-deſſus ou <lb/>au-deſſous du point O. </s> |
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1978 <s xml:id="echoid-s1106" xml:space="preserve">4°. </s> |
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1979 <s xml:id="echoid-s1107" xml:space="preserve">Cette même ligne doit <lb/>encore paſſer par quelqu’un des points où ce poids <lb/>touche cette ſurface, c’eſt-à-dire, par quelqu’un des <lb/>points de ſa baze: </s> |
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1980 <s xml:id="echoid-s1108" xml:space="preserve">autrement, & </s> |
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1981 <s xml:id="echoid-s1109" xml:space="preserve">pour la même rai-<lb/>ſon, il rouleroit, ou couleroit encore du côté qu’elle <lb/>s’en écarteroit. </s> |
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1982 <s xml:id="echoid-s1110" xml:space="preserve">5°. </s> |
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1983 <s xml:id="echoid-s1111" xml:space="preserve">La force dont ce poids eſt ainſi <lb/>pouſſé ou tiré ſuivant AD par le concours d’action <lb/>de ſa peſanteur & </s> |
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1984 <s xml:id="echoid-s1112" xml:space="preserve">de la puiſſance R, eſt à celle de <lb/>cette puiſſance, (Lemm. </s> |
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1985 <s xml:id="echoid-s1113" xml:space="preserve">4. </s> |
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1986 <s xml:id="echoid-s1114" xml:space="preserve">Cor. </s> |
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1987 <s xml:id="echoid-s1115" xml:space="preserve">3.) </s> |
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1988 <s xml:id="echoid-s1116" xml:space="preserve">comme AD à AB; </s> |
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1989 <s xml:id="echoid-s1117" xml:space="preserve"><lb/>c’eſt-à-dire, (Lem. </s> |
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1990 <s xml:id="echoid-s1118" xml:space="preserve">5.) </s> |
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1991 <s xml:id="echoid-s1119" xml:space="preserve">commele ſinus de l’angle DBA, <lb/>ou de ſon complement BAC, au ſinus de l’an-<lb/>gle BDA, ou de DAC qui luy eſt égal. </s> |
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1992 <s xml:id="echoid-s1120" xml:space="preserve">Elle <lb/>eſt auſſi pour la même raiſon à la peſanteur de ce <lb/>poids, comme le ſinus du même angle BAC, au ſinus <lb/>de BAD: </s> |
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1993 <s xml:id="echoid-s1121" xml:space="preserve">Ainſi la peſanteur de ce poids eſt à la <lb/>force de cette puiſſance, comme le ſinus de l’angle <lb/>BAD au ſinus de l’angle DAC; </s> |
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1994 <s xml:id="echoid-s1122" xml:space="preserve">& </s> |
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1995 <s xml:id="echoid-s1123" xml:space="preserve">par conſéquent <lb/>ce poids, & </s> |
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1996 <s xml:id="echoid-s1124" xml:space="preserve">cette puiſſance ſont entr’eux en raiſon <lb/>réciproque des ſinus des angles que font leurs li-<lb/>gnes de diréction avec la ligne tirée de leur point de <lb/>concours perpendiculairement à la ſurfacc GH, <lb/>telle quelle ſoit. </s> |
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1997 <s xml:id="echoid-s1125" xml:space="preserve">Ce qu’il F.</s> |
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1998 <s xml:id="echoid-s1126" xml:space="preserve">D.</s> |
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1999 <s xml:id="echoid-s1127" xml:space="preserve"/> |
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2000 </p> |
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2001 <div xml:id="echoid-div119" type="float" level="2" n="1"> |
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2002 <note position="right" xlink:label="note-0067-01" xlink:href="note-0067-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2003 </div> |
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2004 <pb o="42" file="0068" n="68" rhead="NOUVELLE"/> |
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2005 <note position="left" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2006 <p style="it"> |
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2007 <s xml:id="echoid-s1128" xml:space="preserve">Les cas ou le point de concours de ces lignes de direction <lb/>ſe trouve encore dans ce poids, mais au-deſſous de ſon centre <lb/>de gravité, ſe réſoudront comme ceux des figures 33. </s> |
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2008 <s xml:id="echoid-s1129" xml:space="preserve">34. </s> |
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2009 <s xml:id="echoid-s1130" xml:space="preserve">& </s> |
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2010 <s xml:id="echoid-s1131" xml:space="preserve"><lb/>36. </s> |
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2011 <s xml:id="echoid-s1132" xml:space="preserve">& </s> |
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2012 <s xml:id="echoid-s1133" xml:space="preserve">ceux où il ſe trouvera debors, ſe réſoudront auſſi de <lb/>même, en regardant ſeulement ce point comme apparte-<lb/>nant à ce poids, de la maniére que nous avons fait en traitant <lb/>des poids ſoutenus avec des cordes ſeulement, figure 16. </s> |
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2013 <s xml:id="echoid-s1134" xml:space="preserve">& </s> |
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2014 <s xml:id="echoid-s1135" xml:space="preserve">17. <lb/></s> |
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2015 <s xml:id="echoid-s1136" xml:space="preserve">Tout cela eſt aiſé; </s> |
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2016 <s xml:id="echoid-s1137" xml:space="preserve">c’eſt pourquoy on n’exprime point ici les <lb/>figures de tous ces cas.</s> |
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2017 <s xml:id="echoid-s1138" xml:space="preserve"/> |
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2018 </p> |
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2019 <p style="it"> |
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2020 <s xml:id="echoid-s1139" xml:space="preserve">On n’exprime point non plus la figure d’aucune ſurface <lb/>borizontale: </s> |
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2021 <s xml:id="echoid-s1140" xml:space="preserve">parce que la ligne de direction de quelque poids <lb/>que ce ſoit, lui étant toujours perpendiculaire, il s’y ſoutient <lb/>de lui-même, & </s> |
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2022 <s xml:id="echoid-s1141" xml:space="preserve">ſans le ſecours d’aucune puiſſance, par la <lb/>même raiſon qu’il en a beſoin, comme l’on vient de voir, pour <lb/>demeurer ſur quelque autre ſurface que ce ſoit. </s> |
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2023 <s xml:id="echoid-s1142" xml:space="preserve">Cette propo-<lb/>ſition ne laiſſe pas cependant de s’étendre encore juſques-là, <lb/>comme on le verra dans les Corollaires 9. </s> |
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2024 <s xml:id="echoid-s1143" xml:space="preserve">& </s> |
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2025 <s xml:id="echoid-s1144" xml:space="preserve">10. </s> |
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2026 <s xml:id="echoid-s1145" xml:space="preserve">ainſi on <lb/>n’en peut pas concevoir une plus générale.</s> |
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2027 <s xml:id="echoid-s1146" xml:space="preserve"/> |
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2028 </p> |
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2029 </div> |
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2030 <div xml:id="echoid-div121" type="section" level="1" n="82"> |
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2031 <head xml:id="echoid-head82" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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2032 <p> |
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2033 <s xml:id="echoid-s1147" xml:space="preserve">On voit des articles 3. </s> |
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2034 <s xml:id="echoid-s1148" xml:space="preserve">& </s> |
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2035 <s xml:id="echoid-s1149" xml:space="preserve">4. </s> |
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2036 <s xml:id="echoid-s1150" xml:space="preserve">de cette démonſtra-<lb/>tion que le poids EO ne peut-être ſoutenu par quel-<lb/>que puiſſance R que ce ſoit, ſur quelque ſurface <lb/>quece puiſſe être, à moins que la ligne AD ne tombe <lb/>perpendiculairement ſur cette ſurface, & </s> |
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2037 <s xml:id="echoid-s1151" xml:space="preserve">qu’elle ne <lb/>paſſe en même temps par quelqu’un des points ou <lb/>ce poids touche cette même ſurface; </s> |
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2038 <s xml:id="echoid-s1152" xml:space="preserve">c’eſt-à-dire, <lb/>par quelqu’un des points de la baze de ce même <lb/>poids.</s> |
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2039 <s xml:id="echoid-s1153" xml:space="preserve"/> |
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2040 </p> |
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2041 </div> |
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2042 <div xml:id="echoid-div122" type="section" level="1" n="83"> |
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2043 <head xml:id="echoid-head83" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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2044 <p> |
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2045 <s xml:id="echoid-s1154" xml:space="preserve">Mais auſſi pour la même raiſon dés que l’un &</s> |
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2046 <s xml:id="echoid-s1155" xml:space="preserve"> |
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2047 <pb o="43" file="0069" n="69" rhead="MECHANIQUE."/> |
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2048 l’autre arrivera, la puiſſance qui y ſera alors appli-<lb/> |
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2049 <anchor type="note" xlink:label="note-0069-01a" xlink:href="note-0069-01"/> |
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2050 quée ne manquera pas de l’y ſoutenir.</s> |
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2051 <s xml:id="echoid-s1156" xml:space="preserve"/> |
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2052 </p> |
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2053 <div xml:id="echoid-div122" type="float" level="2" n="1"> |
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2054 <note position="right" xlink:label="note-0069-01" xlink:href="note-0069-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſutfaces.</note> |
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2055 </div> |
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2056 </div> |
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2057 <div xml:id="echoid-div124" type="section" level="1" n="84"> |
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2058 <head xml:id="echoid-head84" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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2059 <p> |
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2060 <s xml:id="echoid-s1157" xml:space="preserve">De-là on voit qu’il n’y a point non plus de puiſſan-<lb/>ce capable de ſoutenir un poids rond, ou quelque <lb/>ſphére que ce ſoit, ſur quelque ſurface que ce puiſſe <lb/>être, à moins que le concours de leurs lignes de di-<lb/>rection ne ſe faſſe dans ſon centre de grandeur; </s> |
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2061 <s xml:id="echoid-s1158" xml:space="preserve">parce <lb/>que c’eſt le ſeul point de ce corps, d’où l’on puiſſe <lb/>tirer une ligne qui paſſe par ſa baze, & </s> |
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2062 <s xml:id="echoid-s1159" xml:space="preserve">qui ſoit en <lb/>même temps perpendiculaire à la ſurface ſur laquelle <lb/>il eſt ſoutenu. </s> |
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2063 <s xml:id="echoid-s1160" xml:space="preserve">Dans tout autre configuration de poids, <lb/>il en va tout autrement: </s> |
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2064 <s xml:id="echoid-s1161" xml:space="preserve">parce que l’on y peut trou-<lb/>ver pluſieurs points, d’où il eſt poſſible de tirer de <lb/>telles perpendiculaires.</s> |
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2065 <s xml:id="echoid-s1162" xml:space="preserve"/> |
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2066 </p> |
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2067 </div> |
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2068 <div xml:id="echoid-div125" type="section" level="1" n="85"> |
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2069 <head xml:id="echoid-head85" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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2070 <p> |
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2071 <s xml:id="echoid-s1163" xml:space="preserve">Il n’y a point encore de puiſſance R, telle quelle <lb/>ſoit, qui puiſſe ſoutenir aucun poids ſur quelque ſur-<lb/>face que ce puiſſe être, à moins que ſa ligne de di-<lb/>rection AR ne ſe trouve dans le complement NAO <lb/>de l’angle CAO, que fait la ligne de direction AC <lb/>de ce poids avec AO tirée du point A perpendiculai-<lb/>rement à cette ſurface GH. </s> |
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2072 <s xml:id="echoid-s1164" xml:space="preserve">Car 1°. </s> |
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2073 <s xml:id="echoid-s1165" xml:space="preserve">ſi elle concou-<lb/>roit avec AN elle ne feroit plus aueun angle avec <lb/>AC: </s> |
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2074 <s xml:id="echoid-s1166" xml:space="preserve">ainſi cette puiſſance porteroit ſeule tout ce poids, <lb/>& </s> |
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2075 <s xml:id="echoid-s1167" xml:space="preserve">non avec ce plan; </s> |
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2076 <s xml:id="echoid-s1168" xml:space="preserve">ce qui eſt contre l’hypothêſe. <lb/></s> |
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2077 <s xml:id="echoid-s1169" xml:space="preserve">2°. </s> |
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2078 <s xml:id="echoid-s1170" xml:space="preserve">Si cette ligne de direction concouroit avec AO, <lb/>ou ſi elle ſortoit de l’angle NAO, la diagonale AD <lb/>du parallelogramme BC ſe tourneroit vers G; </s> |
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2079 <s xml:id="echoid-s1171" xml:space="preserve">ce <lb/>qui feroit néceſſairement (Corol. </s> |
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2080 <s xml:id="echoid-s1172" xml:space="preserve">Lemm. </s> |
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2081 <s xml:id="echoid-s1173" xml:space="preserve">I.) </s> |
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2082 <s xml:id="echoid-s1174" xml:space="preserve">tomber ce <lb/>poids de ce côté-là, ce qui eſt encore contre l’hypo-<lb/>thêſe. </s> |
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2083 <s xml:id="echoid-s1175" xml:space="preserve">Donc la ligne de direction AB de la puiſſance <lb/>R, doit toujours ſe trouver dans le complement NAO |
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2084 <pb o="44" file="0070" n="70" rhead="NOUVELLE"/> |
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2085 <anchor type="note" xlink:label="note-0070-01a" xlink:href="note-0070-01"/> |
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2086 de l’angle CAO: </s> |
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2087 <s xml:id="echoid-s1176" xml:space="preserve">de ſorte que c’eſt-là tout l’eſpace <lb/>du mouvement qu’elle peut avoir.</s> |
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2088 <s xml:id="echoid-s1177" xml:space="preserve"/> |
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2089 </p> |
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2090 <div xml:id="echoid-div125" type="float" level="2" n="1"> |
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2091 <note position="left" xlink:label="note-0070-01" xlink:href="note-0070-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2092 </div> |
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2093 </div> |
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2094 <div xml:id="echoid-div127" type="section" level="1" n="86"> |
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2095 <head xml:id="echoid-head86" xml:space="preserve"><emph style="sc">Corollaire</emph> V.</head> |
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2096 <p> |
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2097 <s xml:id="echoid-s1178" xml:space="preserve">Le plan BAC, ou le parallelogramme BC de <lb/>cette ligne avec AC ligne de direction du poids <lb/>EO, eſt auſſi toujours perpendiculaire à la ſur-<lb/>face que la ligne GH repreſente, & </s> |
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2098 <s xml:id="echoid-s1179" xml:space="preserve">ſur laquelle ce <lb/>poids eſt ſoutenu; </s> |
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2099 <s xml:id="echoid-s1180" xml:space="preserve">puiſque la diagonale AD de ce pa-<lb/>rallelogramme BC, l’eſt toujours à cette même ſur-<lb/>face.</s> |
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2100 <s xml:id="echoid-s1181" xml:space="preserve"/> |
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2101 </p> |
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2102 </div> |
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2103 <div xml:id="echoid-div128" type="section" level="1" n="87"> |
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2104 <head xml:id="echoid-head87" xml:space="preserve"><emph style="sc">Corollaire</emph> VI.</head> |
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2105 <p> |
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2106 <s xml:id="echoid-s1182" xml:space="preserve">On voit auſſi de l’article cinquiéme de la demonſ-<lb/>tration ci-deſſus, que le poids EO eſt à la charge de <lb/>cette ſurface, c’eſt-à-dire, à l’impreſſion que lui & </s> |
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2107 <s xml:id="echoid-s1183" xml:space="preserve">la <lb/>puiſſance R font enſemble deſſus, ou à la réſiſtance <lb/>qu’elle leur fait, comme le ſinus de l’angle BAD, au <lb/>ſinus de l’angle BAC.</s> |
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2108 <s xml:id="echoid-s1184" xml:space="preserve"/> |
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2109 </p> |
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2110 </div> |
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2111 <div xml:id="echoid-div129" type="section" level="1" n="88"> |
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2112 <head xml:id="echoid-head88" xml:space="preserve"><emph style="sc">Corollaire</emph> VII.</head> |
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2113 <p> |
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2114 <s xml:id="echoid-s1185" xml:space="preserve">D’où il ſuit que le poids EO, la charge de la ſur-<lb/>face GH, & </s> |
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2115 <s xml:id="echoid-s1186" xml:space="preserve">la puiſſance R, ſont entr’eux comme <lb/>les ſinus des angles BAD, BAC, ou ABD ſon com-<lb/>plement, & </s> |
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2116 <s xml:id="echoid-s1187" xml:space="preserve">DAC, ou ADB qui lui eſt égal; </s> |
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2117 <s xml:id="echoid-s1188" xml:space="preserve">c’eſt-à-<lb/>dire, (Lemm. </s> |
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2118 <s xml:id="echoid-s1189" xml:space="preserve">5.) </s> |
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2119 <s xml:id="echoid-s1190" xml:space="preserve">comme les lignes BD, AD, & </s> |
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2120 <s xml:id="echoid-s1191" xml:space="preserve"><lb/>AB.</s> |
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2121 <s xml:id="echoid-s1192" xml:space="preserve"/> |
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2122 </p> |
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2123 </div> |
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2124 <div xml:id="echoid-div130" type="section" level="1" n="89"> |
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2125 <head xml:id="echoid-head89" xml:space="preserve"><emph style="sc">Corollaire</emph> VIII.</head> |
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2126 <p> |
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2127 <s xml:id="echoid-s1193" xml:space="preserve">D’où il ſuit encore que plus l’angle BAC eſt obtus, <lb/>moins la charge de cette ſurface eſt grande: </s> |
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2128 <s xml:id="echoid-s1194" xml:space="preserve">de ſorte <lb/>qu’il le peut devenir juſqu’à un tel point, quelle ſera <lb/>ſi petite qu’on voudra; </s> |
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2129 <s xml:id="echoid-s1195" xml:space="preserve">c’eſt ainſi qu’elle peut dimi-<lb/>nuer à l’infini.</s> |
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2130 <s xml:id="echoid-s1196" xml:space="preserve"/> |
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2131 </p> |
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2132 <pb o="45" file="0071" n="71" rhead="MECHANIQUE."/> |
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2133 </div> |
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2134 <div xml:id="echoid-div131" type="section" level="1" n="90"> |
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2135 <head xml:id="echoid-head90" xml:space="preserve"><emph style="sc">Corollaire</emph> IX.</head> |
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2136 <note position="right" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2137 <p> |
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2138 <s xml:id="echoid-s1197" xml:space="preserve">Mais elle ne peut pas augmenter de même; </s> |
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2139 <s xml:id="echoid-s1198" xml:space="preserve">parce <lb/>que ne pouvant jamais être plus grande, que lorſque <lb/>cet angle eſt infiniment aigu; </s> |
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2140 <s xml:id="echoid-s1199" xml:space="preserve">c’eſt-à-dire, lorſque <lb/>les lignes AC & </s> |
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2141 <s xml:id="echoid-s1200" xml:space="preserve">AB concourent avec AO: </s> |
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2142 <s xml:id="echoid-s1201" xml:space="preserve">& </s> |
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2143 <s xml:id="echoid-s1202" xml:space="preserve">AD <lb/>n’étant encore alors qu’égale à la ſomme de AB & </s> |
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2144 <s xml:id="echoid-s1203" xml:space="preserve">de <lb/>BD; </s> |
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2145 <s xml:id="echoid-s1204" xml:space="preserve">la charge de cette ſurface, qui eſt alors hori-<lb/>zontale ne peut jamais être plus grande que la ſomme <lb/>de ce poids, & </s> |
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2146 <s xml:id="echoid-s1205" xml:space="preserve">de cette puiſſance.</s> |
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2147 <s xml:id="echoid-s1206" xml:space="preserve"/> |
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2148 </p> |
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2149 <p style="it"> |
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2150 <s xml:id="echoid-s1207" xml:space="preserve">On entend ici par ſurface horizontale unplan qui le ſoit, <lb/>ou bien un point d’une ſurface courbe dont toutes les tangentes <lb/>ſoient auſſi borizontales.</s> |
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2151 <s xml:id="echoid-s1208" xml:space="preserve"/> |
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2152 </p> |
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2153 </div> |
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2154 <div xml:id="echoid-div132" type="section" level="1" n="91"> |
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2155 <head xml:id="echoid-head91" xml:space="preserve"><emph style="sc">Corollaire</emph> X.</head> |
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2156 <p> |
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2157 <s xml:id="echoid-s1209" xml:space="preserve">On voit encore qu’il faut d’autant moins de force <lb/> |
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2158 <anchor type="note" xlink:label="note-0071-02a" xlink:href="note-0071-02"/> |
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2159 pour ſoutenir ainſi un poids ſuivant la même direc-<lb/>tion AB ſur un même point de quelque ſurface <lb/>que ce ſoit, que cette ſurface, ſi elle eſt droite <lb/>(fig. </s> |
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2160 <s xml:id="echoid-s1210" xml:space="preserve">30. </s> |
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2161 <s xml:id="echoid-s1211" xml:space="preserve">& </s> |
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2162 <s xml:id="echoid-s1212" xml:space="preserve">33.) </s> |
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2163 <s xml:id="echoid-s1213" xml:space="preserve">ou bien ſi elle eſt courbe; </s> |
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2164 <s xml:id="echoid-s1214" xml:space="preserve">(fig. </s> |
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2165 <s xml:id="echoid-s1215" xml:space="preserve">32. <lb/></s> |
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2166 <s xml:id="echoid-s1216" xml:space="preserve">36.)</s> |
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2167 <s xml:id="echoid-s1217" xml:space="preserve">, que ſa tangente au point ou la perpendiculai-<lb/>re AO la rencontre, eſt plus inclinée, quoi qu’en <lb/>proportion différente: </s> |
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2168 <s xml:id="echoid-s1218" xml:space="preserve">parce que la raiſon du ſinus <lb/>de l’angle CAD, au ſinus de l’angle BAD, en eſt <lb/>toujours moindre; </s> |
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2169 <s xml:id="echoid-s1219" xml:space="preserve">& </s> |
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2170 <s xml:id="echoid-s1220" xml:space="preserve">comme cette inclinaiſon avec <lb/>l’horizon peut diminuer à l’infini, la force qu’il faut <lb/>pour ſoutenir quelque poids ſuivant la même direc-<lb/>tion ſur quelqu’une de ces ſurfaces, ſoit droite, ſoit <lb/>courbe, peut auſſi diminuer à l’infini: </s> |
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2171 <s xml:id="echoid-s1221" xml:space="preserve">De ſorte que <lb/>lorſqu’elle ſera infiniment inclinée; </s> |
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2172 <s xml:id="echoid-s1222" xml:space="preserve">c’eſt-à-dire, ho-<lb/>rizontale, du moins dans le point où la perpendicu-<lb/>laire AO la rencontre, cette force ſera nulle, & </s> |
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2173 <s xml:id="echoid-s1223" xml:space="preserve">ré-<lb/>duite à zéro; </s> |
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2174 <s xml:id="echoid-s1224" xml:space="preserve">c’eſt-à-dire, qu’il n’en faudra plus du <lb/>tout pour l’y ſoutenir.</s> |
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2175 <s xml:id="echoid-s1225" xml:space="preserve"/> |
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2176 </p> |
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2177 <div xml:id="echoid-div132" type="float" level="2" n="1"> |
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2178 <note position="right" xlink:label="note-0071-02" xlink:href="note-0071-02a" xml:space="preserve">fig 30. <lb/>32. <lb/>33. <lb/>36.</note> |
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2179 </div> |
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2180 <pb o="46" file="0072" n="72" rhead="NOUVELLE"/> |
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2181 <note position="left" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2182 </div> |
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2183 <div xml:id="echoid-div134" type="section" level="1" n="92"> |
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2184 <head xml:id="echoid-head92" xml:space="preserve"><emph style="sc">Corollaire</emph> XI.</head> |
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2185 <p> |
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2186 <s xml:id="echoid-s1226" xml:space="preserve">Au contraire pour ſoutenir ce poids ſur le même <lb/>point d’une ſurface toujours également inclinée, telle <lb/>quelle ſoit, mais ſuivant différentes directions de <lb/>puiſſance; </s> |
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2187 <s xml:id="echoid-s1227" xml:space="preserve">il faut d’autant plus de forces que l’angle <lb/>DAB fait dans l’eſpace NAD par la perpendiculaire <lb/>AO avec la ligne de direction AB de la puiſſance qui <lb/>ſoutient ce poids, differe davantage de l’angle droit: <lb/></s> |
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2188 <s xml:id="echoid-s1228" xml:space="preserve">parce qu’alors la raiſon du ſinus de l’angle CAD, au ſi-<lb/>nus de l’angle BAD, en ſera d’autant plus grande, quoi <lb/>qu’en proportion différente: </s> |
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2189 <s xml:id="echoid-s1229" xml:space="preserve">& </s> |
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2190 <s xml:id="echoid-s1230" xml:space="preserve">conime cet angle peut-<lb/>être plus ou moins grand qu’un angle droit, & </s> |
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2191 <s xml:id="echoid-s1231" xml:space="preserve">en diffé-<lb/>rer de plus en plus juſqu’au concours de AB avec AN, <lb/>ou avec AO, ſans que AB ſorte de l’eſpace NAO; </s> |
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2192 <s xml:id="echoid-s1232" xml:space="preserve">la <lb/>puiſſance qui ſoutient ce poids peut auſſi augmenter <lb/>juſques-là: </s> |
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2193 <s xml:id="echoid-s1233" xml:space="preserve">mais différemment ſelon que AB s’appro-<lb/>che de l’une, ou de l’autre de ces deux lignes. </s> |
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2194 <s xml:id="echoid-s1234" xml:space="preserve">Car <lb/>1°. </s> |
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2195 <s xml:id="echoid-s1235" xml:space="preserve">ne pouvant jamais être plus grande par l’appro-<lb/>che de AB vers AN, que lorſque l’angle NAB, que <lb/>ces lignes font entr’elles, eſt le plus petit qu’elles <lb/>puiſſent faire; </s> |
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2196 <s xml:id="echoid-s1236" xml:space="preserve">c’eſt-à-dire, celui qu’elles font immé-<lb/>diatement avant que de concourir; </s> |
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2197 <s xml:id="echoid-s1237" xml:space="preserve">& </s> |
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2198 <s xml:id="echoid-s1238" xml:space="preserve">le ſinus de CAD <lb/>étant encore alors un peu moindre que celui de <lb/>BAO, quoique d’une difference infiniment petite: </s> |
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2199 <s xml:id="echoid-s1239" xml:space="preserve"><lb/>Cette puiſſance ne peut être tout au plus de ce côté-là, <lb/>qu’un peu moindre que ce poids d’une différence qui <lb/>ſoit auſſi infiniment petite. </s> |
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2200 <s xml:id="echoid-s1240" xml:space="preserve">2°. </s> |
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2201 <s xml:id="echoid-s1241" xml:space="preserve">Au contraire du côté de <lb/>AO elle pent augmenter à l’infini: </s> |
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2202 <s xml:id="echoid-s1242" xml:space="preserve">parce que la raiſon <lb/>du ſinus de CAD, à celuy de BAD, augmentant à <lb/>meſure quela ligne AB s’approche de AO, en s’éloi-<lb/>gnant de la ſituation qu’elle auroit ſi elle faiſoit un an-<lb/>gle droit avec AO; </s> |
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2203 <s xml:id="echoid-s1243" xml:space="preserve">cette force peut auſſi augmenter <lb/>de ce côté-là juſqu’à ce que AB, & </s> |
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2204 <s xml:id="echoid-s1244" xml:space="preserve">AO concourent. </s> |
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2205 <s xml:id="echoid-s1245" xml:space="preserve"><lb/>Or en ce cas l’angle BAD étant infiniment petit, la |
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2206 <pb o="47" file="0073" n="73" rhead="MECHANIQUE."/> |
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2207 raiſon du ſinus de CAD à celui de cet angle, ſera auſſi <lb/> |
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2208 <anchor type="note" xlink:label="note-0073-01a" xlink:href="note-0073-01"/> |
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2209 infinie; </s> |
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2210 <s xml:id="echoid-s1246" xml:space="preserve">& </s> |
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2211 <s xml:id="echoid-s1247" xml:space="preserve">par conſéquent auſſi celle de cette puiſ-<lb/>ſance à ce poids. </s> |
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2212 <s xml:id="echoid-s1248" xml:space="preserve">Ce qui fait voir que cette puiſ-<lb/>ſance peut augmenter à l’infini dans le mouvement <lb/>qu’elle peut avoir depuis la ſituation où ſa ligne de <lb/>direction feroit un angle droit avec la perpendiculaire <lb/>AO, juſqu’au concours de ces deux mêmes lignes, & </s> |
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2213 <s xml:id="echoid-s1249" xml:space="preserve"><lb/>demeurer cependant toûjours en équilibre avec le <lb/>même poids, & </s> |
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2214 <s xml:id="echoid-s1250" xml:space="preserve">ſur le même point d’une ſurface in-<lb/>clinée, telle quelle ſoit.</s> |
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2215 <s xml:id="echoid-s1251" xml:space="preserve"/> |
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2216 </p> |
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2217 <div xml:id="echoid-div134" type="float" level="2" n="1"> |
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2218 <note position="right" xlink:label="note-0073-01" xlink:href="note-0073-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2219 </div> |
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2220 </div> |
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2221 <div xml:id="echoid-div136" type="section" level="1" n="93"> |
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2222 <head xml:id="echoid-head93" xml:space="preserve"><emph style="sc">Corollaire</emph> XII.</head> |
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2223 <p> |
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2224 <s xml:id="echoid-s1252" xml:space="preserve">Pour les plans perpendiculaires à l’horizon, ou plu-<lb/> |
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2225 <anchor type="note" xlink:label="note-0073-02a" xlink:href="note-0073-02"/> |
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2226 tôt paralleles à la ligne de direction de ce poids; </s> |
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2227 <s xml:id="echoid-s1253" xml:space="preserve">& </s> |
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2228 <s xml:id="echoid-s1254" xml:space="preserve"><lb/>pour les points des ſurfaces courbes, d’où l’on peut <lb/>tirer des tangentes qui ſoient auſſi perpendiculai-<lb/>res à l’horizon: </s> |
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2229 <s xml:id="echoid-s1255" xml:space="preserve">la ligne de direction AB de la puiſ-<lb/>ſance qui ſoutient ce poids ſur, ou contre ces plans, <lb/>ou ces points de ſurfaces courbes, ne pouvant (Co-<lb/>rol. </s> |
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2230 <s xml:id="echoid-s1256" xml:space="preserve">4.) </s> |
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2231 <s xml:id="echoid-s1257" xml:space="preserve">s’éloigner de la ſituation où elle ſeroit, ſi <lb/>elle faiſoit un angle droit avec AO, qu’en s’appro-<lb/>chant de AO, puiſque l’angle NAO en ce cas eſt <lb/>droit; </s> |
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2232 <s xml:id="echoid-s1258" xml:space="preserve">cette puiſſance ne peut auſſi augmenter que <lb/>de ce côté-là: </s> |
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2233 <s xml:id="echoid-s1259" xml:space="preserve">De ſorte qu’elle peut à la vérité aug-<lb/>menter à l’infini de même que ſur les ſurfaces incli-<lb/>nées: </s> |
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2234 <s xml:id="echoid-s1260" xml:space="preserve">mais elle ne peut jamais être moins grande <lb/>que lorſque ſa ligne de direction AB fait le plus petit <lb/>angle qu’elle puiſſe faire avec AN; </s> |
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2235 <s xml:id="echoid-s1261" xml:space="preserve">c’eſt-à-dire, <lb/>qu’en ne ſurpaſſant ce poids que d’une différence in-<lb/>finiment petite.</s> |
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2236 <s xml:id="echoid-s1262" xml:space="preserve"/> |
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2237 </p> |
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2238 <div xml:id="echoid-div136" type="float" level="2" n="1"> |
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2239 <note position="right" xlink:label="note-0073-02" xlink:href="note-0073-02a" xml:space="preserve">fig. 31. <lb/>34. <lb/>35.</note> |
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2240 </div> |
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2241 </div> |
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2242 <div xml:id="echoid-div138" type="section" level="1" n="94"> |
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2243 <head xml:id="echoid-head94" xml:space="preserve"><emph style="sc">Corollaire</emph> XIII.</head> |
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2244 <note position="right" xml:space="preserve">fig. 30. <lb/>31. <lb/>32. <lb/>33. <lb/>34. <lb/>35. <lb/>36.</note> |
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2245 <p> |
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2246 <s xml:id="echoid-s1263" xml:space="preserve">De ſorte que dés le moment que AB & </s> |
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2247 <s xml:id="echoid-s1264" xml:space="preserve">AN vien-<lb/>nent à concourir enſemble, le ſinus de CAD deve-<lb/>nant alors égal à celui de BAD, cette puiſſance de- |
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2248 <pb o="48" file="0074" n="74" rhead="NOUVELLE"/> |
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2249 <anchor type="note" xlink:label="note-0074-01a" xlink:href="note-0074-01"/> |
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2250 vient auſſi égale à ce poids, qui ceſſe auſſi-tôt de s’ap-<lb/>puyer ſur, ou contre la ſurface GH, telle qu’elle <lb/>ſoit.</s> |
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2251 <s xml:id="echoid-s1265" xml:space="preserve"/> |
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2252 </p> |
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2253 <div xml:id="echoid-div138" type="float" level="2" n="1"> |
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2254 <note position="left" xlink:label="note-0074-01" xlink:href="note-0074-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2255 </div> |
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2256 <p style="it"> |
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2257 <s xml:id="echoid-s1266" xml:space="preserve">Ce n’eſt que pour ne pas embaraſſer l’imagination de ceux <lb/>qui ſont accoutumez à regarder une ſurface perpendiculaire à <lb/>l’horizon, comme parallele à la ligne de direction d’un poids, & </s> |
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2258 <s xml:id="echoid-s1267" xml:space="preserve"><lb/>une horizontale, comme lui étant perpendiculaire; </s> |
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2259 <s xml:id="echoid-s1268" xml:space="preserve">que l’on s’eſt <lb/>accommodé à cette bypotbêſe dans ces trois derniers Corollaires: <lb/></s> |
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2260 <s xml:id="echoid-s1269" xml:space="preserve">car pour les rendre auſſi généraux qu’on les puiſſe imaginer, & </s> |
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2261 <s xml:id="echoid-s1270" xml:space="preserve"><lb/>pour toutes ſortes d’bypotbêſes, il ne faut que regarder les plans, <lb/>ou les tangentes des ſurfaces courbes, que l’on dit ici perpen-<lb/>diculaires à l’borizon, comme paralleles ſeulement à la ligne <lb/>de direction de ce poids, ſans avoir égard à l’angle qu’elles <lb/>font, ou qu’elles peuvent faire avec l’borizon. </s> |
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2262 <s xml:id="echoid-s1271" xml:space="preserve">De même celles <lb/>que l’on appelle ici borizontales, ſe doivent ſeulement regar-<lb/>der comme perpendiculaires à cette ligne. </s> |
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2263 <s xml:id="echoid-s1272" xml:space="preserve">De cette maniére ces <lb/>Corollaires ſeront ſi généraux, qu’ils ſe pourront appliquer à <lb/>toutes les directions poſſibles d’un corps ſoutenu ſur ou contre <lb/>quelque ſurface que ce puiſſe être.</s> |
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2264 <s xml:id="echoid-s1273" xml:space="preserve"/> |
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2265 </p> |
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2266 <p style="it"> |
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2267 <s xml:id="echoid-s1274" xml:space="preserve">Il eſt encore bon de remarquer que lorſqu’on dit ici qu’un <lb/>poids eſt ſoutenu ſur le même point d’une ſurface, l’on ne pré-<lb/>tend pas dire qu’il ne la rencontre jamais qu’en un ſeul point; <lb/></s> |
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2268 <s xml:id="echoid-s1275" xml:space="preserve">mais on entend ſeulement que la ligne AD, qui tombe du <lb/>point A perpendiculairement deſſus, la rencontre toujours dans <lb/>le même point O, tant que ce poids eſt ſoutenu deſſus, quoi que <lb/>ce ſoit ſuivant différentes directions de puiſſances. </s> |
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2269 <s xml:id="echoid-s1276" xml:space="preserve">La raiſon <lb/>de cette précaution eſt évidente du côté des ſurfaces courbes, <lb/>dont tous les points ont cbacun une tangente d’une direction <lb/>particuliére. </s> |
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2270 <s xml:id="echoid-s1277" xml:space="preserve">Pour du côté des plans, on la reconnoîtra dans <lb/>le Corollaire 23. </s> |
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2271 <s xml:id="echoid-s1278" xml:space="preserve">où l’on verra que dans l’bypotbêſe du con-<lb/>cours des lignes de direction des poids en quelque points de la <lb/>terre que ce ſoit, ils ne péſent pas toujours également deſſus, <lb/>quoique la ligne de direction de la puiſſance qui leur eſt appli- |
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2272 <pb o="49" file="0075" n="75" rhead="MECHANIQUE"/> |
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2273 quée demeure toujours la même. </s> |
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2274 <s xml:id="echoid-s1279" xml:space="preserve">Au contraire, ils péſent tou-<lb/> |
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2275 <anchor type="note" xlink:label="note-0075-01a" xlink:href="note-0075-01"/> |
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2276 jours également ſur le même point de quelque ſurface que ce <lb/>ſoit, à moins qu’on ne change la ligne de direction de cotte <lb/>puiſſance, ou la ſi@uation de cette ſurface. </s> |
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2277 <s xml:id="echoid-s1280" xml:space="preserve">C’eſt pour cela <lb/>que dans les trois Corollaires précédens, où l’on examine ſépa-<lb/>rément le changement que peut cauſer dans l’action d’un poids <lb/>les différentes inclinaiſons de la même, ou des différentes ſurfaces <lb/>ſur leſquelles il eſt ſoutenu, & </s> |
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2278 <s xml:id="echoid-s1281" xml:space="preserve">les différentes lignes de direction des <lb/>puiſſances qui l’yſoutiennent;</s> |
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2279 <s xml:id="echoid-s1282" xml:space="preserve">on l’aregardé comme appliqué non-<lb/>ſeulement à la même ſurface, mais auſſi toujours au même point.</s> |
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2280 <s xml:id="echoid-s1283" xml:space="preserve"/> |
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2281 </p> |
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2282 <div xml:id="echoid-div139" type="float" level="2" n="2"> |
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2283 <note position="right" xlink:label="note-0075-01" xlink:href="note-0075-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2284 </div> |
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2285 </div> |
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2286 <div xml:id="echoid-div141" type="section" level="1" n="95"> |
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2287 <head xml:id="echoid-head95" xml:space="preserve"><emph style="sc">Corollaire</emph> XIV.</head> |
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2288 <p> |
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2289 <s xml:id="echoid-s1284" xml:space="preserve">Puiſque la puiſſance qui ſoutient quelque poids <lb/>que ce ſoit ſur le même point de quelque ſurface <lb/>que ce puiſſe être, eſt d’autant plus grande que <lb/>ſa ligne de direction AB s’éloigne davantage de la <lb/>ſituaton où elle feroit un angle droit avec AO, ſans <lb/>cependant ſortir de l’eſpace NAO: </s> |
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2290 <s xml:id="echoid-s1285" xml:space="preserve">Il s’enſuit qu’elle <lb/>n’eſt jamais moindre que lorſqu’elle eſt parallele au <lb/>plan, ou à quelqu’une des tangentes au point de la ſur-<lb/>face courbe, ſur lequel ce poids eſt ſoutenu.</s> |
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2291 <s xml:id="echoid-s1286" xml:space="preserve"/> |
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2292 </p> |
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2293 </div> |
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2294 <div xml:id="echoid-div142" type="section" level="1" n="96"> |
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2295 <head xml:id="echoid-head96" xml:space="preserve"><emph style="sc">Corollaire</emph> XV.</head> |
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2296 <p> |
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2297 <s xml:id="echoid-s1287" xml:space="preserve">D’où l’on voit dans l’hypothêſe ordinaire, ou l’on <lb/> |
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2298 <anchor type="note" xlink:label="note-0075-02a" xlink:href="note-0075-02"/> |
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2299 regarde HK comme parallele à AC, que les triangles <lb/>BAD, HKG étant alors ſemblables, cette puiſſance qui <lb/>eſt à ce poids (Cor. </s> |
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2300 <s xml:id="echoid-s1288" xml:space="preserve">7.) </s> |
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2301 <s xml:id="echoid-s1289" xml:space="preserve">comme AB à BD, lui ſera auſſi <lb/>comme HK à HG: </s> |
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2302 <s xml:id="echoid-s1290" xml:space="preserve">& </s> |
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2303 <s xml:id="echoid-s1291" xml:space="preserve">comme elle eſt alors la moin-<lb/>dre qu’elle puiſſe jamais être ſelon le Corollaire précé-<lb/>dent; </s> |
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2304 <s xml:id="echoid-s1292" xml:space="preserve">il s’enſuit qu’elle ne peut jamais être en moindre <lb/>raiſon au poids qu’elle ſoutient ſur un plan incliné, <lb/>qu’eſt celle de la hauteur de ce plan à ſa longueur.</s> |
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2305 <s xml:id="echoid-s1293" xml:space="preserve"/> |
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2306 </p> |
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2307 <div xml:id="echoid-div142" type="float" level="2" n="1"> |
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2308 <note position="right" xlink:label="note-0075-02" xlink:href="note-0075-02a" xml:space="preserve">fig. 30.</note> |
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2309 </div> |
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2310 </div> |
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2311 <div xml:id="echoid-div144" type="section" level="1" n="97"> |
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2312 <head xml:id="echoid-head97" xml:space="preserve"><emph style="sc">Corollaire</emph> XVI.</head> |
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2313 <p> |
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2314 <s xml:id="echoid-s1294" xml:space="preserve">On voit encore que toute puiſſance qui peut ſoute- |
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2315 <pb o="50" file="0076" n="76" rhead="NOUVELLE"/> |
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2316 <anchor type="note" xlink:label="note-0076-01a" xlink:href="note-0076-01"/> |
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2317 nir un poids ſur un plan incliné ſuivant une ligne <lb/>de direction, qui faſſe avec une perpendiculaire faite <lb/>ſur AD au point A, un angle moindre que celui de <lb/>cette perpendiculaire avec AN; </s> |
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2318 <s xml:id="echoid-s1295" xml:space="preserve">l’y peut ſoutenir <lb/> |
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2319 <anchor type="note" xlink:label="note-0076-02a" xlink:href="note-0076-02"/> |
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2320 encore, & </s> |
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2321 <s xml:id="echoid-s1296" xml:space="preserve">ſur le même point, ſuivant une autre ligne <lb/>de direction, qui paſſant de l’autre coté de cette per-<lb/>pendiculaire, faſſe avec elle un angle égal au pre-<lb/>mier: </s> |
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2322 <s xml:id="echoid-s1297" xml:space="preserve">car les deux angles que font alors ces deux li-<lb/>gnes de direction avec AD, étant complemens à deux <lb/>droits, l’un de l’autre, leurs ſinus ſeront égaux; </s> |
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2323 <s xml:id="echoid-s1298" xml:space="preserve">& </s> |
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2324 <s xml:id="echoid-s1299" xml:space="preserve"><lb/>par conſéquent ils ſeront en même raiſon au ſinus de <lb/>l’angle CAD; </s> |
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2325 <s xml:id="echoid-s1300" xml:space="preserve">& </s> |
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2326 <s xml:id="echoid-s1301" xml:space="preserve">par conſéquent auſſi ce même poids <lb/>ſeroit alors en même raiſon aux puiſſances, qui pla-<lb/>cées ſuivant ces différentes directions, le ſoutien-<lb/>droient l’une aprés l’autre; </s> |
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2327 <s xml:id="echoid-s1302" xml:space="preserve">ainſi elles ſeroient égales <lb/>entr’elles: </s> |
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2328 <s xml:id="echoid-s1303" xml:space="preserve">Donc la même puiſſance qui ſoutient ce <lb/>poids ſuivant une de ces directions, le peut encore <lb/>ſoutenir ſuivant l’autre ſur le même plan incliné <lb/>GH.</s> |
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2329 <s xml:id="echoid-s1304" xml:space="preserve"/> |
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2330 </p> |
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2331 <div xml:id="echoid-div144" type="float" level="2" n="1"> |
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2332 <note position="left" xlink:label="note-0076-01" xlink:href="note-0076-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2333 <note position="left" xlink:label="note-0076-02" xlink:href="note-0076-02a" xml:space="preserve">fig 30. <lb/>33.</note> |
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2334 </div> |
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2335 <p style="it"> |
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2336 <s xml:id="echoid-s1305" xml:space="preserve">On verra par le Corollaire 23. </s> |
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2337 <s xml:id="echoid-s1306" xml:space="preserve">que pour rendre ce dernier <lb/>Corollaire général pour toutes ſortes d’hypotbéſes, il faut que <lb/>ce poids ſe trouve alors ſur le même point d’un plan toujours <lb/>également incliné.</s> |
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2338 <s xml:id="echoid-s1307" xml:space="preserve"/> |
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2339 </p> |
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2340 </div> |
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2341 <div xml:id="echoid-div146" type="section" level="1" n="98"> |
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2342 <head xml:id="echoid-head98" xml:space="preserve"><emph style="sc">Corollaire</emph> XVII.</head> |
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2343 <p> |
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2344 <s xml:id="echoid-s1308" xml:space="preserve">1°. </s> |
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2345 <s xml:id="echoid-s1309" xml:space="preserve">Si AB ne concourt point avec la perpendiculaire <lb/>faite ſur AD au point A, la puiſſance R qui ſoutiet le <lb/>poid EO ſuivant cette même ligne AB, eſt à ce même <lb/>poids en plus grande raiſon que le ſinus de CAD au ſi-<lb/>nus total; </s> |
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2346 <s xml:id="echoid-s1310" xml:space="preserve">c’eſt-à-dire, dans l’hypoth êſe ordinaire, en <lb/>plus grande raiſon que la hauteur dé ce plan (Cor. <lb/></s> |
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2347 <s xml:id="echoid-s1311" xml:space="preserve">14. </s> |
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2348 <s xml:id="echoid-s1312" xml:space="preserve">& </s> |
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2349 <s xml:id="echoid-s1313" xml:space="preserve">15.) </s> |
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2350 <s xml:id="echoid-s1314" xml:space="preserve">à ſa longueur. </s> |
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2351 <s xml:id="echoid-s1315" xml:space="preserve">2°. </s> |
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2352 <s xml:id="echoid-s1316" xml:space="preserve">Si l’angle de cette per-<lb/>pendiculaire avec la ligne de direction AB de cette <lb/>puiſſance, eſt moindre que l’angle de cette même per- |
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2353 <pb o="51" file="0077" n="77" rhead="MECHANIQUE."/> |
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2354 pendiculaire avec AN, cette puiſſance eſt auſſi moin-<lb/> |
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2355 <anchor type="note" xlink:label="note-0077-01a" xlink:href="note-0077-01"/> |
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2356 dre que ce poids: </s> |
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2357 <s xml:id="echoid-s1317" xml:space="preserve">puiſque de quelque côté que AB <lb/>faſſe cet angle avec cette pendiculaire, la puiſſance qui <lb/>ſoutiendra ce poids, (Cor. </s> |
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2358 <s xml:id="echoid-s1318" xml:space="preserve">16.) </s> |
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2359 <s xml:id="echoid-s1319" xml:space="preserve">ſera la même; </s> |
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2360 <s xml:id="echoid-s1320" xml:space="preserve">il s’enſuit <lb/>(Cor. </s> |
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2361 <s xml:id="echoid-s1321" xml:space="preserve">II. </s> |
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2362 <s xml:id="echoid-s1322" xml:space="preserve">n. </s> |
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2363 <s xml:id="echoid-s1323" xml:space="preserve">I.) </s> |
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2364 <s xml:id="echoid-s1324" xml:space="preserve">qu’elle ſera moindre que ce poids dans <lb/>l’un & </s> |
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2365 <s xml:id="echoid-s1325" xml:space="preserve">l’autrecas: </s> |
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2366 <s xml:id="echoid-s1326" xml:space="preserve">ainſi l’on peut conclure en général <lb/>qu’une même puiſſance peut ſoutenir un même poids <lb/>ſur un même plan incliné ſuivant deux différentes di-<lb/>rections: </s> |
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2367 <s xml:id="echoid-s1327" xml:space="preserve">pourvu qu’elle ſoit moindre que ce poids, & </s> |
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2368 <s xml:id="echoid-s1328" xml:space="preserve"><lb/>qu’elle lui ſoit cependant en plus grande raiſon que le <lb/>ſinus de l’angle CAD au ſinus total; </s> |
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2369 <s xml:id="echoid-s1329" xml:space="preserve">c’eſt-à-dire, dans <lb/>l’hypothêſe ordinaire, où l’on regarde la ligne de di-<lb/>rection de ce poids comme parallele à la hauteur de ce <lb/>plan: </s> |
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2370 <s xml:id="echoid-s1330" xml:space="preserve">pourvu que cette puiſſance moindre que ce <lb/>poids, lui ſoit cependant en plus grande raiſon que la <lb/>hauteur de ce plan à ſa longueur.</s> |
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2371 <s xml:id="echoid-s1331" xml:space="preserve"/> |
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2372 </p> |
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2373 <div xml:id="echoid-div146" type="float" level="2" n="1"> |
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2374 <note position="right" xlink:label="note-0077-01" xlink:href="note-0077-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2375 </div> |
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2376 </div> |
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2377 <div xml:id="echoid-div148" type="section" level="1" n="99"> |
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2378 <head xml:id="echoid-head99" xml:space="preserve"><emph style="sc">Corollaire</emph> XVIII.</head> |
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2379 <p> |
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2380 <s xml:id="echoid-s1332" xml:space="preserve">En tout autre cas; </s> |
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2381 <s xml:id="echoid-s1333" xml:space="preserve">c’eſt-à-dire, lorſque cette puiſ-<lb/>ſance eſt plus grande que ce poids, ou du moins qu’el-<lb/>le lui eſt égale, ou bien lorſqu’elle lui eſt en même <lb/>raiſon que le ſinus de l’angle CAD au ſinus total, <lb/>elle ne le peut ſoutenir ſur le même point de ce plan <lb/>que ſuivant une ſeule direction. </s> |
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2382 <s xml:id="echoid-s1334" xml:space="preserve">Tout cela eſt mani-<lb/>feſte par une raiſon toute contraire à celle du Corol-<lb/>laire précédent.</s> |
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2383 <s xml:id="echoid-s1335" xml:space="preserve"/> |
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2384 </p> |
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2385 <p style="it"> |
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2386 <s xml:id="echoid-s1336" xml:space="preserve">On voit aſſez comment ces quatre derniers Corollaires ſe <lb/>peuvent appliquer à toutes ſortes de ſurfaces courbes, pour les <lb/>points ou elles peuvent être touchées par des plans inclinez. <lb/></s> |
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2387 <s xml:id="echoid-s1337" xml:space="preserve">Il n’eſt pas difficile non plus de reconnoitre ce qui leur peut <lb/>convenir de ce que nous allons encore dire des ſurfaces planes; </s> |
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2388 <s xml:id="echoid-s1338" xml:space="preserve"><lb/>c’eſt pourquoi nous ne parlerons plus d’orénavant que de <lb/>celles-ci.</s> |
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2389 <s xml:id="echoid-s1339" xml:space="preserve"/> |
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2390 </p> |
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2391 <pb o="52" file="0078" n="78" rhead="NOUVELLE"/> |
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2392 <note position="left" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2393 </div> |
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2394 <div xml:id="echoid-div149" type="section" level="1" n="100"> |
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2395 <head xml:id="echoid-head100" xml:space="preserve"><emph style="sc">Corollaire</emph> XIX.</head> |
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2396 <p> |
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2397 <s xml:id="echoid-s1340" xml:space="preserve">Puiſque (Cor. </s> |
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2398 <s xml:id="echoid-s1341" xml:space="preserve">7.) </s> |
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2399 <s xml:id="echoid-s1342" xml:space="preserve">le poids EO, la puiſſance R, & </s> |
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2400 <s xml:id="echoid-s1343" xml:space="preserve"><lb/>la charge du plan GH, ſont entr’eux comme les li-<lb/> |
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2401 <anchor type="note" xlink:label="note-0078-02a" xlink:href="note-0078-02"/> |
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2402 gnes BD, BA, & </s> |
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2403 <s xml:id="echoid-s1344" xml:space="preserve">AD; </s> |
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2404 <s xml:id="echoid-s1345" xml:space="preserve">ſi la ligne de direction de la <lb/>puiſſance R eſt parallele au plan GH, & </s> |
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2405 <s xml:id="echoid-s1346" xml:space="preserve">AC celle de <lb/>ce poids parallele auſſi à HK hauteur de ce plan: </s> |
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2406 <s xml:id="echoid-s1347" xml:space="preserve">ce <lb/>poids, cette puiſſance, & </s> |
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2407 <s xml:id="echoid-s1348" xml:space="preserve">la charge de ce même plan, <lb/>ſeront entr’eux comme la longueur de ce plan, ſa hau-<lb/>teur, & </s> |
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2408 <s xml:id="echoid-s1349" xml:space="preserve">ſa baſe; </s> |
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2409 <s xml:id="echoid-s1350" xml:space="preserve">c’eſt-à-dire, comme GH, HK, & </s> |
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2410 <s xml:id="echoid-s1351" xml:space="preserve"><lb/>KG; </s> |
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2411 <s xml:id="echoid-s1352" xml:space="preserve">parce qu’alors les triangles GHK, & </s> |
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2412 <s xml:id="echoid-s1353" xml:space="preserve">DBA ſont <lb/>ſemblables.</s> |
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2413 <s xml:id="echoid-s1354" xml:space="preserve"/> |
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2414 </p> |
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2415 <div xml:id="echoid-div149" type="float" level="2" n="1"> |
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2416 <note position="left" xlink:label="note-0078-02" xlink:href="note-0078-02a" xml:space="preserve">fig. 30.</note> |
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2417 </div> |
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2418 </div> |
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2419 <div xml:id="echoid-div151" type="section" level="1" n="101"> |
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2420 <head xml:id="echoid-head101" xml:space="preserve"><emph style="sc">Corollaire</emph> XX.</head> |
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2421 <p> |
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2422 <s xml:id="echoid-s1355" xml:space="preserve">Et pour la même raiſon, ſi cette ligne de direction <lb/> |
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2423 <anchor type="note" xlink:label="note-0078-03a" xlink:href="note-0078-03"/> |
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2424 AB eſt parallele à l’horizon; </s> |
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2425 <s xml:id="echoid-s1356" xml:space="preserve">c’eſt-à-dire, à la baze <lb/>GK de ce plan; </s> |
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2426 <s xml:id="echoid-s1357" xml:space="preserve">& </s> |
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2427 <s xml:id="echoid-s1358" xml:space="preserve">que AC ſoit encore parallele à ſa <lb/>hauteur HK: </s> |
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2428 <s xml:id="echoid-s1359" xml:space="preserve">Ce poids, cette puiſſance, & </s> |
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2429 <s xml:id="echoid-s1360" xml:space="preserve">la charge <lb/>de ce plan, ſeront alors entr’eux comme la baze de <lb/>de ce plan, ſa hauteur, & </s> |
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2430 <s xml:id="echoid-s1361" xml:space="preserve">ſa longueur; </s> |
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2431 <s xml:id="echoid-s1362" xml:space="preserve">c’eſt-à-dire, <lb/>comme GK, KH, HG; </s> |
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2432 <s xml:id="echoid-s1363" xml:space="preserve">parce qu’alors les triangles <lb/>GKH, & </s> |
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2433 <s xml:id="echoid-s1364" xml:space="preserve">DBA ſont encore ſemblables.</s> |
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2434 <s xml:id="echoid-s1365" xml:space="preserve"/> |
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2435 </p> |
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2436 <div xml:id="echoid-div151" type="float" level="2" n="1"> |
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2437 <note position="left" xlink:label="note-0078-03" xlink:href="note-0078-03a" xml:space="preserve">fig. 33.</note> |
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2438 </div> |
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2439 <p style="it"> |
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2440 <s xml:id="echoid-s1366" xml:space="preserve">Fuſqu’ici nous n’avons regardé le même poids que comme <lb/>appliqué au même endroit d’un plan toujours également incli-<lb/>né: </s> |
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2441 <s xml:id="echoid-s1367" xml:space="preserve">Mais s’il ſe trouvoit ſucceſſivement en différens points, <lb/>qu’arriveroit-il? </s> |
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2442 <s xml:id="echoid-s1368" xml:space="preserve">Le voici.</s> |
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2443 <s xml:id="echoid-s1369" xml:space="preserve"/> |
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2444 </p> |
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2445 </div> |
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2446 <div xml:id="echoid-div153" type="section" level="1" n="102"> |
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2447 <head xml:id="echoid-head102" xml:space="preserve"><emph style="sc">Corollaire</emph> XXI.</head> |
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2448 <p> |
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2449 <s xml:id="echoid-s1370" xml:space="preserve">Il ſuit encore de cette propoſition que les puiſſances <lb/> |
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2450 <anchor type="note" xlink:label="note-0078-04a" xlink:href="note-0078-04"/> |
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2451 P & </s> |
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2452 <s xml:id="echoid-s1371" xml:space="preserve">R qui ſoutiennent ſucceſſivement le même poids <lb/>A, ou des poids égaux ſur les points O, & </s> |
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2453 <s xml:id="echoid-s1372" xml:space="preserve">Q d’un <lb/>même plan HG, ſont entr’elles en raiſon compoſée <lb/>de celles des ſinus des angles QAD, & </s> |
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2454 <s xml:id="echoid-s1373" xml:space="preserve">QAP; </s> |
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2455 <s xml:id="echoid-s1374" xml:space="preserve">OAR <lb/>& </s> |
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2456 <s xml:id="echoid-s1375" xml:space="preserve">OAD: </s> |
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2457 <s xml:id="echoid-s1376" xml:space="preserve">car puiſque la puiſſance P eſt au poids A |
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2458 <pb o="53" file="0079" n="79" rhead="MECHANIQUE"/> |
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2459 appliqué en Q, comme le ſinus de l’angle QAD, au <lb/> |
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2460 <anchor type="note" xlink:label="note-0079-01a" xlink:href="note-0079-01"/> |
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2461 ſinus de l’angle QAP; </s> |
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2462 <s xml:id="echoid-s1377" xml:space="preserve">& </s> |
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2463 <s xml:id="echoid-s1378" xml:space="preserve">quele même poids appliqué <lb/>en O, eſt à la puiſſance R, comme le ſinus de l’angle <lb/>OAR, à celui de l’angle OAD: </s> |
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2464 <s xml:id="echoid-s1379" xml:space="preserve">Il ſuit en multipliant <lb/>par ordre ces deux rangées de proportionnelles; </s> |
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2465 <s xml:id="echoid-s1380" xml:space="preserve">que <lb/>la puiſſance P eſt à la puiſſance R, comme le produit <lb/>des finus des angles QAD, & </s> |
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2466 <s xml:id="echoid-s1381" xml:space="preserve">OAR, au produit de <lb/>ceux des angles QAP, & </s> |
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2467 <s xml:id="echoid-s1382" xml:space="preserve">OAD; </s> |
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2468 <s xml:id="echoid-s1383" xml:space="preserve">c’eſt-à-dire, en <lb/>raiſon compoſée de celles des ſinus des angles QAD, <lb/>& </s> |
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2469 <s xml:id="echoid-s1384" xml:space="preserve">QAP; </s> |
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2470 <s xml:id="echoid-s1385" xml:space="preserve">OAR, & </s> |
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|
2471 <s xml:id="echoid-s1386" xml:space="preserve">OAD.</s> |
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|
2472 <s xml:id="echoid-s1387" xml:space="preserve"/> |
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|
2473 </p> |
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2474 <div xml:id="echoid-div153" type="float" level="2" n="1"> |
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2475 <note position="left" xlink:label="note-0078-04" xlink:href="note-0078-04a" xml:space="preserve">fig. 37. <lb/>38.</note> |
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2476 <note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2477 </div> |
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2478 </div> |
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2479 <div xml:id="echoid-div155" type="section" level="1" n="103"> |
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2480 <head xml:id="echoid-head103" xml:space="preserve"><emph style="sc">Corollaire</emph> XXII.</head> |
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2481 <p> |
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2482 <s xml:id="echoid-s1388" xml:space="preserve">D’où l’on voit que tant que les lignes de direction <lb/>AP, & </s> |
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2483 <s xml:id="echoid-s1389" xml:space="preserve">AR ſont la même, ou paralleles entr’elles, <lb/>& </s> |
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2484 <s xml:id="echoid-s1390" xml:space="preserve">que celles du poids A appliqué en Q, & </s> |
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2485 <s xml:id="echoid-s1391" xml:space="preserve">en O, ſont <lb/>auſſi paralleles; </s> |
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2486 <s xml:id="echoid-s1392" xml:space="preserve">les angles QAP, & </s> |
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2487 <s xml:id="echoid-s1393" xml:space="preserve">OAR étant <lb/>alors égaux entr’eux, de même que les angles QAD, <lb/>& </s> |
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2488 <s xml:id="echoid-s1394" xml:space="preserve">OAD, les puiſſances P & </s> |
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2489 <s xml:id="echoid-s1395" xml:space="preserve">R ſont auſſi pour lors <lb/>égales; </s> |
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2490 <s xml:id="echoid-s1396" xml:space="preserve">ce qui fait voir que ce même poids A péſe <lb/>alors également ſur quelque point O, ou Q de ce <lb/>plan, qu’il ſoit appliqué.</s> |
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2491 <s xml:id="echoid-s1397" xml:space="preserve"/> |
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2492 </p> |
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2493 </div> |
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2494 <div xml:id="echoid-div156" type="section" level="1" n="104"> |
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2495 <head xml:id="echoid-head104" xml:space="preserve"><emph style="sc">Corollaire</emph> XXIII.</head> |
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2496 <p> |
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2497 <s xml:id="echoid-s1398" xml:space="preserve">Au contraire, s’il n’y a que les lignes de de direc-<lb/>tion AP, & </s> |
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2498 <s xml:id="echoid-s1399" xml:space="preserve">AR, de ces puiſſances qui ſoient paral-<lb/>leles entr’elles, & </s> |
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2499 <s xml:id="echoid-s1400" xml:space="preserve">que celles de ce même poids A ap-<lb/>pliqué ſucceſſivement en O, & </s> |
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2500 <s xml:id="echoid-s1401" xml:space="preserve">en Q, concourent en <lb/>quelque point D, que ce ſoit; </s> |
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2501 <s xml:id="echoid-s1402" xml:space="preserve">par exemple, au cen-<lb/>tre de la terre: </s> |
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2502 <s xml:id="echoid-s1403" xml:space="preserve">les angles QAP, & </s> |
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2503 <s xml:id="echoid-s1404" xml:space="preserve">OAR étant en-<lb/>core égaux, les puiſſances P & </s> |
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2504 <s xml:id="echoid-s1405" xml:space="preserve">R ſeront entr’elles <lb/>comme les ſinus des angles QAD, & </s> |
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2505 <s xml:id="echoid-s1406" xml:space="preserve">OAD; </s> |
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2506 <s xml:id="echoid-s1407" xml:space="preserve">ou bien, <lb/>à cauſe des paralleles QA, AO, ces puiſſances ſeront <lb/>entr’elles comme les ſinus des angles SAD, & </s> |
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2507 <s xml:id="echoid-s1408" xml:space="preserve">ASA, <lb/>ou ASD ſon complement; </s> |
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2508 <s xml:id="echoid-s1409" xml:space="preserve">c’eſt-à-dire, (Lem. </s> |
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2509 <s xml:id="echoid-s1410" xml:space="preserve">5.) </s> |
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2510 <s xml:id="echoid-s1411" xml:space="preserve">com-<lb/>me DS à AD. </s> |
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2511 <s xml:id="echoid-s1412" xml:space="preserve">Ce qui fait voir qu’en ce cas plus le poids</s> |
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2512 </p> |
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2513 <pb o="54" file="0080" n="80" rhead="NOUVELLE"/> |
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2514 <note position="left" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2515 <p> |
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2516 <s xml:id="echoid-s1413" xml:space="preserve">A eſt haut ſur le plan HG, plus auſſi la puiſſance qui l’y <lb/>doit ſoutenir ſuivant une certaine direction, doit être <lb/>grande.</s> |
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2517 <s xml:id="echoid-s1414" xml:space="preserve"/> |
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2518 </p> |
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2519 <p style="it"> |
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2520 <s xml:id="echoid-s1415" xml:space="preserve">On voit préſentement qu’il peut y avoir bien de la diffé-<lb/>rence entre un poids ſoutenu ſur un même plan, & </s> |
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2521 <s xml:id="echoid-s1416" xml:space="preserve">un poids <lb/>ſoutenu ſur le même point du plan; </s> |
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2522 <s xml:id="echoid-s1417" xml:space="preserve">c’eſt auſſi pour cela qu’on <lb/>à pris ſoin ci-deſſus de ne les pas confondre, & </s> |
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2523 <s xml:id="echoid-s1418" xml:space="preserve">de faire re-<lb/>marquer cette différence dans la ſeconde réfléxion qui ſuit le <lb/>Corollaire 13.</s> |
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2524 <s xml:id="echoid-s1419" xml:space="preserve"/> |
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2525 </p> |
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2526 </div> |
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2527 <div xml:id="echoid-div157" type="section" level="1" n="105"> |
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2528 <head xml:id="echoid-head105" xml:space="preserve"><emph style="sc">Corollaire</emph> XXIV.</head> |
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2529 <p> |
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2530 <s xml:id="echoid-s1420" xml:space="preserve">Mais s’il n’y a que les lignes de direction du poids <lb/>A placé tantôt en O, & </s> |
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2531 <s xml:id="echoid-s1421" xml:space="preserve">tantôt en Q, qui ſoient pa-<lb/>ralleles entr’elles; </s> |
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2532 <s xml:id="echoid-s1422" xml:space="preserve">les puiſſances P & </s> |
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2533 <s xml:id="echoid-s1423" xml:space="preserve">R ſeront alors <lb/>entr’elles comme les ſinus des angles OAR, & </s> |
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2534 <s xml:id="echoid-s1424" xml:space="preserve">QAP; <lb/></s> |
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2535 <s xml:id="echoid-s1425" xml:space="preserve">c’eſt-à-dire, en raiſon réciproque des ſinus des angles <lb/>que font leurs lignes de direction avec AO, & </s> |
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2536 <s xml:id="echoid-s1426" xml:space="preserve">AQ, <lb/>tirées des points A ou ces lignes de direction con-<lb/>courent avec celles de ce poids, perpendiculairement <lb/>au plan GH.</s> |
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2537 <s xml:id="echoid-s1427" xml:space="preserve"/> |
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2538 </p> |
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2539 </div> |
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2540 <div xml:id="echoid-div158" type="section" level="1" n="106"> |
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2541 <head xml:id="echoid-head106" xml:space="preserve"><emph style="sc">Corollaire</emph> XXV.</head> |
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2542 <p> |
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2543 <s xml:id="echoid-s1428" xml:space="preserve">Si préſentement on conçoit que les puiſſances P & </s> |
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2544 <s xml:id="echoid-s1429" xml:space="preserve">R <lb/>ſoient égales, & </s> |
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2545 <s xml:id="echoid-s1430" xml:space="preserve">que les poids A & </s> |
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2546 <s xml:id="echoid-s1431" xml:space="preserve">A ſoient différens; <lb/></s> |
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2547 <s xml:id="echoid-s1432" xml:space="preserve">on trouvera de méme que ces poids, qu’elles ſoutien-<lb/>nent ſur les points Q & </s> |
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2548 <s xml:id="echoid-s1433" xml:space="preserve">O du plan GH, ſeront entr’-<lb/>eux en raiſon compoſée de celles des ſinus des angles <lb/>QAP, & </s> |
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2549 <s xml:id="echoid-s1434" xml:space="preserve">QAD; </s> |
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2550 <s xml:id="echoid-s1435" xml:space="preserve">OAD, & </s> |
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2551 <s xml:id="echoid-s1436" xml:space="preserve">OAR; </s> |
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2552 <s xml:id="echoid-s1437" xml:space="preserve">c’eſt-à-dire, com-<lb/>me le produit des ſinus des angles QAP & </s> |
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2553 <s xml:id="echoid-s1438" xml:space="preserve">OAD, au <lb/>produit de ceux des angles QAD & </s> |
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2554 <s xml:id="echoid-s1439" xml:space="preserve">OAR: </s> |
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2555 <s xml:id="echoid-s1440" xml:space="preserve">De ſorte <lb/>que 1°. </s> |
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2556 <s xml:id="echoid-s1441" xml:space="preserve">Lorſque les lignes de direction de ces puiſ-<lb/>ſances ſont paralleles entr’elles, & </s> |
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2557 <s xml:id="echoid-s1442" xml:space="preserve">celles de ces poids <lb/>paralleles auſſi; </s> |
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2558 <s xml:id="echoid-s1443" xml:space="preserve">ces poids ſont égaux. </s> |
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2559 <s xml:id="echoid-s1444" xml:space="preserve">2°. </s> |
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2560 <s xml:id="echoid-s1445" xml:space="preserve">Mais s’il <lb/>n’y a que celles de ces puiſſances qui le ſoient; </s> |
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2561 <s xml:id="echoid-s1446" xml:space="preserve">ces |
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2562 <pb o="55" file="0081" n="81" rhead="MECHANIQUE."/> |
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2563 poids ſont entr’eux en raiſon réciproque des <lb/> |
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2564 <anchor type="note" xlink:label="note-0081-01a" xlink:href="note-0081-01"/> |
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2565 ſinus des angles que font leurs lignes de direction <lb/>avec les perpendiculaires au plan GH en Q, & </s> |
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2566 <s xml:id="echoid-s1447" xml:space="preserve">en O. <lb/></s> |
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2567 <s xml:id="echoid-s1448" xml:space="preserve">3°. </s> |
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2568 <s xml:id="echoid-s1449" xml:space="preserve">Au contraire s’il n’y a que les lignes de direction <lb/>de ces poids qui ſoient paralleles entr’elles; </s> |
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2569 <s xml:id="echoid-s1450" xml:space="preserve">ils ſeront <lb/>entr’eux en même raiſon que les ſinus des angles que <lb/>font ces mêmes perpendiculaires avec les lignes de di-<lb/>rection des puiſſances qui les ſoutiennent.</s> |
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2570 <s xml:id="echoid-s1451" xml:space="preserve"/> |
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2571 </p> |
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2572 <div xml:id="echoid-div158" type="float" level="2" n="1"> |
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2573 <note position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2574 </div> |
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2575 <p style="it"> |
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2576 <s xml:id="echoid-s1452" xml:space="preserve">Il y auroit encore bien des Corollaires à tirer de cette pro-<lb/>poſition non-ſeulement par raport aux plans, mais auſſi par <lb/>raport aux poli-plans: </s> |
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2577 <s xml:id="echoid-s1453" xml:space="preserve">en voilà aſſés pour en pouvoir juger.</s> |
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2578 <s xml:id="echoid-s1454" xml:space="preserve"/> |
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2579 </p> |
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2580 <figure> |
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2581 <image file="0081-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0081-01"/> |
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2582 </figure> |
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2583 </div> |
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2584 <div xml:id="echoid-div160" type="section" level="1" n="107"> |
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2585 <head xml:id="echoid-head107" xml:space="preserve">PROBLEME.</head> |
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2586 <p style="it"> |
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2587 <s xml:id="echoid-s1455" xml:space="preserve">L Apaiſſance R étant donnée, la diſpoſer tellement qu’elle <lb/> |
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2588 <anchor type="note" xlink:label="note-0081-02a" xlink:href="note-0081-02"/> |
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2589 puiſſe ſoutenir le poids EO auſſi donné, ſur le <lb/>plan GHMN incliné, & </s> |
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2590 <s xml:id="echoid-s1456" xml:space="preserve">ſuivant ſa longueur GH, de la <lb/>hauteur HK; </s> |
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2591 <s xml:id="echoid-s1457" xml:space="preserve">& </s> |
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2592 <s xml:id="echoid-s1458" xml:space="preserve">ſuivant ſa largeur GN, de la hauteur <lb/>NL.</s> |
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2593 <s xml:id="echoid-s1459" xml:space="preserve"/> |
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2594 </p> |
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2595 <div xml:id="echoid-div160" type="float" level="2" n="1"> |
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2596 <note position="right" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">fig. 39. <lb/>40.</note> |
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2597 </div> |
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2598 </div> |
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2599 <div xml:id="echoid-div162" type="section" level="1" n="108"> |
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2600 <head xml:id="echoid-head108" xml:space="preserve"><emph style="sc">Solution.</emph></head> |
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2601 <p> |
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2602 <s xml:id="echoid-s1460" xml:space="preserve">Aiant placé ce poids en quelque point, ou partie <lb/>de ce plan qu’il vous plaira, de quelqu’un des points <lb/>ou ſa baze le touche; </s> |
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2603 <s xml:id="echoid-s1461" xml:space="preserve">par exemple, du point O, tirez <lb/>OD perpendiculaire à ce plan, marquez auſſi la ligne <lb/>de direction FC de ce poids, qui rencontre auſſi ce <lb/>plan en L, & </s> |
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2604 <s xml:id="echoid-s1462" xml:space="preserve">OD prolongée en A. </s> |
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2605 <s xml:id="echoid-s1463" xml:space="preserve">Enſuite de quel-<lb/>que point C qu’il vous plaira de la ligne AC, faite <lb/>AC à CD, comme le poids EO à la puiſſance R. <lb/></s> |
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2606 <s xml:id="echoid-s1464" xml:space="preserve">1°. </s> |
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2607 <s xml:id="echoid-s1465" xml:space="preserve">Si CD n’eſt pas aſſez longue pour atteindre de C <lb/>juſqu’en quelque point D de la ligne AD, ce Pro-<lb/>blême eſt impoſſible: </s> |
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2608 <s xml:id="echoid-s1466" xml:space="preserve">parce que la diagonale tirée du |
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2609 <pb o="56" file="0082" n="82" rhead="NOUVELLE"/> |
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2610 <anchor type="note" xlink:label="note-0082-01a" xlink:href="note-0082-01"/> |
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2611 point A dans le parallelogramme fait ſous ces deux <lb/>lignes; </s> |
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2612 <s xml:id="echoid-s1467" xml:space="preserve">c’eft-à-dire, ſous AC & </s> |
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2613 <s xml:id="echoid-s1468" xml:space="preserve">CD, étant alors dif-<lb/>férente de AD, elle ne ſeroit pas perpendiculaire à <lb/>ce plan: </s> |
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2614 <s xml:id="echoid-s1469" xml:space="preserve">ainſi ce poids rouleroit alors (n. </s> |
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2615 <s xml:id="echoid-s1470" xml:space="preserve">3. </s> |
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2616 <s xml:id="echoid-s1471" xml:space="preserve">Demonſt.) <lb/></s> |
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2617 <s xml:id="echoid-s1472" xml:space="preserve">du côté de L. </s> |
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2618 <s xml:id="echoid-s1473" xml:space="preserve">2°. </s> |
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2619 <s xml:id="echoid-s1474" xml:space="preserve">Mais ſi CD peut atteindre juſqu’en <lb/>quelque point D de la ligne AD, achevez le paral-<lb/>lelogramme BC, & </s> |
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2620 <s xml:id="echoid-s1475" xml:space="preserve">placez la puiſſance R ſuivant <lb/>AB: </s> |
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2621 <s xml:id="echoid-s1476" xml:space="preserve">alors elle ſoutiendra ce poids ſur ce plan.</s> |
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2622 <s xml:id="echoid-s1477" xml:space="preserve"/> |
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2623 </p> |
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2624 <div xml:id="echoid-div162" type="float" level="2" n="1"> |
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2625 <note position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2626 </div> |
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2627 </div> |
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2628 <div xml:id="echoid-div164" type="section" level="1" n="109"> |
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2629 <head xml:id="echoid-head109" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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2630 <p> |
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2631 <s xml:id="echoid-s1478" xml:space="preserve">Puiſque (Hyp.) </s> |
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2632 <s xml:id="echoid-s1479" xml:space="preserve">cette puiſſance eſt à ce poids com-<lb/>me CD, ou AB qui lui eſt égale, eſt à AC; </s> |
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2633 <s xml:id="echoid-s1480" xml:space="preserve">leur con-<lb/>cours d’action doit le pouſſer (Lemm. </s> |
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2634 <s xml:id="echoid-s1481" xml:space="preserve">4. </s> |
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2635 <s xml:id="echoid-s1482" xml:space="preserve">Cor. </s> |
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2636 <s xml:id="echoid-s1483" xml:space="preserve">2.) <lb/></s> |
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2637 <s xml:id="echoid-s1484" xml:space="preserve">ſuivant AD perpendiculaire (Hyp.) </s> |
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2638 <s xml:id="echoid-s1485" xml:space="preserve">au plan GM, <lb/>& </s> |
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2639 <s xml:id="echoid-s1486" xml:space="preserve">qui paſſe auſſi (Hyp.) </s> |
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2640 <s xml:id="echoid-s1487" xml:space="preserve">par la baſe de ce poids: </s> |
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2641 <s xml:id="echoid-s1488" xml:space="preserve"><lb/>Donc (Cor. </s> |
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2642 <s xml:id="echoid-s1489" xml:space="preserve">2.) </s> |
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2643 <s xml:id="echoid-s1490" xml:space="preserve">il doit demeurer deſſus en équilibre <lb/>avec cette puiſſance. </s> |
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2644 <s xml:id="echoid-s1491" xml:space="preserve">Ce qu’il F. </s> |
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2645 <s xml:id="echoid-s1492" xml:space="preserve">D.</s> |
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2646 <s xml:id="echoid-s1493" xml:space="preserve"/> |
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2647 </p> |
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2648 </div> |
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2649 <div xml:id="echoid-div165" type="section" level="1" n="110"> |
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2650 <head xml:id="echoid-head110" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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2651 <p> |
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2652 <s xml:id="echoid-s1494" xml:space="preserve">Il eſt clair que ſi la puiſſance R ceſſoit de retenir le <lb/>poids EO, il couleroit le long de OL.</s> |
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2653 <s xml:id="echoid-s1495" xml:space="preserve"/> |
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2654 </p> |
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2655 </div> |
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2656 <div xml:id="echoid-div166" type="section" level="1" n="111"> |
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2657 <head xml:id="echoid-head111" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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2658 <p> |
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2659 <s xml:id="echoid-s1496" xml:space="preserve">Si CD eſt la plus petite ligne qui puiſſe atteindre <lb/>de C juſqu’en AD; </s> |
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2660 <s xml:id="echoid-s1497" xml:space="preserve">c’eſt-à-dire, ſi l’angle ADC eſt <lb/>droit, l’angle BAD le ſera auſſi; </s> |
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2661 <s xml:id="echoid-s1498" xml:space="preserve">& </s> |
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2662 <s xml:id="echoid-s1499" xml:space="preserve">par conſéquent <lb/>cette puiſſance eſt la plus petite (Cor. </s> |
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2663 <s xml:id="echoid-s1500" xml:space="preserve">14.) </s> |
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2664 <s xml:id="echoid-s1501" xml:space="preserve">qui puiſ-<lb/>ſe ſoutenir ce poids ſur ce plan, & </s> |
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2665 <s xml:id="echoid-s1502" xml:space="preserve">elle ne l’y poura <lb/>ſoutenir non plus que (Cor. </s> |
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2666 <s xml:id="echoid-s1503" xml:space="preserve">16.) </s> |
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2667 <s xml:id="echoid-s1504" xml:space="preserve">ſuivant cette ſeule <lb/>direction.</s> |
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2668 <s xml:id="echoid-s1505" xml:space="preserve"/> |
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2669 </p> |
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2670 </div> |
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2671 <div xml:id="echoid-div167" type="section" level="1" n="112"> |
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2672 <head xml:id="echoid-head112" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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2673 <p> |
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2674 <s xml:id="echoid-s1506" xml:space="preserve">Si CD n’eſt pas la plus petite qui puiſſe atteindre <lb/>depuis C juſqu’en AD, mais qu’elle ſoit cependant <lb/>cncore moindre que AC; </s> |
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2675 <s xml:id="echoid-s1507" xml:space="preserve">cette même puiſſance poura |
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2676 <pb o="57" file="0083" n="83" rhead="MECHANIQUE."/> |
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2677 ſoutenir ce poids ſuivant deux directions différentes; <lb/></s> |
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2678 <s xml:id="echoid-s1508" xml:space="preserve"> |
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2679 <anchor type="note" xlink:label="note-0083-01a" xlink:href="note-0083-01"/> |
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2680 parce qu’en ce cas CD poura rencontrer AD en deux <lb/>points également éloignez de la perpendiculaire tirée <lb/>du point C ſur AD. </s> |
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2681 <s xml:id="echoid-s1509" xml:space="preserve">Ce qui revient au Corollaire 16. <lb/></s> |
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2682 <s xml:id="echoid-s1510" xml:space="preserve">de la propoſition précédente.</s> |
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2683 <s xml:id="echoid-s1511" xml:space="preserve"/> |
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2684 </p> |
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2685 <div xml:id="echoid-div167" type="float" level="2" n="1"> |
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2686 <note position="right" xlink:label="note-0083-01" xlink:href="note-0083-01a" xml:space="preserve">DESPOIDS <lb/>ſoutenus ſur <lb/>des ſurfaces.</note> |
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2687 </div> |
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2688 </div> |
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2689 <div xml:id="echoid-div169" type="section" level="1" n="113"> |
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2690 <head xml:id="echoid-head113" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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2691 <p> |
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2692 <s xml:id="echoid-s1512" xml:space="preserve">Enfin ſi CD eſt plus grande que AC, elle ne poura <lb/>encore ſoutenir ce poids que ſuivant cette ſeule di-<lb/>rection. </s> |
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2693 <s xml:id="echoid-s1513" xml:space="preserve">Ce qui revient auſſi au Corollaire 18.</s> |
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2694 <s xml:id="echoid-s1514" xml:space="preserve"/> |
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2695 </p> |
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2696 </div> |
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2697 <div xml:id="echoid-div170" type="section" level="1" n="114"> |
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2698 <head xml:id="echoid-head114" xml:space="preserve"><emph style="sc">Corollaire</emph> V.</head> |
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2699 <p> |
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2700 <s xml:id="echoid-s1515" xml:space="preserve">Mais auſſi CD pouvant être infiniment plus gran-<lb/>de que AC, cette puiſſance peut auſſi être infiniment <lb/>plus grande que ce poids, & </s> |
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2701 <s xml:id="echoid-s1516" xml:space="preserve">demeurer cependant tou-<lb/>jours en équilibre avec lui. </s> |
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2702 <s xml:id="echoid-s1517" xml:space="preserve">Ce qui revient encore au <lb/>nombre 2. </s> |
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2703 <s xml:id="echoid-s1518" xml:space="preserve">du Corollaire 11.</s> |
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2704 <s xml:id="echoid-s1519" xml:space="preserve"/> |
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2705 </p> |
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2706 <p style="it"> |
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2707 <s xml:id="echoid-s1520" xml:space="preserve">Tout cela ſe peut aiſément appliquer à toutes ſortes de <lb/>ſurfaces courbes: </s> |
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2708 <s xml:id="echoid-s1521" xml:space="preserve">ceux pour qui ce Projet eſt écrit le voyent <lb/>aſſez.</s> |
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2709 <s xml:id="echoid-s1522" xml:space="preserve"/> |
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2710 </p> |
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2711 <figure> |
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2712 <image file="0083-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0083-01"/> |
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2713 </figure> |
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2714 <pb o="58" file="0084" n="84" rhead="NOUVELLE"/> |
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2715 <figure> |
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2716 <image file="0084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0084-01"/> |
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2717 </figure> |
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2718 </div> |
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2719 <div xml:id="echoid-div171" type="section" level="1" n="115"> |
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2720 <head xml:id="echoid-head115" xml:space="preserve">PROPOSITION <lb/>FONDAMENTALE <lb/>POUR <lb/>TOUTES SOR TES DE LEVIERS,</head> |
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2721 <p> |
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2722 <s xml:id="echoid-s1523" xml:space="preserve">De quelque eſpéce, & </s> |
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2723 <s xml:id="echoid-s1524" xml:space="preserve">dans quelque ſituation <lb/>qu’ils ſoient; </s> |
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2724 <s xml:id="echoid-s1525" xml:space="preserve">& </s> |
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2725 <s xml:id="echoid-s1526" xml:space="preserve">pour toutes les directions <lb/>poſſibles des puiſſances, ou des poids qui y <lb/>ſont appliquez.</s> |
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2726 <s xml:id="echoid-s1527" xml:space="preserve"/> |
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2727 </p> |
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2728 <p style="it"> |
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2729 <s xml:id="echoid-s1528" xml:space="preserve">SOIENT les puißances E & </s> |
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2730 <s xml:id="echoid-s1529" xml:space="preserve">F appliquées aux points <lb/> |
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2731 <anchor type="note" xlink:label="note-0084-01a" xlink:href="note-0084-01"/> |
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2732 O & </s> |
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2733 <s xml:id="echoid-s1530" xml:space="preserve">X du Levier MN, de quelque eſpéce, & </s> |
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2734 <s xml:id="echoid-s1531" xml:space="preserve">en <lb/>quelque ſituation qu’il ſoit; </s> |
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2735 <s xml:id="echoid-s1532" xml:space="preserve">quelque angle OAX que faſ-<lb/>ſent auſſi entr’elles, les lignes de direction de ces puiſſances, <lb/>indéfiniment prolongées vers A: </s> |
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2736 <s xml:id="echoid-s1533" xml:space="preserve">Ces deux puißances feroni <lb/>équilibre ſur le point fixe B de ce levier, par ou paſſe la dia-<lb/>gonale AG du parallelogramme RS, dont les côtez AS & </s> |
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2737 <s xml:id="echoid-s1534" xml:space="preserve">AR <lb/>ſont entr’eux, comme les puiſſances E, & </s> |
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2738 <s xml:id="echoid-s1535" xml:space="preserve">F.</s> |
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2739 <s xml:id="echoid-s1536" xml:space="preserve"/> |
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2740 </p> |
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2741 <div xml:id="echoid-div171" type="float" level="2" n="1"> |
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2742 <note position="left" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve">fig 41. <lb/>42. <lb/>43. <lb/>44. <lb/>45. <lb/>46.</note> |
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2743 </div> |
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2744 </div> |
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2745 <div xml:id="echoid-div173" type="section" level="1" n="116"> |
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2746 <head xml:id="echoid-head116" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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2747 <p> |
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2748 <s xml:id="echoid-s1537" xml:space="preserve">Concevons pour un moment que MAN eſt la <lb/>figure de ce Levier, & </s> |
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2749 <s xml:id="echoid-s1538" xml:space="preserve">qu’au lieu d’être tiré, ou <lb/>pouſſé par les puiſſances E & </s> |
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2750 <s xml:id="echoid-s1539" xml:space="preserve">F, ſon point A ſoit ſeu- |
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2751 <pb o="59" file="0085" n="85" rhead="MECHANIQUE."/> |
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2752 lement pouſſé, mais en même-tems, vers R ſuivant <lb/> |
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2753 <anchor type="note" xlink:label="note-0085-01a" xlink:href="note-0085-01"/> |
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2754 AR par une puiſſance égale à F, & </s> |
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2755 <s xml:id="echoid-s1540" xml:space="preserve">vers S ſuivant AS <lb/>par une autre puiſſance égale à E. </s> |
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2756 <s xml:id="echoid-s1541" xml:space="preserve">Il eſt conſtant <lb/>(Lemm. </s> |
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2757 <s xml:id="echoid-s1542" xml:space="preserve">3.) </s> |
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2758 <s xml:id="echoid-s1543" xml:space="preserve">que l’impreſſion compoſée que ce point <lb/>recevroit alors du concours d’action de ces deux <lb/>puiſſances, s’il étoit ainſi pouſſé, ne tendroit qu’à le <lb/>mouvoir ſuivant la diagonale AG du parallelogram-<lb/>me RS; </s> |
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2759 <s xml:id="echoid-s1544" xml:space="preserve">ainſi ne faiſant d’impreſſion ſur tout le corps <lb/>MAN, qu’autant que le point A, à raiſon de l’ob-<lb/>ſtacle qu’il leur fait, lui en communique, toute l’ac-<lb/>tion de ces deux puiſſances ſur ce corps, ſe trouveroit <lb/>réünie dans la ſeule ligne AG, ou AB; </s> |
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2760 <s xml:id="echoid-s1545" xml:space="preserve">ſi donc il <lb/>ſe trouvoit quelque point fixe dans cette ligne, par <lb/>exemple B, ce point ſoutiendroit, lui ſeul, toute <lb/>l’impreſſion de ces deux puiſſances ſur ce corps, ou <lb/>ce Levier; </s> |
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2761 <s xml:id="echoid-s1546" xml:space="preserve">& </s> |
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2762 <s xml:id="echoid-s1547" xml:space="preserve">par conſéquent ce corps n’en ayant <lb/>alors que ce qu’elles lui en communiquent, demeu-<lb/>reroit ainſi en équilibre ſur ce point, ſans qu’aucune <lb/>d’elles l’emportât ſur l’autre. </s> |
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2763 <s xml:id="echoid-s1548" xml:space="preserve">Oſtons préſentement <lb/>ces deux puiſſances, & </s> |
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2764 <s xml:id="echoid-s1549" xml:space="preserve">remettons les deux premiéres <lb/>E, & </s> |
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2765 <s xml:id="echoid-s1550" xml:space="preserve">F en action comme auparavant, prenant encore <lb/>MAN pour la figure du Levier, ou elles ſont appli-<lb/>quées. </s> |
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2766 <s xml:id="echoid-s1551" xml:space="preserve">Il eſt clair que ces deux puiſſances faiſant <lb/>toute la même impreſſion ſur le point A de ce Levier, <lb/>& </s> |
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2767 <s xml:id="echoid-s1552" xml:space="preserve">ſuivant la même direction AG, que faiſoient <lb/>auparavant celles que nous leur avions ſuppoſées <lb/>égales; </s> |
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2768 <s xml:id="echoid-s1553" xml:space="preserve">leur action doit ſe trouver de même que <lb/>celle de ces deux ſuppoſées, toute réünie dans la <lb/>ſeule ligne AB: </s> |
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2769 <s xml:id="echoid-s1554" xml:space="preserve">& </s> |
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2770 <s xml:id="echoid-s1555" xml:space="preserve">par conſéquent le point fixe B la <lb/>ſoutenant, lui ſeul, toute entiére, elles doivent encore <lb/>demeurer en équilibre ſur ce point. </s> |
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2771 <s xml:id="echoid-s1556" xml:space="preserve">Et ſi enfin on <lb/>retranche la partie MAN du corps AMN, en ſorte <lb/>qu’il n’en reſte plus que le Levier MN: </s> |
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2772 <s xml:id="echoid-s1557" xml:space="preserve">Il eſt encore <lb/>clair que les puiſſances E & </s> |
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2773 <s xml:id="echoid-s1558" xml:space="preserve">F agiſſant encore ſur ce <lb/>levier de même que lors qu’il étoit joint à la partie |
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2774 <pb o="60" file="0086" n="86" rhead="NOUVELLE"/> |
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2775 <anchor type="note" xlink:label="note-0086-01a" xlink:href="note-0086-01"/> |
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2776 retranchée, toute leur action doit encore ſe trouver <lb/>réünie dans le ſeul point B de ce levier, par ou paſſe <lb/>la diagonale AG du parallelogramme RS; </s> |
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2777 <s xml:id="echoid-s1559" xml:space="preserve">& </s> |
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2778 <s xml:id="echoid-s1560" xml:space="preserve">par <lb/>conſéquent, elles doivent encore demeurer en équi-<lb/>libre ſur ce point. </s> |
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2779 <s xml:id="echoid-s1561" xml:space="preserve">Ce qu’il faloit démontrer.</s> |
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2780 <s xml:id="echoid-s1562" xml:space="preserve"/> |
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2781 </p> |
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2782 <div xml:id="echoid-div173" type="float" level="2" n="1"> |
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2783 <note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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2784 <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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2785 </div> |
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2786 </div> |
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2787 <div xml:id="echoid-div175" type="section" level="1" n="117"> |
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2788 <head xml:id="echoid-head117" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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2789 <p> |
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2790 <s xml:id="echoid-s1563" xml:space="preserve">On voit aſſez qu’en quelque ſituation, de quel-<lb/>que eſpéce, & </s> |
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2791 <s xml:id="echoid-s1564" xml:space="preserve">de quelque figure, que ſoit le levier <lb/>auquel deux puiſſances, telles qu’elles ſoient, ſont <lb/>appliquées, elles ſeront toujours en équilibre, quelque <lb/>angle que faſſent entr’elles leurs lignes de direction, <lb/>tant qu’il y aura un point fixe de ce levier dans la <lb/>diagonale AG; </s> |
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2792 <s xml:id="echoid-s1565" xml:space="preserve">c’eſt pourquoi on ne s’arrête point <lb/>ici à exprimer les figures detous les cas de cette pro-<lb/>poſition, chacun le pourra faire à ſon loiſir.</s> |
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2793 <s xml:id="echoid-s1566" xml:space="preserve"/> |
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2794 </p> |
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2795 </div> |
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2796 <div xml:id="echoid-div176" type="section" level="1" n="118"> |
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2797 <head xml:id="echoid-head118" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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2798 <p> |
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2799 <s xml:id="echoid-s1567" xml:space="preserve">On voit encore que les deux mêmes puiſſances E <lb/>& </s> |
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2800 <s xml:id="echoid-s1568" xml:space="preserve">F peuvent faire ſucceſſivement équilibre ſur une <lb/>infinité de points B de ce même levier en changeant <lb/>ſeulement leurs directions: </s> |
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2801 <s xml:id="echoid-s1569" xml:space="preserve">puis qu’on les peut varier <lb/>en tant de maniéres que AG paſſera ſucceſſivement <lb/>par tous les points imaginables de ce levier, excepté <lb/>par les points O & </s> |
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2802 <s xml:id="echoid-s1570" xml:space="preserve">X, où ces deux puiſſances ſont <lb/>appliquées.</s> |
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2803 <s xml:id="echoid-s1571" xml:space="preserve"/> |
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2804 </p> |
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2805 </div> |
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2806 <div xml:id="echoid-div177" type="section" level="1" n="119"> |
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2807 <head xml:id="echoid-head119" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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2808 <p> |
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2809 <s xml:id="echoid-s1572" xml:space="preserve">Ce qui fait voir que dans la ſuppoſition du concours <lb/>des lignes de direction des poids au centre de la terre, <lb/>leurs centres de gravité, ou de direction peuvent chan-<lb/>ger inceſſamment à meſure qu’ils s’en approchent, ou <lb/>qu’ils s’en éloignent, ſelon la différente ſituation qu’ils <lb/>peuvent avoir par raport à lui, excepté dans les ſphéri-<lb/>ques. </s> |
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2810 <s xml:id="echoid-s1573" xml:space="preserve">On nes’arrête point à démontrer cela ſur des fi- |
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2811 <pb o="61" file="0087" n="87" rhead="MECHANIQUE."/> |
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2812 gures particuliéres, parce qu’il ſuit ſi naturellement <lb/> |
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2813 <anchor type="note" xlink:label="note-0087-01a" xlink:href="note-0087-01"/> |
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2814 du Corollaire 2. </s> |
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2815 <s xml:id="echoid-s1574" xml:space="preserve">qu’il n’y a perſonne qui ne le puiſſe <lb/>faire de ſoi-même.</s> |
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2816 <s xml:id="echoid-s1575" xml:space="preserve"/> |
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2817 </p> |
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2818 <div xml:id="echoid-div177" type="float" level="2" n="1"> |
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2819 <note position="right" xlink:label="note-0087-01" xlink:href="note-0087-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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2820 </div> |
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2821 </div> |
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2822 <div xml:id="echoid-div179" type="section" level="1" n="120"> |
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2823 <head xml:id="echoid-head120" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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2824 <p> |
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2825 <s xml:id="echoid-s1576" xml:space="preserve">On voit de plus de cette propoſition que le point fixe <lb/>de ce levier, où bien ſon appui B eſt pouſſé de A vers <lb/>G ſuivant AG par l’impreſſion compoſée qu’il reçoit <lb/>du concours d’action de ces deux puiſſances, & </s> |
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2826 <s xml:id="echoid-s1577" xml:space="preserve">que <lb/>la réſiſtance qu’il leur fait, étant égale à cette même <lb/>impreſſion, eſt à la force de chacune d’elles (Lemm. <lb/></s> |
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2827 <s xml:id="echoid-s1578" xml:space="preserve">3. </s> |
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2828 <s xml:id="echoid-s1579" xml:space="preserve">Cor. </s> |
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2829 <s xml:id="echoid-s1580" xml:space="preserve">3.) </s> |
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2830 <s xml:id="echoid-s1581" xml:space="preserve">Comme la diagonale AG à chacun des <lb/>côtez du parallelogramme RS, qui les répréſen-<lb/>tent; </s> |
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2831 <s xml:id="echoid-s1582" xml:space="preserve">c’eſt-à-dire, que cette réſiſtance du point fixe, <lb/>où bien de l’appui B de ce levier, eſt à la force de la <lb/>puiſſance E, comme AG à AS; </s> |
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2832 <s xml:id="echoid-s1583" xml:space="preserve">& </s> |
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2833 <s xml:id="echoid-s1584" xml:space="preserve">à celle de la puiſ-<lb/>ſance F, comme la même AG à AR.</s> |
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2834 <s xml:id="echoid-s1585" xml:space="preserve"/> |
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2835 </p> |
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2836 </div> |
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2837 <div xml:id="echoid-div180" type="section" level="1" n="121"> |
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2838 <head xml:id="echoid-head121" xml:space="preserve"><emph style="sc">Corollaire</emph> V.</head> |
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2839 <p> |
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2840 <s xml:id="echoid-s1586" xml:space="preserve">D’où il ſuit que lors que l’angle OAX eſt infini-<lb/>ment aigu, c’eſt-à-dire, lors que les lignes de direc-<lb/>tion EX & </s> |
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2841 <s xml:id="echoid-s1587" xml:space="preserve">OF des puiſſances E & </s> |
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2842 <s xml:id="echoid-s1588" xml:space="preserve">F ſont paralleles, <lb/>le point A étant alors infiniment éloigné de B, la <lb/>ligne AG, c’eſt-à-dire, (Cor. </s> |
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2843 <s xml:id="echoid-s1589" xml:space="preserve">4.) </s> |
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2844 <s xml:id="echoid-s1590" xml:space="preserve">la direction de <lb/>l’appui B leur eſt auſſi parallele, & </s> |
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2845 <s xml:id="echoid-s1591" xml:space="preserve">toujours vers <lb/>l’endroit, où tendent ces deux puiſſances, lors qu’elles <lb/>tirent du même côté; </s> |
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2846 <s xml:id="echoid-s1592" xml:space="preserve">ou bien vers celui, ou tend la <lb/>plus proche de cet appui, lors qu’elles tirent de diffé-<lb/>rens cótez.</s> |
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2847 <s xml:id="echoid-s1593" xml:space="preserve"/> |
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2848 </p> |
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2849 </div> |
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2850 <div xml:id="echoid-div181" type="section" level="1" n="122"> |
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2851 <head xml:id="echoid-head122" xml:space="preserve"><emph style="sc">Corollaire</emph> VI.</head> |
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2852 <p> |
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2853 <s xml:id="echoid-s1594" xml:space="preserve">Il ſuit encore du Corollaire 4. </s> |
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2854 <s xml:id="echoid-s1595" xml:space="preserve">pour tous les leviers <lb/> |
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2855 <anchor type="note" xlink:label="note-0087-02a" xlink:href="note-0087-02"/> |
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2856 de l’eſpéce exprimée dans les figures 41. </s> |
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2857 <s xml:id="echoid-s1596" xml:space="preserve">& </s> |
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2858 <s xml:id="echoid-s1597" xml:space="preserve">42. </s> |
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2859 <s xml:id="echoid-s1598" xml:space="preserve">que <lb/>plus l’angle OAX, que les lignes de direction des <lb/>puiſſances E & </s> |
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2860 <s xml:id="echoid-s1599" xml:space="preserve">F, font entr’elles, ſera obtus, moins |
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2861 <pb o="62" file="0088" n="88" rhead="NOUVELLE"/> |
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2862 <anchor type="note" xlink:label="note-0088-01a" xlink:href="note-0088-01"/> |
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2863 ſera grande la charge de l’appui B de chacun de ces le-<lb/>viers; </s> |
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2864 <s xml:id="echoid-s1600" xml:space="preserve">parce que plus cet angle ſera obtus, moins ſera <lb/>grande la raiſon de AG aux côtez du parallelogramme <lb/>RS, dont elle eſt diagonale, quoi qu’en proportion <lb/>différente: </s> |
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2865 <s xml:id="echoid-s1601" xml:space="preserve">De ſorte que l’on peut faire cet angle <lb/>ſi obtus que la charge de l’appui B de ce levier ſera <lb/>ſi petite qu’on voudra, quoi que les deux mêmes <lb/>puiſſances demeurent toujours en équilibre deſſus; <lb/></s> |
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2866 <s xml:id="echoid-s1602" xml:space="preserve">juſque-là même qu’elle peut devenir indéfiniment <lb/>petite, c’eſt-à-dire, moindre que quelque poids don-<lb/>né que ce ſoit. </s> |
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2867 <s xml:id="echoid-s1603" xml:space="preserve">Il ne faut pour cela qu’ouvrir l’angle <lb/>OAX juſqu’à ce que la diagonale AG du paralle-<lb/>logramme RS, ſoit à chacun de ſes côtez AR & </s> |
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2868 <s xml:id="echoid-s1604" xml:space="preserve"><lb/>AS en moindre raiſon que celle qui eſt entre ce poids <lb/>donné, & </s> |
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2869 <s xml:id="echoid-s1605" xml:space="preserve">chacune des puiſſances F & </s> |
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2870 <s xml:id="echoid-s1606" xml:space="preserve">E que l’on ſup-<lb/>poſe appliquées à ce levier.</s> |
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2871 <s xml:id="echoid-s1607" xml:space="preserve"/> |
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2872 </p> |
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2873 <div xml:id="echoid-div181" type="float" level="2" n="1"> |
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2874 <note position="right" xlink:label="note-0087-02" xlink:href="note-0087-02a" xml:space="preserve">fig. 41. <lb/>42.</note> |
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2875 <note position="left" xlink:label="note-0088-01" xlink:href="note-0088-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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2876 </div> |
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2877 </div> |
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2878 <div xml:id="echoid-div183" type="section" level="1" n="123"> |
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2879 <head xml:id="echoid-head123" xml:space="preserve"><emph style="sc">Corollaire</emph> VII.</head> |
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2880 <p> |
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2881 <s xml:id="echoid-s1608" xml:space="preserve">La charge de ce point ne peut pas de même <lb/>augmenter à l’infini: </s> |
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2882 <s xml:id="echoid-s1609" xml:space="preserve">Car ne pouvant jamais être <lb/>plus grande que lors que l’angle OAX eſt infini-<lb/>ment aigu, c’eſt-à-dire, lors que les lignes de direc-<lb/>tion de ces deux puiſſances ſont paralleles; </s> |
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2883 <s xml:id="echoid-s1610" xml:space="preserve">& </s> |
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2884 <s xml:id="echoid-s1611" xml:space="preserve">la <lb/>diagonale AG n’étant encore alors qu’égale à la <lb/>ſomme des côtez AR & </s> |
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2885 <s xml:id="echoid-s1612" xml:space="preserve">RG du parallelogramme <lb/>RS alors infiniment long; </s> |
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2886 <s xml:id="echoid-s1613" xml:space="preserve">la charge de cet appui ne <lb/>peut être, tout au plus, qu’égale à la ſomme des puiſ-<lb/>ſances E & </s> |
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2887 <s xml:id="echoid-s1614" xml:space="preserve">F.</s> |
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2888 <s xml:id="echoid-s1615" xml:space="preserve"/> |
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2889 </p> |
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2890 </div> |
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2891 <div xml:id="echoid-div184" type="section" level="1" n="124"> |
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2892 <head xml:id="echoid-head124" xml:space="preserve"><emph style="sc">Corollaire</emph> VIII.</head> |
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2893 <note position="left" xml:space="preserve">fig. 43. <lb/>44. <lb/>45. <lb/>46.</note> |
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2894 <p> |
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2895 <s xml:id="echoid-s1616" xml:space="preserve">Pour les leviers des eſpeces exprimées dans les <lb/>figures 43. </s> |
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2896 <s xml:id="echoid-s1617" xml:space="preserve">44. </s> |
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2897 <s xml:id="echoid-s1618" xml:space="preserve">45. </s> |
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2898 <s xml:id="echoid-s1619" xml:space="preserve">& </s> |
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2899 <s xml:id="echoid-s1620" xml:space="preserve">46. </s> |
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2900 <s xml:id="echoid-s1621" xml:space="preserve">Il en va tout autrement: <lb/></s> |
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2901 <s xml:id="echoid-s1622" xml:space="preserve">car plus l’angle OAX eſt obtus, plus la charge, <lb/>ou la réſiſtance de l’appui B eſt grande; </s> |
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2902 <s xml:id="echoid-s1623" xml:space="preserve">parce que <lb/>la raiſon de la diagonale AG à chacun des côtez du |
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|
2903 <pb o="63" file="0089" n="89" rhead="MECHANIQUE."/> |
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2904 parallelogramme RS, en eſt plus grande, quoi qu’en <lb/> |
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2905 <anchor type="note" xlink:label="note-0089-01a" xlink:href="note-0089-01"/> |
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2906 proportion différente; </s> |
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2907 <s xml:id="echoid-s1624" xml:space="preserve">mais elle ne peut pas pour <lb/>cela augmenter à l’infini: </s> |
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2908 <s xml:id="echoid-s1625" xml:space="preserve">car ne pouvant jamais être <lb/>plus grande que lors que cet angle eſt infiniment <lb/>obtus, c’eſt-à-dire, lors que les lignes de direction <lb/>de ces puiſſances concourent en une ſeule ligne <lb/>droite; </s> |
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2909 <s xml:id="echoid-s1626" xml:space="preserve">& </s> |
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2910 <s xml:id="echoid-s1627" xml:space="preserve">la diagonale AG n’étant alors qu’égale à <lb/>la ſomme des côtez AR & </s> |
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2911 <s xml:id="echoid-s1628" xml:space="preserve">GR du parallelogramme <lb/>RS alors encore infiniment long; </s> |
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2912 <s xml:id="echoid-s1629" xml:space="preserve">la réſiſtance de cet <lb/>appui ne peut par conféquent être encore, toutau plus, <lb/>qu’égale à la ſomme des forces de ces deux puiſſances.</s> |
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2913 <s xml:id="echoid-s1630" xml:space="preserve"/> |
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2914 </p> |
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2915 <div xml:id="echoid-div184" type="float" level="2" n="1"> |
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2916 <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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2917 </div> |
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2918 </div> |
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2919 <div xml:id="echoid-div186" type="section" level="1" n="125"> |
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2920 <head xml:id="echoid-head125" xml:space="preserve"><emph style="sc">Corollaire</emph> IX.</head> |
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2921 <p> |
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2922 <s xml:id="echoid-s1631" xml:space="preserve">Au contraire, plus cet angle OAX eſt aigu, <lb/>moins eſt grande la charge, ou la réſiſtance de l’ap-<lb/>pui B dece levier: </s> |
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2923 <s xml:id="echoid-s1632" xml:space="preserve">car plus cet angle eſt aigu, moins <lb/>eſt grande la raiſon de la diagonale AG aux côtez <lb/>du parallelogramme RS, quoi qu’en proportion dif-<lb/>férente; </s> |
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2924 <s xml:id="echoid-s1633" xml:space="preserve">mais elle ne peut pas non plus ainſi diminuer <lb/>à l’infini de même que nous venons de dire (Cor. </s> |
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2925 <s xml:id="echoid-s1634" xml:space="preserve">6.) <lb/></s> |
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2926 <s xml:id="echoid-s1635" xml:space="preserve">qu’elle le peut dans les leviers de l’eſpece exprimée <lb/>dans les figures 41. </s> |
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2927 <s xml:id="echoid-s1636" xml:space="preserve">& </s> |
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2928 <s xml:id="echoid-s1637" xml:space="preserve">42. </s> |
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2929 <s xml:id="echoid-s1638" xml:space="preserve">Car ne pouvant jamais être <lb/>moindre que lors que cet angle eſt infiniment aigu, <lb/>c’eſt-à-dire, lors que les lignes de direction de ces <lb/>puiſſances deviennent parallel’es; </s> |
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2930 <s xml:id="echoid-s1639" xml:space="preserve">& </s> |
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2931 <s xml:id="echoid-s1640" xml:space="preserve">le point G, qui <lb/>à meſure que cet angle devient plus aigu, s’approche <lb/>de plus en plus de la ligne AR, (fig. </s> |
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2932 <s xml:id="echoid-s1641" xml:space="preserve">43. </s> |
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2933 <s xml:id="echoid-s1642" xml:space="preserve">& </s> |
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2934 <s xml:id="echoid-s1643" xml:space="preserve">44.) </s> |
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2935 <s xml:id="echoid-s1644" xml:space="preserve"><lb/>ou AS (fig. </s> |
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2936 <s xml:id="echoid-s1645" xml:space="preserve">45. </s> |
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2937 <s xml:id="echoid-s1646" xml:space="preserve">& </s> |
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2938 <s xml:id="echoid-s1647" xml:space="preserve">46.) </s> |
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2939 <s xml:id="echoid-s1648" xml:space="preserve">entrant alors dans cette <lb/>ligne, AG demeure encore égale à la différence de <lb/>AR à AS; </s> |
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2940 <s xml:id="echoid-s1649" xml:space="preserve">& </s> |
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2941 <s xml:id="echoid-s1650" xml:space="preserve">par conſéquent la charge, ou la réſiſ-<lb/>tance d’e l’appui B ne peut jamais être moindre que <lb/>la différence des forces des puiſſances E & </s> |
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2942 <s xml:id="echoid-s1651" xml:space="preserve">F.</s> |
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2943 <s xml:id="echoid-s1652" xml:space="preserve"/> |
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|
2944 </p> |
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2945 </div> |
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2946 <div xml:id="echoid-div187" type="section" level="1" n="126"> |
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2947 <head xml:id="echoid-head126" xml:space="preserve"><emph style="sc">Corollaire</emph> X.</head> |
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2948 <p> |
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2949 <s xml:id="echoid-s1653" xml:space="preserve">D’où l’on voit en général 1°. </s> |
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2950 <s xml:id="echoid-s1654" xml:space="preserve">que dans toutes ſor- |
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2951 <pb o="64" file="0090" n="90" rhead="NOUVELLE"/> |
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2952 <anchor type="note" xlink:label="note-0090-01a" xlink:href="note-0090-01"/> |
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2953 tes de Leviers, de quelque figure, en quelque ſitua-<lb/>tion, & </s> |
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2954 <s xml:id="echoid-s1655" xml:space="preserve">de quelque eſpéce qu’ils ſoient, quelles que <lb/>ſoient auſſi les lignes de direction de puiſſances, ou <lb/>des poids qui y ſont appliquez, la charge de leur apui <lb/> |
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2955 <anchor type="note" xlink:label="note-0090-02a" xlink:href="note-0090-02"/> |
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|
2956 ne peut être jamais plus grande (Corol. </s> |
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2957 <s xml:id="echoid-s1656" xml:space="preserve">7. </s> |
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2958 <s xml:id="echoid-s1657" xml:space="preserve">& </s> |
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2959 <s xml:id="echoid-s1658" xml:space="preserve">8.) <lb/></s> |
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2960 <s xml:id="echoid-s1659" xml:space="preserve">que la ſomme de ces poids, ou de ces puiſſances. </s> |
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2961 <s xml:id="echoid-s1660" xml:space="preserve"><lb/>2°. </s> |
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2962 <s xml:id="echoid-s1661" xml:space="preserve">que dans les leviers de l’eſpéce exprimée par les <lb/>figures 41. </s> |
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2963 <s xml:id="echoid-s1662" xml:space="preserve">& </s> |
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2964 <s xml:id="echoid-s1663" xml:space="preserve">42. </s> |
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2965 <s xml:id="echoid-s1664" xml:space="preserve">elle peut (Cor. </s> |
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2966 <s xml:id="echoid-s1665" xml:space="preserve">6.) </s> |
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2967 <s xml:id="echoid-s1666" xml:space="preserve">diminuer à l’infi-<lb/>ni. </s> |
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2968 <s xml:id="echoid-s1667" xml:space="preserve">3°. </s> |
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2969 <s xml:id="echoid-s1668" xml:space="preserve">Mais que dans toute autre eſpéce (fig. </s> |
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2970 <s xml:id="echoid-s1669" xml:space="preserve">43. </s> |
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2971 <s xml:id="echoid-s1670" xml:space="preserve">44. </s> |
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2972 <s xml:id="echoid-s1671" xml:space="preserve"><lb/>45. </s> |
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|
2973 <s xml:id="echoid-s1672" xml:space="preserve">& </s> |
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|
2974 <s xml:id="echoid-s1673" xml:space="preserve">46.) </s> |
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|
2975 <s xml:id="echoid-s1674" xml:space="preserve">elle ne peut jamais être moindre (Cor. </s> |
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2976 <s xml:id="echoid-s1675" xml:space="preserve">9.) </s> |
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2977 <s xml:id="echoid-s1676" xml:space="preserve"><lb/>que la différence des deux puiſſances, ou des deux <lb/>poids qui y ſont appliquez.</s> |
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2978 <s xml:id="echoid-s1677" xml:space="preserve"/> |
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2979 </p> |
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2980 <div xml:id="echoid-div187" type="float" level="2" n="1"> |
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2981 <note position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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2982 <note position="left" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve">fig. 41. <lb/>42. <lb/>43. <lb/>44. <lb/>45. <lb/>46.</note> |
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2983 </div> |
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2984 <p> |
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2985 <s xml:id="echoid-s1678" xml:space="preserve">Perſonne que je fçache n’avoit encore démontré la charge, <lb/>n’y la direction des points d’apuy des leviers: </s> |
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2986 <s xml:id="echoid-s1679" xml:space="preserve">il ne paroit p@ls <lb/>même qu’il ſoit aiſé de le faire par les principes ordinaires; <lb/></s> |
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2987 <s xml:id="echoid-s1680" xml:space="preserve">ſans cela cependant il y à bien des Problêmes qu’on ne ſçau-<lb/>roit réſoudre. </s> |
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2988 <s xml:id="echoid-s1681" xml:space="preserve">Par exemple, ſans la connoiſſance de la direc-<lb/>tion des apuis, il n’eſt pas poſſible de démontrer qu’elles doi-<lb/>vent être les directions de deux puiſſances, ſoit égales, <lb/>ſoit inégales, pour qu’elles puiſſent faire équilibre ſur <lb/>quelque levier que ce ſoit, dont l’apui eſt une ſphére; </s> |
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2989 <s xml:id="echoid-s1682" xml:space="preserve">n’y <lb/>ſur combien de points de ce levier ainſi apuié, il eſt poſſi-<lb/>ble qu’elles faſſent équilibre en changeant ſeulement <lb/>leurs directions. </s> |
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2990 <s xml:id="echoid-s1683" xml:space="preserve">Il n’eſt pas poſſible non plus ſans la connoiſ-<lb/>ſance & </s> |
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2991 <s xml:id="echoid-s1684" xml:space="preserve">de la direction, & </s> |
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2992 <s xml:id="echoid-s1685" xml:space="preserve">de la charge des apuis des leviers de <lb/>trouver le point d’apui de celui auquel tant de puiſ-<lb/>ſances qu’on voudra, ſoient appliquées, pour toutes <lb/>les directions poſſibles dans leſquelles on les peut ſup-<lb/>poſer; </s> |
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2993 <s xml:id="echoid-s1686" xml:space="preserve">ny deux puiſſances étant données avec leurs <lb/>directions & </s> |
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2994 <s xml:id="echoid-s1687" xml:space="preserve">leurs points d’application à un levier, <lb/>de trouver quelle doit être la direction, & </s> |
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2995 <s xml:id="echoid-s1688" xml:space="preserve">le point <lb/>d’application d’une troiſiéme puiſſance auſſi donnée, <lb/>pour que toutes trois enſemble faſſent équilibre ſur <lb/>quelque point donné, que ce ſoit, de ce levier. </s> |
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2996 <s xml:id="echoid-s1689" xml:space="preserve">Ilfaut |
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2997 <pb o="65" file="0091" n="91" rhead="MECHANIQUE."/> |
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2998 penſer la même choſe de tout autre Problême ſur les leviers <lb/> |
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2999 <anchor type="note" xlink:label="note-0091-01a" xlink:href="note-0091-01"/> |
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3000 dont la ſolution dépend de la détermination de la charge, <lb/>& </s> |
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3001 <s xml:id="echoid-s1690" xml:space="preserve">de la direction de leurs apuis.</s> |
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3002 <s xml:id="echoid-s1691" xml:space="preserve"/> |
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3003 </p> |
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3004 <div xml:id="echoid-div188" type="float" level="2" n="2"> |
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3005 <note position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3006 </div> |
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3007 </div> |
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3008 <div xml:id="echoid-div190" type="section" level="1" n="127"> |
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3009 <head xml:id="echoid-head127" xml:space="preserve"><emph style="sc">Corollaire</emph> XI.</head> |
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3010 <p> |
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3011 <s xml:id="echoid-s1692" xml:space="preserve">Il ſuit encore de cette propoſition que les puiſſan-<lb/>ces E & </s> |
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3012 <s xml:id="echoid-s1693" xml:space="preserve">F, qui demeurent ainſi en équilibre ſur le <lb/>levier MN, ſont en raiſon réciproque des lignes BD <lb/>& </s> |
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3013 <s xml:id="echoid-s1694" xml:space="preserve">BP tirées de ſon point d’apui B perpendiculaire-<lb/>ment ſur leurs lignes de direction, qu’elles quelles <lb/>ſoient: </s> |
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3014 <s xml:id="echoid-s1695" xml:space="preserve">Car puiſque la puiſſance E eſt à la puiſſance <lb/>F, comme AS, ou GR à AR; </s> |
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3015 <s xml:id="echoid-s1696" xml:space="preserve">c’eſt-à-dire, (Lemm. <lb/></s> |
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3016 <s xml:id="echoid-s1697" xml:space="preserve">5.) </s> |
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3017 <s xml:id="echoid-s1698" xml:space="preserve">comme le ſinus de l’angle GAR, ou de OAB ſon <lb/>(fig. </s> |
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3018 <s xml:id="echoid-s1699" xml:space="preserve">41. </s> |
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3019 <s xml:id="echoid-s1700" xml:space="preserve">42. </s> |
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3020 <s xml:id="echoid-s1701" xml:space="preserve">43. </s> |
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3021 <s xml:id="echoid-s1702" xml:space="preserve">& </s> |
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3022 <s xml:id="echoid-s1703" xml:space="preserve">44.) </s> |
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3023 <s xml:id="echoid-s1704" xml:space="preserve">égal, ou (fig. </s> |
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3024 <s xml:id="echoid-s1705" xml:space="preserve">45. </s> |
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3025 <s xml:id="echoid-s1706" xml:space="preserve">& </s> |
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3026 <s xml:id="echoid-s1707" xml:space="preserve">46.) </s> |
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3027 <s xml:id="echoid-s1708" xml:space="preserve"><lb/>ſon complement, eſt au ſinus de l’angle RGA, ou de <lb/>XAB ſon (fig. </s> |
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3028 <s xml:id="echoid-s1709" xml:space="preserve">41. </s> |
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3029 <s xml:id="echoid-s1710" xml:space="preserve">42. </s> |
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3030 <s xml:id="echoid-s1711" xml:space="preserve">43. </s> |
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3031 <s xml:id="echoid-s1712" xml:space="preserve">45. </s> |
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3032 <s xml:id="echoid-s1713" xml:space="preserve">& </s> |
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3033 <s xml:id="echoid-s1714" xml:space="preserve">46.) </s> |
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3034 <s xml:id="echoid-s1715" xml:space="preserve">égal, ou (fig. </s> |
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3035 <s xml:id="echoid-s1716" xml:space="preserve"><lb/>44.) </s> |
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3036 <s xml:id="echoid-s1717" xml:space="preserve">ſon complement; </s> |
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3037 <s xml:id="echoid-s1718" xml:space="preserve">& </s> |
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3038 <s xml:id="echoid-s1719" xml:space="preserve">que d’ailleurs BP eſt le <lb/>ſinus de l’angle OAB, & </s> |
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3039 <s xml:id="echoid-s1720" xml:space="preserve">BD celui de l’angle XAB: </s> |
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3040 <s xml:id="echoid-s1721" xml:space="preserve">Il <lb/>ſuit quela puiſſance E eſt à la puiſſance F, comme BP <lb/>à BD; </s> |
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3041 <s xml:id="echoid-s1722" xml:space="preserve">c’eſt-à-dire, en raiſon réciproque des diſtances <lb/>de leurs lignes de direction, au point d’appui de leur <lb/>levier. </s> |
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3042 <s xml:id="echoid-s1723" xml:space="preserve">Ce qui fait que lors que l’angle OAX eſt <lb/>infiniment aigu, c’eſt-à-dire, lors que les lignes de <lb/>direction de ces deux puiſſances ſont paralleles, & </s> |
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3043 <s xml:id="echoid-s1724" xml:space="preserve"><lb/>que ce levier eſt droit, quelque ſituation qu’il ait, <lb/>ces deux puiſſances ſont toujours entr’elles, tant <lb/>que dure leur équilibre, en raiſon réciproque des <lb/>bras de ce levier pris depuis ſon point d’appui, juſ-<lb/>qu’aux points où elles lui ſont appliquées.</s> |
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3044 <s xml:id="echoid-s1725" xml:space="preserve"/> |
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3045 </p> |
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3046 </div> |
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3047 <div xml:id="echoid-div191" type="section" level="1" n="128"> |
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3048 <head xml:id="echoid-head128" xml:space="preserve"><emph style="sc">Corollaire</emph> XII.</head> |
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3049 <p> |
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3050 <s xml:id="echoid-s1726" xml:space="preserve">L’inverſe de ce dernier Corollaire ſuit encore ma-<lb/>nifeſtement de cette propoſition: </s> |
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3051 <s xml:id="echoid-s1727" xml:space="preserve">ſçavoir que lors |
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3052 <pb o="66" file="0092" n="92" rhead="NOUVELLE"/> |
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3053 que ces deux puiſſances ſont en raiſon réciproque <lb/> |
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3054 <anchor type="note" xlink:label="note-0092-01a" xlink:href="note-0092-01"/> |
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3055 des diſtances de leurs lignes de direction au point <lb/>d’appui de leur levier, de quelque eſpece qu’il ſoit, <lb/>elles demeurent toûjours en équilibre; </s> |
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3056 <s xml:id="echoid-s1728" xml:space="preserve">puis - qu’un tel <lb/>point ne ſe peut trouver ailleurs que dans la diagonale <lb/>AG du parallelogramme RS: </s> |
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3057 <s xml:id="echoid-s1729" xml:space="preserve">ainſi lorſque, leurs lignes <lb/>de direction étant paralleles, & </s> |
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3058 <s xml:id="echoid-s1730" xml:space="preserve">leur levier droit, <lb/>elles ſont en raiſon réciproque des bras de ce levier, <lb/>elles demeurent toujours enéquilibre deſſus.</s> |
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3059 <s xml:id="echoid-s1731" xml:space="preserve"/> |
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3060 </p> |
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3061 <div xml:id="echoid-div191" type="float" level="2" n="1"> |
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3062 <note position="left" xlink:label="note-0092-01" xlink:href="note-0092-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3063 </div> |
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3064 </div> |
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3065 <div xml:id="echoid-div193" type="section" level="1" n="129"> |
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3066 <head xml:id="echoid-head129" xml:space="preserve"><emph style="sc">Corollaire</emph> XIII.</head> |
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3067 <p style="it"> |
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3068 <s xml:id="echoid-s1732" xml:space="preserve">D’où l’on voit en général que lors que deux puiſſances <lb/>font équilibre ſur un levier, de quelque eſpece, & </s> |
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3069 <s xml:id="echoid-s1733" xml:space="preserve">en quelque <lb/>ſituation qu’il ſoit, elles ſont toujours entr’elles en raiſon <lb/>réciproque des diſtances de leurs lignes de direction au point <lb/>d’appui de ce levier. </s> |
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3070 <s xml:id="echoid-s1734" xml:space="preserve">Et réciproquement auſſi, lors qu’elles <lb/>ſont en raiſon réciproque des diſtances de ces mémes lignes au <lb/>point d’appui de ce levier, de quelque eſpece, de quelque figure, <lb/>& </s> |
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3071 <s xml:id="echoid-s1735" xml:space="preserve">en quelque ſituation qu’il ſoit, elles font toujours équilibre <lb/>deſſus.</s> |
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3072 <s xml:id="echoid-s1736" xml:space="preserve"/> |
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3073 </p> |
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3074 <p style="it"> |
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3075 <s xml:id="echoid-s1737" xml:space="preserve">Voila ce qu’on appelle ordinairement le premier principe <lb/>de Méchanique, & </s> |
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3076 <s xml:id="echoid-s1738" xml:space="preserve">ce que perſonne, du moins que je con-<lb/>noiſſe, n’avoit encore démontré de cette maniére, n’y ſi gé-<lb/>néralement. </s> |
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3077 <s xml:id="echoid-s1739" xml:space="preserve">Le voici encore d’une autre façon.</s> |
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3078 <s xml:id="echoid-s1740" xml:space="preserve"/> |
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3079 </p> |
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3080 <figure> |
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3081 <image file="0092-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0092-01"/> |
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3082 </figure> |
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3083 </div> |
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3084 <div xml:id="echoid-div194" type="section" level="1" n="130"> |
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3085 <head xml:id="echoid-head130" xml:space="preserve">LEMME VI.</head> |
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3086 <p style="it"> |
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3087 <s xml:id="echoid-s1741" xml:space="preserve">S I deux puiſſances D & </s> |
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3088 <s xml:id="echoid-s1742" xml:space="preserve">E appliquées au même point A <lb/> |
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3089 <anchor type="note" xlink:label="note-0092-02a" xlink:href="note-0092-02"/> |
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3090 d’un levier AB, dont le point fixe ſoit B, ſont entr’elles <lb/>en raiſon réciproque des ſinus des angles que font leurs lignes <lb/>de direction, qu’elles quelles ſoient, avec ce levier; </s> |
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3091 <s xml:id="echoid-s1743" xml:space="preserve">elles <lb/>demeureront en équilibre.</s> |
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3092 <s xml:id="echoid-s1744" xml:space="preserve"/> |
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3093 </p> |
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3094 <div xml:id="echoid-div194" type="float" level="2" n="1"> |
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3095 <note position="left" xlink:label="note-0092-02" xlink:href="note-0092-02a" xml:space="preserve">fig. 47. <lb/>48. <lb/>49.</note> |
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3096 </div> |
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3097 <pb o="67" file="0093" n="93" rhead="MECHANIQUE."/> |
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3098 </div> |
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3099 <div xml:id="echoid-div196" type="section" level="1" n="131"> |
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3100 <head xml:id="echoid-head131" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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3101 <note position="right" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3102 <p> |
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3103 <s xml:id="echoid-s1745" xml:space="preserve">Le point A ainſi tiré par les puiſſances D & </s> |
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3104 <s xml:id="echoid-s1746" xml:space="preserve">E, <lb/>doit en recevoir une impreſſion ſuivant quelque <lb/>ligne AG qui ſoit la diagonale d’un parallelogramme <lb/>RS fait ſous des parties de leurs lignes de direction <lb/>AS & </s> |
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3105 <s xml:id="echoid-s1747" xml:space="preserve">AR qui ſoient entr’elles, (Lemm. </s> |
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3106 <s xml:id="echoid-s1748" xml:space="preserve">3.) </s> |
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3107 <s xml:id="echoid-s1749" xml:space="preserve">comme <lb/>ces mêmes puiſſances; </s> |
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3108 <s xml:id="echoid-s1750" xml:space="preserve">& </s> |
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3109 <s xml:id="echoid-s1751" xml:space="preserve">la force de cette impreſſion <lb/>doit être à chacune des puiſſances D & </s> |
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3110 <s xml:id="echoid-s1752" xml:space="preserve">E, comme <lb/>(Lem. </s> |
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3111 <s xml:id="echoid-s1753" xml:space="preserve">3. </s> |
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3112 <s xml:id="echoid-s1754" xml:space="preserve">Cor. </s> |
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3113 <s xml:id="echoid-s1755" xml:space="preserve">3.) </s> |
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3114 <s xml:id="echoid-s1756" xml:space="preserve">AG à chacune des lignes AS & </s> |
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3115 <s xml:id="echoid-s1757" xml:space="preserve">AR, <lb/>ou SG qui lui eſt égale; </s> |
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3116 <s xml:id="echoid-s1758" xml:space="preserve">c’eſt-à-dire, (Lem. </s> |
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3117 <s xml:id="echoid-s1759" xml:space="preserve">5.) </s> |
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3118 <s xml:id="echoid-s1760" xml:space="preserve">comme <lb/>le ſinus de l’angle ASG, à chacun des ſinus des angles <lb/>AGS, ou GAR qui lui eſt égal, & </s> |
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3119 <s xml:id="echoid-s1761" xml:space="preserve">GAS; </s> |
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3120 <s xml:id="echoid-s1762" xml:space="preserve">& </s> |
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3121 <s xml:id="echoid-s1763" xml:space="preserve">par conſé-<lb/>quent les puiſſances D & </s> |
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3122 <s xml:id="echoid-s1764" xml:space="preserve">E ſont entr’elles, commeles ſi-<lb/>nus GAR & </s> |
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3123 <s xml:id="echoid-s1765" xml:space="preserve">GAS. </s> |
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3124 <s xml:id="echoid-s1766" xml:space="preserve">Elles ſont auſſi (hyp.) </s> |
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3125 <s xml:id="echoid-s1767" xml:space="preserve">entr’elles, com-<lb/>me les ſinus des angles RAB & </s> |
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3126 <s xml:id="echoid-s1768" xml:space="preserve">SAB; </s> |
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3127 <s xml:id="echoid-s1769" xml:space="preserve">& </s> |
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3128 <s xml:id="echoid-s1770" xml:space="preserve">par conſé-<lb/>quent les ſinus de GAR & </s> |
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3129 <s xml:id="echoid-s1771" xml:space="preserve">de RAB, de même que <lb/>ceux de GAS & </s> |
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3130 <s xml:id="echoid-s1772" xml:space="preserve">SAB ſont égaux entr’eux: </s> |
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3131 <s xml:id="echoid-s1773" xml:space="preserve">donc les an-<lb/>gles GAR & </s> |
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3132 <s xml:id="echoid-s1774" xml:space="preserve">RAB, auſſi-bien que GAS & </s> |
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3133 <s xml:id="echoid-s1775" xml:space="preserve">SAB, ſont <lb/>auſſi égaux, ou, du moins, complemens l’un de l’autre à <lb/>deux droits. </s> |
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3134 <s xml:id="echoid-s1776" xml:space="preserve">D’où il ſuit que AG eſt en ligne droite avec <lb/>AB; </s> |
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3135 <s xml:id="echoid-s1777" xml:space="preserve">& </s> |
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3136 <s xml:id="echoid-s1778" xml:space="preserve">par conſéquent le point fixe B dulevier AB ſou-<lb/>tient, lui ſeul, l’impreſſion toute entiére que le point A <lb/>reçoit du concours d’action des puiſſances D & </s> |
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3137 <s xml:id="echoid-s1779" xml:space="preserve">E; </s> |
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3138 <s xml:id="echoid-s1780" xml:space="preserve">& </s> |
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3139 <s xml:id="echoid-s1781" xml:space="preserve">ce <lb/>point demeurant ainſi en repos, ces puiſſances doivent <lb/>auſſi par conſéquent demeurer en équilibre. </s> |
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3140 <s xml:id="echoid-s1782" xml:space="preserve">Ce qu’il <lb/>faloit démontrer.</s> |
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3141 <s xml:id="echoid-s1783" xml:space="preserve"/> |
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3142 </p> |
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3143 </div> |
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3144 <div xml:id="echoid-div197" type="section" level="1" n="132"> |
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3145 <head xml:id="echoid-head132" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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3146 <p> |
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3147 <s xml:id="echoid-s1784" xml:space="preserve">On voit de-là qu’une même puiſſance peut ainſi <lb/>faire ſucceſſivement équilibre avec pluſieurs autres, <lb/>quelques grandes, ou quelques petites qu’on les ſuppo-<lb/>ſe, pourvu qu’elle ſoit à chacune d’elles en raiſon ré- |
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3148 <pb o="68" file="0094" n="94" rhead="NOUVELLE"/> |
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3149 <anchor type="note" xlink:label="note-0094-01a" xlink:href="note-0094-01"/> |
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3150 ciproque des ſinus des angles que font avec ce levier <lb/>ſa ligne de direction, & </s> |
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3151 <s xml:id="echoid-s1785" xml:space="preserve">celle de la puiſſance avec <lb/>laquelle on la compare; </s> |
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3152 <s xml:id="echoid-s1786" xml:space="preserve">c’eſt-à-dire, pourvû que les <lb/>produits de ces deux puiſſances par les perpendicu-<lb/>laires tirées du point d’appui de ce levier ſur leurs <lb/>lignes de direction, ſoient égaux.</s> |
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3153 <s xml:id="echoid-s1787" xml:space="preserve"/> |
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3154 </p> |
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3155 <div xml:id="echoid-div197" type="float" level="2" n="1"> |
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3156 <note position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3157 </div> |
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3158 </div> |
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3159 <div xml:id="echoid-div199" type="section" level="1" n="133"> |
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3160 <head xml:id="echoid-head133" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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3161 <p> |
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3162 <s xml:id="echoid-s1788" xml:space="preserve">D’où l’on voit que l’action d’une puiſſance ne ſe <lb/>prend pas ſeulement de la grandeur de ſa force; </s> |
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3163 <s xml:id="echoid-s1789" xml:space="preserve">mais <lb/>auſſi de la diſtance de ſa ligne de direction au point <lb/>d’appui du levier ſur lequel elle agit: </s> |
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3164 <s xml:id="echoid-s1790" xml:space="preserve">De ſorte que <lb/>le produit de cette diſtance par la force de cette puiſ-<lb/>ſance, eſt la meſure juſte de ſon action, ou de l’im-<lb/>preſſion qu’elle fait ſur ce levier.</s> |
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3165 <s xml:id="echoid-s1791" xml:space="preserve"/> |
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|
3166 </p> |
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|
3167 </div> |
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3168 <div xml:id="echoid-div200" type="section" level="1" n="134"> |
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3169 <head xml:id="echoid-head134" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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3170 <p> |
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3171 <s xml:id="echoid-s1792" xml:space="preserve">Ainſi en quelque point que ce ſoit d’un levier <lb/>quelle ſoit appliquée, pourvû que la diſtance du <lb/>point d’appui de ce levier à ſa ligne de direction ſoit <lb/>toujours la même, ſon action ſur ce levier ſera auſſi <lb/>toujours la même.</s> |
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3172 <s xml:id="echoid-s1793" xml:space="preserve"/> |
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|
3173 </p> |
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|
3174 </div> |
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3175 <div xml:id="echoid-div201" type="section" level="1" n="135"> |
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3176 <head xml:id="echoid-head135" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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|
3177 <p> |
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3178 <s xml:id="echoid-s1794" xml:space="preserve">Et par la même raiſon ſi différentes puiſſances éga-<lb/>les agiſſoient ſucceſſivement ſuivant la même direc-<lb/>tion, ou ſuivant des directions également diſtantes <lb/>du point d’appui du levier auquel elles ſeroient appli-<lb/>quées; </s> |
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3179 <s xml:id="echoid-s1795" xml:space="preserve">leurs actions ſur ce levier ſeroient auſſi-<lb/>égales.</s> |
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3180 <s xml:id="echoid-s1796" xml:space="preserve"/> |
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|
3181 </p> |
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|
3182 </div> |
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3183 <div xml:id="echoid-div202" type="section" level="1" n="136"> |
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3184 <head xml:id="echoid-head136" xml:space="preserve"><emph style="sc">Corollaire</emph> V.</head> |
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|
3185 <p> |
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3186 <s xml:id="echoid-s1797" xml:space="preserve">Et réciproquement ſi ces puiſſances ainſi appliquées <lb/>à ce levier agiſſent également ſur lui, elles ſeront |
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3187 <pb o="69" file="0095" n="95" rhead="MECHANIQUE."/> |
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3188 auſſi égales entr’elles: </s> |
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3189 <s xml:id="echoid-s1798" xml:space="preserve">puis que les diſtances de leurs <lb/> |
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3190 <anchor type="note" xlink:label="note-0095-01a" xlink:href="note-0095-01"/> |
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3191 lignes de direction au point d’appui du levier auquel <lb/>elles ſont appliquées, ſont (hyp.) </s> |
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3192 <s xml:id="echoid-s1799" xml:space="preserve">égales, & </s> |
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3193 <s xml:id="echoid-s1800" xml:space="preserve">que les <lb/>produits de chacune d’elles par la force de chacune <lb/>de ces puiſſances, ſont (Cor. </s> |
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3194 <s xml:id="echoid-s1801" xml:space="preserve">2.) </s> |
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3195 <s xml:id="echoid-s1802" xml:space="preserve">auſſi égaux.</s> |
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3196 <s xml:id="echoid-s1803" xml:space="preserve"/> |
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3197 </p> |
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3198 <div xml:id="echoid-div202" type="float" level="2" n="1"> |
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3199 <note position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3200 </div> |
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3201 <figure> |
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3202 <image file="0095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0095-01"/> |
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3203 </figure> |
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3204 <pb o="70" file="0096" n="96" rhead="NOUVELLE"/> |
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3205 <figure> |
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3206 <image file="0096-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0096-01"/> |
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3207 </figure> |
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3208 </div> |
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3209 <div xml:id="echoid-div204" type="section" level="1" n="137"> |
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3210 <head xml:id="echoid-head137" xml:space="preserve">AUTRE <lb/>PROPOSITION <lb/>DES LEVIERS, <lb/>Pour tous les cas poſſibles de la fondamentale <lb/>précédente.</head> |
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3211 <p style="it"> |
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3212 <s xml:id="echoid-s1804" xml:space="preserve">SI les puiſſances E & </s> |
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3213 <s xml:id="echoid-s1805" xml:space="preserve">F appliquées à diſſérens points X <lb/> |
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3214 <anchor type="note" xlink:label="note-0096-01a" xlink:href="note-0096-01"/> |
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3215 & </s> |
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3216 <s xml:id="echoid-s1806" xml:space="preserve">O du levier BO, de quelque ſigure, de quelque eſpéce, <lb/>& </s> |
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3217 <s xml:id="echoid-s1807" xml:space="preserve">en quelque ſituation qu’il ſoit; </s> |
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3218 <s xml:id="echoid-s1808" xml:space="preserve">ſont entr’elles en raiſon <lb/>rèciproque des diſtances BD & </s> |
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3219 <s xml:id="echoid-s1809" xml:space="preserve">BP de leurs lignes de direction <lb/>XE & </s> |
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3220 <s xml:id="echoid-s1810" xml:space="preserve">OF, qu’elles quelles ſoient, au point ſixe B de ce <lb/>levier; </s> |
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3221 <s xml:id="echoid-s1811" xml:space="preserve">c’eſt-à-dire, ſi E. </s> |
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3222 <s xml:id="echoid-s1812" xml:space="preserve">F. </s> |
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3223 <s xml:id="echoid-s1813" xml:space="preserve">:</s> |
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3224 <s xml:id="echoid-s1814" xml:space="preserve">: BP. </s> |
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3225 <s xml:id="echoid-s1815" xml:space="preserve">BD. </s> |
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3226 <s xml:id="echoid-s1816" xml:space="preserve">Ces deux <lb/>puiſſances ainſi appliquées demeureront en équilibre ſur ce <lb/>levier.</s> |
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3227 <s xml:id="echoid-s1817" xml:space="preserve"/> |
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3228 </p> |
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3229 <div xml:id="echoid-div204" type="float" level="2" n="1"> |
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3230 <note position="left" xlink:label="note-0096-01" xlink:href="note-0096-01a" xml:space="preserve">ſig 50. <lb/>51. <lb/>52.</note> |
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3231 </div> |
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3232 </div> |
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3233 <div xml:id="echoid-div206" type="section" level="1" n="138"> |
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3234 <head xml:id="echoid-head138" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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3235 <p> |
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3236 <s xml:id="echoid-s1818" xml:space="preserve">Si la puiſſance E étoit appliquée en O ſuivant une <lb/>ligne de direction OQ, dont la diſtance BQ au point <lb/>d’appui B de ce levier, fût égale à BD qui eſt celle <lb/>de ce même point à la ligne de direction XE qu’elle <lb/>a préſentement, cette puiſſance (Lemm. </s> |
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3237 <s xml:id="echoid-s1819" xml:space="preserve">6.) </s> |
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3238 <s xml:id="echoid-s1820" xml:space="preserve">demeu-<lb/>reroit en équilibre avec la puiſſance F. </s> |
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3239 <s xml:id="echoid-s1821" xml:space="preserve">Or l’action <lb/>de cette puiſſance appliquée en X ſuivant XE, eſt <lb/>la même (Lemm. </s> |
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3240 <s xml:id="echoid-s1822" xml:space="preserve">6. </s> |
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3241 <s xml:id="echoid-s1823" xml:space="preserve">Corol. </s> |
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3242 <s xml:id="echoid-s1824" xml:space="preserve">3.) </s> |
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3243 <s xml:id="echoid-s1825" xml:space="preserve">qu’elle ſeroit alors ſur <lb/>ce levier: </s> |
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3244 <s xml:id="echoid-s1826" xml:space="preserve">Donc ces deux puiſſances ainſi appliquées |
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3245 <pb o="71" file="0097" n="97" rhead="MECHANIQUE."/> |
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3246 en X & </s> |
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3247 <s xml:id="echoid-s1827" xml:space="preserve">en O, doivent demeurer en équilibre. </s> |
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3248 <s xml:id="echoid-s1828" xml:space="preserve">Ce qu’il <lb/> |
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3249 <anchor type="note" xlink:label="note-0097-01a" xlink:href="note-0097-01"/> |
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3250 faloit démontrer.</s> |
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3251 <s xml:id="echoid-s1829" xml:space="preserve"/> |
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3252 </p> |
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3253 <div xml:id="echoid-div206" type="float" level="2" n="1"> |
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3254 <note position="right" xlink:label="note-0097-01" xlink:href="note-0097-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3255 </div> |
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3256 </div> |
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3257 <div xml:id="echoid-div208" type="section" level="1" n="139"> |
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3258 <head xml:id="echoid-head139" xml:space="preserve"><emph style="sc">Corollaire</emph>.</head> |
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3259 <p> |
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|
3260 <s xml:id="echoid-s1830" xml:space="preserve">Il ſuit réciproquement de cette propoſition que ſi <lb/>les puiſſances E & </s> |
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3261 <s xml:id="echoid-s1831" xml:space="preserve">F font équilibre ſur quelque levier <lb/>que ce ſoit, elles ſeront entr’elles en raiſon récipro-<lb/>que des diſtances de ſon point d’appui à leurs lignes de <lb/>direction: </s> |
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3262 <s xml:id="echoid-s1832" xml:space="preserve">puis que ſi quelque nouvelle puiſſance miſe <lb/>en la place, par exemple, de la puiſſance E, & </s> |
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3263 <s xml:id="echoid-s1833" xml:space="preserve">appli-<lb/>quée comme elle au levier BO, étoit en telle raiſon à la <lb/>puiſſance F, elle feroit équilibre avec elle. </s> |
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3264 <s xml:id="echoid-s1834" xml:space="preserve">Orune telle <lb/>puiſſance (Lemm. </s> |
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3265 <s xml:id="echoid-s1835" xml:space="preserve">6. </s> |
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3266 <s xml:id="echoid-s1836" xml:space="preserve">Cor. </s> |
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3267 <s xml:id="echoid-s1837" xml:space="preserve">5.) </s> |
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3268 <s xml:id="echoid-s1838" xml:space="preserve">ſeroit égale à la puiſſance <lb/>E: </s> |
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3269 <s xml:id="echoid-s1839" xml:space="preserve">Donc la puiſſance E ſeroit auſſi alors à la puiſſance <lb/>F en raiſon réciproque des diſtances de leurs lignes <lb/>de direction au point d’appui du levier ſur lequel <lb/>elles feroient équilibre.</s> |
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3270 <s xml:id="echoid-s1840" xml:space="preserve"/> |
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3271 </p> |
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3272 <p style="it"> |
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3273 <s xml:id="echoid-s1841" xml:space="preserve">On ne met point ici tous les Corollaires qu’on pourroit tirer <lb/>tant de cette propoſition, que de la précédente, par raport à la <lb/>Balance, à la Romaine, au Tour, aux Rouës à dent, aux Ci-<lb/>ſeaux, aux Tenailles, aux Etocs, &</s> |
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3274 <s xml:id="echoid-s1842" xml:space="preserve">c. </s> |
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3275 <s xml:id="echoid-s1843" xml:space="preserve">ce ſera lors qu’on en <lb/>fera l’application à la phyſique; </s> |
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3276 <s xml:id="echoid-s1844" xml:space="preserve">D’ailleurs tres-peu d’atten-<lb/>tion ſuſſit préſentement pour en déduire beaucoup plus que la <lb/>breveté, qu’on s’eſt propoſée dans ce projet, ne permet de ſaire.</s> |
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3277 <s xml:id="echoid-s1845" xml:space="preserve"/> |
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3278 </p> |
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3279 <figure> |
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3280 <image file="0097-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0097-01"/> |
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3281 </figure> |
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3282 </div> |
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3283 <div xml:id="echoid-div209" type="section" level="1" n="140"> |
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3284 <head xml:id="echoid-head140" xml:space="preserve">PROBLEME.</head> |
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3285 <p style="it"> |
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3286 <s xml:id="echoid-s1846" xml:space="preserve">TANT de puiſſances qu’on voudra appliquées à un <lb/> |
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3287 <anchor type="note" xlink:label="note-0097-02a" xlink:href="note-0097-02"/> |
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3288 même levier; </s> |
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3289 <s xml:id="echoid-s1847" xml:space="preserve">par exemple, les cinq que voici M, N, <lb/>O, P, Q, étant données avec leurs lignes de direction AM, <lb/>CN, EO, HP, & </s> |
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3290 <s xml:id="echoid-s1848" xml:space="preserve">GQ, quelles quelles ſoient; </s> |
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3291 <s xml:id="echoid-s1849" xml:space="preserve">trouver le <lb/>point de ce levier ſur lequel elles peuvent ainſi appliquées de-<lb/>meurer toutes enſemble en équilibre.</s> |
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3292 <s xml:id="echoid-s1850" xml:space="preserve"/> |
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3293 </p> |
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3294 <div xml:id="echoid-div209" type="float" level="2" n="1"> |
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3295 <note position="right" xlink:label="note-0097-02" xlink:href="note-0097-02a" xml:space="preserve">ſig. 53. <lb/>54. <lb/>55. <lb/>56. <lb/>57. <lb/>58. <lb/>59.</note> |
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3296 </div> |
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3297 <pb o="72" file="0098" n="98" rhead="NOUVELLE"/> |
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3298 </div> |
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3299 <div xml:id="echoid-div211" type="section" level="1" n="141"> |
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3300 <head xml:id="echoid-head141" xml:space="preserve"><emph style="sc">Solution</emph>.</head> |
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3301 <note position="left" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3302 <p> |
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3303 <s xml:id="echoid-s1851" xml:space="preserve">Premiérement ſi ces lignes de direction ſont toutes <lb/> |
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3304 <anchor type="note" xlink:label="note-0098-02a" xlink:href="note-0098-02"/> |
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3305 paralleles entr’elles, de quelque côté que ces puiſ-<lb/>ſances tirent, il faut prendre ſur le levier AH pro-<lb/>longé s’il en eſt beſoin, H λ à G λ, commela puiſſance <lb/>Q eſt à la puiſſance P, & </s> |
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3306 <s xml:id="echoid-s1852" xml:space="preserve">I’on aura le point λ ſur le-<lb/>quel ces deux puiſſances ainſi appliquées feroient <lb/>é<unsure/>quilibre, (Corol. </s> |
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3307 <s xml:id="echoid-s1853" xml:space="preserve">12.) </s> |
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3308 <s xml:id="echoid-s1854" xml:space="preserve">ſi elles étoient ſeules. </s> |
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3309 <s xml:id="echoid-s1855" xml:space="preserve">La <lb/>direction de ce point (Cor. </s> |
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3310 <s xml:id="echoid-s1856" xml:space="preserve">5.) </s> |
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3311 <s xml:id="echoid-s1857" xml:space="preserve">étant vers Q paralle-<lb/>lement à HP, c’eſt-à-dire, (hyp.) </s> |
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3312 <s xml:id="echoid-s1858" xml:space="preserve">à EO; </s> |
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3313 <s xml:id="echoid-s1859" xml:space="preserve">& </s> |
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3314 <s xml:id="echoid-s1860" xml:space="preserve">ſa charge <lb/>étant (Cor. </s> |
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3315 <s xml:id="echoid-s1861" xml:space="preserve">7. </s> |
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3316 <s xml:id="echoid-s1862" xml:space="preserve">ſig. </s> |
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3317 <s xml:id="echoid-s1863" xml:space="preserve">53.) </s> |
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3318 <s xml:id="echoid-s1864" xml:space="preserve">égale à la ſomme des forces de <lb/>ces deux puiſſances, ou (Cor. </s> |
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3319 <s xml:id="echoid-s1865" xml:space="preserve">9. </s> |
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3320 <s xml:id="echoid-s1866" xml:space="preserve">ſig. </s> |
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3321 <s xml:id="echoid-s1867" xml:space="preserve">54. </s> |
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3322 <s xml:id="echoid-s1868" xml:space="preserve">& </s> |
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3323 <s xml:id="echoid-s1869" xml:space="preserve">55.) </s> |
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3324 <s xml:id="echoid-s1870" xml:space="preserve">à leur <lb/>diffèrence: </s> |
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3325 <s xml:id="echoid-s1871" xml:space="preserve">au lieu d’elles on en peut ſuppoſer une <lb/>nouvelle de cette valeur appliquée en ce point λ, & </s> |
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3326 <s xml:id="echoid-s1872" xml:space="preserve"><lb/>dirigée du côté de la puiſſance Q parallelement à EO. <lb/></s> |
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3327 <s xml:id="echoid-s1873" xml:space="preserve">Il eſt clair que cette nouvelle puiſſance faiſant la <lb/>même impreſſion ſur ce levier que les puiſſances P & </s> |
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3328 <s xml:id="echoid-s1874" xml:space="preserve"><lb/>Q y en faiſoient auparavant, ſon centre d’équilibre <lb/>avec la puiſſance O, ſera le point lequel les trois <lb/>puiſſances O, P, & </s> |
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3329 <s xml:id="echoid-s1875" xml:space="preserve">Q feroient équilibre, ſi elles <lb/>étoient ſeules, & </s> |
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3330 <s xml:id="echoid-s1876" xml:space="preserve">appliquées comme elles ſont: </s> |
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3331 <s xml:id="echoid-s1877" xml:space="preserve"><lb/>l’ayant donc trouvé comme l’on vient de faire le point <lb/>λ; </s> |
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3332 <s xml:id="echoid-s1878" xml:space="preserve">c’eſt-à-dire, ayant fait λF à FE, comme la puiſ-<lb/>ſance O, à la charge qui réſulte au point λ du concours <lb/>d’action des puiſſances P & </s> |
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3333 <s xml:id="echoid-s1879" xml:space="preserve">Q; </s> |
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3334 <s xml:id="echoid-s1880" xml:space="preserve">on aura le point F <lb/>dont la direction ſera encore (Cor. </s> |
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3335 <s xml:id="echoid-s1881" xml:space="preserve">5.) </s> |
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3336 <s xml:id="echoid-s1882" xml:space="preserve">parallele à celle <lb/>de ces puiſſances, & </s> |
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3337 <s xml:id="echoid-s1883" xml:space="preserve">du côté de Q; </s> |
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3338 <s xml:id="echoid-s1884" xml:space="preserve">& </s> |
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3339 <s xml:id="echoid-s1885" xml:space="preserve">la charge en <lb/>ſera égale (Cor. </s> |
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3340 <s xml:id="echoid-s1886" xml:space="preserve">7. </s> |
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3341 <s xml:id="echoid-s1887" xml:space="preserve">ſig. </s> |
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3342 <s xml:id="echoid-s1888" xml:space="preserve">53.) </s> |
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3343 <s xml:id="echoid-s1889" xml:space="preserve">à la ſomme de ces trois-ci <lb/>O, P, & </s> |
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3344 <s xml:id="echoid-s1890" xml:space="preserve">Q; </s> |
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3345 <s xml:id="echoid-s1891" xml:space="preserve">ou (ſig. </s> |
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3346 <s xml:id="echoid-s1892" xml:space="preserve">54.) </s> |
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3347 <s xml:id="echoid-s1893" xml:space="preserve">à la ſomme de la puiſſance <lb/>O, & </s> |
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3348 <s xml:id="echoid-s1894" xml:space="preserve">de la diſſérence qui eſt entre les puiſſances P & </s> |
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3349 <s xml:id="echoid-s1895" xml:space="preserve"><lb/>Q; </s> |
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3350 <s xml:id="echoid-s1896" xml:space="preserve">ou enſin (Cor. </s> |
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3351 <s xml:id="echoid-s1897" xml:space="preserve">9. </s> |
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3352 <s xml:id="echoid-s1898" xml:space="preserve">ſig. </s> |
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3353 <s xml:id="echoid-s1899" xml:space="preserve">55.) </s> |
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3354 <s xml:id="echoid-s1900" xml:space="preserve">à la diſſérence qui eſt <lb/>entre la puiſſance O, & </s> |
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3355 <s xml:id="echoid-s1901" xml:space="preserve">la diſſèrence des puiſſances <lb/>P & </s> |
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3356 <s xml:id="echoid-s1902" xml:space="preserve">Q: </s> |
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3357 <s xml:id="echoid-s1903" xml:space="preserve">ainſi au lieu de la puiſſance O, & </s> |
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3358 <s xml:id="echoid-s1904" xml:space="preserve">de celle que <lb/>nous avons ſuppoſée en λ, ſi nous en concevons en- |
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3359 <pb o="73" file="0099" n="99" rhead="MECHANIQUE."/> |
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3360 core un autre de la valeur de la charge du point F, <lb/> |
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3361 <anchor type="note" xlink:label="note-0099-01a" xlink:href="note-0099-01"/> |
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3362 appliquée en ce point, & </s> |
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3363 <s xml:id="echoid-s1905" xml:space="preserve">dirigée du côté de la puiſ-<lb/>ſance Q parallelement à NC; </s> |
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3364 <s xml:id="echoid-s1906" xml:space="preserve">nous trouverons ſon <lb/>centre d’equilibre D avec la puiſſance N, de même <lb/>que nous avons déja trouvé les points F, & </s> |
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3365 <s xml:id="echoid-s1907" xml:space="preserve">λ. </s> |
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3366 <s xml:id="echoid-s1908" xml:space="preserve">Enſin <lb/>ôtant encore la puiſſance N avec celle qui étoit appli-<lb/>quée en F, & </s> |
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3367 <s xml:id="echoid-s1909" xml:space="preserve">mettant à leur défaut au point D une <lb/>autre puiſſance égale à ſa charge, & </s> |
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3368 <s xml:id="echoid-s1910" xml:space="preserve">dirigée du côté <lb/>de la puiſſance O parallelement à AM; </s> |
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3369 <s xml:id="echoid-s1911" xml:space="preserve">on trouvera <lb/>encore le centre de direction B qui lui eſt commun <lb/>avec la puiſſance M, de même que l’on vient de faire <lb/>les points λ, F, & </s> |
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3370 <s xml:id="echoid-s1912" xml:space="preserve">D; </s> |
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3371 <s xml:id="echoid-s1913" xml:space="preserve">& </s> |
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3372 <s xml:id="echoid-s1914" xml:space="preserve">ce point B ſera (Cor. </s> |
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3373 <s xml:id="echoid-s1915" xml:space="preserve">12.) <lb/></s> |
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3374 <s xml:id="echoid-s1916" xml:space="preserve">celui ſur lequel les cinq puiſſances M, N, O, P, & </s> |
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3375 <s xml:id="echoid-s1917" xml:space="preserve">Q, <lb/>ainſi dirigées demeureront en équilibre. </s> |
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3376 <s xml:id="echoid-s1918" xml:space="preserve">Ce qu’il <lb/>faloit premiérement trouver.</s> |
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3377 <s xml:id="echoid-s1919" xml:space="preserve"/> |
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3378 </p> |
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3379 <div xml:id="echoid-div211" type="float" level="2" n="1"> |
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3380 <note position="left" xlink:label="note-0098-02" xlink:href="note-0098-02a" xml:space="preserve">ſig. 53. <lb/>54. <lb/>55.</note> |
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3381 <note position="right" xlink:label="note-0099-01" xlink:href="note-0099-01a" xml:space="preserve">DES <lb/>LEVIERS</note> |
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3382 </div> |
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3383 </div> |
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3384 <div xml:id="echoid-div213" type="section" level="1" n="142"> |
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3385 <head xml:id="echoid-head142" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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3386 <p> |
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3387 <s xml:id="echoid-s1920" xml:space="preserve">On voit aſſez que ſi ce levier AH, (ſig. </s> |
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3388 <s xml:id="echoid-s1921" xml:space="preserve">55.)</s> |
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3389 <s xml:id="echoid-s1922" xml:space="preserve">ſe fû@t <lb/>terminé en H, ce Problême en ce cas auroit été im-<lb/>poſſible.</s> |
|
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3390 <s xml:id="echoid-s1923" xml:space="preserve"/> |
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|
3391 </p> |
|
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|
3392 </div> |
|
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|
3393 <div xml:id="echoid-div214" type="section" level="1" n="143"> |
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3394 <head xml:id="echoid-head143" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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3395 <p> |
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3396 <s xml:id="echoid-s1924" xml:space="preserve">Ce que nous venons de démontrer des leviers <lb/> |
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3397 <anchor type="note" xlink:label="note-0099-02a" xlink:href="note-0099-02"/> |
|
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3398 droits, ſe peut fort aiſément appliquer à toutes ſor-<lb/>tes de leviers courbes; </s> |
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3399 <s xml:id="echoid-s1925" xml:space="preserve">par exemple, à celui de la fig. <lb/></s> |
|
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3400 <s xml:id="echoid-s1926" xml:space="preserve">56. </s> |
|
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|
3401 <s xml:id="echoid-s1927" xml:space="preserve">en faiſant ſeulement à diſcretion quelque ligne <lb/>droite ah, qui rencontre (il n’importe comment) <lb/>toutes les lignes de direction des puiſſances M, N, <lb/>O, P, & </s> |
|
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3402 <s xml:id="echoid-s1928" xml:space="preserve">Q, en a, c, e, h, & </s> |
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3403 <s xml:id="echoid-s1929" xml:space="preserve">g: </s> |
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3404 <s xml:id="echoid-s1930" xml:space="preserve">car la regardant com-<lb/>me un levier auquel ces puiſſances ſont appliquées <lb/>en ces mêmes points, on en trouvera, comme l’on <lb/>vient de faire, le point d’appui b, avec ſa ligne de <lb/>direction bB, qui rencontrant le levier AH, donnera <lb/>le point B qui ſera ſon point d’appui: </s> |
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3405 <s xml:id="echoid-s1931" xml:space="preserve">Puis que les <lb/>rapports de diſtances de ce point aux lignes de di- |
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3406 <pb o="74" file="0100" n="100" rhead="NOUVELLE"/> |
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3407 rection de ces puiſſ nces, qui ſont (hyp & </s> |
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3408 <s xml:id="echoid-s1932" xml:space="preserve">Cor. </s> |
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3409 <s xml:id="echoid-s1933" xml:space="preserve">5. <lb/></s> |
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3410 <s xml:id="echoid-s1934" xml:space="preserve"> |
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3411 <anchor type="note" xlink:label="note-0100-01a" xlink:href="note-0100-01"/> |
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3412 paralleles à b B, ſont les mêmes que ceux des diſtances <lb/>du point b à ces mêmes lignes.</s> |
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3413 <s xml:id="echoid-s1935" xml:space="preserve"/> |
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3414 </p> |
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3415 <div xml:id="echoid-div214" type="float" level="2" n="1"> |
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3416 <note position="right" xlink:label="note-0099-02" xlink:href="note-0099-02a" xml:space="preserve">ſig. 56.</note> |
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3417 <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3418 </div> |
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3419 <p> |
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3420 <s xml:id="echoid-s1936" xml:space="preserve">Secondement, s’il ſe trouve quelques -unes des <lb/> |
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3421 <anchor type="note" xlink:label="note-0100-02a" xlink:href="note-0100-02"/> |
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3422 lignes de direction des puiſſances données, qui ne ſoient <lb/>point paralleles entr’elles, quelles que ſoient les autres, <lb/>& </s> |
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3423 <s xml:id="echoid-s1937" xml:space="preserve">de quelque côté que ces puiſſances tirent encore; <lb/></s> |
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3424 <s xml:id="echoid-s1938" xml:space="preserve">Voici comment on pourra trouver le point d’appui <lb/>du levier AH auquel elles ſont appliquées. </s> |
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3425 <s xml:id="echoid-s1939" xml:space="preserve">Soient, ſi <lb/>l’on veut, les directions HP & </s> |
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3426 <s xml:id="echoid-s1940" xml:space="preserve">GQ des puiſſan-<lb/>ces P & </s> |
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3427 <s xml:id="echoid-s1941" xml:space="preserve">Q, non paralleles, & </s> |
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3428 <s xml:id="echoid-s1942" xml:space="preserve">qu’elles ſe rencon-<lb/>trent en V: </s> |
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3429 <s xml:id="echoid-s1943" xml:space="preserve">faite VR à VS, comme la puiſſance P à <lb/>la puiſſance Q; </s> |
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3430 <s xml:id="echoid-s1944" xml:space="preserve">achevez le parallelogramme RS, <lb/>& </s> |
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3431 <s xml:id="echoid-s1945" xml:space="preserve">faite la diagonale VK qui rencontre en λ le <lb/>levier AH prolongé juſqu’où il en ſera beſoin: </s> |
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3432 <s xml:id="echoid-s1946" xml:space="preserve">ce <lb/>point ſera (prop. </s> |
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3433 <s xml:id="echoid-s1947" xml:space="preserve">ſond.) </s> |
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3434 <s xml:id="echoid-s1948" xml:space="preserve">celui ſur lequel ces deux puiſ-<lb/>ſances ainſi appliquées feroient équilibre, ſi elles <lb/>étoient ſeules; </s> |
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3435 <s xml:id="echoid-s1949" xml:space="preserve">& </s> |
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3436 <s xml:id="echoid-s1950" xml:space="preserve">ſa charge, dont la direction eſt <lb/>de V vers K ſuivant VK, (Cor. </s> |
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3437 <s xml:id="echoid-s1951" xml:space="preserve">4.) </s> |
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3438 <s xml:id="echoid-s1952" xml:space="preserve">ſera à chacune <lb/>des puiſſances P, & </s> |
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3439 <s xml:id="echoid-s1953" xml:space="preserve">Q, comme VK à chacune des <lb/>lignes VR & </s> |
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3440 <s xml:id="echoid-s1954" xml:space="preserve">VS qui les répréſentent: </s> |
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3441 <s xml:id="echoid-s1955" xml:space="preserve">De ſorte que <lb/>ſi au lieu de ces deux puiſſances, on en appliquoit <lb/>quelqu’autre au point λ de ce levier, ſuivant cette <lb/>même direction VK, & </s> |
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3442 <s xml:id="echoid-s1956" xml:space="preserve">qui eût ce même raport à <lb/>chacune d’elles, c’eſt-à-dire, qui ſût égale à la <lb/>charge de ce point; </s> |
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3443 <s xml:id="echoid-s1957" xml:space="preserve">elle feroit ſeule ainſi appliquée <lb/>la même impreſſion ſur ce levier que font préſente-<lb/>ment ces deux enſemble; </s> |
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3444 <s xml:id="echoid-s1958" xml:space="preserve">& </s> |
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3445 <s xml:id="echoid-s1959" xml:space="preserve">par conſéquent ſon <lb/>centre d’équilibre avec la puiſſance O, ſeroit celui <lb/>des trois puiſſances, O, P, & </s> |
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3446 <s xml:id="echoid-s1960" xml:space="preserve">Q; </s> |
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3447 <s xml:id="echoid-s1961" xml:space="preserve">c’eſt-à-dire, le <lb/>point ſur lequel elles feroient equilibre, ſi elles <lb/>étoient ſeules, & </s> |
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3448 <s xml:id="echoid-s1962" xml:space="preserve">ainſi appliquées. </s> |
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3449 <s xml:id="echoid-s1963" xml:space="preserve">S’il arrive que <lb/>VK & </s> |
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3450 <s xml:id="echoid-s1964" xml:space="preserve">OE ſoient paralleles, on trouvera ce point <lb/>comme l’on a fait dans l’hypothêſe des directions |
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3451 <pb o="75" file="0101" n="101" rhead="MECHANIQUE."/> |
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3452 paralleles; </s> |
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3453 <s xml:id="echoid-s1965" xml:space="preserve">mais ſi elles ſe rencontrent en quelque <lb/> |
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3454 <anchor type="note" xlink:label="note-0101-01a" xlink:href="note-0101-01"/> |
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3455 point T, il faut, comme l’on vient de faire, prendre <lb/>TY à TZ, comme la puiſſance ſuppoſée en λ, eſt à <lb/>la puiſſance O; </s> |
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3456 <s xml:id="echoid-s1966" xml:space="preserve">& </s> |
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3457 <s xml:id="echoid-s1967" xml:space="preserve">ayant achevé le parallelogramme <lb/>YZ, faite ſa diagonale TX qui rencontre en F le <lb/>levier AH: </s> |
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3458 <s xml:id="echoid-s1968" xml:space="preserve">ce point ſera encore (Prop. </s> |
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3459 <s xml:id="echoid-s1969" xml:space="preserve">fond.) </s> |
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3460 <s xml:id="echoid-s1970" xml:space="preserve">celui <lb/>ſur lequel ces deux puiſſances, ou bien ces trois-ici O, <lb/>P, & </s> |
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3461 <s xml:id="echoid-s1971" xml:space="preserve">Q, feroient équilibre, ſi elles étoient ſeules, & </s> |
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3462 <s xml:id="echoid-s1972" xml:space="preserve"><lb/>appliquees ſuivant les conditions de ce Problême; </s> |
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3463 <s xml:id="echoid-s1973" xml:space="preserve">& </s> |
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3464 <s xml:id="echoid-s1974" xml:space="preserve"><lb/>ſa charge, dont la direction eſt de T vers X, (Cor. </s> |
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3465 <s xml:id="echoid-s1975" xml:space="preserve">4.) <lb/></s> |
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3466 <s xml:id="echoid-s1976" xml:space="preserve">eſt en ce cas à la puiſſance O, comme TX à TZ: </s> |
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3467 <s xml:id="echoid-s1977" xml:space="preserve">ôtant <lb/>donc encore cette puiſſance avec celle que nous <lb/>avions ſuppoſée en λ au lieu des puiſſances P & </s> |
|
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|
3468 <s xml:id="echoid-s1978" xml:space="preserve">Q; </s> |
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|
3469 <s xml:id="echoid-s1979" xml:space="preserve"><lb/>& </s> |
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|
3470 <s xml:id="echoid-s1980" xml:space="preserve">en mettant une autre en F, dirigée de T vers X <lb/>ſuivant TX, & </s> |
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3471 <s xml:id="echoid-s1981" xml:space="preserve">qui ſoit à la puiſſance O, comme <lb/>TX à TZ; </s> |
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3472 <s xml:id="echoid-s1982" xml:space="preserve">elle fera encore ſeule ainſi appliquée la <lb/>même impreſſion ſur le leuier AH, que lui faiſoient <lb/>auparavant les trois puiſſances O, P, & </s> |
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3473 <s xml:id="echoid-s1983" xml:space="preserve">Q; </s> |
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3474 <s xml:id="echoid-s1984" xml:space="preserve">& </s> |
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3475 <s xml:id="echoid-s1985" xml:space="preserve">par <lb/>conſéquent ſon centre d’équilibre avec la puiſſance <lb/>N, ſera celui des quatres puiſſances N, O, P, & </s> |
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3476 <s xml:id="echoid-s1986" xml:space="preserve">Q. </s> |
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3477 <s xml:id="echoid-s1987" xml:space="preserve"><lb/>S’il arrive que TX & </s> |
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3478 <s xml:id="echoid-s1988" xml:space="preserve">NC ſoient paralleles, on trou-<lb/>vera encore ce point comme dans la première partie <lb/>de cette ſolution; </s> |
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3479 <s xml:id="echoid-s1989" xml:space="preserve">mais ſi elles ſe rencontrent en quel-<lb/>que point β, il faut encore prendre βγ à βε, comme <lb/>la puiſſance ſuppoſée en F, eſt à la puiſſance N; </s> |
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3480 <s xml:id="echoid-s1990" xml:space="preserve">& </s> |
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3481 <s xml:id="echoid-s1991" xml:space="preserve"><lb/>ayant achevé le parallelogramme εγ, il faut prolon-<lb/>ger ſa diagonale βδ juſqu’à ce qu’elle rencontre le <lb/>levier AH en D, & </s> |
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3482 <s xml:id="echoid-s1992" xml:space="preserve">ce point ſera (prop. </s> |
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3483 <s xml:id="echoid-s1993" xml:space="preserve">fond.) </s> |
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3484 <s xml:id="echoid-s1994" xml:space="preserve">celui <lb/>ſur lequel ces deux puiſſances, ou bien ces quatre-ci <lb/>N, O, P, & </s> |
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3485 <s xml:id="echoid-s1995" xml:space="preserve">Q, feroient équilibre, ſi elles étoient <lb/>ſeules, & </s> |
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3486 <s xml:id="echoid-s1996" xml:space="preserve">appliquées ſuivant les directions données <lb/>de ce problême. </s> |
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3487 <s xml:id="echoid-s1997" xml:space="preserve">La direction de ce point ſera encore <lb/>de β vers δ ſuivant βδ, (Cor. </s> |
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3488 <s xml:id="echoid-s1998" xml:space="preserve">4.) </s> |
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3489 <s xml:id="echoid-s1999" xml:space="preserve">& </s> |
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3490 <s xml:id="echoid-s2000" xml:space="preserve">ſa charge ſera <lb/>auſſi à la puiſſance N, comme βδ à βε: </s> |
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3491 <s xml:id="echoid-s2001" xml:space="preserve">ainſi au lieu <lb/>de la puiſſance N, & </s> |
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3492 <s xml:id="echoid-s2002" xml:space="preserve">de celle que nous venons de |
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3493 <pb o="76" file="0102" n="102" rhead="NOUVELLE"/> |
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3494 ſuppoſer en F, ſi l’on en ſuppoſe encore quelqu’autre <lb/> |
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3495 <anchor type="note" xlink:label="note-0102-01a" xlink:href="note-0102-01"/> |
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3496 en D, dirigée de β vers δ ſuivant βδ, & </s> |
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3497 <s xml:id="echoid-s2003" xml:space="preserve">qui ſoit à la <lb/>puiſſance N, comme βδ à βε; </s> |
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3498 <s xml:id="echoid-s2004" xml:space="preserve">cette nouvelle puiſ-<lb/>ſance ainſi appliquée au levier AH, fera encore <lb/>feule ſur lui la même impreſſion que faiſoient aupa-<lb/>ravant les quatre puiſſances N, O, P, & </s> |
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3499 <s xml:id="echoid-s2005" xml:space="preserve">Q; </s> |
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3500 <s xml:id="echoid-s2006" xml:space="preserve">& </s> |
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3501 <s xml:id="echoid-s2007" xml:space="preserve">par <lb/>conſéquent ſon centre d’équilibre avec la puiſſance <lb/>M, ſera celui des cinq puiſſances données dans ce <lb/>problême. </s> |
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3502 <s xml:id="echoid-s2008" xml:space="preserve">S’il arrive que βδ ſoit parallele à AM, on <lb/>trouvera encore ce point comme l’'on a fait dans le cas <lb/>des directions paralleles; </s> |
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3503 <s xml:id="echoid-s2009" xml:space="preserve">mais ſi elles ſe rencontrent <lb/>en quelque point L, il faut encore prendre L θ à Lω, <lb/>comme la puiſſance qu’on ſuppoſe en D, eſt à la puiſ-<lb/>ſance M; </s> |
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3504 <s xml:id="echoid-s2010" xml:space="preserve">& </s> |
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3505 <s xml:id="echoid-s2011" xml:space="preserve">ayant achevé le parallelogramme ωθ, il <lb/>faut tirer la diagonale LI, qui rencontrant le levier <lb/>AH, donnera le point B pour centre d’equilibre <lb/>(Prop. </s> |
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3506 <s xml:id="echoid-s2012" xml:space="preserve">fond.) </s> |
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3507 <s xml:id="echoid-s2013" xml:space="preserve">de ces deux puiſſances; </s> |
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3508 <s xml:id="echoid-s2014" xml:space="preserve">c’eſt-à-dire en <lb/>remettant à la place de celle qu’on ſuppoſe en D, les <lb/>quatre N, O, P, & </s> |
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3509 <s xml:id="echoid-s2015" xml:space="preserve">Q, qu’elle ſuppléoit; </s> |
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3510 <s xml:id="echoid-s2016" xml:space="preserve">ſur lequel <lb/>les cinq puiſſances données, & </s> |
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3511 <s xml:id="echoid-s2017" xml:space="preserve">appliquées ſuivant <lb/>les conditions de ce Problême, feront équilibre. </s> |
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3512 <s xml:id="echoid-s2018" xml:space="preserve">Ce <lb/>qu’il faloit encore trouver.</s> |
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3513 <s xml:id="echoid-s2019" xml:space="preserve"/> |
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|
3514 </p> |
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3515 <div xml:id="echoid-div215" type="float" level="2" n="2"> |
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3516 <note position="left" xlink:label="note-0100-02" xlink:href="note-0100-02a" xml:space="preserve">ſig 57. <lb/>58. <lb/>59.</note> |
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3517 <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3518 <note position="left" xlink:label="note-0102-01" xlink:href="note-0102-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3519 </div> |
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3520 <p style="it"> |
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3521 <s xml:id="echoid-s2020" xml:space="preserve">Ce Problème, tout facile qu’il paroit à réſoudre par les <lb/>principes q@’on ſuit ici, eſt peut - é<unsure/>tre un des plus diſſiciles <lb/>qu’on puiſſe propoſer à ceux qui ſont dans les principes ordi-<lb/>naires; </s> |
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3522 <s xml:id="echoid-s2021" xml:space="preserve">non ſeulement quant à la maniére de déterminer les <lb/>points d’appui des levi<unsure/>ers pour toutes les directions poſſibles <lb/>des puiſſances, ou des poids qui y ſont appliquez; </s> |
|
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3523 <s xml:id="echoid-s2022" xml:space="preserve">mais auſſi <lb/>quant à celle de reconnoitre leur direction, & </s> |
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3524 <s xml:id="echoid-s2023" xml:space="preserve">leur charge, <lb/>de quelque eſpece, & </s> |
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3525 <s xml:id="echoid-s2024" xml:space="preserve">dans quelque ſituation qu’ils ſoient: <lb/></s> |
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3526 <s xml:id="echoid-s2025" xml:space="preserve">C’eſt peut ètre auſſi ce qui a fait que les Mécbaniciens, qui <lb/>ont entrepris de démontrer le cas de la figu<unsure/>re 53. </s> |
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3527 <s xml:id="echoid-s2026" xml:space="preserve">n’ont oſé tou-<lb/>ch@r aux autres.</s> |
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|
3528 <s xml:id="echoid-s2027" xml:space="preserve"/> |
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|
3529 </p> |
|
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3530 <pb o="77" file="0103" n="103" rhead="MECHANIQUE."/> |
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|
3531 <p style="it"> |
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3532 <s xml:id="echoid-s2028" xml:space="preserve">Outre les Poulies, les Surfaces, & </s> |
|
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3533 <s xml:id="echoid-s2029" xml:space="preserve">les Leviers, on met <lb/> |
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|
3534 <anchor type="note" xlink:label="note-0103-01a" xlink:href="note-0103-01"/> |
|
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|
3535 encore la Vis au rang des machines qu’on regarde comme <lb/>capitales entre celles qui ſont propres à faciliter les mouve-<lb/>mens; </s> |
|
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3536 <s xml:id="echoid-s2030" xml:space="preserve">mais parce que cette dernière ſe rapporte toute au plan <lb/>incliné & </s> |
|
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3537 <s xml:id="echoid-s2031" xml:space="preserve">au levier, dont on va voir qu’elle eſt compoſée, <lb/>nous n’en dirons ici que tres@ peu de choſes.</s> |
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3538 <s xml:id="echoid-s2032" xml:space="preserve"/> |
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3539 </p> |
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3540 <div xml:id="echoid-div216" type="float" level="2" n="3"> |
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3541 <note position="right" xlink:label="note-0103-01" xlink:href="note-0103-01a" xml:space="preserve">DES <lb/>LEVIERS.</note> |
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3542 </div> |
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3543 <figure> |
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3544 <image file="0103-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0103-01"/> |
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3545 </figure> |
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3546 <pb o="78" file="0104" n="104" rhead="NOUVELLE"/> |
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3547 <figure> |
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3548 <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0104-01"/> |
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3549 </figure> |
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3550 </div> |
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3551 <div xml:id="echoid-div218" type="section" level="1" n="144"> |
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3552 <head xml:id="echoid-head144" xml:space="preserve">DE LA VIS <lb/>REMARQUES. <lb/>I.</head> |
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3553 <p> |
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3554 <s xml:id="echoid-s2033" xml:space="preserve">ON voit aſſez que tout l’uſage de la Vis eſt de <lb/>tirer, ou de repouſſer ſuivantla direction de ſon <lb/>axe tout ce qui lui fait quelque réſiſtance; </s> |
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3555 <s xml:id="echoid-s2034" xml:space="preserve">& </s> |
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3556 <s xml:id="echoid-s2035" xml:space="preserve">ſi elle <lb/>eſtſixe, la force, ou le corps contre lequel on s’en ſert, <lb/>doit tirer, ou preſſer ſon écrouë du côté diametra-<lb/>lement oppoſé à celui vers lequel il eſt forcé d’avan-<lb/>cer. </s> |
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3557 <s xml:id="echoid-s2036" xml:space="preserve">Au contraire ſi c’eſt l’écrouë qui ſoit ſixe, cette <lb/>force, où ce corps doit tirer, ou preſſer la vis elle-<lb/>même de ce même côté.</s> |
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3558 <s xml:id="echoid-s2037" xml:space="preserve"/> |
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3559 </p> |
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3560 </div> |
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3561 <div xml:id="echoid-div219" type="section" level="1" n="145"> |
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3562 <head xml:id="echoid-head145" xml:space="preserve">II.</head> |
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3563 <p> |
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3564 <s xml:id="echoid-s2038" xml:space="preserve">De ſorte, que dans l’uſage de la vis, lors qu’elle <lb/>eſt ſixe, l’on doit regarder tous les points de ſon <lb/>écrouë, comme tirez ou preſſez parallelement à ſon <lb/>axe du côté que cette écrouë eſt preſſée, ou tirée par <lb/>la force, ou par le poids dont elle eſt chargée.</s> |
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3565 <s xml:id="echoid-s2039" xml:space="preserve"/> |
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3566 </p> |
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3567 </div> |
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3568 <div xml:id="echoid-div220" type="section" level="1" n="146"> |
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3569 <head xml:id="echoid-head146" xml:space="preserve">III.</head> |
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3570 <p> |
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3571 <s xml:id="echoid-s2040" xml:space="preserve">D’où l’on voit que les lignes de direction de tous <lb/>ces points, ſont toutes obliques à celui des pas de <lb/>cette vis ſur lequel ceux de ces points qui le tou-<lb/>chent, s’appuyent; </s> |
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3572 <s xml:id="echoid-s2041" xml:space="preserve">& </s> |
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3573 <s xml:id="echoid-s2042" xml:space="preserve">par conſéquent (démonſt. </s> |
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3574 <s xml:id="echoid-s2043" xml:space="preserve">des |
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3575 <pb o="79" file="0105" n="105" rhead="MECHANIQUE."/> |
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3576 ſurf. </s> |
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3577 <s xml:id="echoid-s2044" xml:space="preserve">n. </s> |
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3578 <s xml:id="echoid-s2045" xml:space="preserve">3.) </s> |
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3579 <s xml:id="echoid-s2046" xml:space="preserve">ſi cette vis, & </s> |
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3580 <s xml:id="echoid-s2047" xml:space="preserve">ſon écrouë étoient Mathé-<lb/> |
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3581 <anchor type="note" xlink:label="note-0105-01a" xlink:href="note-0105-01"/> |
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3582 matiquement juſtes, chacun d’eux tendroit à couler <lb/>du côté que ſa ligne de direction s’écarteroit de la <lb/>perpendiculaire tirée de lui à ce pas; </s> |
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3583 <s xml:id="echoid-s2048" xml:space="preserve">& </s> |
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3584 <s xml:id="echoid-s2049" xml:space="preserve">parce que <lb/>cet écartement ſe feroit pour tous du même côté, à <lb/>cauſe du paralleliſme de toutes ces lignes, & </s> |
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3585 <s xml:id="echoid-s2050" xml:space="preserve">de la <lb/>pente uniforme du cordon de cette vis dans toute <lb/>ſa longueur: </s> |
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3586 <s xml:id="echoid-s2051" xml:space="preserve">Il ſuit évidemment que tous ces points <lb/>devroient s’accorder dans un même mouvement qui <lb/>emportât cette écrouë ſuivant le fil de ce cordon, <lb/>c’eſt-à-dire, en tournoyant du côté de cet écartement; <lb/></s> |
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3587 <s xml:id="echoid-s2052" xml:space="preserve">ſi dans ſon frotement avec la vis, l’inégalité de leurs <lb/>parties ne les acrochoient point enſemble.</s> |
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3588 <s xml:id="echoid-s2053" xml:space="preserve"/> |
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3589 </p> |
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3590 <div xml:id="echoid-div220" type="float" level="2" n="1"> |
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3591 <note position="right" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">DELA VIS.</note> |
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3592 </div> |
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3593 </div> |
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3594 <div xml:id="echoid-div222" type="section" level="1" n="147"> |
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3595 <head xml:id="echoid-head147" xml:space="preserve">IV.</head> |
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3596 <p> |
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3597 <s xml:id="echoid-s2054" xml:space="preserve">La même choſe ſe doit entendre de tous les points <lb/>de la vis, ſi c’eſt l’écrouë qui ſoit fixe.</s> |
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3598 <s xml:id="echoid-s2055" xml:space="preserve"/> |
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3599 </p> |
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3600 </div> |
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3601 <div xml:id="echoid-div223" type="section" level="1" n="148"> |
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3602 <head xml:id="echoid-head148" xml:space="preserve">V.</head> |
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3603 <p> |
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3604 <s xml:id="echoid-s2056" xml:space="preserve">Ainſi à regarder l’une & </s> |
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3605 <s xml:id="echoid-s2057" xml:space="preserve">l’autre dans une juſteſſe <lb/>Mathématique, il faut néceſſairement quelque force <lb/>pour retenir celle des deux qui eſt mobile, contre <lb/>l’impreſſion de la force, ou du poids qui la charge. <lb/></s> |
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3606 <s xml:id="echoid-s2058" xml:space="preserve">La voici.</s> |
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3607 <s xml:id="echoid-s2059" xml:space="preserve"/> |
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3608 </p> |
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3609 <figure> |
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3610 <image file="0105-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0105-01"/> |
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3611 </figure> |
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3612 </div> |
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3613 <div xml:id="echoid-div224" type="section" level="1" n="149"> |
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3614 <head xml:id="echoid-head149" xml:space="preserve">PROPOSITION <lb/>DE LA VIS.</head> |
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3615 <p style="it"> |
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3616 <s xml:id="echoid-s2060" xml:space="preserve">LOrſqu’une puiſſance ſoutient quelque poids, ou l’action <lb/>de quelque autre force à l’aide d’une vis, ſoit que<unsure/> <lb/>cette vis ſoit fixe, ou que ce ſoit ſon écrouë cette puiſſance |
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3617 <pb o="80" file="0106" n="106" rhead="NOUVELLE"/> |
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3618 eſt toujours à ce poids, ou a cette force, quelle qu’elle ſoit, <lb/> |
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3619 <anchor type="note" xlink:label="note-0106-01a" xlink:href="note-0106-01"/> |
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3620 comme la diſtance qui eſt entre deux des pas de cette vis, à <lb/>la circonfèrence a’un cercle, dont le rayon eſt égal à la diſtance <lb/>qui eſt entre cette puiſſance & </s> |
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3621 <s xml:id="echoid-s2061" xml:space="preserve">l’axe de cette mème vis.</s> |
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3622 <s xml:id="echoid-s2062" xml:space="preserve"/> |
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3623 </p> |
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3624 <div xml:id="echoid-div224" type="float" level="2" n="1"> |
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3625 <note position="left" xlink:label="note-0106-01" xlink:href="note-0106-01a" xml:space="preserve">DELAVIS</note> |
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3626 </div> |
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3627 </div> |
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3628 <div xml:id="echoid-div226" type="section" level="1" n="150"> |
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3629 <head xml:id="echoid-head150" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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3630 <p> |
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3631 <s xml:id="echoid-s2063" xml:space="preserve">Premiérement ſi la vis VXYZ eſt fixe, concevons que <lb/> |
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3632 <anchor type="note" xlink:label="note-0106-02a" xlink:href="note-0106-02"/> |
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3633 le point A de ſon écrouë PQ ſoit retenu ſur un de ſes <lb/>pas GH par quelque puiſſance R dont la direction AB <lb/>ſoit dans le plan de cette écrouë, & </s> |
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3634 <s xml:id="echoid-s2064" xml:space="preserve">perpendiculaire à <lb/>EP qui y eſt auſſi, & </s> |
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3635 <s xml:id="echoid-s2065" xml:space="preserve">qui paſſe par le point A. </s> |
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3636 <s xml:id="echoid-s2066" xml:space="preserve">Il eſt clair <lb/>que cette puiſſance retenant par ce moyen toute l’é-<lb/>crouë PQ, ce point A fait ſur elle la même impreſſion <lb/>que s’il ſoutenoit lui ſeul toute l’action du poids, ou de <lb/>la force, quelle qu’elle ſoit, qui pouſſe cette écrouë, <lb/>ou qui la tire (Remarq. </s> |
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3637 <s xml:id="echoid-s2067" xml:space="preserve">1.) </s> |
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3638 <s xml:id="echoid-s2068" xml:space="preserve">vers ZY parallelement à <lb/>l’axe MS de cette vis: </s> |
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3639 <s xml:id="echoid-s2069" xml:space="preserve">Ainſi l’on peut regarder le <lb/>point A de cette écrouë, comme ayant lui ſeul ſuivant <lb/>AC perpendiculaire au plan de cette écrouë, & </s> |
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3640 <s xml:id="echoid-s2070" xml:space="preserve">pa-<lb/>rallele à MS, toute l’impreſſion qu’elle reçoit de ſa <lb/>charge; </s> |
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3641 <s xml:id="echoid-s2071" xml:space="preserve">de ſorte que ſi l’on fait AD perpendiculaire <lb/>au pas GH de cette vis, & </s> |
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3642 <s xml:id="echoid-s2072" xml:space="preserve">que de quelque point D <lb/>de cette ligne, l’on acheve le parallelogramme BC, <lb/>on verra (prop. </s> |
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3643 <s xml:id="echoid-s2073" xml:space="preserve">fond. </s> |
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3644 <s xml:id="echoid-s2074" xml:space="preserve">des ſurf.) </s> |
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3645 <s xml:id="echoid-s2075" xml:space="preserve">que la puiſſance R ſera à <lb/>la charge de l’écrouë PQ, comme AB, à AC, ou à BD <lb/>qui lui eſt égale; </s> |
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3646 <s xml:id="echoid-s2076" xml:space="preserve">c’eſt-à-dire, à cauſe que le triangle <lb/>HFG roulé ſur la vis VXYZ, eſt ſemblable au <lb/>triangle ABD; </s> |
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3647 <s xml:id="echoid-s2077" xml:space="preserve">comme HF au demi tour FG de cette <lb/>vis, ou comme 2HF, c’eſt-à-dire, HK à un tour <lb/>entier. </s> |
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3648 <s xml:id="echoid-s2078" xml:space="preserve">Or regardant EAP comme un levier dont <lb/>l’appui eſt le point E de l’axe MS de cette vis, & </s> |
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3649 <s xml:id="echoid-s2079" xml:space="preserve">qui <lb/>ſe trouve dans le plan de ſon écrouë; </s> |
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3650 <s xml:id="echoid-s2080" xml:space="preserve">la puiſſance P, <lb/>dont la direction eſt auſſi dans ce même plan, & </s> |
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3651 <s xml:id="echoid-s2081" xml:space="preserve">per-<lb/>pendiculaire à EP, & </s> |
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3652 <s xml:id="echoid-s2082" xml:space="preserve">conſéquemment parallele à AB, |
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3653 <pb o="81" file="0107" n="107" rhead="MECHANIQUE."/> |
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3654 ſoutenant ainſi (Hyp.) </s> |
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3655 <s xml:id="echoid-s2083" xml:space="preserve">le point A, ou la charge de <lb/> |
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3656 <anchor type="note" xlink:label="note-0107-01a" xlink:href="note-0107-01"/> |
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3657 l’écrouë PQ au lieu de la puiſſance R, eſt à cette der-<lb/>niére puiſſance, (Lemm 6. </s> |
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3658 <s xml:id="echoid-s2084" xml:space="preserve">Cor. </s> |
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3659 <s xml:id="echoid-s2085" xml:space="preserve">2.) </s> |
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3660 <s xml:id="echoid-s2086" xml:space="preserve">comme EA à EP, <lb/>ou comme le tour entier de cette vis à la circonfé-<lb/>rence d’un cercle dont le rayon ſoit EP: </s> |
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3661 <s xml:id="echoid-s2087" xml:space="preserve">Ainſi en <lb/>multipliant par ordre ces deux rangées de proportio-<lb/>nelles, l’on aura la puiſſance P à la charge de l’écrouë <lb/>PQ, comme la diſtance HK qui eſt entre deux des <lb/>pas de cette vis, à la circonference d’un cercle dont <lb/>le rayon eſt égal à la diſtance EP qui eſt entre cette <lb/>fance & </s> |
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3662 <s xml:id="echoid-s2088" xml:space="preserve">l’axe de cette même vis.</s> |
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3663 <s xml:id="echoid-s2089" xml:space="preserve"/> |
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3664 </p> |
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3665 <div xml:id="echoid-div226" type="float" level="2" n="1"> |
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3666 <note position="left" xlink:label="note-0106-02" xlink:href="note-0106-02a" xml:space="preserve">ſig. 60.</note> |
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3667 <note position="right" xlink:label="note-0107-01" xlink:href="note-0107-01a" xml:space="preserve">DELA VIS.</note> |
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3668 </div> |
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3669 <p> |
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3670 <s xml:id="echoid-s2090" xml:space="preserve">Secondement, ſi c’eſt l’écrouë PQ qui ſoit fixe, <lb/>concevons que le point A appartient à la vis VXYZ, & </s> |
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3671 <s xml:id="echoid-s2091" xml:space="preserve"><lb/>qu’il eſt retenu ſur le pas de cette écrouë par quelque <lb/>puiſſance R dont la direction ſoit encore ſuivant AB <lb/>qu’on ſuppoſe dans le plan de cetteécrouë, & </s> |
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3672 <s xml:id="echoid-s2092" xml:space="preserve">perpen-<lb/>diculaire à EP qui y eſt auſſi. </s> |
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3673 <s xml:id="echoid-s2093" xml:space="preserve">Il eſt encore clair que <lb/>cette puiſſance retenant par ce moyen toute la vis <lb/>VXYZ, ce point A fait encore ſur elle la même <lb/>impreſſion ſuivant AC parallele à MS, que s’il ſou-<lb/>tenoit, lui ſeul, toute l’action de ce qui pouſſe, (re-<lb/>marq. </s> |
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3674 <s xml:id="echoid-s2094" xml:space="preserve">1.) </s> |
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3675 <s xml:id="echoid-s2095" xml:space="preserve">ou de ce qui tire cette vis vers ZY: </s> |
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3676 <s xml:id="echoid-s2096" xml:space="preserve">ainſi pour <lb/>la même raiſon que ci-deſſus, la puiſſance R ſera <lb/>encore à la charge de cette vis, comme AB à BD; <lb/></s> |
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3677 <s xml:id="echoid-s2097" xml:space="preserve">c’eſt-à-dire, comme HF à FG, ou bien comme HK <lb/>au circuit de cette vis; </s> |
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3678 <s xml:id="echoid-s2098" xml:space="preserve">& </s> |
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3679 <s xml:id="echoid-s2099" xml:space="preserve">la puiſſance T, qui au lieu de <lb/>la puiſſance R retient cette vis, eſt auſſi à cette dernié-<lb/>re puiſſance, (Lemm. </s> |
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3680 <s xml:id="echoid-s2100" xml:space="preserve">6. </s> |
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3681 <s xml:id="echoid-s2101" xml:space="preserve">Cor. </s> |
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3682 <s xml:id="echoid-s2102" xml:space="preserve">2.) </s> |
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3683 <s xml:id="echoid-s2103" xml:space="preserve">comme EA à ST, ou <lb/>comme un tour entier de cette vis à la circonférence <lb/>d’un cercle dont ST ſoit le rayon: </s> |
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3684 <s xml:id="echoid-s2104" xml:space="preserve">ainſi en multi-<lb/>pliant encore par ordre ces deux rangées de propor-<lb/>tionnelles, on aura encore la puiſſance T à la charge <lb/>de cette vis, comme la diſtance qui eſt entre deux de <lb/>ſes pas, à la circonférence d’un cercle dont le rayon eſt <lb/>égal à la diſtance qui eſt entre cette puiſſance & </s> |
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3685 <s xml:id="echoid-s2105" xml:space="preserve">l’axe de <lb/>cette même vis.</s> |
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3686 <s xml:id="echoid-s2106" xml:space="preserve"/> |
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3687 </p> |
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3688 <pb o="82" file="0108" n="108" rhead="NOUVELLE"/> |
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3689 <p> |
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3690 <s xml:id="echoid-s2107" xml:space="preserve">Donc lors qu’une puiſſance ſoutient un poids, ou <lb/> |
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3691 <anchor type="note" xlink:label="note-0108-01a" xlink:href="note-0108-01"/> |
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3692 l’action de quelqu’autre force que ce ſoit, à l’aide <lb/>d’une vis, ſoit que cette vis ſoit fixe, ou que ce ſoit <lb/>ſon écrouë, cette puiſſance eſt toujours à ce poids, ou <lb/>à cette force, commela diſtance qui eſt entre deux des <lb/>pas de cette vis, à la circonférence d’un cercle, dont <lb/>le rayon eſt égal à la diſtance qui eſt entre cette puiſ-<lb/>ſance & </s> |
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3693 <s xml:id="echoid-s2108" xml:space="preserve">l’axe de cette même vis. </s> |
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3694 <s xml:id="echoid-s2109" xml:space="preserve">Ce qu’il faloit dé-<lb/>montrer.</s> |
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3695 <s xml:id="echoid-s2110" xml:space="preserve"/> |
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3696 </p> |
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3697 <div xml:id="echoid-div227" type="float" level="2" n="2"> |
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3698 <note position="left" xlink:label="note-0108-01" xlink:href="note-0108-01a" xml:space="preserve">DE LA VIS.</note> |
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3699 </div> |
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3700 </div> |
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3701 <div xml:id="echoid-div229" type="section" level="1" n="151"> |
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3702 <head xml:id="echoid-head151" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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3703 <p> |
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3704 <s xml:id="echoid-s2111" xml:space="preserve">D’où l’on voit que pour peu que la raiſon d’une <lb/>puiſſance à un poids, ou à quelqu’autre force, ſur-<lb/>paſſe celle de la diſtance, qui eſt entre deux des pas <lb/>d’une vis, à la circonférence d’un cercle, dont le <lb/>rayon ſoit la diſtance de l’axe de cette vis à cette <lb/>puiſſance, elle pourra ainſi appliquée ſurmonter ce <lb/>poids, ou cette force à l’aide de cette vis, & </s> |
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3705 <s xml:id="echoid-s2112" xml:space="preserve">elle le <lb/>fera dautant plus aiſément que cette raiſon ſera plus <lb/>grande.</s> |
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3706 <s xml:id="echoid-s2113" xml:space="preserve"/> |
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3707 </p> |
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3708 <p style="it"> |
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3709 <s xml:id="echoid-s2114" xml:space="preserve">L’obſtacle que le frotement de la vis avec ſon écrouë <lb/>fait à ce mouvement, doit être compté comme faiſant partie <lb/>de ſa charge: </s> |
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3710 <s xml:id="echoid-s2115" xml:space="preserve">c’eſt ainſi qu’on la peut réduire à une juſteſſe <lb/>Mathématique, de meme que toute autre machine.</s> |
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3711 <s xml:id="echoid-s2116" xml:space="preserve"/> |
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3712 </p> |
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3713 </div> |
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3714 <div xml:id="echoid-div230" type="section" level="1" n="152"> |
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3715 <head xml:id="echoid-head152" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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3716 <p> |
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3717 <s xml:id="echoid-s2117" xml:space="preserve">D’où il ſuit que plus les pas d’une vis ſont ſerrez, <lb/>& </s> |
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3718 <s xml:id="echoid-s2118" xml:space="preserve">que la diſtance de ſon axe à la puiſſance qui y eſt <lb/>appliquée, eſt grande, plus il eſt facile à cette puiſ-<lb/>ſance de ſurmonter le poids, ou la force qui agit <lb/>contr’elle.</s> |
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3719 <s xml:id="echoid-s2119" xml:space="preserve"/> |
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3720 </p> |
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3721 </div> |
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3722 <div xml:id="echoid-div231" type="section" level="1" n="153"> |
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3723 <head xml:id="echoid-head153" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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3724 <p> |
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3725 <s xml:id="echoid-s2120" xml:space="preserve">Il ſuit encore de cette propoſition qu’une même |
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3726 <pb o="83" file="0109" n="109" rhead="MECHANIQUE."/> |
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3727 puiſſance peut également mouvoir un même poids, <lb/> |
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3728 <anchor type="note" xlink:label="note-0109-01a" xlink:href="note-0109-01"/> |
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3729 ou ſurmonter une même force, à l’aide d’une même <lb/>vis, ſoit qu’on la ſuppoſe appliquée à cette vis, où <lb/>qu’elle le ſoit à ſon écrouë pourvû qu’elle ſoit éga-<lb/>lement diſtante de ſon axe dans l’un & </s> |
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3730 <s xml:id="echoid-s2121" xml:space="preserve">l’autre cas.</s> |
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3731 <s xml:id="echoid-s2122" xml:space="preserve"/> |
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3732 </p> |
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3733 <div xml:id="echoid-div231" type="float" level="2" n="1"> |
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3734 <note position="right" xlink:label="note-0109-01" xlink:href="note-0109-01a" xml:space="preserve">DELA VIS.</note> |
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3735 </div> |
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3736 <p style="it"> |
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3737 <s xml:id="echoid-s2123" xml:space="preserve">On ne dit rien ici du Coin, de la Scie, du Mortier, &</s> |
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3738 <s xml:id="echoid-s2124" xml:space="preserve">c. <lb/></s> |
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3739 <s xml:id="echoid-s2125" xml:space="preserve">ce ſont plûtôt des inſtrumens, ou des outils propres à faciliter <lb/>la diviſion d’un corps, que des machines qui puiſſent en fa-<lb/>ciliter le mouvement; </s> |
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3740 <s xml:id="echoid-s2126" xml:space="preserve">on aura peut-ê<unsure/>tre un jour occaſion d’en <lb/>parler.</s> |
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3741 <s xml:id="echoid-s2127" xml:space="preserve"/> |
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|
3742 </p> |
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3743 <pb file="0110" n="110"/> |
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|
3744 <pb file="0111" n="111"/> |
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|
3745 </div> |
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|
3746 <div xml:id="echoid-div233" type="section" level="1" n="154"> |
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3747 <head xml:id="echoid-head154" xml:space="preserve">EXAMEN <lb/>DE L’OPINION <lb/>DE M BORELLI <lb/>SUR LES PROPRIETEZ DES POIDS <lb/>ſuſpendus par des cordes.</head> |
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|
3748 <pb file="0112" n="112"/> |
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3749 <pb file="0113" n="113"/> |
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3750 <figure> |
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3751 <image file="0113-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0113-01"/> |
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3752 </figure> |
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3753 </div> |
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3754 <div xml:id="echoid-div234" type="section" level="1" n="155"> |
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3755 <head xml:id="echoid-head155" xml:space="preserve">AVERTISSEMENT.</head> |
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3756 <p style="it"> |
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3757 <s xml:id="echoid-s2128" xml:space="preserve">C’EST ici l’éxamen promis dans la réfléxion qui <lb/>ſuit la preuve de la premiére propoſition du Trojet <lb/>précédent. </s> |
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3758 <s xml:id="echoid-s2129" xml:space="preserve">On ne croyoit pas d’abord le pouvoir donner <lb/>ici; </s> |
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3759 <s xml:id="echoid-s2130" xml:space="preserve">mais s’étant trouvé fait plûtôt qu’on ne s’y étoit <lb/>attendu, on le joint à ce projet. </s> |
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3760 <s xml:id="echoid-s2131" xml:space="preserve">On a été naturelle-<lb/>ment conduit par les principes qu’on y ſuit, à une <lb/>propoſition ſur les proprietez des poids ſuſpendus par <lb/>des cordes, qui s’eſt trouvée la meſme que celle que <lb/>Monſieur Borelli avoit critiquée dans Stévin, <lb/>& </s> |
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3761 <s xml:id="echoid-s2132" xml:space="preserve">dans Hérigone; </s> |
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3762 <s xml:id="echoid-s2133" xml:space="preserve">& </s> |
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3763 <s xml:id="echoid-s2134" xml:space="preserve">ç’a été par la neceſſité de <lb/>la juſtiſier qu’on s’eſt trouvé engagé à l’examen de ſa <lb/>critique.</s> |
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3764 <s xml:id="echoid-s2135" xml:space="preserve"/> |
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3765 </p> |
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3766 <p style="it"> |
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3767 <s xml:id="echoid-s2136" xml:space="preserve">On diviſe cet examen en deux Cbapitres: </s> |
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3768 <s xml:id="echoid-s2137" xml:space="preserve">dans le <lb/>premier on fait voir que le ſentiment que M. <lb/></s> |
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3769 <s xml:id="echoid-s2138" xml:space="preserve">Borelli reprend dans H’erigone, dans Stévin, & </s> |
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3770 <s xml:id="echoid-s2139" xml:space="preserve">dans <lb/>les autres; </s> |
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3771 <s xml:id="echoid-s2140" xml:space="preserve">bien loin d’ètre contraire, comme il l’a <lb/>crû, à la 68. </s> |
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3772 <s xml:id="echoid-s2141" xml:space="preserve">propoſition du Tome premier de ſon traité <lb/>du mouvement des Animaux, en eſt une ſuite ſi né-<lb/>ceſſaire, que s’il eut fait encore quelques pas, il y ſeroit <lb/>infailliblement entré. </s> |
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3773 <s xml:id="echoid-s2142" xml:space="preserve">On indique enſuite dans ce <lb/>meſme Chapitre quelques paralogiſmes que cet Au-<lb/>theur a commis, lors meſme qu’il croyoit en voir dans <lb/>les raiſonnemens qu’il a critiquez.</s> |
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3774 <s xml:id="echoid-s2143" xml:space="preserve"/> |
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3775 </p> |
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3776 <pb file="0114" n="114" rhead="AVERTISSEMENT."/> |
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3777 <p style="it"> |
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3778 <s xml:id="echoid-s2144" xml:space="preserve">Dans le ſecond Cbapitre, apres avoir encore donné <lb/>quelques démonſtrations du ſentiment d’Hèrigone & </s> |
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3779 <s xml:id="echoid-s2145" xml:space="preserve"><lb/>des autres, toutes différentes de celles que M. </s> |
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3780 <s xml:id="echoid-s2146" xml:space="preserve">Borelli <lb/>a critiqu@es; </s> |
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3781 <s xml:id="echoid-s2147" xml:space="preserve">on rend par la metbode du Projet <lb/>précedent les Lemmes ſur leſquels cet Au beur a fondé <lb/>tout ce qu’il a dit de la force des Muſcles, beaucoup <lb/>plus généraux qu’ils ne le peuvent eſtre par la ſienne.</s> |
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3782 <s xml:id="echoid-s2148" xml:space="preserve"/> |
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3783 </p> |
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3784 <p style="it"> |
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3785 <s xml:id="echoid-s2149" xml:space="preserve">Au reſte ſi l’on attaque une erreur ou M. <lb/></s> |
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3786 <s xml:id="echoid-s2150" xml:space="preserve">Borelli eſt tombé, on n’en eſt pas moins perſuadé <lb/>du mérite ex@raordinaire de ce grand bomme, dont <lb/>les principaux Ouvrages doivent eſtre mis au nombre <lb/>des Livres les plus originaux qui ayent paru dans ce <lb/>ſiecle-ci; </s> |
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3787 <s xml:id="echoid-s2151" xml:space="preserve">mais il n’y a perſonne qui ne puiſſe faire un <lb/>fauxpas, ſur tout dans des matieres auſſi delicates que <lb/>celles-ci, & </s> |
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3788 <s xml:id="echoid-s2152" xml:space="preserve">où le paralogiſme ſe gliſſe auſſi facile-<lb/>ment.</s> |
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3789 <s xml:id="echoid-s2153" xml:space="preserve"/> |
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3790 </p> |
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3791 <p style="it"> |
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3792 <s xml:id="echoid-s2154" xml:space="preserve">Tout ce qu’on citera de cet Auteur dans cet exa-<lb/>men, ſera pris du Tome premier de ſon Traité du mou-<lb/>vement des Animaux, de l’édition de Rome, faite en <lb/>1680. </s> |
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3793 <s xml:id="echoid-s2155" xml:space="preserve">On ſpécifie l’édition à cauſe des pages qu’on en <lb/>citera quelques fois.</s> |
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3794 <s xml:id="echoid-s2156" xml:space="preserve"/> |
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3795 </p> |
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3796 <pb o="89" file="0115" n="115"/> |
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3797 <figure> |
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3798 <image file="0115-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-01"/> |
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3799 </figure> |
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3800 </div> |
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3801 <div xml:id="echoid-div235" type="section" level="1" n="156"> |
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3802 <head xml:id="echoid-head156" xml:space="preserve">EXAMEN <lb/>DE L’OPINION <lb/>DE M. BORELLI <lb/>Sur les propriétez des Poids ſuſpendus <lb/>par des cordes.</head> |
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3803 <figure> |
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3804 <image file="0115-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0115-02"/> |
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3805 </figure> |
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3806 </div> |
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3807 <div xml:id="echoid-div236" type="section" level="1" n="157"> |
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3808 <head xml:id="echoid-head157" style="it" xml:space="preserve">ET AT DE LA QUESTION.</head> |
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3809 <p> |
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3810 <s xml:id="echoid-s2157" xml:space="preserve"><emph style="sc">MOnsieur</emph> <emph style="sc">Borelli</emph> dans ſon Traité du <lb/>mouvement des Animaux Tome 1. </s> |
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3811 <s xml:id="echoid-s2158" xml:space="preserve">Chapi-<lb/>tre 13. </s> |
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3812 <s xml:id="echoid-s2159" xml:space="preserve">a fait une fort longue digreſſion pour prou-<lb/>ver que Hérigone, Stévin, & </s> |
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3813 <s xml:id="echoid-s2160" xml:space="preserve">pluſieurs autres ſe <lb/>ſont trompez d’avoir avancé comme propoſition gé-<lb/>nérale que le poids T ſoutenu avec les cordes obliques AC <lb/> |
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3814 <anchor type="note" xlink:label="note-0115-01a" xlink:href="note-0115-01"/> |
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3815 & </s> |
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3816 <s xml:id="echoid-s2161" xml:space="preserve">BC par deux poids, ou deux puiſſances R & </s> |
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3817 <s xml:id="echoid-s2162" xml:space="preserve">S; </s> |
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3818 <s xml:id="echoid-s2163" xml:space="preserve">eſt à chacun |
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3819 <pb o="90" file="0116" n="116" rhead="EXAMEN DE L’OPINION"/> |
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3820 d’eux, ou d’elles, comme la partie HC de ſa ligne de di-<lb/> |
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3821 <anchor type="note" xlink:label="note-0116-01a" xlink:href="note-0116-01"/> |
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3822 rection à chacun des côtez CN & </s> |
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3823 <s xml:id="echoid-s2164" xml:space="preserve">MC du parallelogramme <lb/>MN, dont elle eſt diagonale. </s> |
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3824 <s xml:id="echoid-s2165" xml:space="preserve">Cet Autheur dit (pag. <lb/></s> |
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3825 <s xml:id="echoid-s2166" xml:space="preserve">” 137.) </s> |
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3826 <s xml:id="echoid-s2167" xml:space="preserve">que cette propoſition priſe dans toute ſon <lb/>étenduë & </s> |
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3827 <s xml:id="echoid-s2168" xml:space="preserve">ſans reſtriction, lui paroît ſuſpecte <lb/>pour bien des raiſons; </s> |
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3828 <s xml:id="echoid-s2169" xml:space="preserve">& </s> |
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3829 <s xml:id="echoid-s2170" xml:space="preserve">même qu’il la croit capa-<lb/>ble de jetter dans l’erreur.</s> |
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3830 <s xml:id="echoid-s2171" xml:space="preserve"/> |
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3831 </p> |
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3832 <div xml:id="echoid-div236" type="float" level="2" n="1"> |
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3833 <note position="right" xlink:label="note-0115-01" xlink:href="note-0115-01a" xml:space="preserve">ſig. @@</note> |
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3834 <note position="left" xlink:label="note-0116-01" xlink:href="note-0116-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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3835 </div> |
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3836 <p> |
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3837 <s xml:id="echoid-s2172" xml:space="preserve">Il réduit toutes ces prétenduës raiſons à trois: <lb/></s> |
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3838 <s xml:id="echoid-s2173" xml:space="preserve">1°. </s> |
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3839 <s xml:id="echoid-s2174" xml:space="preserve">il dit (pag. </s> |
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3840 <s xml:id="echoid-s2175" xml:space="preserve">138.) </s> |
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3841 <s xml:id="echoid-s2176" xml:space="preserve">avoir démontré dans le ſcholie <lb/>” de la 68. </s> |
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3842 <s xml:id="echoid-s2177" xml:space="preserve">propoſition du Tome 1. </s> |
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3843 <s xml:id="echoid-s2178" xml:space="preserve">de ce traité, que <lb/>les deux puiſſances R & </s> |
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3844 <s xml:id="echoid-s2179" xml:space="preserve">S appliquées au poids T <lb/>ſuivant des direction obliques, peuvent demeurer <lb/>en équilibre avec lui, non ſeulement quelque <lb/>raport qu’elles ayent entr’elles, fût-il plus grand, <lb/>ou moindre que celui de NC à CM, mais encore de <lb/>quelque maniére que le raport de la ſomme de ces <lb/>deux puiſſances à ce poids, fût différent de celui <lb/>de la ſomme de NC & </s> |
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3845 <s xml:id="echoid-s2180" xml:space="preserve">MC à CH. </s> |
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3846 <s xml:id="echoid-s2181" xml:space="preserve">2°. </s> |
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3847 <s xml:id="echoid-s2182" xml:space="preserve">il a fait, dit-<lb/>il, auſſi pluſieurs expériences qui lui paroiſſent <lb/>confirmer ce ſentiment. </s> |
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3848 <s xml:id="echoid-s2183" xml:space="preserve">3°. </s> |
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3849 <s xml:id="echoid-s2184" xml:space="preserve">Enfin il a crû voir du <lb/>paralogiſme dans deux démonſtrations qu’il a criti-<lb/>quées, dont la premiére paroît être du P.</s> |
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3850 <s xml:id="echoid-s2185" xml:space="preserve">Pardie, & </s> |
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3851 <s xml:id="echoid-s2186" xml:space="preserve">l’au-<lb/>tre commune au reſte des Autheurs qu’il attaque.</s> |
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3852 <s xml:id="echoid-s2187" xml:space="preserve"/> |
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3853 </p> |
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3854 <p> |
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3855 <s xml:id="echoid-s2188" xml:space="preserve">Il eſt conſtant que de toutes ces raiſons la premiére <lb/>eſt non ſeulement la principale, mais encore l’unique <lb/>qui puiſſe ſervir à la deciſion de ce différent: </s> |
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3856 <s xml:id="echoid-s2189" xml:space="preserve">Car 1°. </s> |
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3857 <s xml:id="echoid-s2190" xml:space="preserve">en <lb/>fait d’exactitude & </s> |
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3858 <s xml:id="echoid-s2191" xml:space="preserve">de préciſion, l’expérience ne <lb/>prouve rien; </s> |
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3859 <s xml:id="echoid-s2192" xml:space="preserve">ſur tout ici, ou la réſiſtance qui vient <lb/>du frotement des poulies avec leurs pivots, &</s> |
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3860 <s xml:id="echoid-s2193" xml:space="preserve">c. </s> |
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3861 <s xml:id="echoid-s2194" xml:space="preserve">rend <lb/>ces ſortes d’expériences poſſibles en tant de manieres <lb/>différentes, qu’il n’y a preſque point de ſentiment <lb/>pour, ou contre lequel on n’en puiſſe faire à ſon gré. <lb/></s> |
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3862 <s xml:id="echoid-s2195" xml:space="preserve">2°. </s> |
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3863 <s xml:id="echoid-s2196" xml:space="preserve">Qu’il y ait, ou qu’il n’y ait point de paralogiſme |
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3864 <pb o="91" file="0117" n="117" rhead="DE M. BORELLI."/> |
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3865 dans les raiſonnemens qué cet Autheur critique, on <lb/> |
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3866 <anchor type="note" xlink:label="note-0117-01a" xlink:href="note-0117-01"/> |
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3867 n’en peut rien conclure non plus contre le ſentiment <lb/>qu’il attaque; </s> |
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3868 <s xml:id="echoid-s2197" xml:space="preserve">puiſque la vérité ne dépend point du <lb/>tout de la maniere dont on la démontre.</s> |
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3869 <s xml:id="echoid-s2198" xml:space="preserve"/> |
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3870 </p> |
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3871 <div xml:id="echoid-div237" type="float" level="2" n="2"> |
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3872 <note position="right" xlink:label="note-0117-01" xlink:href="note-0117-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſe@-<lb/>lemen@.</note> |
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3873 </div> |
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3874 <p> |
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3875 <s xml:id="echoid-s2199" xml:space="preserve">Toute la queſtion préſente ſe réduit donc à ſça-<lb/>voir ſi en effet M. </s> |
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3876 <s xml:id="echoid-s2200" xml:space="preserve">Borelli a démontré dans le <lb/>ſcholie de ſa 6 8. </s> |
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3877 <s xml:id="echoid-s2201" xml:space="preserve">Propoſition Tome 1. </s> |
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3878 <s xml:id="echoid-s2202" xml:space="preserve">que les “ <lb/>deux puiſſances R & </s> |
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3879 <s xml:id="echoid-s2203" xml:space="preserve">S appliquées au poids T <lb/>ſuivant des directions obliques, peuvent demeu-<lb/>rer en équilibre avec lui, non ſeulement quelque <lb/>raport qu’elles ayent entr’elles, fût-il plus grand, <lb/>ou moindre que celui de NC à CM; </s> |
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3880 <s xml:id="echoid-s2204" xml:space="preserve">mais encore <lb/>de quelque maniére que le raport de la ſomme de <lb/>ces deux puiſſances à ce poids, fût différent de <lb/>celui de la ſomme de NC & </s> |
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3881 <s xml:id="echoid-s2205" xml:space="preserve">MC à CH. </s> |
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3882 <s xml:id="echoid-s2206" xml:space="preserve">Que dî-je? <lb/></s> |
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3883 <s xml:id="echoid-s2207" xml:space="preserve">Ce ſeroit aſſez pour détruire la propoſition qu’il <lb/>rejette, s’il avoit ſeulement démontré un cas ou ce <lb/>poids pût ainſi demeurer en équilibré avec ces puiſ-<lb/>ſances, ſans être à chacune d’elles, comme la partie <lb/>CH de ſa ligne de direction, qui fait la diagonale du <lb/>parallelogramme MN, à chacune des parties de leurs <lb/>cordes, qui lui ſervent de côtez. </s> |
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3884 <s xml:id="echoid-s2208" xml:space="preserve">Mais bien loin de <lb/>l’avoir fait, la propoſition d’où il tire le ſcholie en <lb/>queſtion, prouve tout le contraire, je veux dire, le <lb/>ſentiment d’où il a crû qu’elle le devoit cloigner.</s> |
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3885 <s xml:id="echoid-s2209" xml:space="preserve"/> |
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|
3886 </p> |
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3887 <p> |
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3888 <s xml:id="echoid-s2210" xml:space="preserve">C’eſt ce qu’on va faire voir dans le premier <lb/>Chapitre de cet Examen; </s> |
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3889 <s xml:id="echoid-s2211" xml:space="preserve">& </s> |
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3890 <s xml:id="echoid-s2212" xml:space="preserve">dans le ſecond, aprés <lb/>avoir encore donné quelques démonſtrations de ce <lb/>même ſentiment, toutes différentes de celles que <lb/>M. </s> |
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3891 <s xml:id="echoid-s2213" xml:space="preserve">Borelli a critiquées, on rendra par la méthode <lb/>du Projet précédent les Lemmes qu’il a déduits de ſa <lb/>68. </s> |
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3892 <s xml:id="echoid-s2214" xml:space="preserve">propoſition, beaucoup plus généraux qu’ils ne le <lb/>peuvent être par la ſienne.</s> |
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3893 <s xml:id="echoid-s2215" xml:space="preserve"/> |
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3894 </p> |
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3895 <pb o="92" file="0118" n="118" rhead="EXAMEN DE L’OPINION"/> |
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3896 <figure> |
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3897 <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0118-01"/> |
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3898 </figure> |
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3899 </div> |
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3900 <div xml:id="echoid-div239" type="section" level="1" n="158"> |
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3901 <head xml:id="echoid-head158" xml:space="preserve">CHAPITRE I. <lb/>SENTIMENT D’HERIGONE, <lb/>DE STEVIN, &c. <lb/>SUR LES PROPRIETEZ DES POIDS <lb/>ſuſpendus par des cordes, <lb/>Démontré par la propoſition même que M. BORELLI <lb/>avoit cru leur être contraire.</head> |
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3902 <p> |
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3903 <s xml:id="echoid-s2216" xml:space="preserve">LE ſcholie de la 68. </s> |
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3904 <s xml:id="echoid-s2217" xml:space="preserve">propoſition de M. </s> |
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3905 <s xml:id="echoid-s2218" xml:space="preserve">Borel-<lb/>li, dont il eſt ici queſtion, porte ” 1°. </s> |
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3906 <s xml:id="echoid-s2219" xml:space="preserve">Qu’a-<lb/>” vec les mêmes inclinaiſons de cordes, le poids qui <lb/>y eſt ſuſpendu, & </s> |
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3907 <s xml:id="echoid-s2220" xml:space="preserve">les forces qui le ſoutiennent, <lb/>peuvent varier en mille manieres différentes ſans <lb/> |
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3908 <anchor type="note" xlink:label="note-0118-01a" xlink:href="note-0118-01"/> |
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3909 que pour cela il ceſſe de faire équilibre avec elles; <lb/></s> |
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3910 <s xml:id="echoid-s2221" xml:space="preserve">pourvû que la puiſſance R ſoit à la partie X de ce poids, <lb/>comme GC à GF, ou comme AC à CH; </s> |
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3911 <s xml:id="echoid-s2222" xml:space="preserve">& </s> |
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3912 <s xml:id="echoid-s2223" xml:space="preserve">que <lb/>la puiſſance S ſoit à ſon autre partie Z, comme IC à <lb/>IK, ou comme BC à CH.</s> |
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3913 <s xml:id="echoid-s2224" xml:space="preserve">..</s> |
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3914 <s xml:id="echoid-s2225" xml:space="preserve">..</s> |
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3915 <s xml:id="echoid-s2226" xml:space="preserve">..</s> |
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3916 <s xml:id="echoid-s2227" xml:space="preserve">. 2° Ce même ſcholie <lb/>porte réciproquement qu’en retenant les mêmes <lb/>poids; </s> |
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3917 <s xml:id="echoid-s2228" xml:space="preserve">c’eſt - à - dire ici, les mêmes forces, (pourvû que <lb/>celui du milieu ſoit moindre que les deux extrê-<lb/>mes) on peut changer l’inclinaiſon de leurs cordes <lb/>ſans en rompre l’équilibre.</s> |
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3918 <s xml:id="echoid-s2229" xml:space="preserve"/> |
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3919 </p> |
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3920 <div xml:id="echoid-div239" type="float" level="2" n="1"> |
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3921 <note position="left" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">ſig. 1.</note> |
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3922 </div> |
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3923 <p> |
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3924 <s xml:id="echoid-s2230" xml:space="preserve">Il eſt clair que la premiére partie de ce ſcholie <lb/>peut avoir deux ſens bien différens. </s> |
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3925 <s xml:id="echoid-s2231" xml:space="preserve">1°. </s> |
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3926 <s xml:id="echoid-s2232" xml:space="preserve">Elle peut <lb/>ſignifier que dans cette variation de poids & </s> |
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3927 <s xml:id="echoid-s2233" xml:space="preserve">de |
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3928 <pb o="93" file="0119" n="119" rhead="DE M. BORELLI."/> |
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3929 forces, ou cet Autheur veut que l’équilibre ſe con-<lb/> |
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3930 <anchor type="note" xlink:label="note-0119-01a" xlink:href="note-0119-01"/> |
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3931 ſerve ſans changer l’inclinaiſon de leurs cordes, ce <lb/>poids demeure toujours à chacune de ces puiſſances <lb/>en même raiſon que la diagonale CH du parallelo-<lb/>gramme MN, à chaque partie de leurs cordes, qui <lb/>lui ſert de côté; </s> |
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3932 <s xml:id="echoid-s2234" xml:space="preserve">& </s> |
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3933 <s xml:id="echoid-s2235" xml:space="preserve">en cela on va voir que cette conſé-<lb/>quence eſt parfaitement juſte, mais auſſi (Cor. </s> |
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3934 <s xml:id="echoid-s2236" xml:space="preserve">12. <lb/></s> |
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3935 <s xml:id="echoid-s2237" xml:space="preserve">de la Prop. </s> |
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3936 <s xml:id="echoid-s2238" xml:space="preserve">fond. </s> |
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3937 <s xml:id="echoid-s2239" xml:space="preserve">des poids ſuſpendus par des cordes, du <lb/>Proiet précéd.) </s> |
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3938 <s xml:id="echoid-s2240" xml:space="preserve">parfaitement conforme au ſentiment <lb/>que cet Autheur attaque. </s> |
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3939 <s xml:id="echoid-s2241" xml:space="preserve">2°. </s> |
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3940 <s xml:id="echoid-s2242" xml:space="preserve">Au contraire, ſi on lui <lb/>fait ſigniſier que cet équilibre puiſſe ſubſiſter ſans un <lb/>tel raport; </s> |
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3941 <s xml:id="echoid-s2243" xml:space="preserve">alors on conclud tres-mal, & </s> |
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3942 <s xml:id="echoid-s2244" xml:space="preserve">même au-<lb/>tant contre cet Autheur que contre Hérigone, <lb/>&</s> |
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3943 <s xml:id="echoid-s2245" xml:space="preserve">c. </s> |
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3944 <s xml:id="echoid-s2246" xml:space="preserve">J’en dis tout autant de la ſeconde partie de <lb/>ce même ſcholie; </s> |
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3945 <s xml:id="echoid-s2247" xml:space="preserve">& </s> |
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3946 <s xml:id="echoid-s2248" xml:space="preserve">pour le démontrer, je vais <lb/>faire voir que la propoſition d’où M. </s> |
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3947 <s xml:id="echoid-s2249" xml:space="preserve">Borelli le <lb/>tire, prouve tout le contraire, & </s> |
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3948 <s xml:id="echoid-s2250" xml:space="preserve">que s’il y eût <lb/>fait un peu plus d’attention, elle l’auroit infaillible-<lb/>ment conduit au ſentiment d’où il a crû qu’elle le <lb/>devoit éloigner; </s> |
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3949 <s xml:id="echoid-s2251" xml:space="preserve">je veux dire, à croire (du moins <lb/>pour tous les cas qu’elle comprend) que le poids T <lb/>ſoutenu avec les cordes obliques AC & </s> |
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3950 <s xml:id="echoid-s2252" xml:space="preserve">BC par deux poids, <lb/>ou deux puiſſances R & </s> |
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3951 <s xml:id="echoid-s2253" xml:space="preserve">S, eſt toujours à chacun d’eux, ou <lb/>d’elles, comme la partie HC de ſa ligne de direction, à cbacun <lb/>descôtez CN & </s> |
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3952 <s xml:id="echoid-s2254" xml:space="preserve">MC du parallelogramme MN, dont elle <lb/>eſt diagonale. </s> |
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3953 <s xml:id="echoid-s2255" xml:space="preserve">Voici comment.</s> |
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3954 <s xml:id="echoid-s2256" xml:space="preserve"/> |
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3955 </p> |
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3956 <div xml:id="echoid-div240" type="float" level="2" n="2"> |
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3957 <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avcc <lb/>des cordes ſeu-<lb/>lement.</note> |
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3958 </div> |
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3959 <p> |
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3960 <s xml:id="echoid-s2257" xml:space="preserve">Selon cet Autheur (Prop. </s> |
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3961 <s xml:id="echoid-s2258" xml:space="preserve">68) lorſque les puiſ-<lb/>ſances R & </s> |
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3962 <s xml:id="echoid-s2259" xml:space="preserve">S ſoutiennent enſemble le poids T, la <lb/>puiſſance R ſoutient pour ſa part une partie X de ce <lb/>poids, de même qu’elle feroit, ſi elle étoit appliquée <lb/>ſuivant ſa même direction AC avec cette partie X au <lb/>levier horizontal CG; </s> |
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3963 <s xml:id="echoid-s2260" xml:space="preserve">& </s> |
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3964 <s xml:id="echoid-s2261" xml:space="preserve">la puiſſance S ſoutient auſſi <lb/>pour la ſienne l’autre partie Z de ce même poids, <lb/>de même qu’elle feroit, ſi elle étoit auſſi appliquée |
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3965 <pb o="94" file="0120" n="120" rhead="EXAMEN DE L’OPINION"/> |
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3966 ſuivant ſa même direction CB avec cette partie Z au <lb/> |
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3967 <anchor type="note" xlink:label="note-0120-01a" xlink:href="note-0120-01"/> |
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3968 levier CI qu’on ſuppoſe encore horizontal & </s> |
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3969 <s xml:id="echoid-s2262" xml:space="preserve">égal <lb/>au premier: </s> |
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3970 <s xml:id="echoid-s2263" xml:space="preserve">& </s> |
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3971 <s xml:id="echoid-s2264" xml:space="preserve">par conſéquent ſi l’on regarde (Cor 2. <lb/></s> |
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3972 <s xml:id="echoid-s2265" xml:space="preserve">Lem. </s> |
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3973 <s xml:id="echoid-s2266" xml:space="preserve">3. </s> |
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3974 <s xml:id="echoid-s2267" xml:space="preserve">du Projet précéd.) </s> |
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3975 <s xml:id="echoid-s2268" xml:space="preserve">l’impreſſion que la puiſſance <lb/>S fait ſuivant CB ſur le noeud C qui retient enſemble <lb/>les cordes de ces puiſſances & </s> |
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3976 <s xml:id="echoid-s2269" xml:space="preserve">de ce poids, comme <lb/>compoſée de deux impreſſions particuliéres, dont <lb/>l’une eſt ſuivant l’horizontale CO, & </s> |
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3977 <s xml:id="echoid-s2270" xml:space="preserve">l’autre ſuivant <lb/>la perpendiculaire CH; </s> |
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3978 <s xml:id="echoid-s2271" xml:space="preserve">on trouvera que ce que cette <lb/>puiſſance lui en fait ſuivant CO, eſt égal à la réſiſ-<lb/>tance que feroit alors contre ce même point, & </s> |
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3979 <s xml:id="echoid-s2272" xml:space="preserve">ſui-<lb/>vant cette même ligne, le levier CG pour empêcher <lb/>la corde ACX de ſe redreſſer; </s> |
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3980 <s xml:id="echoid-s2273" xml:space="preserve">c’eſt-à-dire, égal à la <lb/>charge de l’apui G de ce même levier. </s> |
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3981 <s xml:id="echoid-s2274" xml:space="preserve">Or (Cor. </s> |
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3982 <s xml:id="echoid-s2275" xml:space="preserve">4. </s> |
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3983 <s xml:id="echoid-s2276" xml:space="preserve"><lb/>Prop. </s> |
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3984 <s xml:id="echoid-s2277" xml:space="preserve">fond. </s> |
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3985 <s xml:id="echoid-s2278" xml:space="preserve">des leviers du Proj. </s> |
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3986 <s xml:id="echoid-s2279" xml:space="preserve">précéd.) </s> |
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3987 <s xml:id="echoid-s2280" xml:space="preserve">la puiſſance R <lb/>eſt à la charge de cet apui, comme le côté AC du <lb/>parallelogramme AE, à ſa diagonale CG; </s> |
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3988 <s xml:id="echoid-s2281" xml:space="preserve">& </s> |
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3989 <s xml:id="echoid-s2282" xml:space="preserve">la force <lb/>de l’impreſſion que fait la puiſſance S ſur ce même <lb/>point C ſuivant CO, eſt (Cor. </s> |
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3990 <s xml:id="echoid-s2283" xml:space="preserve">3. </s> |
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3991 <s xml:id="echoid-s2284" xml:space="preserve">Lemm. </s> |
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3992 <s xml:id="echoid-s2285" xml:space="preserve">3. </s> |
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3993 <s xml:id="echoid-s2286" xml:space="preserve">du Projet <lb/>précéd.) </s> |
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3994 <s xml:id="echoid-s2287" xml:space="preserve">à celle de cette même puiſſance ſuivant CB, <lb/>c’eſt-à-dire, à cette puiſſance, elle-même, comme <lb/>le côté OC du parallelogramme OH, à ſa diagonale <lb/>BC; </s> |
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3995 <s xml:id="echoid-s2288" xml:space="preserve">c’eſt-à-dire, en faiſant IK perpendiculaire ſur <lb/>BC, comme CK à CI égale (Hyp.) </s> |
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3996 <s xml:id="echoid-s2289" xml:space="preserve">à CG: </s> |
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3997 <s xml:id="echoid-s2290" xml:space="preserve">Donc la <lb/>puiſſance R eſt à la puiſſance S, comme le produit <lb/>de AC par CK, au quarré de CG. </s> |
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3998 <s xml:id="echoid-s2291" xml:space="preserve">Or en faiſant GF <lb/>perpendiculaire ſur AC, les triangles AGC & </s> |
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3999 <s xml:id="echoid-s2292" xml:space="preserve">GFC <lb/>étant ſemblables, le produit de AC par CF eſt égal <lb/>au quarré de CG: </s> |
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4000 <s xml:id="echoid-s2293" xml:space="preserve">Donc la puiſſance R eſt à la puiſ-<lb/>ſance S, comme le produit de AC par CK au produit <lb/>de la même AC par CF, c’eſt-à-dire, comme CK à <lb/>CF; </s> |
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4001 <s xml:id="echoid-s2294" xml:space="preserve">ou bien, à cauſe des rayons IC & </s> |
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4002 <s xml:id="echoid-s2295" xml:space="preserve">CG (byp.) </s> |
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4003 <s xml:id="echoid-s2296" xml:space="preserve"><lb/>égaux, comme le ſinus de KIC égal à BCH, au ſinus <lb/>de FGC égal à ACH: </s> |
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4004 <s xml:id="echoid-s2297" xml:space="preserve">Donc la puiſſance R eſt à la <lb/>puiſſance S, comme le ſinus de l’angle BCH à celui |
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4005 <pb o="95" file="0121" n="121" rhead="DE M. BORELLI."/> |
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4006 de l’angle ACH qui, à cauſe du parallelogramme <lb/> |
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4007 <anchor type="note" xlink:label="note-0121-01a" xlink:href="note-0121-01"/> |
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4008 MN, eſt égal à CHM: </s> |
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4009 <s xml:id="echoid-s2298" xml:space="preserve">Donc (Lemm. </s> |
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4010 <s xml:id="echoid-s2299" xml:space="preserve">5. </s> |
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4011 <s xml:id="echoid-s2300" xml:space="preserve">du Projet <lb/>précéd) la puiſſance R eſt à la puiſſance S, comme <lb/>HM, ou comme ſon égale NC à CM.</s> |
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4012 <s xml:id="echoid-s2301" xml:space="preserve"/> |
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4013 </p> |
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4014 <div xml:id="echoid-div241" type="float" level="2" n="3"> |
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4015 <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>l@ment.</note> |
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4016 <note position="right" xlink:label="note-0121-01" xlink:href="note-0121-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4017 </div> |
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4018 <p> |
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4019 <s xml:id="echoid-s2302" xml:space="preserve">Voilà ce que M. </s> |
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4020 <s xml:id="echoid-s2303" xml:space="preserve">Borelli devoit premiérement <lb/>conclure de ſa 68. </s> |
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4021 <s xml:id="echoid-s2304" xml:space="preserve">propoſition, ſinon en géné-<lb/>ral, du moins pour tous les cas qu’elle com-<lb/>prend: </s> |
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4022 <s xml:id="echoid-s2305" xml:space="preserve">Sçavoir que lorſque deux puiſſances R & </s> |
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4023 <s xml:id="echoid-s2306" xml:space="preserve">S ſou-<lb/>tiennent enſemble quelque poids T avec des cordes ſeulement, <lb/>elles ſont toujours @ntr’elles en même raiſon que les parties <lb/>CN & </s> |
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4024 <s xml:id="echoid-s2307" xml:space="preserve">MC de leurs cordes, qui ſervent de côtez au pa-<lb/>rallelogramme MN, qui a pour diagonale une partie CH <lb/>de la li@ne de direction du poids qu’elles ſoutiennent. </s> |
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4025 <s xml:id="echoid-s2308" xml:space="preserve">De là <lb/>en faiſant MP & </s> |
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4026 <s xml:id="echoid-s2309" xml:space="preserve">NQ perpendiculaires ſur HC, ces <lb/>lignes marquant toujours CP égale à HQ, cet Au-<lb/>theur auroit trouvé, comme il a fait (pag. </s> |
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4027 <s xml:id="echoid-s2310" xml:space="preserve">137.) <lb/></s> |
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4028 <s xml:id="echoid-s2311" xml:space="preserve">que chacune des puiſſances R & </s> |
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4029 <s xml:id="echoid-s2312" xml:space="preserve">S, étant toujours (par <lb/>le Cor. </s> |
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4030 <s xml:id="echoid-s2313" xml:space="preserve">de ſa 69. </s> |
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4031 <s xml:id="echoid-s2314" xml:space="preserve">Prop.) </s> |
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4032 <s xml:id="echoid-s2315" xml:space="preserve">à tout ce poids, comme chacun <lb/>des côtez CN & </s> |
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4033 <s xml:id="echoid-s2316" xml:space="preserve">MC du parallelogramme MN, à la <lb/>ſomme de leurs ſublimitez CP & </s> |
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4034 <s xml:id="echoid-s2317" xml:space="preserve">CQ; </s> |
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4035 <s xml:id="echoid-s2318" xml:space="preserve">lui eſt auſſi <lb/>toujours comme cbacun de ces mêmes côtez à la diagonale <lb/>CH de ce même para@lelogramme. </s> |
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4036 <s xml:id="echoid-s2319" xml:space="preserve">Ce qu’il faloit démon-<lb/>trer.</s> |
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4037 <s xml:id="echoid-s2320" xml:space="preserve"/> |
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4038 </p> |
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4039 <p> |
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4040 <s xml:id="echoid-s2321" xml:space="preserve">Quoi que cette conſéquence ſuive néceſſairement de la <lb/>68. </s> |
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4041 <s xml:id="echoid-s2322" xml:space="preserve">Propoſition de M. </s> |
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4042 <s xml:id="echoid-s2323" xml:space="preserve">Borelli, cependant parce-que cette <lb/>Propoſition ne peut pas s’appliquer aux cas ou une de <lb/>ces pu@ſſances ſe trouve avoir ſa direction au deſſous de <lb/>l’borizontale qui paſſe par le point où leurs cordes ſe com-<lb/>muniquent, elle n’en eſt pas une ſuitte ſi générale que de la <lb/>Propoſition fondamentale des poids ſuſpendus par des cordes <lb/>du Projet précédent: </s> |
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4043 <s xml:id="echoid-s2324" xml:space="preserve">C’eſt pour cela qu’on ſe contente ici de <lb/>dire, que ſi cet Autbeur eût fait un peu plus d’attention à <lb/>ſa 68. </s> |
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4044 <s xml:id="echoid-s2325" xml:space="preserve">Prop. </s> |
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4045 <s xml:id="echoid-s2326" xml:space="preserve">il auroit aperçû que tout ce que nous venons <lb/>d’en conclure, eſt abſolument vrai, du moins pour tous <lb/>les cas qu’elle comprend.</s> |
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4046 <s xml:id="echoid-s2327" xml:space="preserve"/> |
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4047 </p> |
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4048 <pb o="96" file="0122" n="122" rhead="EXAMEN DE L’OPINION"/> |
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4049 <p> |
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4050 <s xml:id="echoid-s2328" xml:space="preserve">Telle eſt la conſéquence que Monſieur Borelli <lb/> |
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4051 <anchor type="note" xlink:label="note-0122-01a" xlink:href="note-0122-01"/> |
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4052 devoit tirer de ſa 68. </s> |
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4053 <s xml:id="echoid-s2329" xml:space="preserve">Propoſition; </s> |
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4054 <s xml:id="echoid-s2330" xml:space="preserve">s’il l’eût fait, il <lb/>auroit aperçû 1°. </s> |
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4055 <s xml:id="echoid-s2331" xml:space="preserve">que la premiére partie du ſcholie <lb/>qu’il en tire, n’eſt vraye qu’en cas que la variation <lb/>du poids T & </s> |
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4056 <s xml:id="echoid-s2332" xml:space="preserve">des forces ſ & </s> |
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4057 <s xml:id="echoid-s2333" xml:space="preserve">S, entre leſquels il dit <lb/>que l’équilibre ſe peut conſerver ſans changer l’in-<lb/>clinaiſon de leurs cordes, ſoit telle que ce poids de-<lb/>meure toujours à chacune de ces puiſſances en même <lb/>raiſon que la diagonale CH du parallelogramme <lb/>MN, à chaque partie de leurs cordes qui lui ſert de <lb/>côté. </s> |
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4058 <s xml:id="echoid-s2334" xml:space="preserve">2°. </s> |
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4059 <s xml:id="echoid-s2335" xml:space="preserve">Il auroit encore vû que la ſeconde partie <lb/>de ce même ſcholie eſt abſolument fauſſe; </s> |
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4060 <s xml:id="echoid-s2336" xml:space="preserve">puis qu’il <lb/>n’eſt pas poſſible de faire le moindre changement <lb/>auquel que ce ſoit des angles ACB, ACH, & </s> |
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4061 <s xml:id="echoid-s2337" xml:space="preserve">BCH, <lb/>ſans changer en même - tems le raport qui eſt, ou <lb/>entre les côtez du parallelogramme MN, ou entre <lb/>quelqu’un d’eux & </s> |
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4062 <s xml:id="echoid-s2338" xml:space="preserve">ſa diagonale; </s> |
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4063 <s xml:id="echoid-s2339" xml:space="preserve">c’eſt - à - dire, puis <lb/>que (byp.) </s> |
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4064 <s xml:id="echoid-s2340" xml:space="preserve">on ne change rien au raport qui eſt entre <lb/>ce poids & </s> |
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4065 <s xml:id="echoid-s2341" xml:space="preserve">chacune de ces puiſſances, ſans faire ceſſer <lb/>la reſſemblance de ces deux raports: </s> |
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4066 <s xml:id="echoid-s2342" xml:space="preserve">& </s> |
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4067 <s xml:id="echoid-s2343" xml:space="preserve">par conſe-<lb/>quent auſſi, ſuivant ce qui vient d’être conclu de la <lb/>68. </s> |
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4068 <s xml:id="echoid-s2344" xml:space="preserve">Propoſition de M. </s> |
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4069 <s xml:id="echoid-s2345" xml:space="preserve">Borelli, ſans rompre l’équili-<lb/>bre de ce poids avec ces puiſſances.</s> |
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4070 <s xml:id="echoid-s2346" xml:space="preserve"/> |
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4071 </p> |
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4072 <div xml:id="echoid-div242" type="float" level="2" n="4"> |
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4073 <note position="left" xlink:label="note-0122-01" xlink:href="note-0122-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des c<unsure/>otdes ſeu-<lb/>lement.</note> |
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4074 </div> |
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4075 </div> |
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4076 <div xml:id="echoid-div244" type="section" level="1" n="159"> |
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4077 <head xml:id="echoid-head159" xml:space="preserve"><emph style="sc">Remarque.</emph></head> |
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4078 <p> |
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4079 <s xml:id="echoid-s2347" xml:space="preserve">Ayant demontré, comme l’on vient de faire, <lb/>que le ſentiment, dont il eſt ici queſtion, bien loin <lb/>d’être contraire à la 68. </s> |
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4080 <s xml:id="echoid-s2348" xml:space="preserve">Propoſit. </s> |
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4081 <s xml:id="echoid-s2349" xml:space="preserve">de M. </s> |
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4082 <s xml:id="echoid-s2350" xml:space="preserve">Borelli, <lb/>comme cet Autheur l’a crû, en eſt une ſuitte ſi né-<lb/>ceſſaire que, s’il eût fait encore quelques pas, il <lb/>l’auroit linfailliblement trouvé: </s> |
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4083 <s xml:id="echoid-s2351" xml:space="preserve">c’eſt encore une nou-<lb/>velle raiſon de ne nous point arrêter aux expériences <lb/>qu’il objecte à Stévin, à Hérigone, & </s> |
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4084 <s xml:id="echoid-s2352" xml:space="preserve">aux autres, & </s> |
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4085 <s xml:id="echoid-s2353" xml:space="preserve"><lb/>de ne toucher à la critique qu’il a faite de leurs rai- |
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4086 <pb o="97" file="0123" n="123" rhead="DE M. BORELLI."/> |
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4087 ſonnemens, que pour indiquer les fauſſes ſuppo-<lb/> |
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4088 <anchor type="note" xlink:label="note-0123-01a" xlink:href="note-0123-01"/> |
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4089 ſitions ſur leſquelles il s’eſt appuyé pour y trouver <lb/>du paralogiſme: </s> |
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4090 <s xml:id="echoid-s2354" xml:space="preserve">Il y en a trois que voici.</s> |
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4091 <s xml:id="echoid-s2355" xml:space="preserve"/> |
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4092 </p> |
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4093 <div xml:id="echoid-div244" type="float" level="2" n="1"> |
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4094 <note position="right" xlink:label="note-0123-01" xlink:href="note-0123-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4095 </div> |
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4096 <p> |
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4097 <s xml:id="echoid-s2356" xml:space="preserve">1°. </s> |
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4098 <s xml:id="echoid-s2357" xml:space="preserve">Dans la Critique qu’il a faite du premier de <lb/>ces raiſonnemens, qui paroît être du P. </s> |
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4099 <s xml:id="echoid-s2358" xml:space="preserve">Pardie, <lb/>aprés avoir dit que, ſi l’on regarde la corde AC com-<lb/>me une verge de fer mobile autour du point fixe A, <lb/> |
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4100 <anchor type="note" xlink:label="note-0123-02a" xlink:href="note-0123-02"/> |
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4101 à laquelle le poids T ſoit attaché, ce poids ſera ſou-<lb/>tenu avec cette verge par ce point fixe, de même que <lb/>ſur un plan CI perpendiculaire à AC; </s> |
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4102 <s xml:id="echoid-s2359" xml:space="preserve">il fait IL per-<lb/>pendiculaire à l’horizontale LC, & </s> |
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4103 <s xml:id="echoid-s2360" xml:space="preserve">(pag. </s> |
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4104 <s xml:id="echoid-s2361" xml:space="preserve">139.) </s> |
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4105 <s xml:id="echoid-s2362" xml:space="preserve">il <lb/>dit: </s> |
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4106 <s xml:id="echoid-s2363" xml:space="preserve">patet quod pondus T.</s> |
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4107 <s xml:id="echoid-s2364" xml:space="preserve">..</s> |
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4108 <s xml:id="echoid-s2365" xml:space="preserve">..</s> |
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4109 <s xml:id="echoid-s2366" xml:space="preserve">..</s> |
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4110 <s xml:id="echoid-s2367" xml:space="preserve">. ad vim quâ idem T inni-<lb/>titur, & </s> |
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4111 <s xml:id="echoid-s2368" xml:space="preserve">comprimit idem planum IC, eſt ut IC ad LC.</s> |
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4112 <s xml:id="echoid-s2369" xml:space="preserve"/> |
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4113 </p> |
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4114 <div xml:id="echoid-div245" type="float" level="2" n="2"> |
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4115 <note position="right" xlink:label="note-0123-02" xlink:href="note-0123-02a" xml:space="preserve">ſig. 2.</note> |
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4116 </div> |
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4117 <p> |
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4118 <s xml:id="echoid-s2370" xml:space="preserve">2°. </s> |
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4119 <s xml:id="echoid-s2371" xml:space="preserve">Dans la Critique qu’il fait enſuite du rai-<lb/>ſonnement de Hérigone, de Stévin, &</s> |
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4120 <s xml:id="echoid-s2372" xml:space="preserve">c. </s> |
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4121 <s xml:id="echoid-s2373" xml:space="preserve">aprés <lb/> |
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4122 <anchor type="note" xlink:label="note-0123-03a" xlink:href="note-0123-03"/> |
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4123 avoir regardé le poids T ſoutenu par les cordes AC <lb/>& </s> |
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4124 <s xml:id="echoid-s2374" xml:space="preserve">BC, comme s’il l’étoit ſur les plans CK perpendi-<lb/>culaire à AC, & </s> |
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4125 <s xml:id="echoid-s2375" xml:space="preserve">CG perpendiculaire à CB, inéga-<lb/>lement inclinez, il dit (pag. </s> |
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4126 <s xml:id="echoid-s2376" xml:space="preserve">141.) </s> |
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4127 <s xml:id="echoid-s2377" xml:space="preserve">Tunc pondus T <lb/>dum moveri niteretur per duas rectas inclinatas CK & </s> |
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4128 <s xml:id="echoid-s2378" xml:space="preserve">CG, <lb/>cogeretur moveri, aut niſum exercere per diagonalem CO <lb/>ſecantem angulum GCK bifariam.</s> |
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4129 <s xml:id="echoid-s2379" xml:space="preserve"/> |
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4130 </p> |
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4131 <div xml:id="echoid-div246" type="float" level="2" n="3"> |
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4132 <note position="right" xlink:label="note-0123-03" xlink:href="note-0123-03a" xml:space="preserve">ſig. 3.</note> |
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4133 </div> |
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4134 <p> |
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4135 <s xml:id="echoid-s2380" xml:space="preserve">Outre cette ſuppoſition, M. </s> |
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4136 <s xml:id="echoid-s2381" xml:space="preserve">Borelli ſe ſert en-<lb/>core ici de la premiére qu’il a déja faite contre le <lb/>P. </s> |
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4137 <s xml:id="echoid-s2382" xml:space="preserve">Pardie. </s> |
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4138 <s xml:id="echoid-s2383" xml:space="preserve">Il dit (pag. </s> |
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4139 <s xml:id="echoid-s2384" xml:space="preserve">141.) </s> |
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4140 <s xml:id="echoid-s2385" xml:space="preserve">aprés avoir fait CP <lb/>perpendiculaire à l’horizontale KG: </s> |
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4141 <s xml:id="echoid-s2386" xml:space="preserve">Idem pondus ab-<lb/>ſolutum T ad vim, quâ comprimit planum CO, eandem <lb/>rationem babebit quàm CO ad OP.</s> |
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4142 <s xml:id="echoid-s2387" xml:space="preserve"/> |
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4143 </p> |
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4144 <p> |
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4145 <s xml:id="echoid-s2388" xml:space="preserve">3°. </s> |
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4146 <s xml:id="echoid-s2389" xml:space="preserve">Enfin ces deux ſuppoſitions ne lui ſuffiſant pas <lb/>encore pour trouver à redire au raiſonnement d’Hé- |
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4147 <pb o="98" file="0124" n="124" rhead="EXAMEN DE L’OPINION"/> |
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4148 rigone, de Stévin, &</s> |
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4149 <s xml:id="echoid-s2390" xml:space="preserve">c. </s> |
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4150 <s xml:id="echoid-s2391" xml:space="preserve">il y en ajoûte une troi-<lb/> |
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4151 <anchor type="note" xlink:label="note-0124-01a" xlink:href="note-0124-01"/> |
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4152 ſiéme qui ne vaut pas mieux. </s> |
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4153 <s xml:id="echoid-s2392" xml:space="preserve">Vis, dit-il au même en-<lb/>droit, quam patitur planum CO à compreſſione ponderis T <lb/>aqualis eſt viribus ambarum potentiarum R & </s> |
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4154 <s xml:id="echoid-s2393" xml:space="preserve">S, quæ <lb/>ſuſtinendo idem pondus in tali ſitu plani CO inclinati vicem <lb/>ſupplent.</s> |
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4155 <s xml:id="echoid-s2394" xml:space="preserve"/> |
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4156 </p> |
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4157 <div xml:id="echoid-div247" type="float" level="2" n="4"> |
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4158 <note position="left" xlink:label="note-0124-01" xlink:href="note-0124-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4159 </div> |
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4160 <p style="it"> |
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4161 <s xml:id="echoid-s2395" xml:space="preserve">On ne démontre point ici la fauſſeté de toutes ces ſup-<lb/>poſitions: </s> |
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4162 <s xml:id="echoid-s2396" xml:space="preserve">elle eſt trop évidente par la propoſition des Sur-<lb/>faces du Projet précédent, pour s’y arrêter davantage. <lb/></s> |
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4163 <s xml:id="echoid-s2397" xml:space="preserve">D’ailleurs c’eſt, ce me ſemble, avoir ſuffiſamment répondu <lb/>à M. </s> |
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4164 <s xml:id="echoid-s2398" xml:space="preserve">Borelli que d’avoir démontré, comme l’on vient de <lb/>faire, le ſentiment d’Hérigone, de Stévin, &</s> |
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4165 <s xml:id="echoid-s2399" xml:space="preserve">c. </s> |
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4166 <s xml:id="echoid-s2400" xml:space="preserve">par la <lb/>Propoſition même que cet Autbeur croyoit leur être contraire: </s> |
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4167 <s xml:id="echoid-s2401" xml:space="preserve"><lb/>c’eſt auſſi tout ce qu’on s’étoit propoſé dans ce premier Cba-<lb/>pitre; </s> |
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4168 <s xml:id="echoid-s2402" xml:space="preserve">paſſons au ſecond.</s> |
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4169 <s xml:id="echoid-s2403" xml:space="preserve"/> |
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4170 </p> |
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4171 <figure> |
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4172 <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0124-01"/> |
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4173 </figure> |
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4174 <pb o="99" file="0125" n="125" rhead="DE M. BORELLI"/> |
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4175 <figure> |
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4176 <image file="0125-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-01"/> |
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4177 </figure> |
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4178 </div> |
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4179 <div xml:id="echoid-div249" type="section" level="1" n="160"> |
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4180 <head xml:id="echoid-head160" xml:space="preserve">CHAPITRE II. <lb/>NOUVELLES DEMONSTRATIONS <lb/>du ſentiment d’Hérigone, de Stévin, &c.</head> |
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4181 <head xml:id="echoid-head161" xml:space="preserve">Sur les propriétez des poids ſuspendus par <lb/>des cordes.</head> |
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4182 <head xml:id="echoid-head162" xml:space="preserve">AVEC QUELQUES PROPOSITIONS <lb/>de M. Borelli renduës par la méthode du Projet <lb/>précédent beaucoup plus générales qu’elles <lb/>ne le peuvent être par la ſienne.</head> |
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4183 <figure> |
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4184 <image file="0125-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0125-02"/> |
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4185 </figure> |
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4186 </div> |
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4187 <div xml:id="echoid-div250" type="section" level="1" n="161"> |
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4188 <head xml:id="echoid-head163" xml:space="preserve">AVER TISSEMENT.</head> |
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4189 <p style="it"> |
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4190 <s xml:id="echoid-s2404" xml:space="preserve">LE Poids T étant ſoutenu par deux, ou pluſieurs puiſ-<lb/>ſances R, S, &</s> |
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4191 <s xml:id="echoid-s2405" xml:space="preserve">c. </s> |
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4192 <s xml:id="echoid-s2406" xml:space="preserve">Si des extrémitez G, H, &</s> |
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4193 <s xml:id="echoid-s2407" xml:space="preserve">c. </s> |
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4194 <s xml:id="echoid-s2408" xml:space="preserve">des <lb/> |
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4195 <anchor type="note" xlink:label="note-0125-01a" xlink:href="note-0125-01"/> |
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4196 parties CG, CH, &</s> |
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4197 <s xml:id="echoid-s2409" xml:space="preserve">c. </s> |
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4198 <s xml:id="echoid-s2410" xml:space="preserve">de leurs cordes qui leur ſoient pro-<lb/>portionnelles, on fait GP, HQ, &</s> |
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4199 <s xml:id="echoid-s2411" xml:space="preserve">c. </s> |
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4200 <s xml:id="echoid-s2412" xml:space="preserve">perpendiculaires ſur <lb/>ſa ligne de direction CD; </s> |
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4201 <s xml:id="echoid-s2413" xml:space="preserve">elles y déſigncront depuis leurs <lb/>points de rencontre P, Q, &</s> |
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4202 <s xml:id="echoid-s2414" xml:space="preserve">c. </s> |
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4203 <s xml:id="echoid-s2415" xml:space="preserve">juſqu’au point C ou cette <lb/>ligne concourt avec ces cordes, certaines parties CP, CQ <lb/>&</s> |
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4204 <s xml:id="echoid-s2416" xml:space="preserve">c. </s> |
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4205 <s xml:id="echoid-s2417" xml:space="preserve">d@nt nous parlerons ſouvent dans la ſuite; </s> |
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4206 <s xml:id="echoid-s2418" xml:space="preserve">C’eſt pour-<lb/>quoy nous leur allons donner des noms.</s> |
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4207 <s xml:id="echoid-s2419" xml:space="preserve"/> |
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4208 </p> |
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4209 <div xml:id="echoid-div250" type="float" level="2" n="1"> |
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4210 <note position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">ſig. 4. <lb/>5.</note> |
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4211 </div> |
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4212 <pb o="100" file="0126" n="126" rhead="EXAMEN DE L’OPINION"/> |
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4213 </div> |
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4214 <div xml:id="echoid-div252" type="section" level="1" n="162"> |
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4215 <head xml:id="echoid-head164" xml:space="preserve"><emph style="sc">Definition</emph> I.</head> |
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4216 <note position="left" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4217 <p> |
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4218 <s xml:id="echoid-s2420" xml:space="preserve">Lorſque ces parties CP, CQ, &</s> |
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4219 <s xml:id="echoid-s2421" xml:space="preserve">c. </s> |
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4220 <s xml:id="echoid-s2422" xml:space="preserve">ſe trouveront <lb/>au-deſſus du point C, nous les appellerons les ſublimitez <lb/>des puiſſances qui les auront déterminées par leurs <lb/>proportionnelles.</s> |
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4221 <s xml:id="echoid-s2423" xml:space="preserve"/> |
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4222 </p> |
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4223 </div> |
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4224 <div xml:id="echoid-div253" type="section" level="1" n="163"> |
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4225 <head xml:id="echoid-head165" xml:space="preserve"><emph style="sc">Definition</emph> II.</head> |
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4226 <p> |
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4227 <s xml:id="echoid-s2424" xml:space="preserve">Et celles de ces lignes qui ſe trouveront au-deſſous <lb/>de ce même point C, nous les appellerons les Pro-<lb/>fondeurs de ces mêmes puiſſances.</s> |
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4228 <s xml:id="echoid-s2425" xml:space="preserve"/> |
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4229 </p> |
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4230 <p> |
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4231 <s xml:id="echoid-s2426" xml:space="preserve">Selon ces définitions C P eſt la Sublimité de la puiſſance R <lb/>dans les fig. </s> |
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4232 <s xml:id="echoid-s2427" xml:space="preserve">4. </s> |
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4233 <s xml:id="echoid-s2428" xml:space="preserve">& </s> |
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4234 <s xml:id="echoid-s2429" xml:space="preserve">5. </s> |
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4235 <s xml:id="echoid-s2430" xml:space="preserve">CL eſt encore la Sublimité de la <lb/>puiſſance S dans la fig. </s> |
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4236 <s xml:id="echoid-s2431" xml:space="preserve">4. </s> |
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4237 <s xml:id="echoid-s2432" xml:space="preserve">Mais dans la fig. </s> |
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4238 <s xml:id="echoid-s2433" xml:space="preserve">5. </s> |
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4239 <s xml:id="echoid-s2434" xml:space="preserve">CL eſt la <lb/>Profondeur de cette mème puiſſance.</s> |
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4240 <s xml:id="echoid-s2435" xml:space="preserve"/> |
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4241 </p> |
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4242 <p style="it"> |
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4243 <s xml:id="echoid-s2436" xml:space="preserve">On avertit encore que lorſqu’on comparera à la ſublimi-<lb/>té, ou à la profondeur de ces puiſſances, des parties de leurs <lb/>cordes qui leur ſoient proportionnelles, on ne l’entendra pas <lb/>indiffèremment de toutes les proportionnelles qu’on pouroit <lb/>leur aſſigner; </s> |
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4244 <s xml:id="echoid-s2437" xml:space="preserve">mais ſeulement de celles qui déterminent les ſu-<lb/>blimitez, ou les profondeurs en queſtion.</s> |
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4245 <s xml:id="echoid-s2438" xml:space="preserve"/> |
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4246 </p> |
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4247 <figure> |
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4248 <image file="0126-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-01"/> |
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4249 </figure> |
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4250 </div> |
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4251 <div xml:id="echoid-div254" type="section" level="1" n="164"> |
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4252 <head xml:id="echoid-head166" xml:space="preserve">PROPOSITION I.</head> |
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4253 <p style="it"> |
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4254 <s xml:id="echoid-s2439" xml:space="preserve">LE poids T ſoutenu avec les cordes AC & </s> |
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4255 <s xml:id="echoid-s2440" xml:space="preserve">BC par les <lb/> |
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4256 <anchor type="note" xlink:label="note-0126-02a" xlink:href="note-0126-02"/> |
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4257 puiſſances R & </s> |
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4258 <s xml:id="echoid-s2441" xml:space="preserve">S, & </s> |
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4259 <s xml:id="echoid-s2442" xml:space="preserve">en équilibre avec elles, eſt tou-<lb/>jours à chacune d’elles, comme la partie DC de ſa ligne de ái-<lb/>rection, à chacun des còtez GC & </s> |
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4260 <s xml:id="echoid-s2443" xml:space="preserve">HC du parallelogramme <lb/>GH, dont elle eſt diagonale.</s> |
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4261 <s xml:id="echoid-s2444" xml:space="preserve"/> |
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4262 </p> |
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4263 <div xml:id="echoid-div254" type="float" level="2" n="1"> |
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4264 <note position="left" xlink:label="note-0126-02" xlink:href="note-0126-02a" xml:space="preserve">ſig. 4. <lb/>5. <lb/>6. <lb/>7.</note> |
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4265 </div> |
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4266 <figure> |
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4267 <image file="0126-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0126-02"/> |
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4268 </figure> |
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4269 <pb o="101" file="0127" n="127" rhead="DE M. BORELLI."/> |
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4270 </div> |
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4271 <div xml:id="echoid-div256" type="section" level="1" n="165"> |
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4272 <head xml:id="echoid-head167" xml:space="preserve"><emph style="sc">Demonstrations.</emph></head> |
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4273 <note position="right" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4274 <p> |
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4275 <s xml:id="echoid-s2445" xml:space="preserve">1°. </s> |
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4276 <s xml:id="echoid-s2446" xml:space="preserve">Voyez celle qu’on a donnée de cette même <lb/>propoſition dans le Projet précédent.</s> |
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4277 <s xml:id="echoid-s2447" xml:space="preserve"/> |
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4278 </p> |
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4279 <p> |
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4280 <s xml:id="echoid-s2448" xml:space="preserve">2°. </s> |
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4281 <s xml:id="echoid-s2449" xml:space="preserve">Voyez ci-aprés la Remarque qui ſuitle Corol-<lb/>laire de la Prop. </s> |
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4282 <s xml:id="echoid-s2450" xml:space="preserve">3.</s> |
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4283 <s xml:id="echoid-s2451" xml:space="preserve"/> |
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4284 </p> |
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4285 <p> |
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4286 <s xml:id="echoid-s2452" xml:space="preserve">3°. </s> |
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4287 <s xml:id="echoid-s2453" xml:space="preserve">Soient conçûs les leviers MC & </s> |
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4288 <s xml:id="echoid-s2454" xml:space="preserve">NC placez <lb/> |
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4289 <anchor type="note" xlink:label="note-0127-02a" xlink:href="note-0127-02"/> |
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4290 chacun en ligne droite avec chacune des directions <lb/>AC & </s> |
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4291 <s xml:id="echoid-s2455" xml:space="preserve">BC des puiſſances R & </s> |
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4292 <s xml:id="echoid-s2456" xml:space="preserve">S. </s> |
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4293 <s xml:id="echoid-s2457" xml:space="preserve">De leurs points <lb/>d’appui M & </s> |
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4294 <s xml:id="echoid-s2458" xml:space="preserve">N pris à diſcretion, ſoient tirées MF <lb/>& </s> |
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4295 <s xml:id="echoid-s2459" xml:space="preserve">NK perpendiculairement à ces mêmes lignes ré-<lb/>ciproquement priſes, & </s> |
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4296 <s xml:id="echoid-s2460" xml:space="preserve">ML avec NO perpendicu-<lb/>laires auſſi à la ligne de direction DCE de ce même <lb/>poids. </s> |
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4297 <s xml:id="echoid-s2461" xml:space="preserve">Enfin de quelqu’un des points D de cette <lb/>même ligne faite DH & </s> |
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4298 <s xml:id="echoid-s2462" xml:space="preserve">DG paralleles à AC & </s> |
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4299 <s xml:id="echoid-s2463" xml:space="preserve">à <lb/>CB. </s> |
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4300 <s xml:id="echoid-s2464" xml:space="preserve">Cela fait, il eſt clair que le levier CN, étant <lb/>(hyp.) </s> |
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4301 <s xml:id="echoid-s2465" xml:space="preserve">en ligne droite avec la ligne de dìrection CB <lb/>de la puiſſance S, ſupplée néceſſairement tout l’effet <lb/>de cette puiſſance; </s> |
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4302 <s xml:id="echoid-s2466" xml:space="preserve">& </s> |
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4303 <s xml:id="echoid-s2467" xml:space="preserve">que par conſéquent la puiſ-<lb/>ſance R pourroit ſuivant ſa même direction AC ſou-<lb/>tenir ſeule le poids T avec ce levier ainſi placé, de <lb/>même qu’elle le ſoutient préſentement avec la puiſ-<lb/>ſance S. </s> |
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4304 <s xml:id="echoid-s2468" xml:space="preserve">Pour la même raiſon la puiſſance S pourroit <lb/>auſſi le ſoutenir ſeule avec le levier CM, de même <lb/>qu’elle le ſoutient préſentement avec la puiſſance <lb/>R: </s> |
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4305 <s xml:id="echoid-s2469" xml:space="preserve">lepoids T eſt donc ſoutenu par le concours d’ac-<lb/>tion des puiſſances R & </s> |
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4306 <s xml:id="echoid-s2470" xml:space="preserve">S, de même qu’il le ſeroit <lb/>par la ſeule puiſſance R appliquée avec lui au levier <lb/>NC, ou bien par la ſeule puiſſance S appliquée auſſi <lb/>avec lui au levier CM. </s> |
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4307 <s xml:id="echoid-s2471" xml:space="preserve">Or dans le premier cas la <lb/>puiſſance R ſeroit (Prop. </s> |
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4308 <s xml:id="echoid-s2472" xml:space="preserve">fond. </s> |
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4309 <s xml:id="echoid-s2473" xml:space="preserve">des leviers Cor. </s> |
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4310 <s xml:id="echoid-s2474" xml:space="preserve">13. </s> |
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4311 <s xml:id="echoid-s2475" xml:space="preserve">du <lb/>Projet précéd.) </s> |
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4312 <s xml:id="echoid-s2476" xml:space="preserve">au poids T, comme NO à NK; </s> |
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4313 <s xml:id="echoid-s2477" xml:space="preserve">c’eſt-<lb/>à-dire, comme le ſinus de l’angle NCO, ou de |
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4314 <pb o="102" file="0128" n="128" rhead="EXAMEN DE L’OPINION"/> |
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4315 DCH, à celui de l’angle NCK, ou de CHD. </s> |
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4316 <s xml:id="echoid-s2478" xml:space="preserve">Et <lb/> |
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4317 <anchor type="note" xlink:label="note-0128-01a" xlink:href="note-0128-01"/> |
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4318 dans le ſecond cas le poids T, pour la même raiſon, <lb/>ſeroit à la puiſſance S, comme MF à ML; </s> |
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4319 <s xml:id="echoid-s2479" xml:space="preserve">c’eſt-à-dire <lb/>encore, comme le ſinus de l’angle MCF, ou de CHD, <lb/>à celui de l’angle MCL, ou de HDC: </s> |
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4320 <s xml:id="echoid-s2480" xml:space="preserve">Donc la puiſ-<lb/>ſance R, le poids T, & </s> |
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4321 <s xml:id="echoid-s2481" xml:space="preserve">la puiſſance S, ſont entr’eux, <lb/>comme les ſinus des angles DCH, CHD, & </s> |
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4322 <s xml:id="echoid-s2482" xml:space="preserve">HDC; <lb/></s> |
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4323 <s xml:id="echoid-s2483" xml:space="preserve">c’eſt-à-dire, ( Demm. </s> |
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4324 <s xml:id="echoid-s2484" xml:space="preserve">5. </s> |
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4325 <s xml:id="echoid-s2485" xml:space="preserve">du Projet précéd.) </s> |
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4326 <s xml:id="echoid-s2486" xml:space="preserve">comme les <lb/>lignes DH, CD, & </s> |
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4327 <s xml:id="echoid-s2487" xml:space="preserve">CH: </s> |
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4328 <s xml:id="echoid-s2488" xml:space="preserve">Le poids T eſt done à la <lb/>puiſſance R, comme CD à DH, ou à CG; </s> |
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4329 <s xml:id="echoid-s2489" xml:space="preserve">& </s> |
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4330 <s xml:id="echoid-s2490" xml:space="preserve">à la <lb/>puiſſance S, comme la même CD à CH. </s> |
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4331 <s xml:id="echoid-s2491" xml:space="preserve">Ce qu’il faloit <lb/>démontrer.</s> |
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4332 <s xml:id="echoid-s2492" xml:space="preserve"/> |
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4333 </p> |
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4334 <div xml:id="echoid-div256" type="float" level="2" n="1"> |
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4335 <note position="right" xlink:label="note-0127-02" xlink:href="note-0127-02a" xml:space="preserve">fig. 4. <lb/>5.</note> |
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4336 <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">DES POIDS <lb/>foutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4337 </div> |
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4338 <p> |
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4339 <s xml:id="echoid-s2493" xml:space="preserve">4°. </s> |
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4340 <s xml:id="echoid-s2494" xml:space="preserve">Si au lieu des puiſſances R & </s> |
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4341 <s xml:id="echoid-s2495" xml:space="preserve">S, les cordes AC <lb/>& </s> |
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4342 <s xml:id="echoid-s2496" xml:space="preserve">BC étoient attachees aux extrémitez de quelque le-<lb/>vier AB, dont l’appui D fut dans la ligne direction de <lb/> |
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4343 <anchor type="note" xlink:label="note-0128-02a" xlink:href="note-0128-02"/> |
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4344 DCE du poids T. </s> |
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4345 <s xml:id="echoid-s2497" xml:space="preserve">Il eſt clair qu’en quelque fitua-<lb/>tion que ce levier ſe trouvât alors, (Lemm. </s> |
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4346 <s xml:id="echoid-s2498" xml:space="preserve">@. </s> |
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4347 <s xml:id="echoid-s2499" xml:space="preserve">du <lb/>Projet précéd.) </s> |
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4348 <s xml:id="echoid-s2500" xml:space="preserve">il y demeureroit, & </s> |
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4349 <s xml:id="echoid-s2501" xml:space="preserve">que la charge de <lb/>ſon point d’appui ſeroit alors égale au poids T. </s> |
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4350 <s xml:id="echoid-s2502" xml:space="preserve">Il <lb/>eſt encore clair que les extrémitez A & </s> |
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4351 <s xml:id="echoid-s2503" xml:space="preserve">B de ce mê-<lb/>me levier ſeroient auſſi tirées ſuivant AC & </s> |
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4352 <s xml:id="echoid-s2504" xml:space="preserve">BC, <lb/>chacune avec une force égale à celle de la puiſſance <lb/>R, ou S qu’elle ſupplée. </s> |
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4353 <s xml:id="echoid-s2505" xml:space="preserve">Or les forces avec leſquelles <lb/>les points A & </s> |
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4354 <s xml:id="echoid-s2506" xml:space="preserve">B de ce levier ſeroient ainſi tirez ſui-<lb/>vant AC & </s> |
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4355 <s xml:id="echoid-s2507" xml:space="preserve">BC, ſeroient entr’elles, ( Cor. </s> |
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4356 <s xml:id="echoid-s2508" xml:space="preserve">13. </s> |
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4357 <s xml:id="echoid-s2509" xml:space="preserve">prop. <lb/></s> |
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4358 <s xml:id="echoid-s2510" xml:space="preserve">fond. </s> |
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4359 <s xml:id="echoid-s2511" xml:space="preserve">des leviers du Projet précéd.) </s> |
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4360 <s xml:id="echoid-s2512" xml:space="preserve">comme DF & </s> |
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4361 <s xml:id="echoid-s2513" xml:space="preserve">DK <lb/>tirées du point D perpendiculairement ſur BC & </s> |
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4362 <s xml:id="echoid-s2514" xml:space="preserve"><lb/>AC; </s> |
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4363 <s xml:id="echoid-s2515" xml:space="preserve">c’eſt-à-dire, en faiſant le parallelogramme GH, <lb/>comme les ſinus des angles DCH & </s> |
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4364 <s xml:id="echoid-s2516" xml:space="preserve">CDH, ou <lb/>(Lemm. </s> |
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4365 <s xml:id="echoid-s2517" xml:space="preserve">5. </s> |
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4366 <s xml:id="echoid-s2518" xml:space="preserve">du Proiet précéd.) </s> |
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4367 <s xml:id="echoid-s2519" xml:space="preserve">comme les côtez DH & </s> |
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4368 <s xml:id="echoid-s2520" xml:space="preserve"><lb/>HC de ce parallelogramme. </s> |
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4369 <s xml:id="echoid-s2521" xml:space="preserve">Ces mêmes forces ſe-<lb/>roient auſſi ( Cor. </s> |
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4370 <s xml:id="echoid-s2522" xml:space="preserve">4. </s> |
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4371 <s xml:id="echoid-s2523" xml:space="preserve">Prop. </s> |
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4372 <s xml:id="echoid-s2524" xml:space="preserve">fond. </s> |
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4373 <s xml:id="echoid-s2525" xml:space="preserve">des leviers au Projet <lb/>précèd.) </s> |
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4374 <s xml:id="echoid-s2526" xml:space="preserve">chacune à la charge du point d’appui D de <lb/>ce levier, c’eſt-à-dire, au poids T, comme chacun |
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4375 <pb o="103" file="0129" n="129" rhead="DE M. BORELLI."/> |
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4376 ces de mêmes côtez à la diagonale DC: </s> |
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4377 <s xml:id="echoid-s2527" xml:space="preserve">les forces <lb/> |
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4378 <anchor type="note" xlink:label="note-0129-01a" xlink:href="note-0129-01"/> |
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4379 des puiſſances R & </s> |
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4380 <s xml:id="echoid-s2528" xml:space="preserve">S, c’eſt-à-dire, ces mêmes puiſ-<lb/>ſances, elles-mêmes, ſont donc entr’elles, comme <lb/>DH, ou GC & </s> |
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4381 <s xml:id="echoid-s2529" xml:space="preserve">HC; </s> |
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4382 <s xml:id="echoid-s2530" xml:space="preserve">& </s> |
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4383 <s xml:id="echoid-s2531" xml:space="preserve">au poids T, comme chacun <lb/>de ces mêmes côtez du parallelogramme GH, à ſa <lb/>diagonale DC. </s> |
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4384 <s xml:id="echoid-s2532" xml:space="preserve">Cequ’il faloit démontrer.</s> |
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4385 <s xml:id="echoid-s2533" xml:space="preserve"/> |
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4386 </p> |
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4387 <div xml:id="echoid-div257" type="float" level="2" n="2"> |
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4388 <note position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">fig. 6. <lb/>7.</note> |
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4389 <note position="right" xlink:label="note-0129-01" xlink:href="note-0129-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement</note> |
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4390 </div> |
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4391 <p style="it"> |
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4392 <s xml:id="echoid-s2534" xml:space="preserve">On pourroit encore démontrer cette mème Propoſition en <lb/>ſe ſervant des plans inclinez, pourvû qu’on en prit un qui <lb/>fut perpendiculaire à la direction de quelqu’une des deux <lb/>puiſſances qui ſoutiennent ce poids: </s> |
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4393 <s xml:id="echoid-s2535" xml:space="preserve">Car cette puiſſance & </s> |
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4394 <s xml:id="echoid-s2536" xml:space="preserve"><lb/>la cbarge de ce plan alors égales, n’ayant qu’un mème <lb/>rapport avec ce poids, non plus qu’avec l’autre puiſſance <lb/>qu’on conſidére en ce cas comme le ſoutenant ſeule ſur ce plan; <lb/></s> |
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4395 <s xml:id="echoid-s2537" xml:space="preserve">on trouveroit par le Cor. </s> |
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4396 <s xml:id="echoid-s2538" xml:space="preserve">7. </s> |
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4397 <s xml:id="echoid-s2539" xml:space="preserve">de la Prop. </s> |
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4398 <s xml:id="echoid-s2540" xml:space="preserve">des Surfaces du <lb/>Projet précédent, que ce poids eſt toujours à chacune de ces <lb/>puiſſances, comme le ſinus de l’angle que leurs cordes font <lb/>entr’elles, à chacun des ſinus des angles que font avec la <lb/>ligne de direction de ce poids chacune de ces cordes récipro-<lb/>quement priſes. </s> |
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4399 <s xml:id="echoid-s2541" xml:space="preserve">Tout cela eſt préſentement trop clair pour <lb/>s’y arréter davantage.</s> |
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4400 <s xml:id="echoid-s2542" xml:space="preserve"/> |
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4401 </p> |
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4402 </div> |
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4403 <div xml:id="echoid-div259" type="section" level="1" n="166"> |
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4404 <head xml:id="echoid-head168" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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4405 <p> |
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4406 <s xml:id="echoid-s2543" xml:space="preserve">On peut conclure généralement de ces démon-<lb/> |
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4407 <anchor type="note" xlink:label="note-0129-02a" xlink:href="note-0129-02"/> |
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4408 ſtrations, ce que nous n’avons conclu ( chap. </s> |
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4409 <s xml:id="echoid-s2544" xml:space="preserve">1.) </s> |
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4410 <s xml:id="echoid-s2545" xml:space="preserve">dela <lb/>68. </s> |
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4411 <s xml:id="echoid-s2546" xml:space="preserve">Propoſition de M. </s> |
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4412 <s xml:id="echoid-s2547" xml:space="preserve">Borelli, quepour les cas qu’elle <lb/>comprend: </s> |
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4413 <s xml:id="echoid-s2548" xml:space="preserve">Sçavoir qu’il n’y en à aucun de poſſible, <lb/>ou l’on puiſſe conſerver l’équilibre du poids T avec <lb/>les puiſſances R & </s> |
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4414 <s xml:id="echoid-s2549" xml:space="preserve">S, en changeant le rapport qu’elles <lb/>ont entr’elles, ou avec lui; </s> |
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4415 <s xml:id="echoid-s2550" xml:space="preserve">à moins qu’on ne change <lb/>en même-tems l’inclinaiſon de leurs cordes: </s> |
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4416 <s xml:id="echoid-s2551" xml:space="preserve">non plus <lb/>qu’en changeant l’inclinaiſon de ces cordes, ſans <lb/>changer auſſi le rapport de ces mêmes puiſſances, <lb/>ou entr’elles, ou avec ce poids: </s> |
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4417 <s xml:id="echoid-s2552" xml:space="preserve">parce que ſans cela <lb/>il n’eſt pas poſſible de faire que chacun des côtez CH |
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4418 <pb o="104" file="0130" n="130" rhead="EXAMEN DE L’OPINION"/> |
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4419 & </s> |
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4420 <s xml:id="echoid-s2553" xml:space="preserve">CG du parallelogramme GH, continuë d’être à ſa <lb/> |
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4421 <anchor type="note" xlink:label="note-0130-01a" xlink:href="note-0130-01"/> |
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4422 diagonale DC, comme chacune des puiſſances R & </s> |
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4423 <s xml:id="echoid-s2554" xml:space="preserve">S <lb/>au poids T; </s> |
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4424 <s xml:id="echoid-s2555" xml:space="preserve">ce qui doit cependant être, comme onle <lb/>vient de voir, pour qu’elles faſſent équilibre avec lui.</s> |
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4425 <s xml:id="echoid-s2556" xml:space="preserve"/> |
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4426 </p> |
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4427 <div xml:id="echoid-div259" type="float" level="2" n="1"> |
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4428 <note position="right" xlink:label="note-0129-02" xlink:href="note-0129-02a" xml:space="preserve">fig. 4. <lb/>5. <lb/>6. <lb/>7.</note> |
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4429 <note position="left" xlink:label="note-0130-01" xlink:href="note-0130-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4430 </div> |
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4431 <p style="it"> |
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4432 <s xml:id="echoid-s2557" xml:space="preserve">On peut comparer ce Corollaire aux Scholies des Pro-<lb/>poſitions 68. </s> |
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4433 <s xml:id="echoid-s2558" xml:space="preserve">& </s> |
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4434 <s xml:id="echoid-s2559" xml:space="preserve">69. </s> |
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4435 <s xml:id="echoid-s2560" xml:space="preserve">M. </s> |
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4436 <s xml:id="echoid-s2561" xml:space="preserve">Borelli.</s> |
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4437 <s xml:id="echoid-s2562" xml:space="preserve"/> |
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4438 </p> |
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4439 </div> |
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4440 <div xml:id="echoid-div261" type="section" level="1" n="167"> |
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4441 <head xml:id="echoid-head169" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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4442 <p> |
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4443 <s xml:id="echoid-s2563" xml:space="preserve">Il ſuit encore de ces démonſtrations que chacune <lb/>des puiſſances R & </s> |
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4444 <s xml:id="echoid-s2564" xml:space="preserve">S eſt au poids T, comme chacune <lb/> |
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4445 <anchor type="note" xlink:label="note-0130-02a" xlink:href="note-0130-02"/> |
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4446 des parties GC & </s> |
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4447 <s xml:id="echoid-s2565" xml:space="preserve">HC de leurs cordes, qui leurs ſont <lb/>proportionelles, à la ſomme ( fig. </s> |
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4448 <s xml:id="echoid-s2566" xml:space="preserve">4.) </s> |
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4449 <s xml:id="echoid-s2567" xml:space="preserve">de leurs ſublimi-<lb/>tez, ou à la difference (fig. </s> |
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4450 <s xml:id="echoid-s2568" xml:space="preserve">5.) </s> |
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4451 <s xml:id="echoid-s2569" xml:space="preserve">quieſt entre la ſublimité <lb/>de l’une & </s> |
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4452 <s xml:id="echoid-s2570" xml:space="preserve">la profondeur de l’autre: </s> |
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4453 <s xml:id="echoid-s2571" xml:space="preserve">parce que dans <lb/>le parallelogramme GH les angles GCD & </s> |
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4454 <s xml:id="echoid-s2572" xml:space="preserve">CDH <lb/>étant égaux, auſſi-bien que les lignes GC & </s> |
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4455 <s xml:id="echoid-s2573" xml:space="preserve">DH; <lb/></s> |
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4456 <s xml:id="echoid-s2574" xml:space="preserve">de plus les angles qui ſe font en P & </s> |
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4457 <s xml:id="echoid-s2575" xml:space="preserve">en Q, étant auſſi <lb/>(avert.) </s> |
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4458 <s xml:id="echoid-s2576" xml:space="preserve">égaux, les triangles GPC & </s> |
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4459 <s xml:id="echoid-s2577" xml:space="preserve">HQD ſont <lb/>non ſeulement ſemblables, mais encore leurs côtez <lb/>CP & </s> |
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4460 <s xml:id="echoid-s2578" xml:space="preserve">DQ ſont égaux: </s> |
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4461 <s xml:id="echoid-s2579" xml:space="preserve">Donc (fig. </s> |
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4462 <s xml:id="echoid-s2580" xml:space="preserve">4.) </s> |
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4463 <s xml:id="echoid-s2581" xml:space="preserve">CP plus CQ <lb/>eſt égal à DQ plus CQ, & </s> |
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4464 <s xml:id="echoid-s2582" xml:space="preserve">( fig. </s> |
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4465 <s xml:id="echoid-s2583" xml:space="preserve">5.) </s> |
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4466 <s xml:id="echoid-s2584" xml:space="preserve">CP moins CQ <lb/>ſera auſſi égal à DQ moins CQ. </s> |
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4467 <s xml:id="echoid-s2585" xml:space="preserve">Or ( fig. </s> |
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4468 <s xml:id="echoid-s2586" xml:space="preserve">4.) </s> |
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4469 <s xml:id="echoid-s2587" xml:space="preserve">DQ <lb/>plus CQ eſt égal à CD, de même (fig. </s> |
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4470 <s xml:id="echoid-s2588" xml:space="preserve">5.) </s> |
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4471 <s xml:id="echoid-s2589" xml:space="preserve">que <lb/>DQ moins CQ: </s> |
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4472 <s xml:id="echoid-s2590" xml:space="preserve">Donc ( fig. </s> |
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4473 <s xml:id="echoid-s2591" xml:space="preserve">4.) </s> |
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4474 <s xml:id="echoid-s2592" xml:space="preserve">CP plus CQ eſt égal <lb/>à CD, auſſi-bien (fig. </s> |
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4475 <s xml:id="echoid-s2593" xml:space="preserve">5.) </s> |
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4476 <s xml:id="echoid-s2594" xml:space="preserve">que CP moins CQ. </s> |
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4477 <s xml:id="echoid-s2595" xml:space="preserve">Or <lb/>ſelon les démonſtrations précédentes chacune des <lb/>puiſſances R & </s> |
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4478 <s xml:id="echoid-s2596" xml:space="preserve">S eſt au poids T, comme chacune de <lb/>leurs proportionelles CG & </s> |
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4479 <s xml:id="echoid-s2597" xml:space="preserve">HC à CD: </s> |
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4480 <s xml:id="echoid-s2598" xml:space="preserve">Donc cha-<lb/>cune de ces mêmes puiſſances eſt à ce poids, comme <lb/>chacune de ces mêmes proportionelles à CP ( fig. </s> |
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4481 <s xml:id="echoid-s2599" xml:space="preserve">4.) </s> |
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4482 <s xml:id="echoid-s2600" xml:space="preserve"><lb/>plus CQ, ou (fig. </s> |
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4483 <s xml:id="echoid-s2601" xml:space="preserve">5.) </s> |
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4484 <s xml:id="echoid-s2602" xml:space="preserve">à CP moins CQ; </s> |
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4485 <s xml:id="echoid-s2603" xml:space="preserve">c’eſt-à-dire, <lb/>(Def. </s> |
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4486 <s xml:id="echoid-s2604" xml:space="preserve">1. </s> |
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4487 <s xml:id="echoid-s2605" xml:space="preserve">& </s> |
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4488 <s xml:id="echoid-s2606" xml:space="preserve">2.) </s> |
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4489 <s xml:id="echoid-s2607" xml:space="preserve">à la ſomme ( fig. </s> |
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4490 <s xml:id="echoid-s2608" xml:space="preserve">4.) </s> |
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4491 <s xml:id="echoid-s2609" xml:space="preserve">de leurs ſublimitez, <lb/>ou bien ( fig. </s> |
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4492 <s xml:id="echoid-s2610" xml:space="preserve">5.) </s> |
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4493 <s xml:id="echoid-s2611" xml:space="preserve">à la différence qui eſt entre la ſublimi-<lb/>té de l’une & </s> |
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4494 <s xml:id="echoid-s2612" xml:space="preserve">la profondeur de l’autre.</s> |
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4495 <s xml:id="echoid-s2613" xml:space="preserve"/> |
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4496 </p> |
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4497 <div xml:id="echoid-div261" type="float" level="2" n="1"> |
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4498 <note position="left" xlink:label="note-0130-02" xlink:href="note-0130-02a" xml:space="preserve">fig. 4. <lb/>5.</note> |
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4499 </div> |
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4500 <pb o="105" file="0131" n="131" rhead="DE M. BORELLI."/> |
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4501 </div> |
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4502 <div xml:id="echoid-div263" type="section" level="1" n="168"> |
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4503 <head xml:id="echoid-head170" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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4504 <note position="right" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4505 <p> |
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4506 <s xml:id="echoid-s2614" xml:space="preserve">D’où l’on voit que la ſomme des deux puiſſances <lb/>qui ſoutiennent un poids avec des cordes, eſt tou-<lb/>jours à ce poids, comme la ſomme des longueurs de <lb/>leurs cordes, qui leur ſont proportionelles, à la ſomme <lb/>de leurs ſublimitez, ou à la différence qui eſt entre de <lb/>la ſublimité de l’une & </s> |
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4507 <s xml:id="echoid-s2615" xml:space="preserve">la profondeur de l’autre.</s> |
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4508 <s xml:id="echoid-s2616" xml:space="preserve"/> |
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4509 </p> |
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4510 <p style="it"> |
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4511 <s xml:id="echoid-s2617" xml:space="preserve">On peut comparer encore ces deux derniers Corollaires à la <lb/>69. </s> |
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4512 <s xml:id="echoid-s2618" xml:space="preserve">Prop. </s> |
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4513 <s xml:id="echoid-s2619" xml:space="preserve">de M. </s> |
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4514 <s xml:id="echoid-s2620" xml:space="preserve">Borelli, & </s> |
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4515 <s xml:id="echoid-s2621" xml:space="preserve">au Corollaire qu’il entire.</s> |
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4516 <s xml:id="echoid-s2622" xml:space="preserve"/> |
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4517 </p> |
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4518 <figure> |
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4519 <image file="0131-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0131-01"/> |
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4520 </figure> |
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4521 </div> |
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4522 <div xml:id="echoid-div264" type="section" level="1" n="169"> |
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4523 <head xml:id="echoid-head171" xml:space="preserve">PROPOSITION II.</head> |
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4524 <p style="it"> |
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4525 <s xml:id="echoid-s2623" xml:space="preserve">DE quelque maniére qu’un poids T ſoit ſoutenu avee <lb/> |
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4526 <anchor type="note" xlink:label="note-0131-02a" xlink:href="note-0131-02"/> |
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4527 des cordes par quelque nombre de puiſſances A, B, D, <lb/>E, F, & </s> |
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4528 <s xml:id="echoid-s2624" xml:space="preserve">c. </s> |
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4529 <s xml:id="echoid-s2625" xml:space="preserve">que ce ſoit, appliquèes à un même nœud C; </s> |
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4530 <s xml:id="echoid-s2626" xml:space="preserve">ſi l’ on <lb/>prend ſur leurs cordes autant de parties CG, CR, CM, CN, <lb/>CP, &</s> |
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4531 <s xml:id="echoid-s2627" xml:space="preserve">c. </s> |
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4532 <s xml:id="echoid-s2628" xml:space="preserve">qui leurs ſoient proportionelles, & </s> |
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4533 <s xml:id="echoid-s2629" xml:space="preserve">que ſous deux <lb/>de ces parties, par exemple, ſous GC & </s> |
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4534 <s xml:id="echoid-s2630" xml:space="preserve">RC, l’on faſſe un <lb/>parallelogramme RG, dont la diagonale CH faſſe encore <lb/>avecune autre de ces parties CM le parallelogramme HM, <lb/>dont la diagonale CL faſſe encore avec une autre de ces <lb/>parties CN le parallelogramme LN, dont la diagonale <lb/>CQ faſſe encore avec une autre de ces parties CP le paral-<lb/>lelogramme PQ, & </s> |
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4535 <s xml:id="echoid-s2631" xml:space="preserve">ainſi juſqu’à la derniére de ces propor-<lb/>tionelles. </s> |
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4536 <s xml:id="echoid-s2632" xml:space="preserve">On verra 1°. </s> |
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4537 <s xml:id="echoid-s2633" xml:space="preserve">Que la diagonale du dernier de ces <lb/>parallelogrammes, qui eſt ici CK, ſera dans la ligne de di-<lb/>rection du poids T. </s> |
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4538 <s xml:id="echoid-s2634" xml:space="preserve">2°. </s> |
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4539 <s xml:id="echoid-s2635" xml:space="preserve">Et que chacune de ces puiſſances ſera <lb/>à ce poids, comme chacune de ces proportionelles, ſelon qu’el-<lb/>les leurs répoudent, eſt à cette même diagonale.</s> |
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4540 <s xml:id="echoid-s2636" xml:space="preserve"/> |
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4541 </p> |
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4542 <div xml:id="echoid-div264" type="float" level="2" n="1"> |
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4543 <note position="right" xlink:label="note-0131-02" xlink:href="note-0131-02a" xml:space="preserve">fig. 2.</note> |
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4544 </div> |
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4545 </div> |
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4546 <div xml:id="echoid-div266" type="section" level="1" n="170"> |
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4547 <head xml:id="echoid-head172" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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4548 <p> |
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4549 <s xml:id="echoid-s2637" xml:space="preserve">1°. </s> |
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4550 <s xml:id="echoid-s2638" xml:space="preserve">Puiſque ( hyp.) </s> |
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4551 <s xml:id="echoid-s2639" xml:space="preserve">la puiſſance A eſt à la puiſ- |
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4552 <pb o="106" file="0132" n="132" rhead="EXAMEN DE L’OPINION"/> |
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4553 ſance B, comme CG à CR, il réſultera (Lemm. </s> |
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4554 <s xml:id="echoid-s2640" xml:space="preserve">3. </s> |
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4555 <s xml:id="echoid-s2641" xml:space="preserve">du <lb/> |
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4556 <anchor type="note" xlink:label="note-0132-01a" xlink:href="note-0132-01"/> |
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4557 Projet précèd.) </s> |
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4558 <s xml:id="echoid-s2642" xml:space="preserve">de leur concours d’action ſur le point <lb/>C, un@ impreſſion compoſée ſuivant CH, d’une force <lb/>qui ſera (Cor. </s> |
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4559 <s xml:id="echoid-s2643" xml:space="preserve">3. </s> |
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4560 <s xml:id="echoid-s2644" xml:space="preserve">du même Lemm.) </s> |
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4561 <s xml:id="echoid-s2645" xml:space="preserve">à chacune de ces <lb/>puiſſances, comme CH à chacune des lignes CG & </s> |
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4562 <s xml:id="echoid-s2646" xml:space="preserve"><lb/>CR qui les répreſentent: </s> |
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4563 <s xml:id="echoid-s2647" xml:space="preserve">l’impreſſion, que font en-<lb/>ſemble ces deux puiſſances ſur le point C, eſt donc <lb/>la même que celle que feroit ſeule ſur ce même point <lb/>quelque nouvelle puiſſance qui, lui étant appliquée <lb/>ſuivant CH, au lieu d’elles, leur ſeroit à chacune, <lb/>comme CH à chacune des lignes CG & </s> |
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4564 <s xml:id="echoid-s2648" xml:space="preserve">CR: </s> |
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4565 <s xml:id="echoid-s2649" xml:space="preserve">& </s> |
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4566 <s xml:id="echoid-s2650" xml:space="preserve">par <lb/>conſèquent les 3. </s> |
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4567 <s xml:id="echoid-s2651" xml:space="preserve">puiſſances A, B, D, doivent faire <lb/>enſemble la même impreſſion ſur le point C que cette <lb/>nouvelle puiſſance ( je l’appelle H ) feroit alors avec <lb/>la puiſſance D. </s> |
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4568 <s xml:id="echoid-s2652" xml:space="preserve">Or (Lemm 3. </s> |
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4569 <s xml:id="echoid-s2653" xml:space="preserve">du Projet précéd.) </s> |
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4570 <s xml:id="echoid-s2654" xml:space="preserve">l’im-<lb/>preſſion qui réſulteroit alors du concours d’action <lb/>des puiſſances D & </s> |
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4571 <s xml:id="echoid-s2655" xml:space="preserve">H ſur le point C, ſe feroit ſui-<lb/>vant CL, d’une force qui ſeroit (Cor. </s> |
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4572 <s xml:id="echoid-s2656" xml:space="preserve">3. </s> |
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4573 <s xml:id="echoid-s2657" xml:space="preserve">du même <lb/>Lemm.) </s> |
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4574 <s xml:id="echoid-s2658" xml:space="preserve">à celle de la puiſſance D, comme CL à CM: <lb/></s> |
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4575 <s xml:id="echoid-s2659" xml:space="preserve">Donc l’impreſſion compoſée qui réſulte du concours <lb/>d’action des 3. </s> |
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4576 <s xml:id="echoid-s2660" xml:space="preserve">puiſſances A, B, D, ſur le point C, <lb/>ſe fait en effet ſuivant CL, d’une force qui eſt à <lb/>celle de la puiſſance D, comme CL à CM: </s> |
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4577 <s xml:id="echoid-s2661" xml:space="preserve">elles ne <lb/>font donc toutes trois enſemble ſur ce point que la <lb/>même impreſſion que feroit ſeule quelqu’autre puiſ-<lb/>ſance (je l’appelle L) qui appliquée ſuivant CL, au <lb/>lieu de ces trois, ſeroit à la puiſſance D, comme CL <lb/>à CM: </s> |
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4578 <s xml:id="echoid-s2662" xml:space="preserve">& </s> |
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4579 <s xml:id="echoid-s2663" xml:space="preserve">par conſéquent les 4. </s> |
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4580 <s xml:id="echoid-s2664" xml:space="preserve">puiſſances A, B, D, E, <lb/>ne doivent faire ſur le point C que la même impreſ-<lb/>ſion que feroit alors la puiſſance L avec la puiſſance <lb/>E. </s> |
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4581 <s xml:id="echoid-s2665" xml:space="preserve">Or (Lemm. </s> |
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4582 <s xml:id="echoid-s2666" xml:space="preserve">3. </s> |
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4583 <s xml:id="echoid-s2667" xml:space="preserve">du Projet Projet précéd.) </s> |
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4584 <s xml:id="echoid-s2668" xml:space="preserve">l’impreſſion qui <lb/>réſulteroit alors du concours d’action de ces deux <lb/>dernieres puiſſances ſur le point C, ſe feroit ſuivant <lb/>CQ, d’une force qui ſeroit ( Cor. </s> |
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4585 <s xml:id="echoid-s2669" xml:space="preserve">3. </s> |
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4586 <s xml:id="echoid-s2670" xml:space="preserve">du même Lemm.) </s> |
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4587 <s xml:id="echoid-s2671" xml:space="preserve"><lb/>à celle de la puiſſance E, comme CQ à CN: </s> |
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4588 <s xml:id="echoid-s2672" xml:space="preserve">Donc |
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4589 <pb o="107" file="0133" n="133" rhead="DE M. BORELLI."/> |
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4590 l’impreſſion compoſée qui réſulte du concours d’ac-<lb/> |
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4591 <anchor type="note" xlink:label="note-0133-01a" xlink:href="note-0133-01"/> |
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4592 tion des 4. </s> |
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4593 <s xml:id="echoid-s2673" xml:space="preserve">puiſſances A, B, D, E, ſur le point C, <lb/>ſe fait en effet ſuivant la ligne CQ, d’une force qui <lb/>eſt à celle de la puiſſance E, comme CQ à CN. </s> |
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4594 <s xml:id="echoid-s2674" xml:space="preserve">On <lb/>prouvera de même que l’impreſſion compoſée qui <lb/>réſulte du concours d’action des 5. </s> |
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4595 <s xml:id="echoid-s2675" xml:space="preserve">puiſſances A, B, <lb/>D, E, F, ſe fait auſſi ſuivant CK, d’une force qui <lb/>eſt à la puiſſance F, comme CK à CP. </s> |
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4596 <s xml:id="echoid-s2676" xml:space="preserve">Et ainſi tou-<lb/>jours de même juſqu’à la derniére des puiſſances <lb/>appliquées à ce poids: </s> |
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4597 <s xml:id="echoid-s2677" xml:space="preserve">D’où il ſuit que l’impreſſion <lb/>compoſée qui réſulte du concours d’action de toutes <lb/>ces puiſſances ſur le point C, en quelque nombre <lb/>qu’elles ſoient, ſe fait toujours ſuivant la diagonale <lb/>du dernier des parallelogrammes faits comme l’on <lb/>vient de dire, c’eſt-à-dire ici, ſuivant CK: </s> |
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4598 <s xml:id="echoid-s2678" xml:space="preserve">& </s> |
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4599 <s xml:id="echoid-s2679" xml:space="preserve">par <lb/>conſéquent (n. </s> |
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4600 <s xml:id="echoid-s2680" xml:space="preserve">2. </s> |
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4601 <s xml:id="echoid-s2681" xml:space="preserve">Demonſt. </s> |
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4602 <s xml:id="echoid-s2682" xml:space="preserve">Prop. </s> |
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4603 <s xml:id="echoid-s2683" xml:space="preserve">fond. </s> |
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4604 <s xml:id="echoid-s2684" xml:space="preserve">des poids ſoutenus <lb/>par des cordes du Projet précéd.) </s> |
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4605 <s xml:id="echoid-s2685" xml:space="preserve">cette diagonale eſt <lb/>toujours en ligne droite avec CT, c’eſt-à-dire, dans <lb/>la ligne de direction du poids T. </s> |
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4606 <s xml:id="echoid-s2686" xml:space="preserve">Ce qu’il faloit dé-<lb/>montrer.</s> |
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4607 <s xml:id="echoid-s2687" xml:space="preserve"/> |
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4608 </p> |
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4609 <div xml:id="echoid-div266" type="float" level="2" n="1"> |
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4610 <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſcu-<lb/>lement.</note> |
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4611 <note position="right" xlink:label="note-0133-01" xlink:href="note-0133-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4612 </div> |
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4613 <p> |
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4614 <s xml:id="echoid-s2688" xml:space="preserve">2°. </s> |
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4615 <s xml:id="echoid-s2689" xml:space="preserve">On vient de voir que le poids T eſt ſoutenu <lb/>par les puiſſances A, B, D, E, F, &</s> |
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4616 <s xml:id="echoid-s2690" xml:space="preserve">c. </s> |
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4617 <s xml:id="echoid-s2691" xml:space="preserve">De même qu’il <lb/>le ſeroit, par exemple ici, par la puiſſance F aidée <lb/>d’une autre appliquée ſuivant CQ, à qui elle ſeroit <lb/>comme CP à CQ ( les directions de toutes demeu-<lb/>rant toujours les mêmes): </s> |
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4618 <s xml:id="echoid-s2692" xml:space="preserve">Donc (prop. </s> |
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4619 <s xml:id="echoid-s2693" xml:space="preserve">1.) </s> |
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4620 <s xml:id="echoid-s2694" xml:space="preserve">la puiſ-<lb/>ſance F eſt au poids T, comme CP à CK. </s> |
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4621 <s xml:id="echoid-s2695" xml:space="preserve">Or ( hyp.) <lb/></s> |
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4622 <s xml:id="echoid-s2696" xml:space="preserve">la puiſſance F eſt à chacune des puiſſances E, D, B, A, <lb/>&</s> |
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4623 <s xml:id="echoid-s2697" xml:space="preserve">c. </s> |
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4624 <s xml:id="echoid-s2698" xml:space="preserve">comme CP à chacune des parties de leurs cordes, <lb/>CN, CM, CR, CG, &</s> |
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4625 <s xml:id="echoid-s2699" xml:space="preserve">c. </s> |
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4626 <s xml:id="echoid-s2700" xml:space="preserve">Donc chacune de ces <lb/>puiſſances eſt au poids T, comme chacune de ces <lb/>proportionelles, ſelon qu’elles leurs répondent, eſt à la <lb/>diagonale CK. </s> |
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4627 <s xml:id="echoid-s2701" xml:space="preserve">Ce qu’on vient de dire de la puiſſance <lb/>F, ſe prouvera de même de toute autre dont la pro- |
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4628 <pb o="108" file="0134" n="134" rhead="EXAMEN DE L’OPINION"/> |
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4629 portionelle feroit un des côtez du parallelogramme <lb/> |
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4630 <anchor type="note" xlink:label="note-0134-01a" xlink:href="note-0134-01"/> |
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4631 qu’on vient de démontrer avoir toujours ſa diago-<lb/>nale, comme ici CK, dans la ligne de direction du <lb/>poids T: </s> |
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4632 <s xml:id="echoid-s2702" xml:space="preserve">Ainſi en général de quelque maniére qu’un <lb/>poids ſoit ſoutenu avec des cordes par quelque nom-<lb/>bre de puiſſances que ce ſoit, appliquées à un même <lb/>nœud, chacune de ces puiſſances eſt toujours à ce <lb/>poids, comme chacune de leurs proportionelles qui <lb/>ſervent de côtez aux parallelogrammes dont il eſt ici <lb/>queſtion, eſt à la diagonale du dernier, qu’on vient <lb/>de voir ſe trouver toujours dans ſa ligne de direction. <lb/></s> |
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4633 <s xml:id="echoid-s2703" xml:space="preserve">Ce qu’il faloit démontrer.</s> |
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4634 <s xml:id="echoid-s2704" xml:space="preserve"/> |
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4635 </p> |
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4636 <div xml:id="echoid-div267" type="float" level="2" n="2"> |
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4637 <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cord@s ſeu-<lb/>lement.</note> |
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4638 </div> |
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4639 </div> |
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4640 <div xml:id="echoid-div269" type="section" level="1" n="171"> |
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4641 <head xml:id="echoid-head173" xml:space="preserve"><emph style="sc">Corollaire.</emph></head> |
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4642 <p> |
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4643 <s xml:id="echoid-s2705" xml:space="preserve">D’où l’on voit que toutes ces puiſſances priſes <lb/>enſemble ſont toujours au poids T qu’elles ſoutien-<lb/>nent, comme la ſomme de leurs proportionelles CG, <lb/>CR, CM, CN, CP, &</s> |
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4644 <s xml:id="echoid-s2706" xml:space="preserve">c. </s> |
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4645 <s xml:id="echoid-s2707" xml:space="preserve">à la diagonale du paralle-<lb/>logramme qu’on vient de démontrer (n. </s> |
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4646 <s xml:id="echoid-s2708" xml:space="preserve">1.) </s> |
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4647 <s xml:id="echoid-s2709" xml:space="preserve">ſe trou-<lb/>ver toujours dans la ligne de direction de ce poids: <lb/></s> |
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4648 <s xml:id="echoid-s2710" xml:space="preserve">De ſorte que, lorſque toutes ces puiſſances ſont éga-<lb/>les entr’elles, ces mêmes proportionelles l’étant auſſi, <lb/>la ſomme de toutes ces puiſſances eſt à ce poids, com-<lb/>me une de ces proportionelles à une partie de cette <lb/>diagonale diviſée en autant d’égales qu’il y a de telles <lb/>puiſſances; </s> |
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4649 <s xml:id="echoid-s2711" xml:space="preserve">c’eſt-à-dire ici, comme laquelle que ce <lb/>ſoit, des lignes CG, CR, CM, CN, CP, à {1/5} de <lb/>CK.</s> |
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4650 <s xml:id="echoid-s2712" xml:space="preserve"/> |
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4651 </p> |
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4652 <p style="it"> |
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4653 <s xml:id="echoid-s2713" xml:space="preserve">Pour exprimer le raport que nous venons de trouver <lb/>entre ce poids & </s> |
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4654 <s xml:id="echoid-s2714" xml:space="preserve">les puiſſances qui le ſoutiennent, d’une <lb/>maniére qui en rende le calcul plus facile, ſoit le Lemme <lb/>ſuivant.</s> |
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4655 <s xml:id="echoid-s2715" xml:space="preserve"/> |
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4656 </p> |
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4657 <figure> |
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4658 <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0134-01"/> |
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4659 </figure> |
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4660 <pb o="109" file="0135" n="135" rhead="DE M. BORELLI."/> |
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4661 <note position="right" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſcu-<lb/>lement.</note> |
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4662 <figure> |
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4663 <image file="0135-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0135-01"/> |
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4664 </figure> |
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4665 </div> |
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4666 <div xml:id="echoid-div270" type="section" level="1" n="172"> |
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4667 <head xml:id="echoid-head174" xml:space="preserve">LEMME.</head> |
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4668 <p style="it"> |
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4669 <s xml:id="echoid-s2716" xml:space="preserve">DE quelque maniére que la ligne droite CP paſſe par <lb/> |
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4670 <anchor type="note" xlink:label="note-0135-02a" xlink:href="note-0135-02"/> |
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4671 une des pointes C du parallelogramme IE, ſi des trois <lb/>autres pointes G, I, E, on tire ſur la même CP les trois <lb/>perpendiculaires GL, IP, VE: </s> |
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4672 <s xml:id="echoid-s2717" xml:space="preserve">ſa partie CL compriſe <lb/>entre le point C, & </s> |
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4673 <s xml:id="echoid-s2718" xml:space="preserve">la perpendiculaire GL qui part de la <lb/>pointe G qui lui eſt oppoſée, eſt toujours égale à la ſomme de <lb/>ſes deux autres parties CP & </s> |
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4674 <s xml:id="echoid-s2719" xml:space="preserve">CV compriſes entre ce même <lb/>point C & </s> |
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4675 <s xml:id="echoid-s2720" xml:space="preserve">les perpendiculaires IP & </s> |
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4676 <s xml:id="echoid-s2721" xml:space="preserve">EV, lors que ces <lb/>deux perpendiculaires tombent du même côté de C; </s> |
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4677 <s xml:id="echoid-s2722" xml:space="preserve">ou à la <lb/>diffèrence de ces deux parties, lors que ces deux perpendiculaires <lb/>tombent de différens côtez.</s> |
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4678 <s xml:id="echoid-s2723" xml:space="preserve"/> |
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4679 </p> |
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4680 <div xml:id="echoid-div270" type="float" level="2" n="1"> |
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4681 <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">fig. 9. <lb/>10. <lb/>11. <lb/>12. <lb/>13. <lb/>14. <lb/>15. <lb/>16.</note> |
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4682 </div> |
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4683 </div> |
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4684 <div xml:id="echoid-div272" type="section" level="1" n="173"> |
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4685 <head xml:id="echoid-head175" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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4686 <p> |
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4687 <s xml:id="echoid-s2724" xml:space="preserve">Joignez IE & </s> |
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4688 <s xml:id="echoid-s2725" xml:space="preserve">GC qui ſe coupent par la moitié <lb/>l’une & </s> |
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4689 <s xml:id="echoid-s2726" xml:space="preserve">l’autre en K, & </s> |
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4690 <s xml:id="echoid-s2727" xml:space="preserve">apres avoir fait QK perpen-<lb/>diculaire à CP, concevez un plan qui paſſe par QK, <lb/>à qui CP ſoit perpendiculaire, & </s> |
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4691 <s xml:id="echoid-s2728" xml:space="preserve">ſur lequel des <lb/>points I & </s> |
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4692 <s xml:id="echoid-s2729" xml:space="preserve">E, tombent auſſi perpendiculairement <lb/>IM, & </s> |
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4693 <s xml:id="echoid-s2730" xml:space="preserve">EN; </s> |
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4694 <s xml:id="echoid-s2731" xml:space="preserve">Enfin joignez QM & </s> |
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4695 <s xml:id="echoid-s2732" xml:space="preserve">QN. </s> |
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4696 <s xml:id="echoid-s2733" xml:space="preserve">Cela fait, <lb/>ſoit que QK, QM, & </s> |
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4697 <s xml:id="echoid-s2734" xml:space="preserve">QN, ſe confondent en une <lb/>ſeule ligne, ſoit qu’elles en faſſent trois différentes, <lb/>il eſt clair que puis que les lignes IM, PQ, NE, & </s> |
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4698 <s xml:id="echoid-s2735" xml:space="preserve"><lb/>VQ, ſont toutes (Hyp.) </s> |
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4699 <s xml:id="echoid-s2736" xml:space="preserve">perpendiculaires à ce plan, <lb/>elles ſont auſſi toutes paralleles entr’elles; </s> |
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4700 <s xml:id="echoid-s2737" xml:space="preserve">& </s> |
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4701 <s xml:id="echoid-s2738" xml:space="preserve">par <lb/>conſéquent 1°. </s> |
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4702 <s xml:id="echoid-s2739" xml:space="preserve">IM & </s> |
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4703 <s xml:id="echoid-s2740" xml:space="preserve">PQ ſont dans un même plan <lb/>avec PI & </s> |
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4704 <s xml:id="echoid-s2741" xml:space="preserve">QM: </s> |
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4705 <s xml:id="echoid-s2742" xml:space="preserve">Ainſi les angles en M, Q, & </s> |
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4706 <s xml:id="echoid-s2743" xml:space="preserve">P, <lb/>étant (hyp) droits, MP ſera un parallelogramme. <lb/></s> |
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4707 <s xml:id="echoid-s2744" xml:space="preserve">On prouvera de même que VN eſt auſſi un paralle-<lb/>logramme: </s> |
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4708 <s xml:id="echoid-s2745" xml:space="preserve">Donc IM eſt égale à PQ, & </s> |
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4709 <s xml:id="echoid-s2746" xml:space="preserve">EN égale <lb/>à VQ. </s> |
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4710 <s xml:id="echoid-s2747" xml:space="preserve">2°. </s> |
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4711 <s xml:id="echoid-s2748" xml:space="preserve">De ce que IM & </s> |
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4712 <s xml:id="echoid-s2749" xml:space="preserve">EN ſont paralleles en- |
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4713 <pb o="110" file="0136" n="136" rhead="EXAMEN DE L’OPINION"/> |
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4714 tr’elles, il ſuit auſſi que les angles MIK & </s> |
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4715 <s xml:id="echoid-s2750" xml:space="preserve">NEK <lb/> |
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4716 <anchor type="note" xlink:label="note-0136-01a" xlink:href="note-0136-01"/> |
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4717 ſont égaux; </s> |
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4718 <s xml:id="echoid-s2751" xml:space="preserve">& </s> |
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4719 <s xml:id="echoid-s2752" xml:space="preserve">par conſéquent, ſi l’on joint KM & </s> |
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4720 <s xml:id="echoid-s2753" xml:space="preserve"><lb/>KN, les angles en M & </s> |
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4721 <s xml:id="echoid-s2754" xml:space="preserve">en N étant (hyp.) </s> |
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4722 <s xml:id="echoid-s2755" xml:space="preserve">égaux, <lb/>auſſi-bien que les lignes IK & </s> |
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4723 <s xml:id="echoid-s2756" xml:space="preserve">KE, les triangles IMK <lb/>& </s> |
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4724 <s xml:id="echoid-s2757" xml:space="preserve">ENK ſeront non ſeulement ſemblables, mais en-<lb/>core IM ſera égale à EN. </s> |
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4725 <s xml:id="echoid-s2758" xml:space="preserve">Or on vient de voir (n. </s> |
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4726 <s xml:id="echoid-s2759" xml:space="preserve">1.) <lb/></s> |
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4727 <s xml:id="echoid-s2760" xml:space="preserve">que IM eſt égale à PQ, & </s> |
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4728 <s xml:id="echoid-s2761" xml:space="preserve">EN égale à VQ: </s> |
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4729 <s xml:id="echoid-s2762" xml:space="preserve"><lb/>Donc PQ eſt égale à VQ: </s> |
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4730 <s xml:id="echoid-s2763" xml:space="preserve">Donc (fig. </s> |
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4731 <s xml:id="echoid-s2764" xml:space="preserve">9. </s> |
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4732 <s xml:id="echoid-s2765" xml:space="preserve">11. </s> |
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4733 <s xml:id="echoid-s2766" xml:space="preserve">12. </s> |
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4734 <s xml:id="echoid-s2767" xml:space="preserve">13. </s> |
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4735 <s xml:id="echoid-s2768" xml:space="preserve"><lb/>& </s> |
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4736 <s xml:id="echoid-s2769" xml:space="preserve">14.) </s> |
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4737 <s xml:id="echoid-s2770" xml:space="preserve">CP plus CV, ou ( fig. </s> |
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4738 <s xml:id="echoid-s2771" xml:space="preserve">10. </s> |
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4739 <s xml:id="echoid-s2772" xml:space="preserve">14. </s> |
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4740 <s xml:id="echoid-s2773" xml:space="preserve">15. </s> |
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4741 <s xml:id="echoid-s2774" xml:space="preserve">& </s> |
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4742 <s xml:id="echoid-s2775" xml:space="preserve">16.) </s> |
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4743 <s xml:id="echoid-s2776" xml:space="preserve"><lb/>CP moins CV, eſt égal à deux fois CQ. </s> |
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4744 <s xml:id="echoid-s2777" xml:space="preserve">Or à cauſe <lb/>que les triangles CGL, & </s> |
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4745 <s xml:id="echoid-s2778" xml:space="preserve">CKQ ſont ſemblables, & </s> |
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4746 <s xml:id="echoid-s2779" xml:space="preserve"><lb/>que CG eſt double de CK; </s> |
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4747 <s xml:id="echoid-s2780" xml:space="preserve">CL ſera auſſi double de <lb/>CQ: </s> |
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4748 <s xml:id="echoid-s2781" xml:space="preserve">Donc (fig. </s> |
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4749 <s xml:id="echoid-s2782" xml:space="preserve">9. </s> |
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4750 <s xml:id="echoid-s2783" xml:space="preserve">11. </s> |
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4751 <s xml:id="echoid-s2784" xml:space="preserve">12. </s> |
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4752 <s xml:id="echoid-s2785" xml:space="preserve">13. </s> |
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4753 <s xml:id="echoid-s2786" xml:space="preserve">& </s> |
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4754 <s xml:id="echoid-s2787" xml:space="preserve">14.) </s> |
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4755 <s xml:id="echoid-s2788" xml:space="preserve">CP plus CV, <lb/>ou (fig. </s> |
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4756 <s xml:id="echoid-s2789" xml:space="preserve">10. </s> |
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4757 <s xml:id="echoid-s2790" xml:space="preserve">14. </s> |
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4758 <s xml:id="echoid-s2791" xml:space="preserve">16. </s> |
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4759 <s xml:id="echoid-s2792" xml:space="preserve">& </s> |
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4760 <s xml:id="echoid-s2793" xml:space="preserve">16.) </s> |
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4761 <s xml:id="echoid-s2794" xml:space="preserve">CP moins CV, eſt égale <lb/>à CL. </s> |
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4762 <s xml:id="echoid-s2795" xml:space="preserve">Ce qu’il faloit dèmontrer.</s> |
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4763 <s xml:id="echoid-s2796" xml:space="preserve"/> |
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4764 </p> |
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4765 <div xml:id="echoid-div272" type="float" level="2" n="1"> |
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4766 <note position="left" xlink:label="note-0136-01" xlink:href="note-0136-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4767 </div> |
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4768 <figure> |
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4769 <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0136-01"/> |
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4770 </figure> |
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4771 </div> |
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4772 <div xml:id="echoid-div274" type="section" level="1" n="174"> |
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4773 <head xml:id="echoid-head176" xml:space="preserve">PROPOSITION III.</head> |
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4774 <p style="it"> |
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4775 <s xml:id="echoid-s2797" xml:space="preserve">T Outes choſes étant les mèmes que dans la propoſition <lb/> |
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4776 <anchor type="note" xlink:label="note-0136-02a" xlink:href="note-0136-02"/> |
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4777 précédente, on trouvera préſentement que chacune des <lb/>puiſſances A, B, D, E, F, &</s> |
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4778 <s xml:id="echoid-s2798" xml:space="preserve">c. </s> |
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4779 <s xml:id="echoid-s2799" xml:space="preserve">eſt au poids T qu’elles <lb/>ſoutiennent, comme chacune de leurs proportionelles CG, CR, <lb/>CM, CN, CP, &</s> |
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4780 <s xml:id="echoid-s2800" xml:space="preserve">c. </s> |
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4781 <s xml:id="echoid-s2801" xml:space="preserve">à la ſomme de leurs ſublimitez moins <lb/>celle de leurs profondeurs.</s> |
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4782 <s xml:id="echoid-s2802" xml:space="preserve"/> |
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4783 </p> |
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4784 <div xml:id="echoid-div274" type="float" level="2" n="1"> |
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4785 <note position="left" xlink:label="note-0136-02" xlink:href="note-0136-02a" xml:space="preserve">fig. 8. <lb/>17.</note> |
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4786 </div> |
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4787 </div> |
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4788 <div xml:id="echoid-div276" type="section" level="1" n="175"> |
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4789 <head xml:id="echoid-head177" xml:space="preserve"><emph style="sc">Demonstration.</emph></head> |
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4790 <p> |
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4791 <s xml:id="echoid-s2803" xml:space="preserve">De toutes les pointes des parallelogrammes GR, <lb/> |
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4792 <anchor type="note" xlink:label="note-0136-03a" xlink:href="note-0136-03"/> |
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4793 HM, LN, QP, &</s> |
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4794 <s xml:id="echoid-s2804" xml:space="preserve">c. </s> |
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4795 <s xml:id="echoid-s2805" xml:space="preserve">tirez Gg, Hh, Rr, Ll, Mm, Qq, <lb/>Nn, Pp, &</s> |
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4796 <s xml:id="echoid-s2806" xml:space="preserve">c. </s> |
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4797 <s xml:id="echoid-s2807" xml:space="preserve">perpendiculairement ſur la ligne de di-<lb/>rection du poids T, prolongée indéfiniment de part <lb/>& </s> |
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4798 <s xml:id="echoid-s2808" xml:space="preserve">d’autre. </s> |
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4799 <s xml:id="echoid-s2809" xml:space="preserve">Cela fait, vous trouverez par le Lemme <lb/>précédent. </s> |
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4800 <s xml:id="echoid-s2810" xml:space="preserve">1°. </s> |
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4801 <s xml:id="echoid-s2811" xml:space="preserve">Ch = Cg Cr. </s> |
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4802 <s xml:id="echoid-s2812" xml:space="preserve">2°. </s> |
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4803 <s xml:id="echoid-s2813" xml:space="preserve">Cl = Cm -<lb/>Ch: </s> |
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4804 <s xml:id="echoid-s2814" xml:space="preserve">Donc Cl = Cm - Cg + Cr. </s> |
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4805 <s xml:id="echoid-s2815" xml:space="preserve">3°. </s> |
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4806 <s xml:id="echoid-s2816" xml:space="preserve">Cq = |
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|
4807 <pb o="111" file="0137" n="137" rhead="DE M. BORELLI."/> |
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4808 Cl + Cn: </s> |
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4809 <s xml:id="echoid-s2817" xml:space="preserve">Donc Cq = Cm - Cg + Cr + Cn. <lb/></s> |
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4810 <s xml:id="echoid-s2818" xml:space="preserve"> |
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4811 <anchor type="note" xlink:label="note-0137-01a" xlink:href="note-0137-01"/> |
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4812 4°. </s> |
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4813 <s xml:id="echoid-s2819" xml:space="preserve">Ck = Cq - Cp: </s> |
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4814 <s xml:id="echoid-s2820" xml:space="preserve">Donc Ck = Cm - Cg + <lb/>Cr + Cn - Cp. </s> |
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4815 <s xml:id="echoid-s2821" xml:space="preserve">Enfin continuant toujours ainſi <lb/>juſqu’à la diagonale qui ſetrouve toujours ( Prop. </s> |
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4816 <s xml:id="echoid-s2822" xml:space="preserve">2.) <lb/></s> |
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4817 <s xml:id="echoid-s2823" xml:space="preserve">dans la ligne de ditection du poids T, on trouvera <lb/>de même que cette diagonale eſt toujours égale à <lb/>Cm - Cg + Cr + Cn - Cp ± &</s> |
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4818 <s xml:id="echoid-s2824" xml:space="preserve">c. </s> |
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4819 <s xml:id="echoid-s2825" xml:space="preserve">Or on vient <lb/>de voir ( Prop. </s> |
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4820 <s xml:id="echoid-s2826" xml:space="preserve">2.) </s> |
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4821 <s xml:id="echoid-s2827" xml:space="preserve">que chacune des puiſſances A, B, <lb/>D, E, F, &</s> |
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4822 <s xml:id="echoid-s2828" xml:space="preserve">c. </s> |
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4823 <s xml:id="echoid-s2829" xml:space="preserve">eſt auſſi toujours au poids T qu’elles <lb/>ſoutiennent, comme chacune de leurs proportio-<lb/>nelles CG, CR, CM, CN, CP, &</s> |
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4824 <s xml:id="echoid-s2830" xml:space="preserve">c. </s> |
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4825 <s xml:id="echoid-s2831" xml:space="preserve">à cette même <lb/>diagonale: </s> |
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4826 <s xml:id="echoid-s2832" xml:space="preserve">Donc chacune de ces puiſſances eſt à ce <lb/>poids, comme chacune de ces proportionelles à Cm + <lb/>Cr + Cn - Cg - Cp ± &</s> |
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4827 <s xml:id="echoid-s2833" xml:space="preserve">c. </s> |
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4828 <s xml:id="echoid-s2834" xml:space="preserve">C’eſt-à-dire, ( Def. </s> |
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4829 <s xml:id="echoid-s2835" xml:space="preserve"><lb/>1. </s> |
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4830 <s xml:id="echoid-s2836" xml:space="preserve">& </s> |
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4831 <s xml:id="echoid-s2837" xml:space="preserve">2.) </s> |
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4832 <s xml:id="echoid-s2838" xml:space="preserve">à la ſomme de leurs ſublimitez Cm, Cr, <lb/>Cn, &</s> |
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4833 <s xml:id="echoid-s2839" xml:space="preserve">c. </s> |
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4834 <s xml:id="echoid-s2840" xml:space="preserve">moins la ſomme de leurs profondeurs Cg, <lb/>Cp, &</s> |
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4835 <s xml:id="echoid-s2841" xml:space="preserve">c. </s> |
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4836 <s xml:id="echoid-s2842" xml:space="preserve">D’où l’on voit en général, que de qu@lque <lb/>maniére qu’un poids ſoit ſoutenu avec des cordes <lb/>par quelque nombre de puiſſances que ce ſoit, appli-<lb/>quées à un même nœud, chacune de ces puiſſances <lb/>eſt toujours à ce poids, comme chacune de leurs pro-<lb/>portionelles, à la ſomme de leurs ſublimitez moins <lb/>celle de leurs profondeurs. </s> |
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4837 <s xml:id="echoid-s2843" xml:space="preserve">Ce qu’il faloit démon-<lb/>trer.</s> |
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4838 <s xml:id="echoid-s2844" xml:space="preserve"/> |
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4839 </p> |
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4840 <div xml:id="echoid-div276" type="float" level="2" n="1"> |
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4841 <note position="left" xlink:label="note-0136-03" xlink:href="note-0136-03a" xml:space="preserve">fig. 8.</note> |
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4842 <note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4843 </div> |
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4844 </div> |
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4845 <div xml:id="echoid-div278" type="section" level="1" n="176"> |
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4846 <head xml:id="echoid-head178" xml:space="preserve"><emph style="sc">Autre</emph> <emph style="sc">Demonstration.</emph></head> |
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4847 <p> |
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4848 <s xml:id="echoid-s2845" xml:space="preserve">Soient encore les lignes CG, CR, CM, CN, CP, <lb/>&</s> |
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4849 <s xml:id="echoid-s2846" xml:space="preserve">c. </s> |
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4850 <s xml:id="echoid-s2847" xml:space="preserve">proportionelles aux puiſſances A, B, D, E, F, <lb/> |
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4851 <anchor type="note" xlink:label="note-0137-02a" xlink:href="note-0137-02"/> |
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4852 &</s> |
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4853 <s xml:id="echoid-s2848" xml:space="preserve">c. </s> |
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4854 <s xml:id="echoid-s2849" xml:space="preserve">proportionelles aux puiſſances A, B, D, E, F, <lb/>&</s> |
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4855 <s xml:id="echoid-s2850" xml:space="preserve">c. </s> |
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4856 <s xml:id="echoid-s2851" xml:space="preserve">concevez par le point C, où elles ſe communi-<lb/>quent, un plan horizontal OH, c’eſt-à-dire, per-<lb/>pendiculaire à la ligne de direction du poids T; </s> |
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4857 <s xml:id="echoid-s2852" xml:space="preserve">tirez <lb/>enſuite des extrémitez de ces proportionelles G, R, <lb/>M, N, P, &</s> |
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4858 <s xml:id="echoid-s2853" xml:space="preserve">c. </s> |
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4859 <s xml:id="echoid-s2854" xml:space="preserve">autant de perpendiculaires ſur le <lb/>plan OH, & </s> |
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4860 <s xml:id="echoid-s2855" xml:space="preserve">ſur la ligne de direction du poids T <lb/>indéfiniment prolongée de part & </s> |
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4861 <s xml:id="echoid-s2856" xml:space="preserve">d’™autre: </s> |
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4862 <s xml:id="echoid-s2857" xml:space="preserve">en faiſant |
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4863 <pb o="112" file="0138" n="138" rhead="EXAMEN DE L’OPINION"/> |
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4864 depuis C ſur le plan OH autant de lignes CH, CQ, <lb/> |
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4865 <anchor type="note" xlink:label="note-0138-01a" xlink:href="note-0138-01"/> |
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4866 CL, CO, CK, &</s> |
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4867 <s xml:id="echoid-s2858" xml:space="preserve">c. </s> |
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4868 <s xml:id="echoid-s2859" xml:space="preserve">qui joignent ce point avec les <lb/>perpendiculaires qui tombent ſur ce plan, on aura <lb/>autant de parallelogrammes rectangles Hg, Qr, Lm, <lb/>On, Kp, &</s> |
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4869 <s xml:id="echoid-s2860" xml:space="preserve">c. </s> |
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4870 <s xml:id="echoid-s2861" xml:space="preserve">qui exprimeront ( Lemm 3. </s> |
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4871 <s xml:id="echoid-s2862" xml:space="preserve">Cor. </s> |
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4872 <s xml:id="echoid-s2863" xml:space="preserve">2. </s> |
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4873 <s xml:id="echoid-s2864" xml:space="preserve">du <lb/>Projet précédent) que chacune de ces puiſſances, par <lb/>exemple la puiſſance A, fait la même impreſſion ſur le <lb/>point C, que feroient deux autres puiſſances appliquées <lb/>à ce point, l’une ſuivant CH, & </s> |
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4874 <s xml:id="echoid-s2865" xml:space="preserve">l’autre ſuivant Cg, à <lb/>chacune deſquelles celle-ci ſeroit comme @G à cha-<lb/>cune de ces mêmes lignes: </s> |
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4875 <s xml:id="echoid-s2866" xml:space="preserve">Le point C eſt donc tiré <lb/>vers bas ſuivant la ligne de direction du poids T par <lb/>la puiſſance A, d’une force (Cor. </s> |
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4876 <s xml:id="echoid-s2867" xml:space="preserve">3. </s> |
|
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parents:
diff
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|
4877 <s xml:id="echoid-s2868" xml:space="preserve">du même Lemm) <lb/>à qui cette puiſſance eſt comme CG à C@. </s> |
|
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parents:
diff
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|
4878 <s xml:id="echoid-s2869" xml:space="preserve">Pour la <lb/>même raiſon, il eſt encore tiré ſuivant la ligne de di-<lb/>rection de même poids, 1°. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4879 <s xml:id="echoid-s2870" xml:space="preserve">Vers bas, par la puiſſance <lb/>F, d’une force à qui elle eſt comme CP à Cp; </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
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|
4880 <s xml:id="echoid-s2871" xml:space="preserve">&</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4881 <s xml:id="echoid-s2872" xml:space="preserve">c. <lb/></s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4882 <s xml:id="echoid-s2873" xml:space="preserve">2°. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4883 <s xml:id="echoid-s2874" xml:space="preserve">Vers haut, par la puiſſance B, d’une force à qui <lb/>elle eſt comme CR à Cr; </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4884 <s xml:id="echoid-s2875" xml:space="preserve">par la puiſſance D, d’une <lb/>force à qui elle eſt comme CM à Cm; </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4885 <s xml:id="echoid-s2876" xml:space="preserve">par la puiſſance <lb/>E, d’une force à qui elle eſt, comme CN à Cn; </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
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|
4886 <s xml:id="echoid-s2877" xml:space="preserve">&</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4887 <s xml:id="echoid-s2878" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4888 <s xml:id="echoid-s2879" xml:space="preserve"><lb/>Or (hyp.) </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4889 <s xml:id="echoid-s2880" xml:space="preserve">la puiſſance A eſt à chacune des puiſſances <lb/>B, D, E, F, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4890 <s xml:id="echoid-s2881" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4891 <s xml:id="echoid-s2882" xml:space="preserve">comme ſa proportionelle CG à cha-<lb/>cune des leurs CR, CM, CN, CP, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4892 <s xml:id="echoid-s2883" xml:space="preserve">c. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4893 <s xml:id="echoid-s2884" xml:space="preserve">Donc la <lb/>puiſſance A eſt à chacune des forces avec leſquelles <lb/>le point C eſt tiré ſuivant la ligne de direction du <lb/>poids T, 1°. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
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|
4894 <s xml:id="echoid-s2885" xml:space="preserve">Vers bas par les puiſſances A, F, <lb/>&</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4895 <s xml:id="echoid-s2886" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4896 <s xml:id="echoid-s2887" xml:space="preserve">comme CG à chacune de leurs profondeurs <lb/>Cg, Cp, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4897 <s xml:id="echoid-s2888" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4898 <s xml:id="echoid-s2889" xml:space="preserve">2°. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4899 <s xml:id="echoid-s2890" xml:space="preserve">Vers haut par les puiſſances <lb/>B, D, E, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4900 <s xml:id="echoid-s2891" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4901 <s xml:id="echoid-s2892" xml:space="preserve">comme la même CG à chacune de <lb/>leurs ſublimitez Cr, Cm, Cn, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4902 <s xml:id="echoid-s2893" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4903 <s xml:id="echoid-s2894" xml:space="preserve">Donc cette <lb/>même puiſſance A eſt à la ſomme de toutes les forces <lb/>avec leſquelles le point C eſt tiré ſuivant la ligne de <lb/>direction du poids T, 1°. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4904 <s xml:id="echoid-s2895" xml:space="preserve">Vers bas par les puiſſances <lb/>A, F, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4905 <s xml:id="echoid-s2896" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4906 <s xml:id="echoid-s2897" xml:space="preserve">comme ſa proportionelle CG à la ſomme |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4907 <pb o="113" file="0139" n="139" rhead="DE M. BORELLI."/> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4908 de leurs profondeurs Cg, Cp, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4909 <s xml:id="echoid-s2898" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4910 <s xml:id="echoid-s2899" xml:space="preserve">2°. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4911 <s xml:id="echoid-s2900" xml:space="preserve">Vers haut <lb/> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
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|
4912 <anchor type="note" xlink:label="note-0139-01a" xlink:href="note-0139-01"/> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4913 par les puiſſances B, D, E, &</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4914 <s xml:id="echoid-s2901" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4915 <s xml:id="echoid-s2902" xml:space="preserve">comme la même CG <lb/>à la ſomme de leurs ſublimitez Cr, Cm, Cn, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4916 <s xml:id="echoid-s2903" xml:space="preserve">c. <lb/></s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4917 <s xml:id="echoid-s2904" xml:space="preserve">Or la ſomme faite de la peſanteur de ce poids, & </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4918 <s xml:id="echoid-s2905" xml:space="preserve"><lb/>des forces avec leſquelles le point C eſt tiré vers <lb/>bas ſuivant la ligne de direction de ce même poids <lb/>par les puiſſances A, F, &</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4919 <s xml:id="echoid-s2906" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4920 <s xml:id="echoid-s2907" xml:space="preserve">étant diamétralement <lb/>oppoſée à la ſomme de celles avec leſquelles ce même <lb/>point eſt tiré en même-tems vers haut ſuivant cette <lb/>même ligne par les puiſſances B, D, E, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4921 <s xml:id="echoid-s2908" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4922 <s xml:id="echoid-s2909" xml:space="preserve">& </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4923 <s xml:id="echoid-s2910" xml:space="preserve">au-<lb/>cune de ces deux ſommes de forces ne l’emportant <lb/>ſur l’autre; </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4924 <s xml:id="echoid-s2911" xml:space="preserve">puiſque (hyp.) </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4925 <s xml:id="echoid-s2912" xml:space="preserve">le poids T ne monte n’y <lb/>deſcend: </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4926 <s xml:id="echoid-s2913" xml:space="preserve">c’eſt une conſéquence néceſſaire qu’elles <lb/>ſoient égales: </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4927 <s xml:id="echoid-s2914" xml:space="preserve">Donc la puiſſance A eſt non ſeulement <lb/>à la ſomme des forces avec leſquelles le point C eſt <lb/>tiré vers bas, ſuivant la ligne de direction du poids <lb/>T par les puiſſances A, F, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4928 <s xml:id="echoid-s2915" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4929 <s xml:id="echoid-s2916" xml:space="preserve">comme ſa propor-<lb/>tionelle CG à la ſomme de leurs profondeurs Cg, <lb/>Cp, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4930 <s xml:id="echoid-s2917" xml:space="preserve">c. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4931 <s xml:id="echoid-s2918" xml:space="preserve">Mais auſſi à la ſomme faite de cette pre-<lb/>miére & </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4932 <s xml:id="echoid-s2919" xml:space="preserve">de la peſanteur de ce même poids, comme <lb/>la même CG à la ſomme des ſublimitez Cr, Cm, <lb/>Cn, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4933 <s xml:id="echoid-s2920" xml:space="preserve">c. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4934 <s xml:id="echoid-s2921" xml:space="preserve">des puiſſances B, D, E, &</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4935 <s xml:id="echoid-s2922" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4936 <s xml:id="echoid-s2923" xml:space="preserve">Donc la puiſ-<lb/>ſance A eſt à cette derniére ſomme moins la pre-<lb/>miére; </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4937 <s xml:id="echoid-s2924" xml:space="preserve">c’eſt-à-dire, à la peſanteur ſeule du poids <lb/>T, où à ce poids lui - même, comme ſa proportio-<lb/>nelle CG à la ſomme des ſublimitez Cr, Cm, Cn, <lb/>&</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4938 <s xml:id="echoid-s2925" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4939 <s xml:id="echoid-s2926" xml:space="preserve">moins la ſomme des profondeurs Cg, Cp, &</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4940 <s xml:id="echoid-s2927" xml:space="preserve">c. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff
changeset
|
4941 <s xml:id="echoid-s2928" xml:space="preserve"><lb/>Or ( Hyp.) </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4942 <s xml:id="echoid-s2929" xml:space="preserve">chacune des puiſſances B, D, E, F, <lb/>&</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff
changeset
|
4943 <s xml:id="echoid-s2930" xml:space="preserve">c. </s> |
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4944 <s xml:id="echoid-s2931" xml:space="preserve">eſt à la puiſſance A, comme chacune de leurs <lb/>proportionelles CR, CM, CN, CP, &</s> |
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4945 <s xml:id="echoid-s2932" xml:space="preserve">c. </s> |
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4946 <s xml:id="echoid-s2933" xml:space="preserve">à ſa pro-<lb/>portionelle CG: </s> |
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4947 <s xml:id="echoid-s2934" xml:space="preserve">Donc chacune des puiſſances A, <lb/>B, D, E, F, &</s> |
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4948 <s xml:id="echoid-s2935" xml:space="preserve">c. </s> |
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4949 <s xml:id="echoid-s2936" xml:space="preserve">eſt au poids T qu’elles ſoutien-<lb/>nent, comme chacune de leurs proportionelles à la <lb/>ſomme de leurs ſublimitez moins celle de leurs pro-<lb/>fondeurs. </s> |
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4950 <s xml:id="echoid-s2937" xml:space="preserve">Ce qu’il faloit démontrer.</s> |
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4951 <s xml:id="echoid-s2938" xml:space="preserve"/> |
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4952 </p> |
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4953 <div xml:id="echoid-div278" type="float" level="2" n="1"> |
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4954 <note position="right" xlink:label="note-0137-02" xlink:href="note-0137-02a" xml:space="preserve">fig. 17.</note> |
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4955 <note position="left" xlink:label="note-0138-01" xlink:href="note-0138-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4956 <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4957 </div> |
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4958 <pb o="114" file="0140" n="140" rhead="EXAMEN DE L’OPINION"/> |
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4959 </div> |
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4960 <div xml:id="echoid-div280" type="section" level="1" n="177"> |
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4961 <head xml:id="echoid-head179" xml:space="preserve"><emph style="sc">Corollaire.</emph></head> |
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4962 <note position="left" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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4963 <p> |
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4964 <s xml:id="echoid-s2939" xml:space="preserve">On voit préſentement en général que la ſomme <lb/>de toutes les puiſſances qui ſoutiennent un poids <lb/>avec des cordes qui ſe tiennent par un même nœud, <lb/>en quelque nombre qu’elles ſoient, quelque pro-<lb/>portion qu’elles ayent entr’elles, & </s> |
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4965 <s xml:id="echoid-s2940" xml:space="preserve">de quelque ma-<lb/>niére qu’elles lui ſoient appliquées; </s> |
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4966 <s xml:id="echoid-s2941" xml:space="preserve">eſt toujours à <lb/>ce poids, comme la ſomme des parties de leurs cor-<lb/>des qui leurs ſont (Chap. </s> |
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4967 <s xml:id="echoid-s2942" xml:space="preserve">2. </s> |
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4968 <s xml:id="echoid-s2943" xml:space="preserve">Avert ) proportionelles, <lb/>à la ſomme de leurs ſublimitez moins celle de leurs <lb/>profondeurs.</s> |
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4969 <s xml:id="echoid-s2944" xml:space="preserve"/> |
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4970 </p> |
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4971 <p style="it"> |
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4972 <s xml:id="echoid-s2945" xml:space="preserve">On peut comparer tout ceci avec les Propoſitions 70. </s> |
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4973 <s xml:id="echoid-s2946" xml:space="preserve">73. <lb/></s> |
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4974 <s xml:id="echoid-s2947" xml:space="preserve">74. </s> |
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4975 <s xml:id="echoid-s2948" xml:space="preserve">de M. </s> |
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4976 <s xml:id="echoid-s2949" xml:space="preserve">Borelli, & </s> |
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4977 <s xml:id="echoid-s2950" xml:space="preserve">on verra non ſeulement qu’elles ſont <lb/>tres-limitées; </s> |
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4978 <s xml:id="echoid-s2951" xml:space="preserve">mais encore qu’avec ſa méthode on ne peut pas <lb/>aller ſi loin.</s> |
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4979 <s xml:id="echoid-s2952" xml:space="preserve"/> |
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4980 </p> |
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4981 </div> |
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4982 <div xml:id="echoid-div281" type="section" level="1" n="178"> |
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4983 <head xml:id="echoid-head180" xml:space="preserve"><emph style="sc">Remarque.</emph></head> |
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4984 <p> |
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4985 <s xml:id="echoid-s2953" xml:space="preserve">En faiſant la ſeconde des deux démonſtrations <lb/>précédentes, il m’en eſt encore venu une de la pre-<lb/>miére Propoſition: </s> |
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4986 <s xml:id="echoid-s2954" xml:space="preserve">la voici.</s> |
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4987 <s xml:id="echoid-s2955" xml:space="preserve"/> |
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4988 </p> |
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4989 <p style="it"> |
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4990 <s xml:id="echoid-s2956" xml:space="preserve">Le poids T étant donc ſoutenu avec des cordes par deux <lb/>puiſſances R & </s> |
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4991 <s xml:id="echoid-s2957" xml:space="preserve">S; </s> |
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4992 <s xml:id="echoid-s2958" xml:space="preserve">des angles G & </s> |
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4993 <s xml:id="echoid-s2959" xml:space="preserve">H du parallelogramme <lb/> |
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4994 <anchor type="note" xlink:label="note-0140-02a" xlink:href="note-0140-02"/> |
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4995 GH, dont la diagonale CD fait partie de la ligne de di-<lb/>rection de ce poids, ſoient faites GM & </s> |
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4996 <s xml:id="echoid-s2960" xml:space="preserve">HN paralleles à <lb/>cette diagonale, & </s> |
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4997 <s xml:id="echoid-s2961" xml:space="preserve">perpendiculaires à MCN; </s> |
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4998 <s xml:id="echoid-s2962" xml:space="preserve">achevez <lb/>les parallelogrammes MP & </s> |
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4999 <s xml:id="echoid-s2963" xml:space="preserve">NQ. </s> |
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5000 <s xml:id="echoid-s2964" xml:space="preserve">Cela fait, vous trou-<lb/>verez encore de la maniére que nous avons fait la ſeconde <lb/>des deux démonſtrations précédentes, que le poids T eſt aux <lb/>puiſſances R & </s> |
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5001 <s xml:id="echoid-s2965" xml:space="preserve">S, comme la partie CD de ſa ligne de di-<lb/>rection aux parties CG & </s> |
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5002 <s xml:id="echoid-s2966" xml:space="preserve">CH de leurs cordes, qui font <lb/>les côtez du parallelogramme GH, dont elle eſt diagonale.</s> |
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5003 <s xml:id="echoid-s2967" xml:space="preserve"/> |
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5004 </p> |
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5005 <div xml:id="echoid-div281" type="float" level="2" n="1"> |
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5006 <note position="left" xlink:label="note-0140-02" xlink:href="note-0140-02a" xml:space="preserve">fig. 18. <lb/>19.</note> |
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5007 </div> |
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5008 <pb o="115" file="0141" n="141" rhead="DE M. BORELLI."/> |
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5009 <p> |
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5010 <s xml:id="echoid-s2968" xml:space="preserve">Car (Cor. </s> |
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5011 <s xml:id="echoid-s2969" xml:space="preserve">2. </s> |
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5012 <s xml:id="echoid-s2970" xml:space="preserve">Lem. </s> |
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5013 <s xml:id="echoid-s2971" xml:space="preserve">3. </s> |
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5014 <s xml:id="echoid-s2972" xml:space="preserve">du Projet précéd.) </s> |
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5015 <s xml:id="echoid-s2973" xml:space="preserve">la puiſſance <lb/> |
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5016 <anchor type="note" xlink:label="note-0141-01a" xlink:href="note-0141-01"/> |
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5017 R fait ſur le point C la même impreſſion que fe-<lb/>roient deux autres puiſſances appliquées à ce point, <lb/>l’une ſuivant CP, & </s> |
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5018 <s xml:id="echoid-s2974" xml:space="preserve">l’autre ſuivant CM, à chacune <lb/>deſquelles celle-ci ſeroit, comme CG à chacune de <lb/>ces lignes: </s> |
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5019 <s xml:id="echoid-s2975" xml:space="preserve">Le point C reçoit donc en même - tems <lb/>deux impreſſions différentes de la puiſſance R, l’une <lb/>ſuivant CP, d’une force qui eſt à celle de cette puiſ-<lb/>ſance, (Cor. </s> |
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5020 <s xml:id="echoid-s2976" xml:space="preserve">3. </s> |
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5021 <s xml:id="echoid-s2977" xml:space="preserve">du même Lemm.) </s> |
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5022 <s xml:id="echoid-s2978" xml:space="preserve">comme CP à CG, & </s> |
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5023 <s xml:id="echoid-s2979" xml:space="preserve"><lb/>l’autre ſuivant CM, d’une force qui eſt auſſi (par le <lb/>mème Cor.) </s> |
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5024 <s xml:id="echoid-s2980" xml:space="preserve">à celle de cette même puiſſance, comme CM <lb/>à CG. </s> |
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5025 <s xml:id="echoid-s2981" xml:space="preserve">Pour la même raiſon ce même point C reçoit <lb/>encore en même - tems deux impreſſions différentes <lb/>de la puiſſance S, l’une ſuivant CQ, d’une force <lb/>qui eſt à celle de cette puiſſance, comme CQ à CH; </s> |
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5026 <s xml:id="echoid-s2982" xml:space="preserve">& </s> |
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5027 <s xml:id="echoid-s2983" xml:space="preserve"><lb/>l’autre ſuivant CN, d’une force qui eſt auſſi à celle de <lb/>cette même puiſſance, comme CN à CH. </s> |
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5028 <s xml:id="echoid-s2984" xml:space="preserve">Or 1°. </s> |
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5029 <s xml:id="echoid-s2985" xml:space="preserve">La <lb/>force de l’impreſſion que reçoit le point C de la puiſ-<lb/>ſance R ſuivant CM, eſt égale à celle qu’il reçoit <lb/>en même - tems de la puiſſance S ſuivant CN; </s> |
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5030 <s xml:id="echoid-s2986" xml:space="preserve">puis <lb/>qu’elles ſont diamétralement oppoſées, & </s> |
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5031 <s xml:id="echoid-s2987" xml:space="preserve">qu’aucu-<lb/>ne des deux (byp.) </s> |
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5032 <s xml:id="echoid-s2988" xml:space="preserve">ne ſurmonte l’autre: </s> |
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5033 <s xml:id="echoid-s2989" xml:space="preserve">La force <lb/>de la puiſſance R eſt donc à celle de l’impreſſion que <lb/>reçoit le point C de la puiſſance S ſuivant CN, com-<lb/>me CG à CM. </s> |
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5034 <s xml:id="echoid-s2990" xml:space="preserve">Or CM eſt égale à CN; </s> |
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5035 <s xml:id="echoid-s2991" xml:space="preserve">puis que <lb/>les triangles GPD & </s> |
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5036 <s xml:id="echoid-s2992" xml:space="preserve">HQC ſemblables, & </s> |
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5037 <s xml:id="echoid-s2993" xml:space="preserve">GD <lb/>égale à CH rendent GP égale à HQ; </s> |
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5038 <s xml:id="echoid-s2994" xml:space="preserve">& </s> |
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5039 <s xml:id="echoid-s2995" xml:space="preserve">que les <lb/>parallelogrammes MP & </s> |
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5040 <s xml:id="echoid-s2996" xml:space="preserve">NQ rendent auſſi GP <lb/>égale à CM, & </s> |
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5041 <s xml:id="echoid-s2997" xml:space="preserve">HQ égale à CN: </s> |
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5042 <s xml:id="echoid-s2998" xml:space="preserve">Donc la puiſſance <lb/>R eſt à la force de l’impreſſion que le point C reçoit <lb/>de la puiſſance S ſuivant CN, comme CG à CN. <lb/></s> |
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5043 <s xml:id="echoid-s2999" xml:space="preserve">Or on vient de voir que la force de cette même im-<lb/>preſſion eſt à la puiſſance S, comme CN à CH: </s> |
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5044 <s xml:id="echoid-s3000" xml:space="preserve"><lb/>Donc la puiſſance R eſt à la puiſſance S, comme <lb/>CG à CH: </s> |
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5045 <s xml:id="echoid-s3001" xml:space="preserve">2°. </s> |
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5046 <s xml:id="echoid-s3002" xml:space="preserve">On vient de voir auſſi que la puiſſan- |
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5047 <pb o="116" file="0142" n="142" rhead="EXAMEN DE L’OPINION"/> |
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5048 ce S eſt à la force de l’impreſſion qu’elle fait ſur le <lb/> |
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5049 <anchor type="note" xlink:label="note-0142-01a" xlink:href="note-0142-01"/> |
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5050 point C ſuivant CQ, comme CH à CQ: </s> |
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5051 <s xml:id="echoid-s3003" xml:space="preserve">Donc la <lb/>puiſſance R eſt auſſi à la force de cette même im-<lb/>preſſion, comme CG à CQ; </s> |
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5052 <s xml:id="echoid-s3004" xml:space="preserve">c’eſt - à - dire, comme <lb/>CG à DP; </s> |
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5053 <s xml:id="echoid-s3005" xml:space="preserve">puis que les triangles GPD & </s> |
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5054 <s xml:id="echoid-s3006" xml:space="preserve">HQC <lb/>ſemblables, & </s> |
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5055 <s xml:id="echoid-s3007" xml:space="preserve">GD égale à CH, rendent DP égale <lb/>à CQ. </s> |
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5056 <s xml:id="echoid-s3008" xml:space="preserve">On vient de voir encore que cette même <lb/>puiſſance R eſt à la force de l’impreſſion qu’elle fait <lb/>ſur ce même point C ſuivant CP, comme CG à CP: <lb/></s> |
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5057 <s xml:id="echoid-s3009" xml:space="preserve">Donc la puiſſance R eſt à la ſomme, où à la diffé-<lb/>rence des forces de ces deux impreſſions faites ſur <lb/>le point C ſuivant CP & </s> |
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5058 <s xml:id="echoid-s3010" xml:space="preserve">CQ, par elle & </s> |
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5059 <s xml:id="echoid-s3011" xml:space="preserve">par la puiſ-<lb/>ſance S, comme CG à la ſomme, où à la différence <lb/>de ces deux lignes. </s> |
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5060 <s xml:id="echoid-s3012" xml:space="preserve">Or (fig. </s> |
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5061 <s xml:id="echoid-s3013" xml:space="preserve">18.) </s> |
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5062 <s xml:id="echoid-s3014" xml:space="preserve">la ſomme de ces <lb/>deux lignes, où (fig. </s> |
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5063 <s xml:id="echoid-s3015" xml:space="preserve">19.) </s> |
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5064 <s xml:id="echoid-s3016" xml:space="preserve">leur différence, eſt égale <lb/>à la diagonale CD du parallelogramme GH; </s> |
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5065 <s xml:id="echoid-s3017" xml:space="preserve">& </s> |
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5066 <s xml:id="echoid-s3018" xml:space="preserve"><lb/>(fig. </s> |
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5067 <s xml:id="echoid-s3019" xml:space="preserve">18.) </s> |
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5068 <s xml:id="echoid-s3020" xml:space="preserve">la ſomme, où (fig. </s> |
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5069 <s xml:id="echoid-s3021" xml:space="preserve">19.) </s> |
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5070 <s xml:id="echoid-s3022" xml:space="preserve">la différence des <lb/>forces de ces deux impreſſions, eſt auſſi égale au <lb/>poids T: </s> |
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5071 <s xml:id="echoid-s3023" xml:space="preserve">Donc la puiſſance R eſt au poids T, com-<lb/>me CG à CD: </s> |
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5072 <s xml:id="echoid-s3024" xml:space="preserve">On vient de démontrer (n. </s> |
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5073 <s xml:id="echoid-s3025" xml:space="preserve">1.) </s> |
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5074 <s xml:id="echoid-s3026" xml:space="preserve">que <lb/>cettemême puiſſance R eſt auſſi à la puiſſance S, com-<lb/>me CG à CH: </s> |
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5075 <s xml:id="echoid-s3027" xml:space="preserve">Donc les puiſſances R & </s> |
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5076 <s xml:id="echoid-s3028" xml:space="preserve">S, & </s> |
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|
5077 <s xml:id="echoid-s3029" xml:space="preserve">le <lb/>poids T ſont entr’eux , comme les lignes CG, CH, <lb/>& </s> |
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5078 <s xml:id="echoid-s3030" xml:space="preserve">CD: </s> |
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5079 <s xml:id="echoid-s3031" xml:space="preserve">& </s> |
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5080 <s xml:id="echoid-s3032" xml:space="preserve">par conſéquent ce poids eſt à chacune <lb/>d’elles, comme la partie CD de ſa ligne de direction <lb/>à chacune des parties de leurs cordes, qui font les <lb/>côtez du parallelogramme GH, dont elle eſt diago-<lb/>nale. </s> |
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|
5081 <s xml:id="echoid-s3033" xml:space="preserve">Ce qu’il faloit démontrer.</s> |
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5082 <s xml:id="echoid-s3034" xml:space="preserve"/> |
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5083 </p> |
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5084 <div xml:id="echoid-div282" type="float" level="2" n="2"> |
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5085 <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement</note> |
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5086 <note position="left" xlink:label="note-0142-01" xlink:href="note-0142-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5087 </div> |
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5088 <p> |
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5089 <s xml:id="echoid-s3035" xml:space="preserve">On voit de-là, que ſi par le point C où ſe com-<lb/>muniquent les deux cordes qui ſoutiennent quel-<lb/>que poids que ce ſoit, on fait MN perpendiculaire à <lb/>la ligne de direction de ce poids, & </s> |
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5090 <s xml:id="echoid-s3036" xml:space="preserve">qu’aprés avoir pris <lb/>de part & </s> |
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5091 <s xml:id="echoid-s3037" xml:space="preserve">d’autre ſur cette ligne CM & </s> |
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5092 <s xml:id="echoid-s3038" xml:space="preserve">CN ègales en-<lb/>tr’elles, on faſſe aux points M & </s> |
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5093 <s xml:id="echoid-s3039" xml:space="preserve">N les perpendiculaires |
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5094 <pb o="117" file="0143" n="143" rhead="DE M. BORELLI."/> |
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5095 MG & </s> |
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5096 <s xml:id="echoid-s3040" xml:space="preserve">NH qui rencontrent auxpoints G & </s> |
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5097 <s xml:id="echoid-s3041" xml:space="preserve">H les <lb/> |
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5098 <anchor type="note" xlink:label="note-0143-01a" xlink:href="note-0143-01"/> |
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5099 cordes des puiſſances qui ſoutiennent ce poids: </s> |
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5100 <s xml:id="echoid-s3042" xml:space="preserve">elles <lb/>en détermineront des parties CG, CH, qui ſeront <lb/>toujours proportionelles à ces mêmes puiſſances.</s> |
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5101 <s xml:id="echoid-s3043" xml:space="preserve"/> |
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5102 </p> |
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5103 <div xml:id="echoid-div283" type="float" level="2" n="3"> |
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5104 <note position="right" xlink:label="note-0143-01" xlink:href="note-0143-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5105 </div> |
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5106 <p style="it"> |
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5107 <s xml:id="echoid-s3044" xml:space="preserve">Si M. </s> |
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5108 <s xml:id="echoid-s3045" xml:space="preserve">Borelli eut fait rèflèxion que les puiſſances R & </s> |
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5109 <s xml:id="echoid-s3046" xml:space="preserve"><lb/>S n’agiſſent pas ſeulement contre le poids T, mais auſſi <lb/>l’une contre l’autre ; </s> |
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5110 <s xml:id="echoid-s3047" xml:space="preserve">& </s> |
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5111 <s xml:id="echoid-s3048" xml:space="preserve">que de même qu’elles concourent en-<lb/>ſemble pour empêcber que ce poids n’attire à lui (fig. </s> |
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5112 <s xml:id="echoid-s3049" xml:space="preserve">18.) <lb/></s> |
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5113 <s xml:id="echoid-s3050" xml:space="preserve">le nœud C, de même auſſi cbacune d’elles concourt avec <lb/>lui pour empêcber que l’autre ne l’emporte. </s> |
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5114 <s xml:id="echoid-s3051" xml:space="preserve">Si, dî - je, il avoit <lb/>fait cette rèfléxion, il auroit vû ſans doute que chacune. </s> |
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5115 <s xml:id="echoid-s3052" xml:space="preserve">de <lb/>ces puiſſances fait impreſſion ſur ce nœud, non ſeulement <lb/>ſuivant la direction du poids qu’elles ſoutiennent, pour le <lb/>tenir toujours à même hauteur; </s> |
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5116 <s xml:id="echoid-s3053" xml:space="preserve">mais auſſi ſuivant l’hori-<lb/>zontale MCN, pour empêcher qu’aucune d’elles ne l’attire <lb/>n’y à droit, n’y à gaucbe: </s> |
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5117 <s xml:id="echoid-s3054" xml:space="preserve">D'où il auroit infailliblement conclu <lb/>que ces impreſſions horizontales, ètant diamétralement <lb/>oppoſées, doivent toujours être égales. </s> |
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5118 <s xml:id="echoid-s3055" xml:space="preserve">De-là voyant qu’el-<lb/>les augmentent, où diminuent néceſſairement à meſure que <lb/>les angles que font les cordes de ces puiſſances avec la ligne <lb/>de direction du poids qu’elles ſoutiennent, s’aprochent, où <lb/>s’éloignent de l’angle droit, il auroit enfin aperçû l’impoſſibi-<lb/>litè de faire, finon aucun, du moins un tel changement à leurs <lb/>d. </s> |
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5119 <s xml:id="echoid-s3056" xml:space="preserve">rections ſans en rompre l’équilibre.</s> |
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5120 <s xml:id="echoid-s3057" xml:space="preserve"/> |
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5121 </p> |
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5122 <p> |
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5123 <s xml:id="echoid-s3058" xml:space="preserve">@e dis ſinon aucun changement, parce qu’il a été <lb/>démontré (Cor. </s> |
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5124 <s xml:id="echoid-s3059" xml:space="preserve">1. </s> |
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5125 <s xml:id="echoid-s3060" xml:space="preserve">Prop. </s> |
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5126 <s xml:id="echoid-s3061" xml:space="preserve">1.) </s> |
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5127 <s xml:id="echoid-s3062" xml:space="preserve">qu’il n’eſt pas poſſible d’y <lb/>en faire aucun ſans rompre l’équilibre qui eſt (hyp.) </s> |
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5128 <s xml:id="echoid-s3063" xml:space="preserve">entre <lb/>ces puiſſances, & </s> |
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5129 <s xml:id="echoid-s3064" xml:space="preserve">le poids qu’elles ſoutiennent. </s> |
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5130 <s xml:id="echoid-s3065" xml:space="preserve">Nous <lb/>l’avons même conclu (Chap. </s> |
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5131 <s xml:id="echoid-s3066" xml:space="preserve">1.) </s> |
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5132 <s xml:id="echoid-s3067" xml:space="preserve">de la 68. </s> |
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5133 <s xml:id="echoid-s3068" xml:space="preserve">Prop. </s> |
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5134 <s xml:id="echoid-s3069" xml:space="preserve">d’où cet <lb/>Autheur tire un ſcbolie tout contraire par un raiſonnement dont <lb/>le défaut eſt préſentement aiſé à découvrir; </s> |
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5135 <s xml:id="echoid-s3070" xml:space="preserve">Voyez-le.</s> |
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5136 <s xml:id="echoid-s3071" xml:space="preserve"/> |
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5137 </p> |
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5138 <p style="it"> |
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5139 <s xml:id="echoid-s3072" xml:space="preserve">Sur ce qu’on vient de dire de l’uſage des impreſſions hori- |
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5140 <pb o="118" file="0144" n="144" rhead="EXAMEN DE L’OPINION"/> |
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5141 zontales que font ſur le nœud C (fig. </s> |
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5142 <s xml:id="echoid-s3073" xml:space="preserve">18. </s> |
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5143 <s xml:id="echoid-s3074" xml:space="preserve">& </s> |
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5144 <s xml:id="echoid-s3075" xml:space="preserve">19.) </s> |
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5145 <s xml:id="echoid-s3076" xml:space="preserve">les puiſſan-<lb/> |
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5146 <anchor type="note" xlink:label="note-0144-01a" xlink:href="note-0144-01"/> |
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5147 ces R & </s> |
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5148 <s xml:id="echoid-s3077" xml:space="preserve">S, il eſt aiſé de juger de celui des impreſſions ſem-<lb/>blables que font auſſi ſur le nœud C de leurs cordes ſuivant <lb/>le plan OH (fig. </s> |
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5149 <s xml:id="echoid-s3078" xml:space="preserve">17.) </s> |
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5150 <s xml:id="echoid-s3079" xml:space="preserve">les puiſſances A, B, D, E, F, <lb/>& </s> |
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5151 <s xml:id="echoid-s3080" xml:space="preserve">C. </s> |
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5152 <s xml:id="echoid-s3081" xml:space="preserve">auſſi ne s’y arrêtera-t-on pas davantage.</s> |
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5153 <s xml:id="echoid-s3082" xml:space="preserve"/> |
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5154 </p> |
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5155 <div xml:id="echoid-div284" type="float" level="2" n="4"> |
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5156 <note position="left" xlink:label="note-0144-01" xlink:href="note-0144-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5157 </div> |
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5158 <figure> |
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5159 <image file="0144-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0144-01"/> |
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5160 </figure> |
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5161 </div> |
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5162 <div xml:id="echoid-div286" type="section" level="1" n="179"> |
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5163 <head xml:id="echoid-head181" xml:space="preserve">PROPOSITION IV.</head> |
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5164 <p style="it"> |
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5165 <s xml:id="echoid-s3083" xml:space="preserve">DE quelque maniére qu’un poids ſoit ſoutenu avec des <lb/>cordes par quelque nombre de puiſſances que ce ſoit, <lb/>appliquées à tant de nœuds qu’on voudra; </s> |
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5166 <s xml:id="echoid-s3084" xml:space="preserve">chacune d’elles eſt <lb/>toujours à ce poids en raiſon compoſée d’autant d’autres raiſons <lb/>qu’il y a de nœuds entre cette puiſſance & </s> |
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5167 <s xml:id="echoid-s3085" xml:space="preserve">ce poids: </s> |
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5168 <s xml:id="echoid-s3086" xml:space="preserve">Sçavoir <lb/>par chaque nœud, de la raiſon qui eſt entre la proportionelle <lb/>à la force dont ce nœud eſt tiré ſuivant la corde qui lui donne <lb/>communication avec cette puiſſance, & </s> |
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5169 <s xml:id="echoid-s3087" xml:space="preserve">la ſomme des ſu-<lb/>blimitez moins celle des profondeurs de toutes les forces dont <lb/>les branches dans leſquelles ce même nœud ſe diviſe, ſont <lb/>tirèes chacune ſuivant ſa direction contre la réſiſtance qui leur <lb/>vient par la corde de communication de lui à ce poids.</s> |
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5170 <s xml:id="echoid-s3088" xml:space="preserve"/> |
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5171 </p> |
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5172 </div> |
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5173 <div xml:id="echoid-div287" type="section" level="1" n="180"> |
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5174 <head xml:id="echoid-head182" xml:space="preserve"><emph style="sc">Demonstration</emph>.</head> |
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5175 <p> |
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5176 <s xml:id="echoid-s3089" xml:space="preserve">Soit le poids T dont la corde C p ſe diviſe en tant <lb/> |
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5177 <anchor type="note" xlink:label="note-0144-02a" xlink:href="note-0144-02"/> |
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5178 de branches CZ, CX, CY, Cφ, &</s> |
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5179 <s xml:id="echoid-s3090" xml:space="preserve">c. </s> |
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5180 <s xml:id="echoid-s3091" xml:space="preserve">qu’on vou-<lb/>dra, dont celles qu’on voudra, ſe diviſent encore <lb/>en pluſieurs branches, & </s> |
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5181 <s xml:id="echoid-s3092" xml:space="preserve">celles qu’on voudra encore <lb/>de celles-ci en pluſieurs autres de la maniére qu’on <lb/>voit ici; </s> |
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5182 <s xml:id="echoid-s3093" xml:space="preserve">& </s> |
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5183 <s xml:id="echoid-s3094" xml:space="preserve">toujours de même juſqu’auſſi loin qu’on <lb/>voudra. </s> |
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5184 <s xml:id="echoid-s3095" xml:space="preserve">Commencez au premier nœud C à marquer <lb/>ſur les branches CZ, XC, YC, Cφ, &</s> |
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5185 <s xml:id="echoid-s3096" xml:space="preserve">c. </s> |
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5186 <s xml:id="echoid-s3097" xml:space="preserve">des parties <lb/>CM, CN, CP, Cθ, &</s> |
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5187 <s xml:id="echoid-s3098" xml:space="preserve">c. </s> |
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5188 <s xml:id="echoid-s3099" xml:space="preserve">qui ſoient entr’elles com-<lb/>me les forces avec leſquelles ces cordes ſont tirées <lb/>chacune ſuivant ſa direction. </s> |
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5189 <s xml:id="echoid-s3100" xml:space="preserve">Faites - en autant ſur |
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5190 <pb o="119" file="0145" n="145" rhead="DE M. BORELLI"/> |
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5191 les branches dans leſquelles celles-ci ſe ſubdiviſent; <lb/></s> |
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5192 <s xml:id="echoid-s3101" xml:space="preserve"> |
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5193 <anchor type="note" xlink:label="note-0145-01a" xlink:href="note-0145-01"/> |
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5194 & </s> |
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5195 <s xml:id="echoid-s3102" xml:space="preserve">toujours de même juſqu’aux derniéres auſquelles <lb/>les puiſſances A, E, D, B, F, G, H, I, K, φ, &</s> |
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5196 <s xml:id="echoid-s3103" xml:space="preserve">c. <lb/></s> |
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5197 <s xml:id="echoid-s3104" xml:space="preserve">ſont appliquées. </s> |
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5198 <s xml:id="echoid-s3105" xml:space="preserve">Cela fait, aprés avoir marqué des <lb/>extrémitez de toutes ces proportionelles (Avertiſſ. </s> |
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5199 <s xml:id="echoid-s3106" xml:space="preserve"><lb/>Chap. </s> |
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5200 <s xml:id="echoid-s3107" xml:space="preserve">2.) </s> |
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5201 <s xml:id="echoid-s3108" xml:space="preserve">les ſublimitez & </s> |
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5202 <s xml:id="echoid-s3109" xml:space="preserve">les profondeurs de toutes <lb/>ces forces, on trouvera que chacune de ces puiſ-<lb/>ſances, par exemple, la puiſſance D eſt toujours à <lb/>ce poids en raiſon compoſée d’autant d’autres rai-<lb/>ſons telles que cette propoſition porte, qu’il y a de <lb/>nœuds entre cette puiſſance & </s> |
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5203 <s xml:id="echoid-s3110" xml:space="preserve">lui: </s> |
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5204 <s xml:id="echoid-s3111" xml:space="preserve">Car 1°. </s> |
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5205 <s xml:id="echoid-s3112" xml:space="preserve">La puiſ-<lb/>ſance D étant (hyp) à la puiſſance E, comme O S <lb/>à OV.</s> |
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5206 <s xml:id="echoid-s3113" xml:space="preserve">, elle eſt auſſi (Prop. </s> |
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5207 <s xml:id="echoid-s3114" xml:space="preserve">3.) </s> |
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5208 <s xml:id="echoid-s3115" xml:space="preserve">à la force dont<unsure/> le <lb/>nœud O leur réſiſte ſuivant OZ, comme OS à la <lb/>ſomme de leurs ſublimitez O ſ & </s> |
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5209 <s xml:id="echoid-s3116" xml:space="preserve">O u. </s> |
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5210 <s xml:id="echoid-s3117" xml:space="preserve">2°. </s> |
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5211 <s xml:id="echoid-s3118" xml:space="preserve">Cette <lb/>même force étant auſſi (hyp.) </s> |
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5212 <s xml:id="echoid-s3119" xml:space="preserve">aux puiſſances A & </s> |
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5213 <s xml:id="echoid-s3120" xml:space="preserve">B, <lb/>comme ZR à ZL & </s> |
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5214 <s xml:id="echoid-s3121" xml:space="preserve">ZQ, elle eſt de méme (Prop. </s> |
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5215 <s xml:id="echoid-s3122" xml:space="preserve"><lb/>3.) </s> |
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5216 <s xml:id="echoid-s3123" xml:space="preserve">à la réſiſtance que leur fait le nœud Z ſuivant <lb/>Z C, comme Z R à la ſomme des ſublimitez Z r & </s> |
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5217 <s xml:id="echoid-s3124" xml:space="preserve"><lb/>Z q moins la profondeur Z l. </s> |
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5218 <s xml:id="echoid-s3125" xml:space="preserve">3°. </s> |
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5219 <s xml:id="echoid-s3126" xml:space="preserve">Enfin la valeur <lb/>de cette réſiſtance étant encore (hyp.) </s> |
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5220 <s xml:id="echoid-s3127" xml:space="preserve">aux forces <lb/>dont le nœud C eſt tiré ſuivant C X, C Y, C φ. </s> |
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5221 <s xml:id="echoid-s3128" xml:space="preserve">&</s> |
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5222 <s xml:id="echoid-s3129" xml:space="preserve">c. </s> |
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5223 <s xml:id="echoid-s3130" xml:space="preserve"><lb/>comme CM à CN, CP, C θ, &</s> |
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5224 <s xml:id="echoid-s3131" xml:space="preserve">c. </s> |
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5225 <s xml:id="echoid-s3132" xml:space="preserve">elle eſt auſſi <lb/>(Prop. </s> |
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5226 <s xml:id="echoid-s3133" xml:space="preserve">3.) </s> |
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5227 <s xml:id="echoid-s3134" xml:space="preserve">au poids T, comme CM à la ſomme des <lb/>ſublimitez C m, C n, &</s> |
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5228 <s xml:id="echoid-s3135" xml:space="preserve">c. </s> |
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5229 <s xml:id="echoid-s3136" xml:space="preserve">moins celle des profondeurs <lb/>Cλ, C p, &</s> |
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5230 <s xml:id="echoid-s3137" xml:space="preserve">c. </s> |
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5231 <s xml:id="echoid-s3138" xml:space="preserve">Donc en multipliant par ordre ces <lb/>trois rangées de proportionelles, la puiſſance D ſe <lb/>trouvera au poids T, comme le produit fait des <lb/>trois antécédens OS, ZR, & </s> |
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5232 <s xml:id="echoid-s3139" xml:space="preserve">CM, au produit fait <lb/>de leur trois conſéquens Oſ + Ou, Zr + Zq -<lb/>Zl, & </s> |
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5233 <s xml:id="echoid-s3140" xml:space="preserve">Cm + Cn - Cp - Cλ. </s> |
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5234 <s xml:id="echoid-s3141" xml:space="preserve">C’eſt - à - dire, en <lb/>raiſon compoſée des trois raiſons de OS à Oſ + <lb/>Ou, de Z R à Zr + Zq - Zl, & </s> |
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5235 <s xml:id="echoid-s3142" xml:space="preserve">de CM à Cm + <lb/>Cn - Cp - Cλ, qu’on voit telles que cette pro-<lb/>poſition porte. </s> |
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5236 <s xml:id="echoid-s3143" xml:space="preserve">Or il n’y a en eſfet que trois nœuds |
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5237 <pb o="120" file="0146" n="146" rhead="EXAMEN DE L’OPINION"/> |
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5238 O, Z, & </s> |
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5239 <s xml:id="echoid-s3144" xml:space="preserve">C, entre cette puiſſance & </s> |
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5240 <s xml:id="echoid-s3145" xml:space="preserve">ce poids: </s> |
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5241 <s xml:id="echoid-s3146" xml:space="preserve">Donc <lb/> |
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5242 <anchor type="note" xlink:label="note-0146-01a" xlink:href="note-0146-01"/> |
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5243 la puiſſance D eſt au poids T en raiſon compoſée <lb/>d’autant d’autres raiſons telles que cette propoſition <lb/>porte, qu’il y a de nœuds entre cette puiſſance & </s> |
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5244 <s xml:id="echoid-s3147" xml:space="preserve"><lb/>ce poids. </s> |
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5245 <s xml:id="echoid-s3148" xml:space="preserve">On prouvera de même que la puiſſance A <lb/>eſt à ce poids en raiſon compoſée de ZL à Z r + <lb/>Z q - Zl, & </s> |
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5246 <s xml:id="echoid-s3149" xml:space="preserve">de CM à C m + C n - C p - C λ. <lb/></s> |
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5247 <s xml:id="echoid-s3150" xml:space="preserve">On trouvera encore de même que la puiſſance F <lb/>eſt à ce même poids en raiſon compoſée de X β à <lb/>X b + X f, & </s> |
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5248 <s xml:id="echoid-s3151" xml:space="preserve">de CN à C m + C n - C p - C λ; </s> |
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5249 <s xml:id="echoid-s3152" xml:space="preserve"><lb/>& </s> |
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5250 <s xml:id="echoid-s3153" xml:space="preserve">ainſi de toutes les autres puiſſances, en quelque <lb/>nombre qu’elles ſoient, de quelque maniére, & </s> |
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5251 <s xml:id="echoid-s3154" xml:space="preserve">à <lb/>quelque nombre de nœuds qu’elles ſoient appli-<lb/>quées. </s> |
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5252 <s xml:id="echoid-s3155" xml:space="preserve">D’où l’on voit en général, que de quelque <lb/>maniére qu’un poids ſoit ſoutenu avec des cordes <lb/>par quelque nombre de puiſſances que ce ſoit, ap-<lb/>pliquées à tant de nœuds qu’on voudra, chacune <lb/>d’elles eſt toujours à ce poids en raiſon compoſée <lb/>d’autant d’autres telles que cette propoſition porte, <lb/>qu’il y a de nœuds entre cette puiſſance & </s> |
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5253 <s xml:id="echoid-s3156" xml:space="preserve">ce poids. </s> |
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5254 <s xml:id="echoid-s3157" xml:space="preserve"><lb/>Ce qu’il faloit démontrer.</s> |
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5255 <s xml:id="echoid-s3158" xml:space="preserve"/> |
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5256 </p> |
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5257 <div xml:id="echoid-div287" type="float" level="2" n="1"> |
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5258 <note position="left" xlink:label="note-0144-02" xlink:href="note-0144-02a" xml:space="preserve">fig. 20.</note> |
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5259 <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5260 <note position="left" xlink:label="note-0146-01" xlink:href="note-0146-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5261 </div> |
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5262 </div> |
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5263 <div xml:id="echoid-div289" type="section" level="1" n="181"> |
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5264 <head xml:id="echoid-head183" xml:space="preserve"><emph style="sc">Corollaire</emph> I.</head> |
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5265 <p> |
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5266 <s xml:id="echoid-s3159" xml:space="preserve">On voit qu’en prenant ZR égale à O ſ + O u, <lb/>avec ZL & </s> |
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5267 <s xml:id="echoid-s3160" xml:space="preserve">ZQ à ZR en même proportion qu’elles <lb/>ſont ici; </s> |
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5268 <s xml:id="echoid-s3161" xml:space="preserve">de plus CM égale à Zq + Zr - Zl, <lb/>avec CN, CP, Cθ, &</s> |
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5269 <s xml:id="echoid-s3162" xml:space="preserve">c. </s> |
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5270 <s xml:id="echoid-s3163" xml:space="preserve">auſſi à CM en même <lb/>proportion qu’elles ſont ici; </s> |
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5271 <s xml:id="echoid-s3164" xml:space="preserve">la puiſſance D ſera au <lb/>poids T, comme OS à Cm + Cn - Cλ - Cp ±<unsure/> <lb/>&</s> |
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5272 <s xml:id="echoid-s3165" xml:space="preserve">c. </s> |
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5273 <s xml:id="echoid-s3166" xml:space="preserve">c’eſt-à-dire, comme ſa proportionelle à la ſomme <lb/>des ſublimitez moins celle des profondeurs des for-<lb/>ces avec leſquelles les branches du premier nœud <lb/>C ſont tirées chacune ſuivant ſa direction. </s> |
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5274 <s xml:id="echoid-s3167" xml:space="preserve">Il en faut <lb/>penſer autant de toutes les autres puiſſances appli-<lb/>quées au poids T, ſoit de prés, ſoit de loin.</s> |
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5275 <s xml:id="echoid-s3168" xml:space="preserve"/> |
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5276 </p> |
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5277 <pb o="121" file="0147" n="147" rhead="DE M. BORELLI."/> |
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5278 <p style="it"> |
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5279 <s xml:id="echoid-s3169" xml:space="preserve">On peut comparer cette propoſition avec ce Corollaire à la <lb/> |
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5280 <anchor type="note" xlink:label="note-0147-01a" xlink:href="note-0147-01"/> |
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5281 propoſition 78. </s> |
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5282 <s xml:id="echoid-s3170" xml:space="preserve">de M. </s> |
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5283 <s xml:id="echoid-s3171" xml:space="preserve">Borelli.</s> |
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5284 <s xml:id="echoid-s3172" xml:space="preserve"/> |
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5285 </p> |
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5286 <div xml:id="echoid-div289" type="float" level="2" n="1"> |
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5287 <note position="right" xlink:label="note-0147-01" xlink:href="note-0147-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5288 </div> |
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5289 </div> |
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5290 <div xml:id="echoid-div291" type="section" level="1" n="182"> |
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5291 <head xml:id="echoid-head184" xml:space="preserve"><emph style="sc">Corollaire</emph> II.</head> |
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5292 <p> |
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5293 <s xml:id="echoid-s3173" xml:space="preserve">Lors qu’un poids attaché à une corde qui a plu-<lb/> |
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5294 <anchor type="note" xlink:label="note-0147-02a" xlink:href="note-0147-02"/> |
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5295 ſieurs nœuds par chacun deſquels, entre toutes <lb/>les branches qui en naiſſent, il n’y en a qu’une qui <lb/>ſe ſubdiviſe en d’autres branches: </s> |
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5296 <s xml:id="echoid-s3174" xml:space="preserve">lors dî-je que le <lb/>poids T attaché à une telle corde, eſt ſoutenu par <lb/>pluſieurs puiſſances Y, X, S, R, V, Z, &</s> |
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5297 <s xml:id="echoid-s3175" xml:space="preserve">c. </s> |
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5298 <s xml:id="echoid-s3176" xml:space="preserve">telle-<lb/>ment appliquées aux derniéres de ces branches que <lb/>tous les nœuds F, E, C, &</s> |
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5299 <s xml:id="echoid-s3177" xml:space="preserve">c. </s> |
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5300 <s xml:id="echoid-s3178" xml:space="preserve">d’où elles naiſſent, ſe <lb/>trouvent dans la ligne de direction de ce poids; <lb/></s> |
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5301 <s xml:id="echoid-s3179" xml:space="preserve">chacune de ces puiſſances, en quelque nombre qu’el-<lb/>les ſoient, eſt toujours à ce poids, comme la pro-<lb/>portionelle de cette même puiſſance à la ſomme des <lb/>ſublimitez moins celle des profondeurs de tout ce <lb/>qu’il y en a d’appliquées à ce même poids: </s> |
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5302 <s xml:id="echoid-s3180" xml:space="preserve">car ſi l’on <lb/>prend ſur les branches de chaque nœud des parties <lb/>OF, EI, CB, CA, EH, FK, FN, EM, &</s> |
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5303 <s xml:id="echoid-s3181" xml:space="preserve">c. </s> |
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5304 <s xml:id="echoid-s3182" xml:space="preserve"><lb/>proportionelles aux forces avec leſquelles chacune <lb/>d’elles eſt tirée ſuivant ſa direction, & </s> |
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5305 <s xml:id="echoid-s3183" xml:space="preserve">que des ex-<lb/>trémitez de ces mêmes parties on marque (avert. </s> |
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5306 <s xml:id="echoid-s3184" xml:space="preserve"><lb/>Chap. </s> |
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5307 <s xml:id="echoid-s3185" xml:space="preserve">2.) </s> |
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5308 <s xml:id="echoid-s3186" xml:space="preserve">leurs ſublimitez avec leurs profondeurs; </s> |
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5309 <s xml:id="echoid-s3187" xml:space="preserve"><lb/>on trouvera 1°. </s> |
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5310 <s xml:id="echoid-s3188" xml:space="preserve">que les proportionelles FN, EM, <lb/>&</s> |
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5311 <s xml:id="echoid-s3189" xml:space="preserve">c. </s> |
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5312 <s xml:id="echoid-s3190" xml:space="preserve">qui ſe trouvent dans la ligne de direction de ce <lb/>poids, ſont égales aux ſublimitez FN, FM, &</s> |
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5313 <s xml:id="echoid-s3191" xml:space="preserve">c. </s> |
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5314 <s xml:id="echoid-s3192" xml:space="preserve">des <lb/>forces avec leſquelles elles ſont tirées ſuivant leur <lb/>direction, c’eſt-à-dire, ſuivant cette même ligne. </s> |
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5315 <s xml:id="echoid-s3193" xml:space="preserve"><lb/>2°. </s> |
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5316 <s xml:id="echoid-s3194" xml:space="preserve">On trouvera encore que chacune de ces mêmes <lb/>proportionelles, par exemple FN eſt auſſi toujours <lb/>égale à la ſomme des ſublimitez moins celle des pro-<lb/>fondeurs des forces, ou des puiſſances appliquées au |
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5317 <pb o="122" file="0148" n="148" rhead="EXAMEN DE L’OPINION"/> |
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5318 nœud E qui eſt immédiatement au-deſſus du nœud <lb/> |
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5319 <anchor type="note" xlink:label="note-0148-01a" xlink:href="note-0148-01"/> |
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5320 F depuis lequel cette proportionelle a été priſe: <lb/></s> |
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5321 <s xml:id="echoid-s3195" xml:space="preserve">puis que (hyp) cette même proportionelle, & </s> |
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5322 <s xml:id="echoid-s3196" xml:space="preserve">(Prop. </s> |
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5323 <s xml:id="echoid-s3197" xml:space="preserve"><lb/>3.) </s> |
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5324 <s xml:id="echoid-s3198" xml:space="preserve">cette même ſomme ſont à la proportionelle EI <lb/>de la puiſſance X, comme la force dont le nœud E <lb/>eſt tire ſuivant la corde EF, eſt à cette même puiſſan-<lb/>ce. </s> |
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5325 <s xml:id="echoid-s3199" xml:space="preserve">Pour la même raiſon EM eſt égale à la ſomme <lb/>des ſublimitez moins celle des profondeurs des forces <lb/>où des puiſſances appliquées au nœud C qui eſt im-<lb/>médiatement au-deſſus de E; </s> |
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5326 <s xml:id="echoid-s3200" xml:space="preserve">& </s> |
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5327 <s xml:id="echoid-s3201" xml:space="preserve">ainſi des autres <lb/>proportionelles qui ſe trouvent dans la ligne de di-<lb/>rection du poids T. </s> |
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5328 <s xml:id="echoid-s3202" xml:space="preserve">De-là on verra que chacune des <lb/>ſublimitez FN, EM, &</s> |
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5329 <s xml:id="echoid-s3203" xml:space="preserve">c. </s> |
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5330 <s xml:id="echoid-s3204" xml:space="preserve">des forces qui ſuivent la direc-<lb/>tion de ce poids, eſt toujours égale à la ſomme des ſu-<lb/>blimitez moins celle des profondeurs des forces, ou <lb/>des puiſſances appliquées au nœud qui eſt immédia-<lb/>tement au-deſſus de celui depuis lequel elle ſe prend: </s> |
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5331 <s xml:id="echoid-s3205" xml:space="preserve"><lb/>D’où il ſuit que la ſublimité FN qui ſe prend depuis <lb/>le plus bas de tous ces nœuds, eſt égale à la ſomme <lb/>des ſublimitez moins celle des profondeurs de toutes <lb/>les puiſſances X, V, S, R, &</s> |
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5332 <s xml:id="echoid-s3206" xml:space="preserve">c. </s> |
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5333 <s xml:id="echoid-s3207" xml:space="preserve">appliquées à tous <lb/>les autres nœuds E, C, &</s> |
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5334 <s xml:id="echoid-s3208" xml:space="preserve">c. </s> |
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5335 <s xml:id="echoid-s3209" xml:space="preserve">Or on vient de voir <lb/>dans le Corollaire précédent que chacune de toutes <lb/>les puiſſances qui ſoutiennent le poids T, par exem-<lb/>ple S, ou Y, eſt à ce poids, comme ſa proportio-<lb/>nelle CB, ou OF à la ſomme des ſublimitez moins <lb/>celle des profondeurs des forces avec leſquelles <lb/>toutes les branches du plus bas nœud F ſont tirées <lb/>chacune ſuivant ſa direction contre le poids T; </s> |
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5336 <s xml:id="echoid-s3210" xml:space="preserve"><lb/>c’eſt-à-dire, à la ſomme faite de la ſublimité FN, <lb/>& </s> |
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5337 <s xml:id="echoid-s3211" xml:space="preserve">de la ſomme des ſublimitez moins les profondeurs <lb/>des puiſſances Y, Z, &</s> |
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5338 <s xml:id="echoid-s3212" xml:space="preserve">c. </s> |
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5339 <s xml:id="echoid-s3213" xml:space="preserve">immédiatement appliquées <lb/>au nœud F: </s> |
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5340 <s xml:id="echoid-s3214" xml:space="preserve">Donc chacune des puiſſances Y, X, S, <lb/>R, V, Z, &</s> |
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5341 <s xml:id="echoid-s3215" xml:space="preserve">c. </s> |
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5342 <s xml:id="echoid-s3216" xml:space="preserve">eſt en ce cas au poids T, comme ſa |
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5343 <pb o="123" file="0149" n="149" rhead="DE M. BORELLI."/> |
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5344 proportionelle à la ſomme des ſublimitez, moins celle <lb/> |
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5345 <anchor type="note" xlink:label="note-0149-01a" xlink:href="note-0149-01"/> |
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5346 des profondeurs de tout ce qu’il y en a d’appliquées <lb/>à ce même poids.</s> |
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5347 <s xml:id="echoid-s3217" xml:space="preserve"/> |
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5348 </p> |
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5349 <div xml:id="echoid-div291" type="float" level="2" n="1"> |
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5350 <note position="right" xlink:label="note-0147-02" xlink:href="note-0147-02a" xml:space="preserve">fig. 21. <lb/>22.</note> |
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5351 <note position="left" xlink:label="note-0148-01" xlink:href="note-0148-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5352 <note position="right" xlink:label="note-0149-01" xlink:href="note-0149-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5353 </div> |
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5354 </div> |
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5355 <div xml:id="echoid-div293" type="section" level="1" n="183"> |
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5356 <head xml:id="echoid-head185" xml:space="preserve"><emph style="sc">Corollaire</emph> III.</head> |
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5357 <p> |
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5358 <s xml:id="echoid-s3218" xml:space="preserve">D’où l’on voit que la ſomme de toutes ces puiſ-<lb/>ſances eſt à ce poids, comme la ſomme de leurs pro-<lb/>portionelles à la ſomme de leurs ſublimitez moins <lb/>celle de leurs profondeurs: </s> |
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5359 <s xml:id="echoid-s3219" xml:space="preserve">De ſorte que s’il n’y <lb/>en avoit que deux d’appliquées à chaque nœud <lb/>dont l’une tirât à droit & </s> |
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5360 <s xml:id="echoid-s3220" xml:space="preserve">l’autre à gauche, & </s> |
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5361 <s xml:id="echoid-s3221" xml:space="preserve">que <lb/>toutes celles de chaque côté fuſſent égales entr’elles, <lb/>& </s> |
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5362 <s xml:id="echoid-s3222" xml:space="preserve">avec des directions paralleles entr’elles; </s> |
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5363 <s xml:id="echoid-s3223" xml:space="preserve">la ſomme <lb/>(fig. </s> |
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5364 <s xml:id="echoid-s3224" xml:space="preserve">21.) </s> |
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5365 <s xml:id="echoid-s3225" xml:space="preserve">des ſublimitez, par exemple F o, + F k, où <lb/>Ei + Eh, où Cb + Ca, &</s> |
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5366 <s xml:id="echoid-s3226" xml:space="preserve">c. </s> |
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5367 <s xml:id="echoid-s3227" xml:space="preserve">des deux puiſſances ap-<lb/>pliquées au quel que ce ſoit des nœuds F, E, C, &</s> |
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5368 <s xml:id="echoid-s3228" xml:space="preserve">c. <lb/></s> |
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5369 <s xml:id="echoid-s3229" xml:space="preserve">ou bien la différence (fig. </s> |
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5370 <s xml:id="echoid-s3230" xml:space="preserve">22.) </s> |
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5371 <s xml:id="echoid-s3231" xml:space="preserve">de la ſublimité de l’une <lb/>à la profondeur de l’autre, par exemple Fk,- Fo, <lb/>ou Eh - Ei, au Ca - Cb, &</s> |
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5372 <s xml:id="echoid-s3232" xml:space="preserve">c. </s> |
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5373 <s xml:id="echoid-s3233" xml:space="preserve">étant alors la même <lb/>pour tous ces nœuds, auſſi-bien que les proportio-<lb/>nelles de ces puiſſances; </s> |
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5374 <s xml:id="echoid-s3234" xml:space="preserve">la ſomme de ces mêmes <lb/>puiſſances ſeroit alors au poids T, comme la ſomme <lb/>des proportionelles de deux d’entr’elles appliquées à un <lb/>même nœud, quel qu’il ſoit, eſt à la ſomme (fig. </s> |
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5375 <s xml:id="echoid-s3235" xml:space="preserve">21.) </s> |
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5376 <s xml:id="echoid-s3236" xml:space="preserve"><lb/>des ſublimitez de ces deux puiſſances, où (fig. </s> |
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5377 <s xml:id="echoid-s3237" xml:space="preserve">22.) </s> |
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5378 <s xml:id="echoid-s3238" xml:space="preserve">à la <lb/>différence qui eſt entre la ſublimité de l’une, & </s> |
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5379 <s xml:id="echoid-s3239" xml:space="preserve">la <lb/>profondeur del ’autre.</s> |
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5380 <s xml:id="echoid-s3240" xml:space="preserve"/> |
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5381 </p> |
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5382 </div> |
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5383 <div xml:id="echoid-div294" type="section" level="1" n="184"> |
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5384 <head xml:id="echoid-head186" xml:space="preserve"><emph style="sc">Corollaire</emph> IV.</head> |
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5385 <p> |
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5386 <s xml:id="echoid-s3241" xml:space="preserve">Ce qui fait enfin voir que ſi toutes les puiſſances <lb/>Y, X, S, R, V, Z, &</s> |
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5387 <s xml:id="echoid-s3242" xml:space="preserve">c. </s> |
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5388 <s xml:id="echoid-s3243" xml:space="preserve">étoient égales entr’elles, & </s> |
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5389 <s xml:id="echoid-s3244" xml:space="preserve"><lb/>que toutes leurs directions fiſſent avec celle de ce <lb/>poids des angles égaux auſſi entr’eux, leur ſomme <lb/>ſeroit alors à ce même poids, (fig. </s> |
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5390 <s xml:id="echoid-s3245" xml:space="preserve">21.) </s> |
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5391 <s xml:id="echoid-s3246" xml:space="preserve">comme une <lb/>de leurs proportionelles à une de leurs ſublimitez, |
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5392 <pb o="124" file="0150" n="150" rhead="EXAMEN DE L’OPINION"/> |
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5393 l’une & </s> |
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5394 <s xml:id="echoid-s3247" xml:space="preserve">l’autre choiſie à diſcretion; </s> |
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5395 <s xml:id="echoid-s3248" xml:space="preserve">c’eſt - à - dire, <lb/> |
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5396 <anchor type="note" xlink:label="note-0150-01a" xlink:href="note-0150-01"/> |
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5397 comme le ſinus total au ſinus du complement de <lb/>celui qu’on voudra de ces mêmes angles.</s> |
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5398 <s xml:id="echoid-s3249" xml:space="preserve"/> |
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5399 </p> |
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5400 <div xml:id="echoid-div294" type="float" level="2" n="1"> |
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5401 <note position="left" xlink:label="note-0150-01" xlink:href="note-0150-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5402 </div> |
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5403 <p style="it"> |
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5404 <s xml:id="echoid-s3250" xml:space="preserve">On peut encore comparer ces trois Corollaires à la Propo-<lb/>ſition 71. </s> |
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5405 <s xml:id="echoid-s3251" xml:space="preserve">de M. </s> |
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5406 <s xml:id="echoid-s3252" xml:space="preserve">Borelli & </s> |
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5407 <s xml:id="echoid-s3253" xml:space="preserve">au Corollaire qu’il en tire.</s> |
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5408 <s xml:id="echoid-s3254" xml:space="preserve"/> |
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5409 </p> |
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|
5410 </div> |
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5411 <div xml:id="echoid-div296" type="section" level="1" n="185"> |
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5412 <head xml:id="echoid-head187" xml:space="preserve"><emph style="sc">Corollaire</emph> V.</head> |
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5413 <p> |
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5414 <s xml:id="echoid-s3255" xml:space="preserve">On voit encore de cette propoſition que dans l’hy-<lb/> |
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5415 <anchor type="note" xlink:label="note-0150-02a" xlink:href="note-0150-02"/> |
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5416 pothéſe ou les lignes de direction de tous les points <lb/>du corps A D concourent au centre E de la terre, <lb/>de quelque maniére que ce poids ſoit ſoutenu par <lb/>tant de puiſſances F, G, H, I, K, L, M, N, &</s> |
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5417 <s xml:id="echoid-s3256" xml:space="preserve">c. <lb/></s> |
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5418 <s xml:id="echoid-s3257" xml:space="preserve">qu’on voudra avec des cordes qui lui ſoient appli-<lb/>quées en tant de points A, B, C, D, &</s> |
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5419 <s xml:id="echoid-s3258" xml:space="preserve">c. </s> |
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5420 <s xml:id="echoid-s3259" xml:space="preserve">qu’on vou-<lb/>dra; </s> |
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5421 <s xml:id="echoid-s3260" xml:space="preserve">chacune de ces puiſſances ſera toujours à ce <lb/>poids, comme chacune de leurs proportionelles à la <lb/>ſomme des ſublimitez des forces avec leſquelles ces <lb/>points A, B, C, D, &</s> |
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5422 <s xml:id="echoid-s3261" xml:space="preserve">c. </s> |
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5423 <s xml:id="echoid-s3262" xml:space="preserve">ſont tirez ſuivant les lignes <lb/>AE, BE, CE, DE, &</s> |
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5424 <s xml:id="echoid-s3263" xml:space="preserve">c. </s> |
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5425 <s xml:id="echoid-s3264" xml:space="preserve">par le concours d’action <lb/>des puiſſances qui y ſont appliquées: </s> |
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5426 <s xml:id="echoid-s3265" xml:space="preserve">des ſublimitez, <lb/>dî-je, déterminées comme dans le Corollaire 1. </s> |
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5427 <s xml:id="echoid-s3266" xml:space="preserve">Car <lb/>il eſt clair que ce poids agit contre toutes ces puiſſan-<lb/>ces de même que feroit une force qui lui ſeroit égale, <lb/>ſi AE, BE, CE, DE, &</s> |
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5428 <s xml:id="echoid-s3267" xml:space="preserve">c. </s> |
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5429 <s xml:id="echoid-s3268" xml:space="preserve">étoient autant de cor-<lb/>des attachées enſemble au point E par un nœud <lb/>commun auquel cette force fut appliquée ſuivant la <lb/>direction ZE du centre de gravité de ce poids. </s> |
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5430 <s xml:id="echoid-s3269" xml:space="preserve">Or <lb/>en ce cas les points A, B, C, D, &</s> |
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5431 <s xml:id="echoid-s3270" xml:space="preserve">c. </s> |
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5432 <s xml:id="echoid-s3271" xml:space="preserve">étant comme <lb/>autant de nœuds auſquels ſont appliquées, chacune <lb/>ſuivant ſa direction, les puiſſances F, G, H, I, K, <lb/>L, M, N, &</s> |
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5433 <s xml:id="echoid-s3272" xml:space="preserve">c. </s> |
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5434 <s xml:id="echoid-s3273" xml:space="preserve">ſi l’on prend depuis E ſur chacune <lb/>des lignes AE, BE, CE, DE, &</s> |
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5435 <s xml:id="echoid-s3274" xml:space="preserve">c. </s> |
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5436 <s xml:id="echoid-s3275" xml:space="preserve">une partie Eg, <lb/>Ef, Ec, Eb, &</s> |
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5437 <s xml:id="echoid-s3276" xml:space="preserve">c. </s> |
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5438 <s xml:id="echoid-s3277" xml:space="preserve">égale à la ſomme des ſublimitez |
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5439 <pb o="125" file="0151" n="151" rhead="DE M. BORELLI."/> |
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5440 moins celle des profondeurs des puiſſances appli-<lb/> |
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5441 <anchor type="note" xlink:label="note-0151-01a" xlink:href="note-0151-01"/> |
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5442 quées à chacun des points A, B, C, D, &</s> |
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5443 <s xml:id="echoid-s3278" xml:space="preserve">c. </s> |
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5444 <s xml:id="echoid-s3279" xml:space="preserve">On <lb/>trouvera (Cor 1.) </s> |
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5445 <s xml:id="echoid-s3280" xml:space="preserve">que chacune de toutes ces puiſ-<lb/>ſances F, G, H, I, K, L, M, N, &</s> |
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5446 <s xml:id="echoid-s3281" xml:space="preserve">c. </s> |
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5447 <s xml:id="echoid-s3282" xml:space="preserve">ſeroit alors à <lb/>la force qu’on ſuppoſe en E, comme chacune de leurs <lb/>proportionelles DO, CP, BQ, DX, AR, CV, BT, <lb/>AS, &</s> |
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5448 <s xml:id="echoid-s3283" xml:space="preserve">c. </s> |
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5449 <s xml:id="echoid-s3284" xml:space="preserve">à la ſomme des ſublimitez, El, Ee, Ed, <lb/>Ea, &</s> |
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5450 <s xml:id="echoid-s3285" xml:space="preserve">c. </s> |
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5451 <s xml:id="echoid-s3286" xml:space="preserve">des forces dont les nœuds A, B, C, D, &</s> |
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5452 <s xml:id="echoid-s3287" xml:space="preserve">c. <lb/></s> |
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5453 <s xml:id="echoid-s3288" xml:space="preserve">ſeroient alors tirez, chacun ſuivant la ligne qui le <lb/>joint avec le point E: </s> |
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5454 <s xml:id="echoid-s3289" xml:space="preserve">Donc chacune de ces mêmes <lb/>puiſſances eſt en effet au poids AD, comme chacune <lb/>de leurs proportionelles à la ſomme de telles ſubli-<lb/>mitez des forces avec leſquelles les points A, B, C, D, <lb/>&</s> |
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5455 <s xml:id="echoid-s3290" xml:space="preserve">c. </s> |
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5456 <s xml:id="echoid-s3291" xml:space="preserve">ſont tirez ſuivant les lignes AE, BE, CE, DE, <lb/>&</s> |
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5457 <s xml:id="echoid-s3292" xml:space="preserve">c. </s> |
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5458 <s xml:id="echoid-s3293" xml:space="preserve">par le concours d’action de celles qui y ſont ap-<lb/>pliquées.</s> |
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5459 <s xml:id="echoid-s3294" xml:space="preserve"/> |
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5460 </p> |
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5461 <div xml:id="echoid-div296" type="float" level="2" n="1"> |
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5462 <note position="left" xlink:label="note-0150-02" xlink:href="note-0150-02a" xml:space="preserve">fig. 23. <lb/>24.</note> |
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5463 <note position="right" xlink:label="note-0151-01" xlink:href="note-0151-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5464 </div> |
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5465 <p style="it"> |
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5466 <s xml:id="echoid-s3295" xml:space="preserve">Si les forces, avec leſquelles les différens points A, B, C, <lb/>D, &</s> |
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5467 <s xml:id="echoid-s3296" xml:space="preserve">c. </s> |
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5468 <s xml:id="echoid-s3297" xml:space="preserve">du corps AD, ſont tirez ſuivant des lignes qui con-<lb/>courent au centre E de la terre, par le concours d’action des <lb/>puiſſances qui y ſont appliquées, avoient quelque profondeur, <lb/>on trouveroit de même que chacune de toutes les puiſſances qui <lb/>ſoutiennent ce poids, lui ſeroit en même raiſon que chacune de <lb/>leurs proportionnelles à la ſomme de telles ſublimitez moins <lb/>celle des profondeurs de ces mêmes forces: </s> |
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5469 <s xml:id="echoid-s3298" xml:space="preserve">mais ce cas étant <lb/>naturellement impoſſible; </s> |
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5470 <s xml:id="echoid-s3299" xml:space="preserve">puiſqu’il faudroit pour cela que ce <lb/>poids comprît pour le moins plus du quart de la circonférence <lb/>de la terre, on n’a pas crû qu’il fût néceſſaire de l’exprimer.</s> |
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5471 <s xml:id="echoid-s3300" xml:space="preserve"/> |
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5472 </p> |
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5473 </div> |
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5474 <div xml:id="echoid-div298" type="section" level="1" n="186"> |
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5475 <head xml:id="echoid-head188" xml:space="preserve"><emph style="sc">Corollaire</emph> VI.</head> |
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5476 <p> |
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5477 <s xml:id="echoid-s3301" xml:space="preserve">On voit préſentement que dans l’hypotheſe ordi-<lb/>naire, ou l’on regarde les directions AE, BE, CE, <lb/>DE, &</s> |
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5478 <s xml:id="echoid-s3302" xml:space="preserve">c. </s> |
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5479 <s xml:id="echoid-s3303" xml:space="preserve">comme paralleles entr’elles, chacune des <lb/>ſublimitez El, Ee, Ed, Ea, &</s> |
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5480 <s xml:id="echoid-s3304" xml:space="preserve">c. </s> |
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5481 <s xml:id="echoid-s3305" xml:space="preserve">déterminées ſur |
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5482 <pb o="126" file="0152" n="152" rhead="EXAMEN DE L’OPINION"/> |
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5483 ZE par chacune des proportionelles Eg, Ef, Ec, <lb/> |
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5484 <anchor type="note" xlink:label="note-0152-01a" xlink:href="note-0152-01"/> |
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5485 Eb, &</s> |
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5486 <s xml:id="echoid-s3306" xml:space="preserve">c. </s> |
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5487 <s xml:id="echoid-s3307" xml:space="preserve">qu’on vient de prendre egales à la ſomme <lb/>des ſublimitez moins celle des profondeurs des puiſ-<lb/>ſances appliquées à chacun des points A, B, C, D, <lb/>&</s> |
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5488 <s xml:id="echoid-s3308" xml:space="preserve">c. </s> |
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5489 <s xml:id="echoid-s3309" xml:space="preserve">étant alors égales à ces mêmes proportionelles; <lb/></s> |
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5490 <s xml:id="echoid-s3310" xml:space="preserve">chacune de ce qu’il y a de puiſſances ainſi appliquées <lb/>à ce poids, ſçavoir F, G, H, I, K, L, M, N, &</s> |
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5491 <s xml:id="echoid-s3311" xml:space="preserve">c. </s> |
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5492 <s xml:id="echoid-s3312" xml:space="preserve">eſt <lb/>toujours en ce cas à ce même poids, comme chacune <lb/>de leurs proportionelles à la ſomme de toutes leurs <lb/>ſublimitez moins celle de toutes leurs profondeurs.</s> |
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5493 <s xml:id="echoid-s3313" xml:space="preserve"/> |
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5494 </p> |
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5495 <div xml:id="echoid-div298" type="float" level="2" n="1"> |
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5496 <note position="left" xlink:label="note-0152-01" xlink:href="note-0152-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5497 </div> |
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5498 </div> |
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5499 <div xml:id="echoid-div300" type="section" level="1" n="187"> |
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5500 <head xml:id="echoid-head189" xml:space="preserve"><emph style="sc">Corollaire</emph> VII.</head> |
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5501 <p> |
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5502 <s xml:id="echoid-s3314" xml:space="preserve">D’où il ſuit que dans la même hypothêſe la ſom-<lb/>me de toutes ces puiſſances eſt à ce poids, comme <lb/>la ſomme de leurs proportionelles à la ſomme de leurs <lb/>ſublimitez moins celle de leurs profondeurs: </s> |
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5503 <s xml:id="echoid-s3315" xml:space="preserve">De <lb/>ſorte que s’il n’y en avoit que deux d’appliquées à <lb/>chaque point, dont l’une tirât à droit, & </s> |
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5504 <s xml:id="echoid-s3316" xml:space="preserve">l’autre à <lb/>gauche; </s> |
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5505 <s xml:id="echoid-s3317" xml:space="preserve">& </s> |
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5506 <s xml:id="echoid-s3318" xml:space="preserve">que toutes celles de chaque côté fuſſent <lb/>égales entr’elles, & </s> |
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5507 <s xml:id="echoid-s3319" xml:space="preserve">avec des directions qui fiſſent <lb/>avec celle du point où elles ſont appliquées, des angles <lb/>de@chaque côté égaux entr’eux: </s> |
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5508 <s xml:id="echoid-s3320" xml:space="preserve">la ſomme (fig. </s> |
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5509 <s xml:id="echoid-s3321" xml:space="preserve">23.) </s> |
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5510 <s xml:id="echoid-s3322" xml:space="preserve">des <lb/>ſublimitez, par exemple Ar + Aſ, ou Bq + Bt, <lb/>ou Cp + Cu, ou Do + Dx, &</s> |
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5511 <s xml:id="echoid-s3323" xml:space="preserve">c. </s> |
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5512 <s xml:id="echoid-s3324" xml:space="preserve">des deux puiſſances <lb/>appliquées au quel que ce ſoit des nœuds A, B, <lb/>C, D, &</s> |
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5513 <s xml:id="echoid-s3325" xml:space="preserve">c. </s> |
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5514 <s xml:id="echoid-s3326" xml:space="preserve">ou bien (fig. </s> |
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5515 <s xml:id="echoid-s3327" xml:space="preserve">24.) </s> |
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5516 <s xml:id="echoid-s3328" xml:space="preserve">la différence de la ſu-<lb/>blimité de l’une à la profondeur de l’autre, par <lb/>exemple Ar - Aſ, ou Bq - Bt, ou Cp - Cu, ou <lb/>Do - Dx, &</s> |
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5517 <s xml:id="echoid-s3329" xml:space="preserve">c. </s> |
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5518 <s xml:id="echoid-s3330" xml:space="preserve">étant alors la même pour tous ces <lb/>points, auſſi-bien que les proportionelles de ces puiſ-<lb/>ſances; </s> |
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5519 <s xml:id="echoid-s3331" xml:space="preserve">la ſomme de toutes ces puiſſances ſeroit <lb/>alors au poids AD, comme la ſomme des proportio-<lb/>nelles de deux d’entr’elles appliquées à un même <lb/>point, quel qu’il ſoit, eſt à la ſomme (fig. </s> |
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5520 <s xml:id="echoid-s3332" xml:space="preserve">23.) </s> |
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5521 <s xml:id="echoid-s3333" xml:space="preserve">de leurs |
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5522 <pb o="127" file="0153" n="153" rhead="DE M. BORELLI."/> |
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5523 ſublimitez, ou (fig. </s> |
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5524 <s xml:id="echoid-s3334" xml:space="preserve">24.) </s> |
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5525 <s xml:id="echoid-s3335" xml:space="preserve">à la différence qui eſt entre <lb/> |
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5526 <anchor type="note" xlink:label="note-0153-01a" xlink:href="note-0153-01"/> |
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5527 la ſublimité de l’une & </s> |
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5528 <s xml:id="echoid-s3336" xml:space="preserve">la profondeur de l’autre.</s> |
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5529 <s xml:id="echoid-s3337" xml:space="preserve"/> |
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5530 </p> |
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5531 <div xml:id="echoid-div300" type="float" level="2" n="1"> |
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5532 <note position="right" xlink:label="note-0153-01" xlink:href="note-0153-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5533 </div> |
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5534 </div> |
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5535 <div xml:id="echoid-div302" type="section" level="1" n="188"> |
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5536 <head xml:id="echoid-head190" xml:space="preserve"><emph style="sc">Corollaire</emph> VIII.</head> |
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5537 <p> |
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5538 <s xml:id="echoid-s3338" xml:space="preserve">Ce qui fait enfin voir que ſi toutes les puiſſances <lb/>F, G, H, I, K, L, M, N, &</s> |
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5539 <s xml:id="echoid-s3339" xml:space="preserve">c. </s> |
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5540 <s xml:id="echoid-s3340" xml:space="preserve">étoient égales en-<lb/>tr’elles, & </s> |
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5541 <s xml:id="echoid-s3341" xml:space="preserve">que toutes leurs directions fiſſent avec <lb/>celles des points où elles ſont appliquées, des angles <lb/>égaux entr’eux; </s> |
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5542 <s xml:id="echoid-s3342" xml:space="preserve">leur ſomme ſeroit alors au poids <lb/>CD (fig. </s> |
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5543 <s xml:id="echoid-s3343" xml:space="preserve">23.) </s> |
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5544 <s xml:id="echoid-s3344" xml:space="preserve">comme une de leurs proportionelles <lb/>à une de leurs ſublimitez, de quelque maniére qu’on <lb/>les prenne; </s> |
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5545 <s xml:id="echoid-s3345" xml:space="preserve">c’eſt-à-dire, comme le ſinus total au ſinus <lb/>du complement de celui qu’on voudra de ces mêmes <lb/>angles.</s> |
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5546 <s xml:id="echoid-s3346" xml:space="preserve"/> |
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5547 </p> |
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5548 <p style="it"> |
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5549 <s xml:id="echoid-s3347" xml:space="preserve">On peut enfin comparer ces quatre derniers corollaires à <lb/>la Propoſition 72. </s> |
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5550 <s xml:id="echoid-s3348" xml:space="preserve">de M. </s> |
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5551 <s xml:id="echoid-s3349" xml:space="preserve">Borelli, & </s> |
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5552 <s xml:id="echoid-s3350" xml:space="preserve">au corollaire qu’il <lb/>en tire.</s> |
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5553 <s xml:id="echoid-s3351" xml:space="preserve"/> |
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5554 </p> |
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5555 <p style="it"> |
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5556 <s xml:id="echoid-s3352" xml:space="preserve">Tels ſont les principes généraux de tout ce que cet Au-<lb/>theur a dit des poids ſuſpendus par des cordes, & </s> |
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5557 <s xml:id="echoid-s3353" xml:space="preserve">de l’uſage <lb/>qu’il en a fait pour exprimer la force des muſcles; </s> |
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5558 <s xml:id="echoid-s3354" xml:space="preserve">c’eſt ce <lb/>qu’on s’étoit propoſé d’établir dans ce Chapitre par la mé-<lb/>@hode du Projet précédent: </s> |
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5559 <s xml:id="echoid-s3355" xml:space="preserve">qu’on voye préſentement ſi la <lb/>ſienne peut aller juſques-là, & </s> |
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5560 <s xml:id="echoid-s3356" xml:space="preserve">ſi elle peut conduire à la So-<lb/>lution du Problême ſuivant.</s> |
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5561 <s xml:id="echoid-s3357" xml:space="preserve"/> |
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5562 </p> |
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5563 <figure> |
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5564 <image file="0153-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0153-01"/> |
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5565 </figure> |
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5566 </div> |
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5567 <div xml:id="echoid-div303" type="section" level="1" n="189"> |
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5568 <head xml:id="echoid-head191" xml:space="preserve">PROBLEME.</head> |
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5569 <p style="it"> |
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5570 <s xml:id="echoid-s3358" xml:space="preserve">DIx puiſſances φ, A, E, D, B, F, G, H, I, K, <lb/> |
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5571 <anchor type="note" xlink:label="note-0153-02a" xlink:href="note-0153-02"/> |
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5572 appliquées à pluſieurs nœuds de cordes, étant données <lb/>avec les angles que toutes ces cordes font entr’elles; </s> |
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5573 <s xml:id="echoid-s3359" xml:space="preserve">trouver |
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5574 <pb o="128" file="0154" n="154" rhead="EXAMEN DE L’OPINION"/> |
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5575 la valeur du poids T que toutes ces puiſſances ainſi appli-<lb/> |
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5576 <anchor type="note" xlink:label="note-0154-01a" xlink:href="note-0154-01"/> |
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5577 quées ſoutiennent enſemble.</s> |
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5578 <s xml:id="echoid-s3360" xml:space="preserve"/> |
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5579 </p> |
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5580 <div xml:id="echoid-div303" type="float" level="2" n="1"> |
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5581 <note position="right" xlink:label="note-0153-02" xlink:href="note-0153-02a" xml:space="preserve">fig. 20.<unsure/></note> |
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5582 <note position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5583 </div> |
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5584 </div> |
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5585 <div xml:id="echoid-div305" type="section" level="1" n="190"> |
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5586 <head xml:id="echoid-head192" xml:space="preserve"><emph style="sc">Solution</emph>.</head> |
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5587 <p> |
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5588 <s xml:id="echoid-s3361" xml:space="preserve">Soit la valeur de chaque puiſſance, & </s> |
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5589 <s xml:id="echoid-s3362" xml:space="preserve">de chaque <lb/>angle donné dans la Table ſuivante.</s> |
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5590 <s xml:id="echoid-s3363" xml:space="preserve"/> |
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5591 </p> |
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5592 <note position="right" xml:space="preserve"> <lb/>Puiſſance. # Livres. # # Angle. # Deg. # M. <lb/>φ # 5. # # θCT # 45. # 30. <lb/>A # 4. # {1/4} # MCT # 150. # 20. <lb/>E # 7. # {1/4} # LZC # 58. # 30. <lb/>D # 12. # {1/2} # RZC # 112. # 15. <lb/>B # 14. # # VOZ # 151. <lb/>F # 11. # {1/2} # SOZ # 110. <lb/>G # 17. # # QZC # 143. <lb/>H # 7. # {1/2} # NCT # 145. <lb/>I # 16. # # βXC # 131. # 30. <lb/>K # 13. # {1/2} # hXC # 123. # 30. <lb/># PCT # 64. # 40. <lb/># δYC # 62. <lb/># zYC # 107. # 20. <lb/># eYC # 151. # 40. <lb/></note> |
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5593 <pb file="0155" n="155"/> |
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5594 <figure> |
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5595 <image file="0155-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0155-01"/> |
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5596 </figure> |
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5597 <pb file="0155a" n="156"/> |
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5598 <figure> |
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5599 <image file="0155a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0155a-01"/> |
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5600 </figure> |
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5601 <pb file="0156" n="157"/> |
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5602 <pb file="0157" n="158"/> |
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5603 <pb file="0157a" n="159"/> |
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5604 <figure> |
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5605 <image file="0157a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0157a-01"/> |
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5606 </figure> |
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5607 <pb file="0158" n="160"/> |
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5608 <pb file="0159" n="161"/> |
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5609 <pb file="0159a" n="162"/> |
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5610 <figure> |
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5611 <image file="0159a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0159a-01"/> |
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5612 </figure> |
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5613 <pb file="0160" n="163"/> |
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5614 <pb file="0161" n="164"/> |
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5615 <pb file="0161a" n="165"/> |
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5616 <figure> |
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5617 <image file="0161a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0161a-01"/> |
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5618 </figure> |
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5619 <pb file="0162" n="166"/> |
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5620 <pb file="0163" n="167"/> |
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5621 <pb file="0163a" n="168"/> |
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5622 <figure> |
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5623 <image file="0163a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0163a-01"/> |
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5624 </figure> |
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5625 <pb file="0164" n="169"/> |
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5626 <pb file="0165" n="170"/> |
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5627 <pb file="0165a" n="171"/> |
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5628 <figure> |
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5629 <image file="0165a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0165a-01"/> |
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5630 </figure> |
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5631 <pb file="0166" n="172"/> |
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5632 <pb file="0167" n="173"/> |
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5633 <pb file="0167a" n="174"/> |
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5634 <figure> |
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5635 <image file="0167a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0167a-01"/> |
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5636 </figure> |
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5637 <pb file="0168" n="175"/> |
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5638 <pb file="0169" n="176"/> |
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5639 <pb file="0169a" n="177"/> |
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5640 <figure> |
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5641 <image file="0169a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0169a-01"/> |
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5642 </figure> |
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5643 <pb file="0170" n="178"/> |
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5644 <pb file="0171" n="179"/> |
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5645 <pb file="0171a" n="180"/> |
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5646 <figure> |
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5647 <image file="0171a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0171a-01"/> |
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5648 </figure> |
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5649 <pb file="0172" n="181"/> |
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5650 <pb file="0173" n="182"/> |
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5651 <pb file="0173a" n="183"/> |
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5652 <figure> |
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5653 <image file="0173a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0173a-01"/> |
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5654 </figure> |
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5655 <pb file="0174" n="184"/> |
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5656 <pb file="0175" n="185"/> |
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5657 <pb file="0175a" n="186"/> |
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5658 <figure> |
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5659 <image file="0175a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0175a-01"/> |
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5660 </figure> |
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5661 <pb file="0176" n="187"/> |
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5662 <pb file="0177" n="188"/> |
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5663 <pb file="0177a" n="189"/> |
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5664 <figure> |
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5665 <image file="0177a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0177a-01"/> |
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5666 </figure> |
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5667 <pb file="0178" n="190"/> |
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5668 <pb file="0179" n="191"/> |
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5669 <pb file="0179a" n="192"/> |
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5670 <figure> |
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5671 <image file="0179a-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0179a-01"/> |
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5672 </figure> |
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5673 <pb file="0180" n="193"/> |
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5674 <pb o="129" file="0181" n="194" rhead="DE M. BORELLI."/> |
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5675 <p> |
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5676 <s xml:id="echoid-s3364" xml:space="preserve">Cela ſuppoſé, ſur les branches des cordes auſquel-<lb/> |
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5677 <anchor type="note" xlink:label="note-0181-01a" xlink:href="note-0181-01"/> |
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5678 les les puiſſances φ, A, E, D, B, F, G, H, I, K, <lb/>ſont immédiatement appliquées, ſoient priſes depuis <lb/>leurs nœuds des parties θC, LZ, VO, SO, QZ, βX, <lb/>hX, δY, zY, eY, qui ſoient entr’elles, comme les <lb/>forces de ces mêmes puiſſances, c’eſt-à-dire, comme <lb/>les chifres qui leur répondent dans la Table pré-<lb/>cédente.</s> |
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5679 <s xml:id="echoid-s3365" xml:space="preserve"/> |
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5680 </p> |
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5681 <div xml:id="echoid-div305" type="float" level="2" n="1"> |
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5682 <note position="right" xlink:label="note-0181-01" xlink:href="note-0181-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
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5683 </div> |
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5684 <p> |
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5685 <s xml:id="echoid-s3366" xml:space="preserve">Préſentement ſi l’on regarde chacune de ces pro-<lb/>portionelles comme un ſinus total, le ſinus de la diffé-<lb/>rence d’un angle droit à l’angle d’application de la <lb/>puiſſance qui rèpond à cette proportionelle, ſera la <lb/>ſublimité, ou la profondeur de cette même puiſſance: <lb/></s> |
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5686 <s xml:id="echoid-s3367" xml:space="preserve">par exemple, ſi l’on prend la proportionelle C θ <lb/>de la puiſſance φ, pour un ſinus total, ſa profondeur <lb/>Cλ ſera le ſinus de l’angle Cθλ, qui eſt la différen-<lb/>ce de θCλ angle d’application de cette puiſſance, à <lb/>un angle droit. </s> |
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5687 <s xml:id="echoid-s3368" xml:space="preserve">De même en prenant la proportio-<lb/>nelle V O de la puiſſance E, pour un ſinus total, ſa <lb/>ſublimité Ou ſera le ſinus de l'angle OVu, qui eſt la <lb/>diffèrence d’un angle droit à ſon angle d’application <lb/>V O Z; </s> |
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5688 <s xml:id="echoid-s3369" xml:space="preserve">de cette facon nous aurons les ſublimi-<lb/>tez & </s> |
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5689 <s xml:id="echoid-s3370" xml:space="preserve">les profondeurs de toutes ces puiſſances par les <lb/>analogies ſuivantes.</s> |
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5690 <s xml:id="echoid-s3371" xml:space="preserve"/> |
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5691 </p> |
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5692 <pb o="130" file="0182" n="195" rhead="EXAMEN DE L’OPINION"/> |
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5693 <note position="right" xml:space="preserve"> <lb/>Comme # au # # # # Ainſi # # à <lb/>Le ſinus total # Sinus # de \\ l’angle # de \\ Deg. M. \\ différence \\ de 90. deg. \\ à l’angle \\ d’applica- \\ tion # de la \\ puiſ- \\ ſan- \\ ce. # La propor- \\ tionelle \\ de cette \\ méme puiſ- \\ ſance # de # Saſubli- \\ mité, ou \\ à ſa pro- \\ fondeur # de <lb/># 7009093. # Cθλ # 44. 30. # φ # Cθ # 5. # Cλ # 3. {1013093./2000000.} <lb/># 5224986. # ZLl # 31. 30. # A # ZL # 4. {1/4} # Z l # 2. {4412381./20000000.} <lb/># 8746197. # OVu # 61. # E # OV # 7. {1/4} # Ou # 6. {13639713./40000000.} <lb/>10000000.{ # 3420202. # OSſ # 20. # D # OS # 12. {1/2} # Oſ # 4. {110101./400000.} <lb/># 7986355. # ZQq # 53. # B # ZQ # 14. # Zq # 11. {180897./1000000.} <lb/># 6626201. # Xβf # 41. 30. # F # X β # 11. {1/2} # Xf # 7. {6439043./20000000.} <lb/># 5519370. # Xhb # 33. 30. # G # Xh # 17. # Xh # 9. {382929./1000000.} <lb/># 4694716. # Yδd # 28. # H # Yδ # 7. {1/2} # Yd # 3. {521037./1000000.} <lb/># 2979303. # Yzx # 17. 20. # I # Yz # 16. # Yx # 4. {479303./625000.} <lb/># 8802014. # Yeg # 61. 40. # K # Ye # 13. {1/2} # Yg # 11. {8827189./10000000.} <lb/></note> |
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5694 <p> |
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5695 <s xml:id="echoid-s3372" xml:space="preserve">Aprés avoir ainſi trouvé la valeur de chacune des ſu-<lb/>blimitez & </s> |
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5696 <s xml:id="echoid-s3373" xml:space="preserve">des profondeurs de toutes les puiſſances qui <lb/>ſoutiennent le poids T; </s> |
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5697 <s xml:id="echoid-s3374" xml:space="preserve">ſoit priſe Z R égale à Ou <lb/>plus O ſ; </s> |
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5698 <s xml:id="echoid-s3375" xml:space="preserve">c’eſt-à-dire, ſuivant les analogies précéden-<lb/>tes, égale à 6. </s> |
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5699 <s xml:id="echoid-s3376" xml:space="preserve">{13639713.</s> |
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5700 <s xml:id="echoid-s3377" xml:space="preserve">/40000000.</s> |
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5701 <s xml:id="echoid-s3378" xml:space="preserve">} plus 4. </s> |
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5702 <s xml:id="echoid-s3379" xml:space="preserve">{110101.</s> |
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5703 <s xml:id="echoid-s3380" xml:space="preserve">/400000.</s> |
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5704 <s xml:id="echoid-s3381" xml:space="preserve">}; </s> |
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5705 <s xml:id="echoid-s3382" xml:space="preserve">ou bien en ré-<lb/>duiſant ces deux fractions à une même dénomina- |
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5706 <pb o="131" file="0183" n="196" rhead="DEM. BORELLI."/> |
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5707 tion, égale à 10. </s> |
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5708 <s xml:id="echoid-s3383" xml:space="preserve">{24649813.</s> |
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5709 <s xml:id="echoid-s3384" xml:space="preserve">/40000000.</s> |
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5710 <s xml:id="echoid-s3385" xml:space="preserve">}. </s> |
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5711 <s xml:id="echoid-s3386" xml:space="preserve">Aprés cela O V étant à Z R, <lb/> |
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5712 <anchor type="note" xlink:label="note-0183-01a" xlink:href="note-0183-01"/> |
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5713 comme la puiſſance E à la force dont le point Z eſt <lb/>tiré ſuivant ZO par le concours d’action des puiſ-<lb/>ſances D & </s> |
|
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|
5714 <s xml:id="echoid-s3387" xml:space="preserve">E; </s> |
|
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|
5715 <s xml:id="echoid-s3388" xml:space="preserve">Z R ſera la proportionelle de cette <lb/>force, & </s> |
|
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|
5716 <s xml:id="echoid-s3389" xml:space="preserve">l’angle R Z C étant (hyp.) </s> |
|
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|
5717 <s xml:id="echoid-s3390" xml:space="preserve">de 112. </s> |
|
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|
5718 <s xml:id="echoid-s3391" xml:space="preserve">deg. </s> |
|
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|
5719 <s xml:id="echoid-s3392" xml:space="preserve">15. <lb/></s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5720 <s xml:id="echoid-s3393" xml:space="preserve">min. </s> |
|
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diff
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|
5721 <s xml:id="echoid-s3394" xml:space="preserve">ſa diffèrence à un angle droit; </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5722 <s xml:id="echoid-s3395" xml:space="preserve">c’eſt-à-dire, <lb/>l’angle ZRr ſera de 22. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5723 <s xml:id="echoid-s3396" xml:space="preserve">deg. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5724 <s xml:id="echoid-s3397" xml:space="preserve">15. </s> |
|
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|
5725 <s xml:id="echoid-s3398" xml:space="preserve">min. </s> |
|
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diff
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|
5726 <s xml:id="echoid-s3399" xml:space="preserve">Ce qui don-<lb/>nera par une analogie ſemblable aux précédentes, <lb/>3. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5727 <s xml:id="echoid-s3400" xml:space="preserve">{74265285916559.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5728 <s xml:id="echoid-s3401" xml:space="preserve">/200000000000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5729 <s xml:id="echoid-s3402" xml:space="preserve">} pour la valeur de Zr ſublimité de cette <lb/>force: </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5730 <s xml:id="echoid-s3403" xml:space="preserve">puiſque ZR de 10. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5731 <s xml:id="echoid-s3404" xml:space="preserve">{24642813.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5732 <s xml:id="echoid-s3405" xml:space="preserve">/40000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5733 <s xml:id="echoid-s3406" xml:space="preserve">} eſt à 3. </s> |
|
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|
5734 <s xml:id="echoid-s3407" xml:space="preserve">{17426@285916559.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5735 <s xml:id="echoid-s3408" xml:space="preserve">/200000000000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5736 <s xml:id="echoid-s3409" xml:space="preserve">} <lb/>comme le ſinus total 10000000. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5737 <s xml:id="echoid-s3410" xml:space="preserve">à 3786486. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5738 <s xml:id="echoid-s3411" xml:space="preserve">ſinus <lb/>de l’angle ZRr de 22. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5739 <s xml:id="echoid-s3412" xml:space="preserve">deg. </s> |
|
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|
5740 <s xml:id="echoid-s3413" xml:space="preserve">15. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5741 <s xml:id="echoid-s3414" xml:space="preserve">min.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5742 <s xml:id="echoid-s3415" xml:space="preserve"/> |
|
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|
5743 </p> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5744 <div xml:id="echoid-div306" type="float" level="2" n="2"> |
|
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|
5745 <note position="right" xlink:label="note-0183-01" xlink:href="note-0183-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5746 </div> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5747 <p> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff
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|
5748 <s xml:id="echoid-s3416" xml:space="preserve">Soit enſuitte 1°. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5749 <s xml:id="echoid-s3417" xml:space="preserve">C M égale à Zq plus Zr moins <lb/>Zl; </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5750 <s xml:id="echoid-s3418" xml:space="preserve">c’eſt-à-dire, ſuivant les analogies que nous ve-<lb/>nons de trouver, égale à 11. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5751 <s xml:id="echoid-s3419" xml:space="preserve">{180897.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5752 <s xml:id="echoid-s3420" xml:space="preserve">/1000000} plus 3. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5753 <s xml:id="echoid-s3421" xml:space="preserve">{174265285916559.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5754 <s xml:id="echoid-s3422" xml:space="preserve">/200000000@00000.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5755 <s xml:id="echoid-s3423" xml:space="preserve">} <lb/>moins 2. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5756 <s xml:id="echoid-s3424" xml:space="preserve">{4412381.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5757 <s xml:id="echoid-s3425" xml:space="preserve">/20000000.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5758 <s xml:id="echoid-s3426" xml:space="preserve">}; </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff
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|
5759 <s xml:id="echoid-s3427" xml:space="preserve">ou bien en réduiſant ces trois frac-<lb/>tions à une même dénomination, égale à 12. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5760 <s xml:id="echoid-s3428" xml:space="preserve">{1663208759165@9.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5761 <s xml:id="echoid-s3429" xml:space="preserve">/200000000000000}. <lb/></s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff
changeset
|
5762 <s xml:id="echoid-s3430" xml:space="preserve">Ce qui donnera par une analogie ſemblable aux pré-<lb/>cédentes, 11. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5763 <s xml:id="echoid-s3431" xml:space="preserve">{74566272432665199141.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5764 <s xml:id="echoid-s3432" xml:space="preserve">/500000000000000000000.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5765 <s xml:id="echoid-s3433" xml:space="preserve">} pour la valeur de la <lb/>ſublimité Cm: </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5766 <s xml:id="echoid-s3434" xml:space="preserve">puis que 12. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5767 <s xml:id="echoid-s3435" xml:space="preserve">{166320875916559.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5768 <s xml:id="echoid-s3436" xml:space="preserve">/200000000000000.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5769 <s xml:id="echoid-s3437" xml:space="preserve">} eſt à 11. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5770 <s xml:id="echoid-s3438" xml:space="preserve"><lb/>{745662724;</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5771 <s xml:id="echoid-s3439" xml:space="preserve">2665199141.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5772 <s xml:id="echoid-s3440" xml:space="preserve">/500000000000000000000.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5773 <s xml:id="echoid-s3441" xml:space="preserve">}, comme le ſinus total 10000000. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff
changeset
|
5774 <s xml:id="echoid-s3442" xml:space="preserve">à <lb/>8689196. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5775 <s xml:id="echoid-s3443" xml:space="preserve">ſinus de l’angle CMm de 60. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5776 <s xml:id="echoid-s3444" xml:space="preserve">deg. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5777 <s xml:id="echoid-s3445" xml:space="preserve">20. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5778 <s xml:id="echoid-s3446" xml:space="preserve"><lb/>min. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5779 <s xml:id="echoid-s3447" xml:space="preserve">qui eſt la différence d’un angle droit à l’angle <lb/>M C T de (hyp.) </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5780 <s xml:id="echoid-s3448" xml:space="preserve">150. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5781 <s xml:id="echoid-s3449" xml:space="preserve">deg. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5782 <s xml:id="echoid-s3450" xml:space="preserve">20. </s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
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changeset
|
5783 <s xml:id="echoid-s3451" xml:space="preserve">min.</s> |
|
22d6a63640c6
moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5784 <s xml:id="echoid-s3452" xml:space="preserve"/> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5785 </p> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5786 <p> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff
changeset
|
5787 <s xml:id="echoid-s3453" xml:space="preserve">2°. </s> |
|
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|
5788 <s xml:id="echoid-s3454" xml:space="preserve">Faite de même C N égale à Xb plus Xf; </s> |
|
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|
5789 <s xml:id="echoid-s3455" xml:space="preserve">c’eſt-<lb/>à-dire, ſuivant les analogies de la table précédente, <lb/>égale à 9. </s> |
|
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|
5790 <s xml:id="echoid-s3456" xml:space="preserve">{382929.</s> |
|
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|
5791 <s xml:id="echoid-s3457" xml:space="preserve">/1000000.</s> |
|
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|
5792 <s xml:id="echoid-s3458" xml:space="preserve">} plus 7. </s> |
|
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|
5793 <s xml:id="echoid-s3459" xml:space="preserve">{64,9043.</s> |
|
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|
5794 <s xml:id="echoid-s3460" xml:space="preserve">/20000000.</s> |
|
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|
5795 <s xml:id="echoid-s3461" xml:space="preserve">}; </s> |
|
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|
5796 <s xml:id="echoid-s3462" xml:space="preserve">ou bien en réduiſant <lb/>ces deux fractions à une même dénomination, égale <lb/>à 16. </s> |
|
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|
5797 <s xml:id="echoid-s3463" xml:space="preserve">{14097623.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5798 <s xml:id="echoid-s3464" xml:space="preserve">/20000000}. </s> |
|
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diff
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|
5799 <s xml:id="echoid-s3465" xml:space="preserve">Ce qui donnera par une analogie ſem-<lb/>blable aux précédentes, 13. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5800 <s xml:id="echoid-s3466" xml:space="preserve">{136767694854583/200000000000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff
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|
5801 <s xml:id="echoid-s3467" xml:space="preserve">} pour la va-<lb/>leur de la ſublimité Cn: </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5802 <s xml:id="echoid-s3468" xml:space="preserve">puis que 16. </s> |
|
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|
5803 <s xml:id="echoid-s3469" xml:space="preserve">{14097623.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5804 <s xml:id="echoid-s3470" xml:space="preserve">/20000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5805 <s xml:id="echoid-s3471" xml:space="preserve">} eſt à <lb/>13. </s> |
|
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|
5806 <s xml:id="echoid-s3472" xml:space="preserve">{136767694854583.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5807 <s xml:id="echoid-s3473" xml:space="preserve">/200000000000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5808 <s xml:id="echoid-s3474" xml:space="preserve">}, comme le ſinus total 10000000. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5809 <s xml:id="echoid-s3475" xml:space="preserve">à |
|
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|
5810 <pb o="132" file="0184" n="197" rhead="EXAMEN DE L’OPINION"/> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5811 8191521. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5812 <s xml:id="echoid-s3476" xml:space="preserve">ſinus de l’angle CNn de 55. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5813 <s xml:id="echoid-s3477" xml:space="preserve">deg. </s> |
|
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|
5814 <s xml:id="echoid-s3478" xml:space="preserve">qui eſt <lb/> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5815 <anchor type="note" xlink:label="note-0184-01a" xlink:href="note-0184-01"/> |
|
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|
5816 la différence d’un angle droit à l’angle NCT de <lb/>(hyp.) </s> |
|
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|
5817 <s xml:id="echoid-s3479" xml:space="preserve">145. </s> |
|
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|
5818 <s xml:id="echoid-s3480" xml:space="preserve">deg.</s> |
|
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|
5819 <s xml:id="echoid-s3481" xml:space="preserve"/> |
|
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|
5820 </p> |
|
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|
5821 <div xml:id="echoid-div307" type="float" level="2" n="3"> |
|
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|
5822 <note position="left" xlink:label="note-0184-01" xlink:href="note-0184-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>de@cordes ſeu-<lb/>lement.</note> |
|
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|
5823 </div> |
|
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|
5824 <p> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5825 <s xml:id="echoid-s3482" xml:space="preserve">3°. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5826 <s xml:id="echoid-s3483" xml:space="preserve">Enſin ſoit encore C P égale à Yg plus Yx <lb/>moins Yd; </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5827 <s xml:id="echoid-s3484" xml:space="preserve">c’eſt-à-dire, ſuivant les analogies de la <lb/>table précédente, égale à 11. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5828 <s xml:id="echoid-s3485" xml:space="preserve">{8827189.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5829 <s xml:id="echoid-s3486" xml:space="preserve">/10000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5830 <s xml:id="echoid-s3487" xml:space="preserve">} plus 4. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5831 <s xml:id="echoid-s3488" xml:space="preserve">{479303.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5832 <s xml:id="echoid-s3489" xml:space="preserve">/625000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5833 <s xml:id="echoid-s3490" xml:space="preserve">} moins <lb/>3. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5834 <s xml:id="echoid-s3491" xml:space="preserve">{521037.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5835 <s xml:id="echoid-s3492" xml:space="preserve">/1000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5836 <s xml:id="echoid-s3493" xml:space="preserve">}; </s> |
|
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|
5837 <s xml:id="echoid-s3494" xml:space="preserve">ou bien en réduiſant ces trois fractions à <lb/>une même dénomination, égale à 12. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5838 <s xml:id="echoid-s3495" xml:space="preserve">{232141683.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5839 <s xml:id="echoid-s3496" xml:space="preserve">/282000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5840 <s xml:id="echoid-s3497" xml:space="preserve">}. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5841 <s xml:id="echoid-s3498" xml:space="preserve">Ce qui <lb/>donnera par une analogie encore ſemblable aux <lb/>précédentes, 5. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5842 <s xml:id="echoid-s3499" xml:space="preserve">{686442223302177.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5843 <s xml:id="echoid-s3500" xml:space="preserve">/1410000000000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5844 <s xml:id="echoid-s3501" xml:space="preserve">} pour la valeur de la pro-<lb/>fondeur C p: </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5845 <s xml:id="echoid-s3502" xml:space="preserve">puis que 12. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5846 <s xml:id="echoid-s3503" xml:space="preserve">{232141683.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5847 <s xml:id="echoid-s3504" xml:space="preserve">/282000000.</s> |
|
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|
5848 <s xml:id="echoid-s3505" xml:space="preserve">} eſt à 5. </s> |
|
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|
5849 <s xml:id="echoid-s3506" xml:space="preserve">{686442223302177.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5850 <s xml:id="echoid-s3507" xml:space="preserve">/1410000000000000.</s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5851 <s xml:id="echoid-s3508" xml:space="preserve">}, <lb/>comme le ſinus total 10000000. </s> |
|
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|
5852 <s xml:id="echoid-s3509" xml:space="preserve">à 4278838. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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|
5853 <s xml:id="echoid-s3510" xml:space="preserve">ſinus <lb/>de l’angle CPp de 25. </s> |
|
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moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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changeset
|
5854 <s xml:id="echoid-s3511" xml:space="preserve">deg. </s> |
|
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changeset
|
5855 <s xml:id="echoid-s3512" xml:space="preserve">20. </s> |
|
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|
5856 <s xml:id="echoid-s3513" xml:space="preserve">min. </s> |
|
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diff
changeset
|
5857 <s xml:id="echoid-s3514" xml:space="preserve">qui eſt la diffè-<lb/>rence d’un angle droit à l’angle P C T de (hyp.) </s> |
|
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|
5858 <s xml:id="echoid-s3515" xml:space="preserve">64. <lb/></s> |
|
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changeset
|
5859 <s xml:id="echoid-s3516" xml:space="preserve">deg. </s> |
|
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|
5860 <s xml:id="echoid-s3517" xml:space="preserve">40. </s> |
|
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changeset
|
5861 <s xml:id="echoid-s3518" xml:space="preserve">min.</s> |
|
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5862 <s xml:id="echoid-s3519" xml:space="preserve"/> |
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5863 </p> |
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5864 <p> |
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5865 <s xml:id="echoid-s3520" xml:space="preserve">De tout cela on voit preſentement que <lb/>la {Subl. </s> |
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5866 <s xml:id="echoid-s3521" xml:space="preserve">Cm \\ Subl. </s> |
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5867 <s xml:id="echoid-s3522" xml:space="preserve">Cn \\ Prof. </s> |
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5868 <s xml:id="echoid-s3523" xml:space="preserve">Cλ \\ Prof. </s> |
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5869 <s xml:id="echoid-s3524" xml:space="preserve">Cp} eſt ègale à {11. </s> |
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5870 <s xml:id="echoid-s3525" xml:space="preserve">{74566272432665199141.</s> |
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5871 <s xml:id="echoid-s3526" xml:space="preserve">/500000000000000000000.</s> |
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5872 <s xml:id="echoid-s3527" xml:space="preserve">}. </s> |
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5873 <s xml:id="echoid-s3528" xml:space="preserve">\\ 13. </s> |
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5874 <s xml:id="echoid-s3529" xml:space="preserve">{136767694854583.</s> |
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5875 <s xml:id="echoid-s3530" xml:space="preserve">/200000000000000.</s> |
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5876 <s xml:id="echoid-s3531" xml:space="preserve">} \\ 3. </s> |
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5877 <s xml:id="echoid-s3532" xml:space="preserve">{1013093.</s> |
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5878 <s xml:id="echoid-s3533" xml:space="preserve">/2000000.</s> |
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5879 <s xml:id="echoid-s3534" xml:space="preserve">} \\ 5. </s> |
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5880 <s xml:id="echoid-s3535" xml:space="preserve">{686442223302377.</s> |
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5881 <s xml:id="echoid-s3536" xml:space="preserve">/1410000000000000.</s> |
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5882 <s xml:id="echoid-s3537" xml:space="preserve">}</s> |
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|
5883 </p> |
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|
5884 <p> |
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5885 <s xml:id="echoid-s3538" xml:space="preserve">De ſorte qu’en réduiſant toutes ces fractions à une <lb/>même dénomination, on aura Cm + Cn - Cλ -<lb/>Cp = 15. </s> |
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5886 <s xml:id="echoid-s3539" xml:space="preserve">{5919081693@137450578881.</s> |
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5887 <s xml:id="echoid-s3540" xml:space="preserve">/70500000000000000000000}. </s> |
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5888 <s xml:id="echoid-s3541" xml:space="preserve">Or ayant pris, comme <lb/>nous venons de faire, 1° CR = Oſ + Ou. </s> |
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5889 <s xml:id="echoid-s3542" xml:space="preserve">2°. </s> |
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5890 <s xml:id="echoid-s3543" xml:space="preserve">CM <lb/>= Zq + Zr - Zl. </s> |
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5891 <s xml:id="echoid-s3544" xml:space="preserve">3° CN = Xf + Xb. </s> |
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5892 <s xml:id="echoid-s3545" xml:space="preserve">4°. </s> |
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5893 <s xml:id="echoid-s3546" xml:space="preserve">CP <lb/>= Yg + Yx - Yd; </s> |
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5894 <s xml:id="echoid-s3547" xml:space="preserve">chacune des puiſſances qui <lb/>ſoutiennent ainſi le poids T; </s> |
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5895 <s xml:id="echoid-s3548" xml:space="preserve">par exemple, la puiſ-<lb/>ſance E eſt (Prop. </s> |
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5896 <s xml:id="echoid-s3549" xml:space="preserve">4. </s> |
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5897 <s xml:id="echoid-s3550" xml:space="preserve">Cor. </s> |
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5898 <s xml:id="echoid-s3551" xml:space="preserve">1.) </s> |
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5899 <s xml:id="echoid-s3552" xml:space="preserve">à ce poids, comme ſa <lb/>proportionnelle OV de (hyp.) </s> |
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5900 <s xml:id="echoid-s3553" xml:space="preserve">7 {1/4} à Cm + Cn - |
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5901 <pb o="133" file="0185" n="198" rhead="DE M. BORELLI."/> |
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5902 Cλ - Cp: </s> |
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5903 <s xml:id="echoid-s3554" xml:space="preserve">Donc cette même puiſſance E eſt à ce <lb/> |
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5904 <anchor type="note" xlink:label="note-0185-01a" xlink:href="note-0185-01"/> |
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|
5905 poids, comme 7. </s> |
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5906 <s xml:id="echoid-s3555" xml:space="preserve">{1/4} à 15. </s> |
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5907 <s xml:id="echoid-s3556" xml:space="preserve">{1919081693413745<unsure/>0578881.</s> |
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5908 <s xml:id="echoid-s3557" xml:space="preserve">/705<unsure/>00000000000000000000.</s> |
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5909 <s xml:id="echoid-s3558" xml:space="preserve">}; </s> |
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5910 <s xml:id="echoid-s3559" xml:space="preserve">& </s> |
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5911 <s xml:id="echoid-s3560" xml:space="preserve">par con-<lb/>ſèquent la valeur de cette puiſſance étant (hyp.) <lb/></s> |
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5912 <s xml:id="echoid-s3561" xml:space="preserve">de 7. </s> |
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5913 <s xml:id="echoid-s3562" xml:space="preserve">{1/4} liv. </s> |
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5914 <s xml:id="echoid-s3563" xml:space="preserve">ce même poids eſt auſſi juſtement de <lb/>15. </s> |
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5915 <s xml:id="echoid-s3564" xml:space="preserve">{5919081692@137450@78881.</s> |
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5916 <s xml:id="echoid-s3565" xml:space="preserve">/70500000000000000000000.</s> |
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5917 <s xml:id="echoid-s3566" xml:space="preserve">} liv. </s> |
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|
5918 <s xml:id="echoid-s3567" xml:space="preserve">c’eſt-à-dire, de 15. </s> |
|
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5919 <s xml:id="echoid-s3568" xml:space="preserve">livres, & </s> |
|
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5920 <s xml:id="echoid-s3569" xml:space="preserve"><lb/>un peu plus de cinq ſeptiémes de livre. </s> |
|
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5921 <s xml:id="echoid-s3570" xml:space="preserve">Ce qu’il faloit <lb/>trouver.</s> |
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|
5922 <s xml:id="echoid-s3571" xml:space="preserve"/> |
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|
5923 </p> |
|
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|
5924 <div xml:id="echoid-div308" type="float" level="2" n="4"> |
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|
5925 <note position="right" xlink:label="note-0185-01" xlink:href="note-0185-01a" xml:space="preserve">DES POIDS <lb/>ſoutenus avec <lb/>des cordes ſeu-<lb/>lement.</note> |
|
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|
5926 </div> |
|
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|
5927 </div> |
|
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|
5928 <div xml:id="echoid-div310" type="section" level="1" n="191"> |
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|
5929 <head xml:id="echoid-head193" xml:space="preserve">FIN.</head> |
|
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|
5930 <head xml:id="echoid-head194" xml:space="preserve">AU RELIEUR.</head> |
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|
5931 <p style="it"> |
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|
5932 <s xml:id="echoid-s3572" xml:space="preserve">LE S neuf planches au pied deſquelles on voit Projet, <lb/>doivent ètre reliées ſelon l’ordre de leurs chifres immé-<lb/>diatement à la fin de la Méchanique; </s> |
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|
5933 <s xml:id="echoid-s3573" xml:space="preserve">en ſorte que le quart <lb/>du papier où il n’y a rien, ſoit enfermé dans le livre, & </s> |
|
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|
5934 <s xml:id="echoid-s3574" xml:space="preserve">que <lb/>l’autre quart où ſont les figures, puiſſe, en les dépliant, en <lb/>ſortir tout entier, pour ſervir à tous les endroits de cette Mé-<lb/>chanique où l’on en aura beſoin. </s> |
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5935 <s xml:id="echoid-s3575" xml:space="preserve">Pour les quatre autres plan-<lb/>ches, au pied deſquelles on voit Examen, elles doivent auſſi <lb/>être reliées de la même maniére à la fin de l’Examen que voicy <lb/>de M. </s> |
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5936 <s xml:id="echoid-s3576" xml:space="preserve">Borelli.</s> |
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5937 <s xml:id="echoid-s3577" xml:space="preserve"/> |
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5938 </p> |
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5939 </div> |
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5940 <div xml:id="echoid-div311" type="section" level="1" n="192"> |
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5941 <head xml:id="echoid-head195" xml:space="preserve">A PARIS,</head> |
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5942 <p> |
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5943 <s xml:id="echoid-s3578" xml:space="preserve">De l’Imprimerie dela Veuve Clement Gaſſe, 1687.</s> |
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5944 <s xml:id="echoid-s3579" xml:space="preserve"/> |
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5945 </p> |
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5946 <pb file="0186" n="199"/> |
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5947 </div> |
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5948 <div xml:id="echoid-div312" type="section" level="1" n="193"> |
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5949 <head xml:id="echoid-head196" xml:space="preserve">EXTRAIT DV PRIVILE’GE</head> |
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5950 <head xml:id="echoid-head197" style="it" xml:space="preserve">du Roy.</head> |
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5951 <p> |
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5952 <s xml:id="echoid-s3580" xml:space="preserve"><emph style="sc">PAr</emph> Lettres Patentes du Roy, données à Ver-<lb/>ſailles 19. </s> |
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5953 <s xml:id="echoid-s3581" xml:space="preserve">jourde Juin 1687. </s> |
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5954 <s xml:id="echoid-s3582" xml:space="preserve">ſignées par le Roy <lb/>en ſon Conſeil, <emph style="sc">Galloys</emph> & </s> |
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5955 <s xml:id="echoid-s3583" xml:space="preserve">ſcellées. </s> |
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5956 <s xml:id="echoid-s3584" xml:space="preserve">Il eſt permis <lb/>à <emph style="sc">Jean</emph> <emph style="sc">Boudot</emph> Libraire à Paris, d’imprimer un <lb/>livre intitulé Projet d’une nouvelle Méchanique, avec un <lb/>Examen de l’Opinion de M. </s> |
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5957 <s xml:id="echoid-s3585" xml:space="preserve">Borelli, ſur les propriétez des <lb/>Poids ſuſpendus par des Cordes, par M. </s> |
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5958 <s xml:id="echoid-s3586" xml:space="preserve">V * * * * * * * en <lb/>tel volume, marge, & </s> |
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5959 <s xml:id="echoid-s3587" xml:space="preserve">caractére, en autant de volumes, <lb/>& </s> |
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5960 <s xml:id="echoid-s3588" xml:space="preserve">tout autant de fois que bon luy ſemblera, pendant <lb/>le tems de huit années conſécutives, à commencer <lb/>du jour qu’il aura été achevé d’imprimer pour la <lb/>premiére fois. </s> |
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5961 <s xml:id="echoid-s3589" xml:space="preserve">Et défenſes ſont faites à toutes ſortes <lb/>de perſonnes d’imprimer ledit livre, d’en vendre n’y <lb/>diſtribuër d’autre impreſſion que de celle dudit <lb/><emph style="sc">Boudot</emph>, ou de ceux qui auront ſon droit, à peine <lb/>de mil livres d’amende, & </s> |
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5962 <s xml:id="echoid-s3590" xml:space="preserve">de tous dèpens, dom-<lb/>mages & </s> |
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5963 <s xml:id="echoid-s3591" xml:space="preserve">intérêts, & </s> |
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5964 <s xml:id="echoid-s3592" xml:space="preserve">de confiſcation des Exemplaires <lb/>contrefaits, ainſi qu’il eſt porté plus au long dans ledit <lb/>Privilége.</s> |
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5965 <s xml:id="echoid-s3593" xml:space="preserve"/> |
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5966 </p> |
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5967 <p> |
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5968 <s xml:id="echoid-s3594" xml:space="preserve">Regiſtré ſur le Livre de la Communauté des Li-<lb/>braires & </s> |
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5969 <s xml:id="echoid-s3595" xml:space="preserve">Imprimeurs de Paris, le 30. </s> |
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5970 <s xml:id="echoid-s3596" xml:space="preserve">Juillet 1687.</s> |
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5971 <s xml:id="echoid-s3597" xml:space="preserve"/> |
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5972 </p> |
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5973 <p> |
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5974 <s xml:id="echoid-s3598" xml:space="preserve">Signé, <emph style="sc">Coignard</emph>, Syndic.</s> |
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5975 <s xml:id="echoid-s3599" xml:space="preserve"/> |
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5976 </p> |
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5977 <p style="it"> |
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5978 <s xml:id="echoid-s3600" xml:space="preserve">Achevè d’imprimer pour la premiére fois le 30. </s> |
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5979 <s xml:id="echoid-s3601" xml:space="preserve">Aouſt 1687.</s> |
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5980 <s xml:id="echoid-s3602" xml:space="preserve"/> |
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5981 </p> |
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5982 <pb file="0187" n="200"/> |
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5983 </div> |
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5984 <div xml:id="echoid-div313" type="section" level="1" n="194"> |
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5985 <head xml:id="echoid-head198" style="it" xml:space="preserve">FAVTES A CORRIGER.</head> |
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5986 <p style="it"> |
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5987 <s xml:id="echoid-s3603" xml:space="preserve">PAg. </s> |
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5988 <s xml:id="echoid-s3604" xml:space="preserve">4. </s> |
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5989 <s xml:id="echoid-s3605" xml:space="preserve">lig. </s> |
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5990 <s xml:id="echoid-s3606" xml:space="preserve">20. </s> |
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5991 <s xml:id="echoid-s3607" xml:space="preserve">AH liſez AK</s> |
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5992 </p> |
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5993 <p style="it"> |
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5994 <s xml:id="echoid-s3608" xml:space="preserve">pag. </s> |
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5995 <s xml:id="echoid-s3609" xml:space="preserve">9. </s> |
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5996 <s xml:id="echoid-s3610" xml:space="preserve">ligne 14. </s> |
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5997 <s xml:id="echoid-s3611" xml:space="preserve">Lemme 3.</s> |
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5998 <s xml:id="echoid-s3612" xml:space="preserve">, liſez Lemme 3.</s> |
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5999 <s xml:id="echoid-s3613" xml:space="preserve"/> |
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6000 </p> |
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6001 <p style="it"> |
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6002 <s xml:id="echoid-s3614" xml:space="preserve">pag. </s> |
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6003 <s xml:id="echoid-s3615" xml:space="preserve">14. </s> |
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6004 <s xml:id="echoid-s3616" xml:space="preserve">ligne 11. </s> |
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6005 <s xml:id="echoid-s3617" xml:space="preserve">poid liſez poids</s> |
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6006 </p> |
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6007 <p style="it"> |
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6008 <s xml:id="echoid-s3618" xml:space="preserve">pag. </s> |
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6009 <s xml:id="echoid-s3619" xml:space="preserve">17. </s> |
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6010 <s xml:id="echoid-s3620" xml:space="preserve">ligne 4. </s> |
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6011 <s xml:id="echoid-s3621" xml:space="preserve">elle ſe liſez elle le</s> |
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6012 </p> |
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6013 <p style="it"> |
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6014 <s xml:id="echoid-s3622" xml:space="preserve">pag. </s> |
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6015 <s xml:id="echoid-s3623" xml:space="preserve">23. </s> |
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6016 <s xml:id="echoid-s3624" xml:space="preserve">à la marge Vis-à-vis du problême marquez fig. </s> |
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6017 <s xml:id="echoid-s3625" xml:space="preserve">19.</s> |
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6018 <s xml:id="echoid-s3626" xml:space="preserve"/> |
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6019 </p> |
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6020 <p style="it"> |
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6021 <s xml:id="echoid-s3627" xml:space="preserve">pag. </s> |
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6022 <s xml:id="echoid-s3628" xml:space="preserve">29. </s> |
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6023 <s xml:id="echoid-s3629" xml:space="preserve">ligne 22. </s> |
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6024 <s xml:id="echoid-s3630" xml:space="preserve">AH liſez AD</s> |
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6025 </p> |
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6026 <p style="it"> |
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6027 <s xml:id="echoid-s3631" xml:space="preserve">pag. </s> |
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6028 <s xml:id="echoid-s3632" xml:space="preserve">35. </s> |
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6029 <s xml:id="echoid-s3633" xml:space="preserve">à la marge fig. </s> |
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6030 <s xml:id="echoid-s3634" xml:space="preserve">26. </s> |
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6031 <s xml:id="echoid-s3635" xml:space="preserve">liſez fig. </s> |
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6032 <s xml:id="echoid-s3636" xml:space="preserve">26. <lb/></s> |
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6033 <s xml:id="echoid-s3637" xml:space="preserve">27.</s> |
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6034 <s xml:id="echoid-s3638" xml:space="preserve"/> |
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|
6035 </p> |
|
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|
6036 <p style="it"> |
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6037 <s xml:id="echoid-s3639" xml:space="preserve">pag. </s> |
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6038 <s xml:id="echoid-s3640" xml:space="preserve">38. </s> |
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6039 <s xml:id="echoid-s3641" xml:space="preserve">ligne 25. </s> |
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6040 <s xml:id="echoid-s3642" xml:space="preserve">à EF; </s> |
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|
6041 <s xml:id="echoid-s3643" xml:space="preserve">liſez HEF; </s> |
|
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6042 <s xml:id="echoid-s3644" xml:space="preserve">& </s> |
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6043 <s xml:id="echoid-s3645" xml:space="preserve">ligne 26. </s> |
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|
6044 <s xml:id="echoid-s3646" xml:space="preserve">effacéz ou EHF,</s> |
|
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|
6045 </p> |
|
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|
6046 <p style="it"> |
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6047 <s xml:id="echoid-s3647" xml:space="preserve">pag. </s> |
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6048 <s xml:id="echoid-s3648" xml:space="preserve">48. </s> |
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6049 <s xml:id="echoid-s3649" xml:space="preserve">ligne 31. </s> |
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|
6050 <s xml:id="echoid-s3650" xml:space="preserve">points liſez point</s> |
|
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|
6051 </p> |
|
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|
6052 <p style="it"> |
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6053 <s xml:id="echoid-s3651" xml:space="preserve">pag. </s> |
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6054 <s xml:id="echoid-s3652" xml:space="preserve">74. </s> |
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6055 <s xml:id="echoid-s3653" xml:space="preserve">ligne 1. </s> |
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|
6056 <s xml:id="echoid-s3654" xml:space="preserve">puiſſnces, liſez puiſſances,</s> |
|
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|
6057 </p> |
|
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6058 <p style="it"> |
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6059 <s xml:id="echoid-s3655" xml:space="preserve">pag. </s> |
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|
6060 <s xml:id="echoid-s3656" xml:space="preserve">99. </s> |
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6061 <s xml:id="echoid-s3657" xml:space="preserve">ligne 14. </s> |
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6062 <s xml:id="echoid-s3658" xml:space="preserve">& </s> |
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6063 <s xml:id="echoid-s3659" xml:space="preserve">pag. </s> |
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6064 <s xml:id="echoid-s3660" xml:space="preserve">100. </s> |
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|
6065 <s xml:id="echoid-s3661" xml:space="preserve">lignes 5. </s> |
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6066 <s xml:id="echoid-s3662" xml:space="preserve">16. </s> |
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|
6067 <s xml:id="echoid-s3663" xml:space="preserve">& </s> |
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6068 <s xml:id="echoid-s3664" xml:space="preserve">17. </s> |
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|
6069 <s xml:id="echoid-s3665" xml:space="preserve">propotionnelles liſez <lb/>proportionelles</s> |
|
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|
6070 </p> |
|
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|
6071 <p style="it"> |
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|
6072 <s xml:id="echoid-s3666" xml:space="preserve">pag. </s> |
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|
6073 <s xml:id="echoid-s3667" xml:space="preserve">103. </s> |
|
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|
6074 <s xml:id="echoid-s3668" xml:space="preserve">ligne 1. </s> |
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|
6075 <s xml:id="echoid-s3669" xml:space="preserve">ces de liſez de ces</s> |
|
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|
6076 </p> |
|
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|
6077 <p style="it"> |
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|
6078 <s xml:id="echoid-s3670" xml:space="preserve">pag. </s> |
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|
6079 <s xml:id="echoid-s3671" xml:space="preserve">104. </s> |
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|
6080 <s xml:id="echoid-s3672" xml:space="preserve">ligne 6. </s> |
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|
6081 <s xml:id="echoid-s3673" xml:space="preserve">69. </s> |
|
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|
6082 <s xml:id="echoid-s3674" xml:space="preserve">M. </s> |
|
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|
6083 <s xml:id="echoid-s3675" xml:space="preserve">liſez 69. </s> |
|
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|
6084 <s xml:id="echoid-s3676" xml:space="preserve">de M.</s> |
|
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|
6085 <s xml:id="echoid-s3677" xml:space="preserve"/> |
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|
6086 </p> |
|
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|
6087 <p style="it"> |
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|
6088 <s xml:id="echoid-s3678" xml:space="preserve">pag. </s> |
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|
6089 <s xml:id="echoid-s3679" xml:space="preserve">105. </s> |
|
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|
6090 <s xml:id="echoid-s3680" xml:space="preserve">ligne 27. </s> |
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changeset
|
6091 <s xml:id="echoid-s3681" xml:space="preserve">répoudent, liſez répondent,</s> |
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6092 </p> |
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6093 <pb file="0188" n="201"/> |
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6094 <pb file="0189" n="202"/> |
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6095 <pb file="0190" n="203"/> |
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6096 <pb file="0191" n="204"/> |
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6097 <pb file="0192" n="205"/> |
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6098 <pb file="0193" n="206"/> |
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6099 <pb file="0194" n="207"/> |
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6100 <pb file="0195" n="208"/> |
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6101 <pb file="0196" n="209"/> |
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6102 </div></text> |
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6103 </echo> |