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Some new special instructions
| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Fri, 02 Dec 2016 14:37:22 +0100 |
| parents | 22d6a63640c6 |
| children |
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<?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"> <metadata> <dcterms:identifier>ECHO:3YQCRPP7.xml</dcterms:identifier> <dcterms:creator identifier="GND:117604917">Bion, Nicolas</dcterms:creator> <dcterms:title xml:lang="fr">Traité de la construction et principaux usages des instruments de mathématique</dcterms:title> <dcterms:date xsi:type="dcterms:W3CDTF">1723</dcterms:date> <dcterms:language xsi:type="dcterms:ISO639-3">fra</dcterms:language> <dcterms:rights>CC-BY-SA</dcterms:rights> <dcterms:license xlink:href="http://creativecommons.org/licenses/by-sa/3.0/">CC-BY-SA</dcterms:license> <dcterms:rightsHolder xlink:href="http://www.mpiwg-berlin.mpg.de">Max Planck Institute for the History of Science, Library</dcterms:rightsHolder> <log>pbsync ok http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?mode=imagepath&url=/mpiwg/online/permanent/library/3YQCRPP7/pageimg&viewMode=images </log> </metadata> <text xml:lang="fr" type="free"> <div xml:id="echoid-div1" type="section" level="1" n="1"><pb file="001" n="1"/> <pb file="002" n="2"/> <pb file="003" n="3"/> <handwritten/> <pb file="004" n="4"/> <pb file="005" n="5"/> <figure> <caption xml:id="echoid-caption1" xml:space="preserve">Usages des INSTRUMENS <lb/>de MATHEMATIQUE.</caption> </figure> <pb file="006" n="6"/> <pb file="007" n="7"/> </div> <div xml:id="echoid-div2" type="section" level="1" n="2"> <head xml:id="echoid-head1" xml:space="preserve"><emph style="red">TRAITÉ</emph> <lb/>DE LA <lb/><emph style="red">CONSTRUCTION</emph> <lb/>ET DES PRINCIPAUX <lb/><emph style="red">USAGES</emph> <lb/>DES INSTRUMENS <lb/><emph style="red">DE MATHEMATIQUE.</emph></head> <p> <s xml:id="echoid-s1" xml:space="preserve">Avec les Figures néceſſaires pour l'intelligence de ce Traité.</s> <s xml:id="echoid-s2" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3" xml:space="preserve"><emph style="red">Par N. BION, Ingenieur du Roi</emph></s> </p> <p> <s xml:id="echoid-s4" xml:space="preserve">Pour les Inſtrumens de Matbematique.</s> <s xml:id="echoid-s5" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6" xml:space="preserve">Nouvelle Edition, revûë, corrigée & </s> <s xml:id="echoid-s7" xml:space="preserve">augmentée.</s> <s xml:id="echoid-s8" xml:space="preserve"/> </p> <figure> <image file="007-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/007-01"/> </figure> <p> <s xml:id="echoid-s9" xml:space="preserve"><emph style="red">ALAHAYE,</emph> <lb/> <anchor type="note" xlink:label="note-007-01a" xlink:href="note-007-01"/> <emph style="red">M. DCC. XXIII. </emph></s> </p> <div xml:id="echoid-div2" type="float" level="2" n="1"> <note position="right" xlink:label="note-007-01" xlink:href="note-007-01a" xml:space="preserve"> <lb/>Chez # P. HUSSON, T. JOHNSON, P. GOSSE, \\ J. SWART, H. SCHEURLEER, J. VAN DUREN, \\ R. ALBERTS, C. LE VIER, & F. BOUCQUET. <lb/></note> </div> <pb file="008" n="8"/> <pb file="009" n="9"/> <figure> <image file="009-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/009-01"/> </figure> </div> <div xml:id="echoid-div4" type="section" level="1" n="3"> <head xml:id="echoid-head2" xml:space="preserve">A SON ALTESSE ROYALE <lb/>MONSEIGNEUR <lb/>LE DUC D'ORLEANS <lb/>REGENT.</head> <p> <s xml:id="echoid-s10" xml:space="preserve">MONSEIGNEUR,</s> </p> <p> <s xml:id="echoid-s11" xml:space="preserve">Un Livre qui regarde les Mathematiques appartient na-<lb/>turellement à <emph style="sc">VOTRE ALTESSE ROYALE</emph>; </s> <s xml:id="echoid-s12" xml:space="preserve">& </s> <s xml:id="echoid-s13" xml:space="preserve">quand <lb/>le reſpectueux attachement que j'ai pour Elle, ne m'auroit <lb/>pas engagé à lui preſenter cet Ouvrage, la convenance ſeu-<lb/>le m'en auroit fait un devoir. </s> <s xml:id="echoid-s14" xml:space="preserve">Perſonne n'ignore, <emph style="sc">MON-<lb/>SEIGNEUR</emph>, à quel point vous poſſedez les Sciences; </s> <s xml:id="echoid-s15" xml:space="preserve">& </s> <s xml:id="echoid-s16" xml:space="preserve"><lb/>toute l'Europe ne parleroit encore que de vos lumieres, ſi <lb/>vous n'attiriez aujourd'hui ſon admiration par un autre en-<lb/>droit. </s> <s xml:id="echoid-s17" xml:space="preserve">J'entends, <emph style="sc">MONSEIGNEUR</emph>, tous ces Actes de <lb/>Sageſſe & </s> <s xml:id="echoid-s18" xml:space="preserve">d'Equité dont <emph style="sc">VOTRE ALTESSE ROYALE</emph> <lb/>a déja ſignalé ſa Regence, mais ſur leſquels un ſilence pru-<lb/>dent eſt tout ce qui convient à ma foibleſſe, auſſi-bien qu'au <lb/>goût de <emph style="sc">VOTRE ALTESSE ROYALE</emph>. </s> <s xml:id="echoid-s19" xml:space="preserve">Je la remercie-<lb/>rai ſeulement d'avoir bien voulu que je lui renouvelaſſe les <lb/>ſinceres aſſurances du profond reſpect & </s> <s xml:id="echoid-s20" xml:space="preserve">du dévouëmenten-<lb/>tier avec lequel je ſuis,</s> </p> <p> <s xml:id="echoid-s21" xml:space="preserve">MONSEIGNEVR,</s> </p> <p> <s xml:id="echoid-s22" xml:space="preserve">DE VOTRE ALTESSE ROYALE,</s> </p> <p> <s xml:id="echoid-s23" xml:space="preserve">Le très-humble & </s> <s xml:id="echoid-s24" xml:space="preserve">très-obéiſſant <lb/>Serviteur</s> </p> <p> <s xml:id="echoid-s25" xml:space="preserve">B<emph style="sc">ION.</emph></s> </p> <pb file="010" n="10"/> <figure> <image file="010-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/010-01"/> </figure> </div> <div xml:id="echoid-div5" type="section" level="1" n="4"> <head xml:id="echoid-head3" xml:space="preserve">AVERTISSEMENT <lb/>DES <lb/>LIBRAIRES.</head> <p style="it"> <s xml:id="echoid-s26" xml:space="preserve">CE Traité de la Conſtruction & </s> <s xml:id="echoid-s27" xml:space="preserve">des uſages des Inſtrumens de Matbe-<lb/>matique eſt un des plus utiles qui ait encore paru. </s> <s xml:id="echoid-s28" xml:space="preserve">Les plus avancez dans <lb/>cette Science y trouveront pluſieurs choſes pour leur uſage, & </s> <s xml:id="echoid-s29" xml:space="preserve">ceux qui <lb/>n'en ont qu'une connoiſſance médiocre en tireront beaucoup de ſecours né-<lb/>ceſſaires pour s'y avancer. </s> <s xml:id="echoid-s30" xml:space="preserve">Les jeunes gens mêmes, qui n'en ſont encore <lb/>qu'aux Elemens, ne ſçauroient choiſir un meilleur Livre, ni qui con-<lb/>tienne les premiers principes & </s> <s xml:id="echoid-s31" xml:space="preserve">les fondemens de cette ſcience, d'une ma-<lb/>niere plus aiſée & </s> <s xml:id="echoid-s32" xml:space="preserve">plus agréable. </s> <s xml:id="echoid-s33" xml:space="preserve">Ils y apprendront en même tems la <lb/>Theorie & </s> <s xml:id="echoid-s34" xml:space="preserve">la pratique.</s> <s xml:id="echoid-s35" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s36" xml:space="preserve">Comme cet Ouvrage n'étoit gueres connu qu'en France, nous avons cru <lb/>rendre ſervice aux Curieux de ces Provinces & </s> <s xml:id="echoid-s37" xml:space="preserve">des Pays étrangers d'en <lb/>faire ici une Edition. </s> <s xml:id="echoid-s38" xml:space="preserve">Celle que nous donnons eſt incomparablement meil-<lb/>leure que la derniere de Paris. </s> <s xml:id="echoid-s39" xml:space="preserve">Le papier & </s> <s xml:id="echoid-s40" xml:space="preserve">le caractere en ſont plus <lb/>beaux, & </s> <s xml:id="echoid-s41" xml:space="preserve">les Planches mieux gravées & </s> <s xml:id="echoid-s42" xml:space="preserve">plus exactes. </s> <s xml:id="echoid-s43" xml:space="preserve">Nous avons <lb/>auſſi eu ſoin de la faire revoir par une perſonne verſée dans ces ſortes de <lb/>choſes, qui a corrigé quantité de fautes qui ſe trouvent dans l'Edition de <lb/>Paris.</s> <s xml:id="echoid-s44" xml:space="preserve"/> </p> <p style="it"> <s xml:id="echoid-s45" xml:space="preserve">Tous ces avantages qu'a notre Edition ſur celle de France, joint à <lb/>l'utilité du Livre, qui eſt d'un uſage univerſel pour les Mathemaliques, <lb/>nous font eſperer que le Public la recevra favorablement. </s> <s xml:id="echoid-s46" xml:space="preserve">Si le débit <lb/>répond à notre attente, nous pourrons donner unjour une ſuite de ce Trai-<lb/>té, qui ne ſera ni moins curieuſe ni moins néceſſaire. </s> <s xml:id="echoid-s47" xml:space="preserve">Elle enſeignera les <lb/>uſages de quantité d'autres Inſtrumens de Mathematique & </s> <s xml:id="echoid-s48" xml:space="preserve">de Phyſique <lb/>dont on ne fait aucune mention ici.</s> <s xml:id="echoid-s49" xml:space="preserve"/> </p> <pb file="011" n="11"/> <figure> <image file="011-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/011-01"/> </figure> </div> <div xml:id="echoid-div6" type="section" level="1" n="5"> <head xml:id="echoid-head4" style="it" xml:space="preserve">PREFACE.</head> <p> <s xml:id="echoid-s50" xml:space="preserve">LE favorable accuëil qui a été fait aux deux Ouvrages <lb/>que j'ai mis au jour il y a quelques années, m'a déter-<lb/>miné à executer lè deſſein que j'avois formé depuis <lb/>long-tems de donner au Public la Conſtruction & </s> <s xml:id="echoid-s51" xml:space="preserve">les <lb/>principaux Uiages des plus curieux & </s> <s xml:id="echoid-s52" xml:space="preserve">plus utiles Inſtrumens de <lb/>Mathematique qui ont été inventez juſqu'à preſent.</s> <s xml:id="echoid-s53" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s54" xml:space="preserve">Pour garder quelque ordre dans cet Ouvrage, après avoir <lb/>donné les définitions néceſſaires pour l'intelligence de ce Trai-<lb/>té, je l'ai partagé en huit Livres, & </s> <s xml:id="echoid-s55" xml:space="preserve">chacun de ces Livres en plu-<lb/>ſieurs Chapitres.</s> <s xml:id="echoid-s56" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s57" xml:space="preserve">Le premier Livre contient la Conſtruction & </s> <s xml:id="echoid-s58" xml:space="preserve">les principaux <lb/>Uſages des Inſtrumens les plus ſimples & </s> <s xml:id="echoid-s59" xml:space="preserve">les plus or dinaires, <lb/>comme ſont le Compas, la Regle, le Tire-ligne, le Porte-<lb/>craïon, l'Equerre, & </s> <s xml:id="echoid-s60" xml:space="preserve">le Rapporteur; </s> <s xml:id="echoid-s61" xml:space="preserve">on y trouvera pluſieurs <lb/>beaux traits de Compas, & </s> <s xml:id="echoid-s62" xml:space="preserve">la maniere de tracer ſur le papier tou-<lb/>tes ſortes de Figures tant regulieres qu'irregulieres.</s> <s xml:id="echoid-s63" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s64" xml:space="preserve">Le ſecond Livre explique aſſez nettement, quoiqu'en peu de <lb/>pages, la maniere de conſtruire le Compas de Proportion, & </s> <s xml:id="echoid-s65" xml:space="preserve">ſes <lb/>principaux Uſages. </s> <s xml:id="echoid-s66" xml:space="preserve">J'y ai joint pluſieurs méthodes de conſtrui-<lb/>re differentes Jauges, & </s> <s xml:id="echoid-s67" xml:space="preserve">les moyens de s'en ſervir pour jauger <lb/>les Tonneaux. </s> <s xml:id="echoid-s68" xml:space="preserve">Le Compas de Proportion avec les autres Inſtru-<lb/>mens expliquez ci-devant, compoſe ce qu'on nomme Etuy de <lb/>Mathematique.</s> <s xml:id="echoid-s69" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s70" xml:space="preserve">Dans le troiſiéme Livre on trouve la Conſtruction & </s> <s xml:id="echoid-s71" xml:space="preserve">les Uſa-<lb/>ges de pluſieurs autres Inſtrumens curieux qui ſervent ordinai-<lb/>rement dans le Cabinet. </s> <s xml:id="echoid-s72" xml:space="preserve">La matiere eſt fort diverſiſiée dans ce <lb/>Livre, où je donne l'explication de quantité de choſes, qui, <lb/>comme je le crois, n'on point encore été vûës. </s> <s xml:id="echoid-s73" xml:space="preserve">On y trouve la <lb/>maniere d'armer les Pierres d'Aiman, & </s> <s xml:id="echoid-s74" xml:space="preserve">la compoſition de dif-<lb/>ferens Microſcopes, & </s> <s xml:id="echoid-s75" xml:space="preserve">pluſieurs autres curioſitez qui pourront <lb/>faire plaiſir aux Lecteurs</s> </p> <p> <s xml:id="echoid-s76" xml:space="preserve">Je donne dans le quatriéme Livre, la Conſtruction & </s> <s xml:id="echoid-s77" xml:space="preserve">les <lb/> <pb file="012" n="12" rhead="PREFACE."/> Uſages des principaux Inſtrumens qui ſervent en Campagne, <lb/>pour arpenter les Terres, lever les Plans, meſurer les diſtan-<lb/>ces & </s> <s xml:id="echoid-s78" xml:space="preserve">les hauteurs, tant acceſſibles qu'inacceſſibles; </s> <s xml:id="echoid-s79" xml:space="preserve">comme <lb/>ſont les Piquets, la Toiſe, la Chaîne, l'Equerre d'Arpenteur, <lb/>les Recipiangles, les Planchetes, le Quart de Cercle, le Demi-<lb/>Cercle & </s> <s xml:id="echoid-s80" xml:space="preserve">la Bouſſole. </s> <s xml:id="echoid-s81" xml:space="preserve">Comme mon deſſein n'eſt que d'inſtruire <lb/>ceux qui commencent d'apprendre ces Sciences, je n'y ai mis <lb/>que les operations les plus faciles & </s> <s xml:id="echoid-s82" xml:space="preserve">à la portée de tout le <lb/>monde; </s> <s xml:id="echoid-s83" xml:space="preserve">y ayant aſſez d'autres Livres qui traitent ces matieres <lb/>plus à fonds.</s> <s xml:id="echoid-s84" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s85" xml:space="preserve">Le cinquiéme Livre contient la Conſtruction de pluſieurs dif-<lb/>ferens Niveaux, comme auſſi la maniere de les rectifier & </s> <s xml:id="echoid-s86" xml:space="preserve">les <lb/>mettre en pratique pour la conduite des Eaux. </s> <s xml:id="echoid-s87" xml:space="preserve">J'y ai joint l'ex-<lb/>plication d'une efpece de Jauge pour meſurer la quantité d'eau <lb/>que fournit une Source, & </s> <s xml:id="echoid-s88" xml:space="preserve">le moyen de partager ces mêmes <lb/>Eaux. </s> <s xml:id="echoid-s89" xml:space="preserve">On trouvera auſſr dans ce Livre la Conſtruction des Inſ-<lb/>trumens d'Artillerie, & </s> <s xml:id="echoid-s90" xml:space="preserve">la maniere de s'en ſervir, tant pour <lb/>les Canons & </s> <s xml:id="echoid-s91" xml:space="preserve">Boulets, que pour les Mortiers & </s> <s xml:id="echoid-s92" xml:space="preserve">les Bombes; <lb/></s> <s xml:id="echoid-s93" xml:space="preserve">ce qui eſt dit à ce ſujet eſt aſſex de pratique, quoiqu'en abregé.</s> <s xml:id="echoid-s94" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s95" xml:space="preserve">Le ſixiéme Livre renferme la Conſtruction & </s> <s xml:id="echoid-s96" xml:space="preserve">les Uſages des <lb/>plus beaux Inſtrumens qui ſervent à l'Aſtronomie; </s> <s xml:id="echoid-s97" xml:space="preserve">& </s> <s xml:id="echoid-s98" xml:space="preserve">comme il <lb/>y a quantité d'Obſervations à faire, Monſieur de la Hire m'a <lb/>fourni beaucoup de lumieres là-deſſus. </s> <s xml:id="echoid-s99" xml:space="preserve">J'ai pris dans ſes Tables <lb/>Aſtronomiques la meilleure partie de ce qui eſt contenu dans ce <lb/>Livre. </s> <s xml:id="echoid-s100" xml:space="preserve">Il y a auſſi quelque choſe de Monſieur Caſſini. </s> <s xml:id="echoid-s101" xml:space="preserve">L'exacti-<lb/>tude admirable que ces grands Hommes apportent pour obſer-<lb/>ver les Aſtres, y eſt expliquée le mieux qu'il m'a été poſſible, <lb/>pour donner une idée générale de l'Aſtronomie.</s> <s xml:id="echoid-s102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s103" xml:space="preserve">On trouve dans le ſeptiéme Livre la Conſtruction & </s> <s xml:id="echoid-s104" xml:space="preserve">les Uſa-<lb/>ges de pluſieurs Inſtrumens propres à la Navigation. </s> <s xml:id="echoid-s105" xml:space="preserve">Après l'ex-<lb/>plication de la Bouſſole Marine & </s> <s xml:id="echoid-s106" xml:space="preserve">des Inſtrumens pour obſerver <lb/>ſur Mer la hauteur des Aſtres, j'explique en peu de mots le Quar-<lb/>tier de réduction; </s> <s xml:id="echoid-s107" xml:space="preserve">comme auſſi la maniere de dreſſer, & </s> <s xml:id="echoid-s108" xml:space="preserve">de ſe ſer-<lb/>vir des Cartes réduites.</s> <s xml:id="echoid-s109" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s110" xml:space="preserve">Le huitiéme & </s> <s xml:id="echoid-s111" xml:space="preserve">dernier Livre explique aſſez amplement la <lb/>Conſtruction & </s> <s xml:id="echoid-s112" xml:space="preserve">les Uſages des Cadrans Solaires, auſſi-bien que <lb/>des Cadrans à la Lune & </s> <s xml:id="echoid-s113" xml:space="preserve">aux Etoiles. </s> <s xml:id="echoid-s114" xml:space="preserve">On y trouve auſſi la Conſ-<lb/>truction d'un Horloge Elementaire ou Pendule à l eau, & </s> <s xml:id="echoid-s115" xml:space="preserve">d'un <lb/>Cadran qui marque le nom des Vents qui ſoufflent. </s> <s xml:id="echoid-s116" xml:space="preserve">Enfin tout <lb/>l'Ouvrage eſt terminé par la Deſeription des principaux Outils <lb/> <pb file="013" n="13" rhead="PREFACE."/> dont on ſe ſert pour conſtruire les Inſtrumens de Mathemati-<lb/>que.</s> <s xml:id="echoid-s117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s118" xml:space="preserve">J'ai enrichi ce Traité de pluſieurs Planches; </s> <s xml:id="echoid-s119" xml:space="preserve">& </s> <s xml:id="echoid-s120" xml:space="preserve">quoique, pour <lb/>n'en pas trop multiplier le nombre, je les aye un peu remplies de <lb/>Figures, elles ne laiſſeront pas de donner une idée aſſez nette <lb/>des choſes qu'elles repreſentent.</s> <s xml:id="echoid-s121" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s122" xml:space="preserve">Les Planches ſont placées dans le corps du Livre, à la fin des <lb/>matieres dont elles traitent, afin qu'en tournant les feüillets, on <lb/>puiſſe les avoir facilement devant les yeux.</s> <s xml:id="echoid-s123" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s124" xml:space="preserve">J'ai retouché dans cette Edition pluſieurs endroits qui ne me <lb/>ſembloient pas aſſez bien expliquez. </s> <s xml:id="echoid-s125" xml:space="preserve">J'ai de plus ajoûté pluſieurs <lb/>choſes conſiderables, qui manquoient à la precedente; </s> <s xml:id="echoid-s126" xml:space="preserve">par exem-<lb/>ple, dans le quatriéme Livre on trouvera un Chapitre nouveau, <lb/>où je donne les Uſages des Inſtrumens appliquez à la Fortifica-<lb/>tion des Places; </s> <s xml:id="echoid-s127" xml:space="preserve">ce Chapitre avec la Planche qui lui eſt jointe, <lb/>ſuffit pour mettre en état les moins verſez dans cette Science, de <lb/>tracer toutes ſortes d'Ouvrages, tant ſur le terrain que ſur le pa-<lb/>pier, & </s> <s xml:id="echoid-s128" xml:space="preserve">d'en faire le toiſé.</s> <s xml:id="echoid-s129" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s130" xml:space="preserve">On trouvera encore le ſixiéme Livre augmenté d'un Chapi-<lb/>tre entier ſur la Conſtruction & </s> <s xml:id="echoid-s131" xml:space="preserve">les Uſages de l'Horloge à Pendule <lb/>pour les Obſervations Aſtronomiques; </s> <s xml:id="echoid-s132" xml:space="preserve">ce que je dis à ce ſujet <lb/>eſt tiré en partie d'un Livre intitulé, De Horologio Oſcillatorio, de <lb/>Monſieur Huygens, & </s> <s xml:id="echoid-s133" xml:space="preserve">eſt auſſi accompagné d'une Planche où <lb/>les differentes pieces qui compoſent cet Horloge, ſont repreſen-<lb/>tées aſſez ſenſiblement. </s> <s xml:id="echoid-s134" xml:space="preserve">A l'égard des autres additions répanduës <lb/>dans tout l'Ouvrage, je n'en parle point; </s> <s xml:id="echoid-s135" xml:space="preserve">ce détail nous mene-<lb/>roit trop loin.</s> <s xml:id="echoid-s136" xml:space="preserve"/> </p> <pb file="014" n="14" rhead="APPROBATION."/> <p> <s xml:id="echoid-s137" xml:space="preserve">J'Ai examiné par ordre de Monſeigneur le Chancelier, un Traité de la <lb/>Conſtruction & </s> <s xml:id="echoid-s138" xml:space="preserve">des principaux Uſages des differens Inſtrumens de Mathemati-<lb/>que, lequel a été compoſé par M. </s> <s xml:id="echoid-s139" xml:space="preserve"><emph style="sc">NICOLAS BION</emph>, Ingenieur pour les Inſ-<lb/>trumens de Mathematique: </s> <s xml:id="echoid-s140" xml:space="preserve">Je crois qu'il ſera très-agréable & </s> <s xml:id="echoid-s141" xml:space="preserve">très utile au <lb/>Public, & </s> <s xml:id="echoid-s142" xml:space="preserve">particulierement aux Ouvriers, qui y trouveront de quoi s'inſtruire <lb/>à fond pour la fabrique de tous les Inſtrumens dont on ſe ſert dans la pra-<lb/>tique des differentes parties de Mathematique. </s> <s xml:id="echoid-s143" xml:space="preserve">A Paris à l'Obſervatoire <lb/>Roïal, le dixiéme Août, Mil ſept cens huit.</s> <s xml:id="echoid-s144" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div7" type="section" level="1" n="6"> <head xml:id="echoid-head5" xml:space="preserve">DE LA HIRE, Profeſſeur Roïal de Mathematique, & de <lb/>l'Académie des Sciences.</head> <figure> <image file="014-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/014-01"/> </figure> </div> <div xml:id="echoid-div8" type="section" level="1" n="7"> <head xml:id="echoid-head6" xml:space="preserve">Fautes à corriger.</head> <p> <s xml:id="echoid-s145" xml:space="preserve">Pag. </s> <s xml:id="echoid-s146" xml:space="preserve">4. </s> <s xml:id="echoid-s147" xml:space="preserve">ligne 10. </s> <s xml:id="echoid-s148" xml:space="preserve">& </s> <s xml:id="echoid-s149" xml:space="preserve">11. </s> <s xml:id="echoid-s150" xml:space="preserve">liſez, degré p. </s> <s xml:id="echoid-s151" xml:space="preserve">7. </s> <s xml:id="echoid-s152" xml:space="preserve">l. </s> <s xml:id="echoid-s153" xml:space="preserve">21. </s> <s xml:id="echoid-s154" xml:space="preserve">la proportion p. </s> <s xml:id="echoid-s155" xml:space="preserve">29. </s> <s xml:id="echoid-s156" xml:space="preserve">à la <lb/>marge, VI. </s> <s xml:id="echoid-s157" xml:space="preserve">p. </s> <s xml:id="echoid-s158" xml:space="preserve">79. </s> <s xml:id="echoid-s159" xml:space="preserve">l. </s> <s xml:id="echoid-s160" xml:space="preserve">30. </s> <s xml:id="echoid-s161" xml:space="preserve">du Compas à r ſſort. </s> <s xml:id="echoid-s162" xml:space="preserve">& </s> <s xml:id="echoid-s163" xml:space="preserve">en marge Fig. </s> <s xml:id="echoid-s164" xml:space="preserve">C. </s> <s xml:id="echoid-s165" xml:space="preserve">p. </s> <s xml:id="echoid-s166" xml:space="preserve">96. </s> <s xml:id="echoid-s167" xml:space="preserve">l. </s> <s xml:id="echoid-s168" xml:space="preserve">4. <lb/></s> <s xml:id="echoid-s169" xml:space="preserve">manier & </s> <s xml:id="echoid-s170" xml:space="preserve">en marge Fig. </s> <s xml:id="echoid-s171" xml:space="preserve">S. </s> <s xml:id="echoid-s172" xml:space="preserve">p. </s> <s xml:id="echoid-s173" xml:space="preserve">163. </s> <s xml:id="echoid-s174" xml:space="preserve">l. </s> <s xml:id="echoid-s175" xml:space="preserve">31. </s> <s xml:id="echoid-s176" xml:space="preserve">le Sinus de 99. </s> <s xml:id="echoid-s177" xml:space="preserve">d. </s> <s xml:id="echoid-s178" xml:space="preserve">p. </s> <s xml:id="echoid-s179" xml:space="preserve">164. </s> <s xml:id="echoid-s180" xml:space="preserve">l. </s> <s xml:id="echoid-s181" xml:space="preserve">16. </s> <s xml:id="echoid-s182" xml:space="preserve"><lb/>de 20. </s> <s xml:id="echoid-s183" xml:space="preserve">deg. </s> <s xml:id="echoid-s184" xml:space="preserve">& </s> <s xml:id="echoid-s185" xml:space="preserve">l. </s> <s xml:id="echoid-s186" xml:space="preserve">18. </s> <s xml:id="echoid-s187" xml:space="preserve">de 22. </s> <s xml:id="echoid-s188" xml:space="preserve">d. </s> <s xml:id="echoid-s189" xml:space="preserve">p. </s> <s xml:id="echoid-s190" xml:space="preserve">180. </s> <s xml:id="echoid-s191" xml:space="preserve">l. </s> <s xml:id="echoid-s192" xml:space="preserve">3. </s> <s xml:id="echoid-s193" xml:space="preserve">on donne. </s> <s xml:id="echoid-s194" xml:space="preserve">p. </s> <s xml:id="echoid-s195" xml:space="preserve">181. </s> <s xml:id="echoid-s196" xml:space="preserve">l. </s> <s xml:id="echoid-s197" xml:space="preserve">11. </s> <s xml:id="echoid-s198" xml:space="preserve">flancs <lb/>11. </s> <s xml:id="echoid-s199" xml:space="preserve">p. </s> <s xml:id="echoid-s200" xml:space="preserve">183. </s> <s xml:id="echoid-s201" xml:space="preserve">l. </s> <s xml:id="echoid-s202" xml:space="preserve">29. </s> <s xml:id="echoid-s203" xml:space="preserve">environ 600. </s> <s xml:id="echoid-s204" xml:space="preserve">p. </s> <s xml:id="echoid-s205" xml:space="preserve">184. </s> <s xml:id="echoid-s206" xml:space="preserve">l. </s> <s xml:id="echoid-s207" xml:space="preserve">28 6. </s> <s xml:id="echoid-s208" xml:space="preserve">pouces, p. </s> <s xml:id="echoid-s209" xml:space="preserve">194. </s> <s xml:id="echoid-s210" xml:space="preserve">l. </s> <s xml:id="echoid-s211" xml:space="preserve">I. </s> <s xml:id="echoid-s212" xml:space="preserve"><lb/>Table qui p. </s> <s xml:id="echoid-s213" xml:space="preserve">197. </s> <s xml:id="echoid-s214" xml:space="preserve">l. </s> <s xml:id="echoid-s215" xml:space="preserve">dern. </s> <s xml:id="echoid-s216" xml:space="preserve">de 500. </s> <s xml:id="echoid-s217" xml:space="preserve">toiſes, p. </s> <s xml:id="echoid-s218" xml:space="preserve">205, l. </s> <s xml:id="echoid-s219" xml:space="preserve">8. </s> <s xml:id="echoid-s220" xml:space="preserve">90. </s> <s xml:id="echoid-s221" xml:space="preserve">lig. </s> <s xml:id="echoid-s222" xml:space="preserve">l. </s> <s xml:id="echoid-s223" xml:space="preserve">10. </s> <s xml:id="echoid-s224" xml:space="preserve">ſecond <lb/>90. </s> <s xml:id="echoid-s225" xml:space="preserve">l. </s> <s xml:id="echoid-s226" xml:space="preserve">14. </s> <s xml:id="echoid-s227" xml:space="preserve">à 90. </s> <s xml:id="echoid-s228" xml:space="preserve">lignes. </s> <s xml:id="echoid-s229" xml:space="preserve">p. </s> <s xml:id="echoid-s230" xml:space="preserve">208. </s> <s xml:id="echoid-s231" xml:space="preserve">l. </s> <s xml:id="echoid-s232" xml:space="preserve">25. </s> <s xml:id="echoid-s233" xml:space="preserve">du 45. </s> <s xml:id="echoid-s234" xml:space="preserve">deg. </s> <s xml:id="echoid-s235" xml:space="preserve">p. </s> <s xml:id="echoid-s236" xml:space="preserve">209. </s> <s xml:id="echoid-s237" xml:space="preserve">l. </s> <s xml:id="echoid-s238" xml:space="preserve">25. </s> <s xml:id="echoid-s239" xml:space="preserve">de 45. </s> <s xml:id="echoid-s240" xml:space="preserve">deg. </s> <s xml:id="echoid-s241" xml:space="preserve"><lb/>p. </s> <s xml:id="echoid-s242" xml:space="preserve">215. </s> <s xml:id="echoid-s243" xml:space="preserve">l, 26. </s> <s xml:id="echoid-s244" xml:space="preserve">à 35; </s> <s xml:id="echoid-s245" xml:space="preserve">donc p. </s> <s xml:id="echoid-s246" xml:space="preserve">218. </s> <s xml:id="echoid-s247" xml:space="preserve">l. </s> <s xml:id="echoid-s248" xml:space="preserve">17. </s> <s xml:id="echoid-s249" xml:space="preserve">de 90. </s> <s xml:id="echoid-s250" xml:space="preserve">deg. </s> <s xml:id="echoid-s251" xml:space="preserve">p. </s> <s xml:id="echoid-s252" xml:space="preserve">231. </s> <s xml:id="echoid-s253" xml:space="preserve">l. </s> <s xml:id="echoid-s254" xml:space="preserve">4. </s> <s xml:id="echoid-s255" xml:space="preserve">eſpece de <lb/>minutes & </s> <s xml:id="echoid-s256" xml:space="preserve">ſecondes. </s> <s xml:id="echoid-s257" xml:space="preserve">p. </s> <s xml:id="echoid-s258" xml:space="preserve">258. </s> <s xml:id="echoid-s259" xml:space="preserve">l. </s> <s xml:id="echoid-s260" xml:space="preserve">14. </s> <s xml:id="echoid-s261" xml:space="preserve">les 12. </s> <s xml:id="echoid-s262" xml:space="preserve">mois p. </s> <s xml:id="echoid-s263" xml:space="preserve">262. </s> <s xml:id="echoid-s264" xml:space="preserve">l. </s> <s xml:id="echoid-s265" xml:space="preserve">14. </s> <s xml:id="echoid-s266" xml:space="preserve">dans le <lb/>p. </s> <s xml:id="echoid-s267" xml:space="preserve">265. </s> <s xml:id="echoid-s268" xml:space="preserve">l. </s> <s xml:id="echoid-s269" xml:space="preserve">1. </s> <s xml:id="echoid-s270" xml:space="preserve">cercle Z. </s> <s xml:id="echoid-s271" xml:space="preserve">p. </s> <s xml:id="echoid-s272" xml:space="preserve">278. </s> <s xml:id="echoid-s273" xml:space="preserve">l 36. </s> <s xml:id="echoid-s274" xml:space="preserve">de 5 pieds & </s> <s xml:id="echoid-s275" xml:space="preserve">l. </s> <s xml:id="echoid-s276" xml:space="preserve">38. </s> <s xml:id="echoid-s277" xml:space="preserve">de 25. </s> <s xml:id="echoid-s278" xml:space="preserve">pieds p. </s> <s xml:id="echoid-s279" xml:space="preserve">348. </s> <s xml:id="echoid-s280" xml:space="preserve"><lb/>l. </s> <s xml:id="echoid-s281" xml:space="preserve">7. </s> <s xml:id="echoid-s282" xml:space="preserve">le 90. </s> <s xml:id="echoid-s283" xml:space="preserve">deg. </s> <s xml:id="echoid-s284" xml:space="preserve">Avec d'autres pareilles fautes qui peuvent avoir écbapé à la <lb/>diligence du Correcteur ou aux mains des Ouvriers.</s> <s xml:id="echoid-s285" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div9" type="section" level="1" n="8"> <head xml:id="echoid-head7" xml:space="preserve">Avis au Relieur.</head> <p style="it"> <s xml:id="echoid-s286" xml:space="preserve">Les planches doivent être pliées de maniere à pouvoir deborder bors du li-<lb/>vre; </s> <s xml:id="echoid-s287" xml:space="preserve">ſuit qu'on les place auprès des pages comme elles ſont marquées, ſoit qu'on <lb/>les mette toutes enſemble à la fin du livre.</s> <s xml:id="echoid-s288" xml:space="preserve"/> </p> <pb file="015" n="15"/> <figure> <image file="015-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/015-01"/> </figure> </div> <div xml:id="echoid-div10" type="section" level="1" n="9"> <head xml:id="echoid-head8" xml:space="preserve">DEFINITIONS</head> <head xml:id="echoid-head9" xml:space="preserve">NECESSAIRES <lb/>POUR <lb/>L'INTELLIGENCE DE CE TRAITÉ.</head> <p> <s xml:id="echoid-s289" xml:space="preserve">LE Point eſt ce qui n'a aucunes parties, & </s> <s xml:id="echoid-s290" xml:space="preserve">qui par con-<lb/> <anchor type="note" xlink:label="note-015-01a" xlink:href="note-015-01"/> ſequent eſt indiviſible.</s> <s xml:id="echoid-s291" xml:space="preserve"/> </p> <div xml:id="echoid-div10" type="float" level="2" n="1"> <note position="right" xlink:label="note-015-01" xlink:href="note-015-01a" xml:space="preserve">Premiere <lb/>Planche. <lb/>Figure 1.</note> </div> <p> <s xml:id="echoid-s292" xml:space="preserve">La Ligne eſt une longueur ſans largeur, & </s> <s xml:id="echoid-s293" xml:space="preserve">c'eſt l'é-<lb/> <anchor type="note" xlink:label="note-015-02a" xlink:href="note-015-02"/> coulement du Point.</s> <s xml:id="echoid-s294" xml:space="preserve"/> </p> <div xml:id="echoid-div11" type="float" level="2" n="2"> <note position="right" xlink:label="note-015-02" xlink:href="note-015-02a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s295" xml:space="preserve">Il y a de trois ſortes de Lignes, la droite, la courbe & </s> <s xml:id="echoid-s296" xml:space="preserve">la <lb/>mixte.</s> <s xml:id="echoid-s297" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s298" xml:space="preserve">La Ligne Droite eſt la plus courte de toutes celles qu'on peut ti-<lb/> <anchor type="note" xlink:label="note-015-03a" xlink:href="note-015-03"/> rer d'un point à l'autre.</s> <s xml:id="echoid-s299" xml:space="preserve"/> </p> <div xml:id="echoid-div12" type="float" level="2" n="3"> <note position="right" xlink:label="note-015-03" xlink:href="note-015-03a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s300" xml:space="preserve">La Ligne Courbe eſt celle qui ne va pas directement d'une de <lb/> <anchor type="note" xlink:label="note-015-04a" xlink:href="note-015-04"/> ſes extremicez à l'autre, mais qui s'en écarte par un détour.</s> <s xml:id="echoid-s301" xml:space="preserve"/> </p> <div xml:id="echoid-div13" type="float" level="2" n="4"> <note position="right" xlink:label="note-015-04" xlink:href="note-015-04a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s302" xml:space="preserve">La Ligne Mixte eſt celle dont une partie eſt droite, & </s> <s xml:id="echoid-s303" xml:space="preserve">l'autre <lb/> <anchor type="note" xlink:label="note-015-05a" xlink:href="note-015-05"/> courbe.</s> <s xml:id="echoid-s304" xml:space="preserve"/> </p> <div xml:id="echoid-div14" type="float" level="2" n="5"> <note position="right" xlink:label="note-015-05" xlink:href="note-015-05a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s305" xml:space="preserve">Les extremitez des Lignes ſont des Points.</s> <s xml:id="echoid-s306" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s307" xml:space="preserve">Les Lignes comparées les unes aux autres ſuivant leurs poſi-<lb/>tions ou ſituations, ſont ou paralleles, ou perpendiculaires, ou <lb/>obliques.</s> <s xml:id="echoid-s308" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s309" xml:space="preserve">On appelle Lignes Paralleles celles qui conſervent toûjours entre <lb/> <anchor type="note" xlink:label="note-015-06a" xlink:href="note-015-06"/> elles une même diſtance, & </s> <s xml:id="echoid-s310" xml:space="preserve">qui étant prolongées de part & </s> <s xml:id="echoid-s311" xml:space="preserve">d'au-<lb/>tre, ne ſe rencontrent jamais, ſoit que les Lignes ſoient toutes <lb/>deux droites, ou toutes deux courbes.</s> <s xml:id="echoid-s312" xml:space="preserve"/> </p> <div xml:id="echoid-div15" type="float" level="2" n="6"> <note position="right" xlink:label="note-015-06" xlink:href="note-015-06a" xml:space="preserve">Fig. 5.</note> </div> <pb o="2" file="016" n="16" rhead="PRINCIPES"/> <p> <s xml:id="echoid-s313" xml:space="preserve">Les Lignes Perpendiculaires ſont celles qui en ſe rencontrant <lb/> <anchor type="note" xlink:label="note-016-01a" xlink:href="note-016-01"/> ne s'inclinent pas plus d'un côté que d'autre; </s> <s xml:id="echoid-s314" xml:space="preserve">c'eſt pourquoi elles <lb/>font deux angles égaux, & </s> <s xml:id="echoid-s315" xml:space="preserve">par conſequent tous deux droits.</s> <s xml:id="echoid-s316" xml:space="preserve"/> </p> <div xml:id="echoid-div16" type="float" level="2" n="7"> <note position="left" xlink:label="note-016-01" xlink:href="note-016-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s317" xml:space="preserve">Les Lignes Obliques ſont celles qui en ſe rencontrant, forment <lb/> <anchor type="note" xlink:label="note-016-02a" xlink:href="note-016-02"/> des angles obliques & </s> <s xml:id="echoid-s318" xml:space="preserve">inégaux entr'eux, c'eſt-à-dire, aigus & </s> <s xml:id="echoid-s319" xml:space="preserve">obtus.</s> <s xml:id="echoid-s320" xml:space="preserve"/> </p> <div xml:id="echoid-div17" type="float" level="2" n="8"> <note position="left" xlink:label="note-016-02" xlink:href="note-016-02a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s321" xml:space="preserve">Ces Lignes prennent encore d'autres dénominations, comme <lb/>ſont celles qui ſuivent.</s> <s xml:id="echoid-s322" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s323" xml:space="preserve">La Ligne à plomb ou Verticale eſt celle qui paſſeroit par le centre <lb/> <anchor type="note" xlink:label="note-016-03a" xlink:href="note-016-03"/> de la Terre ſi elle étoit continuée, comme ſeroit un fil auquel on <lb/>auroit attaché un plomb, ou quelque autre choſe de peſant.</s> <s xml:id="echoid-s324" xml:space="preserve"/> </p> <div xml:id="echoid-div18" type="float" level="2" n="9"> <note position="left" xlink:label="note-016-03" xlink:href="note-016-03a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s325" xml:space="preserve">La Ligne horizontale, ou de niveau apparent, eſt une Ligne <lb/> <anchor type="note" xlink:label="note-016-04a" xlink:href="note-016-04"/> droite qui toucheroit la ſurface de la Terre en un point, ou qui <lb/>ſeroit parellele à cette Tangente.</s> <s xml:id="echoid-s326" xml:space="preserve"/> </p> <div xml:id="echoid-div19" type="float" level="2" n="10"> <note position="left" xlink:label="note-016-04" xlink:href="note-016-04a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s327" xml:space="preserve">La Ligne du vrai niveau eſt celle qui a tous ſes points également <lb/>éloignez du centre de la Terre, comme ſeroit la circonference de <lb/>la Terre.</s> <s xml:id="echoid-s328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s329" xml:space="preserve">La Ligne finie eſt celle dont la longueur eſt déterminée.</s> <s xml:id="echoid-s330" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s331" xml:space="preserve">La Ligne indéfinie eſt celle dont la longueur eſt indéterminée.</s> <s xml:id="echoid-s332" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s333" xml:space="preserve">Il y a encore des Lignes occultes ou blanches, qui ſe font avec <lb/>la pointe du Compas, ou plus proprement avec le Craïon, parce <lb/>qu'on le peut facilement effacer. </s> <s xml:id="echoid-s334" xml:space="preserve">Ces Lignes ne doivent pas paroî-<lb/>tre, l'ouvrage étant achevé. </s> <s xml:id="echoid-s335" xml:space="preserve">Quand on les veut laiſſer pour faire <lb/>voir de quelle maniere s'eſt faite l'operation, on les marque de <lb/>points, & </s> <s xml:id="echoid-s336" xml:space="preserve">pour lors on les appelle Lignes ponctuées, qu'on trace <lb/> <anchor type="note" xlink:label="note-016-05a" xlink:href="note-016-05"/> avec la Roulete.</s> <s xml:id="echoid-s337" xml:space="preserve"/> </p> <div xml:id="echoid-div20" type="float" level="2" n="11"> <note position="left" xlink:label="note-016-05" xlink:href="note-016-05a" xml:space="preserve">Fig. 10.</note> </div> <p> <s xml:id="echoid-s338" xml:space="preserve">Les Lignes qui doivent reſter, qu'on nomme Lignes apparen-<lb/>tes, ſe tracent à l'encre avec le Tire ligne, ſi groſſes & </s> <s xml:id="echoid-s339" xml:space="preserve">ſi ſines <lb/>qu'on veut, par le moyen de la vis ou de la couliſſe qui eſt au Ti-<lb/>re-ligne.</s> <s xml:id="echoid-s340" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s341" xml:space="preserve">La Ligne Tangente ou touchante eſt une Ligne qui touche une <lb/> <anchor type="note" xlink:label="note-016-06a" xlink:href="note-016-06"/> figure ſans la couper, comme la Ligne A B.</s> <s xml:id="echoid-s342" xml:space="preserve"/> </p> <div xml:id="echoid-div21" type="float" level="2" n="12"> <note position="left" xlink:label="note-016-06" xlink:href="note-016-06a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s343" xml:space="preserve">La Ligne ſous-tendante ou Corde, eſt celle qui joint les extre-<lb/> <anchor type="note" xlink:label="note-016-07a" xlink:href="note-016-07"/> mitez d'un arc, comme eſt la Ligne C D.</s> <s xml:id="echoid-s344" xml:space="preserve"/> </p> <div xml:id="echoid-div22" type="float" level="2" n="13"> <note position="left" xlink:label="note-016-07" xlink:href="note-016-07a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s345" xml:space="preserve">Arc eſt une partie de circonference, comme D F E.</s> <s xml:id="echoid-s346" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s347" xml:space="preserve">Le nombre des differentes eſpeces de Lignes courbes eſt infini; <lb/></s> <s xml:id="echoid-s348" xml:space="preserve"> <anchor type="note" xlink:label="note-016-08a" xlink:href="note-016-08"/> mais la plus ſimple, la plus reguliere & </s> <s xml:id="echoid-s349" xml:space="preserve">la plus aiſée à tracer, eſt <lb/>la circulaire.</s> <s xml:id="echoid-s350" xml:space="preserve"/> </p> <div xml:id="echoid-div23" type="float" level="2" n="14"> <note position="left" xlink:label="note-016-08" xlink:href="note-016-08a" xml:space="preserve">Fig. 11.</note> </div> <p> <s xml:id="echoid-s351" xml:space="preserve">La Ligne circulaire, ou la Circonference du Cercle, eſt une Ligne <lb/> <anchor type="note" xlink:label="note-016-09a" xlink:href="note-016-09"/> courbe dont toutes les parties ſont également éloignées d'un même <lb/>point qui eſt au milieu, & </s> <s xml:id="echoid-s352" xml:space="preserve">qui eſt appellé Centre du Cercle.</s> <s xml:id="echoid-s353" xml:space="preserve"/> </p> <div xml:id="echoid-div24" type="float" level="2" n="15"> <note position="left" xlink:label="note-016-09" xlink:href="note-016-09a" xml:space="preserve">Fig. 11.</note> </div> <pb o="3" file="017" n="17" rhead="DE GEOMETRIE."/> <p> <s xml:id="echoid-s354" xml:space="preserve">Les Lignes droites, menées du centre à la circonference, s'ap-<lb/> <anchor type="note" xlink:label="note-017-01a" xlink:href="note-017-01"/> pellent Raïons, ou demi-Diametres, comme N O.</s> <s xml:id="echoid-s355" xml:space="preserve"/> </p> <div xml:id="echoid-div25" type="float" level="2" n="16"> <note position="right" xlink:label="note-017-01" xlink:href="note-017-01a" xml:space="preserve">Fig. 11.</note> </div> <p> <s xml:id="echoid-s356" xml:space="preserve">Les Cordes qui paſſent par le centre du Cercle, s'appellent Dia-<lb/>metres, comme M P.</s> <s xml:id="echoid-s357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s358" xml:space="preserve">Toute circonference de Cercle ſe conçoit diviſée en 360 parties <lb/>égales, qui ſe nomment Degrez.</s> <s xml:id="echoid-s359" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s360" xml:space="preserve">Ce nombre de 360 a été choiſi par les Géometres pour la divi-<lb/>ſion du Cercle, parce qu'il ſe ſubdiviſe plus exactement qu'aucun <lb/>autre en pluſieurs parties égales ſans reſte: </s> <s xml:id="echoid-s361" xml:space="preserve">car, par exemple, la <lb/>moitié de 360 eſt 180, le tiers eſt 120, le quart eſt 90, la cinquié-<lb/>me partie eſt 72, la ſixiéme eſt 60, & </s> <s xml:id="echoid-s362" xml:space="preserve">ainſi de pluſieurs autres <lb/>parties aliquotes.</s> <s xml:id="echoid-s363" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s364" xml:space="preserve">Chaque Degré ſe diviſe en 60 parties égales, que l'on appelle <lb/>Minutes, chaque Minute en 60 Secondes, & </s> <s xml:id="echoid-s365" xml:space="preserve">chaque Seconde en <lb/>60 Tierces, & </s> <s xml:id="echoid-s366" xml:space="preserve">c. </s> <s xml:id="echoid-s367" xml:space="preserve">& </s> <s xml:id="echoid-s368" xml:space="preserve">ſe marquent ainſi, 40 d. </s> <s xml:id="echoid-s369" xml:space="preserve">35′. </s> <s xml:id="echoid-s370" xml:space="preserve">49″. </s> <s xml:id="echoid-s371" xml:space="preserve">57″′. </s> <s xml:id="echoid-s372" xml:space="preserve">ce qui <lb/>ſignifie quarante degrez, trente-cinq minutes, quarante-neuf ſe-<lb/>condes, cinquante-ſept tierces. </s> <s xml:id="echoid-s373" xml:space="preserve">Cette diviſion ſert à meſurer la <lb/>grandeur des Angles; </s> <s xml:id="echoid-s374" xml:space="preserve">mais la ſubdiviſion en ſecondes & </s> <s xml:id="echoid-s375" xml:space="preserve">tierces <lb/>n'eſt en uſage que dans les grandes circonferences.</s> <s xml:id="echoid-s376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s377" xml:space="preserve">L'ouverture des deux lignes differentes quiſe coupent ou ſe ren-<lb/>contrent en un point, ſe nomme Angle.</s> <s xml:id="echoid-s378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s379" xml:space="preserve">Lorſque deux lignes ſe coupent ou ſe rencontrent ſur un plan, <lb/>l'angle qu'elles font s'appelle Plan.</s> <s xml:id="echoid-s380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s381" xml:space="preserve">Quand les lignes qui font l'angle plan, ſont droites, l'angleeſt <lb/> <anchor type="note" xlink:label="note-017-02a" xlink:href="note-017-02"/> appellé Rectiligne.</s> <s xml:id="echoid-s382" xml:space="preserve"/> </p> <div xml:id="echoid-div26" type="float" level="2" n="17"> <note position="right" xlink:label="note-017-02" xlink:href="note-017-02a" xml:space="preserve">Fig. 12.</note> </div> <p> <s xml:id="echoid-s383" xml:space="preserve">Si les deux lignes ſont courbes, l'angle eſt nommé Curviligne. <lb/></s> <s xml:id="echoid-s384" xml:space="preserve"> <anchor type="note" xlink:label="note-017-03a" xlink:href="note-017-03"/> </s> </p> <div xml:id="echoid-div27" type="float" level="2" n="18"> <note position="right" xlink:label="note-017-03" xlink:href="note-017-03a" xml:space="preserve">Fig. 13.</note> </div> <p> <s xml:id="echoid-s385" xml:space="preserve">Si l'une de ces lignes eſt courbe & </s> <s xml:id="echoid-s386" xml:space="preserve">l'autre droite, l'angle eſt <lb/> <anchor type="note" xlink:label="note-017-04a" xlink:href="note-017-04"/> nommé Mixte ou Mixtiligne, ſoit que la courbure ſoit en dedans <lb/>ou en dehors.</s> <s xml:id="echoid-s387" xml:space="preserve"/> </p> <div xml:id="echoid-div28" type="float" level="2" n="19"> <note position="right" xlink:label="note-017-04" xlink:href="note-017-04a" xml:space="preserve">Fig. 14.</note> </div> <p> <s xml:id="echoid-s388" xml:space="preserve">Les deux lignes qui forment cet angle ſont appellées les côtez de <lb/>l'angle. </s> <s xml:id="echoid-s389" xml:space="preserve">Le point où les deux lignes ſe coupent ou ſe rencontrent, <lb/>en eſt le ſommet.</s> <s xml:id="echoid-s390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s391" xml:space="preserve">Lorſqu'on marque un angle avec trois lettres, celle du milieu <lb/>marque le ſommet, & </s> <s xml:id="echoid-s392" xml:space="preserve">les deux autres les deux côtez.</s> <s xml:id="echoid-s393" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s394" xml:space="preserve">Qu'on prolonge les côtez d'un angle, ou qu'on en retranche, <lb/>cela ne le fait ni plus grand ni plus petit. </s> <s xml:id="echoid-s395" xml:space="preserve">Ainſi la grandeur d'un <lb/>angle ne ſe meſure pas par la grandeur de ſes côtez.</s> <s xml:id="echoid-s396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s397" xml:space="preserve">La meſure d'un angle Rectiligne eſt la portion d'un cercle com-<lb/> <anchor type="note" xlink:label="note-017-05a" xlink:href="note-017-05"/> priſe entre les côtez égaux de cct angle, dont le ſommet fait le cen-<lb/>tre du cercle. </s> <s xml:id="echoid-s398" xml:space="preserve">Il n'importe de quel intervalle, puiſque les arcs des <lb/> <pb o="4" file="018" n="18" rhead="PRINCIPES"/> cercles, petits ou grands, compris entre les côtez A B, A C, ſont <lb/>d'un nombre égal de degrez.</s> <s xml:id="echoid-s399" xml:space="preserve"/> </p> <div xml:id="echoid-div29" type="float" level="2" n="20"> <note position="right" xlink:label="note-017-05" xlink:href="note-017-05a" xml:space="preserve">Fig. 15.</note> </div> <p> <s xml:id="echoid-s400" xml:space="preserve">Si, par exemple, l'arc du petit cercle eſt de 60 degrez, qui fait <lb/>la ſixiéme partie de toute la circonference, l'arc du grand cercle <lb/>ſera pareillement de 60 degrez, ou la ſixiéme partie de la circonfe-<lb/>rence du grand cercle, & </s> <s xml:id="echoid-s401" xml:space="preserve">l'angle B A C ſera de 60 degrez.</s> <s xml:id="echoid-s402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s403" xml:space="preserve">Ces arcs ſont égaux en grandeur relative, par rapportaux cercles <lb/>dont ils ſont parties aliquotes égales; </s> <s xml:id="echoid-s404" xml:space="preserve">mais leur grandeur abſoluë <lb/>eſt differente; </s> <s xml:id="echoid-s405" xml:space="preserve">car ſi, par exemple, la circonference d'un cercle con-<lb/>tient 360 pieds, chaque degre@ ſera d'un pied; </s> <s xml:id="echoid-s406" xml:space="preserve">ſi la circonfe-<lb/>rence d'un autre cercle contient 360 toiſes, chaque degre@ de ce <lb/>cercle ſera d'une toiſe.</s> <s xml:id="echoid-s407" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s408" xml:space="preserve">Tout angle eſt droit, aigu ou obtus.</s> <s xml:id="echoid-s409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s410" xml:space="preserve">L'angle Droit a pour ſa meſure un arc de 90 degrez, qui eſt le <lb/> <anchor type="note" xlink:label="note-018-01a" xlink:href="note-018-01"/> quart de la circonference du cercle.</s> <s xml:id="echoid-s411" xml:space="preserve"/> </p> <div xml:id="echoid-div30" type="float" level="2" n="21"> <note position="left" xlink:label="note-018-01" xlink:href="note-018-01a" xml:space="preserve">Fig. 16.</note> </div> <p> <s xml:id="echoid-s412" xml:space="preserve">L'angle Aigu a moins de 90 degrez. <lb/></s> <s xml:id="echoid-s413" xml:space="preserve"> <anchor type="note" xlink:label="note-018-02a" xlink:href="note-018-02"/> </s> </p> <div xml:id="echoid-div31" type="float" level="2" n="22"> <note position="left" xlink:label="note-018-02" xlink:href="note-018-02a" xml:space="preserve">Fig. 17.</note> </div> <p> <s xml:id="echoid-s414" xml:space="preserve">L'angle Obtus a plus de 90 degrez. <lb/></s> <s xml:id="echoid-s415" xml:space="preserve"> <anchor type="note" xlink:label="note-018-03a" xlink:href="note-018-03"/> </s> </p> <div xml:id="echoid-div32" type="float" level="2" n="23"> <note position="left" xlink:label="note-018-03" xlink:href="note-018-03a" xml:space="preserve">Fig. 18.</note> </div> <p> <s xml:id="echoid-s416" xml:space="preserve">Aucun angle ne peut avoir pour ſa meſure 180 degrez, qui font <lb/>la demie circonference du cercle: </s> <s xml:id="echoid-s417" xml:space="preserve">car deux lignes ainſi écartées <lb/>l'une de l'autre ne pourroient pas ſe couper, mais ſe rencontre-<lb/>roient directement, & </s> <s xml:id="echoid-s418" xml:space="preserve">ne feroient qu'une même ligne, qui ſeroit <lb/>le diametre du cercle.</s> <s xml:id="echoid-s419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s420" xml:space="preserve">Le Sinus d'un angleou d'un arc eſt la moitié de la corde dumê-<lb/>me arc double; </s> <s xml:id="echoid-s421" xml:space="preserve">ainſi, par exemple, pour avoir le ſinus de l'angle <lb/>D A E, ou de l'arc D E, qui en eſt la meſure, ayant doublé l'arc <lb/> <anchor type="note" xlink:label="note-018-04a" xlink:href="note-018-04"/> E D, on aura l'arc E D F, dont la corde eſt E F, & </s> <s xml:id="echoid-s422" xml:space="preserve">ſa moitié E H, <lb/>eſt le Sinus droit de l'angle D A E; </s> <s xml:id="echoid-s423" xml:space="preserve">la ligne D G eſt la Tangente du <lb/>même angle, & </s> <s xml:id="echoid-s424" xml:space="preserve">la ligne AG en eſt la Secante.</s> <s xml:id="echoid-s425" xml:space="preserve"/> </p> <div xml:id="echoid-div33" type="float" level="2" n="24"> <note position="left" xlink:label="note-018-04" xlink:href="note-018-04a" xml:space="preserve">Fig. 15.</note> </div> <p> <s xml:id="echoid-s426" xml:space="preserve">Deux arcs qui font un cercle entier, n'ont qu'une même Corde, <lb/>car il eſt aiſé de voir que la ligne E F eſt auſſi-bien la corde du grand <lb/>arc E B C F, que du petit arc E D F.</s> <s xml:id="echoid-s427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s428" xml:space="preserve">Par même raiſon, deux arcs qui font enſemble un demi-cercle, <lb/>n'ont qu'un même ſinus droit; </s> <s xml:id="echoid-s429" xml:space="preserve">ainſi la ligne E H eſt auſſi-bien le <lb/>ſinus de l'angle obtus E A I, ou de l'arc E B I, qui en eſt la meſu-<lb/>re, que de l'angle aigu E A D, ou de l'arc E D.</s> <s xml:id="echoid-s430" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s431" xml:space="preserve">Il en eſt de même des tangentes & </s> <s xml:id="echoid-s432" xml:space="preserve">ſecantes.</s> <s xml:id="echoid-s433" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s434" xml:space="preserve">Le ſinus de 90 degrez, qui eſt le raïon ou demi-diametre du cer-<lb/>cle, comme D A, eſt appellé Sinus total.</s> <s xml:id="echoid-s435" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s436" xml:space="preserve">La Surface ou Superficie eſt ce qui a longueur & </s> <s xml:id="echoid-s437" xml:space="preserve">largeur ſeule-<lb/>ment.</s> <s xml:id="echoid-s438" xml:space="preserve"/> </p> <pb o="5" file="019" n="19" rhead="DE GEOMETRIE."/> <p> <s xml:id="echoid-s439" xml:space="preserve">Elle eſt de deux ſortes, ſçavoir plane & </s> <s xml:id="echoid-s440" xml:space="preserve">courbe.</s> <s xml:id="echoid-s441" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s442" xml:space="preserve">La ſurface plane ou droite eſt celle à laquelle une ligne droite ſe <lb/> <anchor type="note" xlink:label="note-019-01a" xlink:href="note-019-01"/> peut appliquer de tout ſens, comme eſt, par exemple, le deſſus <lb/>d'une table bien unie.</s> <s xml:id="echoid-s443" xml:space="preserve"/> </p> <div xml:id="echoid-div34" type="float" level="2" n="25"> <note position="right" xlink:label="note-019-01" xlink:href="note-019-01a" xml:space="preserve">Fig. 19.</note> </div> <p> <s xml:id="echoid-s444" xml:space="preserve">La ſurface courbe eſt celle à laquelle une ligne droite ne peut s'a-<lb/> <anchor type="note" xlink:label="note-019-02a" xlink:href="note-019-02"/> pliquer en tous ſens. </s> <s xml:id="echoid-s445" xml:space="preserve">Il y en a de concaves & </s> <s xml:id="echoid-s446" xml:space="preserve">de convexes. </s> <s xml:id="echoid-s447" xml:space="preserve">Le de-<lb/>dans d'une calote eſt une ſurface concave, & </s> <s xml:id="echoid-s448" xml:space="preserve">le deſſus eſt une ſur-<lb/>face convexe.</s> <s xml:id="echoid-s449" xml:space="preserve"/> </p> <div xml:id="echoid-div35" type="float" level="2" n="26"> <note position="right" xlink:label="note-019-02" xlink:href="note-019-02a" xml:space="preserve">Fig. 20.</note> </div> <p> <s xml:id="echoid-s450" xml:space="preserve">Terme, eſt ce qui termine quelque choſe. </s> <s xml:id="echoid-s451" xml:space="preserve">Ainſi les points ſont <lb/>les termes de la ligne, les lignes ſont les termes des ſurfaces, & </s> <s xml:id="echoid-s452" xml:space="preserve">les <lb/>ſurfaces ſont les termes des corps.</s> <s xml:id="echoid-s453" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s454" xml:space="preserve">La figure eſt ce qui eſt terminé de tous côtez.</s> <s xml:id="echoid-s455" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s456" xml:space="preserve">Les figures terminées par un ſeul terme ſont les cercles & </s> <s xml:id="echoid-s457" xml:space="preserve">les <lb/>Ellipſes ou ovales, leſquelles ſont terminées par une ſeule ligne <lb/>courbe.</s> <s xml:id="echoid-s458" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s459" xml:space="preserve">Les figures terminées par pluſieurs termes ou lignes ſont le trian-<lb/> <anchor type="note" xlink:label="note-019-03a" xlink:href="note-019-03"/> gle ou Trigone, qui a trois côtez & </s> <s xml:id="echoid-s460" xml:space="preserve">trois angles.</s> <s xml:id="echoid-s461" xml:space="preserve"/> </p> <div xml:id="echoid-div36" type="float" level="2" n="27"> <note position="right" xlink:label="note-019-03" xlink:href="note-019-03a" xml:space="preserve">Fig. 21.</note> </div> <p> <s xml:id="echoid-s462" xml:space="preserve">Le quarré ou Tetragone qui en a quatre. <lb/></s> <s xml:id="echoid-s463" xml:space="preserve"> <anchor type="note" xlink:label="note-019-04a" xlink:href="note-019-04"/> </s> </p> <div xml:id="echoid-div37" type="float" level="2" n="28"> <note position="right" xlink:label="note-019-04" xlink:href="note-019-04a" xml:space="preserve">Fig. 22.</note> </div> <p> <s xml:id="echoid-s464" xml:space="preserve">Le Pentagone cinq. <lb/></s> <s xml:id="echoid-s465" xml:space="preserve"> <anchor type="note" xlink:label="note-019-05a" xlink:href="note-019-05"/> </s> </p> <div xml:id="echoid-div38" type="float" level="2" n="29"> <note position="right" xlink:label="note-019-05" xlink:href="note-019-05a" xml:space="preserve">Fig. 23.</note> </div> <p> <s xml:id="echoid-s466" xml:space="preserve">L'Exagone ſix. <lb/></s> <s xml:id="echoid-s467" xml:space="preserve"> <anchor type="note" xlink:label="note-019-06a" xlink:href="note-019-06"/> </s> </p> <div xml:id="echoid-div39" type="float" level="2" n="30"> <note position="right" xlink:label="note-019-06" xlink:href="note-019-06a" xml:space="preserve">Fig. 24.</note> </div> <p> <s xml:id="echoid-s468" xml:space="preserve">L'Eptagone ſept.</s> <s xml:id="echoid-s469" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s470" xml:space="preserve">L'Octogone huit.</s> <s xml:id="echoid-s471" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s472" xml:space="preserve">L'Enneagone neuf.</s> <s xml:id="echoid-s473" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s474" xml:space="preserve">Le Decagone dix.</s> <s xml:id="echoid-s475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s476" xml:space="preserve">L'Endecagone onze.</s> <s xml:id="echoid-s477" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s478" xml:space="preserve">Et le Dodecagone douze.</s> <s xml:id="echoid-s479" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s480" xml:space="preserve">On parlera ci-après plus au long de ces Polygones, en traitant <lb/>de leur conſtruction.</s> <s xml:id="echoid-s481" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s482" xml:space="preserve">Toutes les ſuſdites figures, & </s> <s xml:id="echoid-s483" xml:space="preserve">celles qui ont encore plus de cô-<lb/>tez, ſe nomment auſſi Polygones, d'un mot general, qui ſignifie <lb/>figures de pluſieurs angles; </s> <s xml:id="echoid-s484" xml:space="preserve">& </s> <s xml:id="echoid-s485" xml:space="preserve">pour les diſtinguer, on ajoûte le nom-<lb/>bre des côtez, comme, par exemple, un Decagone ſe peut appel-<lb/>ler un Polygone de dix côtez, un Dodecagones'appelle auſſi un Po-<lb/>lygone de douze côtez, & </s> <s xml:id="echoid-s486" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s487" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s488" xml:space="preserve">Les figures dont les côtez & </s> <s xml:id="echoid-s489" xml:space="preserve">les angles ſont égaux, comme celles <lb/>ci-devant, ſe nomment Polygones reguliers.</s> <s xml:id="echoid-s490" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s491" xml:space="preserve">Celles dont les angles ou les côtez ſont inégaux, ſe nomment Po-<lb/>lygones irreguliers.</s> <s xml:id="echoid-s492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s493" xml:space="preserve">Les Triangles ſe diſtinguent, ou par leurs côtez, ou par leurs <lb/>angles.</s> <s xml:id="echoid-s494" xml:space="preserve"/> </p> <pb o="6" file="020" n="20" rhead="PRINCIPES"/> <p> <s xml:id="echoid-s495" xml:space="preserve">Ayant égard à leurs côtez; </s> <s xml:id="echoid-s496" xml:space="preserve">celui qui a les trois côtez égaux ſe <lb/> <anchor type="note" xlink:label="note-020-01a" xlink:href="note-020-01"/> nomme Triangle Equilateral, & </s> <s xml:id="echoid-s497" xml:space="preserve">il eſt auſſi Equiangle.</s> <s xml:id="echoid-s498" xml:space="preserve"/> </p> <div xml:id="echoid-div40" type="float" level="2" n="31"> <note position="left" xlink:label="note-020-01" xlink:href="note-020-01a" xml:space="preserve">Fig. 25.</note> </div> <p> <s xml:id="echoid-s499" xml:space="preserve">Celui qui a ſeulement deux côtez égaux ſe nomme Triangle <lb/> <anchor type="note" xlink:label="note-020-02a" xlink:href="note-020-02"/> Iſoſcele.</s> <s xml:id="echoid-s500" xml:space="preserve"/> </p> <div xml:id="echoid-div41" type="float" level="2" n="32"> <note position="left" xlink:label="note-020-02" xlink:href="note-020-02a" xml:space="preserve">Fig. 26.</note> </div> <p> <s xml:id="echoid-s501" xml:space="preserve">Et celui qui a les trois côtez inégaux s'appelle Triangle Scalene. <lb/></s> <s xml:id="echoid-s502" xml:space="preserve"> <anchor type="note" xlink:label="note-020-03a" xlink:href="note-020-03"/> </s> </p> <div xml:id="echoid-div42" type="float" level="2" n="33"> <note position="left" xlink:label="note-020-03" xlink:href="note-020-03a" xml:space="preserve">Fig. 27.</note> </div> <p> <s xml:id="echoid-s503" xml:space="preserve">Ayant égard à leurs Angles; </s> <s xml:id="echoid-s504" xml:space="preserve">le Triangle qui a un angle droit ſe <lb/> <anchor type="note" xlink:label="note-020-04a" xlink:href="note-020-04"/> nomme Rectangle, & </s> <s xml:id="echoid-s505" xml:space="preserve">le côté oppoſée à l'angle droit, ſe nomme <lb/>Hypotenuſe.</s> <s xml:id="echoid-s506" xml:space="preserve"/> </p> <div xml:id="echoid-div43" type="float" level="2" n="34"> <note position="left" xlink:label="note-020-04" xlink:href="note-020-04a" xml:space="preserve">Fig. 28.</note> </div> <p> <s xml:id="echoid-s507" xml:space="preserve">Celui qui a un angle obtus ſe nomme Obtuſangle, ou Ambli-<lb/> <anchor type="note" xlink:label="note-020-05a" xlink:href="note-020-05"/> gone.</s> <s xml:id="echoid-s508" xml:space="preserve"/> </p> <div xml:id="echoid-div44" type="float" level="2" n="35"> <note position="left" xlink:label="note-020-05" xlink:href="note-020-05a" xml:space="preserve">Fig. 29.</note> </div> <p> <s xml:id="echoid-s509" xml:space="preserve">Celui qui a tous les angles aigus ſe nomme Acutangle, ou Oxy-<lb/> <anchor type="note" xlink:label="note-020-06a" xlink:href="note-020-06"/> gone.</s> <s xml:id="echoid-s510" xml:space="preserve"/> </p> <div xml:id="echoid-div45" type="float" level="2" n="36"> <note position="left" xlink:label="note-020-06" xlink:href="note-020-06a" xml:space="preserve">Fig. 30.</note> </div> <p> <s xml:id="echoid-s511" xml:space="preserve">Les Quadrilateres ou figures de quatre côtez, reçoivent auſſi <lb/>differens noms.</s> <s xml:id="echoid-s512" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s513" xml:space="preserve">Si les côtez oppoſez ſont paralleles, le Quadrilatere eſt appellé <lb/>d'un nom general Parallelogramme.</s> <s xml:id="echoid-s514" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s515" xml:space="preserve">Si le Parallelogramme a les quatre côtez égaux, & </s> <s xml:id="echoid-s516" xml:space="preserve">les quatre an-<lb/> <anchor type="note" xlink:label="note-020-07a" xlink:href="note-020-07"/> gles droits, on l'appelle Quarré.</s> <s xml:id="echoid-s517" xml:space="preserve"/> </p> <div xml:id="echoid-div46" type="float" level="2" n="37"> <note position="left" xlink:label="note-020-07" xlink:href="note-020-07a" xml:space="preserve">Fig. 31.</note> </div> <p> <s xml:id="echoid-s518" xml:space="preserve">Si tous les côtez ne ſont pas égaux, mais que les quatres angles <lb/> <anchor type="note" xlink:label="note-020-08a" xlink:href="note-020-08"/> ſoient droits, on l'appelle Quarré long, Parallelogramme Rectan-<lb/>gle, ou ſimplement Rectangle.</s> <s xml:id="echoid-s519" xml:space="preserve"/> </p> <div xml:id="echoid-div47" type="float" level="2" n="38"> <note position="left" xlink:label="note-020-08" xlink:href="note-020-08a" xml:space="preserve">Fig. 32.</note> </div> <p> <s xml:id="echoid-s520" xml:space="preserve">La Ligne tirée dans un Parallelogramme d'un angle à l'autre qui <lb/>lui eſt oppoſé, ſe nomme Diagonale, comme la ligne A B, même <lb/>figure.</s> <s xml:id="echoid-s521" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s522" xml:space="preserve">Si les quatre côtez ſont égaux, & </s> <s xml:id="echoid-s523" xml:space="preserve">que les angles oppoſez ſoient <lb/> <anchor type="note" xlink:label="note-020-09a" xlink:href="note-020-09"/> auſſi égaux, mais non droits, on l'appelle Rhombe ou Lozange. <lb/></s> <s xml:id="echoid-s524" xml:space="preserve"> <anchor type="note" xlink:label="note-020-10a" xlink:href="note-020-10"/> </s> </p> <div xml:id="echoid-div48" type="float" level="2" n="39"> <note position="left" xlink:label="note-020-09" xlink:href="note-020-09a" xml:space="preserve">II. Plan-<lb/>che.</note> <note position="left" xlink:label="note-020-10" xlink:href="note-020-10a" xml:space="preserve">Fig. 1.</note> </div> <p> <s xml:id="echoid-s525" xml:space="preserve">Si des quatre côtez les deux oppoſez ſont égaux, & </s> <s xml:id="echoid-s526" xml:space="preserve">les angles <lb/> <anchor type="note" xlink:label="note-020-11a" xlink:href="note-020-11"/> oppoſez auſſi égaux, mais non droits, le Quadrilatere eſt appellé <lb/>Rhomboïde.</s> <s xml:id="echoid-s527" xml:space="preserve"/> </p> <div xml:id="echoid-div49" type="float" level="2" n="40"> <note position="left" xlink:label="note-020-11" xlink:href="note-020-11a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s528" xml:space="preserve">Ainſi le quarré eſt Equilateral & </s> <s xml:id="echoid-s529" xml:space="preserve">Equiangle. </s> <s xml:id="echoid-s530" xml:space="preserve">Le quarré long eſt <lb/>Equiangle & </s> <s xml:id="echoid-s531" xml:space="preserve">non Equilateral. </s> <s xml:id="echoid-s532" xml:space="preserve">Le Rhombe eſt Equilateral, & </s> <s xml:id="echoid-s533" xml:space="preserve">non <lb/>Equiangle: </s> <s xml:id="echoid-s534" xml:space="preserve">& </s> <s xml:id="echoid-s535" xml:space="preserve">le Romboïden'eſt ni Equilateral, ni Equiangle.</s> <s xml:id="echoid-s536" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s537" xml:space="preserve">Tout Quadrilatere, dont les côtez oppoſez ne ſont ni paralleles <lb/> <anchor type="note" xlink:label="note-020-12a" xlink:href="note-020-12"/> ni égaux, ſe nomme Trapeze.</s> <s xml:id="echoid-s538" xml:space="preserve"/> </p> <div xml:id="echoid-div50" type="float" level="2" n="41"> <note position="left" xlink:label="note-020-12" xlink:href="note-020-12a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s539" xml:space="preserve">Le Cercle eſt une figure plane, bornée par le contour d'une ligne <lb/> <anchor type="note" xlink:label="note-020-13a" xlink:href="note-020-13"/> courbe, qu'on nomme Circonference, laquelle eſt également éloi-<lb/>gnée du point du milieu, appellé Centre.</s> <s xml:id="echoid-s540" xml:space="preserve"/> </p> <div xml:id="echoid-div51" type="float" level="2" n="42"> <note position="left" xlink:label="note-020-13" xlink:href="note-020-13a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s541" xml:space="preserve">Le Demi-cercle eſt une figure terminée par le Diametre & </s> <s xml:id="echoid-s542" xml:space="preserve">la de-<lb/> <anchor type="note" xlink:label="note-020-14a" xlink:href="note-020-14"/> mie circonference.</s> <s xml:id="echoid-s543" xml:space="preserve"/> </p> <div xml:id="echoid-div52" type="float" level="2" n="43"> <note position="left" xlink:label="note-020-14" xlink:href="note-020-14a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s544" xml:space="preserve">Portion, ou Segment du Cercle, eſt une figure compriſe d'une <lb/> <anchor type="note" xlink:label="note-020-15a" xlink:href="note-020-15"/> <pb o="7" file="021" n="21" rhead="DE GEOMETRIE."/> partie de la circonference, & </s> <s xml:id="echoid-s545" xml:space="preserve">d'une corde plus petite quele Diame-<lb/>tre. </s> <s xml:id="echoid-s546" xml:space="preserve">Il y a le grand & </s> <s xml:id="echoid-s547" xml:space="preserve">le petit Segment.</s> <s xml:id="echoid-s548" xml:space="preserve"/> </p> <div xml:id="echoid-div53" type="float" level="2" n="44"> <note position="left" xlink:label="note-020-15" xlink:href="note-020-15a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s549" xml:space="preserve">Secteur du Cercle eſt une figure faite d'une partie de cercle ter-<lb/> <anchor type="note" xlink:label="note-021-01a" xlink:href="note-021-01"/> miné par deux raïons ou demi-diametres, qui ne font pas une mê-<lb/>me ligne droite. </s> <s xml:id="echoid-s550" xml:space="preserve">Il y a le grand & </s> <s xml:id="echoid-s551" xml:space="preserve">petit Secteur.</s> <s xml:id="echoid-s552" xml:space="preserve"/> </p> <div xml:id="echoid-div54" type="float" level="2" n="45"> <note position="right" xlink:label="note-021-01" xlink:href="note-021-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s553" xml:space="preserve">L'Ellipſe, ou ovale, eſt une figure plus longue que large, com-<lb/> <anchor type="note" xlink:label="note-021-02a" xlink:href="note-021-02"/> priſe ſous une ſeule ligne courbe, dans laquelle les deux plus gran-<lb/>des lignes qu'on puiſſe tirer à angles droits, s'appellent les Axes de <lb/>l'Ellipſe; </s> <s xml:id="echoid-s554" xml:space="preserve">la plus grande ligne s'appelle le grand Axe, & </s> <s xml:id="echoid-s555" xml:space="preserve">l'autre le <lb/>petit Axe.</s> <s xml:id="echoid-s556" xml:space="preserve"/> </p> <div xml:id="echoid-div55" type="float" level="2" n="46"> <note position="right" xlink:label="note-021-02" xlink:href="note-021-02a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s557" xml:space="preserve">Le centre de l'Ellipſe eſt le point cù ces deux Axes ſe coupent.</s> <s xml:id="echoid-s558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s559" xml:space="preserve">On appelle figures Concentriques celles qui ont un même centre. <lb/></s> <s xml:id="echoid-s560" xml:space="preserve"> <anchor type="note" xlink:label="note-021-03a" xlink:href="note-021-03"/> </s> </p> <div xml:id="echoid-div56" type="float" level="2" n="47"> <note position="right" xlink:label="note-021-03" xlink:href="note-021-03a" xml:space="preserve">Fig. 8. <lb/>Fig. 9.</note> </div> <p> <s xml:id="echoid-s561" xml:space="preserve">Figures Excentriques ſont celles qui n'ont pas même centre.</s> <s xml:id="echoid-s562" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s563" xml:space="preserve">Figures ſemblables ſont celles qui ont les angles égaux chacun à <lb/> <anchor type="note" xlink:label="note-021-04a" xlink:href="note-021-04"/> chacun, c'eſt-à-dire, que chaque angle d'une figure eſt égal à cha-<lb/>que angle qui lui correſpond dans l'autre figure, & </s> <s xml:id="echoid-s564" xml:space="preserve">pour lors les <lb/>côtez d'une figure ſont proportionnez aux côtez de l'autre; </s> <s xml:id="echoid-s565" xml:space="preserve">de ſorte <lb/>que ſi le côté ab eſt la moitié ou le tiers du côté A B, tous les autres <lb/>côtez de la petite figure abcd ſeront pareillement moitié ou tiers des <lb/>côtez de la grande figure ABCD. </s> <s xml:id="echoid-s566" xml:space="preserve">Les côtez qui ſe répondent dans <lb/>ſa proportion ſe nomment Homologues; </s> <s xml:id="echoid-s567" xml:space="preserve">ainſi le côté A B de la <lb/>grande figure, & </s> <s xml:id="echoid-s568" xml:space="preserve">le côté ab de la petite, ſont côtez Homologues.</s> <s xml:id="echoid-s569" xml:space="preserve"/> </p> <div xml:id="echoid-div57" type="float" level="2" n="48"> <note position="right" xlink:label="note-021-04" xlink:href="note-021-04a" xml:space="preserve">Fig. 10.</note> </div> <p> <s xml:id="echoid-s570" xml:space="preserve">Figures égales ſont celles qui contiennent également; </s> <s xml:id="echoid-s571" xml:space="preserve">c'eſt-à-<lb/>dire, qui contiennent un nombre égal de quantitez égales.</s> <s xml:id="echoid-s572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s573" xml:space="preserve">Il y a des figures qui ſont égales & </s> <s xml:id="echoid-s574" xml:space="preserve">ſemblables.</s> <s xml:id="echoid-s575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s576" xml:space="preserve">D'autres ſont égales & </s> <s xml:id="echoid-s577" xml:space="preserve">non ſemblables.</s> <s xml:id="echoid-s578" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s579" xml:space="preserve">D'autres enfin ſont ſemblables & </s> <s xml:id="echoid-s580" xml:space="preserve">non égales.</s> <s xml:id="echoid-s581" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s582" xml:space="preserve">Figures Iſoperimetres ſont celles dont le circuit eſt égal; </s> <s xml:id="echoid-s583" xml:space="preserve">ainſi, <lb/> <anchor type="note" xlink:label="note-021-05a" xlink:href="note-021-05"/> par exemple, letriangle ABC, & </s> <s xml:id="echoid-s584" xml:space="preserve">le quarré ABCD, ſont figures <lb/>Iſoperimetres; </s> <s xml:id="echoid-s585" xml:space="preserve">puiſque chaque côté du triangle étant 8, ſon cir-<lb/>cuit eſt 24, & </s> <s xml:id="echoid-s586" xml:space="preserve">chaque côté du quarré étant 6, ſon circuit eſt auſſi <lb/>24 parties égales à celles qui font le circuit du triangle.</s> <s xml:id="echoid-s587" xml:space="preserve"/> </p> <div xml:id="echoid-div58" type="float" level="2" n="49"> <note position="right" xlink:label="note-021-05" xlink:href="note-021-05a" xml:space="preserve">Fig. 11.</note> </div> <p> <s xml:id="echoid-s588" xml:space="preserve">Corps ou Solide eſt ce quia longueur, largeur & </s> <s xml:id="echoid-s589" xml:space="preserve">profondeur.</s> <s xml:id="echoid-s590" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s591" xml:space="preserve">Sphere, Globe ou Boule, eſt un ſolide fait par le mouvement en-<lb/> <anchor type="note" xlink:label="note-021-06a" xlink:href="note-021-06"/> tier d'un demi-cercle à l'entour de ſon diametre immobile, qui <lb/>s'appelle Axe, ou Aiſſieu de la Sphere.</s> <s xml:id="echoid-s592" xml:space="preserve"/> </p> <div xml:id="echoid-div59" type="float" level="2" n="50"> <note position="right" xlink:label="note-021-06" xlink:href="note-021-06a" xml:space="preserve">Fig. 12.</note> </div> <p> <s xml:id="echoid-s593" xml:space="preserve">Spheroïque eſt une ſolide fait par le mouvement entier d'une de-<lb/> <anchor type="note" xlink:label="note-021-07a" xlink:href="note-021-07"/> mie Ellipſe, à l'entour d'un de ſes Axes, qui s'appelle Axe ou Aiſ-<lb/>ſieu du Spheroïque.</s> <s xml:id="echoid-s594" xml:space="preserve"/> </p> <div xml:id="echoid-div60" type="float" level="2" n="51"> <note position="right" xlink:label="note-021-07" xlink:href="note-021-07a" xml:space="preserve">Fig. 13.</note> </div> <p> <s xml:id="echoid-s595" xml:space="preserve">La Piramide eſt un ſolide compris par pluſieurs plans triangu-<lb/> <anchor type="note" xlink:label="note-021-08a" xlink:href="note-021-08"/> <pb o="8" file="022" n="22" rhead="PRINCIPES DE GEOMETRIE."/> laires, ſe rencontrans en un même point, & </s> <s xml:id="echoid-s596" xml:space="preserve">ayant un Polygone <lb/>pour baſe.</s> <s xml:id="echoid-s597" xml:space="preserve"/> </p> <div xml:id="echoid-div61" type="float" level="2" n="52"> <note position="right" xlink:label="note-021-08" xlink:href="note-021-08a" xml:space="preserve">Fig. 14.</note> </div> <p> <s xml:id="echoid-s598" xml:space="preserve">Cone eſt une eſpece de piramide qui a un cercle pour baſe. </s> <s xml:id="echoid-s599" xml:space="preserve">Il eſt <lb/> <anchor type="note" xlink:label="note-022-01a" xlink:href="note-022-01"/> fait par le mouvement entier d'un triangle rectangle; </s> <s xml:id="echoid-s600" xml:space="preserve">à l'entour de <lb/>l'un des côtez qui forme l'angle droit, lcquel côté eſt l'Axe du <lb/>Cone droit.</s> <s xml:id="echoid-s601" xml:space="preserve"/> </p> <div xml:id="echoid-div62" type="float" level="2" n="53"> <note position="left" xlink:label="note-022-01" xlink:href="note-022-01a" xml:space="preserve">Fig. 15.</note> </div> <p> <s xml:id="echoid-s602" xml:space="preserve">Cylindre eſt un ſolide qui a deux cercles pour baſes: </s> <s xml:id="echoid-s603" xml:space="preserve">il eſt fait par <lb/> <anchor type="note" xlink:label="note-022-02a" xlink:href="note-022-02"/> le mouvement circulaire d'un Parallelogramme à l'entour d'un de <lb/>ſes côtez, lequel ſe nomme Axe du Cylindre.</s> <s xml:id="echoid-s604" xml:space="preserve"/> </p> <div xml:id="echoid-div63" type="float" level="2" n="54"> <note position="left" xlink:label="note-022-02" xlink:href="note-022-02a" xml:space="preserve">Fig. 16.</note> </div> <p> <s xml:id="echoid-s605" xml:space="preserve">Priſme eſt un ſolide, qui a pourbaſes deux plans paralleles, ſem-<lb/> <anchor type="note" xlink:label="note-022-03a" xlink:href="note-022-03"/> blables & </s> <s xml:id="echoid-s606" xml:space="preserve">égaux; </s> <s xml:id="echoid-s607" xml:space="preserve">quand ces deux plans paralleles ſont des trian-<lb/>gles, il ſe nomme Priſme triangulaire.</s> <s xml:id="echoid-s608" xml:space="preserve"/> </p> <div xml:id="echoid-div64" type="float" level="2" n="55"> <note position="left" xlink:label="note-022-03" xlink:href="note-022-03a" xml:space="preserve">Fig. 17.</note> </div> <p> <s xml:id="echoid-s609" xml:space="preserve">Quand les deux baſes du Priſme font des Parallelogrammes, il <lb/> <anchor type="note" xlink:label="note-022-04a" xlink:href="note-022-04"/> ſe nomme Parallelipipede.</s> <s xml:id="echoid-s610" xml:space="preserve"/> </p> <div xml:id="echoid-div65" type="float" level="2" n="56"> <note position="left" xlink:label="note-022-04" xlink:href="note-022-04a" xml:space="preserve">Fig. 18.</note> </div> <p> <s xml:id="echoid-s611" xml:space="preserve">Si les côtez de ces corps ſont perpendiculaires à la baſe, on les <lb/>appelle droits ou iſoceles.</s> <s xml:id="echoid-s612" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s613" xml:space="preserve">S'ils ſont inclinez, on les appelle Obliques ou Scalenes.</s> <s xml:id="echoid-s614" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s615" xml:space="preserve">Corps regulier eſt celui qui eſt compris de figures regulieres & </s> <s xml:id="echoid-s616" xml:space="preserve"><lb/>égales, & </s> <s xml:id="echoid-s617" xml:space="preserve">duquel tous les angles ſolides ſont égaux.</s> <s xml:id="echoid-s618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s619" xml:space="preserve">Angle ſolide eſt la rencontre de pluſieurs plans qui aboutiſſent <lb/>en un point, comme eſt, par exemple, la pointe d'un diamant.</s> <s xml:id="echoid-s620" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s621" xml:space="preserve">Il faut au moins trois plans pour faire un angle ſolide.</s> <s xml:id="echoid-s622" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s623" xml:space="preserve">Il y a cinq ſortes de corps reguliers repreſentez dans la même <lb/>planche avec leurs developemens; </s> <s xml:id="echoid-s624" xml:space="preserve">ſçavoir,</s> </p> <p> <s xml:id="echoid-s625" xml:space="preserve">Le Tétraedre compris ſous quatre triangles égaux & </s> <s xml:id="echoid-s626" xml:space="preserve">Equilate-<lb/> <anchor type="note" xlink:label="note-022-05a" xlink:href="note-022-05"/> raux; </s> <s xml:id="echoid-s627" xml:space="preserve">c'eſt un piramide triangulaire qui a ſa baſe égale à ſes faces.</s> <s xml:id="echoid-s628" xml:space="preserve"/> </p> <div xml:id="echoid-div66" type="float" level="2" n="57"> <note position="left" xlink:label="note-022-05" xlink:href="note-022-05a" xml:space="preserve">Fig. 19.</note> </div> <p> <s xml:id="echoid-s629" xml:space="preserve">L'Hexaedre ou Cube compris de ſix quarrez égaux. <lb/></s> <s xml:id="echoid-s630" xml:space="preserve"> <anchor type="note" xlink:label="note-022-06a" xlink:href="note-022-06"/> </s> </p> <div xml:id="echoid-div67" type="float" level="2" n="58"> <note position="left" xlink:label="note-022-06" xlink:href="note-022-06a" xml:space="preserve">Fig. 20.</note> </div> <p> <s xml:id="echoid-s631" xml:space="preserve">L'Octaedre compris ſous huit triangles égaux & </s> <s xml:id="echoid-s632" xml:space="preserve">équilateraux. <lb/></s> <s xml:id="echoid-s633" xml:space="preserve"> <anchor type="note" xlink:label="note-022-07a" xlink:href="note-022-07"/> </s> </p> <div xml:id="echoid-div68" type="float" level="2" n="59"> <note position="left" xlink:label="note-022-07" xlink:href="note-022-07a" xml:space="preserve">Fig. 21.</note> </div> <p> <s xml:id="echoid-s634" xml:space="preserve">Le Dodécaedre terminé de douze Pentagones égaux & </s> <s xml:id="echoid-s635" xml:space="preserve">équila-<lb/> <anchor type="note" xlink:label="note-022-08a" xlink:href="note-022-08"/> teraux.</s> <s xml:id="echoid-s636" xml:space="preserve"/> </p> <div xml:id="echoid-div69" type="float" level="2" n="60"> <note position="left" xlink:label="note-022-08" xlink:href="note-022-08a" xml:space="preserve">Fig. 22.</note> </div> <p> <s xml:id="echoid-s637" xml:space="preserve">L'lcoſaedre compris & </s> <s xml:id="echoid-s638" xml:space="preserve">terminé par vingt triangles égaux & </s> <s xml:id="echoid-s639" xml:space="preserve">é-<lb/> <anchor type="note" xlink:label="note-022-09a" xlink:href="note-022-09"/> quilateraux.</s> <s xml:id="echoid-s640" xml:space="preserve"/> </p> <div xml:id="echoid-div70" type="float" level="2" n="61"> <note position="left" xlink:label="note-022-09" xlink:href="note-022-09a" xml:space="preserve">Fig. 23.</note> </div> <p> <s xml:id="echoid-s641" xml:space="preserve">Les developemens marquez à côté de ces cinq corps reguliers <lb/>font voir la maniere de les tracer ſur du cuivre ou carton, afin de <lb/>les découper, & </s> <s xml:id="echoid-s642" xml:space="preserve">enſuite les rejoindre pour en former leſdits corps.</s> <s xml:id="echoid-s643" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s644" xml:space="preserve">Tous les autres Solides ſe peuvent appeller du nom general Po-<lb/>liedres, qui ſignifie corps terminez de pluſieurs ſurfaces.</s> <s xml:id="echoid-s645" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s646" xml:space="preserve">Si dans la ſuite de ce diſcours, il ſe trouve quelque choſe dont <lb/>la définition ne ſoit pas ici compriſe, il ſera défini & </s> <s xml:id="echoid-s647" xml:space="preserve">expliqué en <lb/>ſon lieu.</s> <s xml:id="echoid-s648" xml:space="preserve"/> </p> <pb file="023" n="23"/> <figure> <image file="023-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/023-01"/> </figure> </div> <div xml:id="echoid-div72" type="section" level="1" n="10"> <head xml:id="echoid-head10" xml:space="preserve">CONSTRUCTION <lb/>ET USAGE <lb/>DES INSTRUMENS <lb/>DE MATHEMATIQUES. <lb/>LIVRE PREMIER.</head> <head xml:id="echoid-head11" xml:space="preserve">Des Inſtrumens les plus ordinaires; comme ſont <lb/>le Compas, la Regle, le Tire-ligne, le Porte-<lb/>craïon, l'Equerre, & le Rapporteur.</head> <head xml:id="echoid-head12" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head13" style="it" xml:space="preserve">De la Conſtruction & des Vſages du Compas, de la Regle, <lb/>du Tire-ligne, & du Porte-craïon.</head> <p> <s xml:id="echoid-s649" xml:space="preserve">IL y a pluſieurs ſortes de Compas, dont nous parlerons <lb/>plus amplement dans la ſuite; </s> <s xml:id="echoid-s650" xml:space="preserve">mais celui dont nous <lb/>allons donner les uſages dans ce Chapitre, eſt le Com-<lb/>pas ordinaire. </s> <s xml:id="echoid-s651" xml:space="preserve">Il s'en fait de deux ſortes; </s> <s xml:id="echoid-s652" xml:space="preserve">ſçavoir, <lb/>des Compas ſimples qui n'ont que deux pointes fixes, & </s> <s xml:id="echoid-s653" xml:space="preserve">d'au-<lb/>tres qui changent de pointes: </s> <s xml:id="echoid-s654" xml:space="preserve">les uns & </s> <s xml:id="echoid-s655" xml:space="preserve">les autres de diffe-<lb/>rentes grandeurs; </s> <s xml:id="echoid-s656" xml:space="preserve">mais l'ordinaire eſt depuis trois pouces juſqu'à <lb/> <anchor type="note" xlink:label="note-023-01a" xlink:href="note-023-01"/> ſix de longueur. </s> <s xml:id="echoid-s657" xml:space="preserve">A ceux qui changent de pointes, on en met <lb/>une pour tracer à l'encre, une pour tracer au craïon, & </s> <s xml:id="echoid-s658" xml:space="preserve">quel-<lb/>quefois une autre où il y a une Roulete pour tracer des lignes ponc-<lb/>tuées.</s> <s xml:id="echoid-s659" xml:space="preserve"/> </p> <div xml:id="echoid-div72" type="float" level="2" n="1"> <note position="right" xlink:label="note-023-01" xlink:href="note-023-01a" xml:space="preserve">III. <lb/>Planche. <lb/>Fig. A.</note> </div> <pb o="10" file="024" n="24" rhead="USAGE DES PREMIERS"/> <p> <s xml:id="echoid-s660" xml:space="preserve">La bonté d'un Compas conſiſte principalement en ce que le <lb/>mouvement de ſa tête ſoit bien égal, & </s> <s xml:id="echoid-s661" xml:space="preserve">qu'il ne ſaute point en <lb/>l'ouvrant ou le fermant; </s> <s xml:id="echoid-s662" xml:space="preserve">que les charnieres ſoient bien ajuſtées; <lb/></s> <s xml:id="echoid-s663" xml:space="preserve">que le corps en ſoit limé, plat & </s> <s xml:id="echoid-s664" xml:space="preserve">bien poli; </s> <s xml:id="echoid-s665" xml:space="preserve">& </s> <s xml:id="echoid-s666" xml:space="preserve">enfin que les pointes <lb/>d'acier ſoient bien jointes & </s> <s xml:id="echoid-s667" xml:space="preserve">bien égales. </s> <s xml:id="echoid-s668" xml:space="preserve">Les figures A donneront <lb/>l'idée de ces ſortes de Compas, dont nous expliquerons la con-<lb/>ſtruction au Livre III.</s> <s xml:id="echoid-s669" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s670" xml:space="preserve">Les Regles, ſoit de cuivre ou de bois, doivent être parfaitement <lb/>droites en tous ſens: </s> <s xml:id="echoid-s671" xml:space="preserve">on ſe ſert pour les dreſſer de limes & </s> <s xml:id="echoid-s672" xml:space="preserve">d'un ra-<lb/> <anchor type="note" xlink:label="note-024-01a" xlink:href="note-024-01"/> bot, dont la ſemelle de deſſous ſoit d'acier; </s> <s xml:id="echoid-s673" xml:space="preserve">comme auſſi d'une au-<lb/>tre regle bien droite, qu'on frote l'une contre l'autre par l'épaiſ-<lb/>ſeur. </s> <s xml:id="echoid-s674" xml:space="preserve">Il y a un bizeau à un des bords, afin que l'encre ne ſaliſſe <lb/>point le papier, quand on tire des lignes à l'encre;</s> <s xml:id="echoid-s675" xml:space="preserve">elles doivent être <lb/>un peu épaiſſes.</s> <s xml:id="echoid-s676" xml:space="preserve"/> </p> <div xml:id="echoid-div73" type="float" level="2" n="2"> <note position="left" xlink:label="note-024-01" xlink:href="note-024-01a" xml:space="preserve">Fig. B.</note> </div> <p> <s xml:id="echoid-s677" xml:space="preserve">Pour connoître ſi une Regle eſt bien droite, tracez une ligne ſur <lb/>du papier, & </s> <s xml:id="echoid-s678" xml:space="preserve">retournez ladite Regle bout pour bout; </s> <s xml:id="echoid-s679" xml:space="preserve">ſi la ligne <lb/>tracée convient juſtement le long de la Regle; </s> <s xml:id="echoid-s680" xml:space="preserve">c'eſt une marque <lb/>qu'elle eſt bien droite.</s> <s xml:id="echoid-s681" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s682" xml:space="preserve">Le Tire-ligne eſt fait de deux lames d'acier jointes enſemble, & </s> <s xml:id="echoid-s683" xml:space="preserve"><lb/>attachées au bout d'un baluſtre, à l'autre bout duquel eſt un Por-<lb/>te-craïon; </s> <s xml:id="echoid-s684" xml:space="preserve">les lames doivent être évidées en dedans, afin que l'en-<lb/> <anchor type="note" xlink:label="note-024-02a" xlink:href="note-024-02"/> cre s'y puiſſe mettre avec une plume; </s> <s xml:id="echoid-s685" xml:space="preserve">elles ſe joignent par les poin-<lb/>tes qui doivent être bien égales. </s> <s xml:id="echoid-s686" xml:space="preserve">Il y a un petit coulant qui ſert à ou-<lb/>vrir & </s> <s xml:id="echoid-s687" xml:space="preserve">fermer plus ou moins le Tire-ligne pour tracer des lignes <lb/>fines ou groſſes ſelon le beſoin.</s> <s xml:id="echoid-s688" xml:space="preserve"/> </p> <div xml:id="echoid-div74" type="float" level="2" n="3"> <note position="left" xlink:label="note-024-02" xlink:href="note-024-02a" xml:space="preserve">Fig. C.</note> </div> <p> <s xml:id="echoid-s689" xml:space="preserve">Le Porte-craïon doit être bien égal de groſſeur par tout, & </s> <s xml:id="echoid-s690" xml:space="preserve">fen-<lb/>du bien droit par le milieu avec une ſciebien mince; </s> <s xml:id="echoid-s691" xml:space="preserve">on le courbe <lb/>vers le bout, afin qu'on puiſſe ſerrer le craïon par le moyen du petit <lb/>anneau.</s> <s xml:id="echoid-s692" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div76" type="section" level="1" n="11"> <head xml:id="echoid-head14" xml:space="preserve">USAGE PREMIER.</head> <head xml:id="echoid-head15" style="it" xml:space="preserve">Diviſer une Ligne droite en deux également. <lb/> </head> <note position="left" xml:space="preserve">III. <lb/>Planche. <lb/>Fig. 1.</note> <p> <s xml:id="echoid-s693" xml:space="preserve">Soit la ligne donnée A B, laquelle il faut diviſer en deux par-<lb/>ties égales.</s> <s xml:id="echoid-s694" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s695" xml:space="preserve">Du point A, comme centre, à l'une, des extremitez de la ligne, <lb/>décrivez l'arc de cercle C D d'une ouverture de Compas priſe à vo-<lb/>lonté, plus grande ou plus petite que A B, mais cependant plus <lb/>grande que la moitié de ladite ligne. </s> <s xml:id="echoid-s696" xml:space="preserve">Décrivez auſſi de l'autre ex-<lb/>tremité B, & </s> <s xml:id="echoid-s697" xml:space="preserve">de la même ouverture de compas l'arc de cercle E F, <lb/> <pb o="11" file="025" n="25" rhead="INSTRUMENS. Liv. I. Chap. I."/> coupant le premier arc déja décrit aux points G H, poſez la Re-<lb/>gle ſur ces deux Interſections, & </s> <s xml:id="echoid-s698" xml:space="preserve">tirez la ligne G H, elle diviſera <lb/>la ligne A B en deux parties égales.</s> <s xml:id="echoid-s699" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s700" xml:space="preserve">Remarquez que ces deux arcs ne pourroient pas s'entrecouper ſi <lb/>les ouvertures de compas n'étoient plus grandes que la moitié de la <lb/>ligne donnée.</s> <s xml:id="echoid-s701" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div77" type="section" level="1" n="12"> <head xml:id="echoid-head16" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head17" style="it" xml:space="preserve">Sur une Ligne droite & d'un point donné, élever une <lb/>Perpendiculaire.</head> <p> <s xml:id="echoid-s702" xml:space="preserve">SOit la ligne droite donnée A B, & </s> <s xml:id="echoid-s703" xml:space="preserve">le point donné C, ſur lequel <lb/> <anchor type="note" xlink:label="note-025-01a" xlink:href="note-025-01"/> il faut élever une Perpendiculaire.</s> <s xml:id="echoid-s704" xml:space="preserve"/> </p> <div xml:id="echoid-div77" type="float" level="2" n="1"> <note position="right" xlink:label="note-025-01" xlink:href="note-025-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s705" xml:space="preserve">Du point donné C, marquez avec le Compas ſur la ligne don-<lb/>née les diſtances égales C A, C B, des points A & </s> <s xml:id="echoid-s706" xml:space="preserve">B, & </s> <s xml:id="echoid-s707" xml:space="preserve">d'une ou-<lb/>verture de compas à volonté, mais plus grande que chacune deſ-<lb/>dites diſtances, décrivez les arcs D E, F G, s'entrecoupans au point <lb/>H, tirez la ligne H C, elle ſera perpendiculaire ſur A B.</s> <s xml:id="echoid-s708" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s709" xml:space="preserve">Si le point donné C étoit à l'extremité de la ligne, décrivez de <lb/> <anchor type="note" xlink:label="note-025-02a" xlink:href="note-025-02"/> ce point, comme centre, un arc de cercle à volonté, ſur lequel <lb/>vous porterez deux fois la même ouverture de compas; </s> <s xml:id="echoid-s710" xml:space="preserve">ſçavoir; <lb/></s> <s xml:id="echoid-s711" xml:space="preserve">de B en D, & </s> <s xml:id="echoid-s712" xml:space="preserve">de D en E. </s> <s xml:id="echoid-s713" xml:space="preserve">Des points D & </s> <s xml:id="echoid-s714" xml:space="preserve">E faites deux autres arcs <lb/>de cercle s'entrecoupans au point F, & </s> <s xml:id="echoid-s715" xml:space="preserve">mettant la Regle ſur les <lb/>points F & </s> <s xml:id="echoid-s716" xml:space="preserve">C, tirez la ligne F C, laquelle ſera perpendiculaire ſur <lb/>l'extremité de la ligne C B.</s> <s xml:id="echoid-s717" xml:space="preserve"/> </p> <div xml:id="echoid-div78" type="float" level="2" n="2"> <note position="right" xlink:label="note-025-02" xlink:href="note-025-02a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s718" xml:space="preserve">S'il manquoit d'eſpace pour prendre la grandeur D E, diviſez en <lb/>deux également l'arc B D au point G, & </s> <s xml:id="echoid-s719" xml:space="preserve">portez la moitié D G de D <lb/>en H, la ligne H C ſera perpendiculaire.</s> <s xml:id="echoid-s720" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s721" xml:space="preserve">Ou bien ayant tiré par les points B & </s> <s xml:id="echoid-s722" xml:space="preserve">D la ligne indéfinie BDF, <lb/> <anchor type="note" xlink:label="note-025-03a" xlink:href="note-025-03"/> faites la partie D F, égale à B D, & </s> <s xml:id="echoid-s723" xml:space="preserve">tirez la perpendiculaire F C.</s> <s xml:id="echoid-s724" xml:space="preserve"/> </p> <div xml:id="echoid-div79" type="float" level="2" n="3"> <note position="right" xlink:label="note-025-03" xlink:href="note-025-03a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s725" xml:space="preserve">Ou bien encore ayant choiſi le point P à volonté, au-deſſus de la <lb/> <anchor type="note" xlink:label="note-025-04a" xlink:href="note-025-04"/> ligne donnée dudit point & </s> <s xml:id="echoid-s726" xml:space="preserve">de l'intervalle PC, décrivez l'arc <lb/>BCD, tirez la ligne BP, & </s> <s xml:id="echoid-s727" xml:space="preserve">prolongez-la juſqu'à ce qu'elle cou-<lb/>pe ledit arc au point D. </s> <s xml:id="echoid-s728" xml:space="preserve">de ce point D au point C, tirez la per-<lb/>pendiculaire D C.</s> <s xml:id="echoid-s729" xml:space="preserve"/> </p> <div xml:id="echoid-div80" type="float" level="2" n="4"> <note position="right" xlink:label="note-025-04" xlink:href="note-025-04a" xml:space="preserve">Fig. 5.</note> </div> <figure> <image file="025-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/025-01"/> </figure> <pb o="12" file="026" n="26" rhead="USAGE DES PREMIERS"/> </div> <div xml:id="echoid-div82" type="section" level="1" n="13"> <head xml:id="echoid-head18" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head19" style="it" xml:space="preserve">Abaiſſer une perpendiculaire ſur une ligne donnée d'un point <lb/>hors de ladite ligne.</head> <p> <s xml:id="echoid-s730" xml:space="preserve">SOit le point donné C, duquel il faut abaiſſer une perpendicu-<lb/> <anchor type="note" xlink:label="note-026-01a" xlink:href="note-026-01"/> laire ſur la ligne A B.</s> <s xml:id="echoid-s731" xml:space="preserve"/> </p> <div xml:id="echoid-div82" type="float" level="2" n="1"> <note position="left" xlink:label="note-026-01" xlink:href="note-026-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s732" xml:space="preserve">Du point C, comme centre, décrivez un arc de cercle qui coupe <lb/>la ligne A B en deux points D E; </s> <s xml:id="echoid-s733" xml:space="preserve">de ces points D & </s> <s xml:id="echoid-s734" xml:space="preserve">E, faites la <lb/>Section F, & </s> <s xml:id="echoid-s735" xml:space="preserve">mettant la Regle ſur les points C & </s> <s xml:id="echoid-s736" xml:space="preserve">F, tirez la per-<lb/>pendiculaire C G.</s> <s xml:id="echoid-s737" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s738" xml:space="preserve">On peut faire la Section F au-deſſus ou au deſſous de la ligne <lb/>donnée; </s> <s xml:id="echoid-s739" xml:space="preserve">mais il eſt bon qu'elle ſoit au-deſſous, parce que les points <lb/>C & </s> <s xml:id="echoid-s740" xml:space="preserve">F étant éloignez, on tire plus juſtement la perpendiculaire <lb/>que s'ils étoient proches.</s> <s xml:id="echoid-s741" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s742" xml:space="preserve">Que ſi la portion de cercle décrite du point C ne coupe pas la <lb/>ligne A B en deux points, il faudra continuer la ligne, s'il ſe peut; <lb/></s> <s xml:id="echoid-s743" xml:space="preserve">ſinon il faudra ſe ſervir de la derniere methode ci-devant rapportée <lb/>pour élever une perpendiculaire à l'extremité d'une ligne; </s> <s xml:id="echoid-s744" xml:space="preserve">car dans <lb/>la même figure 5, ſuppoſé qu'on veuille abaiſſer une perpendicu-<lb/>laire du point D ſur la ligne C B, tirez à volonté la ligne D B, divi-<lb/>ſez-la en deux également au point P; </s> <s xml:id="echoid-s745" xml:space="preserve">de ce point comme centre, & </s> <s xml:id="echoid-s746" xml:space="preserve"><lb/>de l'intervalle P D, décrivez l'arc D C B, coupant la ligne A B au <lb/>point C; </s> <s xml:id="echoid-s747" xml:space="preserve">poſez la Regle ſur les points C & </s> <s xml:id="echoid-s748" xml:space="preserve">D, & </s> <s xml:id="echoid-s749" xml:space="preserve">tirez la ligne <lb/>C D, elle ſera la perpendiculaire requiſe.</s> <s xml:id="echoid-s750" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s751" xml:space="preserve">Autrement. </s> <s xml:id="echoid-s752" xml:space="preserve">Soit la ligne A B & </s> <s xml:id="echoid-s753" xml:space="preserve">le point donné C hors icelle, <lb/> <anchor type="note" xlink:label="note-026-02a" xlink:href="note-026-02"/> duquel il faut abaiſſer une perpendiculaire. </s> <s xml:id="echoid-s754" xml:space="preserve">Prenez les deux points <lb/>1 & </s> <s xml:id="echoid-s755" xml:space="preserve">2 à volonté ſur ladite ligne A B; </s> <s xml:id="echoid-s756" xml:space="preserve">puis des points 1 & </s> <s xml:id="echoid-s757" xml:space="preserve">2 & </s> <s xml:id="echoid-s758" xml:space="preserve">des <lb/>intervalles 1 C & </s> <s xml:id="echoid-s759" xml:space="preserve">2 C, décrivez des arcs de cercles qui s'entrecou-<lb/>peront en deux points; </s> <s xml:id="echoid-s760" xml:space="preserve">ſçavoir, une fois au point C, & </s> <s xml:id="echoid-s761" xml:space="preserve">l'autre <lb/>fois au point D, au-deſſous de la ligne; </s> <s xml:id="echoid-s762" xml:space="preserve">poſez la Regleſur les deux <lb/>interſections, & </s> <s xml:id="echoid-s763" xml:space="preserve">tirez une ligne qui ſera perpendiculaire ſur la li-<lb/>gne A B.</s> <s xml:id="echoid-s764" xml:space="preserve"/> </p> <div xml:id="echoid-div83" type="float" level="2" n="2"> <note position="left" xlink:label="note-026-02" xlink:href="note-026-02a" xml:space="preserve">Fig. 7.</note> </div> </div> <div xml:id="echoid-div85" type="section" level="1" n="14"> <head xml:id="echoid-head20" xml:space="preserve">USAGE IV.</head> <head xml:id="echoid-head21" style="it" xml:space="preserve">Couper un angle rectiligne en deux également.</head> <p> <s xml:id="echoid-s765" xml:space="preserve">SOit A C B l'angle qu'il faut couper en deux angles égaux. <lb/></s> <s xml:id="echoid-s766" xml:space="preserve"> <anchor type="note" xlink:label="note-026-03a" xlink:href="note-026-03"/> </s> </p> <div xml:id="echoid-div85" type="float" level="2" n="1"> <note position="left" xlink:label="note-026-03" xlink:href="note-026-03a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s767" xml:space="preserve">Du point C, comme centre, décrivez l'arc D E à volonté:</s> <s xml:id="echoid-s768" xml:space="preserve"><unsure/> <lb/>des points D & </s> <s xml:id="echoid-s769" xml:space="preserve">E décrivez deux arcs qui ſe couperont au point F, <lb/> <pb o="13" file="027" n="27" rhead="INSTRUMENS. Liv. I. Chap. I."/> Du point F par le point C tirez la ligne FC, elle diviſera l'angle <lb/>propoſé en deux également.</s> <s xml:id="echoid-s770" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s771" xml:space="preserve">Si on vouloit diviſer en trois l'angle A CB, il faudroit diviſer <lb/>l'arc DE en trois également en tâtonant, pour ainſi dire, avec le <lb/>compas; </s> <s xml:id="echoid-s772" xml:space="preserve">puiſque la triſection de l'angle par des lignes droites n'a <lb/>point encore été trouvée géométriquement.</s> <s xml:id="echoid-s773" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div87" type="section" level="1" n="15"> <head xml:id="echoid-head22" xml:space="preserve">USAGE V.</head> <head xml:id="echoid-head23" style="it" xml:space="preserve">Sur un angle donné élever une ligne droite qui n'incline pas <lb/>plus d'un côté que de l'autre.</head> <p> <s xml:id="echoid-s774" xml:space="preserve">FAites la même operation que deſſus, & </s> <s xml:id="echoid-s775" xml:space="preserve">prolongez la ligne <lb/> <anchor type="note" xlink:label="note-027-01a" xlink:href="note-027-01"/> F C G.</s> <s xml:id="echoid-s776" xml:space="preserve"/> </p> <div xml:id="echoid-div87" type="float" level="2" n="1"> <note position="right" xlink:label="note-027-01" xlink:href="note-027-01a" xml:space="preserve">Fig. 8.</note> </div> </div> <div xml:id="echoid-div89" type="section" level="1" n="16"> <head xml:id="echoid-head24" xml:space="preserve">USAGE VI.</head> <head xml:id="echoid-head25" style="it" xml:space="preserve">Sur une ligne droite donnée & d'un point pris en icelle, faire <lb/>un angle égal à un angle donné.</head> <p> <s xml:id="echoid-s777" xml:space="preserve">SOit A B la ligne donnée, & </s> <s xml:id="echoid-s778" xml:space="preserve">A le point donné, duquel il faut <lb/> <anchor type="note" xlink:label="note-027-02a" xlink:href="note-027-02"/> faire un angle égal à l'angle E F G.</s> <s xml:id="echoid-s779" xml:space="preserve"/> </p> <div xml:id="echoid-div89" type="float" level="2" n="1"> <note position="right" xlink:label="note-027-02" xlink:href="note-027-02a" xml:space="preserve">Fig. 9.<unsure/></note> </div> <p> <s xml:id="echoid-s780" xml:space="preserve">Du point F, comme centre décrivez une portion de cercle; </s> <s xml:id="echoid-s781" xml:space="preserve">de la <lb/>même ouverture de compas décrivez du point A une ſemblable <lb/>portion; </s> <s xml:id="echoid-s782" xml:space="preserve">prenez avec le compas la grandeur de l'arc E G, & </s> <s xml:id="echoid-s783" xml:space="preserve">portez <lb/>cette ouverture ſur l'arc B C pour le faire égal; </s> <s xml:id="echoid-s784" xml:space="preserve">par les points A & </s> <s xml:id="echoid-s785" xml:space="preserve"><lb/>C tirez la ligne A C, l'angle B A C ſera égal à l'angle E F G.</s> <s xml:id="echoid-s786" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div91" type="section" level="1" n="17"> <head xml:id="echoid-head26" xml:space="preserve">USAGE VII.</head> <head xml:id="echoid-head27" style="it" xml:space="preserve">D'un point donné mener une ligne parallele à une ligne donnée.</head> <p> <s xml:id="echoid-s787" xml:space="preserve">SOit A B la ligne donnée, & </s> <s xml:id="echoid-s788" xml:space="preserve">C le point par lequel il faut mener <lb/> <anchor type="note" xlink:label="note-027-03a" xlink:href="note-027-03"/> une ligne qui ſoit parallele à A B.</s> <s xml:id="echoid-s789" xml:space="preserve"/> </p> <div xml:id="echoid-div91" type="float" level="2" n="1"> <note position="right" xlink:label="note-027-03" xlink:href="note-027-03a" xml:space="preserve">Fig. 10.</note> </div> <p> <s xml:id="echoid-s790" xml:space="preserve">Du point C, comme centre, & </s> <s xml:id="echoid-s791" xml:space="preserve">d'une ouverture de compas priſe <lb/>à volonté, faites l'arc D B qui coupera la ligne donnée au point B: <lb/></s> <s xml:id="echoid-s792" xml:space="preserve">dudit point B, comme centre, & </s> <s xml:id="echoid-s793" xml:space="preserve">de la même ouverture de compas <lb/>faites l'arc C A; </s> <s xml:id="echoid-s794" xml:space="preserve">prenez avec un compas l'ouverture de l'arc C A, <lb/>& </s> <s xml:id="echoid-s795" xml:space="preserve">la portez de B en D, pour faire ces deux arcs égaux. </s> <s xml:id="echoid-s796" xml:space="preserve">Par les points <lb/>C & </s> <s xml:id="echoid-s797" xml:space="preserve">D tirez la ligne C D, elle ſera parallele à A B.</s> <s xml:id="echoid-s798" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s799" xml:space="preserve">Autrement, du point C comme centre, décrivez un arc qui tou-<lb/> <anchor type="note" xlink:label="note-027-04a" xlink:href="note-027-04"/> che la ligne donnée, & </s> <s xml:id="echoid-s800" xml:space="preserve">d'un autre point pris à volonté ſur la ligne <lb/>A B, décrivez avec la même ouverture l'arc D; </s> <s xml:id="echoid-s801" xml:space="preserve">par le point C <lb/> <pb o="14" file="028" n="28" rhead="USAGE DES PREMIERS"/> tirez une ligne touchant l'arc D, la ligne C D ſera parallele à la <lb/>ligne A B.</s> <s xml:id="echoid-s802" xml:space="preserve"/> </p> <div xml:id="echoid-div92" type="float" level="2" n="2"> <note position="right" xlink:label="note-027-04" xlink:href="note-027-04a" xml:space="preserve">Fig. 11.</note> </div> <p> <s xml:id="echoid-s803" xml:space="preserve">Mais comme on ne voit pas bien où eſt le point touchant, on <lb/>pourra ſe ſervir de la maniere ſuivante qui eſt la meilleure.</s> <s xml:id="echoid-s804" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s805" xml:space="preserve">Du point donné C comme centre, & </s> <s xml:id="echoid-s806" xml:space="preserve">d'une ouverture de compas <lb/> <anchor type="note" xlink:label="note-028-01a" xlink:href="note-028-01"/> à volonté, décrivez un arc qui coupera la ligne A B au point A.</s> <s xml:id="echoid-s807" xml:space="preserve"/> </p> <div xml:id="echoid-div93" type="float" level="2" n="3"> <note position="left" xlink:label="note-028-01" xlink:href="note-028-01a" xml:space="preserve">Fig. 12.</note> </div> <p> <s xml:id="echoid-s808" xml:space="preserve">Et d'un autre point comme B ſur ladite ligne, faites un autre <lb/>arc de la même ouverture de compas que le precedent; </s> <s xml:id="echoid-s809" xml:space="preserve">ouvrez le <lb/>c<unsure/>ompas de la diſtance<unsure/> A B, & </s> <s xml:id="echoid-s810" xml:space="preserve">du point C comme centre faites un <lb/>arc de cercle qui coupera le precedent au point D, par les points <lb/>C & </s> <s xml:id="echoid-s811" xml:space="preserve">D tirez une ligne, elle ſera parallele à A B.</s> <s xml:id="echoid-s812" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div95" type="section" level="1" n="18"> <head xml:id="echoid-head28" xml:space="preserve">USAGE VIII.</head> <head xml:id="echoid-head29" style="it" xml:space="preserve">Diviſer une ligne donnée en tant de parties égales <lb/>qu'on voudra. <lb/> </head> <note position="left" xml:space="preserve">IV. <lb/>Planche. <lb/>Fig. 1.</note> <p> <s xml:id="echoid-s813" xml:space="preserve">LA ligne donnée ſoit A B, qu'il faut diviſer en 8 parties éga-<lb/>les. </s> <s xml:id="echoid-s814" xml:space="preserve">Tirez à volonté la ligne B C, faiſant un angle avec la li-<lb/>gne A B, tirez auſſi la ligne A D parallele à B C, mettez ſur <lb/>B C, 8 parties égales de telle grandeur qu'il vous plaira, portez <lb/>les mêmes parties ſur la ligne A D, & </s> <s xml:id="echoid-s815" xml:space="preserve">des diviſions de l'une à l'au-<lb/>tre tirez des lignes, elles diviſeront la ligne A B en 8 parties é-<lb/>gales.</s> <s xml:id="echoid-s816" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s817" xml:space="preserve">Autrement, tirez une ligne a b, parallele à A B propoſée à divi-<lb/> <anchor type="note" xlink:label="note-028-03a" xlink:href="note-028-03"/> ſer; </s> <s xml:id="echoid-s818" xml:space="preserve">marquez ſur cette ligne ab, 8 parties égales à diſcretion: </s> <s xml:id="echoid-s819" xml:space="preserve">par <lb/>les extremitez de ces deux paralleles tirez deux lignes, leſquelles <lb/>formant un triangle s'entrecoupent au point C, duquel point C ti-<lb/>rant des lignes aux diviſions faites ſur la ligne ab, elles couperont <lb/>l'autre ligne A B en autant de parties égales.</s> <s xml:id="echoid-s820" xml:space="preserve"/> </p> <div xml:id="echoid-div95" type="float" level="2" n="1"> <note position="left" xlink:label="note-028-03" xlink:href="note-028-03a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s821" xml:space="preserve">Cette diviſion de ligne ſert à faire des échelles de plans; </s> <s xml:id="echoid-s822" xml:space="preserve">car s'é-<lb/> <anchor type="note" xlink:label="note-028-04a" xlink:href="note-028-04"/> tant propoſé la ligne A B pour en faire une échelle de 80 parties <lb/>ou 80 toiſes, chaque partie de cette ligne diviſée en 8, contien-<lb/>dra 10 toiſes; </s> <s xml:id="echoid-s823" xml:space="preserve">mais comme il ſeroit difficile de diviſer chacune <lb/>deſdites parties en 10, il faut des extremitez de la ligne A B éle-<lb/>ver des perpendiculaires A D, BC, ſur leſquelles il faut mettre 10 <lb/>parties à volonté, & </s> <s xml:id="echoid-s824" xml:space="preserve">de ces parties tirer des lignes paralleles à la li-<lb/>gne A B; </s> <s xml:id="echoid-s825" xml:space="preserve">on mettra ſur la ligne D C les mêmes diviſions de la li-<lb/>gne A B, & </s> <s xml:id="echoid-s826" xml:space="preserve">on tirera des lignes tranſverſales A E, 10 F, 20 G, & </s> <s xml:id="echoid-s827" xml:space="preserve"><lb/>ainſi des autres.</s> <s xml:id="echoid-s828" xml:space="preserve"/> </p> <div xml:id="echoid-div96" type="float" level="2" n="2"> <note position="left" xlink:label="note-028-04" xlink:href="note-028-04a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s829" xml:space="preserve">On prendra facilement autant de toiſes qu'on voudra ſur cette <lb/> <pb o="15" file="029" n="29" rhead="INSTRUMENS. Liv. I. Chap. I."/> échelle. </s> <s xml:id="echoid-s830" xml:space="preserve">Par exemple, ſi on veut en avoir 23 toiſes, on prendra la <lb/>rencontre de la tranſverſale 20 G avec la 3 parallele quieſt au point <lb/>Z, & </s> <s xml:id="echoid-s831" xml:space="preserve">la grandeur Z 3 ſera de 23 toiſes; </s> <s xml:id="echoid-s832" xml:space="preserve">ſi on veut avoir 58 toiſes, <lb/>on prendra la rencontre de la tranſverſale 50 H avec la 8 parallele <lb/>qui eſt à Y, & </s> <s xml:id="echoid-s833" xml:space="preserve">la grandeur Y 8, repreſentera 58 toiſes, & </s> <s xml:id="echoid-s834" xml:space="preserve">ainſi des <lb/>autres: </s> <s xml:id="echoid-s835" xml:space="preserve">on pourroit mettre ſur cette échelle les pieds faiſant les lignes <lb/>paralleles plus éloignées les unes des autres; </s> <s xml:id="echoid-s836" xml:space="preserve">& </s> <s xml:id="echoid-s837" xml:space="preserve">ſi elles étoient aſſez <lb/>éloignées pour être encore ſubdiviſées en 12 parties, on y pren-<lb/>droit les pouces.</s> <s xml:id="echoid-s838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s839" xml:space="preserve">Pour diviſer une très-petite ligne en grand nombre de parties, <lb/> <anchor type="note" xlink:label="note-029-01a" xlink:href="note-029-01"/> comme en 100, ou en 1000 parties égales. </s> <s xml:id="echoid-s840" xml:space="preserve">Soit, par exemple, pro-<lb/>poſée la ligne A D qu'il faut diviſer en 1000.</s> <s xml:id="echoid-s841" xml:space="preserve"/> </p> <div xml:id="echoid-div97" type="float" level="2" n="3"> <note position="right" xlink:label="note-029-01" xlink:href="note-029-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s842" xml:space="preserve">Des extremitez A D élevez les perpendiculaires AB, DC, por-<lb/>tez ſur ces perpendiculaires 10 parties égales; </s> <s xml:id="echoid-s843" xml:space="preserve">tirez par ces diviſions <lb/>autant de lignes paralleles à A D, diviſez les lignes A D, BC cha-<lb/>cune en 10 parties égales, que vous joindrez par autant de perpendi-<lb/>culaires: </s> <s xml:id="echoid-s844" xml:space="preserve">ſubdiviſez enſuite la premiere diſtance AE & </s> <s xml:id="echoid-s845" xml:space="preserve">ſa parallele <lb/>BF en 10 autres parties que vous joindrez par des tranſverſales ou <lb/>lignes obliques tirées d'un intervale de diviſion comme du point E <lb/>au point 1, & </s> <s xml:id="echoid-s846" xml:space="preserve">ainſi des ſuites.</s> <s xml:id="echoid-s847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s848" xml:space="preserve">Par ce moyen cette premiere diſtance AE ſe trouvera diviſée en <lb/>100 parties égales; </s> <s xml:id="echoid-s849" xml:space="preserve">c'eſt pourquoi on continuëra d'écrire les chi-<lb/>fres 200, 300, 400, 500, &</s> <s xml:id="echoid-s850" xml:space="preserve">c. </s> <s xml:id="echoid-s851" xml:space="preserve">juſqu'à 1000 au-deſſus & </s> <s xml:id="echoid-s852" xml:space="preserve">au-<lb/>deſſous de ladite échelle, qui ſera diviſée en 1000 parties égales, <lb/>comme l'on voit en la Figure 4. </s> <s xml:id="echoid-s853" xml:space="preserve">On nomme ordinairement cette <lb/>regle Echelle de dixme.</s> <s xml:id="echoid-s854" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s855" xml:space="preserve">Pour s'en ſervir & </s> <s xml:id="echoid-s856" xml:space="preserve">y prendre telle partie qu'on voudra, il faut <lb/>faire comme il a été dit au ſujet de l'échelle repreſentée en la Figure <lb/>precedente. </s> <s xml:id="echoid-s857" xml:space="preserve">Nous parlerons encore de cette échelle de 1000 par-<lb/>ties dans le Chapitre du Compas de proportion.</s> <s xml:id="echoid-s858" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s859" xml:space="preserve">Il ſe fait auſſi des échelles ſimples des ſinus, des tangentes & </s> <s xml:id="echoid-s860" xml:space="preserve"><lb/>ſecantes ſur des regles en cette maniere.</s> <s xml:id="echoid-s861" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s862" xml:space="preserve">Par exemple, ſi de tous les degrez du quart de cercle IF, à com-<lb/> <anchor type="note" xlink:label="note-029-02a" xlink:href="note-029-02"/> mencer du point I, on abaiſſe des perpendiculaires ſur le raïon A I, <lb/>ces perpendiculaires ſeront les ſinus detous ces degrez, dont le plus <lb/>grand ſera le raïon du cercle ou ſinus total A F, & </s> <s xml:id="echoid-s863" xml:space="preserve">les longueurs de <lb/>tous ces ſinus ſe pourront marquer ſur le raïon AF, pour en faire <lb/>une échelle, à commencer depuis le point A, ainſi les ſinus DK <lb/>ſont marquez depuis A juſqu'en G, &</s> <s xml:id="echoid-s864" xml:space="preserve">c.</s> <s xml:id="echoid-s865" xml:space="preserve"/> </p> <div xml:id="echoid-div98" type="float" level="2" n="4"> <note position="right" xlink:label="note-029-02" xlink:href="note-029-02a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s866" xml:space="preserve">Et ſi l'on prolonge la tangente IE indéſiniment vers E, & </s> <s xml:id="echoid-s867" xml:space="preserve">que du <lb/> <pb o="16" file="030" n="30" rhead="USAGE DES PREMIERS'"/> centre A on tire des lignes comme A E par tous les degrez du quart <lb/>de cercle juſqu'à la tangente I E prolongée, ceslignes ſeront les ſe-<lb/>cantes de tous les degrez, & </s> <s xml:id="echoid-s868" xml:space="preserve">onverra évidemment que la moindre de <lb/>toutes les ſecantes eſt plus grande que le raï<unsure/>on A1. </s> <s xml:id="echoid-s869" xml:space="preserve">Il eſt auſſi évi-<lb/>dent que toutes les tangentes IE de tous les degrez ſont terminées <lb/>par leurs ſecantes AE le long de la ligne IE, qui ſera pour lors l'é-<lb/>chelle des tangentes; </s> <s xml:id="echoid-s870" xml:space="preserve">& </s> <s xml:id="echoid-s871" xml:space="preserve">c'eſt de cette maniere qu'on pourra faire <lb/>ces échelles ſimples des ſinus, tangentes & </s> <s xml:id="echoid-s872" xml:space="preserve">ſecantes, en tranſpor-<lb/>tant avec un compas ſur une regle toutes ces diſtances.</s> <s xml:id="echoid-s873" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s874" xml:space="preserve">Les tables des ſinus, tangentes & </s> <s xml:id="echoid-s875" xml:space="preserve">ſecantes ſont faites ſur ce princi-<lb/>pe. </s> <s xml:id="echoid-s876" xml:space="preserve">Le raïon du cercle ou ſinus de l'angle droit eſt ſuppoſé diviſé <lb/>en 1000 parties égales, & </s> <s xml:id="echoid-s877" xml:space="preserve">l'on a calculé combien de ces mêmes <lb/>parties ſont contenuës à proportion dans tous les ſinus droits, dans <lb/>les tangentes & </s> <s xml:id="echoid-s878" xml:space="preserve">dans les ſecantes de tous les angles, de minute en minu-<lb/>te, depuis une minute juſqu'à 90 degrez; </s> <s xml:id="echoid-s879" xml:space="preserve">& </s> <s xml:id="echoid-s880" xml:space="preserve">l'on a mis ces nom-<lb/>bres par ordre, & </s> <s xml:id="echoid-s881" xml:space="preserve">c'eſt ce qu'on appelle les tables des ſinus, tan-<lb/>gentes & </s> <s xml:id="echoid-s882" xml:space="preserve">ſecantes.</s> <s xml:id="echoid-s883" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s884" xml:space="preserve">Les Logarithmes ſont des nombres en progreſſion arithmetique <lb/>que l'on fait répondre à d'autres nombres en progreſſion géométri-<lb/>que, dont ils ſont les logarithmes, comme le marquent les deux <lb/>progreſſions ſuivantes.</s> <s xml:id="echoid-s885" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s886" xml:space="preserve">Prog. </s> <s xml:id="echoid-s887" xml:space="preserve">géom. </s> <s xml:id="echoid-s888" xml:space="preserve">nomb. </s> <s xml:id="echoid-s889" xml:space="preserve">1, 2, 4, 8, 16, 32, 64, 128, 256, &</s> <s xml:id="echoid-s890" xml:space="preserve">c.</s> <s xml:id="echoid-s891" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s892" xml:space="preserve">Prog. </s> <s xml:id="echoid-s893" xml:space="preserve">arith. </s> <s xml:id="echoid-s894" xml:space="preserve">logarith. </s> <s xml:id="echoid-s895" xml:space="preserve">0, 1, 2, 3, 4, 5, 6, 7, 8, &</s> <s xml:id="echoid-s896" xml:space="preserve">c. </s> <s xml:id="echoid-s897" xml:space="preserve">& </s> <s xml:id="echoid-s898" xml:space="preserve">les <lb/>logarithmes ont été inventez pour abreger les multiplications par <lb/>de ſimples additions, & </s> <s xml:id="echoid-s899" xml:space="preserve">les diviſions par de ſimples ſouſtractions; <lb/></s> <s xml:id="echoid-s900" xml:space="preserve">ce qui épargne un travail infini, principalement dans les calculs <lb/>aſtronomiques.</s> <s xml:id="echoid-s901" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s902" xml:space="preserve">L'uſage de ces Tables eſt expliqué dans les Livres des Tables de <lb/>ſinus, tangentes, ſecantes & </s> <s xml:id="echoid-s903" xml:space="preserve">logarithmes.</s> <s xml:id="echoid-s904" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div100" type="section" level="1" n="19"> <head xml:id="echoid-head30" xml:space="preserve">USAGE IX.</head> <head xml:id="echoid-head31" style="it" xml:space="preserve">Oter d'une ligne donnée telle partie qu'on voudra.</head> <p> <s xml:id="echoid-s905" xml:space="preserve">SOit AB, la ligne donnée de laquelle il faut retrancher la qua-<lb/> <anchor type="note" xlink:label="note-030-01a" xlink:href="note-030-01"/> triéme partie.</s> <s xml:id="echoid-s906" xml:space="preserve"/> </p> <div xml:id="echoid-div100" type="float" level="2" n="1"> <note position="left" xlink:label="note-030-01" xlink:href="note-030-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s907" xml:space="preserve">Tirez la ligne indéfinie AC, faiſant un angle avec la ligne AB, <lb/>portez ſur la ligne AC quatre parties à diſcretion; </s> <s xml:id="echoid-s908" xml:space="preserve">de la derniere <lb/>diviſion tirez la ligne B 4, & </s> <s xml:id="echoid-s909" xml:space="preserve">tirez enſuite la ligne 1 D, parallele <lb/>à B 4, AD ſera la quatriéme partie de AB.</s> <s xml:id="echoid-s910" xml:space="preserve"/> </p> <pb o="17" file="031" n="31" rhead="INSTRUMENS. Liv. I. Chap. I."/> </div> <div xml:id="echoid-div102" type="section" level="1" n="20"> <head xml:id="echoid-head32" xml:space="preserve">USAGE X.</head> <head xml:id="echoid-head33" style="it" xml:space="preserve">Mener une ligne droite quitouche le cercle par un point donné.</head> <p> <s xml:id="echoid-s911" xml:space="preserve">SI le point donné B touche la circonference du cercle, tirez le <lb/> <anchor type="note" xlink:label="note-031-01a" xlink:href="note-031-01"/> rayon A B, & </s> <s xml:id="echoid-s912" xml:space="preserve">du point B élevez la perpendiculaire B C, qu'il <lb/>faut prolonger, elle ſera tangente au cercle.</s> <s xml:id="echoid-s913" xml:space="preserve"/> </p> <div xml:id="echoid-div102" type="float" level="2" n="1"> <note position="right" xlink:label="note-031-01" xlink:href="note-031-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s914" xml:space="preserve">Mais ſi le point donné B étoit hors le cercle, tirez du centre A <lb/> <anchor type="note" xlink:label="note-031-02a" xlink:href="note-031-02"/> au point donné B une ligne droite, que vous diviſerez en deux éga-<lb/>lement au point D, duquel comme centre & </s> <s xml:id="echoid-s915" xml:space="preserve">intervale BD décri-<lb/>vez un demi cercle qui couperale cercle au point E, tirez B E, elle <lb/>ſera tangente.</s> <s xml:id="echoid-s916" xml:space="preserve"/> </p> <div xml:id="echoid-div103" type="float" level="2" n="2"> <note position="right" xlink:label="note-031-02" xlink:href="note-031-02a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s917" xml:space="preserve">Mais ſi le cercle étant donné avec une ligne qui le touche, on cher-<lb/> <anchor type="note" xlink:label="note-031-03a" xlink:href="note-031-03"/> che le point d'attouchement, du centre du cercle abbaiſſez la per-<lb/>pendiculaire A B ſur la touchante, le point où elle la coupera ſera <lb/>celui d'attouchement.</s> <s xml:id="echoid-s918" xml:space="preserve"/> </p> <div xml:id="echoid-div104" type="float" level="2" n="3"> <note position="right" xlink:label="note-031-03" xlink:href="note-031-03a" xml:space="preserve">Fig. 8.</note> </div> </div> <div xml:id="echoid-div106" type="section" level="1" n="21"> <head xml:id="echoid-head34" xml:space="preserve">USAGE XI.</head> <head xml:id="echoid-head35" style="it" xml:space="preserve">Sur une ligne droite donnée, décrire une ligne ſpirale quifaſſe <lb/>autant de revolutions qu'on voudra.</head> <p> <s xml:id="echoid-s919" xml:space="preserve">SOit la ligne donnée AB, ſur laquelle on veut décrire une ſpirale <lb/> <anchor type="note" xlink:label="note-031-04a" xlink:href="note-031-04"/> qui faſſe trois revolutions; </s> <s xml:id="echoid-s920" xml:space="preserve">diviſez premierement cette ligne en <lb/>deux parties égales au point C, duquel point comme centre décrivez <lb/>un demi cercle dont le diametre ſoit toute la ligne donnée AB; <lb/></s> <s xml:id="echoid-s921" xml:space="preserve">diviſez enſuite le demi diametre A C en trois également aux points <lb/>D E, & </s> <s xml:id="echoid-s922" xml:space="preserve">du même centre C tracez du même côté deux autres de-<lb/>mi cercles paſſans par les points des diviſions D E, ſubdiviſez en-<lb/>core l'eſpace C E en deux également au point F, duquel point com-<lb/>me centre décrivez de l'autre côté de la ligne trois autres demi cer-<lb/>cles, & </s> <s xml:id="echoid-s923" xml:space="preserve">la ſpirale de trois révolutions ſera achevée. </s> <s xml:id="echoid-s924" xml:space="preserve">Si l'on veut que <lb/>la ligne ſpirale faſſe quatre révolutions, il n'y a qu'à diviſer en quatre <lb/>le demi diametre A C.</s> <s xml:id="echoid-s925" xml:space="preserve"/> </p> <div xml:id="echoid-div106" type="float" level="2" n="1"> <note position="right" xlink:label="note-031-04" xlink:href="note-031-04a" xml:space="preserve">Fig. 9.</note> </div> </div> <div xml:id="echoid-div108" type="section" level="1" n="22"> <head xml:id="echoid-head36" xml:space="preserve">USAGE XII.</head> <head xml:id="echoid-head37" style="it" xml:space="preserve">Sur une ligne droite donnée décrire un triangle équilateral.</head> <p> <s xml:id="echoid-s926" xml:space="preserve">SOit AB la ligne donnée ſur laquelle il faut faire un triangle <lb/> <anchor type="note" xlink:label="note-031-05a" xlink:href="note-031-05"/> équilateral.</s> <s xml:id="echoid-s927" xml:space="preserve"/> </p> <div xml:id="echoid-div108" type="float" level="2" n="1"> <note position="right" xlink:label="note-031-05" xlink:href="note-031-05a" xml:space="preserve">Fig. 10.</note> </div> <p> <s xml:id="echoid-s928" xml:space="preserve">Du point A pour centre & </s> <s xml:id="echoid-s929" xml:space="preserve">de l'intervale AB, décrivez un arc de <lb/>cercle: </s> <s xml:id="echoid-s930" xml:space="preserve">du point B pour centre & </s> <s xml:id="echoid-s931" xml:space="preserve">de l'intervale B A, décrivez un <lb/>autre arc de cercle qui coupera le precedent au point C; </s> <s xml:id="echoid-s932" xml:space="preserve">tirez les <lb/>lignes CA, CB, le triangle A B C ſera équilateral.</s> <s xml:id="echoid-s933" xml:space="preserve"/> </p> <pb o="18" file="032" n="32" rhead="USAGES DES PREMIERS"/> <p> <s xml:id="echoid-s934" xml:space="preserve">Pour décrire un triangle Iſocele ſur la ligne AB, il ſaut ouvrir le <lb/> <anchor type="note" xlink:label="note-032-01a" xlink:href="note-032-01"/> compas plus grand que toute la ligne, ou plus petit, & </s> <s xml:id="echoid-s935" xml:space="preserve">faire le reſte <lb/>comme ci-devant.</s> <s xml:id="echoid-s936" xml:space="preserve"/> </p> <div xml:id="echoid-div109" type="float" level="2" n="2"> <note position="left" xlink:label="note-032-01" xlink:href="note-032-01a" xml:space="preserve">Fig. 11.</note> </div> </div> <div xml:id="echoid-div111" type="section" level="1" n="23"> <head xml:id="echoid-head38" xml:space="preserve">USAGE XIII.</head> <head xml:id="echoid-head39" style="it" xml:space="preserve">Faire un triangle égal & ſemblable à un autre triangle <lb/>propoſé.</head> <p> <s xml:id="echoid-s937" xml:space="preserve">SOit le triangle donné ABC, auquel il en faut faire un ſemblable <lb/> <anchor type="note" xlink:label="note-032-02a" xlink:href="note-032-02"/> comme DEF.</s> <s xml:id="echoid-s938" xml:space="preserve"/> </p> <div xml:id="echoid-div111" type="float" level="2" n="1"> <note position="left" xlink:label="note-032-02" xlink:href="note-032-02a" xml:space="preserve">Fig. 12.</note> </div> <p> <s xml:id="echoid-s939" xml:space="preserve">Faites la ligne D E égale à AB; </s> <s xml:id="echoid-s940" xml:space="preserve">du point D pour centre & </s> <s xml:id="echoid-s941" xml:space="preserve">pour <lb/> <anchor type="note" xlink:label="note-032-03a" xlink:href="note-032-03"/> rayon A C décrivez un arc, du point E pour centre & </s> <s xml:id="echoid-s942" xml:space="preserve">pour rayon <lb/>B C décrivez un autre arc qui coupera le precedent au point F, tirez <lb/>les lignes DF, EF, & </s> <s xml:id="echoid-s943" xml:space="preserve">le triangle ſera égal & </s> <s xml:id="echoid-s944" xml:space="preserve">ſemblable au triangle <lb/>propoſé.</s> <s xml:id="echoid-s945" xml:space="preserve"/> </p> <div xml:id="echoid-div112" type="float" level="2" n="2"> <note position="left" xlink:label="note-032-03" xlink:href="note-032-03a" xml:space="preserve">Fig. 13.</note> </div> </div> <div xml:id="echoid-div114" type="section" level="1" n="24"> <head xml:id="echoid-head40" xml:space="preserve">USAGE XIV.</head> <head xml:id="echoid-head41" style="it" xml:space="preserve">Sur une ligne donnée, faire un triangle ſemblable à un autre, <lb/>ſans qu'il lui ſoit égal.</head> <p> <s xml:id="echoid-s946" xml:space="preserve">SOit la ligne donnée HI, ſur laquelle il faut faire un triangle ſem-<lb/> <anchor type="note" xlink:label="note-032-04a" xlink:href="note-032-04"/> blable, mais non égal au triangle ABC.</s> <s xml:id="echoid-s947" xml:space="preserve"/> </p> <div xml:id="echoid-div114" type="float" level="2" n="1"> <note position="left" xlink:label="note-032-04" xlink:href="note-032-04a" xml:space="preserve">Fig. 14. <lb/> & 15.</note> </div> <p> <s xml:id="echoid-s948" xml:space="preserve">Faites l'angle H égal à l'angle A, & </s> <s xml:id="echoid-s949" xml:space="preserve">l'angle I égal à l'angle B; </s> <s xml:id="echoid-s950" xml:space="preserve">tirez <lb/>les lignes HG, IG juſqu'à ce qu'elles ſe rencontrent, le triangle HIG <lb/>ſera le requis.</s> <s xml:id="echoid-s951" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div116" type="section" level="1" n="25"> <head xml:id="echoid-head42" xml:space="preserve">USAGE XV.</head> <head xml:id="echoid-head43" style="it" xml:space="preserve">Faire un triangle de trois lignes droites égales à trois lignes <lb/>données, dont les deux plus courtes priſes enſemble ſoient <lb/>plus longues que la troiſiéme.</head> <p> <s xml:id="echoid-s952" xml:space="preserve">SOient les trois lignes droites propoſées A, B, C. </s> <s xml:id="echoid-s953" xml:space="preserve">Faites la ligne <lb/> <anchor type="note" xlink:label="note-032-05a" xlink:href="note-032-05"/> droite D E égale à la ligne A, du point E pour centre & </s> <s xml:id="echoid-s954" xml:space="preserve">pour <lb/>rayon la grandeur de la ligne B, décrivez une portion de cercle; </s> <s xml:id="echoid-s955" xml:space="preserve">pa-<lb/>reillement de D comme centre, & </s> <s xml:id="echoid-s956" xml:space="preserve">pour rayon la grandeur de la ligne <lb/>C, décrivez une autre portion de cercle, coupant la premiere au point <lb/>F, tirez les lignes droites FD, FE, & </s> <s xml:id="echoid-s957" xml:space="preserve">le triangle DFE ſera le propoſé.</s> <s xml:id="echoid-s958" xml:space="preserve"/> </p> <div xml:id="echoid-div116" type="float" level="2" n="1"> <note position="left" xlink:label="note-032-05" xlink:href="note-032-05a" xml:space="preserve">Fig. 16.</note> </div> </div> <div xml:id="echoid-div118" type="section" level="1" n="26"> <head xml:id="echoid-head44" xml:space="preserve">USAGE XVI.</head> <head xml:id="echoid-head45" style="it" xml:space="preserve">Sur une ligne droite donnée, décrire un quarré.</head> <p> <s xml:id="echoid-s959" xml:space="preserve">SOit la ligne droite donnée AB, ſur laquelle il faut décrire un <lb/> <anchor type="note" xlink:label="note-032-06a" xlink:href="note-032-06"/> quarré, dont AB ſoit un côté. </s> <s xml:id="echoid-s960" xml:space="preserve">Du point A pour centre, & </s> <s xml:id="echoid-s961" xml:space="preserve">AB <lb/> <pb o="19" file="033" n="33" rhead="INSTRUMENS. Liv. I. Chap. I."/> pour rayon, décrivez l'arc BD, & </s> <s xml:id="echoid-s962" xml:space="preserve">du point B l'arc AE, l'entrecou-<lb/>pant au point C, diviſez l'arc CA, ou CB en deux également au point <lb/>F. </s> <s xml:id="echoid-s963" xml:space="preserve">Faites les intervales C E & </s> <s xml:id="echoid-s964" xml:space="preserve">CD égaux à CF; </s> <s xml:id="echoid-s965" xml:space="preserve">tirez les lignes AD, <lb/>DE, EB, le quarré ſera fait.</s> <s xml:id="echoid-s966" xml:space="preserve"/> </p> <div xml:id="echoid-div118" type="float" level="2" n="1"> <note position="left" xlink:label="note-032-06" xlink:href="note-032-06a" xml:space="preserve">Fig. 17.</note> </div> <p> <s xml:id="echoid-s967" xml:space="preserve">Autrement: </s> <s xml:id="echoid-s968" xml:space="preserve">ſur l'extremité de la ligne AB, élevez la perpendicu-<lb/> <anchor type="note" xlink:label="note-033-01a" xlink:href="note-033-01"/> laire A D égale à AB, du point D pour centre, & </s> <s xml:id="echoid-s969" xml:space="preserve">de la grandeur <lb/>AB, ſaites un arc; </s> <s xml:id="echoid-s970" xml:space="preserve">du point B, & </s> <s xml:id="echoid-s971" xml:space="preserve">de la même ouverture de compas <lb/>faites un autre arc, coupant le premier au point E, tirez les lignes <lb/>AD, DE, & </s> <s xml:id="echoid-s972" xml:space="preserve">E B, le quarré ſera achevé.</s> <s xml:id="echoid-s973" xml:space="preserve"/> </p> <div xml:id="echoid-div119" type="float" level="2" n="2"> <note position="right" xlink:label="note-033-01" xlink:href="note-033-01a" xml:space="preserve">Fig. 18.</note> </div> <p> <s xml:id="echoid-s974" xml:space="preserve">Dans la pratique precedente la ligne AB a été donnée pour être <lb/> <anchor type="note" xlink:label="note-033-02a" xlink:href="note-033-02"/> le côté d'un quarré; </s> <s xml:id="echoid-s975" xml:space="preserve">mais ſi on propoſoit cette ligne pour en être la <lb/>diagonale, il faudroit la diviſer en deux également par la perpendicu-<lb/>laire CD, faire les parties EC, ED égales à AE & </s> <s xml:id="echoid-s976" xml:space="preserve">BE, & </s> <s xml:id="echoid-s977" xml:space="preserve">tirer les qua-<lb/>tre lignes AC, CB, BD, & </s> <s xml:id="echoid-s978" xml:space="preserve">DA.</s> <s xml:id="echoid-s979" xml:space="preserve"/> </p> <div xml:id="echoid-div120" type="float" level="2" n="3"> <note position="right" xlink:label="note-033-02" xlink:href="note-033-02a" xml:space="preserve">Fig. 19.</note> </div> <p> <s xml:id="echoid-s980" xml:space="preserve">On donnera dans les uſages du Rapporteur & </s> <s xml:id="echoid-s981" xml:space="preserve">du Compas de pro-<lb/>portion des manieres de conſtruire les polygones reguliers ſur une <lb/>ligne donnée, parce que la partique en eſt plus facile. </s> <s xml:id="echoid-s982" xml:space="preserve">Mais en atten-<lb/>dant, voici une méthode generale où il n'eſt beſoin que du ſimple <lb/>compas & </s> <s xml:id="echoid-s983" xml:space="preserve">de la regle.</s> <s xml:id="echoid-s984" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div122" type="section" level="1" n="27"> <head xml:id="echoid-head46" xml:space="preserve">USAGE XVII.</head> <head xml:id="echoid-head47" style="it" xml:space="preserve">Inſcrire dans un cercle tel Polygone regulier qu'on voudra.</head> <note position="right" xml:space="preserve">V. Plan-<lb/>he. <lb/>Fig. 1.</note> <p> <s xml:id="echoid-s985" xml:space="preserve">SOit propoſé pour exemple à faire un Pentagone; </s> <s xml:id="echoid-s986" xml:space="preserve">ſi le cercle eſt <lb/>donné, diviſez ſon diametre AB en cinq parties égales par l'uſage <lb/>8. </s> <s xml:id="echoid-s987" xml:space="preserve">Mais s'il n'e ſt pas donné, tirez au craïon une ligne indefinie, pour <lb/>ſervir de diametre, laquelle étant diviſée en cinq parties égales', <lb/>youvrez le compas de toute la grandeur du diametre, pour décrire <lb/>deux arcs qui s'entrecoupent au point C, comme pour former un <lb/>triangle équilateral; </s> <s xml:id="echoid-s988" xml:space="preserve">puis ayant tracé un cercle autour de ce diame-<lb/>tre, mettez la regle ſur ledit point C, & </s> <s xml:id="echoid-s989" xml:space="preserve">ſur le ſecond point de divi-<lb/>ſion du diametre, pourtirer une ligne quicoupera la circonference du <lb/>cercle au-deſſous du diametre au point D, l'arc AD ſera à peu près la <lb/>cinquiéme partie de ladite circonference; </s> <s xml:id="echoid-s990" xml:space="preserve">c'eſt pourquoi l'ouvertu-<lb/>re A D diviſera le cercle en cinq également, & </s> <s xml:id="echoid-s991" xml:space="preserve">tirant cinq lignes <lb/>droites, on aura le pentagone propoſé.</s> <s xml:id="echoid-s992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s993" xml:space="preserve">Cette méthode eſt generale pour faire toutes ſortes de Polygones <lb/>reguliers; </s> <s xml:id="echoid-s994" xml:space="preserve">car pour faire, par exemple, un eptagone, il n'y a qu'à di-<lb/>viſer en ſept le diametre AB, c'eſt-à-dire, en autant de parties, que <lb/>la figure doit avoir de côtez, & </s> <s xml:id="echoid-s995" xml:space="preserve">tirer toûjours la ligne du point C <lb/>par le ſecond point de diviſion du diametre.</s> <s xml:id="echoid-s996" xml:space="preserve"/> </p> <pb o="20" file="034" n="34" rhead="USAGES DES PREMIERS"/> <p> <s xml:id="echoid-s997" xml:space="preserve">Pour ce qui eſt de l'exagone, la conſtruction en eſt plus ſimple, <lb/>puiſque, ſans aucune preparation, le rayon, ou demi diametre du <lb/>cercle, diviſe la circonſerence en ſix parties égales.</s> <s xml:id="echoid-s998" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s999" xml:space="preserve">Pour le dodecagone, il n'y a qu'à ſubdiviſer en deux parties <lb/>égales l'arc de l'exagone.</s> <s xml:id="echoid-s1000" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1001" xml:space="preserve">De même, pour le decagone, il faut diviſer en deux l'arc du <lb/>pentagone.</s> <s xml:id="echoid-s1002" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1003" xml:space="preserve">Ce problême eſt à peu près le même que celui qui eſt décrit au <lb/>Chapitre 17 du premier livre des Fortiſications du Chevalier de <lb/>Ville, excepté que pour diviſer le cercle, il tire une ligne de l'angle <lb/>exterieur du triangle équilateral par le premier point de diviſion du <lb/>diametre, & </s> <s xml:id="echoid-s1004" xml:space="preserve">qu'enſuite il double l'arc du cercle; </s> <s xml:id="echoid-s1005" xml:space="preserve">mais par ce moyen <lb/>il s'éloigne davantage de l'exactitude: </s> <s xml:id="echoid-s1006" xml:space="preserve">car, par exemple, en la deſ-<lb/>cription du pentagone, l'angle du centre eſt trop grand de quaran-<lb/>te -<unsure/> quatre minutes, à l'eptagone il eſt trop grand d'un degré cinq <lb/>minutes; </s> <s xml:id="echoid-s1007" xml:space="preserve">& </s> <s xml:id="echoid-s1008" xml:space="preserve">ainſi l'erreur s'augmente aux polygones qui ont plus <lb/>de côtez: </s> <s xml:id="echoid-s1009" xml:space="preserve">au lieu que faiſant paſſer cette ligne par le ſecond point <lb/>de diviſion du diametre, l'angle au centre du pentagone n'eſt trop <lb/>petit que d'environ deux minutes; </s> <s xml:id="echoid-s1010" xml:space="preserve">& </s> <s xml:id="echoid-s1011" xml:space="preserve">à l'eptagone, il eſt trop grand <lb/>de ſix minutes, qui ſont des erreurs beaucoup moindres, & </s> <s xml:id="echoid-s1012" xml:space="preserve">preſ-<lb/>qu'inſenſibles dans l'inſcription de ces polygones.</s> <s xml:id="echoid-s1013" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div123" type="section" level="1" n="28"> <head xml:id="echoid-head48" xml:space="preserve">USAGE XVIII.</head> <head xml:id="echoid-head49" style="it" xml:space="preserve">Partrois points donnez faire paſſer la circonference d'un cer-<lb/>cle, pourvû qu'ils ne ſoient pas en ligne droite.</head> <p> <s xml:id="echoid-s1014" xml:space="preserve">SOient les trois points donnez A, B, C; </s> <s xml:id="echoid-s1015" xml:space="preserve">du point A au point B ti-<lb/> <anchor type="note" xlink:label="note-034-01a" xlink:href="note-034-01"/> rez une ligne, & </s> <s xml:id="echoid-s1016" xml:space="preserve">du point B au point C une autre; </s> <s xml:id="echoid-s1017" xml:space="preserve">diviſez-les en <lb/>deux également par les lignes D E, F G, leſquelles ſe rencontreront <lb/>au point H, quiſera le centre du cercle: </s> <s xml:id="echoid-s1018" xml:space="preserve">du point H pour centre, & </s> <s xml:id="echoid-s1019" xml:space="preserve">de <lb/>I'intervale HA, ou HB, ou HC, décrivez le cercle.</s> <s xml:id="echoid-s1020" xml:space="preserve"/> </p> <div xml:id="echoid-div123" type="float" level="2" n="1"> <note position="left" xlink:label="note-034-01" xlink:href="note-034-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s1021" xml:space="preserve">Par cette methode onacheve une circonference commencée, en y <lb/>prenant trois points, comme ſeroient les trois points A,B,C, & </s> <s xml:id="echoid-s1022" xml:space="preserve">faiſant <lb/>le reſte comme ci-devant.</s> <s xml:id="echoid-s1023" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div125" type="section" level="1" n="29"> <head xml:id="echoid-head50" xml:space="preserve">USAGE XIX.</head> <head xml:id="echoid-head51" style="it" xml:space="preserve">Trouver le centre d'un cercle.</head> <p> <s xml:id="echoid-s1024" xml:space="preserve">SOit le cercle donné ACBD, duquel il faut trouver le centre.</s> <s xml:id="echoid-s1025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1026" xml:space="preserve">Tirez dans le cercle la ligne AB, diviſez-la en deux également <lb/> <anchor type="note" xlink:label="note-034-02a" xlink:href="note-034-02"/> par la ligne CD, diviſez la ligne CD en deux par la ligne EF, laquel-<lb/>le coupera la ligne CD au point G, quiſera le centre du cercle.</s> <s xml:id="echoid-s1027" xml:space="preserve"/> </p> <div xml:id="echoid-div125" type="float" level="2" n="1"> <note position="left" xlink:label="note-034-02" xlink:href="note-034-02a" xml:space="preserve">Fig. 3.</note> </div> <pb o="21" file="035" n="35" rhead="INSTRUMENS. Liv. I. Chap. I."/> </div> <div xml:id="echoid-div127" type="section" level="1" n="30"> <head xml:id="echoid-head52" xml:space="preserve">USAGE XX.</head> <head xml:id="echoid-head53" style="it" xml:space="preserve">Tracer une ligne droite égale à la circonference d'un cercle; <lb/>& faire une circonference de cercle égale à une ligne <lb/>droite propoſée.</head> <p> <s xml:id="echoid-s1028" xml:space="preserve">SOit le cercle donné ABCD, dont on veut reduire la circonferen-<lb/> <anchor type="note" xlink:label="note-035-01a" xlink:href="note-035-01"/> ce en ligne droite; </s> <s xml:id="echoid-s1029" xml:space="preserve">portez ſur une ligne droite trois fois le dia-<lb/>metre du cercle, & </s> <s xml:id="echoid-s1030" xml:space="preserve">de plus une ſeptiéme partie du même diame-<lb/>tre qu'il y faut ajoûter. </s> <s xml:id="echoid-s1031" xml:space="preserve">La ligne GH ſera à peu près égale à ladite <lb/>circonference: </s> <s xml:id="echoid-s1032" xml:space="preserve">nous diſons à peu près, car c'eſt en cela que con-<lb/>ſiſte la quadrature du cercle, laquelle n'a point encore été trou-<lb/>vée geometriquement.</s> <s xml:id="echoid-s1033" xml:space="preserve"/> </p> <div xml:id="echoid-div127" type="float" level="2" n="1"> <note position="right" xlink:label="note-035-01" xlink:href="note-035-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s1034" xml:space="preserve">Si la ligne GH étoit donnée pour la réduire en circonference, il <lb/>la faudroit diviſer en vingt-deux parties égales, & </s> <s xml:id="echoid-s1035" xml:space="preserve">en prendre ſept <lb/>pour le diametre du cercle, ou trois & </s> <s xml:id="echoid-s1036" xml:space="preserve">demi pour ſon raïon.</s> <s xml:id="echoid-s1037" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div129" type="section" level="1" n="31"> <head xml:id="echoid-head54" xml:space="preserve">USAGE XXI.</head> <head xml:id="echoid-head55" style="it" xml:space="preserve">Décrire une Ovale ſur une ligne donnée.</head> <p> <s xml:id="echoid-s1038" xml:space="preserve">SOit AB la ligne droite donnée, ſur laquelle il faut décrire une <lb/> <anchor type="note" xlink:label="note-035-02a" xlink:href="note-035-02"/> ovale.</s> <s xml:id="echoid-s1039" xml:space="preserve"/> </p> <div xml:id="echoid-div129" type="float" level="2" n="1"> <note position="right" xlink:label="note-035-02" xlink:href="note-035-02a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s1040" xml:space="preserve">Diviſez-la en trois parties égales, aux points C & </s> <s xml:id="echoid-s1041" xml:space="preserve">D; </s> <s xml:id="echoid-s1042" xml:space="preserve">ſur la par-<lb/>tie CD décrivez des triangles équilateraux, dont vous prolongerez <lb/>les côtez; </s> <s xml:id="echoid-s1043" xml:space="preserve">des points C & </s> <s xml:id="echoid-s1044" xml:space="preserve">D, & </s> <s xml:id="echoid-s1045" xml:space="preserve">intervale CA, DB, décrivez des <lb/>portions de cercle juſqu'aux côtez des triangles prolongez aux <lb/>points EF & </s> <s xml:id="echoid-s1046" xml:space="preserve">GH; </s> <s xml:id="echoid-s1047" xml:space="preserve">des points I & </s> <s xml:id="echoid-s1048" xml:space="preserve">K pour centre, & </s> <s xml:id="echoid-s1049" xml:space="preserve">pour raïon la <lb/>grandeur IE, ou IG décrivez l'arc E G d'une part, & </s> <s xml:id="echoid-s1050" xml:space="preserve">l'arc F H de <lb/>l'autre, vous aurez une ovale.</s> <s xml:id="echoid-s1051" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1052" xml:space="preserve">On en peut tracer d'autres plus grandes ou plus petites par cet-<lb/>te même maniere, comme on le peut voir par celles qui ſont mar-<lb/>quées de points dans la même figure.</s> <s xml:id="echoid-s1053" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div131" type="section" level="1" n="32"> <head xml:id="echoid-head56" xml:space="preserve">USAGE XXII.</head> <head xml:id="echoid-head57" style="it" xml:space="preserve">Décrire une Ellipſe mathematique, dont les deux axes, <lb/>ou diametres ſont donnez.</head> <p> <s xml:id="echoid-s1054" xml:space="preserve">SOit le grand axe AB, & </s> <s xml:id="echoid-s1055" xml:space="preserve">le petit axe CD, ſe coupans par le mi-<lb/> <anchor type="note" xlink:label="note-035-03a" xlink:href="note-035-03"/> lieu à angles droits au point G.</s> <s xml:id="echoid-s1056" xml:space="preserve"/> </p> <div xml:id="echoid-div131" type="float" level="2" n="1"> <note position="right" xlink:label="note-035-03" xlink:href="note-035-03a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s1057" xml:space="preserve">Prenez avec un compas, ou un cordeau, la grandeur de la moitié <lb/>du grand axe, c'eſt-à-dire, AG, ou GB; </s> <s xml:id="echoid-s1058" xml:space="preserve">portez cette ouverture en <lb/>C, & </s> <s xml:id="echoid-s1059" xml:space="preserve">de ce point, comme centre, décrivez un arc de cercle qui <lb/>coupera le grand axe d'un côté en E, & </s> <s xml:id="echoid-s1060" xml:space="preserve">de l'autre en F; </s> <s xml:id="echoid-s1061" xml:space="preserve">ces points <lb/> <pb o="22" file="036" n="36" rhead="USAGES DES PREMIERS"/> E & </s> <s xml:id="echoid-s1062" xml:space="preserve">F ſeront les foyers, auſquels il faudra mettre de petits points <lb/>comme des têtes d'épingle, ou des piquets, ſi le plan eſt aſſez grand, <lb/>comme ſeroit un jardin: </s> <s xml:id="echoid-s1063" xml:space="preserve">attachez aux points E & </s> <s xml:id="echoid-s1064" xml:space="preserve">F un cordeau é-<lb/>gal au grand axe, dont le milieu paſſera par le point C. </s> <s xml:id="echoid-s1065" xml:space="preserve">Mettez <lb/>dans le ply que fait ce cordeau un crayon ou un piquet, que vous <lb/>ferez mouvoir, en bandant regulierement le cordeau juſqu'à ce que <lb/>vous ayez parcouru les extremitez des diametres propoſez.</s> <s xml:id="echoid-s1066" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1067" xml:space="preserve">On appelle ordinairement cette figure 1 Ovale du jardinier, & </s> <s xml:id="echoid-s1068" xml:space="preserve"><lb/>c'eſt la plus ſimple & </s> <s xml:id="echoid-s1069" xml:space="preserve">la plus facile de toutes les methodes pour dé-<lb/>crire une ovale, mais il faut que le plan ſoit aſſez grand.</s> <s xml:id="echoid-s1070" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1071" xml:space="preserve">Si l'on augmente ou diminuë la longueur de la corde, ſans changer <lb/>la diſtance des foyers, on aura des ellipſes d'une autre eſpece. </s> <s xml:id="echoid-s1072" xml:space="preserve">De <lb/>même, ſi ſans changer la longueur de la corde, on diminuoit la <lb/>diſtance des foyers, on auroit encore des ellipſes d'une autre eſpece; <lb/></s> <s xml:id="echoid-s1073" xml:space="preserve">& </s> <s xml:id="echoid-s1074" xml:space="preserve">ſi à force de les approcher, on les joint tout-à-fait, on décrira un <lb/>cercle. </s> <s xml:id="echoid-s1075" xml:space="preserve">Mais ſi l'on augmente ou diminuë la longueur du grand dia-<lb/>metre & </s> <s xml:id="echoid-s1076" xml:space="preserve">de la corde qui luy eſt égale en même proportion que la <lb/>diſtance des foyers, on tracera des ellipſes toutes de même eſpece, <lb/>quoyque differentes en grandeur.</s> <s xml:id="echoid-s1077" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div133" type="section" level="1" n="33"> <head xml:id="echoid-head58" style="it" xml:space="preserve">Autre maniere de tracer l'Ellipſe.</head> <p> <s xml:id="echoid-s1078" xml:space="preserve">LEs deux foyers E, F, étant marquez comme en la figure prece-<lb/> <anchor type="note" xlink:label="note-036-01a" xlink:href="note-036-01"/> dente, on trouvera autant de points qu'on voudra dans la cir-<lb/>conference de l'ellipſe, en cette ſorte. </s> <s xml:id="echoid-s1079" xml:space="preserve">Ouvrez le compas à diſcre-<lb/>tion, mais un peu davantage que de la diſtance AF, comme par <lb/>exemple, de la grandeur AI, mettez une des pointes du compas au <lb/>foyer F, & </s> <s xml:id="echoid-s1080" xml:space="preserve">de l'autre pointe tracez l'arc O R; </s> <s xml:id="echoid-s1081" xml:space="preserve">ouvrez enſuite le com-<lb/>pas de la diſtance I B, quieſt le reſte du grand axe, poſez une de ſes <lb/>pointes à l'autre foyer E, & </s> <s xml:id="echoid-s1082" xml:space="preserve">de cette ouverture tracez l'arc S T, le <lb/>point d'interſection P de ces deux arcs donnera un des points de la <lb/>circonference de l'ellipſe. </s> <s xml:id="echoid-s1083" xml:space="preserve">Faiſant le même des ouvertures de compas <lb/>AL, LB, on aura le point d'interſection H, en traçant toûjours des <lb/>foyers F & </s> <s xml:id="echoid-s1084" xml:space="preserve">E. </s> <s xml:id="echoid-s1085" xml:space="preserve">Enfin ouvrant le compas de differentes grandeurs, on <lb/>aura tant d'autres points qu'on voudra dans la circonference, leſ-<lb/>quels étant joints par une ligne courbe, l'ellipſe ſera achevée.</s> <s xml:id="echoid-s1086" xml:space="preserve"/> </p> <div xml:id="echoid-div133" type="float" level="2" n="1"> <note position="left" xlink:label="note-036-01" xlink:href="note-036-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s1087" xml:space="preserve">Il eſt à remarquer que chaque ouverture de compas ſert à trouver <lb/>quatre points en diſtance égale des axes. </s> <s xml:id="echoid-s1088" xml:space="preserve">Si d'un point pris à volon-<lb/>té dans la circonference de l'ellipſe, on tire deux lignes droites juſ-<lb/>qu'aux foyers F, E, ces deux lignes PF & </s> <s xml:id="echoid-s1089" xml:space="preserve">PE jointes enſemble, ſont <lb/>égales à ſon grand axe AB, comme il ſe yoit par la même figure.</s> <s xml:id="echoid-s1090" xml:space="preserve"/> </p> <pb o="23" file="037" n="37" rhead="INSTRUMENS Liv. I. Chap. I."/> </div> <div xml:id="echoid-div135" type="section" level="1" n="34"> <head xml:id="echoid-head59" xml:space="preserve">USAGE XXIII.</head> <head xml:id="echoid-head60" style="it" xml:space="preserve">Faire une figure égale & ſemblable à une autre.</head> <p> <s xml:id="echoid-s1091" xml:space="preserve">SOit la figure propoſée A B C D E, à laquelle on en veut faire <lb/> <anchor type="note" xlink:label="note-037-01a" xlink:href="note-037-01"/> une égale & </s> <s xml:id="echoid-s1092" xml:space="preserve">ſemblable.</s> <s xml:id="echoid-s1093" xml:space="preserve"/> </p> <div xml:id="echoid-div135" type="float" level="2" n="1"> <note position="right" xlink:label="note-037-01" xlink:href="note-037-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s1094" xml:space="preserve">Diviſez-la en triangles par les lignes A C, A D; </s> <s xml:id="echoid-s1095" xml:space="preserve">tirez enſuite la <lb/>ligne ab, égale à AB, du point b & </s> <s xml:id="echoid-s1096" xml:space="preserve">grandeur BC décrivez un arc; <lb/></s> <s xml:id="echoid-s1097" xml:space="preserve">du point a & </s> <s xml:id="echoid-s1098" xml:space="preserve">grandeur AC, décrivez un autre arc, coupant le pre-<lb/>cedent au point c, tirez la ligne bc, faites le même pour tous les au-<lb/>tres côtez, & </s> <s xml:id="echoid-s1099" xml:space="preserve">la figure abcde ſera ſemblable à la propoſée ABCDE.</s> <s xml:id="echoid-s1100" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div137" type="section" level="1" n="35"> <head xml:id="echoid-head61" xml:space="preserve">USAGE XXIV.</head> <head xml:id="echoid-head62" style="it" xml:space="preserve">Reduire des figures de grand en petit, & de petit en grand.</head> <p> <s xml:id="echoid-s1101" xml:space="preserve">ON donne ici pluſieurs manieres de réduire les plans, parce que <lb/>cela eſt d'un grand uſage; </s> <s xml:id="echoid-s1102" xml:space="preserve">chacun prendra celle dont il s'ac-<lb/>commodera le mieux.</s> <s xml:id="echoid-s1103" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1104" xml:space="preserve">Premierement, on peut réduire une figure, en prenant un point <lb/> <anchor type="note" xlink:label="note-037-02a" xlink:href="note-037-02"/> en dedans, & </s> <s xml:id="echoid-s1105" xml:space="preserve">tirant des lignes à tous les angles. </s> <s xml:id="echoid-s1106" xml:space="preserve">Soit pour exemple <lb/>la figure A B C D E propoſée à réduire en petit.</s> <s xml:id="echoid-s1107" xml:space="preserve"/> </p> <div xml:id="echoid-div137" type="float" level="2" n="1"> <note position="right" xlink:label="note-037-02" xlink:href="note-037-02a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s1108" xml:space="preserve">Prenez le point F, environ dans le milieu de la figure, tirez des lignes <lb/>à tous les angles ABCDE, menez la ligne ab parallele à la ligne AB, <lb/>la ligne bc parallele à BC, & </s> <s xml:id="echoid-s1109" xml:space="preserve">ainſi des autres; </s> <s xml:id="echoid-s1110" xml:space="preserve">& </s> <s xml:id="echoid-s1111" xml:space="preserve">vous aurez la fi-<lb/>gure a b c d e ſemblable, mais plus petite que la figure A B C D E.</s> <s xml:id="echoid-s1112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1113" xml:space="preserve">Si l'on veut avoir une figure plus grande, il n'y a qu'à prolon-<lb/>ger les lignes tirées du centre de la figure, & </s> <s xml:id="echoid-s1114" xml:space="preserve">mener des paralleles <lb/>à ſes côtez.</s> <s xml:id="echoid-s1115" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div139" type="section" level="1" n="36"> <head xml:id="echoid-head63" style="it" xml:space="preserve">Reduire la figure par l'échelle.</head> <p> <s xml:id="echoid-s1116" xml:space="preserve">MEſurez tous les côtez de la figure propoſée ABCDE avec ſon <lb/> <anchor type="note" xlink:label="note-037-03a" xlink:href="note-037-03"/> échelle GH; </s> <s xml:id="echoid-s1117" xml:space="preserve">ayez une échelle plus petite KL qui contienne <lb/>autant de parties égales que la grande. </s> <s xml:id="echoid-s1118" xml:space="preserve">Faites le côté a b d'autant <lb/>de parties de la petite échelle, que le côté A B en contient de la <lb/>grande. </s> <s xml:id="echoid-s1119" xml:space="preserve">Faites b c d'autant de parties que BC, a c d'autant que A C, <lb/>& </s> <s xml:id="echoid-s1120" xml:space="preserve">ainſi des autres côtez, vous aurez votre figure réduite en petit.</s> <s xml:id="echoid-s1121" xml:space="preserve"/> </p> <div xml:id="echoid-div139" type="float" level="2" n="1"> <note position="right" xlink:label="note-037-03" xlink:href="note-037-03a" xml:space="preserve">Fig. 10.</note> </div> <p> <s xml:id="echoid-s1122" xml:space="preserve">Pour la réduire de petit en grand, on fera une échelle plus grande <lb/>que celle de la figure propoſée, & </s> <s xml:id="echoid-s1123" xml:space="preserve">le reſte ſe fera de la même maniere.</s> <s xml:id="echoid-s1124" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div141" type="section" level="1" n="37"> <head xml:id="echoid-head64" style="it" xml:space="preserve">Reduire les Plans par l'Angle de proportion.</head> <p> <s xml:id="echoid-s1125" xml:space="preserve">SOit la figure propoſée ABCDE, qu'il faut diminuer en même <lb/> <anchor type="note" xlink:label="note-037-04a" xlink:href="note-037-04"/> proportion que la ligne AB eſt à la ligne ab.</s> <s xml:id="echoid-s1126" xml:space="preserve"/> </p> <div xml:id="echoid-div141" type="float" level="2" n="1"> <note position="right" xlink:label="note-037-04" xlink:href="note-037-04a" xml:space="preserve">Fig. 11.</note> </div> <pb o="24" file="038" n="38" rhead="USAGES DES PREMIERS"/> <p> <s xml:id="echoid-s1127" xml:space="preserve">Tirez la ligne indefinie GH, prenez la grandeur AB, & </s> <s xml:id="echoid-s1128" xml:space="preserve">la portez <lb/>de G en H; </s> <s xml:id="echoid-s1129" xml:space="preserve">du point G décrivez l'arc HI; </s> <s xml:id="echoid-s1130" xml:space="preserve">prenez la grandeur du <lb/>côté donné a b, pour être la corde de l'arc HI, tirez la ligne GI, <lb/>l'angle IGH donnera toutes les meſures du plan qu'on s'eſt propo-<lb/>ſé de reduire; </s> <s xml:id="echoid-s1131" xml:space="preserve">car pour avoir le point C, prenez la grandeur BC, <lb/>& </s> <s xml:id="echoid-s1132" xml:space="preserve">du point G décrivez l'arc KL. </s> <s xml:id="echoid-s1133" xml:space="preserve">Prenez la corde KL, & </s> <s xml:id="echoid-s1134" xml:space="preserve">du point <lb/>b comme centre décrivez un petit arc. </s> <s xml:id="echoid-s1135" xml:space="preserve">Prenez la grandeur AC, & </s> <s xml:id="echoid-s1136" xml:space="preserve"><lb/>du point G décrivez l'arc MN, & </s> <s xml:id="echoid-s1137" xml:space="preserve">du point a décrivez un arc de <lb/>cercle qui coupera le precedent au point C, qui ſera celui qu'il faut <lb/>avoir pour tirer le petit côté bc. </s> <s xml:id="echoid-s1138" xml:space="preserve">Faites la même choſe pour tous <lb/>les autres angles & </s> <s xml:id="echoid-s1139" xml:space="preserve">côtez de la figure.</s> <s xml:id="echoid-s1140" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1141" xml:space="preserve">Si vous voulez par cette maniere réduire de petit en grand, vous <lb/>ferez la même choſe; </s> <s xml:id="echoid-s1142" xml:space="preserve">mais il faut que le côté de la figure qu'on <lb/>veut augmenter, ſoit moindre que le double de celui qui lui ré-<lb/>pond. </s> <s xml:id="echoid-s1143" xml:space="preserve">Si vous voulez, par exemple, réduire en grand la figure ab <lb/>cde, il faut que le côté AB de la grande ſoit moindre que le dou-<lb/>ble du côté a b de la petite: </s> <s xml:id="echoid-s1144" xml:space="preserve">car s'il étoit double, les deux lignes <lb/>qui doivent former l'angle IGH, ſe rencontreroient directement, <lb/>& </s> <s xml:id="echoid-s1145" xml:space="preserve">feroient une ligne droite.</s> <s xml:id="echoid-s1146" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div143" type="section" level="1" n="38"> <head xml:id="echoid-head65" style="it" xml:space="preserve">Reduire une figure par les quarreaux.</head> <p> <s xml:id="echoid-s1147" xml:space="preserve">CEtte maniere de réduire ſert particulierement pour copier une <lb/>carte, & </s> <s xml:id="echoid-s1148" xml:space="preserve">pour l'augmenter, ou diminuër.</s> <s xml:id="echoid-s1149" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1150" xml:space="preserve">Soit pour exemple la carte ABCD à reduire en petit; </s> <s xml:id="echoid-s1151" xml:space="preserve">diviſez-la <lb/> <anchor type="note" xlink:label="note-038-01a" xlink:href="note-038-01"/> par quarreaux; </s> <s xml:id="echoid-s1152" xml:space="preserve">faites une ſemblable figure abcd qui ſoit plus petite; <lb/></s> <s xml:id="echoid-s1153" xml:space="preserve">diviſez-la en autant de quarreaux, mais plus petits, & </s> <s xml:id="echoid-s1154" xml:space="preserve">deſſignez <lb/>dans chaque quarreau de la petite figure ce qui eſt en chaque quar-<lb/>reau correſpondant de la grande figure, & </s> <s xml:id="echoid-s1155" xml:space="preserve">vous aurez une carte <lb/>plus petite. </s> <s xml:id="echoid-s1156" xml:space="preserve">Plus il y aura de quarreaux, plus la figure ſera j<unsure/>uſte.</s> <s xml:id="echoid-s1157" xml:space="preserve"/> </p> <div xml:id="echoid-div143" type="float" level="2" n="1"> <note position="left" xlink:label="note-038-01" xlink:href="note-038-01a" xml:space="preserve">Fig. 12.</note> </div> </div> <div xml:id="echoid-div145" type="section" level="1" n="39"> <head xml:id="echoid-head66" xml:space="preserve">CHAPITRE, II.</head> <head xml:id="echoid-head67" style="it" xml:space="preserve">De la conſtruction & uſage de l'Equaire.</head> <p> <s xml:id="echoid-s1158" xml:space="preserve">L'Equaire eſt uninſtrument qui ſert à élever des perpendiculai-<lb/> <anchor type="note" xlink:label="note-038-02a" xlink:href="note-038-02"/> res, & </s> <s xml:id="echoid-s1159" xml:space="preserve">à connoître ſi une ligne tombe perpendiculairement <lb/>ſur une autre. </s> <s xml:id="echoid-s1160" xml:space="preserve">Elle eſt compoſée de deux regles de cuivre ou autre <lb/>métal, aſſemblées de telle maniere, qu'elles forment un angle droit. <lb/></s> <s xml:id="echoid-s1161" xml:space="preserve">Il s'en fait où les deux regles ou branches ſont attachées fixement, <lb/>& </s> <s xml:id="echoid-s1162" xml:space="preserve">d'autres qui s'ouvrent & </s> <s xml:id="echoid-s1163" xml:space="preserve">ſe ferment par le moyen d'une char-<lb/>niere qui doit être bien juſte, afin qu'elle ne vacille point, & </s> <s xml:id="echoid-s1164" xml:space="preserve">qu'el-<lb/>le conſerve toûjours ſon angle droit.</s> <s xml:id="echoid-s1165" xml:space="preserve"/> </p> <div xml:id="echoid-div145" type="float" level="2" n="1"> <note position="left" xlink:label="note-038-02" xlink:href="note-038-02a" xml:space="preserve">Fig. D. <lb/>de la III. <lb/>Planche.</note> </div> <pb o="25" file="039" n="39" rhead="INSTRUMENS. Liv. I. Chap. II."/> <p> <s xml:id="echoid-s1166" xml:space="preserve">On ajufte pour cela dans un petit canal fait à l'angle d'une des <lb/>branches de l'équaire trois charnons ou petits bouts de cylindre, <lb/>coupez bien droits, d'une longueur & </s> <s xml:id="echoid-s1167" xml:space="preserve">groſſeur convenables à la <lb/>largeur & </s> <s xml:id="echoid-s1168" xml:space="preserve">épaiſſeur de l'Equaire. </s> <s xml:id="echoid-s1169" xml:space="preserve">Ces charnons doivent être éloi-<lb/>gnez l'un de l'autre de maniere qu'ils puiſſent recevoir juſte deux <lb/>autres charnons qui ſont ajuſtez de même à l'autre branche de l'é-<lb/>quaire. </s> <s xml:id="echoid-s1170" xml:space="preserve">Ces charnons étant ainſi arrêtez, on les ſoude aux bran-<lb/>ches & </s> <s xml:id="echoid-s1171" xml:space="preserve">enſuite on les unit l'un à l'autre par le moyen d'une goupil-<lb/>le qui rempliſſe juſte le trou des charnons, afin que le mouvement <lb/>ſoit ferme.</s> <s xml:id="echoid-s1172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1173" xml:space="preserve">Il y a des équaires où l'on met un fil avec un petit plomb, pour <lb/>ſervir de niveau, c'eſt-à-dire, pour mettre un plan horiſontalement.</s> <s xml:id="echoid-s1174" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1175" xml:space="preserve">On met ſouvent ſur un des côtez de l'équaire pluſieurs meſures <lb/>ou échelles, & </s> <s xml:id="echoid-s1176" xml:space="preserve">ſur l'autre un demi-pied diviſé en ſix pouces, dont <lb/>un eſt ſubdiviſé en douze lignes. </s> <s xml:id="echoid-s1177" xml:space="preserve">On y ajoûte quelquefois plu-<lb/>ſieurs meſures étrangeres, dont on connoît le rapport avec le pied <lb/>de Paris.</s> <s xml:id="echoid-s1178" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div147" type="section" level="1" n="40"> <head xml:id="echoid-head68" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head69" style="it" xml:space="preserve">Elever d'un point donné une ligne perpendiculaire, ſur une <lb/>ligne donnée.</head> <p> <s xml:id="echoid-s1179" xml:space="preserve">SOit la ligne donnée AB, & </s> <s xml:id="echoid-s1180" xml:space="preserve">le point donné C dans la ligne ou <lb/> <anchor type="note" xlink:label="note-039-01a" xlink:href="note-039-01"/> hors la ligne.</s> <s xml:id="echoid-s1181" xml:space="preserve"/> </p> <div xml:id="echoid-div147" type="float" level="2" n="1"> <note position="right" xlink:label="note-039-01" xlink:href="note-039-01a" xml:space="preserve">V. Plan-<lb/>che. <lb/>Fig. 13.</note> </div> <p> <s xml:id="echoid-s1182" xml:space="preserve">Appliquez un des côtez de l'équaire ſur la ligne donnée, en telle <lb/>ſorte que l'autre côté touche le point donné, & </s> <s xml:id="echoid-s1183" xml:space="preserve">tirez la ligne CD, <lb/>elle ſera perpendiculaire. </s> <s xml:id="echoid-s1184" xml:space="preserve">Si l'on retourne l'équaire, en remettant <lb/>deſſus ce qui étoit deſſous, & </s> <s xml:id="echoid-s1185" xml:space="preserve">que l'on tire une autre ligne CD, on <lb/>connoitra ſi l'équaire eſt bien juſte; </s> <s xml:id="echoid-s1186" xml:space="preserve">car en ce cas ces deux lignes <lb/>tirées par le point C, ne feront qu'une ſeule & </s> <s xml:id="echoid-s1187" xml:space="preserve">même ligne.</s> <s xml:id="echoid-s1188" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div149" type="section" level="1" n="41"> <head xml:id="echoid-head70" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head71" style="it" xml:space="preserve">Connoitre ſi une ligne eſt perpendiculaire ſur une autre; c'eſt-<lb/>à-dire, ſi elles font un angle droit.</head> <p> <s xml:id="echoid-s1189" xml:space="preserve">Appliquez un des côtez de l'équaire ſur une des lignes, & </s> <s xml:id="echoid-s1190" xml:space="preserve"><lb/>voyez ſi l'autre côté correſpond juſtement à l'autre ligne, <lb/>comme on voit en la même figure. </s> <s xml:id="echoid-s1191" xml:space="preserve">Ces pratiques ſont aiſées à fai-<lb/>re, c'eſt pourquoi on n'en fait pas un long diſcours.</s> <s xml:id="echoid-s1192" xml:space="preserve"/> </p> <pb o="26" file="040" n="40" rhead="USAGES DES PREMIERS"/> </div> <div xml:id="echoid-div150" type="section" level="1" n="42"> <head xml:id="echoid-head72" xml:space="preserve">CHAPITRE III.</head> <head xml:id="echoid-head73" style="it" xml:space="preserve">De la conſtruction & des Vſages du Rapporteur.</head> <p> <s xml:id="echoid-s1193" xml:space="preserve">LE Rapporteur eſt un demi cercle diviſé en 180. </s> <s xml:id="echoid-s1194" xml:space="preserve">degrez, d'au-<lb/>tant que le cercle ſe diviſe en 360. </s> <s xml:id="echoid-s1195" xml:space="preserve">degrez, comme il a été <lb/>dit dans les définitions.</s> <s xml:id="echoid-s1196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1197" xml:space="preserve">Il doit être limé plat d'un côté, pour être mieux appliqué ſur le <lb/> <anchor type="note" xlink:label="note-040-01a" xlink:href="note-040-01"/> papier, & </s> <s xml:id="echoid-s1198" xml:space="preserve">l'autre côté doit être en talu, c'eſt-à-dire mince ſur le <lb/>bord où eſt la diviſion. </s> <s xml:id="echoid-s1199" xml:space="preserve">Le centre doit être marqué par une petite <lb/>hoche demi circulaire, afin de mieux découvrir le point où doit <lb/>aboutir la pointe de l'angle.</s> <s xml:id="echoid-s1200" xml:space="preserve"/> </p> <div xml:id="echoid-div150" type="float" level="2" n="1"> <note position="left" xlink:label="note-040-01" xlink:href="note-040-01a" xml:space="preserve">De la III. Planche. <lb/>Fig. E.</note> </div> </div> <div xml:id="echoid-div152" type="section" level="1" n="43"> <head xml:id="echoid-head74" style="it" xml:space="preserve">Methode pour faire cette diviſion.</head> <p> <s xml:id="echoid-s1201" xml:space="preserve">SUr la ligne AB & </s> <s xml:id="echoid-s1202" xml:space="preserve">du centre O, décrivez un demi cercle; </s> <s xml:id="echoid-s1203" xml:space="preserve">por-<lb/> <anchor type="note" xlink:label="note-040-02a" xlink:href="note-040-02"/> tez le raïon ou demi diametre AO autour de la circonference, <lb/>il la diviſera en trois arcs égaux de 60. </s> <s xml:id="echoid-s1204" xml:space="preserve">degrez chacun aux points C <lb/>& </s> <s xml:id="echoid-s1205" xml:space="preserve">D, parce que le raïon d'un cercle eſt contenu ſix fois en ſa cir-<lb/>conference. </s> <s xml:id="echoid-s1206" xml:space="preserve">Diviſez l'arc BC en deux également au point E, l'arc <lb/>BE ſera de 30. </s> <s xml:id="echoid-s1207" xml:space="preserve">degrez, & </s> <s xml:id="echoid-s1208" xml:space="preserve">tournant cette ouverture autour du de-<lb/>mi cercle, il ſera diviſé en ſix arcs égaux. </s> <s xml:id="echoid-s1209" xml:space="preserve">Diviſez-les encore en <lb/>trois parties égales, chacune ſera de dix degrez. </s> <s xml:id="echoid-s1210" xml:space="preserve">Diviſez chaque <lb/>dixaine en deux, vous aurez des arcs de cinq degrez chacun; </s> <s xml:id="echoid-s1211" xml:space="preserve">& </s> <s xml:id="echoid-s1212" xml:space="preserve"><lb/>enfin ſubdiviſant chacun de ces derniers arcs en cinq, tout le de-<lb/>mi cercle ſera diviſé en 180. </s> <s xml:id="echoid-s1213" xml:space="preserve">degrez.</s> <s xml:id="echoid-s1214" xml:space="preserve"/> </p> <div xml:id="echoid-div152" type="float" level="2" n="1"> <note position="left" xlink:label="note-040-02" xlink:href="note-040-02a" xml:space="preserve">De la III. Planche. Fig. E.</note> </div> <p> <s xml:id="echoid-s1215" xml:space="preserve">C'eſt de la même maniere qu'on peut diviſer tout le cercle en <lb/>360. </s> <s xml:id="echoid-s1216" xml:space="preserve">degrez; </s> <s xml:id="echoid-s1217" xml:space="preserve">nous en parlerons encore dans la ſuite. </s> <s xml:id="echoid-s1218" xml:space="preserve">On fait auſſi <lb/>quelquefois des rapporteurs de corne; </s> <s xml:id="echoid-s1219" xml:space="preserve">il ſont aſſez commodes, en <lb/>ce qu'ils ſont tranſparens; </s> <s xml:id="echoid-s1220" xml:space="preserve">mais il faut les tenir dans un livre, quand <lb/>on ne s'en ſert pas, afin que la corne ne ſe ride point.</s> <s xml:id="echoid-s1221" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div154" type="section" level="1" n="44"> <head xml:id="echoid-head75" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head76" style="it" xml:space="preserve">Faire des angles de telle grandeur que l'on veut.</head> <p> <s xml:id="echoid-s1222" xml:space="preserve">SOit, par exemple, propoſé de faire au point A un angle de 50 <lb/> <anchor type="note" xlink:label="note-040-03a" xlink:href="note-040-03"/> degrez ſur la ligne CAB.</s> <s xml:id="echoid-s1223" xml:space="preserve"/> </p> <div xml:id="echoid-div154" type="float" level="2" n="1"> <note position="left" xlink:label="note-040-03" xlink:href="note-040-03a" xml:space="preserve">De la V. Planche. Fig. 14.</note> </div> <p> <s xml:id="echoid-s1224" xml:space="preserve">Mettez le centre du rapporteur qui eſt marqué par une petite ca-<lb/>vité ſur le point A, en telle ſorte que le diametre du demi cercle <lb/>ſoit ſur la ligne AB. </s> <s xml:id="echoid-s1225" xml:space="preserve">Marquez un point de craïon vis-à-vis le cin-<lb/>quantiéme degré, & </s> <s xml:id="echoid-s1226" xml:space="preserve">de ce point tirez au point A une ligne, elle <lb/>fera avec la ligne AB un angle de cinquante degrez.</s> <s xml:id="echoid-s1227" xml:space="preserve"/> </p> <pb o="27" file="041" n="41" rhead="INSTRUMENS. Liv. I. Chap. III."/> </div> <div xml:id="echoid-div156" type="section" level="1" n="45"> <head xml:id="echoid-head77" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head78" style="it" xml:space="preserve">L'Angle BAD étant donné, ſçavoir ce qu'il contient de <lb/>degrez.</head> <p> <s xml:id="echoid-s1228" xml:space="preserve">MEttez le centre du repporteur au point A, & </s> <s xml:id="echoid-s1229" xml:space="preserve">ſon rayon ſurle <lb/> <anchor type="note" xlink:label="note-041-01a" xlink:href="note-041-01"/> côté BC; </s> <s xml:id="echoid-s1230" xml:space="preserve">remarquez à quel degré la ligne AD coupe la cir-<lb/>conference, vous connoîtrez que l'angle BAD eſt de 50. </s> <s xml:id="echoid-s1231" xml:space="preserve">degrez.</s> <s xml:id="echoid-s1232" xml:space="preserve"/> </p> <div xml:id="echoid-div156" type="float" level="2" n="1"> <note position="right" xlink:label="note-041-01" xlink:href="note-041-01a" xml:space="preserve">Même <lb/>figure.</note> </div> </div> <div xml:id="echoid-div158" type="section" level="1" n="46"> <head xml:id="echoid-head79" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head80" style="it" xml:space="preserve">Pour inſcrire dans un cercle tout Polygone regulier.</head> <p> <s xml:id="echoid-s1233" xml:space="preserve">POur cette operation, il faut connoître de combien de degrez eſt <lb/> <anchor type="note" xlink:label="note-041-02a" xlink:href="note-041-02"/> l'angle du centre de chaque polygone regulier: </s> <s xml:id="echoid-s1234" xml:space="preserve">ce qui ſe trouve <lb/>en diviſant 360 degrez de la circonference du cercle par le nombre <lb/>des côtez du polygone propoſé. </s> <s xml:id="echoid-s1235" xml:space="preserve">Ainſi par exemple, diviſant 360 <lb/>par 5, le quotien 72 fait voir que l'angle du centre d'un pentagone <lb/>eſt de 72 degrez. </s> <s xml:id="echoid-s1236" xml:space="preserve">En diviſant 360 par 8, le quotien 45 fait con-<lb/>noître que l'angle du centre d'un octogone eſt de 45 degrez, <lb/>& </s> <s xml:id="echoid-s1237" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s1238" xml:space="preserve"/> </p> <div xml:id="echoid-div158" type="float" level="2" n="1"> <note position="right" xlink:label="note-041-02" xlink:href="note-041-02a" xml:space="preserve">Fig. 15.</note> </div> <p> <s xml:id="echoid-s1239" xml:space="preserve">En connoiſſant l'angle du centre, on trouve l'angle formé par les <lb/>deux côtez du polygone, en ôtant de 180 degrez l'angle du centre. <lb/></s> <s xml:id="echoid-s1240" xml:space="preserve">Ainſi ôtant de 180 degrez l'angle du centre d'un pentagone qui eſt <lb/>de 72 degrez, reſte 108. </s> <s xml:id="echoid-s1241" xml:space="preserve">pour l'angle du polygone, c'eſt-à-dire, <lb/>l'angle formé par les deux côtez dudit pentagone.</s> <s xml:id="echoid-s1242" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1243" xml:space="preserve">De même ôtant de 180 l'angle du centre d'un octogone, quieſt <lb/>45 degrez, reſtent 135 pour ſon angle de polygone.</s> <s xml:id="echoid-s1244" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1245" xml:space="preserve">C'eſt pourquoy ſi l'on propoſe d'inſcrire un pentagone dans un <lb/>cercle, mettez le centre du rapporteur au centre du cercle, & </s> <s xml:id="echoid-s1246" xml:space="preserve">fai-<lb/>ſant convenir le diametre du rapporteur avec le diametre du cercle, <lb/>marquez un point vis-à-vis les 72 degrez de la circonference du <lb/>rapporteur, lequel étant ôté, tirez une ligne du centre du cercle <lb/>par ce point que vous avez marqué, juſqu'à ce qu'elle coupe la cir-<lb/>conference au point C. </s> <s xml:id="echoid-s1247" xml:space="preserve">Prenez avec le compas l'ouverture de l'arc <lb/>BC, elle diviſera le cercle en cinq parties égales, & </s> <s xml:id="echoid-s1248" xml:space="preserve">tirant cinq <lb/>lignes le pentagone ſera inſcrit.</s> <s xml:id="echoid-s1249" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1250" xml:space="preserve">S'il s'agit de faire un eptagone, diviſez trois cens ſoixante par <lb/>fept, le quotien 51 degrez, & </s> <s xml:id="echoid-s1251" xml:space="preserve">trois ſeptiémes, fait voir que l'angle <lb/>du centre doit être de 51. </s> <s xml:id="echoid-s1252" xml:space="preserve">& </s> <s xml:id="echoid-s1253" xml:space="preserve">demi à peu près. </s> <s xml:id="echoid-s1254" xml:space="preserve">C'eſt pourquoy <lb/>ayant placé le rapporteur au centre & </s> <s xml:id="echoid-s1255" xml:space="preserve">ſur le diametre du cercle, <lb/>marquez un point vis-à-vis 51 degrez & </s> <s xml:id="echoid-s1256" xml:space="preserve">demi de la circonference <lb/>du rapporteur, la ligne tirée du centre du cerle par ce point mar-<lb/> <pb o="28" file="042" n="42" rhead="USAGES DES PREM. INSTRUM. Liv. I. Chap. III."/> quera ſur la circonference la ſeptiéme partie du cercle; </s> <s xml:id="echoid-s1257" xml:space="preserve">après quoy <lb/>il ſera facile d'achever l'eptagone.</s> <s xml:id="echoid-s1258" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1259" xml:space="preserve">Il y a des rapporteurs, ſur leſquels ſont gravez des nombres qui <lb/>marquent les polygones reguliers, pour épargner la peine de faire <lb/>les diviſions. </s> <s xml:id="echoid-s1260" xml:space="preserve">Le nombre cinq qui ſignifie le pentagone, eſt marqué <lb/>vis-à-vis 72 degrez de la circonference, le nombre ſix qui ſignifie <lb/>l'exagone eſt marqué vis-à-vis 60 degrez; </s> <s xml:id="echoid-s1261" xml:space="preserve">le nombre ſept qui ſignifie <lb/>l'eptagone, eſt marqué vis-à-vis les 51 degrez & </s> <s xml:id="echoid-s1262" xml:space="preserve">demi, &</s> <s xml:id="echoid-s1263" xml:space="preserve">c.</s> <s xml:id="echoid-s1264" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div160" type="section" level="1" n="47"> <head xml:id="echoid-head81" xml:space="preserve">USAGE IV.</head> <head xml:id="echoid-head82" style="it" xml:space="preserve">Pour décrire ſur une ligne donneé tout polygone regulier.</head> <p> <s xml:id="echoid-s1265" xml:space="preserve">SOit la ligne donnée CD, ſur laquelle on veut décrire un pen-<lb/> <anchor type="note" xlink:label="note-042-01a" xlink:href="note-042-01"/> tagone.</s> <s xml:id="echoid-s1266" xml:space="preserve"/> </p> <div xml:id="echoid-div160" type="float" level="2" n="1"> <note position="left" xlink:label="note-042-01" xlink:href="note-042-01a" xml:space="preserve">Fig. 16.</note> </div> <p> <s xml:id="echoid-s1267" xml:space="preserve">Nous avons enſeigné dans l'uſage precedent le moyen de con-<lb/>noitre les angles de tous les polygones reguliers; </s> <s xml:id="echoid-s1268" xml:space="preserve">& </s> <s xml:id="echoid-s1269" xml:space="preserve">comme celui <lb/>que font les deux côtez du pentagone eſt de 108 degrez, ſa moitié <lb/>54 ſera le demi angle du pentagone, & </s> <s xml:id="echoid-s1270" xml:space="preserve">ſervira à le décrire en la <lb/>maniere ſuivante.</s> <s xml:id="echoid-s1271" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1272" xml:space="preserve">Poſez le diametre du rapporteur ſur la ligne CD, & </s> <s xml:id="echoid-s1273" xml:space="preserve">ſon centre à <lb/> <anchor type="note" xlink:label="note-042-02a" xlink:href="note-042-02"/> l'extremité D. </s> <s xml:id="echoid-s1274" xml:space="preserve">Marquez un point vis-à-vis les 54 degrez de ſa cir-<lb/>conference, & </s> <s xml:id="echoid-s1275" xml:space="preserve">tirez la ligne DF faiſant un angle de 54 degrezavec la <lb/>ligne CD. </s> <s xml:id="echoid-s1276" xml:space="preserve">Tranſportez le centre du rapporteur à l'autre extremi-<lb/>té C, pour y faire pareillement un angle de 54 degrez, en tirant <lb/>la ligne CF; </s> <s xml:id="echoid-s1277" xml:space="preserve">le point F où ces deux lignes ſe rencontrent, ſera le <lb/>centre d'un cercle que vous tracerez en ouvrant le compas de la <lb/>grandeur CF. </s> <s xml:id="echoid-s1278" xml:space="preserve">Prenez enſuite la grandeur de la ligne donnée CD, <lb/>pour diviſer en cinq la circonference du cercle, & </s> <s xml:id="echoid-s1279" xml:space="preserve">tirant cinq <lb/>lignes, le pentagone ſera décrit.</s> <s xml:id="echoid-s1280" xml:space="preserve"/> </p> <div xml:id="echoid-div161" type="float" level="2" n="2"> <note position="left" xlink:label="note-042-02" xlink:href="note-042-02a" xml:space="preserve">Fig. 16.</note> </div> <p> <s xml:id="echoid-s1281" xml:space="preserve">Si l'on propoſe de décrire un octogone ſur une ligne donnée, <lb/>ayant reconnu que ſon angle de poligone eſt de 135 degrez, pre-<lb/>nez-en la moitié, 67 degrez & </s> <s xml:id="echoid-s1282" xml:space="preserve">demi, & </s> <s xml:id="echoid-s1283" xml:space="preserve">faites un angle de pareil <lb/>nombre de degrez à chaque extremité de la ligne donnée, pour y <lb/>faire un triangle Iſocele, dont le ſommet ſera le centre d'une cir-<lb/>conference, que vous diviſerez en huit, en y appliquant huit fois <lb/>la ligne donnée, & </s> <s xml:id="echoid-s1284" xml:space="preserve">l'octogone ſera formé.</s> <s xml:id="echoid-s1285" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1286" xml:space="preserve">On peut faire, avec les inſtrumens dont nous venons de parler, <lb/>quantité d'autres operations, ſuivant les differens ſujets; </s> <s xml:id="echoid-s1287" xml:space="preserve">mais on <lb/>s'eſt contenté d'y rapporter les plus utiles, & </s> <s xml:id="echoid-s1288" xml:space="preserve">les plus ordinaires.</s> <s xml:id="echoid-s1289" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div163" type="section" level="1" n="48"> <head xml:id="echoid-head83" style="it" xml:space="preserve">Fin du premier Livre.</head> <pb o="29" file="043" n="43"/> <figure> <image file="043-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/043-01"/> </figure> </div> <div xml:id="echoid-div164" type="section" level="1" n="49"> <head xml:id="echoid-head84" xml:space="preserve">DELA <lb/>CONSTRUCTION <lb/>ET DES USAGES <lb/>DUCOMPAS <lb/>DEPROPORTION.</head> <head xml:id="echoid-head85" style="it" xml:space="preserve">LIVRE SECOND.</head> <head xml:id="echoid-head86" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head87" style="it" xml:space="preserve">De la Conſtruction du Compas de proportion.</head> <p> <s xml:id="echoid-s1290" xml:space="preserve">LE Compas de proportion eſt un Inſtrument de Mathema-<lb/> <anchor type="note" xlink:label="note-043-01a" xlink:href="note-043-01"/> tique, ainſi nommé, parce qu'il ſert à connoître les pro-<lb/>portions entre les quantitez de même eſpece, comme en-<lb/>tre une ligne & </s> <s xml:id="echoid-s1291" xml:space="preserve">une autre ligne, entre une ſurface & </s> <s xml:id="echoid-s1292" xml:space="preserve">une <lb/>autre ſurface, entre un ſolide & </s> <s xml:id="echoid-s1293" xml:space="preserve">un autre ſolide, &</s> <s xml:id="echoid-s1294" xml:space="preserve">c.</s> <s xml:id="echoid-s1295" xml:space="preserve"/> </p> <div xml:id="echoid-div164" type="float" level="2" n="1"> <note position="right" xlink:label="note-043-01" xlink:href="note-043-01a" xml:space="preserve">VI <lb/>Plancbe.</note> </div> <p> <s xml:id="echoid-s1296" xml:space="preserve">Il eſt fair de deux Regles égales de cuivre, d'argent ou d'autre ma-<lb/>tiere ſolide, jointes enſemble par un clou & </s> <s xml:id="echoid-s1297" xml:space="preserve">une charniere, tellement <lb/>travaillée, que le mouvementen ſoit égal & </s> <s xml:id="echoid-s1298" xml:space="preserve">uniforme; </s> <s xml:id="echoid-s1299" xml:space="preserve">ce qui ſe fait <lb/>en fendant avec une ſcie la regle où eſt la tête, environ un pouce de <lb/>long, pour y ajuſter une lame de laiton qu'on rive fortement par le <lb/>moyen du clou. </s> <s xml:id="echoid-s1300" xml:space="preserve">On arrondit enſuite la tête, en limant tout ce qui <lb/>déborde; </s> <s xml:id="echoid-s1301" xml:space="preserve">en ſorte que le ſimple & </s> <s xml:id="echoid-s1302" xml:space="preserve">la tête ſoient à l'uni l'un de l'au-<lb/>tre. </s> <s xml:id="echoid-s1303" xml:space="preserve">Ils'agit preſentement de trouver le centre du clou. </s> <s xml:id="echoid-s1304" xml:space="preserve">Il faut pour <lb/>cela mettre une pointe de compas au bas de la lame qui ſert de <lb/>charniere; </s> <s xml:id="echoid-s1305" xml:space="preserve">puis marquer quatre ſections avec l'autre pointe du com-<lb/>pas au milieu du clou en tournant le ſimple de la charniere à quatre <lb/>côtez oppoſez. </s> <s xml:id="echoid-s1306" xml:space="preserve">Le point du milieu ſera le centre du clou, & </s> <s xml:id="echoid-s1307" xml:space="preserve">par conſe-<lb/>quent celuy du compas de proportion. </s> <s xml:id="echoid-s1308" xml:space="preserve">On tire enſuite une ligne du <lb/>centre au long de la regle, pour limer juſte l'excedent, & </s> <s xml:id="echoid-s1309" xml:space="preserve">dreſſer bien <lb/> <pb o="30" file="044" n="44" rhead="CONSTRUCTION ET USAGES"/> droite ladite regle, & </s> <s xml:id="echoid-s1310" xml:space="preserve">c'eſt ainſi qu'on met le compas de proportion <lb/>au centre; </s> <s xml:id="echoid-s1311" xml:space="preserve">l'autre regle étant auſſi dreſſée en dedans, & </s> <s xml:id="echoid-s1312" xml:space="preserve">fen-<lb/>duë pour recevoir le ſimple de la charniere, on creuſe le bout en de-<lb/>mi cercle concave, de maniere qu'il joigne bien autour de la tête, <lb/>puis on rive le ſimple à cette regle avcc trois ou quatre petits clous, <lb/>afin que ces deux regles, que l'on nomme les jambes du compas de <lb/>proportion, ſe puiſſent ouvrir & </s> <s xml:id="echoid-s1313" xml:space="preserve">fermer facilement, & </s> <s xml:id="echoid-s1314" xml:space="preserve">reſter a telle <lb/>ouverture que l'on peut en avoir beſoin pour mettre les uſages en <lb/>pratique. </s> <s xml:id="echoid-s1315" xml:space="preserve">Mais il faut avoir bien ſoin, en le conſtruiſant, que les <lb/>jambes ſoient limées bien plates, & </s> <s xml:id="echoid-s1316" xml:space="preserve">ne faſſent pas ce qu'on appelle <lb/>l'aîle de moulin. </s> <s xml:id="echoid-s1317" xml:space="preserve">Il faut auſſi prendre garde que le compas ſoit bien <lb/>au centre, c'eſt-à-dire qu'étant ouvert entierement, il ne faſſe qu'u-<lb/>ne ligne droite en dedans comme en dehors, & </s> <s xml:id="echoid-s1318" xml:space="preserve">que les jambes <lb/>ſoient bien égales d'épaiſſeur & </s> <s xml:id="echoid-s1319" xml:space="preserve">de largeur; </s> <s xml:id="echoid-s1320" xml:space="preserve">en un mot qu'il ſoit <lb/>bien droit en tous ſens. </s> <s xml:id="echoid-s1321" xml:space="preserve">La longueur & </s> <s xml:id="echoid-s1322" xml:space="preserve">largeur deſdites regles n'eſt <lb/>pas déterminée, mais on donne pour l'ordinaire ſix pouces de long, <lb/>ſix à ſept lignes de large, & </s> <s xml:id="echoid-s1323" xml:space="preserve">environ deux lignes d'épaiſſeur à chaque <lb/>jambe des compas de proportion que l'on deſtine pour travailler <lb/>dans le cabinet. </s> <s xml:id="echoid-s1324" xml:space="preserve">On en fait de plus petits, pour être commodément <lb/>portez dans la poche, comme auſſi de plus grands, pour travailler <lb/>ſur le terrain, dont on proportionne la largeur & </s> <s xml:id="echoid-s1325" xml:space="preserve">épaiſſeur.</s> <s xml:id="echoid-s1326" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1327" xml:space="preserve">On a coutume d'y tracer ſix ſortes de lignes; </s> <s xml:id="echoid-s1328" xml:space="preserve">ſçavoir la ligne des <lb/>parties égales, celle des plans & </s> <s xml:id="echoid-s1329" xml:space="preserve">celle des poligones d'un côté; </s> <s xml:id="echoid-s1330" xml:space="preserve">la li <lb/>gne des cordes, celle des ſolides & </s> <s xml:id="echoid-s1331" xml:space="preserve">celle des metaux de l'autre côté <lb/>des jambes dudit compas, en la maniere que nous allons expliquer.</s> <s xml:id="echoid-s1332" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1333" xml:space="preserve">On met encore ordinairement ſur le bord du compas de propor-<lb/>tion d'un côté un ligne diviſée, qui ſert à connoître le calibre des <lb/>canons, & </s> <s xml:id="echoid-s1334" xml:space="preserve">de l'autre côté une ligne qui ſert à connoître le diame-<lb/>tre, & </s> <s xml:id="echoid-s1335" xml:space="preserve">le poids des boulets de fer, depuis un quart juſqu'à ſoixante-<lb/>quatre livres, dont nous donnerons la conſtruction & </s> <s xml:id="echoid-s1336" xml:space="preserve">les uſages, <lb/>en parlant des inſtrumens pour l'artillerie.</s> <s xml:id="echoid-s1337" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div166" type="section" level="1" n="50"> <head xml:id="echoid-head88" xml:space="preserve">SECTION I.</head> <head xml:id="echoid-head89" style="it" xml:space="preserve">De la ligne des parties égales.</head> <p> <s xml:id="echoid-s1338" xml:space="preserve">CEtte ligne eſt ainſi nommée, parce qu'elle eſt diviſée en par-<lb/>ties égales, dont le nombre eſt ordinairement 200, lorſqu'elle <lb/>eſt de ſix pouces de long.</s> <s xml:id="echoid-s1339" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1340" xml:space="preserve">A yant tiré ſur une des ſurfaces de chaque jambe les lignes égales <lb/> <anchor type="note" xlink:label="note-044-01a" xlink:href="note-044-01"/> AB depuis le point A, qui eſt le centre de la charniere du compas, <lb/>& </s> <s xml:id="echoid-s1341" xml:space="preserve">par conſequent le centre de ſon mouvement, qui a été trouvé <lb/> <pb o="31" file="045" n="45" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. I."/> de la maniere que nous avons dit ci-devant, excepté qu'on fait les <lb/>ſections ſur la tête, en poſant le compas au bout de la branche du <lb/>ſimple; </s> <s xml:id="echoid-s1342" xml:space="preserve">pour la conſtruire, diviſez premierment les lignes AB en <lb/>deux parties égales, qui ſeront par conſequent de 100 parties cha-<lb/>cune. </s> <s xml:id="echoid-s1343" xml:space="preserve">Diviſez encore chacune de ces deux parties égales en deux <lb/>autres, dont chacune ſera de 50. </s> <s xml:id="echoid-s1344" xml:space="preserve">Diviſez enſuite chacune de ces <lb/>parties en cinq, dont chacune vaudra dix, & </s> <s xml:id="echoid-s1345" xml:space="preserve">chacune de ces nou-<lb/>velles parties en deux; </s> <s xml:id="echoid-s1346" xml:space="preserve">& </s> <s xml:id="echoid-s1347" xml:space="preserve">enfin chacune de ces dernieres en cinq par-<lb/>ties égales: </s> <s xml:id="echoid-s1348" xml:space="preserve">& </s> <s xml:id="echoid-s1349" xml:space="preserve">par ce moyen leſdites lignes ſe trouveront diviſées <lb/>en deux cens parties égales, que vous diſtinguerez de cinq en cinq <lb/>par des petites lignes, & </s> <s xml:id="echoid-s1350" xml:space="preserve">y mettrez les chifres de dix en dix ſeule-<lb/>ment, en commençant du centre A, juſqu'à l'autre extremité, où <lb/>vous mettrez le nombre 200.</s> <s xml:id="echoid-s1351" xml:space="preserve"/> </p> <div xml:id="echoid-div166" type="float" level="2" n="1"> <note position="left" xlink:label="note-044-01" xlink:href="note-044-01a" xml:space="preserve">VI. <lb/>Planche. <lb/>Fig. I.</note> </div> <p> <s xml:id="echoid-s1352" xml:space="preserve">Comme les deux autres lignes, qui ſont à tracer ſur les mêmes <lb/>ſurfaces de chaque jambe, doivent toutes aboutir au même centre <lb/>A, il faut que l'extremité B de la ligne des parties égales, ſoit tirée <lb/>le plus près que l'on poura des bords exterieurs de chaque jam be, <lb/>afin d'avoir place pour tirer la ligne des plans au milieu de la largeur <lb/>deſdites jambes, & </s> <s xml:id="echoid-s1353" xml:space="preserve">la ligne des polygones vers leurs bords inte-<lb/>rieurs; </s> <s xml:id="echoid-s1354" xml:space="preserve">mais il faut bien prendre garde, en tirant ces lignes, que <lb/>chacune des correſpondantes ſoit également diſtante des bords in-<lb/>terieurs de chaque jambe: </s> <s xml:id="echoid-s1355" xml:space="preserve">le tout, comme il eſt aiſé de voir en la <lb/>planche ſixiéme.</s> <s xml:id="echoid-s1356" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div168" type="section" level="1" n="51"> <head xml:id="echoid-head90" xml:space="preserve">SECTION II.</head> <head xml:id="echoid-head91" style="it" xml:space="preserve">De la ligne des Plans.</head> <p> <s xml:id="echoid-s1357" xml:space="preserve">CEtte ligne eſt ainſi nommée, parce qu'elle comprend les côtez <lb/> <anchor type="note" xlink:label="note-045-01a" xlink:href="note-045-01"/> homologues d'un certain nombre de plans ſemblables, multi-<lb/>ples du plus petit, commençant par le centre A, c'eſt-à-dire, dont <lb/>les ſurfaces contiennent deux fois, trois fois, quatre fois, &</s> <s xml:id="echoid-s1358" xml:space="preserve">c. </s> <s xml:id="echoid-s1359" xml:space="preserve">celle <lb/>du plus petit plan depuis l'unité, ſuivant l'ordre naturel des nom-<lb/>bres, juſqu'à ſoixante-quatre, qui eſt ordinairement le plus grand <lb/>terme des diviſions, que l'on marque ſur ladite ligne marquée AD.</s> <s xml:id="echoid-s1360" xml:space="preserve"/> </p> <div xml:id="echoid-div168" type="float" level="2" n="1"> <note position="right" xlink:label="note-045-01" xlink:href="note-045-01a" xml:space="preserve">Même <lb/>Figure.</note> </div> <p> <s xml:id="echoid-s1361" xml:space="preserve">La diviſion de cette ligne ſe peut faire en deux manieres fondées <lb/>ſur la vingtiéme propoſition du ſixiéme livre d'Euclide, qui dé-<lb/>montre que les plans ſemblables ſont entr'eux comme les quarrez <lb/>de leurs côtez homologues.</s> <s xml:id="echoid-s1362" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1363" xml:space="preserve">La premiere maniere ſe fait à l'aide des nombres, & </s> <s xml:id="echoid-s1364" xml:space="preserve">la ſeconde <lb/>maniere ſans nombres, comme nous allons l'expliquer.</s> <s xml:id="echoid-s1365" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1366" xml:space="preserve">A yant tiré la ligne AC depuis le centre A juſqu'aux extremitez <lb/> <pb o="32" file="046" n="46" rhead="CONSTRUCTION ET USAGE"/> C des jambes du compas de proportion, diviſez-la premierement <lb/>en huit parties égales, dont la premiere du côté du centre A, qui <lb/>repreſente le côté du plus petit plan, n'a pas beſoin d'être tracée. <lb/></s> <s xml:id="echoid-s1367" xml:space="preserve">La ſeconde, qui eſt double de la premiere, eſt le côté d'un plan <lb/>quatre fois plus grand que le premier petit plan, parce que le quarré <lb/>de deux eſt quatre.</s> <s xml:id="echoid-s1368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1369" xml:space="preserve">La troiſiéme diviſion, qui contient trois fois la premiere, eſt le <lb/>côté d'un plan neuf fois plus grand que le premier, parce que le <lb/>quarré de trois eſt neuf.</s> <s xml:id="echoid-s1370" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1371" xml:space="preserve">La quatriéme diviſion, qui contient quatre fois la premiere, qui <lb/>par conſequent eſt la moitié de toute ladite ligne, eſt le côté d'un <lb/>plan ſeize fois plus grand que le premier, parce que le quarré de <lb/>quatre eſt ſeize. </s> <s xml:id="echoid-s1372" xml:space="preserve">Enfin, pour abreger, la huitiéme & </s> <s xml:id="echoid-s1373" xml:space="preserve">derniere divi-<lb/>ſion, qui contient huit fois le côté du petit plan, eſt le côté d'un <lb/>plan ſemblable, ſoixante-quatre fois plus grand, parce que le quar-<lb/>ré de huit eſt ſoixante-quatre.</s> <s xml:id="echoid-s1374" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1375" xml:space="preserve">Il y a un peu plus de façon à trouver les côtez homologues des <lb/>plans doubles, triples, quintuples, &</s> <s xml:id="echoid-s1376" xml:space="preserve">c. </s> <s xml:id="echoid-s1377" xml:space="preserve">du plus petit plan. </s> <s xml:id="echoid-s1378" xml:space="preserve">Suivant <lb/>la premiere methode, qui ſe fait par les nombres, il faut avoir une <lb/>échelle diviſée en mille parties égales, comme celle qui eſt repre-<lb/>ſentée en la même planche, dont nous avons ci-devant donné la <lb/>conſtruction en la page 15,<emph style="sub">me</emph>.</s> <s xml:id="echoid-s1379" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1380" xml:space="preserve">Ladite échelle doit être égale à la ligne entiere AC; </s> <s xml:id="echoid-s1381" xml:space="preserve">& </s> <s xml:id="echoid-s1382" xml:space="preserve">comme le <lb/> <anchor type="note" xlink:label="note-046-01a" xlink:href="note-046-01"/> côté du plus petit plan eſt la huitiéme partie de ladite ligne, il ſera <lb/>par conſequent de 125, qui eſt la huitiéme partie de 1000. </s> <s xml:id="echoid-s1383" xml:space="preserve">Enſuite, <lb/>pour avoir en nombres le côté d'un plan double du plus petit, il faut <lb/>chercher la racine quarrée d'un nombre double du quarréde 125. <lb/></s> <s xml:id="echoid-s1384" xml:space="preserve">Ce quarré eſt 15625, le double eſt 31250, & </s> <s xml:id="echoid-s1385" xml:space="preserve">la racine quarrée de ce <lb/>nombre, qui eſt environ 177, eſt le côté d'un plan double du plus <lb/>petit plan, dont le côté a été ſuppoſé de 125. </s> <s xml:id="echoid-s1386" xml:space="preserve">De même pour avoir <lb/>le côté d'un plan qui contienne trois fois le premier, il faut cher-<lb/>cher la racine d'un nombre qui contienne trois fois le quarré de 125. </s> <s xml:id="echoid-s1387" xml:space="preserve"><lb/>Ce nombre eſt 46875, & </s> <s xml:id="echoid-s1388" xml:space="preserve">ſa racine qui eſt environ 216, eſt le côté <lb/>d'un plan triple du plus petit, & </s> <s xml:id="echoid-s1389" xml:space="preserve">ainſi des autres. </s> <s xml:id="echoid-s1390" xml:space="preserve">C'eſt pourquoi en <lb/>portant depuis le centre A ſur la ligne des plans, 177 parties de la-<lb/>dite échelle, on aura la longueur du côté d'un plan double du plus <lb/>petit. </s> <s xml:id="echoid-s1391" xml:space="preserve">Portant enſuite 216 parties de la même echelle depuis ledit <lb/>centre A, on aura la longueur du côté d'un plan qui contiendra <lb/>trois fois ce plus petit plan.</s> <s xml:id="echoid-s1392" xml:space="preserve"/> </p> <div xml:id="echoid-div169" type="float" level="2" n="2"> <note position="left" xlink:label="note-046-01" xlink:href="note-046-01a" xml:space="preserve">VI. <lb/>Planche. <lb/>Figure 2.</note> </div> <p> <s xml:id="echoid-s1393" xml:space="preserve">C'eſt par ce moyen que l'on a calculé la table ſuivante, qui mar-<lb/> <pb o="33" file="047" n="47" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. I."/> que le nombre des parties égales que contiennent les côtez homolo-<lb/>gues de tous les plans ſemblables, doubles, triples, quadruples, &</s> <s xml:id="echoid-s1394" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s1395" xml:space="preserve">d'un plan dont le côté eſt 125 juſqu'au 64 plan, c'eſt-à-dire, quile <lb/>contient ſoixante-quatre fois, & </s> <s xml:id="echoid-s1396" xml:space="preserve">dont le côté eſt de mille parties.</s> <s xml:id="echoid-s1397" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/> ####### Table pour la ligne des Plans. <lb/>1 125 # # 17 515 # # 33 718 # # 49 875 <lb/>2 177 # # 18 530 # # 34 729 # # 50 884 <lb/>3 216 # # 19 545 # # 35 739 # # 51 892 <lb/>4 250 # # 20 559 # # 36 750 # # 52 901 <lb/>5 279 # # 21 573 # # 37 760 # # 53 910 <lb/>6 306 # # 22 586 # # 38 770 # # 54 918 <lb/>7 330 # # 23 599 # # 39 780 # # 55 927 <lb/>8 353 # # 24 612 # # 40 790 # # 56 935 <lb/>9 375 # # 25 625 # # 41 800 # # 57 944 <lb/>10 395 # # 26 637 # # 42 810 # # 58 952 <lb/>11 414 # # 27 650 # # 43 819 # # 59 960 <lb/>12 433 # # 28 661 # # 44 829 # # 60 968 <lb/>13 450 # # 29 673 # # 45 839 # # 61 976 <lb/>14 467 # # 30 684 # # 46 848 # # 62 984 <lb/>15 484 # # 31 696 # # 47 857 # # 63 992 <lb/>16 500 # # 32 707 # # 48 866 # # 64 1000 <lb/></note> <p> <s xml:id="echoid-s1398" xml:space="preserve">Chacun des dix eſpaces que contient la regle de 1000 parties, en <lb/>vaut cent, & </s> <s xml:id="echoid-s1399" xml:space="preserve">chacune des ſubdiviſions de la ligne AB en vaut dix. <lb/></s> <s xml:id="echoid-s1400" xml:space="preserve">C'eſt pourquoi ſi l'on veut s'en ſervir pour diviſer quelqu'une des <lb/>lignes du compas de proportion, comme, par exemple, la ligne des <lb/>plans, on choiſira ſur l'échelle la ligne marquée du nombre des cen-<lb/>taines, & </s> <s xml:id="echoid-s1401" xml:space="preserve">ce qui ſurpaſſera, ſe doit prendre dans l'eſpace entre les <lb/>lignes AB, comme ſi par exemple on veut marquer le premier plan, <lb/>auquel répond le nombre 125, on portera le compas commun ſur la <lb/>cinquiéme ligne de l'eſpace qui eſt marqué 100, & </s> <s xml:id="echoid-s1402" xml:space="preserve">on l'ouvrira de <lb/>la diſtance OP. </s> <s xml:id="echoid-s1403" xml:space="preserve">De la même façon, ſi on veut marquer le 50 plan <lb/>auquel répond le nombre 884, à cauſe des 800 on prendra le hui-<lb/>tiéme eſpace de la regle où eſt marqué 800, & </s> <s xml:id="echoid-s1404" xml:space="preserve">à cauſe des 84, on <lb/>prendra dans l'eſpace AB l'interſection de la huitiéme tranſverſale <lb/>& </s> <s xml:id="echoid-s1405" xml:space="preserve">de la quatriéme parallele qui ſera la diſtance NL.</s> <s xml:id="echoid-s1406" xml:space="preserve"/> </p> <pb o="34" file="048" n="48" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s1407" xml:space="preserve">On peut encore diviſer la ligne des plans ſans calculen la manie-<lb/>re ſuivante, fondée ſur la 47 propoſition du I livre d'Euclide. </s> <s xml:id="echoid-s1408" xml:space="preserve">Fai-<lb/> <anchor type="note" xlink:label="note-048-01a" xlink:href="note-048-01"/> tes le triangle iſocele rectangle KMN, dont le côté KM ou KN <lb/>ſoit égal au côté du plus petit plan, l'hypotenuſe MN ſera le côté <lb/>d'un plan ſemblable double du premier: </s> <s xml:id="echoid-s1409" xml:space="preserve">c'eſt pourquoiayant por-<lb/>té avec le compas commun l'intervale MN ſur le côté KL prolon-<lb/>gé autant qu'il en ſera beſoin depuis K juſqu'en 2, la longueur K <lb/>2 ſera le côté d'un plan double du plus petit. </s> <s xml:id="echoid-s1410" xml:space="preserve">Portez de même l'in-<lb/>tervale M 2 depuis K juſqu'en 3, la ligne K 3 ſera le côté d'un plan <lb/>triple du premier. </s> <s xml:id="echoid-s1411" xml:space="preserve">Portez enſuite l'intervale M 3 depuis K juſqu'en <lb/>4, la ligne K 4, qui doit être double de KM, ſera le côté d'un plan <lb/>quatre fois plus grand, c'eſt à-dire, qui contiendra quatre fois le <lb/>petit plan, & </s> <s xml:id="echoid-s1412" xml:space="preserve">ainfi de ſuite, comme on voit en ladite figure 5.</s> <s xml:id="echoid-s1413" xml:space="preserve"/> </p> <div xml:id="echoid-div170" type="float" level="2" n="3"> <note position="left" xlink:label="note-048-01" xlink:href="note-048-01a" xml:space="preserve">Fig. 5.</note> </div> </div> <div xml:id="echoid-div172" type="section" level="1" n="52"> <head xml:id="echoid-head92" xml:space="preserve">SECTION III.</head> <head xml:id="echoid-head93" style="it" xml:space="preserve">De la ligne des Polygones.</head> <p> <s xml:id="echoid-s1414" xml:space="preserve">CEtte ligne eſt ainſi nommée, parce qu'elle comprend les cô-<lb/>tez homologues des dix premiers polygones reguliers inſcrits <lb/>dans un même cercle, c'eſt-à-dire, depuis le triangle équilateral <lb/>juſqu'au dodecagone.</s> <s xml:id="echoid-s1415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1416" xml:space="preserve">Le côté du triangle étant le plus grand de tous, doit être de la <lb/>longueur de chaque jambe du compas de proportion; </s> <s xml:id="echoid-s1417" xml:space="preserve">& </s> <s xml:id="echoid-s1418" xml:space="preserve">comme <lb/>les côtez des autres polygones reguliers inſcrits dans le même cer-<lb/>cle, diminuent à meſure qu'ils ont plus de côtez, celui du dode-<lb/>cagone eſt le plus petit, & </s> <s xml:id="echoid-s1419" xml:space="preserve">par conſequent doit être plus proche <lb/>du centre dudit compas.</s> <s xml:id="echoid-s1420" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1421" xml:space="preserve">Suppoſant doncle côté du triangle de mille parties, il faur trou-<lb/>ver la longueur des côtez de chacun desautres polygones; </s> <s xml:id="echoid-s1422" xml:space="preserve">& </s> <s xml:id="echoid-s1423" xml:space="preserve">com-<lb/>me les côtez des polygones reguliers inſcrits dans un même cer-<lb/>cle, ſont en même proportion que les cordes ou ſous-tendantes <lb/>des angles du centre de chacun de ces polygones, il eſt à propos de <lb/>rapporter ici le moyen de connoître ces angles.</s> <s xml:id="echoid-s1424" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1425" xml:space="preserve">Pour cet effet, il faut divifer le nombre de 360 degrez que con-<lb/>tient la circonference entiere du cercle, par le nombre des côtez <lb/>de chaque polygone, le quotien de la diviſion marquera le nom-<lb/>bre de degrez que contient l'angle du centre.</s> <s xml:id="echoid-s1426" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1427" xml:space="preserve">Si, par exemple, on veut avoir l'angle du centre d'un exagone <lb/>ou figure de ſix côtez; </s> <s xml:id="echoid-s1428" xml:space="preserve">en diviſant 360 par ſix, le quotien ſera <lb/>60: </s> <s xml:id="echoid-s1429" xml:space="preserve">ce qui ſignifie que l'angle du centre de l'cxagone eſt de 60 <lb/>degrez. </s> <s xml:id="echoid-s1430" xml:space="preserve">Si pareillement on veut avoir l'angle du centre d'un pen-<lb/> <pb o="35" file="049" n="49" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. I."/> tagone, ou figure de cinq côtez, en diviſant 360 par cinq, le <lb/>quotien ſera 72: </s> <s xml:id="echoid-s1431" xml:space="preserve">ce qui marque que l'angle du centre d'un penta-<lb/>gone, eſt de 72 degrez, & </s> <s xml:id="echoid-s1432" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s1433" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1434" xml:space="preserve">L'angle du centre étant connu, ſi on le ſouſtrait de 180 degrez, <lb/>reſtera l'angle du polygone. </s> <s xml:id="echoid-s1435" xml:space="preserve">Comme, par exemple, l'angle du cen-<lb/>tre d'un pentagone étant de 72 degrez, l'angle de la circonfe-<lb/>rence dudit pentagone eſt de 108 degrez, & </s> <s xml:id="echoid-s1436" xml:space="preserve">ainſi des autres, <lb/>comme il ſe voit dans la table ſuivante.</s> <s xml:id="echoid-s1437" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Polygones reguliers. # Angles du centre. # Angles à la circonference. <lb/>Triangle. # 120. d. # 60. d. <lb/>Quarré. # 90. # 90. <lb/>Pentagone. # 72. # 108. <lb/>Exagone. # 60. # 120. <lb/>Eptagone. # 51. 26. m. # 128. 34. <lb/>Octogone. # 45. # 135. <lb/>Enneagone. # 40. # 140. <lb/>Decagone. # 36. # 144. <lb/>Endecagone. # 32. 44. # 147. 16. <lb/>Dodecagone. # 30. # 150. <lb/></note> <p> <s xml:id="echoid-s1438" xml:space="preserve">Pour trouver en nombre les côtez deſdits polygones reguliers <lb/>inſcriptibles dans un même cercle, ayant ſuppoſé celui du trian-<lb/>gle équilateral de mille parties égales, au lieu des cordes ou ſous-<lb/>tendantes des angles du centre, on peut prendre les moitiez des <lb/>mêmes cordes, qui ſont les ſinus de la moitié des angles de leurs <lb/>centres, & </s> <s xml:id="echoid-s1439" xml:space="preserve">faire l'analogie ſuivante.</s> <s xml:id="echoid-s1440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1441" xml:space="preserve">Pour trouver, par exemple, le côté du quarré.</s> <s xml:id="echoid-s1442" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1443" xml:space="preserve">Comme le ſinus de 60 degrez moitié de l'angle du centre du <lb/>triangle équilateral, eſt au côté du même triangle ſuppoſé mil-<lb/>le; </s> <s xml:id="echoid-s1444" xml:space="preserve">ainſi le ſinus de 45 degrez, moitié de l'angle du centre du <lb/>quarré, ſera au côté du même quarré, qui ſe trouvera par le cal-<lb/>cul de 816.</s> <s xml:id="echoid-s1445" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1446" xml:space="preserve">C'eſt de cette maniere qu'a été conſtruite la table ſuivante des <lb/>polygones.</s> <s xml:id="echoid-s1447" xml:space="preserve"/> </p> <figure> <image file="049-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/049-01"/> </figure> <pb o="36" file="050" n="50" rhead="CONSTRUCTION ET USAGES"/> <note position="right" xml:space="preserve"> <lb/> ## Côté du Triangle équilateral marqué ſur le \\ Compas de proportion par le nombre (3) # Parties égales: \\ 1000. <lb/>Du Quarré par le nombre # 4 # 816. <lb/>Du Pentagone par le n. # 5 # 678. <lb/>De l'Exagone par le n. # 6 # 577. <lb/>De l'Eptagone par le n. # 7 # 501. <lb/>De l'Octogone par le n. # 8 # 442. <lb/>De l'Enneagone par le n. # 9 # 395. <lb/>Du Decagone par le n. # 10 # 357. <lb/>De l'Endecagone par le n. # 11 # 325. <lb/>Du Dodecagone par le n. # 12 # 299. <lb/></note> <p> <s xml:id="echoid-s1448" xml:space="preserve">Nous avons negligé les fractions reſtées apres le calcul en cette <lb/>table comme en toutes les autres, parce que n'étant que des mil-<lb/>liémes parties, elles ne ſont pas conſiderables.</s> <s xml:id="echoid-s1449" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1450" xml:space="preserve">Ceux qui ne voudront pas marquer le triangle équilateral ſur le <lb/>compas de proportion, à cauſe de la facilité qu'il y a de le tracer, & </s> <s xml:id="echoid-s1451" xml:space="preserve"><lb/>qui par conſequent commenceront par le quarré, ſe ſerviront de <lb/>la table ſuivante, oû ſon côté eſt ſuppoſé de 1000 parties.</s> <s xml:id="echoid-s1452" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Autre Table des Polygones. # Parties. <lb/>Quarré, # 1000. <lb/>Pentagone, # 831. <lb/>Exagone, # 707. <lb/>Eptagone, # 613. <lb/>Octogone, # 540. <lb/>Enneagone, # 484. <lb/>Decagone, # 437. <lb/>Endecagone, # 398. <lb/>Dodecagone, # 366. <lb/></note> <p> <s xml:id="echoid-s1453" xml:space="preserve">Pour marquer ſurle compas de proportion la ligne des polygo-<lb/> <anchor type="note" xlink:label="note-050-03a" xlink:href="note-050-03"/> nes, on ſe ſervira de la même échelle de mille parties égales, qui a <lb/>ſervi pour y tracer la ligne des plans; </s> <s xml:id="echoid-s1454" xml:space="preserve">& </s> <s xml:id="echoid-s1455" xml:space="preserve">l'on portera du centre A. <lb/></s> <s xml:id="echoid-s1456" xml:space="preserve">ſur la ligne A D de part & </s> <s xml:id="echoid-s1457" xml:space="preserve">d'autre, le nombre des parties marquées. </s> <s xml:id="echoid-s1458" xml:space="preserve"><lb/>dans la table, pour y graver les chifres 3, 4, 5, &</s> <s xml:id="echoid-s1459" xml:space="preserve">c. </s> <s xml:id="echoid-s1460" xml:space="preserve">qui ſignifient <lb/>le nombre des côtez des polygones reguliers.</s> <s xml:id="echoid-s1461" xml:space="preserve"/> </p> <div xml:id="echoid-div172" type="float" level="2" n="1"> <note position="left" xlink:label="note-050-03" xlink:href="note-050-03a" xml:space="preserve">De la VI. <lb/>Planche. <lb/>Fig. 1.</note> </div> <pb o="37" file="051" n="51" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. I."/> </div> <div xml:id="echoid-div174" type="section" level="1" n="53"> <head xml:id="echoid-head94" xml:space="preserve">SECTION IV.</head> <head xml:id="echoid-head95" style="it" xml:space="preserve">De la ligne des Cordes.</head> <p> <s xml:id="echoid-s1462" xml:space="preserve">CEtte ligne eſt ainſi nommée, parce qu'elle comprend les cor-<lb/>des de tous les degrez du demi cercle, qui a pour diametre la <lb/>longueur de cette ligne, laquelle ſe marque ſur l'autre ſurface de <lb/>chaque jambe du compas de proportion, depuis le point A, qui <lb/> <anchor type="note" xlink:label="note-051-01a" xlink:href="note-051-01"/> eſt le centre de ſa charniere juſqu'à l'extremité F de chaque regle, <lb/>de telle ſorte que les deux lignes AF ſoient parfaitement égales, & </s> <s xml:id="echoid-s1463" xml:space="preserve"><lb/>équi-diſtantes des bords interieurs.</s> <s xml:id="echoid-s1464" xml:space="preserve"/> </p> <div xml:id="echoid-div174" type="float" level="2" n="1"> <note position="right" xlink:label="note-051-01" xlink:href="note-051-01a" xml:space="preserve">VI. Plan-che. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s1465" xml:space="preserve">Il eſt à remarquer que la ligne des cordes doit être directement <lb/>tracée au - deſſous de celle des parties égales, à cauſe de quelques <lb/>operations qui demandent de la correſpondance entre ces deux li-<lb/>gnes.</s> <s xml:id="echoid-s1466" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1467" xml:space="preserve">Il eſt auſſi à propos que la ligne des ſolides ſoit tracée ſous celle <lb/>des plans, & </s> <s xml:id="echoid-s1468" xml:space="preserve">celle des metaux ſous celle des Polygones.</s> <s xml:id="echoid-s1469" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1470" xml:space="preserve">Pour la diviſion de cette ligne décrivez un demi cercle qui ait <lb/>pour diametre la longueur de ladite ligne AF, diviſez-le en 180 <lb/> <anchor type="note" xlink:label="note-051-02a" xlink:href="note-051-02"/> degrez; </s> <s xml:id="echoid-s1471" xml:space="preserve">portez enſuite la longueur des cordes de tous ces degrez, <lb/>en les comptant de l'une des extremitez du diametre du demi cer-<lb/>cle, ſur leſdites jambes du compas, & </s> <s xml:id="echoid-s1472" xml:space="preserve">marquez ſur chacune au <lb/>tant de points qui repreſenteront les degrez du demi cercle que <lb/>vous diſtinguerez par de petites lignes de cinq en cinq, & </s> <s xml:id="echoid-s1473" xml:space="preserve">par des <lb/>chifres de 10 en 10, en commençant depuis le point A, centre de <lb/>la charniere dudit compas de proportion, juſqu'à F.</s> <s xml:id="echoid-s1474" xml:space="preserve"/> </p> <div xml:id="echoid-div175" type="float" level="2" n="2"> <note position="right" xlink:label="note-051-02" xlink:href="note-051-02a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s1475" xml:space="preserve">Ces mêmes degrez ſe peuvent encore marquer ſur la ligne des <lb/>cordes par le moyen des nombres, en fuppoſant le demi diametre <lb/>du cercle ou la corde de 180 degrez de 1000 parties égales. </s> <s xml:id="echoid-s1476" xml:space="preserve">Ces <lb/>nombres ſe trouvent tous calculez dans les tables ordinaires des <lb/>ſinus; </s> <s xml:id="echoid-s1477" xml:space="preserve">car au lieu des cordes, il n'y a qu'à prendre leurs moitiez, <lb/>qui ſont les ſinus de la moitié des arcs. </s> <s xml:id="echoid-s1478" xml:space="preserve">Ainſi, par exemple, au <lb/>lieu de la corde de dix degrez, il faut prendre le ſinus de cinq de-<lb/>grez; </s> <s xml:id="echoid-s1479" xml:space="preserve">& </s> <s xml:id="echoid-s1480" xml:space="preserve">comme le calcul en eſt fait pour un raïon de 100000, <lb/>il faut retrancher les deux derniers chifres, commeil ſe voit dans <lb/>la table ci-deſſous, où ſont marquées les cordes de tous les degrez. <lb/></s> <s xml:id="echoid-s1481" xml:space="preserve">Cette diviſion ſe fait avec l'échelle de 1000 parties.</s> <s xml:id="echoid-s1482" xml:space="preserve"/> </p> <figure> <image file="051-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/051-01"/> </figure> <pb o="38" file="052" n="52" rhead="CONSTRUCTION ET USAGES"/> <note position="right" xml:space="preserve"> <lb/>Table pour la ligne des cordes. <lb/>D. # Cord. # D. # Cord. # D. # Cord. # D. # Cord. # D. # Cord. # D. # Cord. <lb/>1 # 8 # 31 # 267 # 61 # 507 # 91 # 713 # 121 # 870 # 151 # 968 <lb/>2 # 17 # 32 # 275 # 62 # 515 # 92 # 719 # 122 # 874 # 152 # 970 <lb/>3 # 26 # 33 # 284 # 63 # 522 # 93 # 725 # 123 # 879 # 153 # 972 <lb/>4 # 35 # 34 # 292 # 64 # 530 # 94 # 731 # 124 # 883 # 154 # 974 <lb/>5 # 43 # 35 # 300 # 65 # 537 # 95 # 737 # 125 # 887 # 155 # 976 <lb/>6 # 52 # 36 # 309 # 66 # 544 # 96 # 743 # 126 # 891 # 156 # 978 <lb/>7 # 61 # 37 # 317 # 67 # 552 # 97 # 749 # 127 # 895 # 157 # 980 <lb/>8 # 70 # 38 # 325 # 68 # 559 # 98 # 754 # 128 # 899 # 158 # 981 <lb/>9 # 78 # 39 # 334 # 69 # 566 # 99 # 760 # 129 # 902 # 159 # 983 <lb/>10 # 87 # 40 # 342 # 70 # 573 # 100 # 766 # 130 # 906 # 160 # 985 <lb/>11 # 96 # 41 # 350 # 71 # 580 # 101 # 771 # 131 # 910 # 161 # 986 <lb/>12 # 104 # 42 # 358 # 72 # 588 # 102 # 777 # 132 # 913 # 162 # 987 <lb/>13 # 113 # 43 # 366 # 73 # 595 # 103 # 782 # 133 # 917 # 163 # 989 <lb/>14 # 122 # 44 # 374 # 74 # 602 # 104 # 788 # 134 # 920 # 164 # 990 <lb/>15 # 130 # 45 # 382 # 75 # 609 # 105 # 793 # 135 # 924 # 165 # 991 <lb/>16 # 139 # 46 # 390 # 76 # 615 # 106 # 798 # 136 # 927 # 166 # 992 <lb/>17 # 145 # 47 # 399 # 77 # 622 # 107 # 804 # 137 # 930 # 167 # 993 <lb/>18 # 156 # 48 # 406 # 78 # 629 # 108 # 809 # 138 # 933 # 168 # 994 <lb/>19 # 165 # 49 # 414 # 79 # 636 # 109 # 814 # 139 # 936 # 169 # 995 <lb/>20 # 173 # 50 # 422 # 80 # 643 # 110 # 819 # 140 # 939 # 170 # 996 <lb/>21 # 182 # 51 # 430 # 81 # 649 # 111 # 824 # 141 # 941 # 171 # 997 <lb/>22 # 191 # 52 # 438 # 82 # 656 # 112 # 829 # 142 # 945 # 172 # 997 <lb/>23 # 199 # 53 # 446 # 83 # 662 # 113 # 834 # 143 # 948 # 173 # 998 <lb/>24 # 208 # 54 # 454 # 84 # 669 # 114 # 838 # 144 # 951 # 174 # 998 <lb/>25 # 216 # 55 # 462 # 85 # 675 # 115 # 843 # 145 # 954 # 175 # 999 <lb/>26 # 225 # 56 # 469 # 86 # 682 # 116 # 848 # 146 # 956 # 176 # 999 <lb/>27 # 233 # 57 # 477 # 87 # 688 # 117 # 852 # 147 # 959 # 177 # 999 <lb/>28 # 242 # 58 # 485 # 88 # 694 # 118 # 857 # 148 # 961 # 178 # 1000 <lb/>29 # 250 # 59 # 492 # 89 # 701 # 119 # 861 # 149 # 963 # 179 # 1000 <lb/>30 # 259 # 60 # 500 # 90 # 707 # 120 # 866 # 150 # 966 # 180 # 1000 <lb/></note> </div> <div xml:id="echoid-div177" type="section" level="1" n="54"> <head xml:id="echoid-head96" xml:space="preserve">SECTION V.</head> <head xml:id="echoid-head97" style="it" xml:space="preserve">De la ligne des Solides.</head> <p> <s xml:id="echoid-s1483" xml:space="preserve">CEtte ligne eſt ainſi nommée, parce qu'elle comprend les cô-<lb/>tez homologues d'un certain nombre de ſolides ſemblables, <lb/> <pb o="39" file="053" n="53" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch.I."/> multiples du plus petit, depuis l'unité, ſuivant l'or l<unsure/>re naturel <lb/> <anchor type="note" xlink:label="note-053-01a" xlink:href="note-053-01"/> des nombres, juſqu'à 64, qui eſt ordinairement le plus grand ter-<lb/>me des diviſions de cette ligne, marquée AH proche la ligne <lb/>des cordes.</s> <s xml:id="echoid-s1484" xml:space="preserve"/> </p> <div xml:id="echoid-div177" type="float" level="2" n="1"> <note position="right" xlink:label="note-053-01" xlink:href="note-053-01a" xml:space="preserve">Planche <lb/>VI. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s1485" xml:space="preserve">Pour en faire la diviſion, on ſe ſert de l'échelle de 1000 par-<lb/>ties, & </s> <s xml:id="echoid-s1486" xml:space="preserve">l'on ſuppoſe le côté du 64<emph style="sub">me</emph> & </s> <s xml:id="echoid-s1487" xml:space="preserve">plus grand ſolide, de 1000 <lb/>parties égales; </s> <s xml:id="echoid-s1488" xml:space="preserve">& </s> <s xml:id="echoid-s1489" xml:space="preserve">comme la racine cubique de 64 eſt 4, & </s> <s xml:id="echoid-s1490" xml:space="preserve">que <lb/>celle d'un eſt 1, il s'enſuit que le côté du 64 ſolide contient qua-<lb/>tre fois le côté du premier & </s> <s xml:id="echoid-s1491" xml:space="preserve">plus petit ſolide, lequel par conſe-<lb/>quent doit être de 250, puiſque les ſolides ſemblables ſont entr'eux, <lb/>comme les cubes de leurs côtez homologues.</s> <s xml:id="echoid-s1492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1493" xml:space="preserve">Le nombre 500, double de 250, doit être le côté du huitié-<lb/>me ſolide, c'eſt-à-dire, d'un ſolide huit fois plus grand que le <lb/>premier, parce que le cube de 2, qui eſt 8, contient huit fois le <lb/>cube de l'unité.</s> <s xml:id="echoid-s1494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1495" xml:space="preserve">Pareillement le nombre 750, triple de 250 eſt le côté du vingt-<lb/>ſeptiéme ſolide, parce que le cube de 3, qui eſt 27, contient vingt-<lb/>ſept fois le cube d'un.</s> <s xml:id="echoid-s1496" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1497" xml:space="preserve">Il y a un peu plus de calcul à faire pour trouver les côtez des <lb/>ſolides doubles, triples, quadruples, &</s> <s xml:id="echoid-s1498" xml:space="preserve">c. </s> <s xml:id="echoid-s1499" xml:space="preserve">du premier, leſquels <lb/>ne peuvent pas même s'exprimer exactement par nombres, par-<lb/>ce que leurs racines ſont incommenſurables; </s> <s xml:id="echoid-s1500" xml:space="preserve">on peut néan-<lb/>moins en approcher ſuffiſamment pour l'uſage, par la methode <lb/>ſuivante.</s> <s xml:id="echoid-s1501" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1502" xml:space="preserve">Pour trouver, par exemple, le nombre qui exprime le côté <lb/>d'un ſolide double du premier & </s> <s xml:id="echoid-s1503" xml:space="preserve">plus petit, il faut cuber ſon cô-<lb/>té 250, le cube eſt 15625000. </s> <s xml:id="echoid-s1504" xml:space="preserve">Enſuite il faut doubler ce nom-<lb/>bre, & </s> <s xml:id="echoid-s1505" xml:space="preserve">en tirer la racine cubique, qui ſe trouvera à peu près <lb/>315, & </s> <s xml:id="echoid-s1506" xml:space="preserve">qui ſera le côté d'un ſolide double. </s> <s xml:id="echoid-s1507" xml:space="preserve">Pour avoir le côté <lb/>d'un ſolide triple du premier, il faut tripler ce même nombre, <lb/>& </s> <s xml:id="echoid-s1508" xml:space="preserve">en tirer la racine cubique, qui ſe trouvera 360, & </s> <s xml:id="echoid-s1509" xml:space="preserve">ainſi du <lb/>reſte; </s> <s xml:id="echoid-s1510" xml:space="preserve">le tout ſuivant qu'il eſt marqué en la table ci-jointe.</s> <s xml:id="echoid-s1511" xml:space="preserve"/> </p> <figure> <image file="053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/053-01"/> </figure> <pb o="40" file="054" n="54" rhead="CONSTRUCTION ET USAGES"/> <note position="right" xml:space="preserve"> <lb/> ######## Table pour la ligne des Solides. <lb/> <lb/>1 # 250 # 17 # 643 # 33 # 802 # 49 # 914 <lb/>2 # 315 # 18 # 655 # 34 # 810 # 50 # 921 <lb/>3 # 360 # 19 # 667 # 35 # 818 # 51 # 927 <lb/>4 # 397 # 20 # 678 # 36 # 825 # 52 # 933 <lb/>5 # 427 # 21 # 689 # 37 # 833 # 53 # 939 <lb/>6 # 454 # 22 # 700 # 38 # 840 # 54 # 945 <lb/>7 # 478 # 23 # 711 # 39 # 848 # 55 # 951 <lb/>8 # 500 # 24 # 721 # 40 # 855 # 56 # 956 <lb/>9 # 520 # 25 # 731 # 41 # 862 # 57 # 962 <lb/>10 # 538 # 26 # 740 # 42 # 869 # 58 # 967 <lb/>11 # 556 # 27 # 750 # 43 # 876 # 59 # 973 <lb/>12 # 572 # 28 # 759 # 44 # 882 # 60 # 978 <lb/>13 # 588 # 29 # 768 # 45 # 889 # 61 # 984 <lb/>14 # 602 # 30 # 777 # 46 # 896 # 62 # 989 <lb/>15 # 616 # 31 # 785 # 47 # 902 # 63 # 995 <lb/>16 # 630 # 32 # 794 # 48 # 908 # 64 # 1000 <lb/></note> <p> <s xml:id="echoid-s1512" xml:space="preserve">Les côtez de tous ces ſolides étant ainſi trouvez en nombre, <lb/>on les marquera ſur ladite ligne des ſolides, en y portant depuis <lb/>le centre A les parties qu'ils contiennnent, priſes ſur l'échelle de <lb/>1000 parties.</s> <s xml:id="echoid-s1513" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div179" type="section" level="1" n="55"> <head xml:id="echoid-head98" xml:space="preserve">SECTION VI.</head> <head xml:id="echoid-head99" style="it" xml:space="preserve">De la ligne des Métaux.</head> <p> <s xml:id="echoid-s1514" xml:space="preserve">CEtte ligne eſt ainſi nommée, parce qu'elle ſert à connoître <lb/>la proportion qu'ont entr'eux les ſix métaux, dont on peut <lb/>faire des ſolides.</s> <s xml:id="echoid-s1515" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1516" xml:space="preserve">Elle ſe marque ſur les jambes du compas de proportion à côté <lb/> <anchor type="note" xlink:label="note-054-02a" xlink:href="note-054-02"/> de la ligne des ſolides, & </s> <s xml:id="echoid-s1517" xml:space="preserve">les métaux y ſont figurez par les carac-<lb/>teres ci joints, qui leur ont été appropriez par les Chimiſtes & </s> <s xml:id="echoid-s1518" xml:space="preserve"><lb/>naturaliſtes.</s> <s xml:id="echoid-s1519" xml:space="preserve"/> </p> <div xml:id="echoid-div179" type="float" level="2" n="1"> <note position="left" xlink:label="note-054-02" xlink:href="note-054-02a" xml:space="preserve">Planche <lb/>VI. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s1520" xml:space="preserve">La diviſion de cette ligne eſt fondée ſur les experiences qui ont <lb/>été faites des differentes peſanteurs de maſſes égales de chacun <lb/>de ces métaux, d'où l'on a calculé leurs proportions, comme on <lb/>les voit marquées en la table ci-après.</s> <s xml:id="echoid-s1521" xml:space="preserve"/> </p> <pb o="41" file="055" n="55" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch.I."/> <note position="right" xml:space="preserve"> <lb/> ### Table pour la ligne des Métaux. <lb/>Or # ☉ # 730. <lb/>Plomb # ♄ # 863. <lb/>Argent # ɔ<unsure/> # 895. <lb/>Cuivre # ☿ # 937. <lb/>Fer # ♂ # 974. <lb/>Eſtain # ♃4 # 1000. <lb/></note> </div> <div xml:id="echoid-div181" type="section" level="1" n="56"> <head xml:id="echoid-head100" xml:space="preserve">Avertiſſement.</head> <p> <s xml:id="echoid-s1522" xml:space="preserve">Le moins peſant de tous ces mé-<lb/>taux, qui eſt l'étain, ſera marqué <lb/> <anchor type="note" xlink:label="note-055-02a" xlink:href="note-055-02"/> au bout de chaque jambe, comme <lb/>ici AG, figure 4. </s> <s xml:id="echoid-s1523" xml:space="preserve">à une diſtance de <lb/>centre qui égale la longueur de tou-<lb/>te l'échelle de 1000 parties, & </s> <s xml:id="echoid-s1524" xml:space="preserve">les <lb/>autres métaux plus proches dudit <lb/>centre, chacun ſuivant les nombres qui leur conviennent, pris <lb/>ſur la même échelle.</s> <s xml:id="echoid-s1525" xml:space="preserve"/> </p> <div xml:id="echoid-div181" type="float" level="2" n="1"> <note position="right" xlink:label="note-055-02" xlink:href="note-055-02a" xml:space="preserve">De la V. <lb/>Planche. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s1526" xml:space="preserve">Comme la plûpart des ſuſdites lignes marquées ſur le compas <lb/>de proportion, ſe diviſent par le moyen d'une échelle de 1000 <lb/>parties égales, il faut qu'elles ſoient toutes parfaitement égales en-<lb/>tr'elles & </s> <s xml:id="echoid-s1527" xml:space="preserve">à ladite échelle; </s> <s xml:id="echoid-s1528" xml:space="preserve">c'eſt pourquoi, comme elles aboutiſ-<lb/>ſent toutes d'une part au même point, qui eſt le centre de la charnie-<lb/>re, il faut qu'elles ſoient toutes terminées de l'autre part, par un arc <lb/>ſur chaque face des regles qui forment ledit compas.</s> <s xml:id="echoid-s1529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1530" xml:space="preserve">Il n'eſt pas toûjours neceſſaire de diviſer les compas de pro-<lb/>portion par les methodes que nous venons de donner; </s> <s xml:id="echoid-s1531" xml:space="preserve">car pour <lb/>abreger le temps, on diſpoſe une regle de la longueur, largeur & </s> <s xml:id="echoid-s1532" xml:space="preserve"><lb/>épaiſſeur des compas de proportion, & </s> <s xml:id="echoid-s1533" xml:space="preserve">on y trace les mêmes li-<lb/>gnes, que l'on diviſe très-exactement, ſuivant les regles que nous <lb/>venons d'expliquer; </s> <s xml:id="echoid-s1534" xml:space="preserve">puis on tranſporte avec un compas à coulice <lb/>les mêmes diviſions ſur les compas de proportion, après y avoir <lb/>tracé les lignes pour les contenir.</s> <s xml:id="echoid-s1535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1536" xml:space="preserve">Nous avons dit qu'il ſe fait des compas de proportion de dif-<lb/>ferentes grandeurs, mais les plus en ulage ſont ceux qui ſe met-<lb/>tent dans les étuis de Mathematique, de ſix pouces de long, d'au-<lb/>tres que l'on met auſſi dans des étuis de quatre pouces, & </s> <s xml:id="echoid-s1537" xml:space="preserve">d'au-<lb/>tres qui n'ont que trois pouces de long, que l'on nomme étuis <lb/>de poche. </s> <s xml:id="echoid-s1538" xml:space="preserve">On voit à peu près la figure de ces ſortes d'étuis dans <lb/>la planche ſixiéme. </s> <s xml:id="echoid-s1539" xml:space="preserve">Il s'en fait auſſi qui ont neuf à dix pouces <lb/>de longueur, où l'on met ordinairement des pinulles, & </s> <s xml:id="echoid-s1540" xml:space="preserve">un ge-<lb/>nouil au compas de proportion, pour ſervir en campagne à lever <lb/>les plans, & </s> <s xml:id="echoid-s1541" xml:space="preserve">meſurer les diſtances & </s> <s xml:id="echoid-s1542" xml:space="preserve">prendre les hauteurs; </s> <s xml:id="echoid-s1543" xml:space="preserve">mais <lb/>les demi cercles ou cercles entiers ſont plus commodes pour ces <lb/>ſortes d'operations.</s> <s xml:id="echoid-s1544" xml:space="preserve"/> </p> <pb o="42" file="056" n="56" rhead="CONSTRUTION ET USAGES"/> </div> <div xml:id="echoid-div183" type="section" level="1" n="57"> <head xml:id="echoid-head101" xml:space="preserve">SECTION VII.</head> <head xml:id="echoid-head102" style="it" xml:space="preserve">Contenant les preuves des diviſions des ſix lignes que l'on <lb/>marque ordinarement ſur le Compas de proportion.</head> <head xml:id="echoid-head103" style="it" xml:space="preserve">Preuve de la ligne des parties égales.</head> <p> <s xml:id="echoid-s1545" xml:space="preserve">LA diviſion de cette ligne eſt ſi facile, qu'elle n'a beſoin d'aucu-<lb/>ne autre preuve, que celle d'examiner avecun compas commun <lb/>fi les deux lignes correſpondantes, tracées ſur les jambes du compas <lb/>de proportion, ſont bien égales & </s> <s xml:id="echoid-s1546" xml:space="preserve">diviſées également: </s> <s xml:id="echoid-s1547" xml:space="preserve">ce que l'on <lb/>connoîtra, en prenant avec un compas ordinaire, dont les pointes <lb/>ſoient fines & </s> <s xml:id="echoid-s1548" xml:space="preserve">déliées, tel nombre que l'on voudra de ces parties é <lb/>gales, commençant par où l'on jugera à propos. </s> <s xml:id="echoid-s1549" xml:space="preserve">Car ſi cetteligne <lb/>des parties égales eſt bien diviſée, en portant ſur ladite ligne l ou-<lb/>verture du compas ainſi ouvert, ſes deux pointes comprendront toû-<lb/>jours le même nombre de parties égales ſur une jambe ou ſur l'autre <lb/>en comptant du centre, ou de tel point de diviſion que l'on voudra.</s> <s xml:id="echoid-s1550" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div184" type="section" level="1" n="58"> <head xml:id="echoid-head104" style="it" xml:space="preserve">Preuve de la ligne des Cordes.</head> <p> <s xml:id="echoid-s1551" xml:space="preserve">LA methode ci-devant expliquée ne peut pas ſervir à connoître <lb/>ſi la ligne des cordes eſt bien diviſée, parce que ces diviſions ne <lb/>ſont pas égales; </s> <s xml:id="echoid-s1552" xml:space="preserve">la corde de 10 degrez, par exemple, étant plus de la <lb/>moitié de celle de 20, pareillement la corde de 20 degrez eſt plus <lb/>de la moitie de celle de 40, & </s> <s xml:id="echoid-s1553" xml:space="preserve">ainſi de ſuite: </s> <s xml:id="echoid-s1554" xml:space="preserve">de telle ſorte que les <lb/>diviſions ſont plus grandes vers le centre du compas que vers les ex-<lb/>tremitez de ſes jambes: </s> <s xml:id="echoid-s1555" xml:space="preserve">ce qui provient de la nature du cercle.</s> <s xml:id="echoid-s1556" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1557" xml:space="preserve">Mais comme nous avons rapporté deux methodes pour diviſer <lb/>la ligne des cordes, l'une par le ſecours des nombres, & </s> <s xml:id="echoid-s1558" xml:space="preserve">l'autre par <lb/>l'étenduë des cordes ou ſous-tendantes des arcs, une de ces metho-<lb/>de peut ſervir de preuve à l'autre.</s> <s xml:id="echoid-s1559" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1560" xml:space="preserve">En voici cependant encore une autre, qui n'eſt point à negliger. <lb/></s> <s xml:id="echoid-s1561" xml:space="preserve">Choiſiſſez à volonté ſur la ligne des cordes deux nombres égale-<lb/>ment éloignez, de 120 degrez comme, par exemple, 110 & </s> <s xml:id="echoid-s1562" xml:space="preserve">130 <lb/>quien ſont éloignez chacun de 10 degrez, le premier par défaut, & </s> <s xml:id="echoid-s1563" xml:space="preserve"><lb/>le ſecond par excez. </s> <s xml:id="echoid-s1564" xml:space="preserve">Prenez avecun compas commun la diſtance de <lb/>ces deux nombres 110 & </s> <s xml:id="echoid-s1565" xml:space="preserve">130, laquelle doit être égale a la corde de <lb/>10 degrez, ou à la diſtance du point marqué 10 ſur la ligne des cor-<lb/>des au centre du compas de proportion.</s> <s xml:id="echoid-s1566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1567" xml:space="preserve">On connoîtra par le même moyen, que la diſtance entre 100 & </s> <s xml:id="echoid-s1568" xml:space="preserve"><lb/>140 degrez eſt égale à la corde de 20 degrez; </s> <s xml:id="echoid-s1569" xml:space="preserve">que pareillement la <lb/> <pb o="43" file="057" n="57" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch.I."/> diſtance entre 90 & </s> <s xml:id="echoid-s1570" xml:space="preserve">150 eſt égale à la corde de 30, qui eſt le nom-<lb/>bre dont 120 ſurpaſſe 90, & </s> <s xml:id="echoid-s1571" xml:space="preserve">dont il eſt ſurpaſſé par 150 & </s> <s xml:id="echoid-s1572" xml:space="preserve">ainſi des <lb/>autres comme il eſt aiſé de remarquer par la table des cordes ci-<lb/>devant marquée, où l'on voit, par exemple, que le nombre 44, qui <lb/>eſt la corde de 5 degrez, eſt la difference entre 843, quieſt la corde de <lb/>115 degrez; </s> <s xml:id="echoid-s1573" xml:space="preserve">& </s> <s xml:id="echoid-s1574" xml:space="preserve">887, qui eſt la corde de 125, que pareillement 87, <lb/>corde de 10 degrez eſt la difference entre la corde de 110 & </s> <s xml:id="echoid-s1575" xml:space="preserve">celle de <lb/>130, &</s> <s xml:id="echoid-s1576" xml:space="preserve">c. </s> <s xml:id="echoid-s1577" xml:space="preserve">leſquelles ſont également éloignées de 120 degrez.</s> <s xml:id="echoid-s1578" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div185" type="section" level="1" n="59"> <head xml:id="echoid-head105" style="it" xml:space="preserve">Preuve de la ligne des Polygones.</head> <p> <s xml:id="echoid-s1579" xml:space="preserve">ON connoítra ſi cette ligne eſt bien diviſée par le moyen de la <lb/>ligne des cordes en la maniere ſuivante.</s> <s xml:id="echoid-s1580" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1581" xml:space="preserve">Prenez avec un compas commun ſur la ligne des Polygones la <lb/>diſtance du centre du compas de proportion juſqu'au point 6, qui <lb/>marque l'exagone. </s> <s xml:id="echoid-s1582" xml:space="preserve">Puis ayant ouvert le compas de proportion, <lb/>portez cette diſtance ſur la ligne des cordes, mettant chaque pointe <lb/>dudit compas commun ſur les points correſpondans de 60 à 60, <lb/>quimarque l'angle du centre de l'exagone.</s> <s xml:id="echoid-s1583" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1584" xml:space="preserve">Le compas de proportion demeurant ainſi ouvert, prenez avec <lb/>le compas ordinaire ſur chaque ligne des cordes la diſtance des deux <lb/>points marquez 72, & </s> <s xml:id="echoid-s1585" xml:space="preserve">la portez ſur la ligne des Polygones, mettant <lb/>une pointe au centre de la charniere du compas deproportion; </s> <s xml:id="echoid-s1586" xml:space="preserve">l'au-<lb/>tre pointe doit rencontrer le point marque 5, qui apartient au pen-<lb/>tagone, dont l'angle du centre eſt de 72 degrez.</s> <s xml:id="echoid-s1587" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1588" xml:space="preserve">Prenant de même ſur la ligne des cordes la diſtance des deux <lb/>points marquez 90, & </s> <s xml:id="echoid-s1589" xml:space="preserve">la portant ſur la ligne des Polygones, l'ou-<lb/>verture du compas commun y rencontrera le point marqué 3, qui <lb/>appartient au quarré, dont l'angle du centre eſt de 90 degrez, & </s> <s xml:id="echoid-s1590" xml:space="preserve"><lb/>ainſi de tous les autres.</s> <s xml:id="echoid-s1591" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div186" type="section" level="1" n="60"> <head xml:id="echoid-head106" style="it" xml:space="preserve">Preuve de la ligne des Plans.</head> <p> <s xml:id="echoid-s1592" xml:space="preserve">COmme nous avons rapporté deux methodes pour diviſer la li-<lb/>gne des plans, l'une peut ſervir de preuve à l'autre; </s> <s xml:id="echoid-s1593" xml:space="preserve">mais on <lb/>peut encore facilement reconnoître ſi la diviſion eſt bien faite par la <lb/>maniere ſuivante. </s> <s xml:id="echoid-s1594" xml:space="preserve">Prenez avec un compas ordinaire la diſtance de <lb/>quelque point que ce ſoit de cette ligne juſqu'au centre de la char-<lb/>niere du compas de proportion, & </s> <s xml:id="echoid-s1595" xml:space="preserve">portez cette diſtance depuis le <lb/>même point de diviſion de l'autre côté de la même ligne des plans, <lb/>la pointe du compas rencontrera un nombre de plan quatre fois plus <lb/>grand que celui quia été pris vers le centre; </s> <s xml:id="echoid-s1596" xml:space="preserve">& </s> <s xml:id="echoid-s1597" xml:space="preserve">ſi l'on tourne encore <lb/> <pb o="44" file="058" n="58" rhead="CONSTRUCTION ET USAGES"/> une fois le compas commun ainſi ouvert vers l'extremité de ladite <lb/>ligne, la pointe tombera ſur un nombre de plan neuf fois plus grand. <lb/></s> <s xml:id="echoid-s1598" xml:space="preserve">Ainſi, par exemple, ſi l'on a pris la diſtance depuis le centre juſqu'au <lb/>plan marqué 2, arrêtant une pointe du compas ſur ledit point 2, <lb/>l'autre pointe doittomber ſur le point 8, & </s> <s xml:id="echoid-s1599" xml:space="preserve">en tournant encore une <lb/>fois le compas, ſans changer l'ouverture, en arrêtant une de ſes <lb/>pointes ſur ledit point 8, l'autre pointe doit rencontrer le dix-hui-<lb/>tiéme plan, qui contient neuf fois le ſecond plan; </s> <s xml:id="echoid-s1600" xml:space="preserve">tournant encore <lb/>une fois le compas, on rencontrera le trente deuxiéme plan, qui <lb/>contient ſeize fois le ſecond plan. </s> <s xml:id="echoid-s1601" xml:space="preserve">Si enfin on tourne encore une au-<lb/>tre fois, on doit rencontrer le cinquantiéme plan, qui contient ce-<lb/>lui de deux 25 fois, & </s> <s xml:id="echoid-s1602" xml:space="preserve">ainſi des autres plans ſemblables, parce qu'ils <lb/>ſont entr'eux, comme les quarrez de leurs côtez homologues. </s> <s xml:id="echoid-s1603" xml:space="preserve"><lb/>C'eſt ce qui facilite la diviſion de cette ligne des plans, puiſqu'ayant <lb/>le premier, on a le quatriéme, le neuviéme, le ſeiziéme, le vingt-<lb/>cinquiéme, le trente-ſixiéme, le quarante-neuviéme, & </s> <s xml:id="echoid-s1604" xml:space="preserve">le ſoixan-<lb/>te-quatriéme; </s> <s xml:id="echoid-s1605" xml:space="preserve">ayant trouvé le ſecond, on a le huitiéme, le dix-<lb/>huitiéme, le trente-deuxiéme, & </s> <s xml:id="echoid-s1606" xml:space="preserve">cinquantiéme; </s> <s xml:id="echoid-s1607" xml:space="preserve">ayant pareille-<lb/>ment trouvé le troiſiéme, on a le douziéme, le vingt-ſeptiéme, & </s> <s xml:id="echoid-s1608" xml:space="preserve"><lb/>le quarante-huitiéme; </s> <s xml:id="echoid-s1609" xml:space="preserve">& </s> <s xml:id="echoid-s1610" xml:space="preserve">ainſi du reſte.</s> <s xml:id="echoid-s1611" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div187" type="section" level="1" n="61"> <head xml:id="echoid-head107" style="it" xml:space="preserve">Preuve de la ligne des Solides.</head> <p> <s xml:id="echoid-s1612" xml:space="preserve">ON connoît ſi cette ligne eſt bien diviſée par la methode ſuivan-<lb/>te. </s> <s xml:id="echoid-s1613" xml:space="preserve">Prenez avec un compas ordinaire la diſtance de quelque <lb/>point que ce ſoit de cette ligne jnſqu'au centre du compas de pro-<lb/>portion; </s> <s xml:id="echoid-s1614" xml:space="preserve">arrêtez une pointe du compas ainſi ouvert ſur le même <lb/>point de diviſion, & </s> <s xml:id="echoid-s1615" xml:space="preserve">tournez l'autre pointe vers l'extremité de ladite <lb/>ligne, elle doit rencontrerun nombre de ſolides huit fois plus grand <lb/>que celui que vous aurez choiſi. </s> <s xml:id="echoid-s1616" xml:space="preserve">Si vous tournez encore une fois le <lb/>compas, une de ſes pointes tombera ſur un ſolide vingt-ſeptfois plus <lb/>grand que le nombre choiſi. </s> <s xml:id="echoid-s1617" xml:space="preserve">Ainſi, par exemple, l'ouverture du pre-<lb/>mier ſolide donnera celle du huitiéme, du vingt-ſeptiéme, & </s> <s xml:id="echoid-s1618" xml:space="preserve">du <lb/>ſoixante-quatriéme; </s> <s xml:id="echoid-s1619" xml:space="preserve">l'ouverture du ſecond ſolide donnera celle du <lb/>ſeiziéme, & </s> <s xml:id="echoid-s1620" xml:space="preserve">du cinquante-quatriéme; </s> <s xml:id="echoid-s1621" xml:space="preserve">l'ouverture du troiſiéme pri-<lb/>ſe deux fois donnera celle du vingt quatriéme. </s> <s xml:id="echoid-s1622" xml:space="preserve">Par le quatriéme <lb/>ſolide on aura le trente-deuxiéme, de même que par le cinquiéme <lb/>on aura le quarantiéme; </s> <s xml:id="echoid-s1623" xml:space="preserve">par le ſixiéme on aura le quarante-huitié-<lb/>me, & </s> <s xml:id="echoid-s1624" xml:space="preserve">enfin par le moyen du ſeptiéme on aura le cinquante-ſixié-<lb/>me ſolide, parce que les ſolides ſemblables ſont entr'eux, comme les <lb/>cubes de leurs côtez homologues; </s> <s xml:id="echoid-s1625" xml:space="preserve">& </s> <s xml:id="echoid-s1626" xml:space="preserve">c'eſt ce qui facilite la diviſion <lb/>de la ligne des ſolides.</s> <s xml:id="echoid-s1627" xml:space="preserve"/> </p> <pb o="45" file="059" n="59" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch.I."/> </div> <div xml:id="echoid-div188" type="section" level="1" n="62"> <head xml:id="echoid-head108" style="it" xml:space="preserve">Preuve de la ligne des Métaux.</head> <p> <s xml:id="echoid-s1628" xml:space="preserve">NOus avons déja dit ci-devant, que la diviſion de cette ligne <lb/>eſt fondée ſur les experiences par leſquelles on a connu les <lb/>differentes peſanteurs d'un pied cube de chacun des ſix métaux, <lb/>comme ils ſont ici marquez.</s> <s xml:id="echoid-s1629" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Mètaux. # ## Poids d'un pied cube. <lb/>Or. # 1326. # livres # 4. # onces. <lb/>Plomb. # 802. # # 2. <lb/>Argent. # 720. # # 12. <lb/>Cuivre. # 627. # # 12. <lb/>Fer. # 558. # # 0. <lb/>Eſtain. # 516. # # 2. <lb/></note> <p> <s xml:id="echoid-s1630" xml:space="preserve">Je vais ici rapporter comme deces differens poids deſdits métaux, <lb/>on a calculé la table ci-devant rapportée des nombres qui ſervent à <lb/>marquer ſur le compas de proportion les côtez homologues des <lb/>corps ſemblables, & </s> <s xml:id="echoid-s1631" xml:space="preserve">d'égale peſanteur, faits deſdits métaux.</s> <s xml:id="echoid-s1632" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1633" xml:space="preserve">Or comme l'étain eſt le moins peſant, il eſt évident que ſi, par <lb/>exemple, on veut en faire une boule qui peſe autant qu'une boule <lb/>de fer ou de cuivre, celle d'étain doit être la plus groſſe de toutes, <lb/>& </s> <s xml:id="echoid-s1634" xml:space="preserve">enſuite celle de fer plus groſſe que celle de cuivre, & </s> <s xml:id="echoid-s1635" xml:space="preserve">ainſi des au-<lb/>tres juſqu'à celle d'or qui ſeroit la plus petite. </s> <s xml:id="echoid-s1636" xml:space="preserve">C'eſt pourquoi, ſup-<lb/>poſant le diametrc de la boule d'étain de 1000 parties égales, il eſt <lb/>queſtion de trouver de combien de ces mêmes parties doit être le <lb/>diametre de la boule de fer, ou de celle de cuivre de pareille peſanteur: <lb/></s> <s xml:id="echoid-s1637" xml:space="preserve">ce qui ſe peut trouver par l'analogie ſuivante, en ſe ſervant de la <lb/>table des ſolides ci-devant marquée.</s> <s xml:id="echoid-s1638" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1639" xml:space="preserve">Il faut faire une regle de proportion, dont le premier terme ſoit <lb/>toûjours le poids du plus peſant des deux métaux que l'on veut <lb/>comparer enſemble; </s> <s xml:id="echoid-s1640" xml:space="preserve">le ſecond terme, ſoit le poids de l'étain; </s> <s xml:id="echoid-s1641" xml:space="preserve">le troi-<lb/>ſiéme ſoit le nombre 64, qui eſt le plus grand ſolide de ladite table, <lb/>auquel convient le nombre 1000. </s> <s xml:id="echoid-s1642" xml:space="preserve">Si, par exemple, on veut com-<lb/>parer le fer, dont le pied cube peſe 558 livres avec l'étain, dont le <lb/>pied cube peſe 516 livres & </s> <s xml:id="echoid-s1643" xml:space="preserve">2 onces, ayant reduit le touten onces <lb/>les 558 liv. </s> <s xml:id="echoid-s1644" xml:space="preserve">feront 8928 onces, & </s> <s xml:id="echoid-s1645" xml:space="preserve">le 516 liv. </s> <s xml:id="echoid-s1646" xml:space="preserve">2 onces feront 8258; <lb/></s> <s xml:id="echoid-s1647" xml:space="preserve">il faut donc dire: </s> <s xml:id="echoid-s1648" xml:space="preserve">ſi 8928; </s> <s xml:id="echoid-s1649" xml:space="preserve">donnent 8258, combien 64; </s> <s xml:id="echoid-s1650" xml:space="preserve">la regle de <lb/>trois étant faite, le quatriéme terme ſera 59, & </s> <s xml:id="echoid-s1651" xml:space="preserve">un petit reſte, je <lb/>cherche dans ladite table des ſolides le 59, & </s> <s xml:id="echoid-s1652" xml:space="preserve">le nombre correſpon-<lb/> <pb o="46" file="060" n="60" rhead="CONSRTUTION ET USAGES"/> dant eſt 973, au lieu duquel je prends 974, à cauſe de la fraction <lb/>reſtée. </s> <s xml:id="echoid-s1653" xml:space="preserve">C'eſt pourquoi je dis que le diametre de la boule de fer de-<lb/>vroit être de 974 parties égales à celles dont le diamettre de la <lb/>boule d'étian eſt ſuppoſé. </s> <s xml:id="echoid-s1654" xml:space="preserve">En faiſant de la mêm maniere quatre <lb/>autres regles de trois, on connoîtra ſi les nombres marquez vis-à-<lb/>vis des quatres autres métaux ſont bien calculez, & </s> <s xml:id="echoid-s1655" xml:space="preserve">par conſequent <lb/>ſi la ligne des métaux eſt bien diviſée.</s> <s xml:id="echoid-s1656" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div189" type="section" level="1" n="63"> <head xml:id="echoid-head109" xml:space="preserve">CHAPITRE II.</head> <head xml:id="echoid-head110" style="it" xml:space="preserve">Des Vſages du Compas de Proportion</head> <p> <s xml:id="echoid-s1657" xml:space="preserve">NOus ne rapporterons ici que les Uſages qui ſont les plus pro-<lb/>pres à cet inſtrument, & </s> <s xml:id="echoid-s1658" xml:space="preserve">qui ſe font mieux par ſon moyen <lb/>que par aucun autre.</s> <s xml:id="echoid-s1659" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div190" type="section" level="1" n="64"> <head xml:id="echoid-head111" xml:space="preserve">SECTION I.</head> <head xml:id="echoid-head112" style="it" xml:space="preserve">Des Uſages de la ligne des parties égales.</head> <head xml:id="echoid-head113" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head114" style="it" xml:space="preserve">Diviſer une ligne donnée en tant de parties égales qu'on <lb/>voudra; comme, par exemple, en ſept.</head> <p> <s xml:id="echoid-s1660" xml:space="preserve">PRenez avec un compas ordinaire l'étenduë de toute la ligne <lb/> <anchor type="note" xlink:label="note-060-01a" xlink:href="note-060-01"/> propoſée, comme AB, & </s> <s xml:id="echoid-s1661" xml:space="preserve">la portez ſur la ligne des parties éga-<lb/>les à un nombre de part & </s> <s xml:id="echoid-s1662" xml:space="preserve">d'autre, quiſe ſe puiſſe facilement diviſer <lb/>par 7, comme pourroit être en cet exemple 70, dont la ſeptiéme <lb/>partie eſt 10, ou bien au nombre 140, dont la ſeptiéme partie eſt 20. <lb/></s> <s xml:id="echoid-s1663" xml:space="preserve">Enſuite laiſſant le compas de proportion ainſi ouvert, reſſerrez le <lb/>compas commun juſqu'à ce que les deux pointes rencontrent les <lb/>deux nombres 10, ſi l'on s'eſtſervi du nombre 70, ou bien les deux <lb/>nombres 20, ſi l'on a pris 140 pour l'étenduë de toute la ligne, cet-<lb/>te ouverture du compas marquée par la figure 2, ſera la ſeptiéme <lb/>partie de la ligne propo@ée.</s> <s xml:id="echoid-s1664" xml:space="preserve"/> </p> <div xml:id="echoid-div190" type="float" level="2" n="1"> <note position="left" xlink:label="note-060-01" xlink:href="note-060-01a" xml:space="preserve">VII. Plan-<lb/>che. <lb/>Fig. I.</note> </div> <p> <s xml:id="echoid-s1665" xml:space="preserve">Si la ligne propoſée à diviſer étoit trop longue pour être appli-<lb/>quée ſur les jambes du compas de proportion, portez en ſeulement <lb/>une partie, comme la moitié ou le quart, que vous diviſerez, com-<lb/>me il vient d'être dit, en 7, le double ou quadruple de cette ſep-<lb/>tiéme partie diviſera en 7 la grande ligne propoſée.</s> <s xml:id="echoid-s1666" xml:space="preserve"/> </p> <pb o="47" file="061" n="61" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> </div> <div xml:id="echoid-div192" type="section" level="1" n="65"> <head xml:id="echoid-head115" xml:space="preserve"><emph style="bf">USAGE II.</emph></head> <p style="it"> <s xml:id="echoid-s1667" xml:space="preserve">Etant donnés pluſieurs lignes droites qui font la circonference <lb/>d'un polygone, l'une deſquelles ſoit eſtirnée contenir autant <lb/>de parties égales qu'on voudra, trouver combien de ces mê-<lb/>mes parties ſont contenuës en chacune des autres lignes.</s> <s xml:id="echoid-s1668" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1669" xml:space="preserve">PRenez avec un compas commun la longueur de la ligne dont la <lb/>meſure eſt connuë, & </s> <s xml:id="echoid-s1670" xml:space="preserve">la portez ſur la ligne des parties égales à <lb/>l'ouverture du nombre qui exprime la meſure; </s> <s xml:id="echoid-s1671" xml:space="preserve">le compas de pro-<lb/>portion demeurant ainſi ouvert, tranſportez-y la longueur de cha-<lb/>cune des autres lignes, les nombres de l'ouverture que chacune <lb/>comprendra, marqueront leur veritable longueur. </s> <s xml:id="echoid-s1672" xml:space="preserve">Que ſi quel-<lb/>qu'une deſdites lignes ne convient pas juſtement au même nombre <lb/>de part & </s> <s xml:id="echoid-s1673" xml:space="preserve">d'autre ſur la ligne des parties égales, mais que, par exem-<lb/>ple, une des pointes du compas tombant ſur le nombre 29, l'autre <lb/>tombe ſur le nombre 30, cette ligne contiendra 29 & </s> <s xml:id="echoid-s1674" xml:space="preserve">demi.</s> <s xml:id="echoid-s1675" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div193" type="section" level="1" n="66"> <head xml:id="echoid-head116" xml:space="preserve">USAGE III.</head> <p style="it"> <s xml:id="echoid-s1676" xml:space="preserve">Etant donnée une ligne droite, & </s> <s xml:id="echoid-s1677" xml:space="preserve">le nombre des parties égales <lb/>qu'elle contient, en retrancher une moindre ligne contenant <lb/>tel nombre de ces parties que l'on voudra.</s> <s xml:id="echoid-s1678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1679" xml:space="preserve">SOit pour exemple la ligne propſée de 120 toiſes, dont on <lb/>veut retrancher une ligne de 25. </s> <s xml:id="echoid-s1680" xml:space="preserve">Prenez avecle compas com-<lb/>mun la longueur de la ligne propoſée; </s> <s xml:id="echoid-s1681" xml:space="preserve">ouvrez le compas de propor-<lb/>tion de telle ſorte que cette longueur convienne de 120 à 120 mar-<lb/>quez ſur les deux lignes des parties égales, & </s> <s xml:id="echoid-s1682" xml:space="preserve">ledit compas de pro-<lb/>portion demeurant ainſi ouvert, prenez ſur la même ligne la diſtan-<lb/>ce de 25 à 25, que vous retrancherez de ladite ligne de 120 toiſes.</s> <s xml:id="echoid-s1683" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1684" xml:space="preserve">Parles trois uſages précedens il eſt aiſé de voir que la ligne des <lb/>parties égales du compas de proportion peut très-commod ément <lb/>ſervir d'échelle pour toutes ſortes de plans, pourvû qu'on fçache <lb/>la quantité d'un de ſes côtez, & </s> <s xml:id="echoid-s1685" xml:space="preserve">que l'on peut par ſon moyen les <lb/>réduire de petit en grand, ou de grand en petit.</s> <s xml:id="echoid-s1686" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div194" type="section" level="1" n="67"> <head xml:id="echoid-head117" xml:space="preserve">USAGE IV.</head> <p style="it"> <s xml:id="echoid-s1687" xml:space="preserve">A deux lignes droites données trouver une troiſiéme propor-<lb/>tionnelle, & </s> <s xml:id="echoid-s1688" xml:space="preserve">à trois une quatriéme.</s> <s xml:id="echoid-s1689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1690" xml:space="preserve">SI l'on ne propoſe que deux lignes, prenez avec un compas <lb/>commun la longueur de la premiere, & </s> <s xml:id="echoid-s1691" xml:space="preserve">la tranſportez ſur une <lb/>des jambes du compas de proportion depuis le centre le long de la <lb/> <pb o="48" file="062" n="62" rhead="CONSTRUCTION ET USAGES"/> ligne des parties égales, pour en connoître la valeur, & </s> <s xml:id="echoid-s1692" xml:space="preserve">du nom-<lb/>bre où elle ſe terminera, ouvrez le compas de proportion, en ſorte <lb/>que la longueur de la ſeconde ligne convienne à ſon ouverture; </s> <s xml:id="echoid-s1693" xml:space="preserve">le-<lb/>dit compas demeurant ainſi ouvert, portez la longueur de ladite ſe-<lb/>conde ligne ſur une des jambes depuis le centre, & </s> <s xml:id="echoid-s1694" xml:space="preserve">remarquez le <lb/>nombre des parties égales, où elle ſe termine, l'ouverture de ce <lb/>nombre donnera la troiſiéme ligne proportionnelle requiſe.</s> <s xml:id="echoid-s1695" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1696" xml:space="preserve">Soit pour exemple la premiere ligne propoſée A B, de 40 parties <lb/> <anchor type="note" xlink:label="note-062-01a" xlink:href="note-062-01"/> égales, & </s> <s xml:id="echoid-s1697" xml:space="preserve">la ſeconde CD, de 20. </s> <s xml:id="echoid-s1698" xml:space="preserve">Portez la longueur des 20 parties <lb/>égales à l'ouverture des 40; </s> <s xml:id="echoid-s1699" xml:space="preserve">& </s> <s xml:id="echoid-s1700" xml:space="preserve">le compas reſtant ainſi ouvert, pre-<lb/>nez l'ouverture de 20 à 20, cette ouverture ſera la longueur de la <lb/>troiſiéme ligne proportionnelle que l'on cherche; </s> <s xml:id="echoid-s1701" xml:space="preserve">& </s> <s xml:id="echoid-s1702" xml:space="preserve">ſi vous la me-<lb/>ſurez ſur la ligne des parties égales depuis le centre, elle en contien-<lb/>dra 10, car 40 ſont à 20, comme 20 ſont à 10.</s> <s xml:id="echoid-s1703" xml:space="preserve"/> </p> <div xml:id="echoid-div194" type="float" level="2" n="1"> <note position="left" xlink:label="note-062-01" xlink:href="note-062-01a" xml:space="preserve">De la VII. <lb/>Planchs. <lb/>Fig. 3.</note> </div> <p> <s xml:id="echoid-s1704" xml:space="preserve">Que ſi à trois lignes données vous cherchez une quatriéme pro-<lb/>portionnelle, portez, comme nous venons de dire, la ſeconde à l'ou-<lb/>verture de la premiere; </s> <s xml:id="echoid-s1705" xml:space="preserve">& </s> <s xml:id="echoid-s1706" xml:space="preserve">le compas de proportion demeurant ainſi <lb/>ouvert, portez la troiſiéme ligne ſur une de ſes jambes depuis le <lb/>centre; </s> <s xml:id="echoid-s1707" xml:space="preserve">l'ouverture du nombre où elle ſe terminera, donnera la <lb/>quatriéme requiſe.</s> <s xml:id="echoid-s1708" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1709" xml:space="preserve">Soit pour exemple la premiere de ces trois lignes de 60 parties <lb/> <anchor type="note" xlink:label="note-062-02a" xlink:href="note-062-02"/> égalcs, la ſeconde de 30, & </s> <s xml:id="echoid-s1710" xml:space="preserve">la troiſiéme de 50; </s> <s xml:id="echoid-s1711" xml:space="preserve">portez la longueur <lb/>de 30 parties égales à l'ouverture de 60; </s> <s xml:id="echoid-s1712" xml:space="preserve">& </s> <s xml:id="echoid-s1713" xml:space="preserve">le compas demeurant <lb/>ainſi ouvert, prenez l'ouverture 50, cette ouverture, qui con-<lb/>tiendra 25, ſera la quatriéme proportionnelle, car 60 ſont à 30, <lb/>comme 50 à 25.</s> <s xml:id="echoid-s1714" xml:space="preserve"/> </p> <div xml:id="echoid-div195" type="float" level="2" n="2"> <note position="left" xlink:label="note-062-02" xlink:href="note-062-02a" xml:space="preserve">Fig. 3.</note> </div> </div> <div xml:id="echoid-div197" type="section" level="1" n="68"> <head xml:id="echoid-head118" xml:space="preserve">USAGE V.</head> <p style="it"> <s xml:id="echoid-s1715" xml:space="preserve">Diviſer une ligne donnée ſelon une raiſon donnée.</s> <s xml:id="echoid-s1716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1717" xml:space="preserve">QU'il faille, par exemple, diviſer la ligne donnée en deux par-<lb/>ties, dont la raiſon ſoit égale à celle de 40 à 70; </s> <s xml:id="echoid-s1718" xml:space="preserve">ajoutez en-<lb/>ſemble ces deux nombres, leur ſomme ſera 110. </s> <s xml:id="echoid-s1719" xml:space="preserve">Prenez avec un <lb/>compas commun la longueur de la ligne propoſée, que je ſuppoſe <lb/>être de 165 parties égales; </s> <s xml:id="echoid-s1720" xml:space="preserve">portez cette longueur à l'ouverture des <lb/>nombres 110 de la ligne des parties égales; </s> <s xml:id="echoid-s1721" xml:space="preserve">& </s> <s xml:id="echoid-s1722" xml:space="preserve">le compas de pro-<lb/>portion demeurant ainſi ouvert, prenez l'ouverture des nombres <lb/>40 & </s> <s xml:id="echoid-s1723" xml:space="preserve">70, la premiere de ces deux ouvertures donnera 60, & </s> <s xml:id="echoid-s1724" xml:space="preserve">la <lb/>ſeconde 105, qui ſeront les parties de la ligne propoſée à diviſer, <lb/>puiſque 40 ſont à 70, comme 60 ſont à 105.</s> <s xml:id="echoid-s1725" xml:space="preserve"/> </p> <pb o="49" file="063" n="63" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> </div> <div xml:id="echoid-div198" type="section" level="1" n="69"> <head xml:id="echoid-head119" xml:space="preserve">USAGE VI.</head> <p style="it"> <s xml:id="echoid-s1726" xml:space="preserve">Ouvrir le Compas de proportion, en ſorte que les deux lignes <lb/>des parties égales faſſent un angle àroit.</s> <s xml:id="echoid-s1727" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1728" xml:space="preserve">CHoiſiſſez trois nombres qui puiſſent exprimer les côtez d'un <lb/>triangle rectangle, comme ſont, par exemple, les nombres 3, <lb/>4, 5, ou leurs multiples; </s> <s xml:id="echoid-s1729" xml:space="preserve">mais comme il eſt mieux de les prendre un <lb/>peu grands, nous choiſirons 60, 80 & </s> <s xml:id="echoid-s1730" xml:space="preserve">100. </s> <s xml:id="echoid-s1731" xml:space="preserve">Prenez avec un com-<lb/>pas commun la diſtance du centre du compas de proportion ſur la <lb/>ligne des parties égales juſqu'au nombre 100; </s> <s xml:id="echoid-s1732" xml:space="preserve">ouvrez enſuite le <lb/>compas de proportions de telle ſorte qu'une des pointes du compas <lb/>commun tombe d'une part ſur le nombre 60 des parties égales, & </s> <s xml:id="echoid-s1733" xml:space="preserve"><lb/>l'autre pointe ſur le nombre 80 des mêmes parties égales de l'autre <lb/>jambe; </s> <s xml:id="echoid-s1734" xml:space="preserve">alors le compas de proportion ſera ouvert, de ſorte que les <lb/>deux lignes de parties égales feront un angle droit.</s> <s xml:id="echoid-s1735" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div199" type="section" level="1" n="70"> <head xml:id="echoid-head120" xml:space="preserve">USAGE VII.</head> <p style="it"> <s xml:id="echoid-s1736" xml:space="preserve">Trouver une ligne droite égale à la circonference d'un cercle <lb/>donné.</s> <s xml:id="echoid-s1737" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1738" xml:space="preserve">LE diametre d'un cercle eſt à la circonference environ comme <lb/>100 à 314, ou comme 50 à 157; </s> <s xml:id="echoid-s1739" xml:space="preserve">c'eſt pourquoi prenez avec un <lb/>compas ordinaire la longueur du diametre du cercle propoſé, & </s> <s xml:id="echoid-s1740" xml:space="preserve">la <lb/>portez ſur les jambes de 50 à 50 de part & </s> <s xml:id="echoid-s1741" xml:space="preserve">d'autre de la ligne des <lb/>parties égales; </s> <s xml:id="echoid-s1742" xml:space="preserve">le compas de proportion demeurant ainſi ouvert, <lb/>prenez avec ledit compas commun la diſtance de 157 à 157, vous <lb/>aurez une ligne droite à peu près égale à la circonference du cercle <lb/>propoſé: </s> <s xml:id="echoid-s1743" xml:space="preserve">je dis à peu près, parce que la veritable proportion du <lb/>diametre d'un cercle à ſa; </s> <s xml:id="echoid-s1744" xml:space="preserve">circonference, n'a point encore été trou-<lb/>véc géometriquement.</s> <s xml:id="echoid-s1745" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div200" type="section" level="1" n="71"> <head xml:id="echoid-head121" xml:space="preserve">SECTION II.</head> <p style="it"> <s xml:id="echoid-s1746" xml:space="preserve">Des Vſages de la ligne des Plans.</s> <s xml:id="echoid-s1747" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div201" type="section" level="1" n="72"> <head xml:id="echoid-head122" xml:space="preserve">USAGE I.</head> <p style="it"> <s xml:id="echoid-s1748" xml:space="preserve">Augmenter ou diminuer toutes ſortes de figures planes, <lb/>ſelon une raiſon donnée.</s> <s xml:id="echoid-s1749" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1750" xml:space="preserve">SOit pour exemple propoſé le triangle A B C, auquel on a deſſein <lb/> <anchor type="note" xlink:label="note-063-01a" xlink:href="note-063-01"/> d'en faire un ſemblable qui ſoit triple en ſurface.</s> <s xml:id="echoid-s1751" xml:space="preserve"/> </p> <div xml:id="echoid-div201" type="float" level="2" n="1"> <note position="right" xlink:label="note-063-01" xlink:href="note-063-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s1752" xml:space="preserve">Prenez avec un compas commun la longueur du côté AB; </s> <s xml:id="echoid-s1753" xml:space="preserve">por-<lb/>tez-la ſur la ligne des plans à l'ouverture du premier plan; </s> <s xml:id="echoid-s1754" xml:space="preserve">le com-<lb/> <pb o="50" file="064" n="64" rhead="CONSTRUCTION ET USAGES"/> pas de proportion reſtant ainſi ouvert, prenez avec le compas com-<lb/>mun l'ouverture du troiſiéme plan, & </s> <s xml:id="echoid-s1755" xml:space="preserve">vous aurez la longueur du <lb/>côté homologue audit côté A B; </s> <s xml:id="echoid-s1756" xml:space="preserve">vous trouverez de la même facon <lb/>les côtez homologues aux deux autres côtez du triangle propoſé, & </s> <s xml:id="echoid-s1757" xml:space="preserve"><lb/>de ces trois côtez vous formerez le triangle triple du propoſé, com-<lb/>me il ſe voit en la figure 4 de la planche 7. </s> <s xml:id="echoid-s1758" xml:space="preserve">Si le plan propoſé a plus <lb/>de trois côtez, reduiſez-le en triangle par une ou pluſieurs diago-<lb/>nales.</s> <s xml:id="echoid-s1759" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1760" xml:space="preserve">Si c'eſt un cercle que l'on veiiille diminuer ou augmenter, il <lb/>faut faire la ſuſditc operation ſur ſon diametre.</s> <s xml:id="echoid-s1761" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div203" type="section" level="1" n="73"> <head xml:id="echoid-head123" xml:space="preserve">USAGE II.</head> <p style="it"> <s xml:id="echoid-s1762" xml:space="preserve">Etant données deux figures planes ſemblables, trouver quelle <lb/>raiſon elles ont entr' elles.</s> <s xml:id="echoid-s1763" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1764" xml:space="preserve">PRenez lequel vous voudrez des côtez de l'une deſdites figures, <lb/>& </s> <s xml:id="echoid-s1765" xml:space="preserve">le portez à l'ouverture de quelque plan; </s> <s xml:id="echoid-s1766" xml:space="preserve">prenez enſuite le <lb/>coté homologue de l'autre figure, & </s> <s xml:id="echoid-s1767" xml:space="preserve">voyez à l'ouverture de quel <lb/>plan il convient; </s> <s xml:id="echoid-s1768" xml:space="preserve">les deux nombres auſquels conviennent les deux <lb/>côtez homologues expriment la raiſon des plans entr'eux; </s> <s xml:id="echoid-s1769" xml:space="preserve">car ſi, <lb/> <anchor type="note" xlink:label="note-064-01a" xlink:href="note-064-01"/> par exemple, le côté a b de la plus petite convient au quatriéme <lb/>plan, & </s> <s xml:id="echoid-s1770" xml:space="preserve">que le côté homologue AB de l'autre convienne au ſixié-<lb/>me, ces deux plans ſont entr'eux comme 4 eſt à 6, c'eſt-à-dire, <lb/>que le grand contient une fois & </s> <s xml:id="echoid-s1771" xml:space="preserve">demie la ſurface du petit; </s> <s xml:id="echoid-s1772" xml:space="preserve">& </s> <s xml:id="echoid-s1773" xml:space="preserve">ſi le <lb/>petit plan contient vingt toiſes quarrées, le grand en contient tren-<lb/>te, comme l'on voit dans les figures.</s> <s xml:id="echoid-s1774" xml:space="preserve"/> </p> <div xml:id="echoid-div203" type="float" level="2" n="1"> <note position="left" xlink:label="note-064-01" xlink:href="note-064-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s1775" xml:space="preserve">Mais ſi le côté d'une figure ayant été mis à l'ouverture d'un <lb/>plan, le côté homologue ne pcut s'ajuſter à l'ouverture d'aucun <lb/>nombre entier, il faudra mettre ledit côté de la premiere figure à <lb/>l'ouverture de quelqu'autre plan, juſqu'a ce qu'on trouve un nom-<lb/>bre entier, dont l'ouverture convienne à la longueur du côté ho-<lb/>mologue de l'autre figure, aſin d'éviter les fractions.</s> <s xml:id="echoid-s1776" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1777" xml:space="preserve">Si les figures propoſées ſont ſi grandes, qu'aucun de leurs côtez <lb/>ne ſe puiſſe appliquer à l'ouverture des jambes du compas de pro-<lb/>portion, prenez les moities, tiers ou quarts de chacun des deux <lb/>côtez homologues deſdites figures, & </s> <s xml:id="echoid-s1778" xml:space="preserve">les comparant enſemble, <lb/>vous aurez la proportion des plans.</s> <s xml:id="echoid-s1779" xml:space="preserve"/> </p> <pb o="51" file="065" n="65" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> </div> <div xml:id="echoid-div205" type="section" level="1" n="74"> <head xml:id="echoid-head124" xml:space="preserve">USAGE III.</head> <p style="it"> <s xml:id="echoid-s1780" xml:space="preserve">Ouvrir le Compas de proportion, en ſorte que les deux lignes <lb/>des Plans faſſent un angle droit.</s> <s xml:id="echoid-s1781" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1782" xml:space="preserve">PRenez avecun compas commun ſur la ligne des plans depuis le <lb/>centre, l'étenduë d'un nombre de plans tel que vous voudrez, <lb/>comme, par exemple, 40; </s> <s xml:id="echoid-s1783" xml:space="preserve">appliquez cette ouverture de compas <lb/>ſur la même ligne des plans de part & </s> <s xml:id="echoid-s1784" xml:space="preserve">d'autre à un nombre quiéga-<lb/>le la moitié du precedent, comme eſt 20 en cet exemple; </s> <s xml:id="echoid-s1785" xml:space="preserve">alors les <lb/>deux lignes des plans feront au centre du compas un angle droit, <lb/>puiſque par la conſtruction de la ligne des plans, le nombre mar-<lb/>qué 40, qui fait comme le plus grand côté d'un trìangle, ſignifie <lb/>un plan égal aux deux autres plans ſemblables, marquez ſur les <lb/>jambes du compas par les nombres 20, d'où il ſuit par la quaran-<lb/>té-huitiéme Prop. </s> <s xml:id="echoid-s1786" xml:space="preserve">du Liv. </s> <s xml:id="echoid-s1787" xml:space="preserve">I. </s> <s xml:id="echoid-s1788" xml:space="preserve">d'Euclide que ledit angle eſt droit.</s> <s xml:id="echoid-s1789" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div206" type="section" level="1" n="75"> <head xml:id="echoid-head125" xml:space="preserve">USAGE IV.</head> <p style="it"> <s xml:id="echoid-s1790" xml:space="preserve">Conſtruire un Plan ſemblable & </s> <s xml:id="echoid-s1791" xml:space="preserve">égla à deux Plans ſembla-<lb/>bles donnez.</s> <s xml:id="echoid-s1792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1793" xml:space="preserve">OUvrez le compas de proportion à angles droits par l'uſage pre-<lb/>cedent, & </s> <s xml:id="echoid-s1794" xml:space="preserve">portez deux côtez homologues tels que vous vou-<lb/>drez des deux plans propoſez ſur la ligne des plans depuis le centre, <lb/>l'un ſur une jambe, & </s> <s xml:id="echoid-s1795" xml:space="preserve">l'autre ſur l'autre jambe, la diſtance des deux <lb/>nombres trouvez donnera le côté homologue d'un plan ſemblable <lb/>& </s> <s xml:id="echoid-s1796" xml:space="preserve">égal aux deux donnez.</s> <s xml:id="echoid-s1797" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1798" xml:space="preserve">Si, par exemple, le côté du moindre plan étant porté ſur une des <lb/>jambes du compas de proportion depuis le centre, recontre le qua-<lb/>triéme plan, & </s> <s xml:id="echoid-s1799" xml:space="preserve">quele côté homologue de l'autre plan porté ſur l'au-<lb/>tre jambe, rencontre le neuviéme plan, la diſtance de 4 à 9 qui ſera <lb/>égale au treiziéme plan, ſi le compas eſt ouvert, comme il eſt dit, <lb/>ſera le côte homologue d'un plan égal aux deux propoſez, par le <lb/>moyen duquel il ſera facile de conſtruire le plan ſemblable.</s> <s xml:id="echoid-s1800" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1801" xml:space="preserve">On peut par cet uſage ajoûter enſemble tant de plans ſemblables <lb/>que l'on voudra, en ajoutant enſemble les deux premiers, puis à <lb/>leur ſomme ajoûtant le troiſiéme & </s> <s xml:id="echoid-s1802" xml:space="preserve">ainſi de ſuite.</s> <s xml:id="echoid-s1803" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div207" type="section" level="1" n="76"> <head xml:id="echoid-head126" xml:space="preserve">USAGE V.</head> <p style="it"> <s xml:id="echoid-s1804" xml:space="preserve">Etant donnez deux Plans ſemblables & </s> <s xml:id="echoid-s1805" xml:space="preserve">ineganx en trouver <lb/>un troiſiéme auſſi ſemblable & </s> <s xml:id="echoid-s1806" xml:space="preserve">égal à leur difference.</s> <s xml:id="echoid-s1807" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1808" xml:space="preserve">OUvrez le compas de proportion de ſorte que les deux lignes des <lb/>plans faſſent un angle droit, & </s> <s xml:id="echoid-s1809" xml:space="preserve">portez un côté du moindre <lb/> <pb o="52" file="066" n="66" rhead="CONSTRUCTION ET USAGES"/> plan ſur une des jambes depuis le centre; </s> <s xml:id="echoid-s1810" xml:space="preserve">portez enſuite le côté ho-<lb/>mologue du plus grand plan, en mettant une des pointes du com-<lb/>pas commun ſur le nombre où ſe termine le premier côté, ſon autre <lb/>pointe rencontrera ſur l'autre jambe le nombre du plan requis.</s> <s xml:id="echoid-s1811" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1812" xml:space="preserve">Si, par exemple, ayant porté le côté du moindre plan depuis le <lb/>centre, l'on trouve qu'il tombe ſur le nombre 9 d'une jambe du <lb/>compas de proportion, prenez avec un compas ordinaire l'étenduë <lb/>du côté homologue du plus grand plan, en mettant une de ſes <lb/>pointes ſur ledit nombre 9, l'autre pointe marquera ſur l'autre jam-<lb/>be le nombre 4; </s> <s xml:id="echoid-s1813" xml:space="preserve">c'eſt pourquoi prenant la diſtance dudit nombre <lb/>4 au centre du compas de proportion, vous aurez le côté homolo-<lb/>gue d'un plan ſemblable & </s> <s xml:id="echoid-s1814" xml:space="preserve">égal à la difference des deux plans don-<lb/>nez, dont la raiſon eſt ici ſuppoſée de 9 à 13.</s> <s xml:id="echoid-s1815" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div208" type="section" level="1" n="77"> <head xml:id="echoid-head127" xml:space="preserve">USAGE VI</head> <p style="it"> <s xml:id="echoid-s1816" xml:space="preserve">Entre deux lignes droites données, trouver une moyene <lb/>proportionnelle.</s> <s xml:id="echoid-s1817" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1818" xml:space="preserve">POrtez chacune des deux lignes données ſur la ligne des parties <lb/>égales du compas de proportion, afin de ſçavoir le nombre que <lb/>chacune en contient, & </s> <s xml:id="echoid-s1819" xml:space="preserve">ſuppoſé, par exemple, que la moindre li-<lb/>gen ſoit de 20 parties égales, & </s> <s xml:id="echoid-s1820" xml:space="preserve">la plus grande de 45; </s> <s xml:id="echoid-s1821" xml:space="preserve">portez la <lb/>plus grande, qui eſt 45 à l'ouverture du quarante-cinquiéme plan <lb/>qui dénote le nombre deſes parties, le com pas de proportion reſtant <lb/>ainſi ouvert, prenez l'ouverture du vingtiéme plan, qui marque le <lb/>nombre des parties égales de la plus petite ligne, cette ouverture, <lb/>qui doit contenir 30 des mêmcs parties donnera la moyene pro-<lb/>portionelle, car 20 ſont à 30, comme 30 ſont à 45.</s> <s xml:id="echoid-s1822" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1823" xml:space="preserve">Mais comme le plus grand nombre de la ligne des plans eſt 64, <lb/>ſi quelqu'une des lignes propoſées contenoit un plus grand nombre <lb/>de parties égales, on pourroit faire ladite operation ſur leurs moi-<lb/>tiez, tiers ou quarts en cette ſorte. </s> <s xml:id="echoid-s1824" xml:space="preserve">Suppoſant, par exemple, que la <lb/>moindre des lignes propoſées ſoit de 32; </s> <s xml:id="echoid-s1825" xml:space="preserve">l'autre de 72, portez la <lb/>moitié de la grande ligne à l'ouverture du trente-fixième plan, & </s> <s xml:id="echoid-s1826" xml:space="preserve"><lb/>prenez l'ouverture du ſeiziéme, cette ouverture étant doublée <lb/>donnera la moyene proportio@nelle que l'on cherche.</s> <s xml:id="echoid-s1827" xml:space="preserve"/> </p> <figure> <image file="066-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/066-01"/> </figure> <pb o="53" file="067" n="67" rhead="DU COMPAS DE PROPORTION. Liv. II. Chap. II."/> </div> <div xml:id="echoid-div209" type="section" level="1" n="78"> <head xml:id="echoid-head128" xml:space="preserve">SECTION III. <lb/>Des Vſages de la ligne des Polygones.</head> <head xml:id="echoid-head129" xml:space="preserve">USAGE I. <lb/>Décrire un Polygone regulier dans un cercle donné.</head> <p> <s xml:id="echoid-s1828" xml:space="preserve">PRenez avec un compas commun la longueur du demi diametre <lb/> <anchor type="note" xlink:label="note-067-01a" xlink:href="note-067-01"/> du cercle donné AC, & </s> <s xml:id="echoid-s1829" xml:space="preserve">l'ajuſtez à l'ouverture du nombre 6, <lb/>marqué de part & </s> <s xml:id="echoid-s1830" xml:space="preserve">d'autre ſur la ligne des polygones; </s> <s xml:id="echoid-s1831" xml:space="preserve">& </s> <s xml:id="echoid-s1832" xml:space="preserve">le compas <lb/>de proportion demeurant ainſi ouvert, prenez l'ouverture des deux <lb/>nombres égaux qui expriment le nombre des côtez du polygone <lb/>que vous voulez décrire. </s> <s xml:id="echoid-s1833" xml:space="preserve">Prenez, par exemple, l'ouverture de 5 à 5, <lb/>pour décrire un pentagone; </s> <s xml:id="echoid-s1834" xml:space="preserve">de 7 à 7 pour un eptagone, & </s> <s xml:id="echoid-s1835" xml:space="preserve">ainſi des <lb/>autres. </s> <s xml:id="echoid-s1836" xml:space="preserve">Cette ouverture étant portée autour de la circonference du <lb/>cercle, le diviſera en autant de parties égales, & </s> <s xml:id="echoid-s1837" xml:space="preserve">il ſera facile de dé-<lb/>crire tout polygone regulier depuis le triangle équilateral juſqu'au <lb/>dodecagone, comme eſt décrit le pentagone en la figure ſixiéme.</s> <s xml:id="echoid-s1838" xml:space="preserve"/> </p> <div xml:id="echoid-div209" type="float" level="2" n="1"> <note position="right" xlink:label="note-067-01" xlink:href="note-067-01a" xml:space="preserve">Fig. 6.</note> </div> </div> <div xml:id="echoid-div211" type="section" level="1" n="79"> <head xml:id="echoid-head130" xml:space="preserve">USAGE II. <lb/>Sur une ligne donnée décrire un Polygone regulier.</head> <p> <s xml:id="echoid-s1839" xml:space="preserve">SI, par exemple, on veut décrire ſur la ligne AB de la ſuſdite fi-<lb/>gure 6, un pentagone, prenez avec un compas commun la lon-<lb/>gureur de ladite ligne, & </s> <s xml:id="echoid-s1840" xml:space="preserve">l'ayant appliquée à l'ouverture des nom-<lb/>bres 5 marquez de part & </s> <s xml:id="echoid-s1841" xml:space="preserve">d'autre ſur la ligne des polygones, laiffez <lb/>le compas de proportion ainſi ouvert, & </s> <s xml:id="echoid-s1842" xml:space="preserve">prenez ſur la même ligne <lb/>l'ouverture de 6 à 6, qui ſera le demi diametre du cercle propre à <lb/>décrire le pentagone regulier propoſé; </s> <s xml:id="echoid-s1843" xml:space="preserve">c'eſt pourquoi ſi avec cette <lb/>ouverture vous décrivez des extremitez de la ligne donnée AB deux <lb/>arcs de cercle, leur interſection ſera le centre dudit cercle.</s> <s xml:id="echoid-s1844" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1845" xml:space="preserve">Si l'on propoſe un eptagone, appliquez la longueur de la ligne <lb/>donnée à l'ouverture des nombres 7 marquez de part & </s> <s xml:id="echoid-s1846" xml:space="preserve">d'autre ſur <lb/>la ligne des polygones, & </s> <s xml:id="echoid-s1847" xml:space="preserve">prenez toûjours l'ouverture de 6 à 6 pour <lb/>trouver comme deffus le centre d'un cercle, danslequel il ſera facile <lb/>d'inſcrire l'eptagone, dont chaque côté fera égal à la ligne donnée.</s> <s xml:id="echoid-s1848" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div212" type="section" level="1" n="80"> <head xml:id="echoid-head131" xml:space="preserve">USAGE III. <lb/>Couper une ligne donnée en moyene & extrême raiſon, <lb/>comme D E, figure 7.</head> <p> <s xml:id="echoid-s1849" xml:space="preserve">APpliquez la longueur de la ligne donnée à l'ouverture des <lb/> <anchor type="note" xlink:label="note-067-02a" xlink:href="note-067-02"/> nombres 6 & </s> <s xml:id="echoid-s1850" xml:space="preserve">6 marquez de part & </s> <s xml:id="echoid-s1851" xml:space="preserve">d'autre ſur la ligne des <lb/> <pb o="54" file="068" n="68" rhead="CONSTRUCTION ET USAGE"/> polygones; </s> <s xml:id="echoid-s1852" xml:space="preserve">& </s> <s xml:id="echoid-s1853" xml:space="preserve">le compas de proportion demeurant ainſi ouvert, pre-<lb/>nez l'ouverture des nombres 10, qui ſont ceux du decagone, Cette <lb/>ouverture donnera D F, qui ſera la mediane, c'eſt à-dire, le plus <lb/>grand ſegment de la ligne propoſée, puiſque la mediane du raïon <lb/>d'un cercle coupé en moyene & </s> <s xml:id="echoid-s1854" xml:space="preserve">extréme raiſon, eſt la corde de 36 <lb/>degrez, qui eſt la dixiéme partie de ſa circonference.</s> <s xml:id="echoid-s1855" xml:space="preserve"/> </p> <div xml:id="echoid-div212" type="float" level="2" n="1"> <note position="right" xlink:label="note-067-02" xlink:href="note-067-02a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s1856" xml:space="preserve">Que ſi l'on ajoûte cette mediane au raïon du cercle, pour n'en <lb/>faire qu'une ligne, ledit raïon deviendra la mediane, & </s> <s xml:id="echoid-s1857" xml:space="preserve">la corde <lb/>de 36 degrez ſera le petit ſegment.</s> <s xml:id="echoid-s1858" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div214" type="section" level="1" n="81"> <head xml:id="echoid-head132" xml:space="preserve">USAGE IV. <lb/>Sur une ligne donnée DF, figure 8. décrire untriangle iſocele, <lb/>qui ait les angles de ſa baſe doubles de celui du ſommet.</head> <p> <s xml:id="echoid-s1859" xml:space="preserve">APpliquez la longueur de la ligne donnée à l'ouverture des <lb/> <anchor type="note" xlink:label="note-068-01a" xlink:href="note-068-01"/> nombres 10 marquez de part & </s> <s xml:id="echoid-s1860" xml:space="preserve">d'autre ſur la ligne des poly-<lb/>gones; </s> <s xml:id="echoid-s1861" xml:space="preserve">& </s> <s xml:id="echoid-s1862" xml:space="preserve">le compas de proportion reſtant ainſi ouvert, prenez <lb/>l'ouverture des nombres 6, pour avoir la longueur des deux côtez <lb/>égaux du triangle qu'on veut conſtruire.</s> <s xml:id="echoid-s1863" xml:space="preserve"/> </p> <div xml:id="echoid-div214" type="float" level="2" n="1"> <note position="left" xlink:label="note-068-01" xlink:href="note-068-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s1864" xml:space="preserve">Il eſt évident que l'angle du ſommet de ce triangle eſt de 36 de-<lb/>grez, & </s> <s xml:id="echoid-s1865" xml:space="preserve">que chacun des angles de la baſe eſt de 72 degrez; </s> <s xml:id="echoid-s1866" xml:space="preserve">or l'an-<lb/>gle de 36 degrez eſt l'angle du centre d'un decagone.</s> <s xml:id="echoid-s1867" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div216" type="section" level="1" n="82"> <head xml:id="echoid-head133" xml:space="preserve">USAGE V. <lb/>Ouvrir le compas de proportion, en ſorte que les deux lignes <lb/>des Polygones faſſent un angle droit.</head> <p> <s xml:id="echoid-s1868" xml:space="preserve">PRenez avec le compas commun ſur la ligne des polygones la di-<lb/>ſtance depuis le centre du compas de proportion juſqu'au nom-<lb/>bre 5, ouvrez enſuite le compas de proportion, de ſorte que cette <lb/>diſtance ſoit appliquée d'une part ſur le nombre 6, & </s> <s xml:id="echoid-s1869" xml:space="preserve">de l'autre part <lb/>ſur le nombre 10 des deux lignes des polygones, elles feront au cen-<lb/>tre un angle droit, parce que le quarré du côté du pentagone eſt égal <lb/>au quarré du côré de l'exagone, & </s> <s xml:id="echoid-s1870" xml:space="preserve">au quarré du côté du decagone.</s> <s xml:id="echoid-s1871" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div217" type="section" level="1" n="83"> <head xml:id="echoid-head134" xml:space="preserve">SECTION IV. <lb/>Des Vſages de la ligne des Cordes.</head> <head xml:id="echoid-head135" xml:space="preserve">USAGE I. <lb/>Ouvrir le compas de proportion de ſorte que les deux lignes des <lb/>cordes faſſent un angle de tant de degrez qu'on voudra.</head> <p> <s xml:id="echoid-s1872" xml:space="preserve">PRenez avec un compas ordinaire le long de la ligne des cordes <lb/>la diſtance depuis le centre de la charniere juſqu'au nombre des <lb/> <pb o="55" file="069" n="69" rhead="DU COMPAS DE PROPORTION. Liv. II. Chap. II."/> degrez propoſez; </s> <s xml:id="echoid-s1873" xml:space="preserve">ouvrez enſuite le compas de proportion de ſorte <lb/>que cette diſtance s'accorde aux deux nombres 60 marquez de part <lb/>& </s> <s xml:id="echoid-s1874" xml:space="preserve">d'autre ſur la ligne de cordes, ellcs feront l'angle requis.</s> <s xml:id="echoid-s1875" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1876" xml:space="preserve">Si, par exemple, vous voulez qu'elles faſſent un angle de 40 de-<lb/>grez, comme en la figure 9 de la planche 7, prenez la diſtance du <lb/>centre au nombre 40, & </s> <s xml:id="echoid-s1877" xml:space="preserve">la portez à l'ouverture de 60 à 60. </s> <s xml:id="echoid-s1878" xml:space="preserve">Si vous <lb/>voulez un angle droit, prenez la diſtance du centre à 90 degrez, & </s> <s xml:id="echoid-s1879" xml:space="preserve"><lb/>la portez pareillement à l'ouverture de 60 à 60, & </s> <s xml:id="echoid-s1880" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s1881" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div218" type="section" level="1" n="84"> <head xml:id="echoid-head136" xml:space="preserve">USAGE II. <lb/>Le compas de proportion étant ouvert, trouver les degrez <lb/>de ſon ouverture.</head> <p> <s xml:id="echoid-s1882" xml:space="preserve">PRenez l'ouverture de 60 degrez, & </s> <s xml:id="echoid-s1883" xml:space="preserve">la portez le long de la ligne <lb/>des cordes depuis le centre, le nombre où elle ſe terminera, <lb/>marquera les degrez de ſon ouverture.</s> <s xml:id="echoid-s1884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1885" xml:space="preserve">C'eſt ſur la ligne des cordes que l'on place quelquefois des pinu-<lb/>les pour meſurer un angle ſur la terre, ou poury en faire un d'autant <lb/>de degrez que l'on veut, en ajoûtant un genoüil au compas de pro-<lb/>portion, & </s> <s xml:id="echoid-s1886" xml:space="preserve">le plaçant ſur un pied, pour l'élever à la hauteur de <lb/>l'œil, en pratiquant ce que nous venons de dire en ces deux ufages; <lb/></s> <s xml:id="echoid-s1887" xml:space="preserve">mais nous eſtimons qu'il eſt plus aiſé de ſe ſervir d'un demi cercle <lb/>diviſé pour faire ces ſortes d'operations.</s> <s xml:id="echoid-s1888" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div219" type="section" level="1" n="85"> <head xml:id="echoid-head137" xml:space="preserve">USAGE III. <lb/>Sur une ligne droite donnée faire un angle rectiligne d'aut ant <lb/>de degrez qu'on voudra.</head> <p> <s xml:id="echoid-s1889" xml:space="preserve">DEcrivez ſur la ligne donnée un arc de cercle ayant pour centre <lb/>le point auquel vous voulez faire l'angle, portez le rayon du-<lb/>dit arc à l'ouverture de la corde de 60 degrez; </s> <s xml:id="echoid-s1890" xml:space="preserve">lecompas de propor-<lb/>tion demeurant ainſi ouvert, prenez l'ouverture de la corde du <lb/>nombre des degrez propoſez, & </s> <s xml:id="echoid-s1891" xml:space="preserve">la portez depuis la ligne ſur l'arc <lb/>que vous avez décrit; </s> <s xml:id="echoid-s1892" xml:space="preserve">tirez enfin une ligne droite du centre par l'ex-<lb/>tremité de cet arc, pour former l'angle requis.</s> <s xml:id="echoid-s1893" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1894" xml:space="preserve">Soit propoſé pour exemple de faire à l'extremité B de la ligne AB, <lb/> <anchor type="note" xlink:label="note-069-01a" xlink:href="note-069-01"/> un angle de 40 degrez; </s> <s xml:id="echoid-s1895" xml:space="preserve">ayant fait dudit point B un arc de cercle à <lb/>diſcretion, portez-en le rayon toûjours à l'ouverture de la corde de <lb/>60 degrez, parce que le rayon d'un cercle eſt toûjours égal à la cor-<lb/>de de 60 degrez du même cercle; </s> <s xml:id="echoid-s1896" xml:space="preserve">prenez enſuite l'ouverture de la <lb/>corde de 40 degrez, & </s> <s xml:id="echoid-s1897" xml:space="preserve">la portez ſur l'arc de cercle CD; </s> <s xml:id="echoid-s1898" xml:space="preserve">enfin tirant <lb/>la droit du pointe B par lepoint D, vousaurez fait un angle de 40 <lb/>degrez, figure 10.</s> <s xml:id="echoid-s1899" xml:space="preserve"/> </p> <div xml:id="echoid-div219" type="float" level="2" n="1"> <note position="right" xlink:label="note-069-01" xlink:href="note-069-01a" xml:space="preserve">Fig. 10.</note> </div> <pb o="56" file="070" n="70" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s1900" xml:space="preserve">On peut par cet uſage tracer une figure, dont les angles & </s> <s xml:id="echoid-s1901" xml:space="preserve">les <lb/>côtez ſont connus.</s> <s xml:id="echoid-s1902" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div221" type="section" level="1" n="86"> <head xml:id="echoid-head138" xml:space="preserve">USAGE IV. <lb/>Etant donné un angle rectiligne, trouver combien de degrez <lb/>il contient.</head> <p> <s xml:id="echoid-s1903" xml:space="preserve">DU ſommet de l'angle donné comme centre, décrivez un arc <lb/>de cercle, & </s> <s xml:id="echoid-s1904" xml:space="preserve">portez ſon rayon à l'ouverture de la corde de 60 <lb/>degrez; </s> <s xml:id="echoid-s1905" xml:space="preserve">prenez enſuite ſur le papier la corde de l'arc décrit entre les <lb/>côtez qui forment l'angle, & </s> <s xml:id="echoid-s1906" xml:space="preserve">cherchez ſur les jambes du compas de <lb/>proportion à quelle ouverture elle convient, le nombre des degrez <lb/>vous indiquera la valeur dudit angle.</s> <s xml:id="echoid-s1907" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div222" type="section" level="1" n="87"> <head xml:id="echoid-head139" xml:space="preserve">USAGE V. <lb/>Prendre ſur la circonference d'un cercle donné un arc d'autant <lb/>de degrez que l'on voudra.</head> <p> <s xml:id="echoid-s1908" xml:space="preserve">APpliquez le rayon du cercle donné ſur les jambes du compas <lb/>de proportion, à l'ouverture de la corde de 50 degrez; </s> <s xml:id="echoid-s1909" xml:space="preserve">& </s> <s xml:id="echoid-s1910" xml:space="preserve">ledit <lb/>compas demeurant ainſi ouvert, prenez l'ouverture de la corde du <lb/>nombre de degrez propoſé, & </s> <s xml:id="echoid-s1911" xml:space="preserve">la portez ſur la circonference du cer-<lb/>cle donné.</s> <s xml:id="echoid-s1912" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1913" xml:space="preserve">On peut par cet uſage inſcrire dans un cercle toutes ſortes de po-<lb/>lygones reguliers, auſſi-bien que par laligne des polygones, en con-<lb/>noiffant ſon angle du centre par la methode & </s> <s xml:id="echoid-s1914" xml:space="preserve">par la table ci-devant <lb/>rapportée, en traitant de la conſtruction de la ligne des polygones.</s> <s xml:id="echoid-s1915" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1916" xml:space="preserve">Soit, par exemple, propoſé de faire un pentagone regulier par la <lb/>ligne des cordes. </s> <s xml:id="echoid-s1917" xml:space="preserve">A yant connu que ſon angle du centre eſt de 72 de-<lb/>grez, portez le rayon du cercle à l'ouverture de la corde de 60 de-<lb/>grez, & </s> <s xml:id="echoid-s1918" xml:space="preserve">prenez enſuite l'ouverture de la corde de 72 degrez, la-<lb/> <anchor type="note" xlink:label="note-070-01a" xlink:href="note-070-01"/> quelle étant portée ſur la circonference du cercle donné, le diviſera <lb/>en cinq également, & </s> <s xml:id="echoid-s1919" xml:space="preserve">les cinq cordes étant tracées, ſeront les côtez <lb/>du pentagone.</s> <s xml:id="echoid-s1920" xml:space="preserve"/> </p> <div xml:id="echoid-div222" type="float" level="2" n="1"> <note position="left" xlink:label="note-070-01" xlink:href="note-070-01a" xml:space="preserve">Fig. @@.</note> </div> </div> <div xml:id="echoid-div224" type="section" level="1" n="88"> <head xml:id="echoid-head140" xml:space="preserve">USAGE VI. <lb/>Sur une ligne donnée F G, decrire un Polygone regulier.</head> <p> <s xml:id="echoid-s1921" xml:space="preserve">SI, par exemple, on propoſe de conſtruire un pentagone, dont <lb/>l'angle du centre eſt de 72 degrez, portez la longueur de la ligne <lb/>donnée à l'ouverture de la corde de 72 degrez, & </s> <s xml:id="echoid-s1922" xml:space="preserve">le compas de pro-<lb/>portion demeurant ainſi ouvert, prenez l'ouverture de la corde de <lb/>60 degrez, avec laquelle, des extremitez de la ligne donnée, vous <lb/> <pb o="57" file="071" n="71" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> décrirez deux arcs de cercle, le point de leur interſection D ſera le <lb/>centre d'un cercle, dont la circonference ſera diviſée en cinq par-<lb/>ties égales par la ligne donnée, & </s> <s xml:id="echoid-s1923" xml:space="preserve">ladite corde de 60 degrez ſera <lb/>égale au raïon de ce cercle.</s> <s xml:id="echoid-s1924" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div225" type="section" level="1" n="89"> <head xml:id="echoid-head141" xml:space="preserve"><emph style="bf">SECTION V.</emph></head> <head xml:id="echoid-head142" style="it" xml:space="preserve">Des Vſages de la ligne des Solides.</head> <head xml:id="echoid-head143" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head144" style="it" xml:space="preserve">Augmenter ou diminuer tous ſolides ſemblables, ſelon une <lb/>raiſon donnée.</head> <p> <s xml:id="echoid-s1925" xml:space="preserve">SOit propoſé, par exemple, un cube, duquel on en demande un <lb/> <anchor type="note" xlink:label="note-071-01a" xlink:href="note-071-01"/> qui ſoit double en ſolidité. </s> <s xml:id="echoid-s1926" xml:space="preserve">Portez le côté du cube donné ſur la <lb/>ligne des ſolides à l'ouverture de tel nombre que vous voudrez, <lb/>commme, par exemple, de 20 à 20, puis prenez l'ouverture d'un <lb/>nombre double, comme eſt en cet exemple le nombre 40; </s> <s xml:id="echoid-s1927" xml:space="preserve">cette <lb/>ouverture eſt le côté d'un cube double du propoſé.</s> <s xml:id="echoid-s1928" xml:space="preserve"/> </p> <div xml:id="echoid-div225" type="float" level="2" n="1"> <note position="right" xlink:label="note-071-01" xlink:href="note-071-01a" xml:space="preserve">Fig. 12.</note> </div> <p> <s xml:id="echoid-s1929" xml:space="preserve">Si l'on propoſe une boule ou ſphere, & </s> <s xml:id="echoid-s1930" xml:space="preserve">qu'on veüille en faire <lb/>une autre qui ſoit trois fois plus groſſe; </s> <s xml:id="echoid-s1931" xml:space="preserve">portez le diametre de la <lb/>boule propoſée à l'ouverture de tel nombre qu'il vous plaira, com-<lb/>me par exemple de 20 à 20, & </s> <s xml:id="echoid-s1932" xml:space="preserve">prenez l'ouverture de 60, ce ſera <lb/>le diametre d'une autre boule triple en ſolidité.</s> <s xml:id="echoid-s1933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1934" xml:space="preserve">Si l'on propoſe encore un coffre parallelipipede rectangle qui con-<lb/>tienne trois meſures de grain, on en veut faire faire un autre ſembla-<lb/>ble qui en contienne cinq; </s> <s xml:id="echoid-s1935" xml:space="preserve">portez la longueur de la bafe à l'ouver-<lb/>ture du trentiéme ſolide, & </s> <s xml:id="echoid-s1936" xml:space="preserve">prenez l'ouverture du cinquantiéme <lb/>pour le côté homologue de celui qui eſt à faire, portez enſuite la <lb/>largeur à l'ouverture du même nombre 30, & </s> <s xml:id="echoid-s1937" xml:space="preserve">prenez l'ouverture du <lb/>cinquantiéme ſolide pour le côté homologue à ladite largeur; </s> <s xml:id="echoid-s1938" xml:space="preserve">de <lb/>ces deux ouvertures ayant conſtruit un parallelograme, prenez <lb/>enfin la profondeur dudit coffre, & </s> <s xml:id="echoid-s1939" xml:space="preserve">l'ayant portée à l'ouverture du <lb/>trentiéme ſolide, vous prendrez l'ouverture du cinquantiéme ſoli-<lb/>de, pour avoir le côté homologue, c'eſt-à-dire, la profondeur, avec <lb/>laquelle il ſera facile de conſures ledit parallelipipede rectangle, <lb/>qui contiendra les cinq meſures propoſées.</s> <s xml:id="echoid-s1940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1941" xml:space="preserve">Si les lignes ſont trop grandes pour être appliquées à l'ouverture <lb/>du compas de proportion, prenez la moitié, tiers ou quart des unes <lb/>& </s> <s xml:id="echoid-s1942" xml:space="preserve">des autres; </s> <s xml:id="echoid-s1943" xml:space="preserve">ce qui en proviendra après l'operation ſera moitié, <lb/>tiers ou quart des dimenſions requiſes.</s> <s xml:id="echoid-s1944" xml:space="preserve"/> </p> <pb o="58" file="072" n="72" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div227" type="section" level="1" n="90"> <head xml:id="echoid-head145" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head146" style="it" xml:space="preserve">Etant donnez deux corps ſemblables, trouver quelle raiſon <lb/>ils ont entr'eux.</head> <p> <s xml:id="echoid-s1945" xml:space="preserve">PRenez lequel vous voudrez des côtez de l'un deſdits corps pro-<lb/>poſez, & </s> <s xml:id="echoid-s1946" xml:space="preserve">l'ayant porté à l'ouverture de quelque ſolide, prenez le <lb/>côté homologue de l'autre corps, & </s> <s xml:id="echoid-s1947" xml:space="preserve">voyez à quel nombre des ſolides <lb/>il convient; </s> <s xml:id="echoid-s1948" xml:space="preserve">les nombres auſquels ces deux côtez homologues con-<lb/>viennent, indiquent la raiſon des deux corps ſemblables entr'eux.</s> <s xml:id="echoid-s1949" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1950" xml:space="preserve">Que ſi le premier ayant été mis à l'ouverture de quelque ſolide, <lb/>le côté homologue du ſecond ne peut s'accommoder à l'ouverture <lb/>d'aucun nombre, portez le côté du premier corps à l'ouverture de <lb/>quelque autre ſolide juſqu'à ce que le côté homo!ogue du ſecond <lb/>corps s'accommode à l'ouverture de quelque nombre des ſolides.</s> <s xml:id="echoid-s1951" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div228" type="section" level="1" n="91"> <head xml:id="echoid-head147" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head148" style="it" xml:space="preserve">Conſtruire & diviſer une ligne ſervant à connoître les calibres <lb/>des boulets & Canons.</head> <p> <s xml:id="echoid-s1952" xml:space="preserve">L'Experience nous ayant appris qu'un boulet de fer fondu de <lb/>trois pouces de diamctre peſe quatre livres, il ſera facile de <lb/>trouver les diametres des autres boulets de differens poids & </s> <s xml:id="echoid-s1953" xml:space="preserve">de <lb/>même' métail, en cette maniere.</s> <s xml:id="echoid-s1954" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1955" xml:space="preserve">Portez l'étenduë de trois pouces à l'ouverture du quatriéme ſo-<lb/>lide, & </s> <s xml:id="echoid-s1956" xml:space="preserve">ſans changer l'ouverture du compas de proportion, prenez <lb/>ſur la même ligne des ſolides les ouvertures de tous les nombres de-<lb/>puis un juſqu'à 64; </s> <s xml:id="echoid-s1957" xml:space="preserve">portez toutes ces longueurs les unes aprés les <lb/>autres ſur une ligne droite tracée ſur une regle ou ſur le long d'une <lb/>des jambes du compas de proportion, & </s> <s xml:id="echoid-s1958" xml:space="preserve">là où ces diametres ſe ter-<lb/>mineront, marquez y les chifres qui feront connoître la péſanteur <lb/>des boulets.</s> <s xml:id="echoid-s1959" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1960" xml:space="preserve">Pour marquer enſuite les fractions de la livre, comme un quarrt, <lb/>une demie, trois quarts, portez le diametre du boulet d'une livre à <lb/>l'ouverture du quatriéme ſolide, & </s> <s xml:id="echoid-s1961" xml:space="preserve">prenez l'ouverture du premier <lb/>ſolide pour le diametre d'un quart de livre, l'ouverture du ſecond <lb/>ſolide pour une demie, & </s> <s xml:id="echoid-s1962" xml:space="preserve">celle du troiſiéme pour trois quarts de li-<lb/>vre, & </s> <s xml:id="echoid-s1963" xml:space="preserve">ainſi du reſte. </s> <s xml:id="echoid-s1964" xml:space="preserve">Quand on connoît le calibre des boulets, on <lb/>connoît auſſi le calibre du canon auquel ces boulets ſont propies, <lb/>parce qu'ordinairement on donne deux ou trois lignes pourle vent <lb/>des gros boulets, afin qu'ils puiſſent facilement y entrer, & </s> <s xml:id="echoid-s1965" xml:space="preserve">les pe-<lb/>tits à proportion.</s> <s xml:id="echoid-s1966" xml:space="preserve"/> </p> <pb o="59" file="073" n="73" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> <p> <s xml:id="echoid-s1967" xml:space="preserve">Les diametres des boulets ſe meſurent avec un compas ſpherique, <lb/>comme il ſera plus amplement expliqué, en parlant des inſtruments <lb/>propres à l'artillerie.</s> <s xml:id="echoid-s1968" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div229" type="section" level="1" n="92"> <head xml:id="echoid-head149" xml:space="preserve">USAGE IV.</head> <head xml:id="echoid-head150" style="it" xml:space="preserve">Etant donnez pluſieurs Solides ſemblables, en conſtruire un <lb/>autre auſſi ſenblable & égal aux donnez.</head> <p> <s xml:id="echoid-s1969" xml:space="preserve">POrtez lequel vous voudrez des côtez de quelqu'un des corps <lb/>propoſez à l'ouverture de quelque ſolide, & </s> <s xml:id="echoid-s1970" xml:space="preserve">ajoûtez à l'ouver-<lb/>ture des autres ſolides les côtez homologues des autres corps. </s> <s xml:id="echoid-s1971" xml:space="preserve">Ajoû-<lb/>tez enſemble les nombres qui expriment ainſi leur proportion, & </s> <s xml:id="echoid-s1972" xml:space="preserve"><lb/>prenez l'ouverture de la ſomme provenuë de cette addition, vous au-<lb/>rez le côté homologue d'un corps égal & </s> <s xml:id="echoid-s1973" xml:space="preserve">ſemblable à tous les autres.</s> <s xml:id="echoid-s1974" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1975" xml:space="preserve">Suppoſons, par exemple, que le côté choiſi du premier corps é-<lb/>tant porté à l'ouverture du cinquiéme ſolide, les côtez homologues <lb/>des autres conviennent, l'un à l'ouverture du ſeptiéme, & </s> <s xml:id="echoid-s1976" xml:space="preserve">l'autre à <lb/>celle du huitiéme ſolide. </s> <s xml:id="echoid-s1977" xml:space="preserve">J'ajoûte enſemble ces trois nombres 5, 7 & </s> <s xml:id="echoid-s1978" xml:space="preserve"><lb/>8, leur ſomme eſt 20, c'eſt pourquoi l'ouverture du 20<emph style="sub">me</emph> ſolide ſe-<lb/>ra le côté homologue d'un corps égal & </s> <s xml:id="echoid-s1979" xml:space="preserve">ſemblable aux trois autres.</s> <s xml:id="echoid-s1980" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div230" type="section" level="1" n="93"> <head xml:id="echoid-head151" xml:space="preserve">USAGE V.</head> <head xml:id="echoid-head152" style="it" xml:space="preserve">Etant donnez deux corps ſemblables & inégaux, en trouver un <lb/>troiſiéme auſſi ſemblable, & égal à la difference des donnez.</head> <p> <s xml:id="echoid-s1981" xml:space="preserve">POrtez lequel côté vous voudrez de l'un des corps à l'ouverture <lb/>de quelque ſolide que ceſoit, & </s> <s xml:id="echoid-s1982" xml:space="preserve">voyez à quelle autre ouverture <lb/>convient le côté homologue de l'autre corps; </s> <s xml:id="echoid-s1983" xml:space="preserve">ôtez le moindre nom-<lb/>bre du plus grand, & </s> <s xml:id="echoid-s1984" xml:space="preserve">prenez l'ouverture du nombre reſtant, vous <lb/>aurez le côté homologue du corps égal à la difference des deux.</s> <s xml:id="echoid-s1985" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1986" xml:space="preserve">Si, par exemple, le côté du plus grand étant porté à l'ouverture <lb/>du quinziéme ſolide, le côté homologue du moindre convient à <lb/>l'ouverture du neuviéme, ôtant 9 de 15, rcſte 6; </s> <s xml:id="echoid-s1987" xml:space="preserve">c'eſt pourquoi <lb/>l'ouverture du ſixiéme ſolide donnera le requis.</s> <s xml:id="echoid-s1988" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div231" type="section" level="1" n="94"> <head xml:id="echoid-head153" xml:space="preserve">USAGE VI.</head> <head xml:id="echoid-head154" style="it" xml:space="preserve">Entre deux lignes donnes, trouver deux moyenes <lb/>proportionnelles.</head> <p> <s xml:id="echoid-s1989" xml:space="preserve">SOient propoſées pour exemple deux lignes, dont l'une contienne <lb/>54 parties égales, & </s> <s xml:id="echoid-s1990" xml:space="preserve">l'autre 16; </s> <s xml:id="echoid-s1991" xml:space="preserve">ouvrez le compas de proportion, <lb/>& </s> <s xml:id="echoid-s1992" xml:space="preserve">portez la longueur de la ligne que contient 54 parties égales à <lb/>l'ouverture du cinquante-quatriéme ſolide, & </s> <s xml:id="echoid-s1993" xml:space="preserve">prenez l'ouverture <lb/> <pb o="60" file="074" n="74" rhead="CONSTRUCTION ET USAGES"/> du ſeiziéme, cette ouverture ſera la plus grande des deux moyenes <lb/>proportionnelles qu'on cherche; </s> <s xml:id="echoid-s1994" xml:space="preserve">& </s> <s xml:id="echoid-s1995" xml:space="preserve">cette ligne qui en cet exemple <lb/>contient 36 des mêmes parties égales étant portée à l'ouverture du-<lb/>dit cinquante-quariéme ſolide, ce qui ſe fait en refferrant les jam-<lb/>bes du compas de proportion, prenez une ſeconde fois l'ouverture <lb/>du ſeiziéme ſolide, vous aurez la moindre des deux moyenes pro-<lb/>portionnelles qu'on cherche, laquelle en cet exemple contiendra 24 <lb/>des mêmes parties égales, tellement que ces quatre lignes ſeront <lb/>en proportion continuë, & </s> <s xml:id="echoid-s1996" xml:space="preserve">en même raiſon que ces quatre nombres <lb/>54, 36, 24, 16.</s> <s xml:id="echoid-s1997" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s1998" xml:space="preserve">Si les lignes ſont trop longues, ou les nombres de leurs parties é-<lb/>gales trop grands, il ne faut que prendre leurs moitiez, tiers, ou <lb/>quarts, &</s> <s xml:id="echoid-s1999" xml:space="preserve">c. </s> <s xml:id="echoid-s2000" xml:space="preserve">& </s> <s xml:id="echoid-s2001" xml:space="preserve">operer comme deſſus. </s> <s xml:id="echoid-s2002" xml:space="preserve">Si, par exemple, on cherche <lb/>deux moyenes proportionnelles entre deux lignes, dont l'une con-<lb/>tient 32, & </s> <s xml:id="echoid-s2003" xml:space="preserve">l'autre 256, je prends le quart de chacune de ces lignes <lb/>qui ſera 8 & </s> <s xml:id="echoid-s2004" xml:space="preserve">64, je porte le premier nombre 8 à l'ouverture du <lb/>huitiéme ſolide, & </s> <s xml:id="echoid-s2005" xml:space="preserve">je prends l'ouverture du 64, qui me donne 16 <lb/>pour la premiere des deux moyenes proportionnelles; </s> <s xml:id="echoid-s2006" xml:space="preserve">puis je porte <lb/>la longueur de la ligne de 16 à l'ouverture du huitiéme ſolide, & </s> <s xml:id="echoid-s2007" xml:space="preserve"><lb/>l'ouverture du ſoixante-quatriéme me donne une ligne de 32 par-<lb/>ties égales, je multiplie ces deux nombres trouvez par quatre, pour <lb/>les remettre en leur entier, tellement qu'entre les deux lignes pro-<lb/>poſées la premiere des deux moyenes eſt de 94, & </s> <s xml:id="echoid-s2008" xml:space="preserve">la ſeconde de <lb/>128, & </s> <s xml:id="echoid-s2009" xml:space="preserve">ces quatre lignes en proportion continuë, ſont en même <lb/>raiſon que ces quatre nombres 32, 64, 128, 256.</s> <s xml:id="echoid-s2010" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div232" type="section" level="1" n="95"> <head xml:id="echoid-head155" xml:space="preserve">USAGE VII.</head> <head xml:id="echoid-head156" style="it" xml:space="preserve">Etant donné un Parallelipipede, trouver le côté d'un cube <lb/>qui lui ſoit égal.</head> <p> <s xml:id="echoid-s2011" xml:space="preserve">CHerchez un moyen proportionnel entre les deux côtez de la <lb/>baſe du parallelipipede, puis entre la valeur du nombre trouvé <lb/>& </s> <s xml:id="echoid-s2012" xml:space="preserve">la hauteur du parallelipipede cherchez le premier des deux nom-<lb/>bres moyens proportionnels, lequel ſera le côté du cube cherché.</s> <s xml:id="echoid-s2013" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2014" xml:space="preserve">Soient les deux côtez d'un parallelipede 24 & </s> <s xml:id="echoid-s2015" xml:space="preserve">54, & </s> <s xml:id="echoid-s2016" xml:space="preserve">ſa hau-<lb/>teur 63, on demande le côté d'un cube quilui ſoit égal; </s> <s xml:id="echoid-s2017" xml:space="preserve">je porte la <lb/>ligne de 54 parties égales à l'ouverture du cinquante-quatriéme <lb/>plan, & </s> <s xml:id="echoid-s2018" xml:space="preserve">je prends l'ouverture du vingt-quatriéme, laquelle portée <lb/>ſur la ligne des parties égales me donne 36 pour moyen proportion-<lb/>nel; </s> <s xml:id="echoid-s2019" xml:space="preserve">enſuite je porte 36 à l'ouverture du trente-ſixiéme ſolide, & </s> <s xml:id="echoid-s2020" xml:space="preserve">je <lb/>prends l'ouverture du ſoixante troiſiéme qui me donne peu moins <lb/> <pb o="61" file="075" n="75" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> de 44 & </s> <s xml:id="echoid-s2021" xml:space="preserve">demi pour le côté du cube égal au parallelipipede propoſé,</s> </p> </div> <div xml:id="echoid-div233" type="section" level="1" n="96"> <head xml:id="echoid-head157" xml:space="preserve">USAGE VIII.</head> <head xml:id="echoid-head158" style="it" xml:space="preserve">Conſtruire & diviſer une jauge, pour meſurer les tonneaux & <lb/>tous vaiſſeaux ſemblables propres à contenir des liqueurs.</head> <p> <s xml:id="echoid-s2022" xml:space="preserve">LA jauge dont je pretends parler ici eſt une regle de quelque <lb/>métal diviſée en certaines parties, qui marquent le nombre des <lb/>pintes contenuës dans le tonneau, l'ayant fait entrer par le bondon <lb/>juſqu'à ce que ſon extremité touche l'angle que fait le fonds avec <lb/>les douves dans la partie la plus éloignée du bondon, comme on <lb/> <anchor type="note" xlink:label="note-075-01a" xlink:href="note-075-01"/> voit la ligne AC, ſituée en forme de diagonale.</s> <s xml:id="echoid-s2023" xml:space="preserve"/> </p> <div xml:id="echoid-div233" type="float" level="2" n="1"> <note position="right" xlink:label="note-075-01" xlink:href="note-075-01a" xml:space="preserve">Fig. 13.</note> </div> <p> <s xml:id="echoid-s2024" xml:space="preserve">Cette jauge étant ainſi poſée, la diviſion qui répond au milieu <lb/>de l'ouverture du bondon au-dedans du tonneau, marque le nom-<lb/>bre des pintes qu'il contient.</s> <s xml:id="echoid-s2025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2026" xml:space="preserve">Mais il eſt à propos de rechanger la poſition de ladite verge, en <lb/>ſorte que ſon extremité C touche l'angle de l'autre fonds B, afin de <lb/>connoître ſi l'ouverture du bondon eſt juſtement au milieu, car s'il <lb/>ſe trouve quelque difference, il en faut prendre la moitié.</s> <s xml:id="echoid-s2027" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2028" xml:space="preserve">L'uſage de cette jauge eſt très-facile, puiſque ſans calcul on trou-<lb/>ve d'abord la capacité des tonneaux; </s> <s xml:id="echoid-s2029" xml:space="preserve">toute l'adreſſe conſiſte à la <lb/>bien divifer.</s> <s xml:id="echoid-s2030" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2031" xml:space="preserve">Pour cet effet on peut faire conſtruire un petit baril contenant un <lb/>ſeptier, c'eſt-à-dire huit pintes, lequel ſoit parfaitement ſemblable <lb/>aux tonneaux qui ſont en uſage dans le païs, car cette jauge ne peut <lb/>être juſte que dans des tonneaux ſemblables; </s> <s xml:id="echoid-s2032" xml:space="preserve">c'eſt-à-dire, qui ont les <lb/>diametres des fonds, & </s> <s xml:id="echoid-s2033" xml:space="preserve">celui à l'endroit du bondon avec la longueur <lb/>dans les mêmes proportions que celui qui a ſervi pour les diviſions.</s> <s xml:id="echoid-s2034" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2035" xml:space="preserve">Suppoſons, par exemple, que le diametre de chacun des fonds d'un <lb/>tonneau ſoit de vingt pouces, le diametre de la coupe à l'endroit du <lb/>bondon de vingt-deux pouces, & </s> <s xml:id="echoid-s2036" xml:space="preserve">ſa longueur interieure de trente <lb/>pouces, ce vaiſſeau contiendra vingt-ſept ſeptiers, meſure de Paris, <lb/>comme ſont les demi-queuës d'Orlcans; </s> <s xml:id="echoid-s2037" xml:space="preserve">& </s> <s xml:id="echoid-s2038" xml:space="preserve">ſa meſure diagonale qui <lb/>répond au milieu de l'ouverture du bondon ſera de vingt-cinq pou-<lb/>ces neuf lignes & </s> <s xml:id="echoid-s2039" xml:space="preserve">demie, comme il eſt aiſé de trouver par le calcul, <lb/> <anchor type="note" xlink:label="note-075-02a" xlink:href="note-075-02"/> puiſque dans le triangle rectangle ADC, on connoît le côté CD <lb/>15 pouces, & </s> <s xml:id="echoid-s2040" xml:space="preserve">DA 21, & </s> <s xml:id="echoid-s2041" xml:space="preserve">qu'ajouûtant leurs quarrez, on aura par la <lb/>quarante-ſeptiéme Prop. </s> <s xml:id="echoid-s2042" xml:space="preserve">du premier livre d'Euclide le quarré de <lb/>la diagonale ou hypotenuſe AC, & </s> <s xml:id="echoid-s2043" xml:space="preserve">enſuite ſa racine.</s> <s xml:id="echoid-s2044" xml:space="preserve"/> </p> <div xml:id="echoid-div234" type="float" level="2" n="2"> <note position="right" xlink:label="note-075-02" xlink:href="note-075-02a" xml:space="preserve">Fig. 13.</note> </div> <p> <s xml:id="echoid-s2045" xml:space="preserve">Suivant les mêmes proportions un baril dont les dimenſions ſe-<lb/>roient le tiers des prccedentes, contiendroit un ſeptier ou huit <lb/> <pb o="62" file="076" n="76" rhead="CONSTRUCTION ET USAGES"/> pintes, c'eſt-à-dire, que le diametre de chacun des fonds ſeroit de <lb/>ſix pouces huit lignes, celui du milieu deſept pouces quatre lignes, & </s> <s xml:id="echoid-s2046" xml:space="preserve"><lb/>ſa longueur interieure de dix pouces, ſa diagonale ſeroit de huit <lb/>pouces ſept lignes.</s> <s xml:id="echoid-s2047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2048" xml:space="preserve">Un autre baril dont les dimenſions ſeroient moitié de celles-ci, <lb/>contiendroit une pinte, c'eſt-à-dire, ſi le diametre de chacun des <lb/>fonds eſt de trois pouces quatre lignes, celui du milieu ſous le bon-<lb/>don de trois pouces huit lignes, & </s> <s xml:id="echoid-s2049" xml:space="preserve">la longueur interieure du baril <lb/>de cinq pouces, la diagonale qui répond au milieu de l'ouverture <lb/>du bondon ſera de quatre pouces trois lignes & </s> <s xml:id="echoid-s2050" xml:space="preserve">demie.</s> <s xml:id="echoid-s2051" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2052" xml:space="preserve">Prenez donc une verge ou regle longue de trois à quatre pieds, & </s> <s xml:id="echoid-s2053" xml:space="preserve"><lb/>ſervez vous de laquelle vous jugerez à propos de ces trois meſures, <lb/>comme, par exemple, ſivous voulez y marquer les ſeptiers, marquez <lb/>un point au milieu de ſa largeur diſtant d'un des bouts de huit pou-<lb/>ces ſept lignes; </s> <s xml:id="echoid-s2054" xml:space="preserve">pour y marquer un ſeptier, doublez cette meſure, & </s> <s xml:id="echoid-s2055" xml:space="preserve"><lb/>y marquez huit ſeptiers; </s> <s xml:id="echoid-s2056" xml:space="preserve">triplez la même meſure, & </s> <s xml:id="echoid-s2057" xml:space="preserve">y marquez <lb/>vingt-ſept ſeptiers; </s> <s xml:id="echoid-s2058" xml:space="preserve">quadruplez-la, & </s> <s xml:id="echoid-s2059" xml:space="preserve">y marquez ſoixante-quatre <lb/>ſeptiers, parce que les ſolides ſemblables ſont entr'eux comme les <lb/>cubes de leurs côtez homologues.</s> <s xml:id="echoid-s2060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2061" xml:space="preserve">Pour y marquer enſuite les autres nombres de ſeptiers, prenez <lb/>avec un compas commun la longueur de huit pouces ſept lignes, & </s> <s xml:id="echoid-s2062" xml:space="preserve"><lb/>l'ayant portée à l'ouverture du premier folide, arrêtez fixement en <lb/>cet état les deux regles ou jambes du compas de proportion, & </s> <s xml:id="echoid-s2063" xml:space="preserve">pre-<lb/>nez l'ouverture du ſecond ſolide, pour marquer ſur ladite jauge l'é-<lb/>tenduë qui convient à deux ſeptiers.</s> <s xml:id="echoid-s2064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2065" xml:space="preserve">Prenez de même l'ouverture du troiſiéme ſolide pour marquer <lb/>ſur la jauge l'étenduë de la diagonale qui convient à trois ſeptiers, <lb/>& </s> <s xml:id="echoid-s2066" xml:space="preserve">ainſi de ſuite, & </s> <s xml:id="echoid-s2067" xml:space="preserve">par ce moyen la jauge ſera diviſée de ſeptier <lb/>en ſeptier.</s> <s xml:id="echoid-s2068" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2069" xml:space="preserve">On pourra avec la même facilité y marquer les pintes; </s> <s xml:id="echoid-s2070" xml:space="preserve">car, par <lb/>exemple, la moitié de l'entenduë qui convient à deux ſeptiers ſervi-<lb/>ra poury marquer deux pintes; </s> <s xml:id="echoid-s2071" xml:space="preserve">la moitié de l'étenduë des trois ſep-<lb/>tiers ſervira pour y marquer trois pintes; </s> <s xml:id="echoid-s2072" xml:space="preserve">la moitié de la diagonale <lb/>de quatre ſeptiers ſera celle de quatre pintes, & </s> <s xml:id="echoid-s2073" xml:space="preserve">ainſi du reſte.</s> <s xml:id="echoid-s2074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2075" xml:space="preserve">Si le compas de proportion n'eſt point affez grand pour porter la <lb/>meſure diagonale d'un ſeptier à l'ouverture du premier ſolide, on y <lb/>portera celle d'une pinte, & </s> <s xml:id="echoid-s2076" xml:space="preserve">ayant marqué ſur la jauge autant de <lb/>pintes qu'on pourra, on aura les diagonales des ſeptiers de même <lb/>nombre, en doublant les meſures des pintes; </s> <s xml:id="echoid-s2077" xml:space="preserve">ainſi, par exemple, <lb/>ſi on double la diagonale de ſix pintes, on aura celle de ſix ſeptiers; <lb/></s> <s xml:id="echoid-s2078" xml:space="preserve"> <pb o="63" file="077" n="77" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> ſi on double la meſure de ſept pintes, on aura celle de ſeptſeptiers, <lb/>& </s> <s xml:id="echoid-s2079" xml:space="preserve">ainſi de toutes les autres meſures.</s> <s xml:id="echoid-s2080" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2081" xml:space="preserve">Si la meſure diagonale d'une pinte eſt encore trop grande pour <lb/>être portée à l'ouverture du premier ſolide, on y portera ſa moitié, <lb/>& </s> <s xml:id="echoid-s2082" xml:space="preserve">le compas de proportion reſtant ainſi ouvert, on prendra l'ouver-<lb/>ture du ſecond ſolide, que l'on doublera pour avoir la diagonale de <lb/>deux pintes; </s> <s xml:id="echoid-s2083" xml:space="preserve">ayant pris de même l'ouverture du troiſiéme ſolide, on <lb/>la doublera pour marquer ſur la jauge la diagonale de trois pintes, <lb/>& </s> <s xml:id="echoid-s2084" xml:space="preserve">ainſi du reſte.</s> <s xml:id="echoid-s2085" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2086" xml:space="preserve">Les marques des ſeptiers traverſeront toute la largeur de la ver-<lb/>ge, & </s> <s xml:id="echoid-s2087" xml:space="preserve">ſur icelles on gravera les chifres quiexpriment leurs nombres; <lb/></s> <s xml:id="echoid-s2088" xml:space="preserve">les marques des pintes ſeront plus petites, pour les diftinguer.</s> <s xml:id="echoid-s2089" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2090" xml:space="preserve">Afin que cette jauge puiſſe ſervir à meſurer pluſieurs ſortes de <lb/>tonneaux diffemblables, on pourra marquer d'autres diviſions ſur <lb/>chacune de ſes faces ſuivant les proportions des diametres, & </s> <s xml:id="echoid-s2091" xml:space="preserve">lon-<lb/>gueurs des differentes eſpeces de tonneaux uſitez dans le païs, & </s> <s xml:id="echoid-s2092" xml:space="preserve"><lb/>l'on marquera ſur un des bouts de chaque face les diametres & </s> <s xml:id="echoid-s2093" xml:space="preserve">lon-<lb/>gueurs qui ont ſervi a faire les diviſions; </s> <s xml:id="echoid-s2094" xml:space="preserve">par exemple, au bout de <lb/>la face où l'on aura marqué la diviſion precedente, on écrira, dia-<lb/>mettre des fonds 20, diamettre du milleu 22, longueur 40; </s> <s xml:id="echoid-s2095" xml:space="preserve">ou pour <lb/>abreger, diametre réduit 21, long. </s> <s xml:id="echoid-s2096" xml:space="preserve">30.</s> <s xml:id="echoid-s2097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2098" xml:space="preserve">Si pour les diviſions d'une autre face on ſert des meſures d'un <lb/>tonneau, dont le diametre de chaque fonds ſoit de vingt & </s> <s xml:id="echoid-s2099" xml:space="preserve">un <lb/>pouces, celui du milieu 23, & </s> <s xml:id="echoid-s2100" xml:space="preserve">la longueur interieure vingt-ſept <lb/>pouces & </s> <s xml:id="echoid-s2101" xml:space="preserve">demi, ce tonneau plus court que l'autre, mais plus gros, <lb/>contiendroit à peu près la même quantité, c'eſt-à-dire, vingt-ſept <lb/>ſeptiers, & </s> <s xml:id="echoid-s2102" xml:space="preserve">ſa diagonale ſeroit de vingt ſix pouces.</s> <s xml:id="echoid-s2103" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2104" xml:space="preserve">Si un autre tonneau a toutes ſes dimenſions du tiers des prece-<lb/>dentes, il contiendra un ſeptier, & </s> <s xml:id="echoid-s2105" xml:space="preserve">ſa diagonale AC ſera de huit <lb/>pouces huit lignes; </s> <s xml:id="echoid-s2106" xml:space="preserve">au moyen de quoi il ſera facile de faire les divi-<lb/>ſions, comme nous avons dit ci-devant, & </s> <s xml:id="echoid-s2107" xml:space="preserve">de marquér ſur ladite <lb/>face, diametre réduit 23, longueur 27 & </s> <s xml:id="echoid-s2108" xml:space="preserve">demi.</s> <s xml:id="echoid-s2109" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2110" xml:space="preserve">Si l'on fait quatre diviſions differentes ſur les quatre faces de la re-<lb/>gle, on aura ſur cette même regle quatre differentes jauges qui ſervi-<lb/>ront à meſurer quatre eſpeces differentes de tonneaux, & </s> <s xml:id="echoid-s2111" xml:space="preserve">l'on choi-<lb/>ſira celle qui conviendra le mieux pour jauger ceux qui ſe preſente-<lb/>ront, en examinant les proportions de leurs diametres & </s> <s xml:id="echoid-s2112" xml:space="preserve">longueurs.</s> <s xml:id="echoid-s2113" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2114" xml:space="preserve">Au lieu de ſe ſervir des jambes du compas de proportion pour di-<lb/>viſer la jauge diagonale dont nous venons de parler, on peut encore <lb/>mieux ſe ſervir de la table des ſolides, rapportée à la page 40 Ainſi <lb/> <pb o="64" file="078" n="78" rhead="CONSTRUCTION ET USAGES"/> ayant reconnu par le calcul, que la diagonale d'un tonneau qui <lb/>contient 47 ſeptiers, eſt de 26 pouces; </s> <s xml:id="echoid-s2115" xml:space="preserve">il ſera facile de trouver les <lb/>autres diagonales des tonneaux de toute grandeur propoſée, qui au-<lb/>ront les mêmes proportions du diametre reduit à la longueur, <lb/>comme de 22 à 27 & </s> <s xml:id="echoid-s2116" xml:space="preserve">demi, ou pour abreger, comme de 4 à 5,</s> </p> <p> <s xml:id="echoid-s2117" xml:space="preserve">Soit propoſé pour exemple à trouver la diagonale d'un quarteau <lb/>contenant 9 ſeptiers; </s> <s xml:id="echoid-s2118" xml:space="preserve">cherchez dans la ſuſdite table le nombre qui <lb/>répond au neuviéme ſolide, vous trouverez 520; </s> <s xml:id="echoid-s2119" xml:space="preserve">cherchez en mê-<lb/>me tems le nombre correſpondant au vingt-ſeptiéme ſolide, vous y <lb/>trouvez 750, formez - en la regle de trois, de la maniere qui ſuit:</s> <s xml:id="echoid-s2120" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div236" type="section" level="1" n="97"> <head xml:id="echoid-head159" xml:space="preserve">750. 520. 26. 18.</head> <p> <s xml:id="echoid-s2121" xml:space="preserve">La regle étant faite, vous trouverez 18 pouces pour diagonale <lb/>de 9 ſeptiers. </s> <s xml:id="echoid-s2122" xml:space="preserve">Les Tonneliers des environs de Paris, font à peu près <lb/>leurs tonneaux dans les proportions de 4 à 5, comme ſeroit, par <lb/>exemple, un demi-muid ayant 19 pouces 2 lignes de diametrre ré-<lb/>duit, & </s> <s xml:id="echoid-s2123" xml:space="preserve">24 pouces de longueur interieure, & </s> <s xml:id="echoid-s2124" xml:space="preserve">dans ce cas ſa diago-<lb/>nale ſeroit de 22 pouces 8 lignes & </s> <s xml:id="echoid-s2125" xml:space="preserve">demie, comme il eſt aiſé dere-<lb/>connoître par le calcul.</s> <s xml:id="echoid-s2126" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2127" xml:space="preserve">L'autre eſpece de tonneau, dont il eſt parlé à la page 61, eſt plus <lb/>long, car ſon diamettre réduit eſt à ſa longueur interieure comme <lb/>7 à 10.</s> <s xml:id="echoid-s2128" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2129" xml:space="preserve">Mais en general, ſi-tôt qu'on a reconnu les proportions uſitées <lb/>dans un païs pour la fabrique destonneaux, on trouvera premiere-<lb/>ment la diagonale d'un vaiffeau contenant certain nombre de ſep-<lb/>tiers, par la quarante-ſeptiéme du premier Livre d'Euclide, ou bien <lb/>par l'experience, & </s> <s xml:id="echoid-s2130" xml:space="preserve">enſuite les diagonales de tous les autres ton-<lb/>neaux faits dans les mêmes proportions, par le moyen de la ſuſdite <lb/>table des ſolides.</s> <s xml:id="echoid-s2131" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div237" type="section" level="1" n="98"> <head xml:id="echoid-head160" xml:space="preserve">SECTION VI.</head> <head xml:id="echoid-head161" style="it" xml:space="preserve">Contenant la conſtruction & l'uſage de pluſieurs autres <lb/>ſortes de jauges.</head> <p> <s xml:id="echoid-s2132" xml:space="preserve">LA jauge que nous avons ci-devant expliquée n'eſt propre qu'à <lb/>meſurer des vaiffeaux ſemblabes; </s> <s xml:id="echoid-s2133" xml:space="preserve">mais celles dont nous allons <lb/>parler, peuvent ſervir à meſurer toutes ſortes de vaiſſeaux cylindri-<lb/>ques, quoiqu'ils ne ſoient pas ſemblables.</s> <s xml:id="echoid-s2134" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2135" xml:space="preserve">Ces methodes de jauger ſont fondées ſur la ſuppoſition que le <lb/>tonneau eſt égal au cylindre qui a ſa hauteur égale à la longueur in-<lb/>terieure du tonneau, & </s> <s xml:id="echoid-s2136" xml:space="preserve">ſa baſe égale au cercle dont le diametre eſt <lb/>moyen proportionnel arithmetique entre les diamettres à l'endroit <lb/> <pb o="65" file="079" n="79" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> des fonds, & </s> <s xml:id="echoid-s2137" xml:space="preserve">celui du milieu ſous le bondon, ce qui eſt affez exact <lb/>pour la pratique, principalement lorſqu'il y a peu de difference en-<lb/>tre les cercles des fonds & </s> <s xml:id="echoid-s2138" xml:space="preserve">celui du milieu du tonneau.</s> <s xml:id="echoid-s2139" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2140" xml:space="preserve">Pour conſtruire la premiere ſorte de jauge; </s> <s xml:id="echoid-s2141" xml:space="preserve">il faut déterminer la <lb/>meſure dont on veut ſeſervir, en la comparant avec quelque vaſe <lb/>regulier, comme un cylindre concave; </s> <s xml:id="echoid-s2142" xml:space="preserve">dans lequel on verſera une <lb/>meſure du païs remplie d'eau ou de quelque autre liqueur, dont on <lb/>marquera exactement le diametre & </s> <s xml:id="echoid-s2143" xml:space="preserve">la profondeur occupée par la-<lb/>dite liqueur.</s> <s xml:id="echoid-s2144" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2145" xml:space="preserve">Si, par exemple, on veut faire cette jauge pour Paris, où la pinte <lb/>contient quarante-huit pouces cubiques, ou bien ſoixante & </s> <s xml:id="echoid-s2146" xml:space="preserve">un pou-<lb/>ces cylindriques, on trouvera par le calcul, qu'un cylindre concave <lb/>ayant trois pouces onze lignes & </s> <s xml:id="echoid-s2147" xml:space="preserve">un tiers de diametre, & </s> <s xml:id="echoid-s2148" xml:space="preserve">autant de <lb/>profondeur, contient une pinte meſure de Paris, & </s> <s xml:id="echoid-s2149" xml:space="preserve">qu'un cylindre <lb/>dont les meſures ſont doubles, c'eſt-à-dire, de ſept pouces dix lignes <lb/>& </s> <s xml:id="echoid-s2150" xml:space="preserve">deux tiers, contient un ſeptier ou huit pintes; </s> <s xml:id="echoid-s2151" xml:space="preserve">car les ſolides ſem-<lb/>blables ſontentr'eux comme les cubes de leurs côtez homologues.</s> <s xml:id="echoid-s2152" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2153" xml:space="preserve">Cela ſuppoſé, portez cette longueur de 3 pouces 11 lignes i tiers <lb/>ſur une des faces de la jauge, autant de fois qu'elle y pourra être <lb/>compriſe, & </s> <s xml:id="echoid-s2154" xml:space="preserve">y marquez des points, ou vous écrirez 1, 2, 3, 4, 5, &</s> <s xml:id="echoid-s2155" xml:space="preserve">c. <lb/></s> <s xml:id="echoid-s2156" xml:space="preserve"> <anchor type="note" xlink:label="note-079-01a" xlink:href="note-079-01"/> vous ſubdiviſerez chacune de ces parties en quatre, ou plus, ſi vous <lb/>voulez. </s> <s xml:id="echoid-s2157" xml:space="preserve">Cette face ainſi diviſée, ſera appellée côté des parties éga-<lb/>les, & </s> <s xml:id="echoid-s2158" xml:space="preserve">ſervira à meſurer la longueur des tonneaux.</s> <s xml:id="echoid-s2159" xml:space="preserve"/> </p> <div xml:id="echoid-div237" type="float" level="2" n="1"> <note position="right" xlink:label="note-079-01" xlink:href="note-079-01a" xml:space="preserve">Fig. 14.</note> </div> <p> <s xml:id="echoid-s2160" xml:space="preserve">Il faut auſſi marquer ſur une autre face de la jauge le diametre du <lb/>même cylindre, que nous ſuppoſons pareillement de trois pouces <lb/>onze lignes & </s> <s xml:id="echoid-s2161" xml:space="preserve">un tiers, & </s> <s xml:id="echoid-s2162" xml:space="preserve">enſuite les diametres des cercles doubles, <lb/>triples, quadruples, &</s> <s xml:id="echoid-s2163" xml:space="preserve">c. </s> <s xml:id="echoid-s2164" xml:space="preserve">par quelqu'une des methodes ci-devant <lb/>expliquées pour diviſer la ligne des plans du compas de proportion, <lb/>dont la plus facile & </s> <s xml:id="echoid-s2165" xml:space="preserve">la plus courte eſt de faire un triangle Iſocele <lb/>rectangle ABC, dont chacune des jambes autour de l'angle droit <lb/> <anchor type="note" xlink:label="note-079-02a" xlink:href="note-079-02"/> ſoit de trois pouces onze lignes un tiers, l'hypotenuſe BC ſera le <lb/>diametre d'un cercle double; </s> <s xml:id="echoid-s2166" xml:space="preserve">c'eſt pourquoi ayant prolongé vers D <lb/>une deſdites jambes AB autant quil eſt beſoin pour y marquer tous <lb/>les diametres des tonneaux qu'on veut meſurer, vous porterez de A <lb/>vers D ladite hypotenuſe, & </s> <s xml:id="echoid-s2167" xml:space="preserve">au point où elle ſe terminera vous <lb/>marquerez le chifre 2; </s> <s xml:id="echoid-s2168" xml:space="preserve">prenez enſuite la diſtance C 2, & </s> <s xml:id="echoid-s2169" xml:space="preserve">l'ayant <lb/>portée ſur la ligne AD, vous marquerez le chifre 3 au point où <lb/>elle ſe terminera; </s> <s xml:id="echoid-s2170" xml:space="preserve">prenez de même la diſtance C 3, & </s> <s xml:id="echoid-s2171" xml:space="preserve">l'ayant portée <lb/>ſur la ligne AD, vous y marquerez le chifre 4, & </s> <s xml:id="echoid-s2172" xml:space="preserve">ainſi de tous les <lb/>autres diametres que vous voudrez marquer ſur la jauge.</s> <s xml:id="echoid-s2173" xml:space="preserve"/> </p> <div xml:id="echoid-div238" type="float" level="2" n="2"> <note position="right" xlink:label="note-079-02" xlink:href="note-079-02a" xml:space="preserve">Fig. 15.</note> </div> <pb o="66" file="080" n="80" rhead="CONSTRUTION ET USAGES"/> <p> <s xml:id="echoid-s2174" xml:space="preserve">Remarquez que la ligne A 4, qui eſt le diametre d'un cercle qua-<lb/>druple du premier eſt aouble de AC, ou AB, parce que les cercles <lb/>ſont entr'eux comme les quarrez de leurs diametres. </s> <s xml:id="echoid-s2175" xml:space="preserve">Or AB étant <lb/>1, ſon quarré eſt 1, & </s> <s xml:id="echoid-s2176" xml:space="preserve">la ligne A 4 étant ſuppoſée 2, ſon quarrée eſt 4.</s> <s xml:id="echoid-s2177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2178" xml:space="preserve">Pour vous ſervir de cette jauge, appliquez le côté des parties éga-<lb/>les ſur la longueur exterieure du tonneau, dont il faudra diminuer <lb/>la profondeur des jables de chaque fond, & </s> <s xml:id="echoid-s2179" xml:space="preserve">l'épaiſſeur des douves <lb/>qui compoſent les mêmes fonds, afin d'avoir au juſte ſa longueur <lb/>interieure.</s> <s xml:id="echoid-s2180" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2181" xml:space="preserve">Appliquez enſuite le côté des diametres de ladite jauge ſur le dia-<lb/>metre des fonds du tonneau, & </s> <s xml:id="echoid-s2182" xml:space="preserve">remarquez le nombre qui leur <lb/>convient, & </s> <s xml:id="echoid-s2183" xml:space="preserve">s'ils ſont égaux ou non; </s> <s xml:id="echoid-s2184" xml:space="preserve">car s'il y a quelque differen-<lb/>ce entre les diametres des fonds, il faut les egaler, en prenant la <lb/>moitié de leur ſomme.</s> <s xml:id="echoid-s2185" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2186" xml:space="preserve">Faites encore entrer la jaūge à plomb par le trou du bondon, <lb/>afin d'avoir le plus grand diametre interieur de la coupe du milieu, <lb/>que vous ajoûterez avec le diametre des fonds, & </s> <s xml:id="echoid-s2187" xml:space="preserve">en prendrez la <lb/>moitié, pour avoir un diametre moyen arithmetique, lequel étant <lb/>multiplié par la longueur interieure du tonneau, le produit vous <lb/>marquera le nombre des meſures qu'il contient.</s> <s xml:id="echoid-s2188" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2189" xml:space="preserve">Soit pour exemple la longueur interieure d'un tonneau de quatre <lb/>meſures & </s> <s xml:id="echoid-s2190" xml:space="preserve">trois quarts, après en avoir diminué deux pouces de cha-<lb/>que côté ſur la longueur exterieure, ſçavoir un pouce & </s> <s xml:id="echoid-s2191" xml:space="preserve">demi pour <lb/>la profondeur des jables, & </s> <s xml:id="echoid-s2192" xml:space="preserve">demi pouce pour l'épaiſſeur des douves <lb/>qui compoſent les fonds: </s> <s xml:id="echoid-s2193" xml:space="preserve">ſoit auſſi le diametre de chaque fonds 15 <lb/>& </s> <s xml:id="echoid-s2194" xml:space="preserve">le diametre du milieu 17 parties, j'ajoûte 15 & </s> <s xml:id="echoid-s2195" xml:space="preserve">17, la ſomme eſt <lb/>32, dont la moitié eſt 16, que je multiplie par la longueur 4 & </s> <s xml:id="echoid-s2196" xml:space="preserve">trois <lb/>quarts, le produit 76 ſera le nombre des pintes ou meſures conte-<lb/>nuës dans le tonneau propoſé.</s> <s xml:id="echoid-s2197" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2198" xml:space="preserve">Pour la ſeconde ſorte de jauge, on trouve par le calcul, qu'un <lb/>cylindre qui a pour diametre trois pieds trois pouces & </s> <s xml:id="echoid-s2199" xml:space="preserve">ſix lignes, <lb/>& </s> <s xml:id="echoid-s2200" xml:space="preserve">autant pour ſa hauteur, contient mille pintes, meſure de Paris.</s> <s xml:id="echoid-s2201" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2202" xml:space="preserve">Prenez donc ſur une regle une longueur de trois pieds trois pou-<lb/>ces & </s> <s xml:id="echoid-s2203" xml:space="preserve">ſix lignes; </s> <s xml:id="echoid-s2204" xml:space="preserve">diviſez cette longueur en dix; </s> <s xml:id="echoid-s2205" xml:space="preserve">chacune de ces par-<lb/>ties ſera le diametre, & </s> <s xml:id="echoid-s2206" xml:space="preserve">la hauteur d'un cylindre contenant une pin-<lb/>te, puiſque les ſolides ſemblables ſont entr'eux comme les cubes de <lb/>leurs côtez homologues: </s> <s xml:id="echoid-s2207" xml:space="preserve">ſubdiviſez encore chacune de ces parties <lb/>en dix, ce qui ſe pourra facilement faire par le moyen de la ligne <lb/>des parties égales du compas de proportion; </s> <s xml:id="echoid-s2208" xml:space="preserve">chacune de ces dernie-<lb/>res parties ſera la hauteur, & </s> <s xml:id="echoid-s2209" xml:space="preserve">le diametre d'un cylindre ſolide con-<lb/> <pb o="67" file="081" n="81" rhead="DU COMPAS DE PROPORTION. Liv.II.Ch.II."/> tenant la milliéme partie d'une pinte. </s> <s xml:id="echoid-s2210" xml:space="preserve">Vous ajoûterez ces petites <lb/>parties juſqu'au bout de vôtre regle, & </s> <s xml:id="echoid-s2211" xml:space="preserve">les ayant chifrées de cinq <lb/> <anchor type="note" xlink:label="note-081-01a" xlink:href="note-081-01"/> en cinq vôtre jauge ſera faite. </s> <s xml:id="echoid-s2212" xml:space="preserve">Vous lui pourrez donner quatre à <lb/>cinq pieds de long, ſi vous voulez qu'elle ſerve pour meſurer de <lb/>grands vaiſſeaux, comme ſont les pipes, &</s> <s xml:id="echoid-s2213" xml:space="preserve">c.</s> <s xml:id="echoid-s2214" xml:space="preserve"/> </p> <div xml:id="echoid-div239" type="float" level="2" n="3"> <note position="right" xlink:label="note-081-01" xlink:href="note-081-01a" xml:space="preserve">Fig. 16.</note> </div> <p> <s xml:id="echoid-s2215" xml:space="preserve">Pour vous en ſervir, voyez combien les diametres des fonds &</s> <s xml:id="echoid-s2216" xml:space="preserve">c <lb/>de la bonde, comme auſſi la longueur du vaiſſcau, contiennent de <lb/>petites parties de vôtre jauge.</s> <s xml:id="echoid-s2217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2218" xml:space="preserve">Par la longueur du vaiſſeau, il faut entendre la longueur interieu-<lb/>re ,qui eſt l'eſpace compris en ligne droite entre les fonds; </s> <s xml:id="echoid-s2219" xml:space="preserve">& </s> <s xml:id="echoid-s2220" xml:space="preserve">par les <lb/>diametres, on entend les diametres pris en-dedans entre les douves.</s> <s xml:id="echoid-s2221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2222" xml:space="preserve">Si les diametres des fonds ſont égaux, comparez l'un d'eux avec <lb/>le diametre de la coupe du millieu, à l'endroit du bondon, le mi-<lb/>lieu entre les deux s'appellera le diametre égalé du tonneau.</s> <s xml:id="echoid-s2223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2224" xml:space="preserve">Si les diametres des fonds ne ſont pas égaux, ajoûtez-les enſem-<lb/>ble & </s> <s xml:id="echoid-s2225" xml:space="preserve">prenez-en la moitié, qui s'appellera le diametre égalé des <lb/>fonds; </s> <s xml:id="echoid-s2226" xml:space="preserve">comparez enſuite le diametre égalé avec le grand diametre <lb/>du milieu au deſſous du bondon; </s> <s xml:id="echoid-s2227" xml:space="preserve">ajoûtez-les enſemble, & </s> <s xml:id="echoid-s2228" xml:space="preserve">prenez <lb/>la moitie de leur ſomme, pour avoir le diametre égalé du vaiſſeau.</s> <s xml:id="echoid-s2229" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2230" xml:space="preserve">Multipliez le diametre égalé du vaſſeau par lui même, & </s> <s xml:id="echoid-s2231" xml:space="preserve">le <lb/>produit par la longueur, vous aurez le nombre de milliéme de <lb/>pintes contenuës dans le vaiſſeau; </s> <s xml:id="echoid-s2232" xml:space="preserve">tranchez donc les trois dernie-<lb/>res figures vers la droite, les reſtantes montreront combien ledit <lb/>vaiſſeau contient de pintes.</s> <s xml:id="echoid-s2233" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2234" xml:space="preserve">Soit pour exemple le diametre de chaque fonds, 58 parties de la-<lb/>dite jauge, & </s> <s xml:id="echoid-s2235" xml:space="preserve">le diametre du milieu 62 ajoûtez enſemble ces deux <lb/>nombres, vous aurez 120, dont la moitie 60 eſt le diametre égalé <lb/>du vaiſſeau; </s> <s xml:id="echoid-s2236" xml:space="preserve">multiplipliez ce nombre par lui-même, pour avoir ſon <lb/>quarré 3600; </s> <s xml:id="echoid-s2237" xml:space="preserve">ſuppoſons la longueur interieure du vaiſſeau 80 des <lb/>mêmes parties; </s> <s xml:id="echoid-s2238" xml:space="preserve">multipliez 3600 par 80, le produit ſera 288000, <lb/>dont ayant retranché les trois dernieres figures, on connoîtra que <lb/>ce vaiſſeau contient 288 pintes, meſure de Paris.</s> <s xml:id="echoid-s2239" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2240" xml:space="preserve">Ces methodes de jauger ſont aſſez exactes dans la pratique, lorſ-<lb/>qu'il y a peu de difference entre les cercles des fonds & </s> <s xml:id="echoid-s2241" xml:space="preserve">celui du mi-<lb/>lieu du tonneau, comme aux muids qui ſe font aux environs de Pa-<lb/>ris; </s> <s xml:id="echoid-s2242" xml:space="preserve">mais lorſque la difference eſt conſiderable, comme elle eſt aux <lb/>pipes d'Anjou, dont le diamettre du milieu eſt beaucoup plus grand <lb/>que celui des fonds, la meſure faite par les methodes que nous ve-<lb/>nons de donner, ſeroit un peu plus petite que la veritable; </s> <s xml:id="echoid-s2243" xml:space="preserve">mais <lb/>pour en approcher, & </s> <s xml:id="echoid-s2244" xml:space="preserve">la rendre plus juſte, diviſez en ſept la diffe-<lb/> <pb o="68" file="082" n="82" rhead="CONSRTUTION ET USAGES"/> rence qui fait l'excès du diametre du milieu, & </s> <s xml:id="echoid-s2245" xml:space="preserve">ajoûtez en quatre <lb/>au diametre égalé desfonds, comme, ſi par exemple le diametre des <lb/>fonds étoit de 50 petites parties, & </s> <s xml:id="echoid-s2246" xml:space="preserve">celui du milieu de 57 des mê-<lb/>mes parties, vous en prendrez 54 pour le diametre égalé du vaiſ-<lb/>ſeau, & </s> <s xml:id="echoid-s2247" xml:space="preserve">ferez le reſte, comme il a été dit ci-devant</s> </p> <p> <s xml:id="echoid-s2248" xml:space="preserve">A yant connu par la jauge combien un tonneau contient de pin-<lb/>tes de Paris, ou pourra ttouver ce que le même vaiſſeau contient de <lb/>toutes autres meſures par la methode ſuivante.</s> <s xml:id="echoid-s2249" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2250" xml:space="preserve">La pinte d'eau douce, meſure de Paris, peſe trente une onces <lb/>poids de marc, c'eſt pourquoi il n'y aura qu'à faire peſer dans le <lb/>païs où l'on ſe trouvera, la meſure d'eau, & </s> <s xml:id="echoid-s2251" xml:space="preserve">par une regle de pro-<lb/>portion on trouvera ce que l'on cherche.</s> <s xml:id="echoid-s2252" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2253" xml:space="preserve">Si, par exemple, la meſure d'eau de quelque païs peſe cinquante <lb/>onces, & </s> <s xml:id="echoid-s2254" xml:space="preserve">que l'on veüille ſçavoir combien de pareilles meſures ſont <lb/>contenuës dans un muid qui contient 288 pintes, meſure de Paris, <lb/>on dira par une regle de trois, comme 50 ſont à 31, ainſi 288 pintes <lb/>ſont a un quatriéme nombre, la regle étant faite, on trouvera 178 <lb/>meſures & </s> <s xml:id="echoid-s2255" xml:space="preserve">demie.</s> <s xml:id="echoid-s2256" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2257" xml:space="preserve">On pouroit marquer ſur une des faces de ladite jauge les pieds <lb/>& </s> <s xml:id="echoid-s2258" xml:space="preserve">pouces, & </s> <s xml:id="echoid-s2259" xml:space="preserve">ſubdiviſer chaque pouce en quatre: </s> <s xml:id="echoid-s2260" xml:space="preserve">ce qui donne-<lb/>roit un ſecond moyen de jauger les tonneaux, qui ſervira comme <lb/>de preuve. </s> <s xml:id="echoid-s2261" xml:space="preserve">On marquera les pieds par des chifres romains, & </s> <s xml:id="echoid-s2262" xml:space="preserve">les <lb/>pouce par d'autres chifres plus petits.</s> <s xml:id="echoid-s2263" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2264" xml:space="preserve">Nous avons dit ci-devant, que la pinte de Paris contient 61 pou-<lb/>ces cylindriques. </s> <s xml:id="echoid-s2265" xml:space="preserve">C'eſt pourquoi ayant réduit la ſolidité du vaiſſeau <lb/>en pouces cylindriques, il faudra les diviſer par 61, pour avoir le <lb/>nombre des pintes qu'il contient. </s> <s xml:id="echoid-s2266" xml:space="preserve">Un exemple ou deux vont don-<lb/>ner tout l'éclairciſſement neceſſaire.</s> <s xml:id="echoid-s2267" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2268" xml:space="preserve">Soit, par exemple, la longueur interieure d'un tonneau 36 pou-<lb/>ces, le diametre des fonds 23 pouces, & </s> <s xml:id="echoid-s2269" xml:space="preserve">celui du millieu du tonneau <lb/>25. </s> <s xml:id="echoid-s2270" xml:space="preserve">Ajoûtez ces deux diametres, leur ſomme eſt 48, dont la moitié <lb/>eſt 24 pour le diametre égalé. </s> <s xml:id="echoid-s2271" xml:space="preserve">Multipliez ce nombre 24 par lui-<lb/>même, le produit eſt 576; </s> <s xml:id="echoid-s2272" xml:space="preserve">& </s> <s xml:id="echoid-s2273" xml:space="preserve">le multipliez encore par 36, vous <lb/>trouverez 20736 pouces cylindriques leſquels étant diviſez par <lb/>61, le quotien eſt 339 pintes, & </s> <s xml:id="echoid-s2274" xml:space="preserve">environ trois quarts.</s> <s xml:id="echoid-s2275" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2276" xml:space="preserve">Si les meſures dont on s'eſt ſervi pour la longueur & </s> <s xml:id="echoid-s2277" xml:space="preserve">les diametres <lb/>ſont des quarts de pouce, on diviſera le dernier produit par 3904, <lb/>pour avoir le nombre des pintes.</s> <s xml:id="echoid-s2278" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2279" xml:space="preserve">Soit, par exemple, la longueur interieure duvaiſſeau propoſe2; </s> <s xml:id="echoid-s2280" xml:space="preserve">35 <lb/>pouces & </s> <s xml:id="echoid-s2281" xml:space="preserve">un quart, le diametre des fonds 23 pouces, & </s> <s xml:id="echoid-s2282" xml:space="preserve">celui du <lb/> <pb o="69" file="083" n="83" rhead="DU COMPAS DE PROPORTION. Liv.II.Ch.II."/> milieu 25 pouces & </s> <s xml:id="echoid-s2283" xml:space="preserve">un demi; </s> <s xml:id="echoid-s2284" xml:space="preserve">ajoûtez enſemble ces deux diame-<lb/>tres, leur ſomme ſera 48 & </s> <s xml:id="echoid-s2285" xml:space="preserve">demi, & </s> <s xml:id="echoid-s2286" xml:space="preserve">ſa moitié 24 un quart, leſ-<lb/>quels pour la facilité du calcul vous reduιrez en quarts, le nombre <lb/>eſt 97 qu'il faut multιplier par lui-même, le produit ſera 9409, <lb/>leſquels il faut multiplier par 141, à quoi ſe réduiſent les 35 pou-<lb/>ces un quart de longueur, ce dernier produit ſera 1326669, le-<lb/>quel étant diviſé par 3904, le quotien ſera, comme ci-devant, 339 <lb/>pintes, & </s> <s xml:id="echoid-s2287" xml:space="preserve">environ trois quarts.</s> <s xml:id="echoid-s2288" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div241" type="section" level="1" n="99"> <head xml:id="echoid-head162" style="it" xml:space="preserve">Conſtruction & Vſage d'une nouvelle jauge.</head> <p> <s xml:id="echoid-s2289" xml:space="preserve">MOnſieur Sauveur, Maître de Mathematiques des Rois d'Eſ-<lb/>pagne & </s> <s xml:id="echoid-s2290" xml:space="preserve">d'Angleterre, & </s> <s xml:id="echoid-s2291" xml:space="preserve">de Meſſeigneurs les Princes Fils de <lb/>France, Profeſſeur Royal, & </s> <s xml:id="echoid-s2292" xml:space="preserve">de l'Academie des Sciences, a bien <lb/>voulu nous communiquer une nouvelle jauge de ſon invention, par <lb/>le moyen de laquelle on trouve par la ſeule addition le contenu de <lb/>toutes ſortes de tonneaux, au lieu que toutes les manieres dejauger <lb/>qui ont paru juſqu'à preſent, ne ſe peuvent executer que par des <lb/>multiplications & </s> <s xml:id="echoid-s2293" xml:space="preserve">diviſions.</s> <s xml:id="echoid-s2294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2295" xml:space="preserve">Pour conſtruire cette jauge, choiſiſſez une piece de bon bois ſec <lb/> <anchor type="note" xlink:label="note-083-01a" xlink:href="note-083-01"/> & </s> <s xml:id="echoid-s2296" xml:space="preserve">ſans nœuds, comme de cormier ou poirier, longue d'environ 5 <lb/>pieds en forme de parallelipipede rectangle, & </s> <s xml:id="echoid-s2297" xml:space="preserve">de 6 ou 7 lignes d'é-<lb/>paiſſeur à chacune de ſes quatre faces qui doivent être égales. </s> <s xml:id="echoid-s2298" xml:space="preserve">La <lb/>figure 17 montre à peu près le dévelopement de ces quatre faces.</s> <s xml:id="echoid-s2299" xml:space="preserve"/> </p> <div xml:id="echoid-div241" type="float" level="2" n="1"> <note position="right" xlink:label="note-083-01" xlink:href="note-083-01a" xml:space="preserve">De laVII. <lb/>Planche. <lb/>Fig. 17.</note> </div> <p> <s xml:id="echoid-s2300" xml:space="preserve">Sur la premiere de ces quatre faces on marquera des nombres qui <lb/>ſerviront à meſurer les diametres des tonneaux.</s> <s xml:id="echoid-s2301" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2302" xml:space="preserve">Les diviſions de la ſeconde face ſerviront à meſurer leurs lon-<lb/>gueurs.</s> <s xml:id="echoid-s2303" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2304" xml:space="preserve">Les diviſions de la troiſiéme face ſeront pour le contenu des ton-<lb/>neaux. </s> <s xml:id="echoid-s2305" xml:space="preserve">Enfin, on trouvera ſur la quatriéme face le nombre desſep-<lb/>tiers & </s> <s xml:id="echoid-s2306" xml:space="preserve">pintes qu'ils contiennent.</s> <s xml:id="echoid-s2307" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2308" xml:space="preserve">Ces diviſions ſe ſeront en la maniere qui ſuit.</s> <s xml:id="echoid-s2309" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2310" xml:space="preserve">Diviſez premierement la quatriéme face de pouce en pouce, & </s> <s xml:id="echoid-s2311" xml:space="preserve"><lb/>chaque pouce en dix parties égales. </s> <s xml:id="echoid-s2312" xml:space="preserve">Ces petites diviſions marque-<lb/>ront des pintes, chifrant 1, 2, 3, 4, 5, 6, &</s> <s xml:id="echoid-s2313" xml:space="preserve">c. </s> <s xml:id="echoid-s2314" xml:space="preserve">& </s> <s xml:id="echoid-s2315" xml:space="preserve">de 8 en 8 ce ſeront <lb/>des ſeptiers, puiſqu'un ſeptier contient huit pintes. </s> <s xml:id="echoid-s2316" xml:space="preserve">Sur undes bouts <lb/>de cette quatriéme face on écrira pintes & </s> <s xml:id="echoid-s2317" xml:space="preserve">ſeptiers.</s> <s xml:id="echoid-s2318" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2319" xml:space="preserve">On diviſera les trois autres faces par le moyen des logarithmes, <lb/>comme nous allons l'expliquer.</s> <s xml:id="echoid-s2320" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2321" xml:space="preserve">Les diviſions de la quatriéme face ſerviront d'échelle pour la <lb/>troiſiéme qui lui doit être contiguë.</s> <s xml:id="echoid-s2322" xml:space="preserve"/> </p> <pb o="70" file="084" n="84" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div243" type="section" level="1" n="100"> <head xml:id="echoid-head163" style="it" xml:space="preserve">Diviſion de la troiſiéme face pour le contenu.</head> <p> <s xml:id="echoid-s2323" xml:space="preserve">POur placer un nombre ſur la troiſiéme face, comme, par exem-<lb/>ple, 240, cherchez dans les logarithmes 2.</s> <s xml:id="echoid-s2324" xml:space="preserve">40, ou le nombre <lb/>qui en approche le plus, vous le trouverez vis-à-vis 251; </s> <s xml:id="echoid-s2325" xml:space="preserve">mettez <lb/>donc 240 dans la troiſiéme face vis-à-vis 251 pintes de la quatrié-<lb/>me face, & </s> <s xml:id="echoid-s2326" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s2327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2328" xml:space="preserve">J'ai dit le nombre qui en approche le plus, car je ne trouve pas <lb/>juſtement 2.</s> <s xml:id="echoid-s2329" xml:space="preserve">40 vis-à-vis de 251, mais en ſa place je trouve 2.</s> <s xml:id="echoid-s2330" xml:space="preserve">3996 <lb/>qui en approche, puiſqu'il ne s'en manque que quatre unitez, en <lb/>negligeant les trois dernieres figures du nombre entier marqué dans <lb/>les tables des logarithmes.</s> <s xml:id="echoid-s2331" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2332" xml:space="preserve">Cependant pour ne rien negliger de l'exactitude neceſſaire, en <lb/>faiſant ces diviſions, j'ajoûte 1 au premier chifre, & </s> <s xml:id="echoid-s2333" xml:space="preserve">au lieu duloga-<lb/>rithme 240, je cherche 340, vis-à-vis duquel je trouve 2512 qui <lb/>ſigniſie qu'il faut placer le logarithme 240 vis-à-vis de 251 divi-<lb/>ſion des pintes, & </s> <s xml:id="echoid-s2334" xml:space="preserve">deux parties davantage d'une pinte, qu'on doit <lb/>ſuppoſer être diviſée en dix. </s> <s xml:id="echoid-s2335" xml:space="preserve">Sur un des bouts de la troiſiéme face <lb/>on écrira Contenu.</s> <s xml:id="echoid-s2336" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div244" type="section" level="1" n="101"> <head xml:id="echoid-head164" style="it" xml:space="preserve">Diviſion de la ſeconde face pour les longueurs.</head> <p> <s xml:id="echoid-s2337" xml:space="preserve">UN vaiſſeau cylindrique ayant 3 pouces 11 lignes & </s> <s xml:id="echoid-s2338" xml:space="preserve">1 tiers de <lb/>diametre, & </s> <s xml:id="echoid-s2339" xml:space="preserve">autant de profondeur ou de longueur, contient <lb/>une pinte, meſure de Paris; </s> <s xml:id="echoid-s2340" xml:space="preserve">c'eſt pourquoi la premiere partie de la <lb/>ſeconde face qui eſt ſans diviſion, doit être de cette longueur qu'il <lb/>faut poſer dix fois & </s> <s xml:id="echoid-s2341" xml:space="preserve">plus, ſi l'on veut, le long de ladite face, en <lb/>marquant ſeulement des points occultes. </s> <s xml:id="echoid-s2342" xml:space="preserve">Une de ces parties doit <lb/>être diviſée en cent ſur une regle ſeparée qui ſervira d'échelle.</s> <s xml:id="echoid-s2343" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2344" xml:space="preserve">Pour placer un nombre ſur la ſeconde face comme 60, cherchez <lb/>dans les logarithmes le nombre 60, qui ſe trouvera entre 39 & </s> <s xml:id="echoid-s2345" xml:space="preserve">40, <lb/>ou plûtôt vis à-vis de 3981, ſans avoir égard aux chifres 1, 2, 3, qui-<lb/>le precedent, & </s> <s xml:id="echoid-s2346" xml:space="preserve">qui ſe nomment Lettres carecteriſtiques. </s> <s xml:id="echoid-s2347" xml:space="preserve">C'eſt pour-<lb/>quoi je prends 98 ou 981, en eſtimant une partie diviſée en dix ſur <lb/>la petite échelle diviſée en 100, & </s> <s xml:id="echoid-s2348" xml:space="preserve">je poſe cet intervale après le troi-<lb/>fiéme point occulte qui marque trois centaines ou trois mille. </s> <s xml:id="echoid-s2349" xml:space="preserve">Il <lb/>faut ainſi marquer toutes les diviſions de cinq en cinq, & </s> <s xml:id="echoid-s2350" xml:space="preserve">les ſub-<lb/>diviſer en cinq parties égales. </s> <s xml:id="echoid-s2351" xml:space="preserve">Enfin, ſur le bout de cette face, on <lb/>écrira Longueurs.</s> <s xml:id="echoid-s2352" xml:space="preserve"/> </p> <pb o="71" file="085" n="85" rhead="DU COMPAS DE PROPORTION. Liv.II.Ch.II."/> </div> <div xml:id="echoid-div245" type="section" level="1" n="102"> <head xml:id="echoid-head165" style="it" xml:space="preserve">Diviſion de la premiere face pour les diametres.</head> <p> <s xml:id="echoid-s2353" xml:space="preserve">LA premiere partie de cette face qui eſt ſans diviſion, repreſente <lb/>le diametre d'un vaiſleau cylindιique contenant une pinte , <lb/>meſure de Paris; </s> <s xml:id="echoid-s2354" xml:space="preserve">c'eſt pourquoi ſa longueur doit être detrois pou-<lb/>ces onze lignes un tiers, de même que la premiere partie de la ſe-<lb/>conde face.</s> <s xml:id="echoid-s2355" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2356" xml:space="preserve">Pour le reſte, portez y les diviſions de la ſeconde face, mais au <lb/>lieu d'écrire 5, 10, 15, 20, 25, &</s> <s xml:id="echoid-s2357" xml:space="preserve">c. </s> <s xml:id="echoid-s2358" xml:space="preserve">écrivez-y leur double 10, 20, <lb/>30, 40, 50, &</s> <s xml:id="echoid-s2359" xml:space="preserve">c. </s> <s xml:id="echoid-s2360" xml:space="preserve">& </s> <s xml:id="echoid-s2361" xml:space="preserve">ſubdiviſez les intervales en 10, & </s> <s xml:id="echoid-s2362" xml:space="preserve">ſur le bout de <lb/>cette face écrivez Diametres.</s> <s xml:id="echoid-s2363" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div246" type="section" level="1" n="103"> <head xml:id="echoid-head166" xml:space="preserve">USAGE</head> <p> <s xml:id="echoid-s2364" xml:space="preserve">MEſurez avec la premiere face des diametres le diametre moyen <lb/>du tonneau: </s> <s xml:id="echoid-s2365" xml:space="preserve">marquez ce diametre par nombres de la jauge, <lb/>ajoûtant les ſubdiviſions par 10, qui ne ſont pas marquées; </s> <s xml:id="echoid-s2366" xml:space="preserve">je ſup-<lb/>poſe que le diametre moyen tombe ſur 153.</s> <s xml:id="echoid-s2367" xml:space="preserve">00.</s> <s xml:id="echoid-s2368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2369" xml:space="preserve">Meſurez de même la longueur interieure du vaiſſeau avec la ſe-<lb/>conde face des longueurs, je ſuppoſe qu'elle tombe ſur <lb/> <anchor type="note" xlink:label="note-085-01a" xlink:href="note-085-01"/> ajoûtez enſemble ces deux logarithmes,</s> </p> <div xml:id="echoid-div246" type="float" level="2" n="1"> <note position="right" xlink:label="note-085-01" xlink:href="note-085-01a" xml:space="preserve"> <lb/> # 92. 85. <lb/>153. 00. <lb/> # 92. 85. <lb/>245. 85. <lb/></note> </div> <p> <s xml:id="echoid-s2370" xml:space="preserve">Cherchez cette ſomme 245.</s> <s xml:id="echoid-s2371" xml:space="preserve">85. </s> <s xml:id="echoid-s2372" xml:space="preserve">ſur la troiſiéme face du contenu, <lb/>vous trouverez vis-à-vis ſur la quatriéme face 36 ſeptiers ou 288 <lb/>pintes de Paris.</s> <s xml:id="echoid-s2373" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div248" type="section" level="1" n="104"> <head xml:id="echoid-head167" style="it" xml:space="preserve">Pour rendre cette Meſure generale.</head> <p> <s xml:id="echoid-s2374" xml:space="preserve">PEſez une pinte d'eau douce, meſure du païs; </s> <s xml:id="echoid-s2375" xml:space="preserve">je ſuppoſe qu'el-<lb/>le peſe cinquante onces, poids de marc.</s> <s xml:id="echoid-s2376" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2377" xml:space="preserve">Cherchez 31 onces, poids de la pinte de Paris ſur la quatriéme <lb/>face des ſptiers, ce nombre 31 répondra vis-à-dis de 239.</s> <s xml:id="echoid-s2378" xml:space="preserve">4. </s> <s xml:id="echoid-s2379" xml:space="preserve">de la <lb/>troiſiéme échelle.</s> <s xml:id="echoid-s2380" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2381" xml:space="preserve">Cherchez de même 50 ſur la quatriéme face, il répond vis-à-<lb/>vis de 260.</s> <s xml:id="echoid-s2382" xml:space="preserve">2.</s> <s xml:id="echoid-s2383" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>De # 260. 2. # Il faut enſuite de # 245. 85.trouvé ci-devant, <lb/>Oſtez # 239. 4 # Oſter # 20. 80. <lb/>Reſtera # 20. 8. # Reſtera # 225. 05. <lb/></note> <p> <s xml:id="echoid-s2384" xml:space="preserve">Vis-à-vis de ce nombre 225.</s> <s xml:id="echoid-s2385" xml:space="preserve">05. </s> <s xml:id="echoid-s2386" xml:space="preserve">pris dans la troiſiéme échelle <lb/>du contenu, vous trouverez dans la quatriéme échelle 22 ſeptiers <lb/>2 pintes, ou 178 pintes du païs propoſé, & </s> <s xml:id="echoid-s2387" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s2388" xml:space="preserve"/> </p> <pb o="72" file="086" n="86" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div249" type="section" level="1" n="105"> <head xml:id="echoid-head168" style="it" xml:space="preserve">Des differentes Meſures du Vin.</head> <p> <s xml:id="echoid-s2389" xml:space="preserve">LE poiſſon eſt la plus petite meſure, dont on ſe ſert pour meſu-<lb/>rer le vin à Paris, il contient environ un verre de ſougere d'une <lb/>moyene grandeur.</s> <s xml:id="echoid-s2390" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2391" xml:space="preserve">Deux poiſſons font le demi-ſeptier.</s> <s xml:id="echoid-s2392" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2393" xml:space="preserve">La chopine contient deux demi-ſeptiers.</s> <s xml:id="echoid-s2394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2395" xml:space="preserve">La pinte deux chopines.</s> <s xml:id="echoid-s2396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2397" xml:space="preserve">Nous avons dit dit ci-devant ce que la pinte contient de pouces.</s> <s xml:id="echoid-s2398" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2399" xml:space="preserve">La quarte contient deux pintes.</s> <s xml:id="echoid-s2400" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2401" xml:space="preserve">Le ſeptier, huit pintes de Paris.</s> <s xml:id="echoid-s2402" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2403" xml:space="preserve">Le quarteau contient neuf ſeptiers.</s> <s xml:id="echoid-s2404" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2405" xml:space="preserve">Le demi-muid, dix-huit ſeptiers; </s> <s xml:id="echoid-s2406" xml:space="preserve">& </s> <s xml:id="echoid-s2407" xml:space="preserve">le muid, trente-ſix.</s> <s xml:id="echoid-s2408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2409" xml:space="preserve">La demi-queuë de Champagne contient vingt-quatre ſeptiers.</s> <s xml:id="echoid-s2410" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2411" xml:space="preserve">La demi-queuë d'Orleans, vingt-ſeptiers.</s> <s xml:id="echoid-s2412" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2413" xml:space="preserve">La demi-queuë de Beaune, trente ſeptiers.</s> <s xml:id="echoid-s2414" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2415" xml:space="preserve">Le buſſard d'Anjou eſt de trente à trente-deux ſeptiers, & </s> <s xml:id="echoid-s2416" xml:space="preserve">le <lb/>gros buſſard en contient trente-ſix à quarante.</s> <s xml:id="echoid-s2417" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2418" xml:space="preserve">Le muid de Mantes contient trente-neuf à quarante ſeptiers.</s> <s xml:id="echoid-s2419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2420" xml:space="preserve">La pipe, cinquante-quatre ſeptiers.</s> <s xml:id="echoid-s2421" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2422" xml:space="preserve">Et la pipe de Coignac ſoixante-ſix à ſeptante ſeptiers.</s> <s xml:id="echoid-s2423" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2424" xml:space="preserve">Il y a encore d'autres meſures rondes ou cylindriques qui ſer-<lb/>vent à meſurer les grains, le ſel, les fruits, & </s> <s xml:id="echoid-s2425" xml:space="preserve">autres choſes ſem-<lb/>blables.</s> <s xml:id="echoid-s2426" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2427" xml:space="preserve">Le litron, dont on ſe ſert à Paris, contient trente-ſix pouces <lb/>cubes, les demis & </s> <s xml:id="echoid-s2428" xml:space="preserve">quarts à proportion.</s> <s xml:id="echoid-s2429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2430" xml:space="preserve">Le boiſſeau contient ſeize litrons.</s> <s xml:id="echoid-s2431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2432" xml:space="preserve">Le minot de ſel contient quatre boiſſeaux, & </s> <s xml:id="echoid-s2433" xml:space="preserve">doit peſer cent <lb/>livres.</s> <s xml:id="echoid-s2434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2435" xml:space="preserve">Le minot de bled contient trois boiſſeaux.</s> <s xml:id="echoid-s2436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2437" xml:space="preserve">Le ſeptier contient quatre minots, ou douze boiſſeaux.</s> <s xml:id="echoid-s2438" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2439" xml:space="preserve">Le muid eſt de douze ſeptiers, mais celui d'avoine eſt double <lb/>de cclui de bled.</s> <s xml:id="echoid-s2440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2441" xml:space="preserve">Le minot de charbon contient huit boiſſeaux, & </s> <s xml:id="echoid-s2442" xml:space="preserve">la voie qui eſt <lb/>un ſac, eſt de deux minots.</s> <s xml:id="echoid-s2443" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2444" xml:space="preserve">Le muid de plâtre contient trente-ſix ſacs, & </s> <s xml:id="echoid-s2445" xml:space="preserve">chaque ſac trois <lb/>boiſſeaux.</s> <s xml:id="echoid-s2446" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2447" xml:space="preserve">Toutes ces meſures doivent être raſes, & </s> <s xml:id="echoid-s2448" xml:space="preserve">les étalons ou matri-<lb/>ces qui ont été reglées en l'année 1669, ſe conſervent en l'Hôtel <lb/>de Ville de Paris au Bureau des Meſureurs de Sel.</s> <s xml:id="echoid-s2449" xml:space="preserve"/> </p> <pb o="73" file="087" n="87" rhead="DU COMPAS DE PROPORTION. Liv.II. Ch.II."/> </div> <div xml:id="echoid-div250" type="section" level="1" n="106"> <head xml:id="echoid-head169" xml:space="preserve">SECTION VII.</head> <head xml:id="echoid-head170" style="it" xml:space="preserve">Des Vſages de la ligne des Métaux.</head> <head xml:id="echoid-head171" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head172" style="it" xml:space="preserve">Etant donné le diametre d'une boule de quelqu'un des ſix mé-<lb/>taux, trouver le diametre d'une autre boule de même <lb/>poids, & duquel on voudra deſdits métaux.</head> <p> <s xml:id="echoid-s2450" xml:space="preserve">PRenez le diametre donné, & </s> <s xml:id="echoid-s2451" xml:space="preserve">le portez à l'ouverture des deux <lb/> <anchor type="note" xlink:label="note-087-01a" xlink:href="note-087-01"/> points marquez du caractere qui dénote le métal de la boule; <lb/></s> <s xml:id="echoid-s2452" xml:space="preserve">& </s> <s xml:id="echoid-s2453" xml:space="preserve">le compas de proportion demeurant ainſiouvert, prenez l'ouver-<lb/>ture des points ottez du caractere qui ſignifie le métal dont on <lb/>veut faire la boule, cette ouverture ſera ſon diametre. </s> <s xml:id="echoid-s2454" xml:space="preserve">Soit pour <lb/>exemple AB, le diamettre d'une boule de plomb, & </s> <s xml:id="echoid-s2455" xml:space="preserve">l'on demande <lb/>le diametre d'une boule defer qui ſoit de même poids; </s> <s xml:id="echoid-s2456" xml:space="preserve">portez la li-<lb/>gne AB à l'ouverture des points ♄ qui marque le plomb, & </s> <s xml:id="echoid-s2457" xml:space="preserve">pre-<lb/>nez enſuite l'ouverture des points ♂ qui dénote le fer, cette ouver-<lb/>ture donne la longueur CD pour diametre de la boule de fer d'un <lb/>poids égal à celle de plomb.</s> <s xml:id="echoid-s2458" xml:space="preserve"/> </p> <div xml:id="echoid-div250" type="float" level="2" n="1"> <note position="right" xlink:label="note-087-01" xlink:href="note-087-01a" xml:space="preserve">Fig. 18.</note> </div> <p> <s xml:id="echoid-s2459" xml:space="preserve">Si au lieu de boules on propoſe des corps ſemblables ayant plu-<lb/>ſieurs faces, faites la même operation que deſſus pour trouver cha-<lb/>cun de côtez homologues, les uns aprés les autres, afin d'avoir les <lb/>longueurs, largeurs & </s> <s xml:id="echoid-s2460" xml:space="preserve">épaiſſeurs des corps qu'on veut conſtruire.</s> <s xml:id="echoid-s2461" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div252" type="section" level="1" n="107"> <head xml:id="echoid-head173" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head174" style="it" xml:space="preserve">Trouver la proportion que les ſix métaux ont entr'eux ſelon <lb/>leur péſanteur.</head> <p> <s xml:id="echoid-s2462" xml:space="preserve">ON demande, par exemple quelle proportion auroient' en-<lb/>tr'eux deux corps ſemblables de même gandeur & </s> <s xml:id="echoid-s2463" xml:space="preserve">volume, <lb/>mais de differens métaux.</s> <s xml:id="echoid-s2464" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2465" xml:space="preserve">Prenez ſur la ligne des métaux la diſtance du centre de la char-<lb/>niere juſqu'au point du caractere qui dénote le métal moins peſant <lb/>des deux propoſez, qui eſt toûjours le plus éloigné dudit centre,; <lb/></s> <s xml:id="echoid-s2466" xml:space="preserve">portez cette diſtance ſur la ligne des ſolides, à l'ouverture de quel <lb/>nombre vous voudrez, & </s> <s xml:id="echoid-s2467" xml:space="preserve">le compas de proportion demeurantainſi <lb/>ouvert, prenez ſur la ligne des métaux la diſtance du centre de la <lb/>charniere juſqu'au point qui marque l'autre métal, & </s> <s xml:id="echoid-s2468" xml:space="preserve">les portant <lb/>ſur la ligne des ſolides, voyez ſi elle peut convenir à l'ouverture de <lb/>quelque nombre, ſi elle y convient, ces deux nombres exprimeront <lb/> <pb o="74" file="088" n="88" rhead="CONSTRUCTION ET USAGES"/> la proportion des deux métaux propoſez, en permutant les nombres.</s> <s xml:id="echoid-s2469" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2470" xml:space="preserve">Soit propoſé, par exemple, de trouver quelle raiſon a le poids <lb/>d'une certaine maſſe ou lingot d'or, au poids d'un autre lingot d'ar-<lb/>gent ſemblable & </s> <s xml:id="echoid-s2471" xml:space="preserve">de même volume. </s> <s xml:id="echoid-s2472" xml:space="preserve">Comme l'argent peſe moins <lb/>que l'or, je prends la diſtance du centre de la charniere juſqu'au <lb/>point cotté Ɔ, &</s> <s xml:id="echoid-s2473" xml:space="preserve">la porte à l'ouverture du cinquantiéme ſolide, puis <lb/>je prends la diſtance du même centre au point marqué ⊙, & </s> <s xml:id="echoid-s2474" xml:space="preserve">trouve <lb/>qu'elle convient environ à l'ouverture du vingt-ſeptiéme ſolide, <lb/>peu plus, d'où je conclus que le poids de l'or eſt à celui de l'argent <lb/>comme 50 à 27 un ſixiême, ou comme 100 à 54 un tiers; </s> <s xml:id="echoid-s2475" xml:space="preserve">c'eſt-à-<lb/>dire, que ſi le lingot d'or peſe 100 liv. </s> <s xml:id="echoid-s2476" xml:space="preserve">celui d'argent peſera 54 liv. <lb/></s> <s xml:id="echoid-s2477" xml:space="preserve">& </s> <s xml:id="echoid-s2478" xml:space="preserve">un tiers; </s> <s xml:id="echoid-s2479" xml:space="preserve">& </s> <s xml:id="echoid-s2480" xml:space="preserve">ainſi des autres métax, dont la proportion eſt expri-<lb/>mée plus exactement par les nombres livres & </s> <s xml:id="echoid-s2481" xml:space="preserve">onces que peſe un <lb/>pied cube de chacun de ces métaux, rapportez ci-devant en parlant <lb/>de la preuve de la ligne des métaux, & </s> <s xml:id="echoid-s2482" xml:space="preserve">en la table ci-après; </s> <s xml:id="echoid-s2483" xml:space="preserve">ſi néan-<lb/>moins on veut exprimer leur proportion par de plus petits nombres, <lb/>on trouvera ſi un lingot d'or eſt ſuppoſé peſer cent marcs, qu'un lin-<lb/>got de plomb de même groſſeur & </s> <s xml:id="echoid-s2484" xml:space="preserve">volume en peſera environ ſoixan-<lb/>te & </s> <s xml:id="echoid-s2485" xml:space="preserve">demi, un d'argent 54 un tiers. </s> <s xml:id="echoid-s2486" xml:space="preserve">un de cuivre 47 un quart, un <lb/>de fer 42 un dixiéme, & </s> <s xml:id="echoid-s2487" xml:space="preserve">un d'étain 39.</s> <s xml:id="echoid-s2488" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div253" type="section" level="1" n="108"> <head xml:id="echoid-head175" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head176" style="it" xml:space="preserve">Etant donné quelque corps que ce ſoit de l'un des ſix métaux, <lb/>trouver combien il faut d'un descinq autres, métaux pour <lb/>faire un autre corps ſemblable & égal au propoſé.</head> <p> <s xml:id="echoid-s2489" xml:space="preserve">SOit pour exemple un reliquaire d'étain, on propoſe d'en faire <lb/>un autre d'argent tout ſemblable, & </s> <s xml:id="echoid-s2490" xml:space="preserve">de même grandeur. </s> <s xml:id="echoid-s2491" xml:space="preserve">Pre-<lb/>mierement je peſece reliquaire d'étain, & </s> <s xml:id="echoid-s2492" xml:space="preserve">trouve qu'il peſe 36 li-<lb/>vers; </s> <s xml:id="echoid-s2493" xml:space="preserve">c'eſt pourquoi je prends ſur la ligne des métaux la diſtance du <lb/>centre du compas de proportion juſqu'au point marqué Ɔ, qui eſt <lb/>le métal dont on veut faire le nouveau reliquaire, & </s> <s xml:id="echoid-s2494" xml:space="preserve">porte cette <lb/>diſtance à l'ouverture du trente ſixiéme ſolide qui eſt le poids ſup-<lb/>poſé du reliquaire d'étain; </s> <s xml:id="echoid-s2495" xml:space="preserve">puis je prends encore ſur ladite ligne <lb/>des métaux la diſtance du centre au point marqué 4, qui dénote <lb/>le métal du reliquaire d'étain, & </s> <s xml:id="echoid-s2496" xml:space="preserve">portant cette diſtance à l'ouver-<lb/>ture de quelque ſolide, je trouve qu'elle convient au cinquantiéme <lb/>un peu plus: </s> <s xml:id="echoid-s2497" xml:space="preserve">ce qui me fait connoître qu'il faut environ cinquante <lb/>livres d'argent & </s> <s xml:id="echoid-s2498" xml:space="preserve">un quart, pour faire un reliquaire ſemblable, & </s> <s xml:id="echoid-s2499" xml:space="preserve"><lb/>de même grandeur que celui d'étain propoſé.</s> <s xml:id="echoid-s2500" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2501" xml:space="preserve">La preuve de cette operation ſe peut faire par le calcul, ſçavoir <lb/> <pb o="75" file="089" n="89" rhead="DU COMPAS DE PROPORTION. Liv. II. Ch. II."/> en multipliant reciproquement ces differens poids par ceux d'un <lb/>pied cube de chacun de ces métaux, comme en cet exemple, mul-<lb/>tipliant 7201.</s> <s xml:id="echoid-s2502" xml:space="preserve">12 onces, qui eſt le poids d'un pied cube d'argent <lb/>par 361. </s> <s xml:id="echoid-s2503" xml:space="preserve">qui eſt le poids dudit reliquaire d'étain, & </s> <s xml:id="echoid-s2504" xml:space="preserve">enſuite mul-<lb/>tipliant 5161.</s> <s xml:id="echoid-s2505" xml:space="preserve">2 onces, qui eſt le poids d'un pied cube d'étain par <lb/>50 livres un quart, qui eſt le poids du reliquaire d'argent, les pro-<lb/>duits de ces deux multiplications doivent être à peu près égaux.</s> <s xml:id="echoid-s2506" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div254" type="section" level="1" n="109"> <head xml:id="echoid-head177" xml:space="preserve">USAGE IV.</head> <head xml:id="echoid-head178" style="it" xml:space="preserve">Etant donnez les diametres, ou côtez de deux corps ſemblables, <lb/>de divers métaux, trouver en quelle raiſon ſont les <lb/>poids de ces deux corps.</head> <p> <s xml:id="echoid-s2507" xml:space="preserve">SOit, par exemple, la ligne droite EF le diametre d'une boule <lb/> <anchor type="note" xlink:label="note-089-01a" xlink:href="note-089-01"/> d'étain, & </s> <s xml:id="echoid-s2508" xml:space="preserve">GH le diametre d'une boule d'argent, il faut trouver <lb/>la raiſon des poids de ces deux boules. </s> <s xml:id="echoid-s2509" xml:space="preserve">Prenez le diametre EF, & </s> <s xml:id="echoid-s2510" xml:space="preserve">le <lb/>portez à l'ouverture des points 4, qui dénotent le métal de cette <lb/>boule; </s> <s xml:id="echoid-s2511" xml:space="preserve">le compas de proportion demeurant ainſi ouvert, prenez <lb/>l'ouverture des points Ɔ, qui dénotent le métal de l'autre boule; <lb/></s> <s xml:id="echoid-s2512" xml:space="preserve">comparez cette ouverture avec le diametre GH, afin de reconnoître <lb/>ſi elle lui eſt égale, car en ce cas les deux boules ſeroient de même <lb/>péſanteur. </s> <s xml:id="echoid-s2513" xml:space="preserve">Mais ſi le diametre de la boule d'argent eſt plus petit que <lb/>l'ouverture des points Ɔ, comme eſt ici KL, c'eſt une marque que <lb/>la boule d'argent peſe moins que celle d'étain, & </s> <s xml:id="echoid-s2514" xml:space="preserve">pour connoître de <lb/>combien, il faut comparer enſemble ſur la ligne des ſolides les dia-<lb/>metres GH & </s> <s xml:id="echoid-s2515" xml:space="preserve">KL, c'eſt pourquoi portez ladite ouverture des points <lb/>Ɔ, qui eſt ici GH à l'ouverture de quelque ſolide, comme, par exem-<lb/>ple, du 60<emph style="sub">me</emph> voyez enſuite à quel autre ſolide convient le diame-<lb/>tre KL, & </s> <s xml:id="echoid-s2516" xml:space="preserve">ſuppoſant qu'il convienne à l'ouverture du 20<emph style="sub">me</emph> ſolide, <lb/>c'eſt une marque que la boule d'argent, dont le diametre eſt KL, <lb/>ne peſe que le tiers de la boule d'étain, dont le diametre eſt EF.</s> <s xml:id="echoid-s2517" xml:space="preserve"/> </p> <div xml:id="echoid-div254" type="float" level="2" n="1"> <note position="right" xlink:label="note-089-01" xlink:href="note-089-01a" xml:space="preserve">Fig. 19.</note> </div> </div> <div xml:id="echoid-div256" type="section" level="1" n="110"> <head xml:id="echoid-head179" xml:space="preserve">USAGE V.</head> <head xml:id="echoid-head180" style="it" xml:space="preserve">Etant donnez le poids & le diametre d'une boule, ou le côte de <lb/>quelqu'autre corps d'un des ſix métaux, trouver le diame-<lb/>tre, ou le côté homologue d'un autre corps ſemblable d'un <lb/>des cinq autres métaux, lequel ſoit d'un poids donné.</head> <p> <s xml:id="echoid-s2518" xml:space="preserve">SOit, par exemple, la ligne droite MN le diametre d'une boule <lb/> <anchor type="note" xlink:label="note-089-02a" xlink:href="note-089-02"/> de cuivre qui peſe dix livres, on demande le diametre d'une <lb/>boule d'or qui peſe quinze livres. </s> <s xml:id="echoid-s2519" xml:space="preserve">Il faut premierement trouver <lb/> <pb o="76" file="090" n="90" rhead="CONSTRUCTION ET USAGES, &c."/> par la ligne des métaux le diametre d'une boule d'or de poids égal <lb/>à celle de cuivre, & </s> <s xml:id="echoid-s2520" xml:space="preserve">puis l'augmenter par la ligne des ſolides. </s> <s xml:id="echoid-s2521" xml:space="preserve">Por-<lb/>tez pour cet effet le diametre MN à l'ouverture des points ☿, qui <lb/>dénote le cuivre, & </s> <s xml:id="echoid-s2522" xml:space="preserve">prenez l'ouverture des points ⊙, qui dénote <lb/>l'or, marquez le diametre de la boule d'or OP du poids de dix li-<lb/>vres, & </s> <s xml:id="echoid-s2523" xml:space="preserve">le portez à l'ouverture du dixiéme ſolide. </s> <s xml:id="echoid-s2524" xml:space="preserve">Prenez enſuite <lb/>l'ouverture du quinziéme; </s> <s xml:id="echoid-s2525" xml:space="preserve">cette derniere ouverture QR donnera <lb/>le diametre d'une boule d'or péſant quinze livres, comme on l'a <lb/>demandé.</s> <s xml:id="echoid-s2526" xml:space="preserve"/> </p> <div xml:id="echoid-div256" type="float" level="2" n="1"> <note position="right" xlink:label="note-089-02" xlink:href="note-089-02a" xml:space="preserve">Fig. 20.</note> </div> <p> <s xml:id="echoid-s2527" xml:space="preserve">Voici une table du poids de differentes matieres, réduit au pied <lb/>& </s> <s xml:id="echoid-s2528" xml:space="preserve">au pouce cubes.</s> <s xml:id="echoid-s2529" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/> ### Le poids d'un pieds cube. # ### Le poids d'un pouce cube. <lb/>Or # 1326. liv. # 4. onces. # 12. onces. # 2. gros. # 52. grains. <lb/>Vif-argent # 946. # 10. # 8. # 6. # 8. <lb/>Plomb # 802. # 2. # 7. # 3. # 30. <lb/>Argent # 720. # 12. # 6. # 5. # 28. <lb/>Cuivre # 627. # 12. # 5. # 6. # 38. <lb/>Fer # 558. # 0. # 5. # 1. # 24. <lb/>Eſtain # 516. # 2. # 4. # 6. # 17. <lb/>Marbre blanc # 188. # 12. # 1. # 6. # 0. <lb/>Pierre de taille # 139. # 8. # 1. # 2. # 24. <lb/>Plâtre # 85. # 0. # 0. # 5. # 6. <lb/>Ardoiſe # 150. # 0. # 1. # 7. # 12, <lb/>Tuile # 127. # 0. # 1. # 0. # 18, <lb/>Eau de Seine # 69. # 12. # 0. # 5. # 12, <lb/>Eau de Mer # 70. # 10. # 0. # 6. # 0. <lb/>Vin # 68. # 6. # 0. # 5. # 5. <lb/>Cire # 66. # 4. # 0. # 4. # 65. <lb/>Huile # 64. # 0. # 0. # 4. # 43. <lb/></note> </div> <div xml:id="echoid-div258" type="section" level="1" n="111"> <head xml:id="echoid-head181" style="it" xml:space="preserve">Fin du ſecond Livre.</head> <figure> <image file="090-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/090-01"/> </figure> <pb file="091" n="91"/> <figure> <image file="091-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/091-01"/> </figure> </div> <div xml:id="echoid-div259" type="section" level="1" n="112"> <head xml:id="echoid-head182" xml:space="preserve">DELA <lb/>CONSTRUCTION <lb/>ET DES USAGES</head> <head xml:id="echoid-head183" xml:space="preserve">DE PLUSIEURS COMPAS <lb/>ET AUTRES INSTRUMENS CURIEUX, <lb/>Qui ſervent ordinairement au Cabinet.</head> <head xml:id="echoid-head184" style="it" xml:space="preserve">LIVRE TROISIÉME.</head> <head xml:id="echoid-head185" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head186" style="it" xml:space="preserve">De la Conſtruction & des Vſages de pluſieurs differens Compas.</head> <p> <s xml:id="echoid-s2530" xml:space="preserve">NOUS avons déja parlé des Compas qui ſe mettent or-<lb/>dinairement dans les Etuis de Mathematique, il nous <lb/>reſte à parler de quelques autres que l'on y place auſſi <lb/>quelquefois, dont les longueurs ſont arbitraires.</s> <s xml:id="echoid-s2531" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div260" type="section" level="1" n="113"> <head xml:id="echoid-head187" style="it" xml:space="preserve">Conſtruction du Compas à pince.</head> <p> <s xml:id="echoid-s2532" xml:space="preserve">CE Compas ſe nomme Compas à pince, à cauſe d'une entraille <lb/> <anchor type="note" xlink:label="note-091-01a" xlink:href="note-091-01"/> qui eſt milieu du corps, enſorte qu'étant fermé, on l'ouvre. <lb/></s> <s xml:id="echoid-s2533" xml:space="preserve">facilement d'une main, en preſſant les doigts l'un contre l'autre <lb/>Nous avons dit que la principale bonté des compas conſiſte en ce <lb/>que leurs mouvemens ſoient bien doux, & </s> <s xml:id="echoid-s2534" xml:space="preserve">qu'ils s'ouvrent & </s> <s xml:id="echoid-s2535" xml:space="preserve">fer-<lb/>ment bien également; </s> <s xml:id="echoid-s2536" xml:space="preserve">il faut pour cela que les charnieres ſoient bien <lb/>fenduës & </s> <s xml:id="echoid-s2537" xml:space="preserve">très-égales d'épaiſſeur; </s> <s xml:id="echoid-s2538" xml:space="preserve">on ſe ſert pour cela d'une ſcie <lb/>d'acier, la tête eſt fendue en deux fois, de maniere qu'il reſte au mi-<lb/>lieu un ſimple de l'épaiſſeur d'une carte à joüer; </s> <s xml:id="echoid-s2539" xml:space="preserve">l'autre jambe du <lb/>compas eſt fenduë par le milieu de la charniere, pour recevoir le <lb/> <pb o="78" file="092" n="92" rhead="CONSTRUTION ET USAGES"/> ſimple qui a été reſervé à la tête; </s> <s xml:id="echoid-s2540" xml:space="preserve">il faut enſuite limer & </s> <s xml:id="echoid-s2541" xml:space="preserve">dreſſer le<emph style="sub">3</emph> <lb/>charnieres, en ſorte qu'elles joignent bien par tout; </s> <s xml:id="echoid-s2542" xml:space="preserve">on perce enſui-<lb/>te le compas au milieu de la tête d'un trou d'une groſſeur propor-<lb/>tionnée à la grandeur du compas, les plus petits ſont ordinairement <lb/>d'une ligne de diametre, & </s> <s xml:id="echoid-s2543" xml:space="preserve">les plus gros environ de deux lignes, <lb/>mais il faut que le clou ſoit bien rond, & </s> <s xml:id="echoid-s2544" xml:space="preserve">qu'il rempliſſe exactement <lb/>le trou de la tête. </s> <s xml:id="echoid-s2545" xml:space="preserve">Quand il eſt rivé, on fait couler un peu de cire <lb/>jaune entre les charnieres, en faiſant chaufer la tête du compas, cela <lb/>empêche que le métal ne s'attache l'un contre l'autre, en l'ouvrant <lb/>ou le fermant; </s> <s xml:id="echoid-s2546" xml:space="preserve">on y met ordinairement deux roſetes tournées qui <lb/>ſervent de contrerivures; </s> <s xml:id="echoid-s2547" xml:space="preserve">& </s> <s xml:id="echoid-s2548" xml:space="preserve">maintiennent la tête. </s> <s xml:id="echoid-s2549" xml:space="preserve">La petite vis qui <lb/>eſt au bas du corps du compas, ſert à avancer ou reculer la pointe <lb/>d'acier tant & </s> <s xml:id="echoid-s2550" xml:space="preserve">ſi peu que l'on veut: </s> <s xml:id="echoid-s2551" xml:space="preserve">c'eſt ce qui fait qu'on le nomme <lb/>compas de diviſion. </s> <s xml:id="echoid-s2552" xml:space="preserve">Cette pointe eſt attachée par deux clous au <lb/>haut du compas, en ſorte qu'elle fait reſſort en tournant la vis; </s> <s xml:id="echoid-s2553" xml:space="preserve">l'au-<lb/>tre pointe d'acier eſt ſoudée au feu, comme toutes les autres pointes <lb/>de compas quiſont fixes. </s> <s xml:id="echoid-s2554" xml:space="preserve">On fait pour cela auſdites pointes une en-<lb/>taille plate, que l'on fait entrer dans une fente faite au bas du corps <lb/>du compas, en ſorte qu'elles ſe joignent bien, afin que la ſoudure <lb/>les faſſe tenir fortement. </s> <s xml:id="echoid-s2555" xml:space="preserve">On ſe ſert ordinairement de ſoudure d'ar-<lb/>gent au tiers de cuivre, c'eſt-à-dire, qu'on met deux fois plus d'ar-<lb/>gent que de cuivre; </s> <s xml:id="echoid-s2556" xml:space="preserve">par exemple, ſur un gros d'argent, on met un <lb/>demi-gros de laiton que l'on fond enſemble dans un creuſet, & </s> <s xml:id="echoid-s2557" xml:space="preserve">qu'-<lb/>on amincit enſuite au marteau de l'épaiſſeur d'une bonne carte, <lb/>pour les couper enſuite en petits morceaux, pour la faire couler plus <lb/>facilement; </s> <s xml:id="echoid-s2558" xml:space="preserve">on ſe ſert auſſi aſſez ſouvent de ſoudure de cuivre mê-<lb/>lée avec du zin, on fond enſemble trois quarts de laiton avec un <lb/>quart de zin qu'on jette enſuite tout fondu dans l'eau froide, afin de <lb/>la rendre en petite grenaille; </s> <s xml:id="echoid-s2559" xml:space="preserve">il faut avoir ſoin de poudrer l'endroit <lb/>qu'on veut ſouder avec du borax broyé bien fin, c'eſt ce qui fait <lb/>couler & </s> <s xml:id="echoid-s2560" xml:space="preserve">penetrer la ſoudure aux jointures qu'on veut ſouder; </s> <s xml:id="echoid-s2561" xml:space="preserve">ce <lb/>que je dis ici de la maniere de ſouder les pointes de compas, ſe doit <lb/>entendre de même de toutes autres pieces qu'on veut ſouder.</s> <s xml:id="echoid-s2562" xml:space="preserve"/> </p> <div xml:id="echoid-div260" type="float" level="2" n="1"> <note position="right" xlink:label="note-091-01" xlink:href="note-091-01a" xml:space="preserve">Planche. <lb/>VIII. <lb/>Fig. A.</note> </div> </div> <div xml:id="echoid-div262" type="section" level="1" n="114"> <head xml:id="echoid-head188" style="it" xml:space="preserve">Du Compas à l'Allemande.</head> <p> <s xml:id="echoid-s2563" xml:space="preserve">CE Compas a ſes branches un peu courbées, en ſorte que les <lb/> <anchor type="note" xlink:label="note-092-01a" xlink:href="note-092-01"/> pointes ne ſe joignent que par les bouts; </s> <s xml:id="echoid-s2564" xml:space="preserve">il change de pointes, <lb/>c'eſt-à-dire, qu'il y en a pluſieurs qui s'ajuſtent dans un petit trou <lb/>quarré fait à la boëte où eſt la vis qui ſert à les tenir fermes. </s> <s xml:id="echoid-s2565" xml:space="preserve">Il faut <lb/>que ces pointes entrent bien juſte dans le petit trou quarré, afin <lb/> <pb o="79" file="093" n="93" rhead="DE DIFFERENS COMPAS. Liv. III. Chap. I."/> qu'elles ne vacillent point. </s> <s xml:id="echoid-s2566" xml:space="preserve">On met quelquefois à ces ſortes de com-<lb/>pas une pointe à tire-ligne, afin de tracer des lignes groſſes ou me-<lb/>nuës par le moyen de la petite vis qui approche ou écarte les poin-<lb/>tes du tire-ligne; </s> <s xml:id="echoid-s2567" xml:space="preserve">on le fait à mouvement parle moyen d'une petite <lb/>charniere à peu près comme la tête du compas, afin de pouvoir <lb/>mettre ladite pointe perpendiculaire ſur le papier, le compas étant <lb/>peu ou beaucoup ouvert; </s> <s xml:id="echoid-s2568" xml:space="preserve">la petite figure marquée 3 donne une idée <lb/>de cette pointe; </s> <s xml:id="echoid-s2569" xml:space="preserve">le porte-craïon marqué 2 eſt auſſi mobile, afin que <lb/>le craïon ſoit auſſi à plomb dans les grandes ouvertures de compas; <lb/></s> <s xml:id="echoid-s2570" xml:space="preserve">la pointe à roulete marquée 1 ſert à faire des lignes ponctuées; </s> <s xml:id="echoid-s2571" xml:space="preserve">elle <lb/>a auſſi un mouvement de la même maniere, & </s> <s xml:id="echoid-s2572" xml:space="preserve">pour la même rai-<lb/>ſon que le tire-ligne. </s> <s xml:id="echoid-s2573" xml:space="preserve">On met dans l'un & </s> <s xml:id="echoid-s2574" xml:space="preserve">dans l'autre de l'encre <lb/>avec une plume entre les lames; </s> <s xml:id="echoid-s2575" xml:space="preserve">afin de ne pas s'expoſer à gâter les <lb/>deſſeins. </s> <s xml:id="echoid-s2576" xml:space="preserve">Ce qu'on appelle roulete eſt une petite rouë de cuivre, ou <lb/>autre métal d'environ trois lignes de diametre, autour de laquelle <lb/>on fait de petites dents pointuës; </s> <s xml:id="echoid-s2577" xml:space="preserve">elle eſt atachée au bout de deux <lb/>petites lames de laiton par une petite goupille, de maniere qu'elle <lb/>tourne librement, à peu près comme un éperon; </s> <s xml:id="echoid-s2578" xml:space="preserve">les pointes des dents <lb/>doivent être aſſez proches l'une de l'autre, pour ne pas faire des <lb/>points trop éloignez; </s> <s xml:id="echoid-s2579" xml:space="preserve">le reſte de ce compas ſe fait de la même ma-<lb/>niere que celui dont je viens de parler; </s> <s xml:id="echoid-s2580" xml:space="preserve">je dirai ſeulement qu'il doit <lb/>être bien ajuſté, & </s> <s xml:id="echoid-s2581" xml:space="preserve">limé bien plat par-tout. </s> <s xml:id="echoid-s2582" xml:space="preserve">La beauté d'un compas <lb/>conſiſte auſſience qu'il ſoit bien adouci & </s> <s xml:id="echoid-s2583" xml:space="preserve">bien poli; </s> <s xml:id="echoid-s2584" xml:space="preserve">on ſe ſert pour <lb/>cela d'une pierre douce qu'on paſſe à l'eau ſur tous les pans du com-<lb/>pas; </s> <s xml:id="echoid-s2585" xml:space="preserve">on prend enſuite un bâton de bois doux qu'on applatit, & </s> <s xml:id="echoid-s2586" xml:space="preserve"><lb/>qu'on paſſe bien droit ſur toutes les parties du compas avec de la <lb/>potée d'émery trempée dans de l'huile ou du tripoli bien fin, on eſ-<lb/>ſuie bien après tout le compas avec un linge blanc, ou un mor-<lb/>ceau de chamois.</s> <s xml:id="echoid-s2587" xml:space="preserve"/> </p> <div xml:id="echoid-div262" type="float" level="2" n="1"> <note position="left" xlink:label="note-092-01" xlink:href="note-092-01a" xml:space="preserve">Fig. B.</note> </div> </div> <div xml:id="echoid-div264" type="section" level="1" n="115"> <head xml:id="echoid-head189" style="it" xml:space="preserve">Conſtruction du Compas.</head> <p> <s xml:id="echoid-s2588" xml:space="preserve">CE Compas eſt fait tout d'acier trempé, c'eſt-à-dire, dur par-tout <lb/> <anchor type="note" xlink:label="note-093-01a" xlink:href="note-093-01"/> en ſorte que la lime ne peut y mordre & </s> <s xml:id="echoid-s2589" xml:space="preserve">ſa tête eſt contournée <lb/>de telle maniere qu'il s'ouvre delui-même par ſon reſſort. </s> <s xml:id="echoid-s2590" xml:space="preserve">La vis <lb/>qui le traverſe en arc, ſert à l'ouvrir & </s> <s xml:id="echoid-s2591" xml:space="preserve">le fermer tant qu'on le veut <lb/>par le moyen de l'écrou qui eſt derriere. </s> <s xml:id="echoid-s2592" xml:space="preserve">Cette ſorte de compas eſt <lb/>fort commode pour prendre de petites meſures, & </s> <s xml:id="echoid-s2593" xml:space="preserve">faire de petites <lb/>diviſions, mais ils doivent être un peu courts, & </s> <s xml:id="echoid-s2594" xml:space="preserve">trempez de ma-<lb/>niere qu'ils faſſent bien reſſort, & </s> <s xml:id="echoid-s2595" xml:space="preserve">qu'ils ne caſſent pas.</s> <s xml:id="echoid-s2596" xml:space="preserve"/> </p> <div xml:id="echoid-div264" type="float" level="2" n="1"> <note position="right" xlink:label="note-093-01" xlink:href="note-093-01a" xml:space="preserve">Fig. C.</note> </div> <pb o="80" file="094" n="94" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div266" type="section" level="1" n="116"> <head xml:id="echoid-head190" style="it" xml:space="preserve">Conſtruction du Compas d'Horlogeur.</head> <p> <s xml:id="echoid-s2597" xml:space="preserve">CE Compas eſt nommé Compas d'Horlogeur; </s> <s xml:id="echoid-s2598" xml:space="preserve">il eſt fort & </s> <s xml:id="echoid-s2599" xml:space="preserve">ſoli-<lb/> <anchor type="note" xlink:label="note-094-01a" xlink:href="note-094-01"/> de, car ſon uſage ordinaire eſt de ſervir à couper le carton, le <lb/>cuivre, & </s> <s xml:id="echoid-s2600" xml:space="preserve">autres choſes ſemblables. </s> <s xml:id="echoid-s2601" xml:space="preserve">Le quart de cercle quile traver-<lb/>ſe eſt pour l'arrêter fixement à une ouverture, en ſerrant la vis qui <lb/>apuie ſur ledit quart de cercle qui eſt le plus ſouvent d'acier; </s> <s xml:id="echoid-s2602" xml:space="preserve">l'écrou <lb/>qui eſt à ſon extremité ſert à ouvrir & </s> <s xml:id="echoid-s2603" xml:space="preserve">fermer le compas tant & </s> <s xml:id="echoid-s2604" xml:space="preserve">ſi <lb/>peu qu'on le veut, en tournant ledit écrou quidoit être rivé de telle <lb/>maniere à la branche du compas, qu'il faſſe avancer ou reculer l'au-<lb/>tre branche; </s> <s xml:id="echoid-s2605" xml:space="preserve">les quatre pointes doivent être d'acier bien trempé, <lb/>comme nous allons l'expliquer. </s> <s xml:id="echoid-s2606" xml:space="preserve">Celle marquée 1 eſt limée en talu à <lb/>peu près comme un burin, pour couper le cuivre; </s> <s xml:id="echoid-s2607" xml:space="preserve">celle marquée 2 <lb/>eſt faite en maniere de champignon pointu, pour remplir les centres <lb/>de differentes grandeurs; </s> <s xml:id="echoid-s2608" xml:space="preserve">les deux autres pointes ſont comme à l'or-<lb/>dinaire, excepté qu'elles doivent être fortes à proportion des com-<lb/>pas; </s> <s xml:id="echoid-s2609" xml:space="preserve">le reſte de la conſtruction eſt comme ci-devant.</s> <s xml:id="echoid-s2610" xml:space="preserve"/> </p> <div xml:id="echoid-div266" type="float" level="2" n="1"> <note position="left" xlink:label="note-094-01" xlink:href="note-094-01a" xml:space="preserve">Fig. D.</note> </div> <p> <s xml:id="echoid-s2611" xml:space="preserve">Pour tremper les pointes de compas ou autres pieces d'acier, on <lb/>doits'y prendre de differentes manieres; </s> <s xml:id="echoid-s2612" xml:space="preserve">par exemple, les bouts des <lb/>pointes des petits compas ſe trempent à la chandelle par le moyen <lb/>d'un chalumeau de cuivre, car en ſouflant dedans, cela fait un raïon <lb/>de flâme fort vif qui rougit en un inſtant les pointes qu'il faut trem-<lb/>per auſſi-tôt dans le ſuif de chandelle; </s> <s xml:id="echoid-s2613" xml:space="preserve">alors quand les pointes ſont <lb/>d'acier, elles deviennent très dures: </s> <s xml:id="echoid-s2614" xml:space="preserve">les pointes des gros compas & </s> <s xml:id="echoid-s2615" xml:space="preserve">au-<lb/>tres outils d'acier ſe trempent au feu, en les faiſant rougir d'une cou-<lb/>leur de ceriſe; </s> <s xml:id="echoid-s2616" xml:space="preserve">les faiſant tremper en cet état dans l'eau, cette matiere <lb/>devient fort dure. </s> <s xml:id="echoid-s2617" xml:space="preserve">Je donnerai à la fin de cet Ouvrage une deſcrip-<lb/>tion des principaux outils dont on ſe ſert pour faire les inſtrumens <lb/>de Mathematique, & </s> <s xml:id="echoid-s2618" xml:space="preserve">j'expliquerai en abregé les principaux uſages.</s> <s xml:id="echoid-s2619" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div268" type="section" level="1" n="117"> <head xml:id="echoid-head191" style="it" xml:space="preserve">Conſtruction du Compas à trois branches.</head> <p> <s xml:id="echoid-s2620" xml:space="preserve">CE Compas ſert à prendre trois points à la fois, pour former un <lb/> <anchor type="note" xlink:label="note-094-02a" xlink:href="note-094-02"/> triangle tel qu'il peut être, & </s> <s xml:id="echoid-s2621" xml:space="preserve">auſſi pour placer trois poſitions <lb/>à la fois d'une carte que l'on veut copier, &</s> <s xml:id="echoid-s2622" xml:space="preserve">c.</s> <s xml:id="echoid-s2623" xml:space="preserve"/> </p> <div xml:id="echoid-div268" type="float" level="2" n="1"> <note position="left" xlink:label="note-094-02" xlink:href="note-094-02a" xml:space="preserve">Fig. E.</note> </div> <p> <s xml:id="echoid-s2624" xml:space="preserve">La conſtruction de ce compas eſt à peu près comme les autres, <lb/>excepté que la troiſiéme branche doit avoir un mouvement en tout <lb/>ſens, & </s> <s xml:id="echoid-s2625" xml:space="preserve">cela ſe fait par le moyen du clou tourné qui ſert à river par <lb/>un bout les deux branches ordinaires, & </s> <s xml:id="echoid-s2626" xml:space="preserve">à l'autre bout il doit y avoir <lb/>une roſete & </s> <s xml:id="echoid-s2627" xml:space="preserve">une plaque ronde qui ſert de charniere à la troiſiéme <lb/> <anchor type="note" xlink:label="note-094-03a" xlink:href="note-094-03"/> branche, quiſe rive commeles autres compas. </s> <s xml:id="echoid-s2628" xml:space="preserve">La petite figure 1 <lb/> <pb o="81" file="095" n="95" rhead="DE DIFFERENS COMPAS. Liv.III.Ch.I."/> marque comment ce clou cſt fait; </s> <s xml:id="echoid-s2629" xml:space="preserve">ce ompas a ſes pointes d'acier <lb/>comme les autres.</s> <s xml:id="echoid-s2630" xml:space="preserve"/> </p> <div xml:id="echoid-div269" type="float" level="2" n="2"> <note position="left" xlink:label="note-094-03" xlink:href="note-094-03a" xml:space="preserve">Fig. I.</note> </div> </div> <div xml:id="echoid-div271" type="section" level="1" n="118"> <head xml:id="echoid-head192" style="it" xml:space="preserve">Du Compas à Cartes Marines.</head> <p> <s xml:id="echoid-s2631" xml:space="preserve">CE Compas a ſes jambes recourbées & </s> <s xml:id="echoid-s2632" xml:space="preserve">rélargies vers la tête, <lb/>afin que l'on puiſſe l'ouvrir d'une ſeule main; </s> <s xml:id="echoid-s2633" xml:space="preserve">ce quiſe fait en <lb/> <anchor type="note" xlink:label="note-095-01a" xlink:href="note-095-01"/> preſſant les deux branches dans la main; </s> <s xml:id="echoid-s2634" xml:space="preserve">ſa figure fait aſſez con-<lb/>noître ſa conſtruction, & </s> <s xml:id="echoid-s2635" xml:space="preserve">nous parlerons de ſon uſage, en traitant <lb/>des inſtrumens de la Navigation.</s> <s xml:id="echoid-s2636" xml:space="preserve"/> </p> <div xml:id="echoid-div271" type="float" level="2" n="1"> <note position="right" xlink:label="note-095-01" xlink:href="note-095-01a" xml:space="preserve">Fig. F.</note> </div> </div> <div xml:id="echoid-div273" type="section" level="1" n="119"> <head xml:id="echoid-head193" style="it" xml:space="preserve">Conſtruction du Compas de reduction ſimple.</head> <p> <s xml:id="echoid-s2637" xml:space="preserve">ON nomme ce Compas de reduction & </s> <s xml:id="echoid-s2638" xml:space="preserve">de diviſion, à cauſe qu'il <lb/> <anchor type="note" xlink:label="note-095-02a" xlink:href="note-095-02"/> eſt fait pour diviſer une ligne, & </s> <s xml:id="echoid-s2639" xml:space="preserve">reduire un plan du petit au <lb/>grand, & </s> <s xml:id="echoid-s2640" xml:space="preserve">du grand au petit. </s> <s xml:id="echoid-s2641" xml:space="preserve">On en fait qui ſervent à diviſer une li-<lb/>gne en deux, d'autres en trois, d'autres en quatre, en cinq, &</s> <s xml:id="echoid-s2642" xml:space="preserve">c. </s> <s xml:id="echoid-s2643" xml:space="preserve">II <lb/>faut bien prendre garde en le conſtruiſant, que la tête ſoit percée en <lb/>ligne droite avec les branches, & </s> <s xml:id="echoid-s2644" xml:space="preserve">que le dedans des pointes d'acier <lb/>n'avance pas plus l'une que l'autre. </s> <s xml:id="echoid-s2645" xml:space="preserve">Si, par exemple, on veut faire <lb/>un compas qui ſerve à prendre la moitié d'une ligne, il faut que <lb/>depuis le centre du clou juſqu'à l'extremité des plus longues poin-<lb/>tes, il y ait bien exactement deux fois la longueur des plus courtes, <lb/>& </s> <s xml:id="echoid-s2646" xml:space="preserve">ainſi à proportion des autres meſures. </s> <s xml:id="echoid-s2647" xml:space="preserve">Le compas de la figure G <lb/>eſt fait pour prendre le tiers d'une figure, c'eſt pourquoi depuis le <lb/>centre marqué 5 juſqu'aux deux extremitez des pointes marquées <lb/>2, il y a trois fois la longueur depuis le même centre juſqu'aux ex-<lb/>tremitez des petites pointes marquées 3 & </s> <s xml:id="echoid-s2648" xml:space="preserve">4; </s> <s xml:id="echoid-s2649" xml:space="preserve">en ſorte que ſi l'on <lb/>veut avoir le tiers de la ligne 2, 2, il faut prendre toute ſa longueur <lb/>avec le plus grand côté du compas, lequel reſtant ainſi ouvert, les <lb/>plus petites branches donneront le tiers qui ſera la ligne 3, 4.</s> <s xml:id="echoid-s2650" xml:space="preserve"/> </p> <div xml:id="echoid-div273" type="float" level="2" n="1"> <note position="right" xlink:label="note-095-02" xlink:href="note-095-02a" xml:space="preserve">Fig. G.</note> </div> </div> <div xml:id="echoid-div275" type="section" level="1" n="120"> <head xml:id="echoid-head194" style="it" xml:space="preserve">Conſtruction du Compas de reduction à tête mobile.</head> <p> <s xml:id="echoid-s2651" xml:space="preserve">CEt inſtrument eſt une autre ſorte de compas de reduction ou <lb/> <anchor type="note" xlink:label="note-095-03a" xlink:href="note-095-03"/> de diviſion à tête mobile; </s> <s xml:id="echoid-s2652" xml:space="preserve">il ſert à diviſer une ligne propoſée <lb/>en parties égales, comme auſſi à diviſer la circonference de tout cer-<lb/>cle, pour y inſcrire tout polygone regulier.</s> <s xml:id="echoid-s2653" xml:space="preserve"/> </p> <div xml:id="echoid-div275" type="float" level="2" n="1"> <note position="right" xlink:label="note-095-03" xlink:href="note-095-03a" xml:space="preserve">Fig. H.</note> </div> <p> <s xml:id="echoid-s2654" xml:space="preserve">Cette ſorte de compas eſt compoſée de deux jambes égales, dont <lb/>chacune eſt garnie de deux pointes d'acier. </s> <s xml:id="echoid-s2655" xml:space="preserve">Ces jambes ſont évi-<lb/>dées pour y faire couler une eſpece de boëte, au milieu de laquelle <lb/>il y a une vis qui ſert de clou pour les joindre, & </s> <s xml:id="echoid-s2656" xml:space="preserve">les ſerrer en di-<lb/>vers endroits avec l'écrou; </s> <s xml:id="echoid-s2657" xml:space="preserve">mais il faut que les branches ſoient évi-<lb/> <pb o="82" file="096" n="96" rhead="CONSTRUCTION ET USAGES"/> dées bien juſte au milieu, enſorte que le centre du clou ſoit en ligne <lb/>droite avec le dedans des pointes, que la boëte coule très-juſtement <lb/>au long des branches, & </s> <s xml:id="echoid-s2658" xml:space="preserve">que la vis à tête rempliſſe exactement le <lb/>trou de la boëte, afin que rien ne vacille quand il eſt ſerré avec <lb/>l'écrou.</s> <s xml:id="echoid-s2659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2660" xml:space="preserve">La figure 1 repreſente la vis, la figure 2 marque l'écrou, la figu-<lb/> <anchor type="note" xlink:label="note-096-01a" xlink:href="note-096-01"/> re 3 montre la moitié de la boëte qui doit ſe joindre avec une pa-<lb/>reille moitié. </s> <s xml:id="echoid-s2661" xml:space="preserve">On voit par cette petite figure qu'il y a une épaiſſeur <lb/>au milieu pour remplir exactement le vuide des branches; </s> <s xml:id="echoid-s2662" xml:space="preserve">ce qui <lb/>eſt ombré des deux côtez eſt pour embraſſer les deux côtez des bran-<lb/>ches, en ſorte que cette moitié de boëte doit être juſte d'épaiſſeur, <lb/>& </s> <s xml:id="echoid-s2663" xml:space="preserve">couler au long d'une des branches; </s> <s xml:id="echoid-s2664" xml:space="preserve">elle doit être auſſi percée <lb/>pour recevoir la vis; </s> <s xml:id="echoid-s2665" xml:space="preserve">il faut ajuſter une pareille moitie de boëte à <lb/>l'autre branche pour joindre les deux enſemble, & </s> <s xml:id="echoid-s2666" xml:space="preserve">on les fait tenir <lb/>ferme à telle ouverture qu'on veut par le moyen de l'écrou; </s> <s xml:id="echoid-s2667" xml:space="preserve">la figu-<lb/>re 1 eſt une des branches ſeparées, où ſont les diviſions des parties <lb/>égales, car ſur une des jambes on marque d'un côté les chifres qui <lb/>ſervent à diviſer toute ligne donnée en parties égales, & </s> <s xml:id="echoid-s2668" xml:space="preserve">ſur l'autre <lb/>jambe on marque de l'autre côté les chifres qui ſervent à inſcrire <lb/>dans un cercle propoſé tout Polygone regulier.</s> <s xml:id="echoid-s2669" xml:space="preserve"/> </p> <div xml:id="echoid-div276" type="float" level="2" n="2"> <note position="left" xlink:label="note-096-01" xlink:href="note-096-01a" xml:space="preserve">Fig. H. 1. 2. 3.</note> </div> <p> <s xml:id="echoid-s2670" xml:space="preserve">Pour faire la diviſion des lignes en parties égales, ayez une échel-<lb/>le biendiviſée qui ſoit de la même grandeur que tout le compas de <lb/>reduction; </s> <s xml:id="echoid-s2671" xml:space="preserve">ou plûtôt ſervez-vous d'un compas de proportion, par-<lb/>ce qu'il peut ſervir d'échelle de pluſieurs grandeurs.</s> <s xml:id="echoid-s2672" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2673" xml:space="preserve">Prenez avec un compas commun la longueur exacte d'une des <lb/>jambes du compas de reduction, & </s> <s xml:id="echoid-s2674" xml:space="preserve">la portez ſur la ligne des parties <lb/>égales du compas de proportion à l'ouverture de 120, lequel reſtant <lb/>ainſi ouvert, prenez avec le compas commun 40 des mêmes par-<lb/>ties, que vous porterez ſur une de jambes du compas de reduction, <lb/>& </s> <s xml:id="echoid-s2675" xml:space="preserve">y marquerez le chifre 2, qui ſervira pour diviſer en deux parties <lb/>égales toute ligne propofée.</s> <s xml:id="echoid-s2676" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2677" xml:space="preserve">Le compas de proportion reſtanttoûjours de la même ouvertu-<lb/>re, prenez 30 parties égales, que vous porterez ſur ladite jambe <lb/>du compas de reduction, pour y marquer le nombre 3 qui ſervira <lb/>pour partager en trois parties égales toute ligne propoſée.</s> <s xml:id="echoid-s2678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2679" xml:space="preserve">Prenez enſuite 24 parties égales, & </s> <s xml:id="echoid-s2680" xml:space="preserve">l'ayant porte ſur la jambe <lb/>du compas de reduction, marquez-y le nombre 5, qui ſervira pour <lb/>diviſer la ligne donnée en quatre parties égales.</s> <s xml:id="echoid-s2681" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2682" xml:space="preserve">Prenez de même 20 parties égales, & </s> <s xml:id="echoid-s2683" xml:space="preserve">l'ayant porté ſur la jambe <lb/>du compas, marquez-y le nombre 5 pour ſervir à diviſer la ligne <lb/>propoſée en cinq parties égales.</s> <s xml:id="echoid-s2684" xml:space="preserve"/> </p> <pb o="83" file="097" n="97" rhead="DE DIFFERENS COMPAS. Liv. III. Ch. I."/> <p> <s xml:id="echoid-s2685" xml:space="preserve">La mêmc ouverture du compas de proportion peut ſervir encore <lb/>à diviſer en 7, en 9, & </s> <s xml:id="echoid-s2686" xml:space="preserve">en 11 parties égales; </s> <s xml:id="echoid-s2687" xml:space="preserve">mais pour éviter les <lb/>fractions, il faudra changer ladite ouverture, pour diviſer en 6, en <lb/>8, en 10 & </s> <s xml:id="echoid-s2688" xml:space="preserve">en 12.</s> <s xml:id="echoid-s2689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2690" xml:space="preserve">Avant que de changer ladite ouverture du compas de propor-<lb/>tion, prenez avec le compas commun quinze deſdites parties éga-<lb/>les, que vous porterez ſur la jambe du compas de reduction, & </s> <s xml:id="echoid-s2691" xml:space="preserve">y <lb/>marquerez le nombre 7, pour diviſer toute ligne donnée en ſept.</s> <s xml:id="echoid-s2692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2693" xml:space="preserve">Prenez enſuite 12, pour marquer ſur ladite jambe le nombre 9.</s> <s xml:id="echoid-s2694" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2695" xml:space="preserve">Prenez enfin 10, pour marquer ſur ladite jambe le nombre 11, qui <lb/>ſervira pour diviſer en onze toute ligne donnée.</s> <s xml:id="echoid-s2696" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2697" xml:space="preserve">Mais pour diviſer en ſix, prenez avec un compas commun la lon-<lb/>gueur exacte d'une des jambes du compas de reduction; </s> <s xml:id="echoid-s2698" xml:space="preserve">portez-la <lb/>ſur la ligne des parties égales du compas de proportion à l'ouver-<lb/>ture de 140; </s> <s xml:id="echoid-s2699" xml:space="preserve">& </s> <s xml:id="echoid-s2700" xml:space="preserve">ce compas reſtant ainſi ouvert, prenez l'ouverture <lb/>de 20, portez-la ſur la jambe du compas de reduction, pour y mar-<lb/>quer le nombre 6, qui ſervira pour diviſer toute ligne donnée en ſix <lb/>parties égales.</s> <s xml:id="echoid-s2701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2702" xml:space="preserve">Ayant pris de même la longueur entiere d'une des jambes du <lb/>compas de reduction, portez-la ſur la ligne des parties égales du <lb/>compas de proportion à l'ouverture de 180, & </s> <s xml:id="echoid-s2703" xml:space="preserve">prenez en vingt, & </s> <s xml:id="echoid-s2704" xml:space="preserve"><lb/>avec cette ouverture marquez ſur la jambe du compas de reduction <lb/>le nombre 8, qui ſervira pour diviſer en huit toute ligne propoſée.</s> <s xml:id="echoid-s2705" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2706" xml:space="preserve">Portez de même toute la longueur du compas de reduction à <lb/>l'ouverture de 110, dont vous prendrez 10 pour marquer ſur la <lb/>jambe du compas de reduction le nombre 10 qui ſervira pour divi-<lb/>ſer en dix toute ligne donnée.</s> <s xml:id="echoid-s2707" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2708" xml:space="preserve">Portez enſin la longueur du compas de reduction à l'ouverture <lb/>de 130, dont vous prendrez 10 pour marquer ſur la jambe du <lb/>compas de reduction le nombre 12, qui ſervira pour diviſer toute <lb/>ligne donnée en douze.</s> <s xml:id="echoid-s2709" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2710" xml:space="preserve">L'uſage en eſt facile: </s> <s xml:id="echoid-s2711" xml:space="preserve">car ſi, par exemple, vous voulez diviſer une <lb/>ligne droite en trois parties égales, pouſſez la boëte, en ſorte que le <lb/>milieu de la vis ſe trouve juſtement ſur le point marqué 3, & </s> <s xml:id="echoid-s2712" xml:space="preserve">l'ayant <lb/>arrêté fixement ſur ce point, ouvrez le compas de reduction, enſor-<lb/>te que les deux pointes des plus longues parties des jambes convien-<lb/>nent exactement à la longueur de la ligne droite propoſée; </s> <s xml:id="echoid-s2713" xml:space="preserve">puis <lb/>ayant tourné le compas, ſans changer ſon ouverture, les deux plus <lb/>courtes parties deſdites jambes diviſeront en trois parties égales la <lb/>ligne droite propoſée; </s> <s xml:id="echoid-s2714" xml:space="preserve">& </s> <s xml:id="echoid-s2715" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s2716" xml:space="preserve"/> </p> <pb o="84" file="098" n="98" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s2717" xml:space="preserve">Pour faire la diviſion des Polygones reguliers, diviſez en deux <lb/>parties égales la jambe du compas de reduction; </s> <s xml:id="echoid-s2718" xml:space="preserve">prenez avec le com-<lb/>pas commun ſa moitié juſte, & </s> <s xml:id="echoid-s2719" xml:space="preserve">la portez à l'ouverture des chifres 6 <lb/>de part & </s> <s xml:id="echoid-s2720" xml:space="preserve">d'autre de la ligne des Polygones du compas de propor-<lb/>tion, lequel reſtant ainſi ouvert, prenez l'ouverture des chiſres 3 pour <lb/>le triangle équilateral, & </s> <s xml:id="echoid-s2721" xml:space="preserve">portez-la ſur la jambe du compas de re-<lb/>duction, commençant par l'extremité de ladite jambe, ſur laquelle <lb/>vous marquerez le même chifre 3; </s> <s xml:id="echoid-s2722" xml:space="preserve">prenez enſuite l'ouverture des <lb/>chifres 4 ſur le compas de proportion pour le quarré, portez-la ſur <lb/>la même jambe du compas de reduction, & </s> <s xml:id="echoid-s2723" xml:space="preserve">du même côté, pour y <lb/>marquer le même nombre 4; </s> <s xml:id="echoid-s2724" xml:space="preserve">prenez de même avec le compas com-<lb/>mun l'ouverture des nombres 5 de part & </s> <s xml:id="echoid-s2725" xml:space="preserve">d'autre ſur la ligne des <lb/>Polygones du compas de proportion, & </s> <s xml:id="echoid-s2726" xml:space="preserve">ayant porté cette longueur <lb/>ſur la jambe du compas de reduction, marquez-y le même nombre <lb/>5 pour le Pentagone; </s> <s xml:id="echoid-s2727" xml:space="preserve">faites la même choſe pour l'Eptagone, & </s> <s xml:id="echoid-s2728" xml:space="preserve">pour <lb/>tous les autres Polygones juſqu'au Dodecagone. </s> <s xml:id="echoid-s2729" xml:space="preserve">Il ſeroit inutile d'y <lb/>marquer l'Exagone, puiſque le demi-diametre de tout cercle diviſe <lb/>ſa circonference en ſix parties égales.</s> <s xml:id="echoid-s2730" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2731" xml:space="preserve">Il eſt aiſé de remarquer que les côtez du triangle, du quarré, & </s> <s xml:id="echoid-s2732" xml:space="preserve"><lb/>du pentagone, ſont plus grands que le demi-diametre du cercle <lb/>dans lequel on les veut inſcrire, & </s> <s xml:id="echoid-s2733" xml:space="preserve">que les côtez de l'eptagone, oc-<lb/>togone; </s> <s xml:id="echoid-s2734" xml:space="preserve">& </s> <s xml:id="echoid-s2735" xml:space="preserve">de tous les autres, ſont plus petits que le demi-diame-<lb/>tre du cercle où ils ſont inſcrits.</s> <s xml:id="echoid-s2736" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2737" xml:space="preserve">L'uſage en eſt facile, & </s> <s xml:id="echoid-s2738" xml:space="preserve">ſe pratique ainſi. </s> <s xml:id="echoid-s2739" xml:space="preserve">Si, par exemple, vous <lb/>ſouhaitez d'inſcrire un Pentagone dans un cercle propoſé, pouſſez <lb/>la couliſſe en ſorte que le milieu de la vis ſoit arrêté fixement ſur le <lb/>chifre 5 des Polygones. </s> <s xml:id="echoid-s2740" xml:space="preserve">Prenez avec les plus courtes jambes du <lb/>compas de reduction le demi-diametre du cercle; </s> <s xml:id="echoid-s2741" xml:space="preserve">& </s> <s xml:id="echoid-s2742" xml:space="preserve">tournez ledit <lb/>compas, ſans y rien changer, l'ouverture des plus longues jambes <lb/>diviſera le cercle en cinq parties égales.</s> <s xml:id="echoid-s2743" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2744" xml:space="preserve">Mais ſi l'on propoſe d'inſcrire un eptagone, arrêtez la vis ſur le <lb/>nombre 7, prenez avec les plus longues jambes le demi-diametre <lb/>du cercle propoſé, & </s> <s xml:id="echoid-s2745" xml:space="preserve">retournant ledit compas, l'ouverture des <lb/>plus courtes jambes diviſera le cercle en ſept parties égales.</s> <s xml:id="echoid-s2746" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div278" type="section" level="1" n="121"> <head xml:id="echoid-head195" style="it" xml:space="preserve">Du Compas à couliſſe.</head> <p> <s xml:id="echoid-s2747" xml:space="preserve">CE Compas ſe nomme Compas à branche ou à couliſſe; </s> <s xml:id="echoid-s2748" xml:space="preserve">il eſt fait <lb/> <anchor type="note" xlink:label="note-098-01a" xlink:href="note-098-01"/> d'une branche quarrée de cuivre ou d'acier bien dreſſée, lon-<lb/>gue depuis un pied juſqu'à 3 ou 4. </s> <s xml:id="echoid-s2749" xml:space="preserve">Il y a deux boëtes de cuivre <lb/>quarrées qui embraſſent exactement ladite branche, à chacune deſ-<lb/> <pb o="85" file="099" n="99" rhead="DE DIFFERENS COMPAS. Liv. III. Chap. I."/> quelles ſe monte à vis une pointe d'acier, que l'on peut démonter <lb/>pour en mettre une autre qui porte encre ou un craïon. </s> <s xml:id="echoid-s2750" xml:space="preserve">Il y a une de <lb/>ces boëtes qui coule au long de la branche, & </s> <s xml:id="echoid-s2751" xml:space="preserve">qui s'arrête à l'en-<lb/>droit où l'on veut par le moyen de la vis qui appuie ſur un petit reſ-<lb/>ſort. </s> <s xml:id="echoid-s2752" xml:space="preserve">L'autre boëte eſt preſque fixe à un des bouts, où il y a un écrou <lb/>qui lui eſt attaché de maniere que le faiſant tourner autour de la vis <lb/>qui eſt à l'extremité de la branche, il fait avancer ou reculer la poin-<lb/>te d'acier, tant & </s> <s xml:id="echoid-s2753" xml:space="preserve">ſi peu qu'on le ſouhaite.</s> <s xml:id="echoid-s2754" xml:space="preserve"/> </p> <div xml:id="echoid-div278" type="float" level="2" n="1"> <note position="left" xlink:label="note-098-01" xlink:href="note-098-01a" xml:space="preserve">VIII. <lb/>Planche. <lb/>Fig. K.</note> </div> <p> <s xml:id="echoid-s2755" xml:space="preserve">Ces ſortes de compas ſervent à prendre de grandes longueurs, <lb/>comme auſſi à tracer bien juſte de grandes circonferences, & </s> <s xml:id="echoid-s2756" xml:space="preserve">à les <lb/>diviſer bien exactement.</s> <s xml:id="echoid-s2757" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div280" type="section" level="1" n="122"> <head xml:id="echoid-head196" style="it" xml:space="preserve">Conſtruction du Compas à tracer les Ellipſes ou ovales.</head> <note position="right" xml:space="preserve">Fig. L.</note> <p> <s xml:id="echoid-s2758" xml:space="preserve">CEt inſtrument eſt fait pour tracer des ovales ou ellipſes de dif-<lb/>ferentes eſpeces; </s> <s xml:id="echoid-s2759" xml:space="preserve">il eſt compoſé d'une branche de cuivre quar-<lb/>rée bien droite & </s> <s xml:id="echoid-s2760" xml:space="preserve">bien égale, d'environ un pied de longueur, ſur la-<lb/>quelle ſont ajuſtées trois boëtes pour couler au long de ladite bran-<lb/>che. </s> <s xml:id="echoid-s2761" xml:space="preserve">A l'une ces boëtes ſe monte à vis une pointe d'acier ordinai-<lb/>re, ou bien une pour tracer à l'encre, & </s> <s xml:id="echoid-s2762" xml:space="preserve">quelquefois un porte-craïon. <lb/></s> <s xml:id="echoid-s2763" xml:space="preserve">Onjoint aux deux autres boëtes deux couliſſes à queuë d'aronde ou <lb/>en talud, comme la petite figure 1 le montre. </s> <s xml:id="echoid-s2764" xml:space="preserve">Ces couliſſes s'ajuſtent <lb/>au long des branches de la croix, ſur laquelle ſont attachées de pe-<lb/>tites regles à bιzeaux, ou en talud par-deſſous, de même que la cou-<lb/>liſſe à queuë d'aronde. </s> <s xml:id="echoid-s2765" xml:space="preserve">Leſdites couliſſes qui ſont attachées par un <lb/>clou rond, & </s> <s xml:id="echoid-s2766" xml:space="preserve">qui tournent en tout ſens ſous les boëtes quarrées, <lb/>font qu'en tournant le compas à verge, elles avancent ou reculent <lb/>au long de la croix, mais il faut faire paſſer pour cela une des couliſ-<lb/>ſes dans une branche de la croix, & </s> <s xml:id="echoid-s2767" xml:space="preserve">l'autre dans l'autre branche <lb/>comme on voit par la figure.</s> <s xml:id="echoid-s2768" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2769" xml:space="preserve">Il faut remarquer que la diſtance qu'il y a entre les deux couliſ-<lb/>ſes, eſt la diſtance des deux foïers de l'ellipſe, car en changeant cette <lb/>diſtance, elle eſt plus ou moins enflée. </s> <s xml:id="echoid-s2770" xml:space="preserve">Aux extremitez des branches <lb/>de la croix, & </s> <s xml:id="echoid-s2771" xml:space="preserve">par-deſſous, il y a quatre petites pointes d'acier <lb/>pour la faire tenir ferme ſur le papier, & </s> <s xml:id="echoid-s2772" xml:space="preserve">au milieu de ladite croix <lb/>il y a un petit quarré entaillé juſqu'aux bizeaux, pour faire paſſer <lb/>les couliſſes d'une branche à l'autre, pendant le mouvement du <lb/>compas. </s> <s xml:id="echoid-s2773" xml:space="preserve">L'uſage de cette machine eſt fort facile, parce qu'en fai-<lb/>fant faire un tour au compas à verge, la pointe à encre ou au craïon <lb/>trace l'ovale ou l'ellipſe telle qu'on la ſouhaite. </s> <s xml:id="echoid-s2774" xml:space="preserve">Sa figure fait aſſez <lb/>connoître ſa conſtruction & </s> <s xml:id="echoid-s2775" xml:space="preserve">ſon uſage.</s> <s xml:id="echoid-s2776" xml:space="preserve"/> </p> <pb o="86" file="100" n="100" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div281" type="section" level="1" n="123"> <head xml:id="echoid-head197" style="it" xml:space="preserve">Du Compas d'épaiſſeur & à repeter les groſſeurs.</head> <p> <s xml:id="echoid-s2777" xml:space="preserve">CEtte figure repreſente un compas d'épaiſſeur & </s> <s xml:id="echoid-s2778" xml:space="preserve">de repetition. <lb/></s> <s xml:id="echoid-s2779" xml:space="preserve">Il ſert à faire connoître l'épaιſſeur de ce qui eſt engagê ſous <lb/>des rebords, comme ſeroit les rebords d'un canon, d'un tuyau, & </s> <s xml:id="echoid-s2780" xml:space="preserve"><lb/>autres choſes ſemblables; </s> <s xml:id="echoid-s2781" xml:space="preserve">ce que l'on ne pourroit pas faire ſi le <lb/>compas n'avoit que deux pointes; </s> <s xml:id="echoid-s2782" xml:space="preserve">il eſt compoſé de deux picces de <lb/>laiton ou autre matiere, auſquelles il y a deux pointes enflées, & </s> <s xml:id="echoid-s2783" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-100-01a" xlink:href="note-100-01"/> deux autres plates un peu recourbées parles bouts. </s> <s xml:id="echoid-s2784" xml:space="preserve">Pour s'cn ſervir, <lb/>on fait entrer une des pointes plates dans le canon, & </s> <s xml:id="echoid-s2785" xml:space="preserve">l'autre par <lb/>dehors, leſquelles étant ſerrées, les autres pointes oppoſées mar-<lb/>quent l'épaiſſeur.</s> <s xml:id="echoid-s2786" xml:space="preserve"/> </p> <div xml:id="echoid-div281" type="float" level="2" n="1"> <note position="left" xlink:label="note-100-01" xlink:href="note-100-01a" xml:space="preserve">Fig. M.</note> </div> <p> <s xml:id="echoid-s2787" xml:space="preserve">Il faut prendre garde, en le conſtruiſant, que la tête ſoit bien per-<lb/>cée dans le centre, c'eſt-à-dire, qu'en tirant une ligne d'une pointe <lb/>à l'autre oppoſée, elle paſſe préciſément par le centre, lequel la doit <lb/>diviſer également, & </s> <s xml:id="echoid-s2788" xml:space="preserve">que fermantle compas, toutes les pointes ſe <lb/>joignent; </s> <s xml:id="echoid-s2789" xml:space="preserve">on y met ordinairement de petites pointes d'acier aux <lb/>extremitez.</s> <s xml:id="echoid-s2790" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div283" type="section" level="1" n="124"> <head xml:id="echoid-head198" style="it" xml:space="preserve">Du Compas Spherique.</head> <p> <s xml:id="echoid-s2791" xml:space="preserve">LE Compas Spherique ou d'épaiſſeur ne differe en rien pour ſa <lb/> <anchor type="note" xlink:label="note-100-02a" xlink:href="note-100-02"/> conſtruction des compas ordinaires, excepté que ſes jambes <lb/>ſont recourbées pour prendre la groſſeur ou diametre des corps <lb/>ronds, comme boulets, globles ou ſpheres, &</s> <s xml:id="echoid-s2792" xml:space="preserve">c.</s> <s xml:id="echoid-s2793" xml:space="preserve"/> </p> <div xml:id="echoid-div283" type="float" level="2" n="1"> <note position="left" xlink:label="note-100-02" xlink:href="note-100-02a" xml:space="preserve">Fig. N.</note> </div> <p> <s xml:id="echoid-s2794" xml:space="preserve">Enfin le Compas marqué O eſt encore un Compas d'épaiſſeur à <lb/> <anchor type="note" xlink:label="note-100-03a" xlink:href="note-100-03"/> repetition, dont les branches doivent être toutes égales en tout <lb/>ſens. </s> <s xml:id="echoid-s2795" xml:space="preserve">Sa figure fait aſſez connoître ſa conſtruction & </s> <s xml:id="echoid-s2796" xml:space="preserve">ſon uſage.</s> <s xml:id="echoid-s2797" xml:space="preserve"/> </p> <div xml:id="echoid-div284" type="float" level="2" n="2"> <note position="left" xlink:label="note-100-03" xlink:href="note-100-03a" xml:space="preserve">Fig. O.</note> </div> </div> <div xml:id="echoid-div286" type="section" level="1" n="125"> <head xml:id="echoid-head199" xml:space="preserve">CHAPITRE II.</head> <head xml:id="echoid-head200" style="it" xml:space="preserve">De la Conſtruction & Vſages de pluſieurs Inſtrumens de <lb/>Mathematique, qui peuvent ſervir dans le Cabinet.</head> <head xml:id="echoid-head201" style="it" xml:space="preserve">Du Porte-craïon à Compas.</head> <p> <s xml:id="echoid-s2798" xml:space="preserve">CEt inſtrument eſt nommé Porte-craïon à compas; </s> <s xml:id="echoid-s2799" xml:space="preserve">il eſt limé à <lb/> <anchor type="note" xlink:label="note-100-04a" xlink:href="note-100-04"/> huit pans en dehors, & </s> <s xml:id="echoid-s2800" xml:space="preserve">on les fait ordinairement de quatre, <lb/>cinq & </s> <s xml:id="echoid-s2801" xml:space="preserve">ſix pouces de long; </s> <s xml:id="echoid-s2802" xml:space="preserve">le dedans doit être parfaitement rond, <lb/>afin d'y placer & </s> <s xml:id="echoid-s2803" xml:space="preserve">faire couler un Porte craïon par le moyen de ſon <lb/>reſſort & </s> <s xml:id="echoid-s2804" xml:space="preserve">deſon bouton, dont nous parlerons ci-après; </s> <s xml:id="echoid-s2805" xml:space="preserve">à un des <lb/>bouts ſe monte à vis un compas; </s> <s xml:id="echoid-s2806" xml:space="preserve">la figure B montre la maniere dont <lb/> <pb o="87" file="101" n="101" rhead="DE DIFFERENS INSTRUMENS. Liv III. Ch. II."/> il eſt fait; </s> <s xml:id="echoid-s2807" xml:space="preserve">ſa conſtruction ne differe en rien de celle des autres com-<lb/>pas, ſi ce n'eſt qu'il eſt rond, & </s> <s xml:id="echoid-s2808" xml:space="preserve">qu'ily a une vis au-deſſous de ſa <lb/>tête, pour le monter dans le Porte craïon. </s> <s xml:id="echoid-s2809" xml:space="preserve">Ladite vis ſe fait par le <lb/>moyen d'une filiere double, puis on la repaſſe enſuite dans une fi-<lb/>liere ſimple, afin de ne pas forcer les charnieres des compas en les <lb/>taraudant, car c'eſt à quoion doit bien prendre garde.</s> <s xml:id="echoid-s2810" xml:space="preserve"/> </p> <div xml:id="echoid-div286" type="float" level="2" n="1"> <note position="left" xlink:label="note-100-04" xlink:href="note-100-04a" xml:space="preserve">IX. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s2811" xml:space="preserve">On trace ordinairement ſur les pans de ce Porte craïon les lignes <lb/>qui ſe mettent ſur le compas de proportion. </s> <s xml:id="echoid-s2812" xml:space="preserve">On les prend ſur une <lb/>regle d'égale longueur, que l'on a diviſée ſuivant les methodes ex-<lb/>pliquées pour le compas de proportion, & </s> <s xml:id="echoid-s2813" xml:space="preserve">que l'on tranſporte ſur <lb/>chacun des pans. </s> <s xml:id="echoid-s2814" xml:space="preserve">L'uſage en eſt à peu près le même, ſinon qu'il ſe <lb/>faut toûjours ſervir de la même grandeur; </s> <s xml:id="echoid-s2815" xml:space="preserve">car ſi, par exemple, ils'a-<lb/>git de tracer un angle de 40 degrez ſur une ligne donnée, on prend <lb/>avec le compas commun l'étenduë depuis le premier point de divi-<lb/>ſion de la ligne des cordes juſqu'au point marqué 60; </s> <s xml:id="echoid-s2816" xml:space="preserve">de cette ou-<lb/>verture on fait un arc ſur la ligne donnée; </s> <s xml:id="echoid-s2817" xml:space="preserve">& </s> <s xml:id="echoid-s2818" xml:space="preserve">enſuite on prend avec <lb/>le même compas la diſtance du premier point de diviſion juſqu'au <lb/>point 40, laquelle on tranſporte ſur l'arc tracé, & </s> <s xml:id="echoid-s2819" xml:space="preserve">de ſon centre on <lb/>tire une ligne qui fera avec la donnée un angle de 40 degrez, & </s> <s xml:id="echoid-s2820" xml:space="preserve"><lb/>ainſi des autres lignes.</s> <s xml:id="echoid-s2821" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2822" xml:space="preserve">On ſait auſſi de ces ſortes de porte craïon à compas qui ſont <lb/>ronds, & </s> <s xml:id="echoid-s2823" xml:space="preserve">ſur leſquels on marque les pouces, dont on diviſe un en <lb/>douze lignes.</s> <s xml:id="echoid-s2824" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div288" type="section" level="1" n="126"> <head xml:id="echoid-head202" style="it" xml:space="preserve">Conſtruction du porte-craïon a couliſſe.</head> <p> <s xml:id="echoid-s2825" xml:space="preserve">CE Porte-craïon eſt rond en dedans & </s> <s xml:id="echoid-s2826" xml:space="preserve">tourné en dehors; </s> <s xml:id="echoid-s2827" xml:space="preserve">on les <lb/> <anchor type="note" xlink:label="note-101-01a" xlink:href="note-101-01"/> fait auſſi quelquefois à pans, & </s> <s xml:id="echoid-s2828" xml:space="preserve">on y marque les pouces & </s> <s xml:id="echoid-s2829" xml:space="preserve">li-<lb/>gnes par des traits fins qui ſe font par le moyen du tour. </s> <s xml:id="echoid-s2830" xml:space="preserve">On prend <lb/>une lame de laiton ou d'autre matiere de la longueur & </s> <s xml:id="echoid-s2831" xml:space="preserve">largeur qu'-<lb/>on veut faire le porte-craïon, puis on la contourne autour d'un ar-<lb/>bre ou verge de fil d'acier bien rond, bien droit & </s> <s xml:id="echoid-s2832" xml:space="preserve">égal de groſ-<lb/>ſeur par tout. </s> <s xml:id="echoid-s2833" xml:space="preserve">On ſoude enſuite la jointure de ladite lame, qu'on <lb/>nomme la charniere ou corps du porte-craïon, qu'il faut tirer & </s> <s xml:id="echoid-s2834" xml:space="preserve">fai-<lb/>re paſſer dans une filiere à trou rond par le moyen d'un banc; </s> <s xml:id="echoid-s2835" xml:space="preserve">on tire <lb/>ladite charniere juſqu'à ce qu'elle preſſe l'arbre d'acier partout é-<lb/>galement, afin que le dedans foit bien rond & </s> <s xml:id="echoid-s2836" xml:space="preserve">égal, puis après l'a-<lb/>voir tourné comme la figure le montre on le fend juſqu'à environ <lb/>demi-pouce des bouts, & </s> <s xml:id="echoid-s2837" xml:space="preserve">on le perce aux extremitez de la ſente & </s> <s xml:id="echoid-s2838" xml:space="preserve"><lb/>au milieu, d'un petit trou rond, pour y recevoir le bouton. </s> <s xml:id="echoid-s2839" xml:space="preserve">La figu-<lb/>re D eſt le dedans du porte-craïon; </s> <s xml:id="echoid-s2840" xml:space="preserve">aux deux extremitez on y place <lb/> <pb o="88" file="102" n="102" rhead="CONSTRUCTION ET USAGES"/> les craïons qui ſont ſerrez avec de petits anneaux; </s> <s xml:id="echoid-s2841" xml:space="preserve">le milieu doit être <lb/>de la groſſeur juſte du dedans du corps marqué C, afin qu'il puiſſe <lb/>y couler facilement. </s> <s xml:id="echoid-s2842" xml:space="preserve">On entaille ladite piece, pour y placer un petit <lb/>reſſort d'acier ou de cuivre bien endurci au marteau. </s> <s xml:id="echoid-s2843" xml:space="preserve">Le millieu dud. <lb/></s> <s xml:id="echoid-s2844" xml:space="preserve">reſſort marqué I eſt percé à vis pour recevoir le petit bouton mar-<lb/>qué E; </s> <s xml:id="echoid-s2845" xml:space="preserve">on le fait d'acier avec une vis par le bout. </s> <s xml:id="echoid-s2846" xml:space="preserve">Au deſſus de la <lb/>vis il y a un petit colet rond de la groſſeur des trous qui ſont au <lb/>corps C; </s> <s xml:id="echoid-s2847" xml:space="preserve">& </s> <s xml:id="echoid-s2848" xml:space="preserve">au-deſſus du colet on fait une entaille de chaque côté <lb/>dudit bouton, pour y faire un tenon de l'epaiſſſeur de la fente dudit <lb/>corps. </s> <s xml:id="echoid-s2849" xml:space="preserve">Le haut doit être limé ou tournéen rond. </s> <s xml:id="echoid-s2850" xml:space="preserve">Enfin, pour mon-<lb/>ter ledit porte-craïon, il faut faire entrer le dedans, en ſorte que le <lb/>trou du reſſort ſoit vis-à-vis un des trous du corps, & </s> <s xml:id="echoid-s2851" xml:space="preserve">enſuite on <lb/>monte à vis le petit bouton juſqu'àce qu'il ſoit appuïé fur le colet <lb/>rond, en telle ſorte que le tenon ſoit au long de la fente-alors en <lb/>preſſant ſur ledit bouton, on fait couler le dedans du porte-craïon <lb/>d'un côté & </s> <s xml:id="echoid-s2852" xml:space="preserve">d'autre. </s> <s xml:id="echoid-s2853" xml:space="preserve">La figure fait aſſez connoître ce que nous <lb/>venons d'expliquer.</s> <s xml:id="echoid-s2854" xml:space="preserve"/> </p> <div xml:id="echoid-div288" type="float" level="2" n="1"> <note position="right" xlink:label="note-101-01" xlink:href="note-101-01a" xml:space="preserve">Fig. C.</note> </div> </div> <div xml:id="echoid-div290" type="section" level="1" n="127"> <head xml:id="echoid-head203" style="it" xml:space="preserve">Conſtruction de la Plume ſans fin.</head> <p> <s xml:id="echoid-s2855" xml:space="preserve">CEt Inſtrument eſt compoſé de differentes pieces de cuivre, d'ar-<lb/> <anchor type="note" xlink:label="note-102-01a" xlink:href="note-102-01"/> gent, ou d'autre matiere; </s> <s xml:id="echoid-s2856" xml:space="preserve">les pieces F G H étant jontes enſem-<lb/>ble font environ 5 pouces de long; </s> <s xml:id="echoid-s2857" xml:space="preserve">ſa groſſeur eſt à peu près de 3 li-<lb/>gnes de diamettre. </s> <s xml:id="echoid-s2858" xml:space="preserve">Le milieu marqué F porte la plume qui doit être <lb/>fenduë & </s> <s xml:id="echoid-s2859" xml:space="preserve">bien taillée, & </s> <s xml:id="echoid-s2860" xml:space="preserve">ajuſtée ſur un petit tuyau taraudé à vis en <lb/>dedans, lequel eſt ſoudé à un autre petit tuyau, de la groſſeur juſte <lb/>du dedans du couvercle G, dans lequel eſt ſoudée une vis qui ſert à <lb/>monter ledit couvercle, & </s> <s xml:id="echoid-s2861" xml:space="preserve">en entrant dans la plume, boucher un <lb/>petit trou qui eſt a l'endroit marqué 1, pour empêcher que l'encre <lb/>ne ſorte, a l'autre bout du corps F il y a un petit tu au taraudé à vis <lb/>en dedans & </s> <s xml:id="echoid-s2862" xml:space="preserve">en dehors. </s> <s xml:id="echoid-s2863" xml:space="preserve">Celle de dehors ſert à monter le couvercle <lb/>marqué A, dans lequel entre un petit porte-craïon qui ſe monte à <lb/>vis au dedans du petit tuyau, dont nous venons de parler, & </s> <s xml:id="echoid-s2864" xml:space="preserve">qui ſert <lb/>à boucher l'ouverture du colet, qui eſt l'endroit par où l'on fait en-<lb/>trer l'encre dans le corps F, par le moyen d'un petit entonoir.</s> <s xml:id="echoid-s2865" xml:space="preserve"/> </p> <div xml:id="echoid-div290" type="float" level="2" n="1"> <note position="left" xlink:label="note-102-01" xlink:href="note-102-01a" xml:space="preserve">Fig. F.</note> </div> <p> <s xml:id="echoid-s2866" xml:space="preserve">Pour ſe ſervir de ladite plume, il faut démonter le couvercle G, <lb/>& </s> <s xml:id="echoid-s2867" xml:space="preserve">un peu ſecoüer la plume, après quoi l'encre ſort doucement à <lb/>meſure qu'on écrit. </s> <s xml:id="echoid-s2868" xml:space="preserve">Ilfaut remarquer que l'autre côté doit être <lb/>bouché du porte-craïon, car autrement la colonne d'air peſeroit ſur <lb/>l'encre, & </s> <s xml:id="echoid-s2869" xml:space="preserve">la feroit ſortir toute à la fois. </s> <s xml:id="echoid-s2870" xml:space="preserve">Aux deux bouts ſont ſou-<lb/>dez deux cachets, pour y graver un chifre & </s> <s xml:id="echoid-s2871" xml:space="preserve">des armes. </s> <s xml:id="echoid-s2872" xml:space="preserve">La conſ-<lb/> <pb o="89" file="103" n="103" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> truction de cette machine eſt à peu près comme le porte-craïon <lb/>dont je viens de parler.</s> <s xml:id="echoid-s2873" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div292" type="section" level="1" n="128"> <head xml:id="echoid-head204" style="it" xml:space="preserve">Conſtruction d'une Pince à tenir le papier.</head> <p> <s xml:id="echoid-s2874" xml:space="preserve">CEtte petite machine ſert à tenir pluſieurs papiers enſemble; </s> <s xml:id="echoid-s2875" xml:space="preserve">elle <lb/> <anchor type="note" xlink:label="note-103-01a" xlink:href="note-103-01"/> eſt ſort commode quand on veut calquer quelque deſſein, on en <lb/>met aux quatre coins du papier. </s> <s xml:id="echoid-s2876" xml:space="preserve">Elle eſt faite de deux lames de cui-<lb/>vre bien battuës au marteau, pour les rendre plus dures; </s> <s xml:id="echoid-s2877" xml:space="preserve">elles ſont <lb/>attachées par le haut, & </s> <s xml:id="echoid-s2878" xml:space="preserve">renforcées par une lame de laiton qui fait <lb/>faire reſſort. </s> <s xml:id="echoid-s2879" xml:space="preserve">Il y a un coulant au milieu qui ſert à preſſer les papiers, <lb/>en faiſant approcher les deux bouts qui ſont élargis pour mieux te-<lb/>nir ce qui eſt entre deux. </s> <s xml:id="echoid-s2880" xml:space="preserve">Toute cette piece a environ deux pouces de <lb/>longueur. </s> <s xml:id="echoid-s2881" xml:space="preserve">La figure fait aſſez connoítre ſa conſtruction & </s> <s xml:id="echoid-s2882" xml:space="preserve">ſon uſage.</s> <s xml:id="echoid-s2883" xml:space="preserve"/> </p> <div xml:id="echoid-div292" type="float" level="2" n="1"> <note position="right" xlink:label="note-103-01" xlink:href="note-103-01a" xml:space="preserve">Fig. I.</note> </div> </div> <div xml:id="echoid-div294" type="section" level="1" n="129"> <head xml:id="echoid-head205" style="it" xml:space="preserve">Conſtruction du Pentographe.</head> <p> <s xml:id="echoid-s2884" xml:space="preserve">L'Inſtrument, dont nous allons parler, eſt nommé Pentographe; <lb/></s> <s xml:id="echoid-s2885" xml:space="preserve">on le nomme auſſi Singe, parce qu'il ſert à copier toutes ſortes <lb/>de deſſeins. </s> <s xml:id="echoid-s2886" xml:space="preserve">Il eſt compoſé de quatre regles de cuivre ou de bois dur, <lb/>très-égales en largeur & </s> <s xml:id="echoid-s2887" xml:space="preserve">en épaiſſeur; </s> <s xml:id="echoid-s2888" xml:space="preserve">il y en a deux qui ont 15 à 18 <lb/> <anchor type="note" xlink:label="note-103-02a" xlink:href="note-103-02"/> pouces de longueur, & </s> <s xml:id="echoid-s2889" xml:space="preserve">deux autres qui n'en ont que la moitié; </s> <s xml:id="echoid-s2890" xml:space="preserve">ces <lb/>regles ont d'ordinaire 2 à 3 lignes d'épaiſſeur, & </s> <s xml:id="echoid-s2891" xml:space="preserve">5 à 6 lignes de lar-<lb/>geur.</s> <s xml:id="echoid-s2892" xml:space="preserve"/> </p> <div xml:id="echoid-div294" type="float" level="2" n="1"> <note position="right" xlink:label="note-103-02" xlink:href="note-103-02a" xml:space="preserve">Fig. K.</note> </div> <p> <s xml:id="echoid-s2893" xml:space="preserve">La juſteſſe de cet inſtrument conſiſte en ce que les trous qui ſont <lb/>aux extremitez & </s> <s xml:id="echoid-s2894" xml:space="preserve">au milieu des grandes regles ſoient très juſtes & </s> <s xml:id="echoid-s2895" xml:space="preserve"><lb/>en égale diſtance des trous qui ſont aux extremitez des petites, afin <lb/>qu'étant montées, elles faffent toûjours un parallelogramme par-<lb/>fait. </s> <s xml:id="echoid-s2896" xml:space="preserve">Il y a ſix petites pieces de cuivre, pour monter & </s> <s xml:id="echoid-s2897" xml:space="preserve">mettre en <lb/>pratique ledit inſtrument.</s> <s xml:id="echoid-s2898" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2899" xml:space="preserve">La piece marquée I eſt un petit baluſtre de cuivre tourné, au bout <lb/>duquel il y a une vis garnie de ſon écrou, qui ſert à joindre & </s> <s xml:id="echoid-s2900" xml:space="preserve">à ſer-<lb/>rer les deux grandes regles enſemble. </s> <s xml:id="echoid-s2901" xml:space="preserve">A l'autre bout il y a une petite <lb/>pomme qui ſert à faire couler l'inſtrument ſur la table de côté & </s> <s xml:id="echoid-s2902" xml:space="preserve"><lb/>d'autre, ſuivant les differens mouvemens qu'on lui donne. </s> <s xml:id="echoid-s2903" xml:space="preserve">La pie-<lb/>ce marquée 2 eſt un clou à tête tournée avec la vis & </s> <s xml:id="echoid-s2904" xml:space="preserve">ſon écrou; </s> <s xml:id="echoid-s2905" xml:space="preserve">il <lb/>en faut deux pareilles pour joindre les petites regles au milieu des <lb/>grandes aux endroits marquez 2. </s> <s xml:id="echoid-s2906" xml:space="preserve">La piece marquée 3 eſt une vis en <lb/>bois qui eſt au-deſſous d'un petit baluſtre avec la vis & </s> <s xml:id="echoid-s2907" xml:space="preserve">ſon écrou, <lb/>pour joindre enſemble les deux petites regles à l'endroit marqué 3. <lb/></s> <s xml:id="echoid-s2908" xml:space="preserve">La piece marquée 4 eſt un porte-craïon, ou une plume qui entre <lb/>dans le baluſtre avec la vis & </s> <s xml:id="echoid-s2909" xml:space="preserve">ſon écrou, pour le tenir ferme au bout <lb/> <pb o="90" file="104" n="104" rhead="CONSTRUCTION ET USAGES"/> de la grande regle à l'endroit marqué 4. </s> <s xml:id="echoid-s2910" xml:space="preserve">Enfin la piece marquée 5 eſt <lb/>une pointe de cuivre un peu mouſſe, qui eſt jointe au baluſtre garni <lb/>de ſa vis & </s> <s xml:id="echoid-s2911" xml:space="preserve">de ſon écrou, pour le placer au bout de l'autre grande <lb/>regle à l'endroit marque 5. </s> <s xml:id="echoid-s2912" xml:space="preserve">L'inſtrument étant monté & </s> <s xml:id="echoid-s2913" xml:space="preserve">diſpoſé <lb/>comme la figure le marque, il nes'agit plus que d'en donner l'uſage.</s> <s xml:id="echoid-s2914" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2915" xml:space="preserve">Lorſqu'on veut copier un deſſein de la même grandeur que l'ori-<lb/>ginal, il faut diſpoſer l'inſtrument comme il paroît dans la figure K, <lb/>c'eſt-à-dire, qu'il faut faire entrer la vis en bois dans la table à l'en-<lb/>droit marqué 3, puis mettre le papier blanc ſous le craïon marqué 4, <lb/>& </s> <s xml:id="echoid-s2916" xml:space="preserve">le deſſein ſous la pointe marquée 5: </s> <s xml:id="echoid-s2917" xml:space="preserve">alors il n'y a qu'à conduire <lb/>ladite pointe ſur tous les traits du deſſein, en même tems le craïon <lb/>trace la même figure ſur le papier blanc. </s> <s xml:id="echoid-s2918" xml:space="preserve">Mais ſi on vouloit reduire <lb/>le deſſein, & </s> <s xml:id="echoid-s2919" xml:space="preserve">le faire plus petit de la moitié que l'original, il faudroit <lb/>placer la vis en bois à un des bouts d'une grande regle, le papier <lb/>blanc & </s> <s xml:id="echoid-s2920" xml:space="preserve">le craïon au milieu, & </s> <s xml:id="echoid-s2921" xml:space="preserve">conduire toûjours la pointe ſur tous <lb/>les traits du deſſein; </s> <s xml:id="echoid-s2922" xml:space="preserve">le craïon executera la même choſe, mais les li-<lb/>gnes ſeront plus petites de la moitié que celles de l'original, dont la <lb/>raiſon eſt, que le craïon placé comme nous venons de dire, fait la <lb/>moitié moins de chemin que la pointe: </s> <s xml:id="echoid-s2923" xml:space="preserve">& </s> <s xml:id="echoid-s2924" xml:space="preserve">par une raiſon contraire, <lb/>ſi l'on veut faire le deſſein plus grand, comme, par exemple, double <lb/>de l'original, il faut placer la pointe & </s> <s xml:id="echoid-s2925" xml:space="preserve">le deſſein au milieu à l'endroit <lb/>marqué 3, le craïon ou la plume avec le papier blanc au bout d'une <lb/>des grandes regles, & </s> <s xml:id="echoid-s2926" xml:space="preserve">la vis en bois attachée au bout de l'autre gran-<lb/>de regle: </s> <s xml:id="echoid-s2927" xml:space="preserve">car de cette maniere on tracera le deſſein double de l'ori-<lb/>ginal, ſoit un plan, une figure, ou tel autre deſſein qu'on voudra.</s> <s xml:id="echoid-s2928" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2929" xml:space="preserve">Pour augmenter ou diminuer le deſſein ſelon d'autres propor-<lb/>tions, on perce pluſieurs trous ſur chaque regle en diſtances égales, <lb/>fçavoir ſur les petites regles, tout le long, & </s> <s xml:id="echoid-s2930" xml:space="preserve">juſqu'à la moitié des <lb/>grandes, afin d'y placer la pointe, le craïon & </s> <s xml:id="echoid-s2931" xml:space="preserve">la vis toûjours en li-<lb/>gne droite; </s> <s xml:id="echoid-s2932" xml:space="preserve">c'eſt-à-dire, que ſi l'on remonte la pointe de trois trous, <lb/>il ſaut remonter pareillement de trois trous les deux autres pieces; <lb/></s> <s xml:id="echoid-s2933" xml:space="preserve">mais en ce cas il faut placer à l'extremité des petites regles une vis à <lb/>tête pareille à celle marquée 2, de maniere quel'inſtrument conſer-<lb/>ve toûjours le parallelogramme.</s> <s xml:id="echoid-s2934" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2935" xml:space="preserve">Il eſt à remarquer que ſi l'on place la pointe & </s> <s xml:id="echoid-s2936" xml:space="preserve">le deſſein à quel-<lb/>qu'un des trous d'une grande regle, & </s> <s xml:id="echoid-s2937" xml:space="preserve">le craïon avec le papier blanc <lb/>ſous un des trous de la petite regle qui fait angle, & </s> <s xml:id="echoid-s2938" xml:space="preserve">ſe joint au mi-<lb/>lieu de la même grande regle, pour lors la copie ſera plus petite que <lb/>la moitié de l'original; </s> <s xml:id="echoid-s2939" xml:space="preserve">mais ſi le craïon & </s> <s xml:id="echoid-s2940" xml:space="preserve">papier ſont placez ſous <lb/>un des trous de la petite regle qui @ſt parallele à la grande, alors la <lb/> <pb o="91" file="105" n="105" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> copie ſera plus grande que la moitié de l'original. </s> <s xml:id="echoid-s2941" xml:space="preserve">Il ſera facile de <lb/>connoître toutes ces differentes proportions par l'experience.</s> <s xml:id="echoid-s2942" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div296" type="section" level="1" n="130"> <head xml:id="echoid-head206" style="it" xml:space="preserve">Conſtruction du Carat, pour connoitre le poids des Perles.</head> <p> <s xml:id="echoid-s2943" xml:space="preserve">CEtte petite machine ſe nomme Carat, elle ſert à connoître le <lb/> <anchor type="note" xlink:label="note-105-01a" xlink:href="note-105-01"/> poids des perles fines & </s> <s xml:id="echoid-s2944" xml:space="preserve">bien rondes; </s> <s xml:id="echoid-s2945" xml:space="preserve">elle eſt compoſée de cinq <lb/>petites lames de laiton ou autre métal, minces, de deux pouces de <lb/>longueur ſur ſix à ſept lignes de largeur. </s> <s xml:id="echoid-s2946" xml:space="preserve">Ces lames ſont percées de <lb/>pluſieurs trous ronds de differens diametres. </s> <s xml:id="echoid-s2947" xml:space="preserve">Les trous de la pre-<lb/>miere lame font connoître le poids des perles depuis un demi-grain <lb/>juſqu'à ſept grains; </s> <s xml:id="echoid-s2948" xml:space="preserve">la ſeconde lame marque depuis huit grains, qui <lb/>ſont deux carats, juſqu'à cinq; </s> <s xml:id="echoid-s2949" xml:space="preserve">la troiſiéme marque les carats de-<lb/>puis deux & </s> <s xml:id="echoid-s2950" xml:space="preserve">demi juſqu'à cinq & </s> <s xml:id="echoid-s2951" xml:space="preserve">demi; </s> <s xml:id="echoid-s2952" xml:space="preserve">la quatriéme ſert depuis <lb/>ſix carats juſqu'à huit; </s> <s xml:id="echoid-s2953" xml:space="preserve">& </s> <s xml:id="echoid-s2954" xml:space="preserve">la cinquiéme marque le poids des perles <lb/>depuis ſix carats & </s> <s xml:id="echoid-s2955" xml:space="preserve">demi juſqu'à huit & </s> <s xml:id="echoid-s2956" xml:space="preserve">demi.</s> <s xml:id="echoid-s2957" xml:space="preserve"/> </p> <div xml:id="echoid-div296" type="float" level="2" n="1"> <note position="right" xlink:label="note-105-01" xlink:href="note-105-01a" xml:space="preserve">1 X. <lb/>Planche. <lb/>Fig. M.</note> </div> <p> <s xml:id="echoid-s2958" xml:space="preserve">Nous allons donner le diametre du plus petit trou & </s> <s xml:id="echoid-s2959" xml:space="preserve">du plus <lb/>grand de chaque lame, les autres ſe pouvant trouver par leurs diffe-<lb/>rentes proportions; </s> <s xml:id="echoid-s2960" xml:space="preserve">leurs diametres ſont fondez ſur l'experience de <lb/>pluſieurs perles qu'on a peſées avec de petites balances bien fines.</s> <s xml:id="echoid-s2961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2962" xml:space="preserve">Le petit trou qui fait connoître le poidsl d'une perle d'un grain a <lb/>une ligne & </s> <s xml:id="echoid-s2963" xml:space="preserve">un quart de ligne de diametre, celui de ſept grains a <lb/>deux lignes & </s> <s xml:id="echoid-s2964" xml:space="preserve">un tiers de ligne; </s> <s xml:id="echoid-s2965" xml:space="preserve">celui qui marque le poids de deux <lb/>carats a deux lignes & </s> <s xml:id="echoid-s2966" xml:space="preserve">demie; </s> <s xml:id="echoid-s2967" xml:space="preserve">celui qui marque 5 carats a 4 lignes; <lb/></s> <s xml:id="echoid-s2968" xml:space="preserve">celui qui marque le poids de 2 carats & </s> <s xml:id="echoid-s2969" xml:space="preserve">demi a 2 lignes 3 quarts <lb/>& </s> <s xml:id="echoid-s2970" xml:space="preserve">celui de 5 carats & </s> <s xml:id="echoid-s2971" xml:space="preserve">demi a 4 lignes & </s> <s xml:id="echoid-s2972" xml:space="preserve">I quart; </s> <s xml:id="echoid-s2973" xml:space="preserve">celui qui donne <lb/>le poids de 6 carats a 4 lignes I tiers; </s> <s xml:id="echoid-s2974" xml:space="preserve">celui de 8 carars a 4 lignes & </s> <s xml:id="echoid-s2975" xml:space="preserve"><lb/>demie; </s> <s xml:id="echoid-s2976" xml:space="preserve">enfin celui qui donne le poids de 8 carats & </s> <s xml:id="echoid-s2977" xml:space="preserve">demi a 4 lignes <lb/>3 quarts.</s> <s xml:id="echoid-s2978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2979" xml:space="preserve">Ces lames ſont attachées enſemble par un de leurs bouts avec un <lb/>clou qui leur laiſſe la liberté de mouvoir en tous ſens, & </s> <s xml:id="echoid-s2980" xml:space="preserve">ſe renfer-<lb/>ment entre deux autres lames de laiton, qui leur ſervent comme <lb/>d'étui. </s> <s xml:id="echoid-s2981" xml:space="preserve">La figure fait aſſez connoître le reſte de ſa conſtruction.</s> <s xml:id="echoid-s2982" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2983" xml:space="preserve">Les Joüailliers ſe ſervent encore de petites balances bien fines & </s> <s xml:id="echoid-s2984" xml:space="preserve"><lb/>de petits poids qu'ils nomment carats, pour peſer les diamans & </s> <s xml:id="echoid-s2985" xml:space="preserve">au-<lb/>tres pierres précieuſes, comme auſſi les perles qui ne ſont pas ron-<lb/>des. </s> <s xml:id="echoid-s2986" xml:space="preserve">Le carat peſe 4 grains; </s> <s xml:id="echoid-s2987" xml:space="preserve">il ſe diviſe en demi, tiers, quart, hui-<lb/>tiéme & </s> <s xml:id="echoid-s2988" xml:space="preserve">ſeiziéme de carat. </s> <s xml:id="echoid-s2989" xml:space="preserve">On ſe ſert auſſi du mot de carat pour <lb/>marquer le titre de l'or. </s> <s xml:id="echoid-s2990" xml:space="preserve">Le carat d'or fin eſt la 24 <emph style="sub">me</emph> partie d'une <lb/>once de pur or, lequel eſt ſi mol, qu'on ne peut le mettre en œuvre. <lb/></s> <s xml:id="echoid-s2991" xml:space="preserve">L'or à 22 carats eſt le titre des Orſévres de Paris, c'eſt-à-dire, qu'il <lb/> <pb o="92" file="106" n="106" rhead="CONSTRUCTION ET USAGES"/> y a 22 parties d'or fin & </s> <s xml:id="echoid-s2992" xml:space="preserve">2 parties de cuivre, afin que par cet alliage <lb/>l'or ſoit plus ferme & </s> <s xml:id="echoid-s2993" xml:space="preserve">ſe puiſſe mieux travailler.</s> <s xml:id="echoid-s2994" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s2995" xml:space="preserve">Les Orfevres ſe ſervent du mot de denier pour ſpecifier le titre & </s> <s xml:id="echoid-s2996" xml:space="preserve"><lb/>la bontéde de l'argent; </s> <s xml:id="echoid-s2997" xml:space="preserve">le marc d'argent fin eſt à douze deniers; </s> <s xml:id="echoid-s2998" xml:space="preserve">l'ar-<lb/>gent au titre de Paris eſt à onze deniers douze grains, en compre-<lb/>nant les deux grains de remede qu'on accorde pour ſaire recevoir <lb/>l'argent, comme s'il étoit au titre, étant très-difficile de faire l'al-<lb/>liage bien juſte, à cauſe des differens degrez du feu.</s> <s xml:id="echoid-s2999" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div298" type="section" level="1" n="131"> <head xml:id="echoid-head207" style="it" xml:space="preserve">Conſtruction de l' Equerre fixe.</head> <p> <s xml:id="echoid-s3000" xml:space="preserve">CEt inſtrument eſt nommé équerre fixe, c'eſt-à-dire, qui ne ſe <lb/> <anchor type="note" xlink:label="note-106-01a" xlink:href="note-106-01"/> plie point. </s> <s xml:id="echoid-s3001" xml:space="preserve">Toute ſa juſteſſe conſiſte en ce qu'elle ſoit bien dref-<lb/>ſée, & </s> <s xml:id="echoid-s3002" xml:space="preserve">quelle faſſe angle droit en dedans & </s> <s xml:id="echoid-s3003" xml:space="preserve">en dehors, & </s> <s xml:id="echoid-s3004" xml:space="preserve">pour cet <lb/>effet il faut que l'interieur de chaque branche ſoit parallele à l'exte-<lb/>rieur, quand l'inſtrument eſt juſte en dehors.</s> <s xml:id="echoid-s3005" xml:space="preserve"/> </p> <div xml:id="echoid-div298" type="float" level="2" n="1"> <note position="left" xlink:label="note-106-01" xlink:href="note-106-01a" xml:space="preserve">Fig. L.</note> </div> </div> <div xml:id="echoid-div300" type="section" level="1" n="132"> <head xml:id="echoid-head208" style="it" xml:space="preserve">De l'Equerre pliante.</head> <p> <s xml:id="echoid-s3006" xml:space="preserve">CEtte Equerre ſe plie dans l'angle par le moyen d'un clou rond <lb/> <anchor type="note" xlink:label="note-106-02a" xlink:href="note-106-02"/> ajuſté dans une branche qui ſert à faire mouvoir une piece min-<lb/>ce de laiton qui ſe@t comme de charniere, & </s> <s xml:id="echoid-s3007" xml:space="preserve">où eſt attachée l'autre <lb/>branche avec quatre petits clous, laquelle étant ouverte à angles <lb/>droits, s'appuie par un de ſes bouts ſur l'épaiſſeur de la plus grande <lb/>branche, & </s> <s xml:id="echoid-s3008" xml:space="preserve">forme l'Equerre. </s> <s xml:id="echoid-s3009" xml:space="preserve">L'on marque ordinairement les pou-<lb/>ces & </s> <s xml:id="echoid-s3010" xml:space="preserve">les lignes ſur ces ſortes d'équerres. </s> <s xml:id="echoid-s3011" xml:space="preserve">Leur principal uſage eſt <lb/>pour tracer des lignes perpendiculaires, & </s> <s xml:id="echoid-s3012" xml:space="preserve">connoître ſi une choſe <lb/>eſt bien à angle droit.</s> <s xml:id="echoid-s3013" xml:space="preserve"/> </p> <div xml:id="echoid-div300" type="float" level="2" n="1"> <note position="left" xlink:label="note-106-02" xlink:href="note-106-02a" xml:space="preserve">Fig. N.</note> </div> </div> <div xml:id="echoid-div302" type="section" level="1" n="133"> <head xml:id="echoid-head209" style="it" xml:space="preserve">Conſtruction du Pied à niveau.</head> <p> <s xml:id="echoid-s3014" xml:space="preserve">CEt inſtrument ſe nomme Pied à niveau; </s> <s xml:id="echoid-s3015" xml:space="preserve">il eſt compoſé de deux <lb/> <anchor type="note" xlink:label="note-106-03a" xlink:href="note-106-03"/> branches de cuivre ou autre matiere, d'environ ſix lignes de <lb/>largeur, dont l'une tourne autour de la tête de l'autre, & </s> <s xml:id="echoid-s3016" xml:space="preserve">eſt atta-<lb/>chée par un clou rond dans ſon centre. </s> <s xml:id="echoid-s3017" xml:space="preserve">Elles ſont fenduës toutle <lb/>long en dedans juſqu'à la moitié de leur largeur, pour y placer une <lb/>languette ou petite lame de laiton, quand l'inſtrument eſt fermé. <lb/></s> <s xml:id="echoid-s3018" xml:space="preserve">Cette languette eſt attachée à une des branches par un petit clou, <lb/>pour la faire mouvoir, & </s> <s xml:id="echoid-s3019" xml:space="preserve">quand elle eſt placée dans l'autre branche <lb/>où il y a une petite goupille qui la retient, le pied demeure ouvert à <lb/>angle droit, tel que la figure le montre. </s> <s xml:id="echoid-s3020" xml:space="preserve">On ajuſte à la tête une pe-<lb/>tite plaque de laiton quarrée, afin que l'inſtrument ſerve d'equerre, <lb/>on perce un petit trou au bas de l'angle de la petite plaque, pour y <lb/> <pb o="93" file="107" n="107" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> paſſer une ſoie fine avecſon plomb, laquelle tombant ſur une ligne <lb/>perpendiculaire tracée au millieu de la languette ſert de niveau. </s> <s xml:id="echoid-s3021" xml:space="preserve">On <lb/>coupe les angles interieurs des branches, afin que l'inſtrument ſe <lb/>puiſſe mieux appuïer ſur le plan que l'on veut niveler.</s> <s xml:id="echoid-s3022" xml:space="preserve"/> </p> <div xml:id="echoid-div302" type="float" level="2" n="1"> <note position="left" xlink:label="note-106-03" xlink:href="note-106-03a" xml:space="preserve">Fig. O.</note> </div> <p> <s xml:id="echoid-s3023" xml:space="preserve">Nous ne nous arrêterons pas davantage à ſa conſtruction, la fi-<lb/>gure la faiſant aſſez connoître: </s> <s xml:id="echoid-s3024" xml:space="preserve">Nous dirons ſeulement qu'il ſert <lb/>d'équerre & </s> <s xml:id="echoid-s3025" xml:space="preserve">de niveau de la maniere dont il eſt placé, de pied droit <lb/>& </s> <s xml:id="echoid-s3026" xml:space="preserve">de regle quand il eſt ouvert tout-à-fait.</s> <s xml:id="echoid-s3027" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div304" type="section" level="1" n="134"> <head xml:id="echoid-head210" style="it" xml:space="preserve">Du pied de Roy & de differentes Meſures.</head> <p> <s xml:id="echoid-s3028" xml:space="preserve">LA conſtruction du Pied de Roy pour le corps ne differe guéres <lb/> <anchor type="note" xlink:label="note-107-01a" xlink:href="note-107-01"/> de celle du compas de proportion dont nous avons ci-devant <lb/>parlé. </s> <s xml:id="echoid-s3029" xml:space="preserve">Quand on n'y veut marquer ſimplement que le pied de Pa-<lb/>ris chaque branche n'a qu'environ cinq lignes de largeur; </s> <s xml:id="echoid-s3030" xml:space="preserve">mais <lb/>quand on y veut mettre les meſures, étrangeres on les fait plus lar-<lb/>ges. </s> <s xml:id="echoid-s3031" xml:space="preserve">Nous allons donner le rapport du pied de Paris avec les prin-<lb/>cipales meſures étrangers de l'Europe.</s> <s xml:id="echoid-s3032" xml:space="preserve"/> </p> <div xml:id="echoid-div304" type="float" level="2" n="1"> <note position="right" xlink:label="note-107-01" xlink:href="note-107-01a" xml:space="preserve">Fig. P.</note> </div> <p> <s xml:id="echoid-s3033" xml:space="preserve">Le point eſt la douziéme partie de l'épaiſſeur d'un moyen grain <lb/>d'orge; </s> <s xml:id="echoid-s3034" xml:space="preserve">la ligne eſt longue de 12 points ou de l'épaiſſeur d'un grain <lb/>d'orge, le pouce contient 12 lignes, & </s> <s xml:id="echoid-s3035" xml:space="preserve">le pied 12 pouces. </s> <s xml:id="echoid-s3036" xml:space="preserve">Le pied de <lb/>Roy ou de Paris eſt de 12 pouces, de ceux dont on vient de parler; <lb/></s> <s xml:id="echoid-s3037" xml:space="preserve">mais on le diviſe quelquefois en 720, ou en 1440 parties égales, <lb/>pour mieux exprimer ſon rapport avec les meſures étrangeres, le <lb/>pied de Lyon & </s> <s xml:id="echoid-s3038" xml:space="preserve">de Grenoble eſt un peu plus grand que celui de Pa-<lb/>ris, car il contient 12 pouces 7 lignes. </s> <s xml:id="echoid-s3039" xml:space="preserve">Le pied de Dijon eſt plus <lb/>petit & </s> <s xml:id="echoid-s3040" xml:space="preserve">ne contient que 11 pouces 7 lignes; </s> <s xml:id="echoid-s3041" xml:space="preserve">celui de Beſançon 11 <lb/>pouces 5 lignes; </s> <s xml:id="echoid-s3042" xml:space="preserve">celui de Mâcon 12 pouces 4 lignes. </s> <s xml:id="echoid-s3043" xml:space="preserve">Le pied de <lb/>Rouen eſt égal à celui de Paris.</s> <s xml:id="echoid-s3044" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3045" xml:space="preserve">Le pied de Sedan a 12 pouces 3 lignes.</s> <s xml:id="echoid-s3046" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3047" xml:space="preserve">Le pied de Lorraine a 10 pouces 9 lignes.</s> <s xml:id="echoid-s3048" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3049" xml:space="preserve">Celui de Bruxelles a pareillement 13 pouces 9 lignes.</s> <s xml:id="echoid-s3050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3051" xml:space="preserve">Le pied d'Amſterdam 10 pouces 5 lignes.</s> <s xml:id="echoid-s3052" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3053" xml:space="preserve">Le pied du Rhin, quieſt fort en uſage dans les païs du Nord, a <lb/>11 pouces 7 lignes.</s> <s xml:id="echoid-s3054" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3055" xml:space="preserve">Celui de Londres 11 pouces 3 lignes.</s> <s xml:id="echoid-s3056" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3057" xml:space="preserve">Celui de Dantzic 14 pouces 7 lignés.</s> <s xml:id="echoid-s3058" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3059" xml:space="preserve">Celui de Suede 10 pouces 1 lignes.</s> <s xml:id="echoid-s3060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3061" xml:space="preserve">Celui de Danemarc 10 pouces 9 lignes.</s> <s xml:id="echoid-s3062" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3063" xml:space="preserve">Le pied Romain 13 pouces 10 lignes,</s> </p> <p> <s xml:id="echoid-s3064" xml:space="preserve">Le pied de Boulogne 14 pouces 1 ligne.</s> <s xml:id="echoid-s3065" xml:space="preserve"/> </p> <pb o="94" file="108" n="108" rhead="CONSTRUCTION ET US AGES"/> <p> <s xml:id="echoid-s3066" xml:space="preserve">Celui de Veniſe 11 pouces 11 lignes,</s> </p> <p> <s xml:id="echoid-s3067" xml:space="preserve">Celui de Milan eſt de deux ſortes, le grand a 1 pied 10 pouces, le <lb/>petit 1 pied 2 pouces 8 lignes.</s> <s xml:id="echoid-s3068" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3069" xml:space="preserve">Celui de Turin a 1 pied 6 pouces 11 lignes.</s> <s xml:id="echoid-s3070" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3071" xml:space="preserve">Celui de Savoye n'a que 10 pouces.</s> <s xml:id="echoid-s3072" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3073" xml:space="preserve">Celui de Genéve 18 pouces.</s> <s xml:id="echoid-s3074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3075" xml:space="preserve">Celui de Vienne a 11 pouces 8 lignes.</s> <s xml:id="echoid-s3076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3077" xml:space="preserve">Celui de Conſtantinople contient 2 pieds 2 pouces 2 lignes.</s> <s xml:id="echoid-s3078" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div306" type="section" level="1" n="135"> <head xml:id="echoid-head211" style="it" xml:space="preserve">Nous allons encore donner quelques autres meſures par <lb/>rapport au pied</head> <p> <s xml:id="echoid-s3079" xml:space="preserve">LA Palme Romaine à 8 pouces 2 lignes; </s> <s xml:id="echoid-s3080" xml:space="preserve">celle de Genes a 9 pou-<lb/>ces 1 ligne; </s> <s xml:id="echoid-s3081" xml:space="preserve">celle de Naples a 9 pouces 9 lignes, & </s> <s xml:id="echoid-s3082" xml:space="preserve">celle de Por-<lb/>tugal 8 pouces 2 lignes. </s> <s xml:id="echoid-s3083" xml:space="preserve">Le pan qui ſert de meſure en pluſieurs au-<lb/>tres Villes d'Italie, contient 8 à 9 pouces de long.</s> <s xml:id="echoid-s3084" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3085" xml:space="preserve">L'Aune de Paris eſt de 3 pieds 8 pouces, L'Aune de Provence, <lb/>de Montpellier & </s> <s xml:id="echoid-s3086" xml:space="preserve">d'Avignon contient une Aune 2 tiers de celle de <lb/>Paris. </s> <s xml:id="echoid-s3087" xml:space="preserve">L'Aune de Flandres & </s> <s xml:id="echoid-s3088" xml:space="preserve">d'Allemagne ne contient que 7 dou-<lb/>ziéme de celle de Paris.</s> <s xml:id="echoid-s3089" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3090" xml:space="preserve">La braſſe de Milan pour les étofes deſoie, eſt d'un pied 7 pouces <lb/>4 lignes; </s> <s xml:id="echoid-s3091" xml:space="preserve">celle pour les draps & </s> <s xml:id="echoid-s3092" xml:space="preserve">autres etófes de laine eſt de 2 pieds <lb/>11 lignes.</s> <s xml:id="echoid-s3093" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3094" xml:space="preserve">La braſſe de Florence eſt d'un pied 9 pouces 6 lignes.</s> <s xml:id="echoid-s3095" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3096" xml:space="preserve">Le Ras de Piemont & </s> <s xml:id="echoid-s3097" xml:space="preserve">de Luque eſt de 22 pouces.</s> <s xml:id="echoid-s3098" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3099" xml:space="preserve">La Verge de Seville eſt de 30 pouces 11 lignes.</s> <s xml:id="echoid-s3100" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3101" xml:space="preserve">La Verge d'Angleterre eſt de 33 pouces 11 lignes.</s> <s xml:id="echoid-s3102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3103" xml:space="preserve">La Barre de Caſtille eſt de 31 pouces 3 lignes.</s> <s xml:id="echoid-s3104" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3105" xml:space="preserve">Celle de Valence eſt de 33 pouces 7 lignes.</s> <s xml:id="echoid-s3106" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3107" xml:space="preserve">La Varre de Madrid & </s> <s xml:id="echoid-s3108" xml:space="preserve">celle de Portugal ſont de 3 pieds 9 lignes.</s> <s xml:id="echoid-s3109" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3110" xml:space="preserve">La Varre d'Eſpagne en general eſt de 5 pieds 5 pouces 6 lignes.</s> <s xml:id="echoid-s3111" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3112" xml:space="preserve">La Canne de Toulouſe eſt de même longueur.</s> <s xml:id="echoid-s3113" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3114" xml:space="preserve">La Canne de Rome contient 6 pieds 11 pouces 7 lignes.</s> <s xml:id="echoid-s3115" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3116" xml:space="preserve">La Canne de Naples 6 pieds 10 pouces 2 lignes.</s> <s xml:id="echoid-s3117" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3118" xml:space="preserve">Le Pic de Conſtantinople 2 pieds 2 pouces 2 lignes.</s> <s xml:id="echoid-s3119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3120" xml:space="preserve">La Geuſe des Indes & </s> <s xml:id="echoid-s3121" xml:space="preserve">celle de Perſe 2 pieds 10 pouces 11 lignes.</s> <s xml:id="echoid-s3122" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div307" type="section" level="1" n="136"> <head xml:id="echoid-head212" style="it" xml:space="preserve">Conſtruction des Regles paralleles.</head> <p> <s xml:id="echoid-s3123" xml:space="preserve">CEs inſtrumens ſe font ordinairement de cuivre ou de bois dur, <lb/>comme ébene & </s> <s xml:id="echoid-s3124" xml:space="preserve">bois de la Chine, depuis 6 pouces juſqu'à 18 <lb/>de long ſur un pouce de large, & </s> <s xml:id="echoid-s3125" xml:space="preserve">environ 2 lignes d'épaiſſeur. </s> <s xml:id="echoid-s3126" xml:space="preserve">Ilſaur <lb/> <pb o="95" file="109" n="109" rhead="DE DIFFERENS INSTRUMENS. Liv III. Ch. II."/> ſur tout que leſdites regles ſoient bien dreſſées en tout ſens, & </s> <s xml:id="echoid-s3127" xml:space="preserve">bien <lb/>paralleles; </s> <s xml:id="echoid-s3128" xml:space="preserve">c'eſt-à dire, très-également larges depuis un bout juſqu'à <lb/>l'autre; </s> <s xml:id="echoid-s3129" xml:space="preserve">car c'eſt en partie d'où dépend la juſteſſe de cet inſtrument.</s> <s xml:id="echoid-s3130" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div308" type="section" level="1" n="137"> <head xml:id="echoid-head213" style="it" xml:space="preserve">Nous allons donner la deſcription de deux differentes ſortes <lb/>de regles paralleles également juſtes.</head> <p> <s xml:id="echoid-s3131" xml:space="preserve">LEs deux regles du premier de ces deux inſtrumens ſont jointes <lb/> <anchor type="note" xlink:label="note-109-01a" xlink:href="note-109-01"/> enſemble par deux petites lames de laiton d'environ 2 à 3 pou-<lb/>ces & </s> <s xml:id="echoid-s3132" xml:space="preserve">demi de long, & </s> <s xml:id="echoid-s3133" xml:space="preserve">de 6 lignes de largeur, limées & </s> <s xml:id="echoid-s3134" xml:space="preserve">façonées à <lb/>pcu près comme la figure le marque; </s> <s xml:id="echoid-s3135" xml:space="preserve">elles ſont percées par les deux <lb/>bouts bien également, & </s> <s xml:id="echoid-s3136" xml:space="preserve">pour cet efſet il eſt à propos de les percer <lb/>l'une ſur l'autre; </s> <s xml:id="echoid-s3137" xml:space="preserve">il faut tourner 4 clous à tête qui rempliſent exac-<lb/>tement les trous deſdites lames, puis on trace une ligne au milieu de <lb/>la largeur des regles, & </s> <s xml:id="echoid-s3138" xml:space="preserve">on les partage en deux également, enſuite <lb/>on diviſe une des moitiez dechaque regle en trois, & </s> <s xml:id="echoid-s3139" xml:space="preserve">à la premiere <lb/>meſure, en comptant du milieu, on perce un trou à chaque regle <lb/>dans la ligne droite qui partage leur largeur, pour y placer une lame <lb/>avec ſon clou. </s> <s xml:id="echoid-s3140" xml:space="preserve">Enſuite les regles étant bien jointes enſemble, il faut <lb/>tracer avec la pointe d'une éguille un trait autour des petites la-<lb/>mes, toûjours ſur la ligne du milieu, & </s> <s xml:id="echoid-s3141" xml:space="preserve">percer exactement les trous <lb/>au milieu de ces traits; </s> <s xml:id="echoid-s3142" xml:space="preserve">mais pour bien faire il n'en faut percer qu'un, <lb/>& </s> <s xml:id="echoid-s3143" xml:space="preserve">y mettre ſon clou, pour voir ſi le trait de l'autre regle eſt toûjours <lb/>vis-à-vis du trou de la lame; </s> <s xml:id="echoid-s3144" xml:space="preserve">car c'eſt ce quatriéme trou qui donne <lb/>toute la préciſion à l'inſtrument, & </s> <s xml:id="echoid-s3145" xml:space="preserve">l'ayant percé & </s> <s xml:id="echoid-s3146" xml:space="preserve">mis le clou, <lb/>on pourra verifier s'il eſt bien juſte en l'ouvrant à droite & </s> <s xml:id="echoid-s3147" xml:space="preserve">à gau-<lb/>che; </s> <s xml:id="echoid-s3148" xml:space="preserve">car ſi les regles ſont bien percées elles ſe joindront auſſi-bien <lb/>d'un côté que de l'autre. </s> <s xml:id="echoid-s3149" xml:space="preserve">Il faut avoir ſoin de river les clous douce-<lb/>ment afin de ne rien forcer ni étendre.</s> <s xml:id="echoid-s3150" xml:space="preserve"/> </p> <div xml:id="echoid-div308" type="float" level="2" n="1"> <note position="right" xlink:label="note-109-01" xlink:href="note-109-01a" xml:space="preserve">Fig. R.</note> </div> </div> <div xml:id="echoid-div310" type="section" level="1" n="138"> <head xml:id="echoid-head214" style="it" xml:space="preserve">Conſtruction d'une autre ſorte de regle parallele.</head> <p> <s xml:id="echoid-s3151" xml:space="preserve">LEs regles qui compoſent cet inſtrument doivent être pareille-<lb/> <anchor type="note" xlink:label="note-109-02a" xlink:href="note-109-02"/> ment droites & </s> <s xml:id="echoid-s3152" xml:space="preserve">égales d'épaiſſeur; </s> <s xml:id="echoid-s3153" xml:space="preserve">les deux grandes ſont atta-<lb/>chées par deux autres un peu plus courtes, percées juſte d'une même <lb/>longueur par les deux bouts & </s> <s xml:id="echoid-s3154" xml:space="preserve">par le milieu, & </s> <s xml:id="echoid-s3155" xml:space="preserve">ajuſtées de maniere <lb/>qu'elles font une eſpece de zig zag, qui en s'écartant & </s> <s xml:id="echoid-s3156" xml:space="preserve">ſe rappro-<lb/>chant font auſſi écarter & </s> <s xml:id="echoid-s3157" xml:space="preserve">rapprocher les autres regles parallele-<lb/>ment, & </s> <s xml:id="echoid-s3158" xml:space="preserve">ce par le moyen des trous qui ſont percez à un des bouts <lb/>de chaque regle & </s> <s xml:id="echoid-s3159" xml:space="preserve">attachez aux regles à zig-zag avec des clous à tê-<lb/>te tournez. </s> <s xml:id="echoid-s3160" xml:space="preserve">Les autres bouts des grandes regles ſont fendus à bî-<lb/>ſeaux pardeſſous environ au quart de leur longueur, pour faire <lb/> <pb o="96" file="110" n="110" rhead="CONSTRUCTION ET USAGES"/> couler les bouts des petites regles par le moyen des clous à chan-<lb/>frain qui rempliſſent les biſeaux, & </s> <s xml:id="echoid-s3161" xml:space="preserve">que l'on rive auſſi pardeſſous. <lb/></s> <s xml:id="echoid-s3162" xml:space="preserve">Enfin on met un bouton tourné de cuivre au milieu de chaque re-<lb/>gle de ces deux inſtrumens pour les manier plus aiſement, le tout <lb/>comme il eſt aiſe de voir par leurs ſigures.</s> <s xml:id="echoid-s3163" xml:space="preserve"/> </p> <div xml:id="echoid-div310" type="float" level="2" n="1"> <note position="right" xlink:label="note-109-02" xlink:href="note-109-02a" xml:space="preserve">Fig. Q.</note> </div> <p> <s xml:id="echoid-s3164" xml:space="preserve">Leur principal uſage eſt pour tracer des lignes parelleles, en les <lb/>ouvrant ou les fermant. </s> <s xml:id="echoid-s3165" xml:space="preserve">Elles ſont fort commodes pour les deſſeins <lb/>d'Architecture & </s> <s xml:id="echoid-s3166" xml:space="preserve">de Fortification où il y a beaucoup de lignes pa-<lb/>ralleles à tracer l'une contre l'autre.</s> <s xml:id="echoid-s3167" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div312" type="section" level="1" n="139"> <head xml:id="echoid-head215" style="it" xml:space="preserve">Conſtruction du Pedometre.</head> <p> <s xml:id="echoid-s3168" xml:space="preserve">CEt inſtrument ſe nomme Pedometre ou Compte-pas; </s> <s xml:id="echoid-s3169" xml:space="preserve">toutes les <lb/> <anchor type="note" xlink:label="note-110-01a" xlink:href="note-110-01"/> pieces de cet inſtrument ſont réunies enſemble dans une boëte <lb/>à peu près ſemblable à celle d'une montre; </s> <s xml:id="echoid-s3170" xml:space="preserve">ſa grandeur eſt environ <lb/>de 2 pouces de diametre, & </s> <s xml:id="echoid-s3171" xml:space="preserve">de 6 à 8 lignes d'épaiſſeur. </s> <s xml:id="echoid-s3172" xml:space="preserve">Nous allons <lb/>donner la conſtruction de toutes les pieces en particulier.</s> <s xml:id="echoid-s3173" xml:space="preserve"/> </p> <div xml:id="echoid-div312" type="float" level="2" n="1"> <note position="left" xlink:label="note-110-01" xlink:href="note-110-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s3174" xml:space="preserve">La plaque marquée T ſe place dans le fond de la boëte. </s> <s xml:id="echoid-s3175" xml:space="preserve">Sur cette <lb/>plaque ſont attachées pluſieurs pieces, comme on les voir diſpoſées <lb/>en la figure. </s> <s xml:id="echoid-s3176" xml:space="preserve">La piece marquée 1 eſt un pietit pied de Biche d'acier <lb/>avec ſes deux reſſorts; </s> <s xml:id="echoid-s3177" xml:space="preserve">il eſt retenu par un tenon rond qui entre dans <lb/>un trou, de maniere qu'en tirant la petite lame, qui déborde ladite <lb/>plaque & </s> <s xml:id="echoid-s3178" xml:space="preserve">qui eſt attachée par un bout au pied de Biche, on lui fait <lb/>faire un mouvement de baſcule qui fait tourner une étoile d'a-<lb/>cier à 6 pointes marquée 2, elle porte un pignon de 6 dents auſſi <lb/>d'acier de la même hauteur des 2 rouës dont nous allons parler. </s> <s xml:id="echoid-s3179" xml:space="preserve">Le <lb/>reſſort d'acier marqué 4, eſt fait pour empêcher que l'étoile ne re-<lb/>cule, & </s> <s xml:id="echoid-s3180" xml:space="preserve">celui marqué 5, eſt pour faire relever le bout du pied de <lb/>Biche, quand il a fait avancer l'étoile d'une pointe.</s> <s xml:id="echoid-s3181" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3182" xml:space="preserve">La plaque marquée V, eſt la même que celle marquée A, ſi ce <lb/>n'eſt qu'elle eſt recouverte de deux rouës d'une même grandeur, & </s> <s xml:id="echoid-s3183" xml:space="preserve"><lb/>placées l'une ſur l'autre; </s> <s xml:id="echoid-s3184" xml:space="preserve">celle de deſſous a 101 dents, & </s> <s xml:id="echoid-s3185" xml:space="preserve">celle de def-<lb/>ſus n'en a que 100; </s> <s xml:id="echoid-s3186" xml:space="preserve">elles ſont toutes deux engrenées par le pignon <lb/>qui eſt ſur l'étoile, en ſorte que par une eſpece de declic ou de dé-<lb/>tente qui fait tourner l'étoile & </s> <s xml:id="echoid-s3187" xml:space="preserve">ſon pignon, quand la premiere <lb/>rouë a fait ſon tour, & </s> <s xml:id="echoid-s3188" xml:space="preserve">parcouru 100 parties avec ſon éguille ſur le <lb/>plus grand cadran de la figure S, la rouë qui a une dent de plus re-<lb/>cule d'un point, & </s> <s xml:id="echoid-s3189" xml:space="preserve">fait avancer l'éguille du milieu ſur le petit ca-<lb/>dran auſſi diviſé en 100 partics, laquelle n'acheve un de ſes tours <lb/>que lorſque l'éguille du grand cadran en fait 100 des ſiens, qui <lb/>@ont autant de pas, & </s> <s xml:id="echoid-s3190" xml:space="preserve">par conſequent l'éguille du petit cadran n'a <lb/> <pb o="97" file="111" n="111" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> fait un tour entier qu'au bout 10000 pas.</s> <s xml:id="echoid-s3191" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3192" xml:space="preserve">Il y a 3 tenons percez & </s> <s xml:id="echoid-s3193" xml:space="preserve">attachez à la plaque de deſſous, pour la <lb/>faire tenir avec des goupilles à la plaque de deſſus, ſur laquelle <lb/>ſont poſez les cadrans de la figure S.</s> <s xml:id="echoid-s3194" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3195" xml:space="preserve">Toute la machine eſt renfermée dans ſa boëte, recouverte d'un <lb/>criſtal, & </s> <s xml:id="echoid-s3196" xml:space="preserve">d'un côté il y a 2 anneaux pour y paſſer un ruban afin d'at-<lb/>tacher cet inſtrument à la ceinture; </s> <s xml:id="echoid-s3197" xml:space="preserve">& </s> <s xml:id="echoid-s3198" xml:space="preserve">à l'autre extremité de la boë-<lb/>te il y a une ouverture par où paſſe la petite lame d'acier pour y re-<lb/>cevoir un cordon qui s attache à la jarretiere.</s> <s xml:id="echoid-s3199" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3200" xml:space="preserve">L'uſage de cet inſtrument eſt qu'étant ainſi attaché, à chaque ten-<lb/>ſion du genoüil que l'on fait pour avancer un pas, le cordon tire la <lb/>lame d'acier, & </s> <s xml:id="echoid-s3201" xml:space="preserve">cette lame fait mouvoir le pied de biche, & </s> <s xml:id="echoid-s3202" xml:space="preserve">par le <lb/>même moyen l'étoile avec le pignon, en même-tems les rouës font <lb/>avancer l'éguille du grand cadran d'une diviſion. </s> <s xml:id="echoid-s3203" xml:space="preserve">A l'inflexion du <lb/>genoüille reſſort ſe replace, & </s> <s xml:id="echoid-s3204" xml:space="preserve">ſe tire de nouveau par une autre ten-<lb/>ſion, & </s> <s xml:id="echoid-s3205" xml:space="preserve">lorſque l'on a pris une meſure, ou qu'on a fait bien du che-<lb/>min, on regarde ſur ſon cadran, & </s> <s xml:id="echoid-s3206" xml:space="preserve">l'on écrit la quantité de pas qu'-<lb/>on a trouvez. </s> <s xml:id="echoid-s3207" xml:space="preserve">Les pas ſont à peu près de deux pieds, & </s> <s xml:id="echoid-s3208" xml:space="preserve">il eſt aiſe <lb/>de s'accoûtumer en marchant de les faire juſtes de cette meſure.</s> <s xml:id="echoid-s3209" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3210" xml:space="preserve">Quand le terrain n'eſt pas de niveau, les pas ne ſont pas égaux; <lb/></s> <s xml:id="echoid-s3211" xml:space="preserve">car en deſcendant ils s'allongent, & </s> <s xml:id="echoid-s3212" xml:space="preserve">en montant ils ſe racourciſſent <lb/>il faut y avoir égard, & </s> <s xml:id="echoid-s3213" xml:space="preserve">les reformer par l'experience.</s> <s xml:id="echoid-s3214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3215" xml:space="preserve">On fait auſſi de ces ſortes d'inſtruments qu'on ajuſte à une rouë <lb/>dont on connoît la circonference, qui eſt, par exemple, d'une toiſe, <lb/>& </s> <s xml:id="echoid-s3216" xml:space="preserve">quand ladite rouë arrive à un certain point où il y a un tenon <lb/>qui tire une branche de fer, le pied de biche ſe détend; </s> <s xml:id="echoid-s3217" xml:space="preserve">& </s> <s xml:id="echoid-s3218" xml:space="preserve">par ce <lb/>moyen fait avancer les rouës, qui font en même-tems avancer l'é-<lb/>guille d'une diviſion, & </s> <s xml:id="echoid-s3219" xml:space="preserve">par là on connoît combien on a parcou-<lb/>ru de toiſes.</s> <s xml:id="echoid-s3220" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3221" xml:space="preserve">On ajuſte auſſi le Compte pas au derriere d'un carroſſe, de telle <lb/>maniere que quand la grande rouë du carroſſe eſt parvenuë à un <lb/>point, elle fait détendre le cliquet & </s> <s xml:id="echoid-s3222" xml:space="preserve">fait avancer l'éguille d'une <lb/>diviſion; </s> <s xml:id="echoid-s3223" xml:space="preserve">en connoiſſant la circonference de ladite rouë, on ſçait <lb/>combien on a fait de chemin. </s> <s xml:id="echoid-s3224" xml:space="preserve">M. </s> <s xml:id="echoid-s3225" xml:space="preserve">Sauveur a perfectionné depuis <lb/>peu cette derniere maniere de Compte. </s> <s xml:id="echoid-s3226" xml:space="preserve">pas.</s> <s xml:id="echoid-s3227" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div314" type="section" level="1" n="140"> <head xml:id="echoid-head216" style="it" xml:space="preserve">Conſtruction de la plate-forme, pour diviſer & fendre les <lb/>rouës & pignons des horloges.</head> <p> <s xml:id="echoid-s3228" xml:space="preserve">L'Inſtrument marqué A de la Planche dixiéme, eſt nommé pla-<lb/>te forme des Horlogeurs; </s> <s xml:id="echoid-s3229" xml:space="preserve">il ſert à diviſer & </s> <s xml:id="echoid-s3230" xml:space="preserve">fendre ou faire les <lb/> <pb o="98" file="112" n="112" rhead="CONSRTUCTION ET USAGES"/> <anchor type="note" xlink:label="note-112-01a" xlink:href="note-112-01"/> dents des rouës & </s> <s xml:id="echoid-s3231" xml:space="preserve">les pignons des pendules & </s> <s xml:id="echoid-s3232" xml:space="preserve">montres de poche. <lb/></s> <s xml:id="echoid-s3233" xml:space="preserve">Cette machine eſt très-commode, & </s> <s xml:id="echoid-s3234" xml:space="preserve">abrege beaucoup le tems aux <lb/>Horlogeurs, pour fendre facilement les dents des rouës, & </s> <s xml:id="echoid-s3235" xml:space="preserve">les diviſer <lb/>bien exactement. </s> <s xml:id="echoid-s3236" xml:space="preserve">La plaque A, eſt faite de laiton bien dreſſée de 7 à <lb/>8 pouces de diametre, & </s> <s xml:id="echoid-s3237" xml:space="preserve">d'une ligne d'épaiſſeur; </s> <s xml:id="echoid-s3238" xml:space="preserve">on y trace pluſieurs <lb/>cercles concentriques qu'on diviſe en differens nombres pairs ou <lb/>impairs, dont les plus grands ſont toûjours les plus près du bord.</s> <s xml:id="echoid-s3239" xml:space="preserve"/> </p> <div xml:id="echoid-div314" type="float" level="2" n="1"> <note position="left" xlink:label="note-112-01" xlink:href="note-112-01a" xml:space="preserve">X. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s3240" xml:space="preserve">Si, par exemple, on veut diviſer un de ces cercles en 120 parties <lb/>égales, on les diviſe premiérement en 2, dont chaque moitié en con-<lb/>tient 60, que l'on ſubdiviſe encore en 2, dont chaque partie en con-<lb/>tient 30, que l'on ſubdiviſe encore en 2, chaque partie ſera de 15, <lb/>leſquelles étant diviſées en 3, feront 5, enfin chacune de ces der-<lb/>nieres parties en 5, & </s> <s xml:id="echoid-s3241" xml:space="preserve">par ce moyen tout le cercle ſe trouvera diviſé <lb/>cn 120 parties.</s> <s xml:id="echoid-s3242" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3243" xml:space="preserve">Mais ſi l'on veut diviſer un de ces cercles en nombre impair, com-<lb/>me par exemple en 81 parties égales, il faut d'abord le diviſer en 3, <lb/>dont chacune ſera de 27, leſquelles étant ſubdiviſées en 3 chaque <lb/>partie ſera de 9, & </s> <s xml:id="echoid-s3244" xml:space="preserve">chacune de ces nouvelles parties en 3, & </s> <s xml:id="echoid-s3245" xml:space="preserve">puis en-<lb/>core en 3, & </s> <s xml:id="echoid-s3246" xml:space="preserve">par ce moyen le cercle ſe trouvera diviſé en 81 parties <lb/>égales.</s> <s xml:id="echoid-s3247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3248" xml:space="preserve">Ainſi de tout autre nombre en cherchant leurs parties aliquotes <lb/>les plus convenables aux diviſions que l'on ſe propoſe de faire.</s> <s xml:id="echoid-s3249" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3250" xml:space="preserve">Les cercles de cette plate-forme étant diviſez, on fait avec une <lb/>pointe d'acier bien fine, de petits points à chaque diviſion.</s> <s xml:id="echoid-s3251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3252" xml:space="preserve">Quand on veut diviſer ſimplement une rouë d'horloge, pour la <lb/>fendre à la main, on place le trou qui eſt à ſon centre à l'arbre qui <lb/>fait le centre de la plate-forme, & </s> <s xml:id="echoid-s3253" xml:space="preserve">l'ayant arrêté fixement, on trace <lb/>avcc une regle à centre d'acier mince, que l'on fait tourner de divi-<lb/>ſion en diviſion d'une des circonferences convenables au nombre <lb/>des dents que l'on veut avoir ſur la rouë, & </s> <s xml:id="echoid-s3254" xml:space="preserve">elle ſe trouvera diviſée.</s> <s xml:id="echoid-s3255" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3256" xml:space="preserve">Enſuite on refend les dents avec une lime mince, laiſſant à peu <lb/>prés autant de plein que de vuide, & </s> <s xml:id="echoid-s3257" xml:space="preserve">la rouë ſe trouve achevée.</s> <s xml:id="echoid-s3258" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3259" xml:space="preserve">Mais quand on veut ſe ſervir de cette machine pour fendre tout <lb/>d'un coup les rouës d'horloge, elle eſt compoſée de la maniere que <lb/>nous allons expliquer.</s> <s xml:id="echoid-s3260" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3261" xml:space="preserve">La figure premiere repreſente le plan de la machine toute montée <lb/> <anchor type="note" xlink:label="note-112-02a" xlink:href="note-112-02"/> & </s> <s xml:id="echoid-s3262" xml:space="preserve">prête à s'en ſervir. </s> <s xml:id="echoid-s3263" xml:space="preserve">La piece marquée I, eſt le touret qui porte une <lb/>rouë d'acier de l'épaiſſeur du vuide que l'on veut laiſſer entre les <lb/>dents, elle eſt taillée en lime par le bord, & </s> <s xml:id="echoid-s3264" xml:space="preserve">eſt montée ſur un arbre <lb/>quarré ſur lequel il y a une petite bobine ou poulie afin de la faire <lb/> <pb o="99" file="113" n="113" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> tourner entre 2 pointes d'acier. </s> <s xml:id="echoid-s3265" xml:space="preserve">L'endroit marqué 2, eſt le porte-<lb/>touret, il a un mouvement aux deux exrremitez comme la tête d'un <lb/>compas, afin d'élever ou baiſſer la rouë à lime.</s> <s xml:id="echoid-s3266" xml:space="preserve"/> </p> <div xml:id="echoid-div315" type="float" level="2" n="2"> <note position="left" xlink:label="note-112-02" xlink:href="note-112-02a" xml:space="preserve">Fig. A.</note> </div> <p> <s xml:id="echoid-s3267" xml:space="preserve">La figure 2, repreſente le touret de face; </s> <s xml:id="echoid-s3268" xml:space="preserve">l'endroit marqué 1, eſt <lb/>la rouë taillée en lime montée ſur ſon arbre avec la bobine entre les <lb/>deux pointes qui ſont arrêtées ferme par les deux vis a tête marquées <lb/>7. </s> <s xml:id="echoid-s3269" xml:space="preserve">A l'endroit marqué 2, eſt le mouvement pour placer le touret vis-<lb/>à-vis de la rouë qu'on veut fendre. </s> <s xml:id="echoid-s3270" xml:space="preserve">Les vis marquées 9, ſont pour <lb/>arrêter le touret qu'on fait entrer dans la piece de fer marquée 3 qui <lb/>eſt une eſpece de regle, par le trou quarré où aboutiſſent leſdites vis. <lb/></s> <s xml:id="echoid-s3271" xml:space="preserve">Ladite regle eſt double; </s> <s xml:id="echoid-s3272" xml:space="preserve">c'eſt-à-dire, qu'il y en a une deſſus la plate-<lb/>forme, & </s> <s xml:id="echoid-s3273" xml:space="preserve">l'autre deſſous. </s> <s xml:id="echoid-s3274" xml:space="preserve">Elles ſont d'une épaiſſeur convenable, & </s> <s xml:id="echoid-s3275" xml:space="preserve"><lb/>ſe tiennent enſemble par les deux bouts avec deux fortes vis, laiſſant <lb/>un vuide entre deux ſuffiſant pour contenir la plate-forme, & </s> <s xml:id="echoid-s3276" xml:space="preserve">y fai-<lb/>re couler le touret, & </s> <s xml:id="echoid-s3277" xml:space="preserve">le reſſort qui porte la pointe dont nous par-<lb/>lerons ci après.</s> <s xml:id="echoid-s3278" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3279" xml:space="preserve">La figure 3, repreſente le profil de toute la machine montée. </s> <s xml:id="echoid-s3280" xml:space="preserve">La <lb/>piece marquée 1, eſt le touret placé proche la rouë qu'on veut fendre <lb/>marquée 6, ladite rouë eſt poſée au centre, & </s> <s xml:id="echoid-s3281" xml:space="preserve">arrêtée par des vis à <lb/>l'arbre qui traverſe la machine. </s> <s xml:id="echoid-s3282" xml:space="preserve">La piece marquée 3, eſt la regle de <lb/>fer ſur laquelle coulent le touret marqué 2, & </s> <s xml:id="echoid-s3283" xml:space="preserve">le reſſort qui porte la <lb/>pointe marquée 4, La piece qui eſt au-deſſous marquée 5, eſt une <lb/>queuë de fer, pour tenir ferme toute la machine dans un étau, <lb/>quand on s'en veut ſervir.</s> <s xml:id="echoid-s3284" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3285" xml:space="preserve">La figure 4, eſt une pointe d'acier bien fine & </s> <s xml:id="echoid-s3286" xml:space="preserve">bien trempée qui <lb/>entre à vis au bout d'une efpece de reſſort qui a un mouvement cir-<lb/>culaire pour placer la pointe dans tous les points de diviſion qui <lb/>ſont ſur la plate-forme; </s> <s xml:id="echoid-s3287" xml:space="preserve">il y a une autre piece qui ſe rejoint ſur le <lb/>reſſort afin d'appuïer par une vis la pointe & </s> <s xml:id="echoid-s3288" xml:space="preserve">l'empêcher de ſortir <lb/>de chaque diviſion où elle eſt poſée.</s> <s xml:id="echoid-s3289" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3290" xml:space="preserve">L'endroit marqué 3, eſt l'ouverture par où ladite piece coule le <lb/>long de la regle de fer, & </s> <s xml:id="echoid-s3291" xml:space="preserve">qu'on arrête où l'on veut, par le moyen <lb/>de la vis qui eſt au bout.</s> <s xml:id="echoid-s3292" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3293" xml:space="preserve">Enfin la figure 5, eſt l'arbre qui ſe met au centre de la machine, <lb/>& </s> <s xml:id="echoid-s3294" xml:space="preserve">ſur lequel on poſe les rouës qu'on veut fendre en les arrêtant fer-<lb/>me par le moyen des écrous qui ſont deſſus & </s> <s xml:id="echoid-s3295" xml:space="preserve">deſſous. </s> <s xml:id="echoid-s3296" xml:space="preserve">On a pour <lb/> <anchor type="note" xlink:label="note-113-01a" xlink:href="note-113-01"/> l'ordinaire pluſieurs arbres de differente groſſeur à proportion des <lb/>ouvertures des centres des rouës qu'on veut fendre.</s> <s xml:id="echoid-s3297" xml:space="preserve"/> </p> <div xml:id="echoid-div316" type="float" level="2" n="3"> <note position="right" xlink:label="note-113-01" xlink:href="note-113-01a" xml:space="preserve">Fig. A.</note> </div> <p> <s xml:id="echoid-s3298" xml:space="preserve">L'uſage de cette machine eſt facile; </s> <s xml:id="echoid-s3299" xml:space="preserve">il n'y a qu'à faire tenir ferme <lb/>les rouës au centre à l'endroit marqué 6, puis ajuſter le reſſort mar-<lb/> <pb o="100" file="114" n="114" rhead="CONSTRUCTION ET USAGES"/> qué 4, dont la pointe doit etre placée bien juſte ſur la diviſion qui <lb/>eſt autour de la circonference qui contient pareil nombre à celui des <lb/>dents qu'on veut faire. </s> <s xml:id="echoid-s3300" xml:space="preserve">On approche enſuite le touret avec ſa rouë <lb/>à refendre par le moyen de la grande vis qui eſt arrêtée par un col-<lb/>let taraudé, & </s> <s xml:id="echoid-s3301" xml:space="preserve">qui eſt attaché au bout de la regle de fer à l'endroit <lb/>marque 5. </s> <s xml:id="echoid-s3302" xml:space="preserve">L'autre bout de la vis qui doit être entaillé, & </s> <s xml:id="echoid-s3303" xml:space="preserve">non ta-<lb/>raudé, entre dans un trou rond qui eſt au bas du touret, & </s> <s xml:id="echoid-s3304" xml:space="preserve">arrêté par <lb/>une goupille, en ſorte qu'en tournant la vis on fait avancer ou re-<lb/>culer le touret tant & </s> <s xml:id="echoid-s3305" xml:space="preserve">ſi peu qu'on veut. </s> <s xml:id="echoid-s3306" xml:space="preserve">A yant ainſi placé le touret, <lb/>il n'y a qu'à faire tourner la rouë à refendre 4 ou 5 tours par le <lb/>moyen d'un archet dont la corde eſt paſſée autour de la petite pou-<lb/>lie, alors la dent ſera fenduë d'un côté, & </s> <s xml:id="echoid-s3307" xml:space="preserve">ayant ſait faire le tour de <lb/>la circonference à la machine en plaçant toûjours bien juſte la poin-<lb/>te du reſſort dans chaque point de diviſion; </s> <s xml:id="echoid-s3308" xml:space="preserve">& </s> <s xml:id="echoid-s3309" xml:space="preserve">donnant toûjours à <lb/>chaque point 4 ou 5 coups d'archet, la rouë fe trouvera fenduë, & </s> <s xml:id="echoid-s3310" xml:space="preserve"><lb/>les dents bien faites: </s> <s xml:id="echoid-s3311" xml:space="preserve">les pignons ſe fendent de même.</s> <s xml:id="echoid-s3312" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3313" xml:space="preserve">Il eſt à remarquer que l'on a des rouës à refendre de differente <lb/>épaiſſeur conformément au vuide que l'on veut faire à chaque dent <lb/>A la fin de cet Ouvrage je donnerai la conſtruction d'une Pendu-<lb/>le à ſecondes, où l'on verra l'utilité de cette machine.</s> <s xml:id="echoid-s3314" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div318" type="section" level="1" n="141"> <head xml:id="echoid-head217" style="it" xml:space="preserve">Conſtruction des armures des pierres d'aiman, comme auſſi la <lb/>maniere de tailler leſdites pierres pour les armer.</head> <p> <s xml:id="echoid-s3315" xml:space="preserve">LEs figures B & </s> <s xml:id="echoid-s3316" xml:space="preserve">C, repreſentent deux pierres d'aiman armées: </s> <s xml:id="echoid-s3317" xml:space="preserve">la <lb/>premiere en forme de parallelipipede, & </s> <s xml:id="echoid-s3318" xml:space="preserve">la ſeconde en forme <lb/>de ſphere; </s> <s xml:id="echoid-s3319" xml:space="preserve">nous allons expliquer la maniere de les bien armer, après <lb/>avoir parlé des vertus & </s> <s xml:id="echoid-s3320" xml:space="preserve">proprietéz de cette pierre.</s> <s xml:id="echoid-s3321" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3322" xml:space="preserve">L'aiman eſt une pierre très-dure, & </s> <s xml:id="echoid-s3323" xml:space="preserve">très-peſante, qui ſe trouve <lb/>dans les minieres de fer, & </s> <s xml:id="echoid-s3324" xml:space="preserve">eſt à peu près de la même couleur, c'eſt <lb/>pourquoi on la met au rang des mineraux; </s> <s xml:id="echoid-s3325" xml:space="preserve">elle à des proprietez mer-<lb/>veilleuſes, dont l'une eſt d'attirer le fer, & </s> <s xml:id="echoid-s3326" xml:space="preserve">l'autre de ſe diriger vers <lb/>les Poles du Monde.</s> <s xml:id="echoid-s3327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3328" xml:space="preserve">L'aiman attire le fer, & </s> <s xml:id="echoid-s3329" xml:space="preserve">reciproquement le fer attire l'aiman, & </s> <s xml:id="echoid-s3330" xml:space="preserve"><lb/>même à travers des corps qui leur ſont interpoſez. </s> <s xml:id="echoid-s3331" xml:space="preserve">Cette pierre <lb/>communique auſſi au fer la faculté d'en attirer un autre; </s> <s xml:id="echoid-s3332" xml:space="preserve">car par <lb/>exemple, un anneau de fer qui a été touché d'une bonne pierre <lb/>d'aiman, enleve un autre anneau par un ſimple attouchement, & </s> <s xml:id="echoid-s3333" xml:space="preserve"><lb/>ce ſecond un troiſiéme, ainſi de ſuite, & </s> <s xml:id="echoid-s3334" xml:space="preserve">font comme une eſpe-<lb/>ce de chaîne; </s> <s xml:id="echoid-s3335" xml:space="preserve">mais il faut que le premier anneau ſoit plus fort que <lb/>le ſecond, & </s> <s xml:id="echoid-s3336" xml:space="preserve">le ſecond plus que le troiſiéme.</s> <s xml:id="echoid-s3337" xml:space="preserve"/> </p> <pb o="101" file="115" n="115" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> <p> <s xml:id="echoid-s3338" xml:space="preserve">On voit auſſi que la lame d'un couteau qui a été touchée d'un <lb/>aiman enleve des éguilles, & </s> <s xml:id="echoid-s3339" xml:space="preserve">de petits morceaux de fer. </s> <s xml:id="echoid-s3340" xml:space="preserve">Si l'on met <lb/>pluſieurs éguilles à coudre ſur une table les unes près des autres, & </s> <s xml:id="echoid-s3341" xml:space="preserve"><lb/>qu'on approche un aiman de la premiere, cette premiere ayant ac-<lb/>quis la vertu magnetique attirera la ſuivante, & </s> <s xml:id="echoid-s3342" xml:space="preserve">celle-ci une autre, <lb/>& </s> <s xml:id="echoid-s3343" xml:space="preserve">toutes paroîtront comme attachées les unes aux autres.</s> <s xml:id="echoid-s3344" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3345" xml:space="preserve">Le fer attire réciproquement l'aiman, lorſque cette pierre ſe peut <lb/>mouvoir librement; </s> <s xml:id="echoid-s3346" xml:space="preserve">car ayant mis une pierre d'aiman dans une eſ-<lb/>pece de petit bateau leger qui puiſſe flotter ſur l'eau d'un baſſin, ſi <lb/>on lui preſente un morceau de fer à une diſtance convenable, on ver-<lb/>ra que ce petit bateau fendra l'eau par la vertu de l'aiman qui veut <lb/>ſe joindre au fer.</s> <s xml:id="echoid-s3347" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3348" xml:space="preserve">Pour éviter l'embarras de ſe ſervir de l'eau & </s> <s xml:id="echoid-s3349" xml:space="preserve">des petits bateaux, <lb/>principalement en hyver; </s> <s xml:id="echoid-s3350" xml:space="preserve">on a depuis peu inventé une eſpece de <lb/>balance magnetique qui conſiſte en un ſil de laiton ou d argent con-<lb/>tourné en maniere d'anſe de petit ſeau; </s> <s xml:id="echoid-s3351" xml:space="preserve">on paſſe cette anſe dans une <lb/>piece en baluſtre qui ſe termine en pointe, & </s> <s xml:id="echoid-s3352" xml:space="preserve">on la poſe ſur <lb/>un petit enfoncement qui eſt au bout d'un morceau de fil de laiton <lb/>ou d'argent, & </s> <s xml:id="echoid-s3353" xml:space="preserve">qui eſt attaché à un petit pied d'eſtal, qui ſert à por-<lb/>ter toute la machine, en ſorte qu'elle puiſſe ſe mouvoir en tous ſens. <lb/></s> <s xml:id="echoid-s3354" xml:space="preserve">Aux deux extremitez de l'anſe ſont deux petits baſſins, dans l'un <lb/>deſquels on met un aiman, & </s> <s xml:id="echoid-s3355" xml:space="preserve">dans l'autre une boule de fer qui faſſe <lb/>équilibre avec l'aiman; </s> <s xml:id="echoid-s3356" xml:space="preserve">on peut faire avec cette petite machine les <lb/>mêmes experiences qu'avec les petits beteaux; </s> <s xml:id="echoid-s3357" xml:space="preserve">car étant poſée ſur <lb/>le pivot, elle tourne très-facilement; </s> <s xml:id="echoid-s3358" xml:space="preserve">en ſorte que préſentant le po-<lb/>le boreal d'un aiman au pole boreal de l'aiman placé dans le baſſin, <lb/>cet aiman fuira avec beaucoup de vîteſſe celui qu'on lui préſente, <lb/>& </s> <s xml:id="echoid-s3359" xml:space="preserve">préſentant le pole boreal de l'aiman qu'on tient à la main au po-<lb/>le auſtral de celui qui eſt dans le baſſin, cet aiman s'approchera auſſi-<lb/>tôt & </s> <s xml:id="echoid-s3360" xml:space="preserve">s'arrêtera dans l'inſtant; </s> <s xml:id="echoid-s3361" xml:space="preserve">on fait auſſi avec cette balance les <lb/>mêmes choſes par les boules d'acier qu'avec les bateaux.</s> <s xml:id="echoid-s3362" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3363" xml:space="preserve">A l'égard de la proprieté de l'aiman, qui eſt de ſe diriger vers les <lb/>Poles du Monde, on la reconnoît par l'experience ſuivante; </s> <s xml:id="echoid-s3364" xml:space="preserve">quand <lb/>on laiſſe flotter un morceau de liege avec une pierre d'aiman ſur une, <lb/>eau dormante, ſans qu'il y ait de fer ou autre choſe qui l'empêche <lb/>de ſe mouvoir librement & </s> <s xml:id="echoid-s3365" xml:space="preserve">de prendre ſa ſituation naturelle, on re-<lb/>marque qu'elle ſe diſpoſe toujours d'une même façon à l'égard du <lb/>Midi & </s> <s xml:id="echoid-s3366" xml:space="preserve">du Septentrion, de ſorte qu'un endroit de cette pierre re-<lb/>garde toûjours le Septentrion, & </s> <s xml:id="echoid-s3367" xml:space="preserve">ſon oppoſé le Midi.</s> <s xml:id="echoid-s3368" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3369" xml:space="preserve">On doit remarquer que l'aiman ne ſe dirige pas droit au Pole du <lb/> <pb o="102" file="116" n="116" rhead="CONSTRUCTION ET USAGES"/> Monde, à cauſe de ſa déclinaiſon, qui eſt à preſent de plus de 12 <lb/>degrez 15 minutes Nord-Oüeſt, en ſorte que le Pole boreal de l'ai-<lb/>man ſe dirige à plus de 12 degrez près de celui du Monde, & </s> <s xml:id="echoid-s3370" xml:space="preserve">ſon <lb/>oppoſe2; </s> <s xml:id="echoid-s3371" xml:space="preserve">également, ce qui a fait appeller Poles de l'aiman ces deux <lb/>endroits qui regardent les deux Poles magnetiques du monde, & </s> <s xml:id="echoid-s3372" xml:space="preserve">a-<lb/>xe principal de l'aiman, la ligne droite qui s'étend d'un Pole à l'au-<lb/>tre. </s> <s xml:id="echoid-s3373" xml:space="preserve">C'eſt autour de cet axe que ſe manifeſte la plus grande force de <lb/>l'aiman, & </s> <s xml:id="echoid-s3374" xml:space="preserve">c'eſt aux deux Poles que ſa vertu ſe communique da-<lb/>vantage. </s> <s xml:id="echoid-s3375" xml:space="preserve">On a auſſi imaginé un équateur, qui eſt un cercle autour <lb/>de la ſurface de l'aiman également diſtant des Poles & </s> <s xml:id="echoid-s3376" xml:space="preserve">même des <lb/>Meridiens, paſſant par ſes deux Poles principaux, & </s> <s xml:id="echoid-s3377" xml:space="preserve">on a nommé-<lb/>cela Sphere magnetique.</s> <s xml:id="echoid-s3378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3379" xml:space="preserve">Pour trouver les Poles principaux d'un aiman il faut percer une <lb/>carte de la figure de la pierre, afin de l'enchaſſer dans le trou, en ſor-<lb/>te que ſon axe principal ſe trouve dans le plan de cette carte; </s> <s xml:id="echoid-s3380" xml:space="preserve">puis ſe-<lb/>mer de la limaille de fer ou d'acier en la tamiſant; </s> <s xml:id="echoid-s3381" xml:space="preserve">enſuite de quoi <lb/>on frape doucement avec uu petit bâton, afin que mettant en mou-<lb/>vement cette limaille la matiere magnetique lui faſſe prendre un ar-<lb/>rangement conforme au chemin que tient cette matiere pour paſſer <lb/>d'un pore boreal dans un autre pore auſtral, & </s> <s xml:id="echoid-s3382" xml:space="preserve">on s'apercevra que <lb/>cette limaille ſera rangée en forme de pluſieurs demi circonferences <lb/>dont les extremitez oppoſécs mar queront les Poles de l'aiman.</s> <s xml:id="echoid-s3383" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3384" xml:space="preserve">On peut encore connoître les Poles d'un aiman en le plongeant <lb/>dans de la limaille de fer ou d'acier, ou pour le mieux dans de petits <lb/>bouts de fil d'acier qu'on a coupé; </s> <s xml:id="echoid-s3385" xml:space="preserve">car pour lors ils feront pluſieurs <lb/>differentes configurations autour de la pierre; </s> <s xml:id="echoid-s3386" xml:space="preserve">il y en aura qui ſeront <lb/>tout-à-fait couchez, d'autres à demi courbez, & </s> <s xml:id="echoid-s3387" xml:space="preserve">enfin d'autres tout <lb/>droits; </s> <s xml:id="echoid-s3388" xml:space="preserve">& </s> <s xml:id="echoid-s3389" xml:space="preserve">ces endroits de la pierre où ces petits bouts d'acier ſeront <lb/>perpendiculaires, ou que la limaille ſera heriſſée, ſeront imman qua-<lb/>blement ſes Poles, & </s> <s xml:id="echoid-s3390" xml:space="preserve">l'endroit où ils ſe tiennent couchez marque <lb/>ſon équateur.</s> <s xml:id="echoid-s3391" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3392" xml:space="preserve">Connoiſſant ainſi les Poles de l'aiman on déterminera leurs noms <lb/>en le faiſſant flotter ſur l'eau avec un petit morceau de liege ou le <lb/>ſuſpendant avec un fil, de telle ſorte que ſon axe ſoit parallele à l'ho-<lb/>riſon; </s> <s xml:id="echoid-s3393" xml:space="preserve">alors le Pole de cette pierre qui ſe tournera vers le Nord du <lb/>Monde ſera le Sud de laiman, & </s> <s xml:id="echoid-s3394" xml:space="preserve">le point oppoſé ſera le Nord.</s> <s xml:id="echoid-s3395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3396" xml:space="preserve">On connoîtra auſſi les Poles d'un aiman avec une bouſſole; </s> <s xml:id="echoid-s3397" xml:space="preserve">car <lb/>preſentant une éguille aimantée à une pierre d'aiman, le bout qui <lb/>aura été touché tournera auſſi-tôt vers le Pole de la pierre qui lui <lb/>convient, & </s> <s xml:id="echoid-s3398" xml:space="preserve">l'autre bout de l'éguille tournera de même vers l'au-<lb/>tre Pole de la pierre.</s> <s xml:id="echoid-s3399" xml:space="preserve"/> </p> <pb o="103" file="117" n="117" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> <p> <s xml:id="echoid-s3400" xml:space="preserve">Les Poles de la pierre étant trouvez il eſt neceſſaire de la tailler, & </s> <s xml:id="echoid-s3401" xml:space="preserve"><lb/>lui donner une forme reguliere, en retranchant ce qui eſt inutile, <lb/>ſoit avec une ſcie & </s> <s xml:id="echoid-s3402" xml:space="preserve">de la poudre d'émery, ou bien ſur une meule de <lb/>Gagne-petit, lui conſervant ſon axe le plus long qu'il ſera poſſible, <lb/>& </s> <s xml:id="echoid-s3403" xml:space="preserve">donnant à ſes Poles une figure ſemblable; </s> <s xml:id="echoid-s3404" xml:space="preserve">pour achever de la <lb/>dreſſer & </s> <s xml:id="echoid-s3405" xml:space="preserve">adoucir, on la frotera ſur une pierre unie avec du grais <lb/>ou du ſable.</s> <s xml:id="echoid-s3406" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3407" xml:space="preserve">Pour faire un grand nombre d'experiences, il eſt à propos de faire <lb/>prendre à la pierre une figure la plus reguliere qu'il eſt poſſible, la-<lb/>quelle figure ſe détermine par rapport à celle de la maſſe irreguliere <lb/>qu'on veut travailler; </s> <s xml:id="echoid-s3408" xml:space="preserve">la cubique, la parallelipipede, l'ovale, & </s> <s xml:id="echoid-s3409" xml:space="preserve">la <lb/>ronde ſont les plus avantageuſes; </s> <s xml:id="echoid-s3410" xml:space="preserve">mais il faut préferer la paralleli-<lb/>pipede & </s> <s xml:id="echoid-s3411" xml:space="preserve">l'ovale, à cauſe que l'axe peincipal de l'aiman en étant <lb/>plus long, l'effet en ſera plus ſenſible. </s> <s xml:id="echoid-s3412" xml:space="preserve">Sion veut tailler une pierre en <lb/>forme de ſphere, il ne faut pas s'embaraſſer de chercher d'abord ſes <lb/>Poles ni ſon axe; </s> <s xml:id="echoid-s3413" xml:space="preserve">il faudra ſeulement la dégroſſir dans un baſſin de <lb/>fer bien concave, ſe ſervant pour cela de poudre d'émery, puis a-<lb/>chever de l'arondir dans une matrice ou baſſin de cuivre concave <lb/>avec du grais, & </s> <s xml:id="echoid-s3414" xml:space="preserve">enſuite pour l'adoucir on ſe ſervira de ſable fin.</s> <s xml:id="echoid-s3415" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3416" xml:space="preserve">La figure ſpherique d'un aiman eſt fort avantageuſe pour plu-<lb/>ſieurs experiences; </s> <s xml:id="echoid-s3417" xml:space="preserve">on trouve ſes Poles de la même maniere que nous <lb/>avons dit ci-devant.</s> <s xml:id="echoid-s3418" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3419" xml:space="preserve">Mais auparavant que de ſe donner la peine de couper & </s> <s xml:id="echoid-s3420" xml:space="preserve">de tailler <lb/>une pierre d'aiman il eſt à propos de s'aſſurer de ſa bonté, en voyant <lb/>ſi elle ſe charge bien de limaille de fer ou de petits morc@aux d'acier, <lb/>& </s> <s xml:id="echoid-s3421" xml:space="preserve">ſi elle n'a point de matiere étrangere qui traverſe ſes pores, & </s> <s xml:id="echoid-s3422" xml:space="preserve">qui <lb/>empêche la matiere magnetique de circuler & </s> <s xml:id="echoid-s3423" xml:space="preserve">de paſſer d'un Pole <lb/>à l'autre.</s> <s xml:id="echoid-s3424" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3425" xml:space="preserve">La bonté d'un aiman conſiſte en deux choſes eſſentielles, qui ſont <lb/>10 d'être homogene, ayant un grand nombre de pores remplis de ma-<lb/>tiere magnetique qui les parcoure formant autour de lui un tour-<lb/>billon très-étendu, & </s> <s xml:id="echoid-s3426" xml:space="preserve">rempli d'un grand nombre de particules ma-<lb/>gnetiques. </s> <s xml:id="echoid-s3427" xml:space="preserve">En ſecond lieu, ſa figure, comme nous avons dit, contri-<lb/>buë beaucoup à ſa force, étant certain que de tous les aimans de pa-<lb/>reille bonté, celui qui ſera le mieux poli, qui aura ſon axe le plus <lb/>long, & </s> <s xml:id="echoid-s3428" xml:space="preserve">dont les Poles ſe rencontreront juſte aux deux extremitez, <lb/>ſera le plus vigoureux.</s> <s xml:id="echoid-s3429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3430" xml:space="preserve">Deux aimans à qui on preſente leurs Poles de divers noms, s'ap-<lb/>prochent, au lieu que quand on leur preſente leurs Poles de même <lb/>nom ils ſe fuïent, étants ſur l'eau dans une petite gondole.</s> <s xml:id="echoid-s3431" xml:space="preserve"/> </p> <pb o="104" file="118" n="118" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s3432" xml:space="preserve">Si un aiman eſt coupé en deux pieces parallelement à ſon axe, les <lb/>côtez des piecez qui étoient enſemble avant la diviſion ſe fuïent.</s> <s xml:id="echoid-s3433" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3434" xml:space="preserve">Si un aiman eſt coupé en deux pieces, ſuivant ſon équateur, les <lb/>côtez des pieces qui étoient enſemble avant la coupe, ſe trouvent <lb/>Poles de divers noms, & </s> <s xml:id="echoid-s3435" xml:space="preserve">s'approchent.</s> <s xml:id="echoid-s3436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3437" xml:space="preserve">Un aiman fort qui en touche un foible l'attire par ſon Pole de <lb/>même nom, &</s> <s xml:id="echoid-s3438" xml:space="preserve">c.</s> <s xml:id="echoid-s3439" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div319" type="section" level="1" n="142"> <head xml:id="echoid-head218" style="it" xml:space="preserve">Deſcription des Armures.</head> <p> <s xml:id="echoid-s3440" xml:space="preserve">L'Armure d'un aiman taillé en parallelipipede rectangle, eſt com-<lb/>poſée de deux morceaux d'acier ou de fer bien doux en forme <lb/>d'equerre; </s> <s xml:id="echoid-s3441" xml:space="preserve">l'acier trempé eſt plus propre que le fer, parce que ſes <lb/>pores ſont plus ſerrez & </s> <s xml:id="echoid-s3442" xml:space="preserve">en plus grande quantité. </s> <s xml:id="echoid-s3443" xml:space="preserve">Il faut avoit grand <lb/>ſoin que les armures embraſſent & </s> <s xml:id="echoid-s3444" xml:space="preserve">touchent bien juſtement les po-<lb/>les, & </s> <s xml:id="echoid-s3445" xml:space="preserve">les faire épaiſſes, à proportion de la bonté de l'aiman: </s> <s xml:id="echoid-s3446" xml:space="preserve">car ſi à <lb/> <anchor type="note" xlink:label="note-118-01a" xlink:href="note-118-01"/> un foible aiman on y mettoit une forte armure, elle ne feroit point <lb/>d'effet, parce que la matiere magnetique n'auroit pas aſſez de force <lb/>pour paſſer à travers; </s> <s xml:id="echoid-s3447" xml:space="preserve">de même ſi l'armure d'une forte pierre étoit <lb/>trop mince, elle ne pourroit pas contenir toute la matiere magne-<lb/>tique qu'elle devroit contenir, & </s> <s xml:id="echoid-s3448" xml:space="preserve">par conſequent ne feroit pas <lb/>tant d'effet.</s> <s xml:id="echoid-s3449" xml:space="preserve"/> </p> <div xml:id="echoid-div319" type="float" level="2" n="1"> <note position="left" xlink:label="note-118-01" xlink:href="note-118-01a" xml:space="preserve">Fig. B.</note> </div> <p> <s xml:id="echoid-s3450" xml:space="preserve">Cela ſe reconnoît en éprouvant & </s> <s xml:id="echoid-s3451" xml:space="preserve">limant peu à peu les armures, <lb/>tant que l'on voit que l'effet s'augmente, & </s> <s xml:id="echoid-s3452" xml:space="preserve">quand il n'augmente <lb/>plus, c'eſt une marque qu'elles ſont dans une juſte proportion, & </s> <s xml:id="echoid-s3453" xml:space="preserve"><lb/>qu'elles ont l'épaiſſeur convenable. </s> <s xml:id="echoid-s3454" xml:space="preserve">Après quoi il faut les adoucir <lb/>en dedans, & </s> <s xml:id="echoid-s3455" xml:space="preserve">les polir en dehors.</s> <s xml:id="echoid-s3456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3457" xml:space="preserve">A l'égard des têtes des armures elles doivent être plus épaiſſes que <lb/>le reſte, & </s> <s xml:id="echoid-s3458" xml:space="preserve">couvrir environ les deux tiers de la longueur de l'axe.</s> <s xml:id="echoid-s3459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3460" xml:space="preserve">On éprouvera de même l'épaiſſeur & </s> <s xml:id="echoid-s3461" xml:space="preserve">la longueur qui convien-<lb/>dront le mieux à la pierre, en limant peu à peu.</s> <s xml:id="echoid-s3462" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3463" xml:space="preserve">Il faut ſur tout avoir grand ſoin que les deux têtes ſoient d'égale <lb/>épaiſſeur, & </s> <s xml:id="echoid-s3464" xml:space="preserve">que leurs baſes ſe rencontrent bien juſte dans un mê-<lb/>me plan Enſuite on ajuſtera une ceinture de laiton ou d'argent mar-<lb/>quée 5 autour de la pierre qui ſervira à ſerrer & </s> <s xml:id="echoid-s3465" xml:space="preserve">maintenir les armu-<lb/>res, par le moyen des deux vis marquées 1; </s> <s xml:id="echoid-s3466" xml:space="preserve">on mettra auſſi au-deſlus <lb/>une platine de laiton, ou autre matiere, qui portera le pendant & </s> <s xml:id="echoid-s3467" xml:space="preserve"><lb/>ſon anneau, ladite platine maintiendra le haut des armures avec <lb/>deux écrous aux endroits marquez 6. </s> <s xml:id="echoid-s3468" xml:space="preserve">On ajuſte enfin un porte-poids <lb/>avec ſon crochet de même matiere. </s> <s xml:id="echoid-s3469" xml:space="preserve">Il eſt compoſé d'une lame d'a-<lb/>cier de longueur, largeur & </s> <s xml:id="echoid-s3470" xml:space="preserve">épaiſſeur convenables, & </s> <s xml:id="echoid-s3471" xml:space="preserve">du côté où il <lb/> <pb o="105" file="119" n="119" rhead="DE DIFFERENS INSTRUMENS. Liv III. Ch. II."/> doit toucher les baſes des têtes des armures, il faut qu'il ſoit bien <lb/>droit, bien adouci, & </s> <s xml:id="echoid-s3472" xml:space="preserve">un peu arrondi par les bords, afin que le <lb/>contact s'en faſſe mieux.</s> <s xml:id="echoid-s3473" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3474" xml:space="preserve">A l'égard de l'armure de l'aiman ſpherique, elle eſt compoſée de <lb/>2 coquilles d'acier qui ſe tiennent par le haut avec une charniere <lb/>aux endroits marquez 6, d'une ceinture à l'endroit 5, d'un anneau <lb/>à l'endroit 4, & </s> <s xml:id="echoid-s3475" xml:space="preserve">d'un porte-poids à l'endroit 2. </s> <s xml:id="echoid-s3476" xml:space="preserve">ll faut ſur tout que <lb/> <anchor type="note" xlink:label="note-119-01a" xlink:href="note-119-01"/> les coquilles ſoient bien fraiſées en rond par dedans, & </s> <s xml:id="echoid-s3477" xml:space="preserve">qu'elles joi-<lb/>gnent bien juſte la ſuperficie; </s> <s xml:id="echoid-s3478" xml:space="preserve">de maniere que chacune embraſſe bien <lb/>ſes poles, & </s> <s xml:id="echoid-s3479" xml:space="preserve">qu'elle couvre une très-grande partie de la convexité de <lb/>la pierre. </s> <s xml:id="echoid-s3480" xml:space="preserve">On connoît l'épaiſſeur & </s> <s xml:id="echoid-s3481" xml:space="preserve">largeur qui convient à cette ar-<lb/>mure par des épreuves ſemblables à celles dont nous avons parlé ci-<lb/>devant. </s> <s xml:id="echoid-s3482" xml:space="preserve">Au reſte les figures B & </s> <s xml:id="echoid-s3483" xml:space="preserve">C font aſſez connoître ce que nous <lb/>venons de dire.</s> <s xml:id="echoid-s3484" xml:space="preserve"/> </p> <div xml:id="echoid-div320" type="float" level="2" n="2"> <note position="right" xlink:label="note-119-01" xlink:href="note-119-01a" xml:space="preserve">Fig. C.</note> </div> <p> <s xml:id="echoid-s3485" xml:space="preserve">C'eſt une choſe merveilleuſe que deux petits morceaux d'acier <lb/>qui font l'armure d'un aiman, ſemblent augmenter tellement ſa <lb/>force, qu'on a vû de bonnes pierres, leſquelles après avoir été ar-<lb/>mées, enlevoient plus de cent cinquante fois plus qu'@lles ne fai-<lb/>ſoient lorſqu'elles étoient nuës.</s> <s xml:id="echoid-s3486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3487" xml:space="preserve">Il y a des pierres paſſablement bonnes, qui peſent nuës environ <lb/>trois onces, & </s> <s xml:id="echoid-s3488" xml:space="preserve">n'enlevent qu'une demie once de fer; </s> <s xml:id="echoid-s3489" xml:space="preserve">mais étant ar-<lb/>mées, elles levent plus de ſept livres.</s> <s xml:id="echoid-s3490" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3491" xml:space="preserve">Pour conſerver un aiman on le tient dans un lieu ſec parmi de pe-<lb/>tits bouts de fil d'acier: </s> <s xml:id="echoid-s3492" xml:space="preserve">car la limaille, qui eſt toûjours pleine de <lb/>pouſſiere, le fait roüiller.</s> <s xml:id="echoid-s3493" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3494" xml:space="preserve">On le ſuſpend auſſi quelquefois, afin qu'ayant la liberté de ſe <lb/>mouvoir, il ſe dirige vers les Poles du Monde.</s> <s xml:id="echoid-s3495" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3496" xml:space="preserve">Dans cette ſituation on lui met ſon porte-poids avec le crochet, <lb/>auquel on attache la charge qu'il porte d'ordinaire, & </s> <s xml:id="echoid-s3497" xml:space="preserve">de tems en <lb/>tems on y ajoûte quelque petit poids nouveau; </s> <s xml:id="echoid-s3498" xml:space="preserve">& </s> <s xml:id="echoid-s3499" xml:space="preserve">ayant continué <lb/>pendant quelques jours, on verra qu'il ſoûtient beaucoup plus de <lb/>poids qu'il ne faiſoit auparavant.</s> <s xml:id="echoid-s3500" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div322" type="section" level="1" n="143"> <head xml:id="echoid-head219" style="it" xml:space="preserve">Nous allons rapporter pluſieurs experiences que l'on fait <lb/>or dinairement avec la pierre d'aiman.</head> <p> <s xml:id="echoid-s3501" xml:space="preserve">LA premiere & </s> <s xml:id="echoid-s3502" xml:space="preserve">la plus utile eſt celle d'aimanter les éguilles des <lb/>bouſſoles. </s> <s xml:id="echoid-s3503" xml:space="preserve">Pour le faire adroitement, on coule doucement & </s> <s xml:id="echoid-s3504" xml:space="preserve"><lb/>on tire de loin l'éguille 3 ou 4 fois ſur un des poles de l'aiman de-<lb/>puis ſon milieu juſqu'à ſon extremité; </s> <s xml:id="echoid-s3505" xml:space="preserve">mais il faut remarquer que le <lb/>bout de l'éguille d'une bouſſole qui a touché à un des poles de l'ai-<lb/> <pb o="106" file="120" n="120" rhead="CONSTRUCTION ET USAGES"/> man, ſe tourne vers l'endroit du Monde oppoſé à celui qui regarde <lb/>ce pole; </s> <s xml:id="echoid-s3506" xml:space="preserve">c'eſt pourquoi ſi on veut que le bout de l'éguille ſe dirige <lb/>vers le Nord, il faut le faire toucher au pole de l'aiman quiregarde <lb/>le Sud. </s> <s xml:id="echoid-s3507" xml:space="preserve">Plus les éguilles ſont longues, moins elles ont de vibration.</s> <s xml:id="echoid-s3508" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3509" xml:space="preserve">Cette merveilleuſe direction de l'aiman & </s> <s xml:id="echoid-s3510" xml:space="preserve">de l'éguille aimantée <lb/>vers les Poles du Monde, n'eſt connuë en Europe que depuis environ <lb/>200 ans, & </s> <s xml:id="echoid-s3511" xml:space="preserve">les Pilotes en tirent la principale connoiſſance de leurs <lb/>routes dans les grandes navigations. </s> <s xml:id="echoid-s3512" xml:space="preserve">Ce qui eſt incommode, c'eſt <lb/>que l'éguille aimantée ne ſe dirige pas toûjours exactement vers les <lb/>Poles du Monde, mais qu'elle décline tantôt plus, tantôt moins vers <lb/>l'Orient ou vers l'Occident, & </s> <s xml:id="echoid-s3513" xml:space="preserve">que ſa déclinaiſon n'eſt pas même é-<lb/>gale par tout. </s> <s xml:id="echoid-s3514" xml:space="preserve">En l'année 1610, elle déclinoit à Paris de 8 degrez du <lb/>Septentrion vers l'Orient; </s> <s xml:id="echoid-s3515" xml:space="preserve">en 1658, elle n'y déclinoit point du tout; </s> <s xml:id="echoid-s3516" xml:space="preserve">en <lb/>1716, elle déclinoit de plus de 2 degrez 15 minutes vers l'Occident.</s> <s xml:id="echoid-s3517" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3518" xml:space="preserve">Outre la déclinaiſon de l'éguille aimantée, on y remarque enco-<lb/>re une inclinaiſon, c'eſt-à-dire, qu'une éguille de bouſſole étant en <lb/>équilibre ſur ſon pivot avant que d'être aimantée, perd cet équili-<lb/>bre en l'aimantant, & </s> <s xml:id="echoid-s3519" xml:space="preserve">le bout qui dans ce païs tourne au Nord, <lb/>panche vers la terre, comme ſi elle étoit devenuë plus peſante de <lb/>ce côté-là; </s> <s xml:id="echoid-s3520" xml:space="preserve">c'eſt ce quifait qu'avant que d'aimanter les éguilles, on <lb/>laiſſe le côté qui doit regarder le Nord, plus leger que celui qui doit <lb/>regarder le Sud. </s> <s xml:id="echoid-s3521" xml:space="preserve">Cette inclinaiſon augmente à meſure qu'on appro-<lb/>che du Pole, & </s> <s xml:id="echoid-s3522" xml:space="preserve">diminuë quand on aproche de l'Equateur; </s> <s xml:id="echoid-s3523" xml:space="preserve">tellement <lb/>queſous la Ligne équinoxiale l'éguille ſe trouve en équilibre; </s> <s xml:id="echoid-s3524" xml:space="preserve">quand <lb/>on a paſſé la Ligne pour aller vers la partie méridionale du Monde, <lb/>pour lors l'aut re bout de l'éguille, qui regarde le Pole du Sud, com-<lb/>mence à pancher vers la terre, tellement que les Pilotes ſont obligez <lb/>de mettre un peu de cire tantôt à un bout de l'éguille, tantôt à l'au-<lb/>tre, pour la mettre en équilibre. </s> <s xml:id="echoid-s3525" xml:space="preserve">Plus l'aiman ſur lequel ou touche <lb/>les éguilles, a de force, plus illes fait pancher.</s> <s xml:id="echoid-s3526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3527" xml:space="preserve">On fait exprès des éguilles pour obſerver cette inclinaiſon. </s> <s xml:id="echoid-s3528" xml:space="preserve">C'eſt <lb/>un morceau d'acier fort uni, traverſé par le milieu à angles droits <lb/>d'un fil de laiton qui ſert à la ſoûtenir ſur deux petits pivots, à la <lb/>maniere que le fleau d'une balance eſt ſoûtenu. </s> <s xml:id="echoid-s3529" xml:space="preserve">Elle eſt d'abord mi-<lb/>ſe en équilïbre; </s> <s xml:id="echoid-s3530" xml:space="preserve">mais après qu'elle a été frotée d'un bon aiman, <lb/>quand on la met dans le plan du Méridien à Paris, le bout ne l'éguil-<lb/>le qui regarde le Nord, trebuche; </s> <s xml:id="echoid-s3531" xml:space="preserve">& </s> <s xml:id="echoid-s3532" xml:space="preserve">quand elle eſt arrêtée, elle incli-<lb/>ne à 1 horiſon environ de 70 degrez.</s> <s xml:id="echoid-s3533" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3534" xml:space="preserve">Si on paſſe une lame d'acier ſur un des poles de l'aiman armé de <lb/>la même maniere que nous avons dit des éguilles de bouſſoles, cette <lb/> <pb o="107" file="121" n="121" rhead="DE DIFFERENS INSTRUMENS. Liv.III.Ch.II."/> lame acquiert en un inſtant la vertu magnetique, & </s> <s xml:id="echoid-s3535" xml:space="preserve">ne la perd que <lb/>peu à peu & </s> <s xml:id="echoid-s3536" xml:space="preserve">après pluſieurs mois, à moins qu'on ne la mette aufeu; <lb/></s> <s xml:id="echoid-s3537" xml:space="preserve">une lame d'acier étant paſſée ſur une bonne pierre, enleve juſqu'a <lb/>douze à quatorze onces.</s> <s xml:id="echoid-s3538" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3539" xml:space="preserve">Les deux bouts de cette lame ainſi aimantée deviennent poles de <lb/>diversnoms; </s> <s xml:id="echoid-s3540" xml:space="preserve">l'un boreal, ſçavoir celui dont l'attouchement finit ſur <lb/>le pole auſtral dela pierre; </s> <s xml:id="echoid-s3541" xml:space="preserve">& </s> <s xml:id="echoid-s3542" xml:space="preserve">auſtral, ſi l'attouchement a été fait ſur <lb/>le pole boreal de la pierre. </s> <s xml:id="echoid-s3543" xml:space="preserve">car ſi cette lame eſt aſſez legere pour na-<lb/>ger ſur l'eau, elle ſe dirigera, comme l'aiman, au Nord & </s> <s xml:id="echoid-s3544" xml:space="preserve">au Sud.</s> <s xml:id="echoid-s3545" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3546" xml:space="preserve">Le bout de cette lame, par lequel l'attouchement a fini, leve beau-<lb/>coup plus de fer que l'autre bout; </s> <s xml:id="echoid-s3547" xml:space="preserve">& </s> <s xml:id="echoid-s3548" xml:space="preserve">ſi l'on paſſe une ſeule fois cette <lb/>lame à contre-ſens ſur la pierre, elle ne levera plus, & </s> <s xml:id="echoid-s3549" xml:space="preserve">aura perdu ſa <lb/>vertu. </s> <s xml:id="echoid-s3550" xml:space="preserve">Il en eſt de même d'une éguille de bouſſole, d'une lame de <lb/>couteau, &</s> <s xml:id="echoid-s3551" xml:space="preserve">c.</s> <s xml:id="echoid-s3552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3553" xml:space="preserve">Deux lames aimantées ſe fuïent, & </s> <s xml:id="echoid-s3554" xml:space="preserve">s'aprochent comme l'aiman.</s> <s xml:id="echoid-s3555" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3556" xml:space="preserve">Siune lame d'acier nage ſur l'eau, on la fera mouvoir comme on <lb/>voudra, ſelon qu'on lui preſentera les poles d'un aiman, ou d'une <lb/>autre lame aimantée.</s> <s xml:id="echoid-s3557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3558" xml:space="preserve">Une éguille fine, enfilée & </s> <s xml:id="echoid-s3559" xml:space="preserve">ſoûtenuë par un fil, fera voir cequ'on <lb/>nommé ſympathie & </s> <s xml:id="echoid-s3560" xml:space="preserve">antipathie: </s> <s xml:id="echoid-s3561" xml:space="preserve">car cette éguille ſera chaſſée par <lb/>un pole d'un aiman, & </s> <s xml:id="echoid-s3562" xml:space="preserve">attirée par l'autre.</s> <s xml:id="echoid-s3563" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3564" xml:space="preserve">L'on fera tenir deboutune éguille, ſans qn'elle touche à l'aiman, <lb/>en ſorte qu'on pourra paſſer entr'elle & </s> <s xml:id="echoid-s3565" xml:space="preserve">l'aiman une piece d'argent, <lb/>ou autre matiere, pourvû que ce ne ſoït pas de fer.</s> <s xml:id="echoid-s3566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3567" xml:space="preserve">Si autour d'un aiman rond, ou d'une autre figure, ſuſpendu par <lb/>un fil, on place circulairement pluſieurs petites éguilles de bouſſole <lb/>aimantées, ſur leurs pivots, & </s> <s xml:id="echoid-s3568" xml:space="preserve">qu'on faſſe mouvoir l'aiman en tout <lb/>ſens, on verra auſſi mouvoir toutes ces éguilles d'une maniere agréa-<lb/>ble, en prenant differentes ſituations, & </s> <s xml:id="echoid-s3569" xml:space="preserve">lorſque l'aiman ceſſer a de <lb/>ſe mouvoir, ces éguilles ceſſeront auſſi, en obſervant chacune à part <lb/>une diſpoſition conſorme à la façon dont on l'aura aimantée.</s> <s xml:id="echoid-s3570" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3571" xml:space="preserve">Nous avons parlé de l'arrangement de la limaille autour d'un ai-<lb/>man poſé ſur un carton; </s> <s xml:id="echoid-s3572" xml:space="preserve">il en ſera à peu près de même autour d'u-<lb/>ne lame d'acier aimantée.</s> <s xml:id="echoid-s3573" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3574" xml:space="preserve">Si on ſeme de la limaille ſur un carton, & </s> <s xml:id="echoid-s3575" xml:space="preserve">qu'on paſſe un aiman <lb/>deſſous, la limaille ſe dreſſera, puis ſe couchera du côté d'où vicnt <lb/>l'aiman.</s> <s xml:id="echoid-s3576" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3577" xml:space="preserve">Si au lieu de limaille on met ſur un carton un ou pluſieurs bouts <lb/>d'éguilles caſſées, ils ſe dreſſeront par un bout en preſentant un des <lb/>poles de l'aiman; </s> <s xml:id="echoid-s3578" xml:space="preserve">mais ſi on preſente l'autre pole, ils feront la culbu-<lb/>@e, puis ſe redreſſeront ſur l'autre bout.</s> <s xml:id="echoid-s3579" xml:space="preserve"/> </p> <pb o="108" file="122" n="122" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s3580" xml:space="preserve">Il n'eſt pas facile de ſeparer une pouſſiere noire mêlée parmi du <lb/>ſable blanc; </s> <s xml:id="echoid-s3581" xml:space="preserve">& </s> <s xml:id="echoid-s3582" xml:space="preserve">le propoſer à faire à une perſonne qui n'en auroit pas <lb/>le ſecret, ce ſeroit demander l'impoſſible: </s> <s xml:id="echoid-s3583" xml:space="preserve">cependant ſi on mêle de <lb/>la limaille de fer avec du ſablon d'Etampes, on les ſepare facilement <lb/>avec une pierre d'aiman ou une lame d'acier aimantée: </s> <s xml:id="echoid-s3584" xml:space="preserve">car enfon-<lb/>çant l'un ou l'autre dans ce mélange, on enleve à diverſes foistout <lb/>ce qu'il y a de fer parmi ce ſable, qui reſte ſeul.</s> <s xml:id="echoid-s3585" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3586" xml:space="preserve">Un aiman enleve une piroüete qui tourne, & </s> <s xml:id="echoid-s3587" xml:space="preserve">dont l'axe eſt d'a-<lb/>cier; </s> <s xml:id="echoid-s3588" xml:space="preserve">& </s> <s xml:id="echoid-s3589" xml:space="preserve">ſi elle eſt un peu péſante, elle tournera plus long-tems en <lb/>l'air qu'elle n'auroit fait ſur une table, où le frotement fait plûtôt <lb/>ceſſer ſon mouvement. </s> <s xml:id="echoid-s3590" xml:space="preserve">Si l'aiman a aſſez de force, la piroüete qui y <lb/>tient peut en enlever une ſeconde, & </s> <s xml:id="echoid-s3591" xml:space="preserve">toutes les deux tourneront à <lb/>contre-fens.</s> <s xml:id="echoid-s3592" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3593" xml:space="preserve">On peut encore faire une experience aſſez divertiſlante, en met-<lb/>tant dans un baſſin plat, oùil y a de l'eau, de petits poiſſons, ou des <lb/>cignes d'émail, qui ſont ordinairement enfilez d'un fil d'acier. </s> <s xml:id="echoid-s3594" xml:space="preserve">On <lb/>aura le plaiſir de les voir nager & </s> <s xml:id="echoid-s3595" xml:space="preserve">courir çà & </s> <s xml:id="echoid-s3596" xml:space="preserve">là en paſſant ſous le <lb/>baſſin une bonne pierre d'aiman. </s> <s xml:id="echoid-s3597" xml:space="preserve">On peut leur donner tel mouve-<lb/>ment qu'on veut en promenant la pierre de differentes facons: </s> <s xml:id="echoid-s3598" xml:space="preserve">car ſi <lb/>on la tourneen ſerpentant, les poiſſons ſerpenteront; </s> <s xml:id="echoid-s3599" xml:space="preserve">ſi on leur pre-<lb/>ſentele pole de l'aiman, ils plongeront comme pour s'y joindre. </s> <s xml:id="echoid-s3600" xml:space="preserve">On <lb/>y peut auſſi mettre de petits ſoldats d'émail, que l'on pourra faire a-<lb/>procher ou écarter les uns des autres en forme de combat, & </s> <s xml:id="echoid-s3601" xml:space="preserve">en leur <lb/>préſentant l'équateur de l'aiman ils ſe couchent & </s> <s xml:id="echoid-s3602" xml:space="preserve">ſemblent tomber.</s> <s xml:id="echoid-s3603" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3604" xml:space="preserve">C'eſt une choſe aſſez curieuſe, de voir une éguille à coudre enfilée, <lb/>ou une petite fleche attachée par un cheveu à l'arc d'un Cupidon, <lb/>demeurer ſuſpendue en l'air à 8 ou 10 lignes de diſtance d'un bon <lb/>aiman; </s> <s xml:id="echoid-s3605" xml:space="preserve">& </s> <s xml:id="echoid-s3606" xml:space="preserve">quoiqu'avec le bout d'une éguille on écarte un peu plus <lb/>cette fleche à droit ou à gauche, elle ſe rapproche auſſi-tôt, & </s> <s xml:id="echoid-s3607" xml:space="preserve">par <lb/>ſon agitation elle ſemble vouloir ſe joindre à cette pierre avec beau-<lb/>coup de viteſſe.</s> <s xml:id="echoid-s3608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3609" xml:space="preserve">Nous laiſſons pluſieurs autres experiences, parce qu'elles nous <lb/>meneroient trop loin, il s'en ſait plus de cent differentes. </s> <s xml:id="echoid-s3610" xml:space="preserve">Le princi-<lb/>pal eſt d'avoir un bon aſſortiment d'aiman pour faire les plus belles <lb/>& </s> <s xml:id="echoid-s3611" xml:space="preserve">les plus curieuſes.</s> <s xml:id="echoid-s3612" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div323" type="section" level="1" n="144"> <head xml:id="echoid-head220" style="it" xml:space="preserve">Conſtruction d'un Aiman artificiel.</head> <p> <s xml:id="echoid-s3613" xml:space="preserve">CEt inſtrument eſt de l'invention de M. </s> <s xml:id="echoid-s3614" xml:space="preserve">Joblot. </s> <s xml:id="echoid-s3615" xml:space="preserve">Il eſt compoſé <lb/> <anchor type="note" xlink:label="note-122-01a" xlink:href="note-122-01"/> de pluſieurs lames d'acier bien dreſſées & </s> <s xml:id="echoid-s3616" xml:space="preserve">bien unies, miſes les <lb/>unes ſur les autres. </s> <s xml:id="echoid-s3617" xml:space="preserve">Pour le faire paſſablement bon, il en faut du <lb/>moins une vingtaine, ſuivant la force de l'aiman qu'on veut faire, <lb/> <pb o="109" file="123" n="123" rhead="DE DIFFERENS INSTRUMENS. Liv.III. Ch. II."/> qui ayent environ dix pouces de longueur, un pouce de largeur, <lb/>& </s> <s xml:id="echoid-s3618" xml:space="preserve">demi-ligne d'épaiſſeur: </s> <s xml:id="echoid-s3619" xml:space="preserve">il ſeroit inutile deles faire plus épaiſſes, <lb/>parce que la vertu magnetique ne ſe communique pas plus avant <lb/>dans l'acier.</s> <s xml:id="echoid-s3620" xml:space="preserve"/> </p> <div xml:id="echoid-div323" type="float" level="2" n="1"> <note position="left" xlink:label="note-122-01" xlink:href="note-122-01a" xml:space="preserve">Fig. BB.</note> </div> <p> <s xml:id="echoid-s3621" xml:space="preserve">Ces lames étant aimantées avec une bonne pierre, on les place l'u-<lb/>ne ſur l'autre, ſuivant leurs plus larges ſurfaces, ayant leurs poles de <lb/>même nom tournez du même côté formant un parallelipipede rec-<lb/>tangle. </s> <s xml:id="echoid-s3622" xml:space="preserve">Ces lames ſont preſlées par quatre étriers de laiton, & </s> <s xml:id="echoid-s3623" xml:space="preserve">au-<lb/>tant de petits coins de même matiere, marquez 3, & </s> <s xml:id="echoid-s3624" xml:space="preserve">terminez par 2 <lb/>armures de fer, de longueur, largeur & </s> <s xml:id="echoid-s3625" xml:space="preserve">épaiſſeur convenables. </s> <s xml:id="echoid-s3626" xml:space="preserve">La ba-<lb/>ſe de leurs têtes a environ 2 pouces de largeur. </s> <s xml:id="echoid-s3627" xml:space="preserve">Ces armures ſont re-<lb/>tenuës par une ceinture de laiton, & </s> <s xml:id="echoid-s3628" xml:space="preserve">ſerrées avec des vis marquées <lb/>2. </s> <s xml:id="echoid-s3629" xml:space="preserve">Il y a une plaque de laiton qui les couvre par deſſus, à laquelle eſt <lb/>attaché le pendant avec ſon anneau, & </s> <s xml:id="echoid-s3630" xml:space="preserve">au-deſſous eſt ſon porte-<lb/>poids marqué 5. </s> <s xml:id="echoid-s3631" xml:space="preserve">Il faut faire en ſorte que le deſſus du porte-poids <lb/>faſſe un contact le plus parfait qu'il eſt poſſible avec les têtes des ar-<lb/>mures. </s> <s xml:id="echoid-s3632" xml:space="preserve">Quand les aimans artificiels ſont bien faits, & </s> <s xml:id="echoid-s3633" xml:space="preserve">touchez avec <lb/>de bonnes pierres, ils ont autant de vertu que les bons aimans natu-<lb/>rels, & </s> <s xml:id="echoid-s3634" xml:space="preserve">on peut s'en ſervir pour faire les mêmes experiences.</s> <s xml:id="echoid-s3635" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div325" type="section" level="1" n="145"> <head xml:id="echoid-head221" style="it" xml:space="preserve">Conſtruction du Peſon àreſſort.</head> <p> <s xml:id="echoid-s3636" xml:space="preserve">CEtte machine eſt un peſon qui ſe peut porter aiſément à la po-<lb/> <anchor type="note" xlink:label="note-123-01a" xlink:href="note-123-01"/> che, & </s> <s xml:id="echoid-s3637" xml:space="preserve">dont on ſe ſert bien facilement pour peſer un poids, de-<lb/>puis une livre juſqu'à environ 40.</s> <s xml:id="echoid-s3638" xml:space="preserve"/> </p> <div xml:id="echoid-div325" type="float" level="2" n="1"> <note position="right" xlink:label="note-123-01" xlink:href="note-123-01a" xml:space="preserve">Fig.D</note> </div> <p> <s xml:id="echoid-s3639" xml:space="preserve">Cet inſtrument eſt compoſé d'un tuïau ou canon de cuivre bou-<lb/>ché par les deux bouts, long de 4 à 5 pouces, & </s> <s xml:id="echoid-s3640" xml:space="preserve">large de 7 à 8 li-<lb/>gnes, dont on voit un bout marqué 3, le reſte étant ouvert pour fai-<lb/>re voir le dedans, quieſtun reſſort de fil d'acier trempé, fait en ma-<lb/>niere de vis, comme un tire-boure d'arquebuſe, marqué 2. </s> <s xml:id="echoid-s3641" xml:space="preserve">Il y a par <lb/>le bout d'en haut une petite virole marquée 6, qui a un trou quarré <lb/>par où paſſe une verge de cuivre marquée 1, quieſt auſſi quarrée, & </s> <s xml:id="echoid-s3642" xml:space="preserve"><lb/>qui traverſe le reſſort, ſur laquelle verge ſont les diviſions des livres <lb/>qu'on y a marquées, en mettant ſuccſſivement au crochet marqué <lb/>4 un poids d'1, 2, 3 livres, &</s> <s xml:id="echoid-s3643" xml:space="preserve">c. </s> <s xml:id="echoid-s3644" xml:space="preserve">ſuivant qu'on veut que le peſon <lb/>porte de poids; </s> <s xml:id="echoid-s3645" xml:space="preserve">on écrit auſſi les chifres de 5 en 5, ſur la verge, & </s> <s xml:id="echoid-s3646" xml:space="preserve">le <lb/>lieu où elle ſe trouvera coupée par le bord du trou quarré, marquera <lb/>les livres; </s> <s xml:id="echoid-s3647" xml:space="preserve">ce qui arrivera en divers points par les differens poids <lb/>attachez au crochet 4, qui par leur péſanteur feront étendre & </s> <s xml:id="echoid-s3648" xml:space="preserve">re-<lb/>trecir le reſſort, & </s> <s xml:id="echoid-s3649" xml:space="preserve">en même tems ſortir en dehors une plus grande <lb/>ou plus petite partie de la verge, qui doit être arrêtée par le bout <lb/>d'en bas au reſſort par une petite vis.</s> <s xml:id="echoid-s3650" xml:space="preserve"/> </p> <pb o="110" file="124" n="124" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s3651" xml:space="preserve">L'uſage en eſt fort facile: </s> <s xml:id="echoid-s3652" xml:space="preserve">car la virole à vis marquée 6, étant miſe <lb/>au haut de la grande virole, le reſſort ſera dans toute ſon étenduëau <lb/>long de la branche, & </s> <s xml:id="echoid-s3653" xml:space="preserve">en mettant un poids au crochet, il fera repliſ-<lb/>ſer ledit reſſort & </s> <s xml:id="echoid-s3654" xml:space="preserve">ſortir la branche en dehors; </s> <s xml:id="echoid-s3655" xml:space="preserve">alors remarquant le <lb/>nombre qui ſera coupé par le bord de la petite virole, ce ſeront au-<lb/>tant de livres que peſera ce qui ſera attaché au crochet.</s> <s xml:id="echoid-s3656" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3657" xml:space="preserve">La principale juſteſſe de cette machine conſiſte en la trempe du <lb/>reſſort, afin qu'il ſe ploye & </s> <s xml:id="echoid-s3658" xml:space="preserve">ſe tende ſuivant la force du poids qu'ou <lb/>lui veut faire porter. </s> <s xml:id="echoid-s3659" xml:space="preserve">Il faut auſſi que le fil d'acier ſoit gros à pro-<lb/>portion du poids que le peſon portera delivres, ce qui déterminera <lb/>auſſi la groſſeur & </s> <s xml:id="echoid-s3660" xml:space="preserve">la longueur de l'inſtrument.</s> <s xml:id="echoid-s3661" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div327" type="section" level="1" n="146"> <head xml:id="echoid-head222" style="it" xml:space="preserve">Conſtruction du Peſon à fléau.</head> <p> <s xml:id="echoid-s3662" xml:space="preserve">CEt inſtrument eſt une eſpece de Peſon ou balance de l'inven-<lb/> <anchor type="note" xlink:label="note-124-01a" xlink:href="note-124-01"/> tion de M. </s> <s xml:id="echoid-s3663" xml:space="preserve">Caſſini. </s> <s xml:id="echoid-s3664" xml:space="preserve">Cette balance conſiſte en une verge ſuſ-<lb/>penduë par un fléau en ſon point d'équilibre 5, qui diviſe ladite ver-<lb/>ge en deux bras, comme celle des balances communes. </s> <s xml:id="echoid-s3665" xml:space="preserve">Chacun de <lb/>ces bras eſt diviſé en parties égales ſuivant la longueur de l'inſtru-<lb/>ment, dont l'ordre commence du point de l'équilibre, allant vers <lb/>les deux extremitez marquées 1 & </s> <s xml:id="echoid-s3666" xml:space="preserve">2.</s> <s xml:id="echoid-s3667" xml:space="preserve"/> </p> <div xml:id="echoid-div327" type="float" level="2" n="1"> <note position="left" xlink:label="note-124-01" xlink:href="note-124-01a" xml:space="preserve">Fig. E.</note> </div> <p> <s xml:id="echoid-s3668" xml:space="preserve">L'uſage de cette balance eſt de connoître le poids & </s> <s xml:id="echoid-s3669" xml:space="preserve">le prix des <lb/>marchandiſes en même tems. </s> <s xml:id="echoid-s3670" xml:space="preserve">Si on veut ſe ſervir de cette balance <lb/>pour peſer les marchandiſes, il faut mettre à un des bras de la balan-<lb/>ce un contrepoids marqué 4, d'une livre ou d'une once, ſuivant que <lb/>les marchandiſes ſe peſent par livres ou par onces, en telle maniere <lb/>qu'il puiſte couler le long du bras, comme dansles Romaines, & </s> <s xml:id="echoid-s3671" xml:space="preserve">de <lb/>l'autre côté il faut mettre un fil de ſoie pour ſoûtenir la marchandi-<lb/>ſe. </s> <s xml:id="echoid-s3672" xml:space="preserve">Pour en ſçavoir le poids, il faut mettre le fil de ſoie à la premiere <lb/>diviſion qui eſt la plus proche du point de l'équilibre, & </s> <s xml:id="echoid-s3673" xml:space="preserve">faifant cou-<lb/>ler le contrepoids juſqu'à ce qu'il faſſe équilibre, il marquera dans <lb/>ce point le nombre des livres ou des onces de la marchandiſe.</s> <s xml:id="echoid-s3674" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3675" xml:space="preserve">Si on veut ſçavoir le prix de toute la marchandiſe, à raiſon du <lb/>prix convenu, comme par exemple à 7 ſols l'once ou la livre, met-<lb/>tez le fil qui ſoûtient la marchandiſe, à la ſeptiéme diviſion du mê-<lb/>me bras, enſuite faiſant couler le contrepoids ſur l'autre bras juſ-<lb/>qu'à ce qu'il ſoit en équilibre, le nombre des diyiſions depuis le <lb/>point de ſuſpenſion juſqu'au contrepoids, ſera le nombre des ſols, <lb/>ou la valeur de la marchandiſe peſée.</s> <s xml:id="echoid-s3676" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3677" xml:space="preserve">Pour les marchandiſes qui ne ſçauroient être peſées que dans un <lb/>@aſſin, prenez en un qui ſoit d'un poids connu, comme d'une on-<lb/> <pb o="111" file="125" n="125" rhead="DE DIFFERENS INSTRUMENS. Liv.III.Ch.II."/> ce ou d'une livre, le crochet pour le ſuſpendre y compris; </s> <s xml:id="echoid-s3678" xml:space="preserve">& </s> <s xml:id="echoid-s3679" xml:space="preserve">pour <lb/>trouver le poids & </s> <s xml:id="echoid-s3680" xml:space="preserve">le prix de la marchandiſe, faites la même choſe <lb/>que vous avez faite avecle fil de ſoie, & </s> <s xml:id="echoid-s3681" xml:space="preserve">en ôrcz celui d'une livre <lb/>ou d'une once, quieſt le poids du baſſin.</s> <s xml:id="echoid-s3682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3683" xml:space="preserve">La livre dont on ſe ſert à Paris eſt de 16 onces, & </s> <s xml:id="echoid-s3684" xml:space="preserve">ſe diviſe en 2 <lb/>marcs, chacun de 8 onces; </s> <s xml:id="echoid-s3685" xml:space="preserve">l'once ſe ſubdiviſe en 8 gros, le gros <lb/>en 72 grains, & </s> <s xml:id="echoid-s3686" xml:space="preserve">le grain, qui eſt à peu près le poids d'un grain de <lb/>froment eſt le plus petit poids qui ſoit en uſage.</s> <s xml:id="echoid-s3687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3688" xml:space="preserve">Le quintal peſe cent livres.</s> <s xml:id="echoid-s3689" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div329" type="section" level="1" n="147"> <head xml:id="echoid-head223" style="it" xml:space="preserve">Rapports du poids de 'Paris à ceux des Païs étrangers.</head> <p> <s xml:id="echoid-s3690" xml:space="preserve">LA livre d'Avignon, Lyon, Montpellier & </s> <s xml:id="echoid-s3691" xml:space="preserve">Thoulouſe peſe 13 <lb/>onces.</s> <s xml:id="echoid-s3692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3693" xml:space="preserve">La livre de Marſeille & </s> <s xml:id="echoid-s3694" xml:space="preserve">de la Rochelle de 19 onces.</s> <s xml:id="echoid-s3695" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3696" xml:space="preserve">La livre de Roüen, Beſancon, Stra@bourg & </s> <s xml:id="echoid-s3697" xml:space="preserve">Amſterdam peſe <lb/>16 onces, comme celle de Paris.</s> <s xml:id="echoid-s3698" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3699" xml:space="preserve">La livre de Milan, Naples & </s> <s xml:id="echoid-s3700" xml:space="preserve">Veniſe peſe 9 onces.</s> <s xml:id="echoid-s3701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3702" xml:space="preserve">La livre de Meſſine & </s> <s xml:id="echoid-s3703" xml:space="preserve">de Gennes peſe 9 onces 3 quarts.</s> <s xml:id="echoid-s3704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3705" xml:space="preserve">La livre de Florence, Ligourne, Piſe Sarragoſſe, Valence peſe <lb/>10 onces.</s> <s xml:id="echoid-s3706" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3707" xml:space="preserve">La livre de Turin & </s> <s xml:id="echoid-s3708" xml:space="preserve">de Modene peſe 10 onces & </s> <s xml:id="echoid-s3709" xml:space="preserve">demie.</s> <s xml:id="echoid-s3710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3711" xml:space="preserve">La livre de Londres, Anvers & </s> <s xml:id="echoid-s3712" xml:space="preserve">Flandres peſe 14 onces.</s> <s xml:id="echoid-s3713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3714" xml:space="preserve">La livre de Baſle, Berne Francfort, Nuremberg peſe 16 onces <lb/>& </s> <s xml:id="echoid-s3715" xml:space="preserve">14 grains.</s> <s xml:id="echoid-s3716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3717" xml:space="preserve">Celle de Genéve 17 onces.</s> <s xml:id="echoid-s3718" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div330" type="section" level="1" n="148"> <head xml:id="echoid-head224" style="it" xml:space="preserve">Conſtruction d'une Moufle.</head> <p> <s xml:id="echoid-s3719" xml:space="preserve">L'Inſtrument marqué F eſt une mouſle double. </s> <s xml:id="echoid-s3720" xml:space="preserve">Elle eſt compoſée <lb/> <anchor type="note" xlink:label="note-125-01a" xlink:href="note-125-01"/> de deux chapes; </s> <s xml:id="echoid-s3721" xml:space="preserve">dont chacune porte huit poulies creuſées dans <lb/>l'épaiſſeur d'un petit canal pour recevoir la corde & </s> <s xml:id="echoid-s3722" xml:space="preserve">l'empêcher de <lb/>ſe détourner. </s> <s xml:id="echoid-s3723" xml:space="preserve">Elle eſt attachée par un bout à la chape ſuperieure, & </s> <s xml:id="echoid-s3724" xml:space="preserve"><lb/>après avoir ſait le contour de toutes les poulies, l'autre bout de la <lb/>corde ſe joint à la puiſſance repreſentée par une main. </s> <s xml:id="echoid-s3725" xml:space="preserve">Quatre de ces <lb/>poulies ſont portées par un même eſſieu, & </s> <s xml:id="echoid-s3726" xml:space="preserve">quatre par un autre, <lb/>auſſi-bien dans la chape ſuperieure que dans l'inferieure. </s> <s xml:id="echoid-s3727" xml:space="preserve">Au-deſſus <lb/>de la chape d'en haut il y a un anneau pour attacher la machine en <lb/>un lieu fixe, & </s> <s xml:id="echoid-s3728" xml:space="preserve">au-deſſous de la chape d'en bas il y a un autre an-<lb/>neau pour attacher le poids.</s> <s xml:id="echoid-s3729" xml:space="preserve"/> </p> <div xml:id="echoid-div330" type="float" level="2" n="1"> <note position="right" xlink:label="note-125-01" xlink:href="note-125-01a" xml:space="preserve">Fig. F.</note> </div> <p> <s xml:id="echoid-s3730" xml:space="preserve">L'uſage de cette machine eſt pour élever ou attirer à ſoi de gros <lb/>fardeaux, en multipliant la force de la puiſſance, laquelle augmente <lb/> <pb o="112" file="126" n="126" rhead="CONSTRUCTION ET USAGES"/> dans la raiſon de l'unité au nombre double des poulies d'en bas: </s> <s xml:id="echoid-s3731" xml:space="preserve">de <lb/>ſorte que dans cet inſtrument, où la moufle d'en bas contient huit <lb/>poulies, ſile poids marqué 4 peſe 16 livres, il ne faudra à peu près <lb/>qu'une livre de force à la puiſſance pour faire équilibre. </s> <s xml:id="echoid-s3732" xml:space="preserve">Je dis à peu <lb/>près, parce qu'il en faut un peu plus à cauſe du frotement de la cor-<lb/>de & </s> <s xml:id="echoid-s3733" xml:space="preserve">des eſſieux. </s> <s xml:id="echoid-s3734" xml:space="preserve">Les poulies de la chape d'en haut ne contribuent <lb/>point à augmenter la force, mais ſeulement à faciliter le mouve-<lb/>ment en évitant le frotement des cordes, parce qu'étant comme des <lb/>leviers de la premiere eſpece, dont le point fixe eſt au milieu, la puiſ-<lb/>ſance eſt égale au poids; </s> <s xml:id="echoid-s3735" xml:space="preserve">mais les poulies de la moufle d'en bas ſont <lb/>comme des leviers de la ſeconde eſpece, dont le point fixe eſt à un des <lb/>bouts: </s> <s xml:id="echoid-s3736" xml:space="preserve">car leur diametre eſt comme apuïé ſur un bout, & </s> <s xml:id="echoid-s3737" xml:space="preserve">levé de <lb/>l'autre; </s> <s xml:id="echoid-s3738" xml:space="preserve">ce qui fait que chacune de ces poulies double la force, parce <lb/>que la diſtance de la puiſſance eſt double de celle du poids.</s> <s xml:id="echoid-s3739" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div332" type="section" level="1" n="149"> <head xml:id="echoid-head225" style="it" xml:space="preserve">Conſtruction de la Canne à vent.</head> <p> <s xml:id="echoid-s3740" xml:space="preserve">CEtte machine repreſente une Canne a vent, ou même une ar-<lb/>quebuſe, dont la diſſerence cſt peu de choſe pour la conſtruc-<lb/>tion. </s> <s xml:id="echoid-s3741" xml:space="preserve">Elle a environ 3 pieds de long ſur 12 ou 15 lignes de groſſeur. <lb/></s> <s xml:id="echoid-s3742" xml:space="preserve">Le tuïau 4 eſt fait de laiton bien rond & </s> <s xml:id="echoid-s3743" xml:space="preserve">bien ſoudé, de 4 à 6 lignes <lb/>de diametre. </s> <s xml:id="echoid-s3744" xml:space="preserve">Il eſt bouché du côté oppoſé à l'ouverture. </s> <s xml:id="echoid-s3745" xml:space="preserve">Le creux <lb/>du tuïau eſt ce que l'on nomme l'âme du canon; </s> <s xml:id="echoid-s3746" xml:space="preserve">l'endroit marqué 1 <lb/>eſt un autre tuïau auſſi de laiton tellement diſpoſé autour du pre-<lb/>mier, qu'il demeure un eſpace marqué 4, dans lequel l'air peut ê-<lb/>tre cnfermé. </s> <s xml:id="echoid-s3747" xml:space="preserve">Ces deux tuïaux doivent être unis enſemble par une <lb/>plaque circulaire attachée au bout & </s> <s xml:id="echoid-s3748" xml:space="preserve">exactement ſoudée à l'un & </s> <s xml:id="echoid-s3749" xml:space="preserve"><lb/>à l'autre, pour que l'air n'en puiſſe ſortir. </s> <s xml:id="echoid-s3750" xml:space="preserve">La piece marquée 8, eſt <lb/>une ſoupape qui bouche une ouverture qui ſe peut faire du dehors <lb/>en dedans, c'eſt-à-dire, qui permet à l'air de paſſer de 2 vers 1, mais <lb/>non pas de retourner de 1 vers 2. </s> <s xml:id="echoid-s3751" xml:space="preserve">Il y a encore deux ouvertures <lb/>au tuïau interieur environ vers le bout, qui reſſemble à la culaſſe <lb/>d'un canon ordinaire; </s> <s xml:id="echoid-s3752" xml:space="preserve">l'une eſt marquée 6, par où l'air pouroit écha-<lb/>per de la cavité 4, dans l'ame du canon, s'il n'en étoit empêché par <lb/>une ſoupape à reſſort, qui ne ſe peut ouvrir que de dehors en dedans, <lb/>& </s> <s xml:id="echoid-s3753" xml:space="preserve">que l'air preſſe d'autant plus contre le trou, qu'il fait plus d'effort <lb/>pourſortir. </s> <s xml:id="echoid-s3754" xml:space="preserve">L'autre ouverture eſt marquée 5, par laquelle il y a com-<lb/>munication du dehors de toute la machine au dedans du canon in-<lb/>téricur, de telle forte cependant que l'air que l'on a renfermé dans <lb/>la cavité 4, ne peut ſortir par l'ouverture 5, en étant empêché par <lb/>le moyen d'un petit bout de tuïau qui eſt ſoudé aux deux tuïaux 1 <lb/> <pb o="113" file="127" n="127" rhead="DE DIFFERENS INSTRUMENS Liv. III. Ch. II."/> & </s> <s xml:id="echoid-s3755" xml:space="preserve">4. </s> <s xml:id="echoid-s3756" xml:space="preserve">Enfin le tuïau 2 repreſente le corps d'une ſeringue par laquelle <lb/>on introduit le plus d'air qu'on peut dans l'eſpace 4, après quoi <lb/>ayant fait couler une bale près le petit tuïau 5 dans l'ame à l'en-<lb/>droit marqué 8, la canne ou arquebuſe ſe trouve toute chargée.</s> <s xml:id="echoid-s3757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3758" xml:space="preserve">Pour la décharger, il ne faut qu'enfoncer dans le petit tuïau 5, <lb/>une petite cheville ou poinçon rond qui rempliſſe le trou par lequel <lb/>on pouſſe la ſoupape à reſſort qui eſt à l'ouverture marquée 6: </s> <s xml:id="echoid-s3759" xml:space="preserve">car <lb/>alors l'air qui étoit preſſé dans la cavité 4, ſe dilate, & </s> <s xml:id="echoid-s3760" xml:space="preserve">ſortant <lb/>par l'ouverture marquée 5 dans l'ame du canon, pouſſe la bale au <lb/>dehors avec impetuoſité, & </s> <s xml:id="echoid-s3761" xml:space="preserve">d'une ſi grande force, qu'elle perce une <lb/>planche d'une moyene épaiſſeur.</s> <s xml:id="echoid-s3762" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3763" xml:space="preserve">Le piſton marqué 6, eſt à peu près ſemblable à celui d'une ſerin-<lb/>gue. </s> <s xml:id="echoid-s3764" xml:space="preserve">L'etrier marqué 12, qui eſtau bout, eſt fait pour paſſer le pied <lb/>dedans, afin de pomper l'air plus facilement. </s> <s xml:id="echoid-s3765" xml:space="preserve">Il faut avoir grand ſoin <lb/>que le corps de la ſeringue ſoit bien juſte & </s> <s xml:id="echoid-s3766" xml:space="preserve">bien rond, afin que l'air <lb/>ne s'en retourne pas. </s> <s xml:id="echoid-s3767" xml:space="preserve">Il eſt auſſi neceſſaire que le piſton rempliſſe <lb/>très-juſte le corps de pompe, & </s> <s xml:id="echoid-s3768" xml:space="preserve">qu'il y ait deux petits trous, afin <lb/>qu'en tirant l'étrier en dehors, l'air preſſé faſſe lever une pétite pla-<lb/>que de cuir qui eſt attachée au bout du dit piſton, pour le laiſſer paſſer <lb/>entre le piſton & </s> <s xml:id="echoid-s3769" xml:space="preserve">la ſoupape; </s> <s xml:id="echoid-s3770" xml:space="preserve">enſuite repouſſant le piſton en dedans, <lb/>l'air ſe trouvant encore preſſé, fait lever la petite ſoupape qui bou-<lb/>che le trou de communication, & </s> <s xml:id="echoid-s3771" xml:space="preserve">par ce moyen l'air paſſe dans la <lb/>capacité 3 & </s> <s xml:id="echoid-s3772" xml:space="preserve">n'en peut ſortir ſans faire ſon effet.</s> <s xml:id="echoid-s3773" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3774" xml:space="preserve">La canne ſe démonte en deux, à l'endroit marqué 7, par le <lb/>moyen d'une groſſe vis creuſe.</s> <s xml:id="echoid-s3775" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3776" xml:space="preserve">La figure 10, qui eſt à part, repreſente la petite ſoupape qui bou-<lb/>che le trou de communication. </s> <s xml:id="echoid-s3777" xml:space="preserve">Il y a une eſpece de vis en tire-bou-<lb/>re, afin que par ſon reſſort elle puiſſe ſe relever & </s> <s xml:id="echoid-s3778" xml:space="preserve">rebaiſſer, ſui-<lb/>vant que l'air la fait agir.</s> <s xml:id="echoid-s3779" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3780" xml:space="preserve">La petite figure 11, repreſente le reſſort en ſoupape. </s> <s xml:id="echoid-s3781" xml:space="preserve">On le met en <lb/>dedans du canon quand la canne eſt démontée. </s> <s xml:id="echoid-s3782" xml:space="preserve">Il ſert à boucher le <lb/>trou qui eſt à l'ame du canon. </s> <s xml:id="echoid-s3783" xml:space="preserve">Il faut ſur tout qu'il ſoit ſi bien ajuſté, <lb/>que l'air ne s'échape point du tout. </s> <s xml:id="echoid-s3784" xml:space="preserve">On attache audit reſſort, à l'en-<lb/>droit qui bouche le trou, un morceau de cuir de Hongrie, afin que <lb/>le trou ſoit bien bouché. </s> <s xml:id="echoid-s3785" xml:space="preserve">L'on démonte auſſi l'étrier qui eſt au bout <lb/>du piſton, pour mettre une pomme de canne ordinaire à ſa place.</s> <s xml:id="echoid-s3786" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div333" type="section" level="1" n="150"> <head xml:id="echoid-head226" style="it" xml:space="preserve">Conſtruction de l'Eolipile.</head> <p> <s xml:id="echoid-s3787" xml:space="preserve">CEt Inſtrument eſt fait de laiton battu & </s> <s xml:id="echoid-s3788" xml:space="preserve">retraint en forme de <lb/> <anchor type="note" xlink:label="note-127-01a" xlink:href="note-127-01"/> boule ou poire creuſe. </s> <s xml:id="echoid-s3789" xml:space="preserve">On ſoude une eſpece de tuïau en forme <lb/> <pb o="114" file="128" n="128" rhead="CONSTRUCTION ET USAGES"/> de goulet, qui eſt percé d'un très-petit trou parle bout. </s> <s xml:id="echoid-s3790" xml:space="preserve">Le vaſe n'eſt <lb/>d'abord rempli que d'air, que l'on fait rarefier en l'aprochant du feu, <lb/>afin qu'il en échape une bonne partie par ſa petite ouverture; </s> <s xml:id="echoid-s3791" xml:space="preserve">en-<lb/>ſuite on plonge l'Eolipile dans de l'eau froide, qui fait condenſer <lb/>l'air contenu dans l'inſtrument, & </s> <s xml:id="echoid-s3792" xml:space="preserve">donne paſſage à l'eau qui entre <lb/>par la petite ouverture, & </s> <s xml:id="echoid-s3793" xml:space="preserve">remplit le vuide.</s> <s xml:id="echoid-s3794" xml:space="preserve"/> </p> <div xml:id="echoid-div333" type="float" level="2" n="1"> <note position="right" xlink:label="note-127-01" xlink:href="note-127-01a" xml:space="preserve">Fig. H.</note> </div> <p> <s xml:id="echoid-s3795" xml:space="preserve">Ayant ainſi rempli en partie d'eau cette Eolipile environ letiers <lb/>de ſa capacité, ſi on la poſe ſur des charbons ardens dans la ſituation <lb/>ſemblable à celle que vous voyez dans la figure, l'eau qui eſt dans la <lb/>partie baſſe venant à s'échaufer, ſe dilatera petit à petit, & </s> <s xml:id="echoid-s3796" xml:space="preserve">s'élevera <lb/>peu à peu en vapeurs, qui volant dans l'eſpace d'en haut, où il n'y a <lb/>que de l'air, ſe chaſſent les unes les autres pour ſortir en foule par la <lb/>petite ouverture, en telle ſorte que celles qui ſont auprès du trou ſor-<lb/>tent par là avec beaucoup de viteſſe. </s> <s xml:id="echoid-s3797" xml:space="preserve">Ces vapeurs entraînant l'air a-<lb/>vecſoi, produiſent un vent & </s> <s xml:id="echoid-s3798" xml:space="preserve">un ſifflement violent qui ſouffle le feu <lb/>& </s> <s xml:id="echoid-s3799" xml:space="preserve">qui continuë juſqu'à ce que toute l'eau ſoit évaporée, ou que la <lb/>chaleur ſoit tout-à-fait éteinte, & </s> <s xml:id="echoid-s3800" xml:space="preserve">ce vent a toutes les proprietez <lb/>qu'on remarque dans ceux que nous ſentons au deſſus de la ſurfa-<lb/>ce de la Terre.</s> <s xml:id="echoid-s3801" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div335" type="section" level="1" n="151"> <head xml:id="echoid-head227" style="it" xml:space="preserve">Conſtruction du Microſcope à liqueur.</head> <p> <s xml:id="echoid-s3802" xml:space="preserve"> <lb/> <anchor type="note" xlink:label="note-128-01a" xlink:href="note-128-01"/> L'Inſtrument marqué I eſt un Microſcope pour voir les plus pe-<lb/>tits objets & </s> <s xml:id="echoid-s3803" xml:space="preserve">les petits animaux qui ſont dans les liqueurs. </s> <s xml:id="echoid-s3804" xml:space="preserve">Il eſt <lb/>compoſéde deux plaques de cuivre, ou d'autre métal, longues d'en-<lb/>viron 3 pouces ſur 8 lignes de large. </s> <s xml:id="echoid-s3805" xml:space="preserve">Elles ſont attachées enſen ble <lb/>par les 2 bouts avec 2 vis marquées 2, & </s> <s xml:id="echoid-s3806" xml:space="preserve">qui ſervent à éloigner ou <lb/>approcher les 2 plaques tant & </s> <s xml:id="echoid-s3807" xml:space="preserve">ſi peu qu il eſt neceſlaire pour laiſſer <lb/>tourner une rouë qui porte 6 ouvertures rondes, dans leſquelles il <lb/>y a de petits verres plats pour mettre les differens objets marquez 3, <lb/>4, 5, &</s> <s xml:id="echoid-s3808" xml:space="preserve">c. </s> <s xml:id="echoid-s3809" xml:space="preserve">Du côté de l'œil il y a une piece de cuivre marquée 1. </s> <s xml:id="echoid-s3810" xml:space="preserve">Elle <lb/>eſt concave comme une petite coquille ronde, dont le trou qui eſt <lb/>au milieu aboutit à une couliſſe qui porte une très-petite lentille ou <lb/>boule de verre. </s> <s xml:id="echoid-s3811" xml:space="preserve">Cette boule doit être bien ronde ou fort convexe & </s> <s xml:id="echoid-s3812" xml:space="preserve"><lb/>bien polie, afin de diſtinguer les objets. </s> <s xml:id="echoid-s3813" xml:space="preserve">Le bout d'en bas de la ma-<lb/>chine eſt limé en maniere de manche pour la tenir à la main.</s> <s xml:id="echoid-s3814" xml:space="preserve"/> </p> <div xml:id="echoid-div335" type="float" level="2" n="1"> <note position="left" xlink:label="note-128-01" xlink:href="note-128-01a" xml:space="preserve">Fig. I.</note> </div> <p> <s xml:id="echoid-s3815" xml:space="preserve">L'uſage de cet inſtrument eſt aſſez facile. </s> <s xml:id="echoid-s3816" xml:space="preserve">Si les objets qu'on veut <lb/>voir ſont tranſ parens ſans être liquides, tels que ſont les pieds d'une <lb/>puce, d'une mouche, leurs aîles, les mittes de fromages, ou autres <lb/>petits animaux, comme auſſi les cheveux, leurs racines, &</s> <s xml:id="echoid-s3817" xml:space="preserve">c. </s> <s xml:id="echoid-s3818" xml:space="preserve">on met-<lb/>tra ces objets du côté de l'œil ſur les verres plats qui ſont joints à la <lb/> <pb o="115" file="129" n="129" rhead="DE DIFFERENS INSTRUMENS. Liv.III. Ch.II."/> rouë, en les faiſant tenir par leurs extremitez avec un peu d'eau <lb/>gommée; </s> <s xml:id="echoid-s3819" xml:space="preserve">& </s> <s xml:id="echoid-s3820" xml:space="preserve">pour voir les petits animaux qui ſont dans l'urine gar-<lb/>dée, dans le vinaigre, dans l'eau en laquelle on aura fait infuſer des <lb/>grains de poivre, de la coriandre, de la paille, du foin & </s> <s xml:id="echoid-s3821" xml:space="preserve">preſque de <lb/>toutes ſortes de legumes ou herbages. </s> <s xml:id="echoid-s3822" xml:space="preserve">Il en faut prendre une petite <lb/>goute avec le bout d'un petit tuïau de verre & </s> <s xml:id="echoid-s3823" xml:space="preserve">l'étendre ſur leſdits <lb/>verres; </s> <s xml:id="echoid-s3824" xml:space="preserve">il faut enſuite tourner la rouë & </s> <s xml:id="echoid-s3825" xml:space="preserve">la hauſſer ou baiſſer parle <lb/>moyen des vis marquées 2, & </s> <s xml:id="echoid-s3826" xml:space="preserve">du reſſort qui eſt entre les deux pla-<lb/>ques, qui ſert à maintenir ladite rouë dans la ſituation qu'on veut <lb/>qu'elle ait, & </s> <s xml:id="echoid-s3827" xml:space="preserve">en telle ſorte que les petits objets, ou la goute de li-<lb/>queur ſoit directemeut au-deſſous de la petite boule de verre. </s> <s xml:id="echoid-s3828" xml:space="preserve">Les <lb/>choſes étant ainſi diſpoſées, prenez à la main le manche du Microſ-<lb/>cope, & </s> <s xml:id="echoid-s3829" xml:space="preserve">ayant appliqué l'œil dans la coquille marquée 1, vis-à-vis de <lb/>la petite boule de verre, regardez fixement l'objet au grand jour, ou <lb/>la nuit à la lumiere d'une bougie, tournez en même tems & </s> <s xml:id="echoid-s3830" xml:space="preserve">peu à <lb/>peu la vis du bout pour approcher ou éloigner l'objet plus ou moins <lb/>de la boule de verre, juſqu'à ce que vous ayez trouvé le point de vûë <lb/>dans lequel le petit objet tranſparent, ou les animaux qui nagent <lb/>dans la goute de liqueur, paroiſſent très-grands & </s> <s xml:id="echoid-s3831" xml:space="preserve">très-diſtincte-<lb/>ment; </s> <s xml:id="echoid-s3832" xml:space="preserve">alors vous remarquerez des choſes très-ſingulieres par la <lb/>diverſité de tant d'animaux de differentes figures.</s> <s xml:id="echoid-s3833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3834" xml:space="preserve">Il faut avoir bien ſoin d'eſſuïer la petite boule ou lentille de ver-<lb/>re, afin qu'elle ſoit toûjours bien claire.</s> <s xml:id="echoid-s3835" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div337" type="section" level="1" n="152"> <head xml:id="echoid-head228" style="it" xml:space="preserve">Conſtruction d'un autre Microſcope à liqueur, & autres <lb/>petis objets.</head> <p> <s xml:id="echoid-s3836" xml:space="preserve">JE fais des Microſcopes à liqueur de differentes façons: </s> <s xml:id="echoid-s3837" xml:space="preserve">celui <lb/>marqué K, me paroît le plus commode, il eſt compoſé d'une <lb/>plaque de cuivre d'environ 3 pouces de hauteur, ſur un demi de <lb/>largeur, taillée en maniere de parallelogramme, au bout de la-<lb/>quelle eſt un manche pour le tenir: </s> <s xml:id="echoid-s3838" xml:space="preserve">l'endroit marqué 1, eſt une <lb/> <anchor type="note" xlink:label="note-129-01a" xlink:href="note-129-01"/> petite couliſſe percée au milieu, au trou de laquelle on place une <lb/>lentille enfermée dans un petit chaſſis; </s> <s xml:id="echoid-s3839" xml:space="preserve">on peut en mettre de diffe-<lb/>rens foyers ſuivant les differens objets qu'on veut obſerver. </s> <s xml:id="echoid-s3840" xml:space="preserve">Il eſt <lb/>bon de ſçavoir que le foyer d'un verre eſt ſa diſtance juſqu'à l'ob-<lb/>jet, & </s> <s xml:id="echoid-s3841" xml:space="preserve">que les lentilles dont on ſe ſert à ces ſortes de Microſcopes, <lb/>ſont depuis demi-ligne juſqu'à quatre lignes de foyer.</s> <s xml:id="echoid-s3842" xml:space="preserve"/> </p> <div xml:id="echoid-div337" type="float" level="2" n="1"> <note position="right" xlink:label="note-129-01" xlink:href="note-129-01a" xml:space="preserve">Fig. K.</note> </div> <p> <s xml:id="echoid-s3843" xml:space="preserve">Au derriere de ladite plaque, à l'endroit marqué 2, eſt attachée <lb/>une petite branche de cuivre ou d'acier quarrée, portant une au-<lb/>tre plaque qui coule aulong de ladite branche par le moyen d'une <lb/> <pb o="116" file="130" n="130" rhead="CONSTRUCTION ET USAGES"/> petite boëte, d'un reſſort & </s> <s xml:id="echoid-s3844" xml:space="preserve">d'une vis qu'on fait tourner par le moyen <lb/>d'une rouë à dents, & </s> <s xml:id="echoid-s3845" xml:space="preserve">qui ſert à éloigner ou approcher parallele-<lb/>ment comme on veut, ladite plaque, de celle qui porte la lentille. <lb/></s> <s xml:id="echoid-s3846" xml:space="preserve">Vers le haut de la ſeconde plaque, qui eſt percée d'un trou aſſez <lb/>grand, eſt auſſi une couliſſe où l'on place de petits verres plats ſur <lb/>leſquels on a fait de petits ronds concaves pour y mettre les li-<lb/>queurs de maniere qu'elles ne ſoient point emportées par la pro-<lb/>ximité de l'autre plaque. </s> <s xml:id="echoid-s3847" xml:space="preserve">On peut ajuſter dàns cette couliſſe diffe-<lb/>rentes pieces pour differens objets. </s> <s xml:id="echoid-s3848" xml:space="preserve">Il faut obſerver ſeulement, que <lb/>tous ces objets répondent au centre de la lentille; </s> <s xml:id="echoid-s3849" xml:space="preserve">de l'autre côté <lb/>de ladite plaque eſt ajuſté un petit tuïau marqué 3, de cuivre, <lb/>de bois ou de chagrin d'environ un pouce de diametre, & </s> <s xml:id="echoid-s3850" xml:space="preserve">d'un ou <lb/>deux de longueur, percé par les deux extremitez; </s> <s xml:id="echoid-s3851" xml:space="preserve">mais dont le <lb/>centre réponde auſſi très-juſte au centre des lentilles: </s> <s xml:id="echoid-s3852" xml:space="preserve">on a remar-<lb/>qué qu'avec un pareil tuiau, ces Microſcopes avoient bien plus <lb/>d'effet dans les objets tranſparens, & </s> <s xml:id="echoid-s3853" xml:space="preserve">on y remarque aſſez diſtincte-<lb/>ment la circulation du ſang dans la queuë des plus petits poiſſons.</s> <s xml:id="echoid-s3854" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3855" xml:space="preserve">L'uſage de cet Inſtrument eſt très-facile: </s> <s xml:id="echoid-s3856" xml:space="preserve">ayant placé l'objet vis-<lb/>à-vis le centre de la lentille, il n'y a qu'à mettre l'œil vis-à-vis la-<lb/>dite lentille au grand jour, ou vis-a-vis la lumiere d'une bougie, <lb/>& </s> <s xml:id="echoid-s3857" xml:space="preserve">approcher ou reculer l'objet par le moyen de la vis, juſqu'à ce <lb/>qu'on voye l'objet diſtinctement; </s> <s xml:id="echoid-s3858" xml:space="preserve">alors on y remarquera des choſes <lb/>très-ſingulieres, & </s> <s xml:id="echoid-s3859" xml:space="preserve">qui feront plaiſir.</s> <s xml:id="echoid-s3860" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div339" type="section" level="1" n="153"> <head xml:id="echoid-head229" style="it" xml:space="preserve">Conſtruction d'un Microſcope à un verre.</head> <p> <s xml:id="echoid-s3861" xml:space="preserve">LE petit Inſtrument marqué L eſt un Microſcope aſſez commo-<lb/>de. </s> <s xml:id="echoid-s3862" xml:space="preserve">Il eſt compoſé d'une branche de laiton, ou autre métal, qui <lb/>a un mouvement vers le haut pour la mettre dans la ſituation que <lb/>la figurele montre. </s> <s xml:id="echoid-s3863" xml:space="preserve">Il y a au bout une piece marquée 1, qui porte <lb/> <anchor type="note" xlink:label="note-130-01a" xlink:href="note-130-01"/> une petite lentille de verre fort convexe qui groſſit beaucoup l'ob-<lb/>jet. </s> <s xml:id="echoid-s3864" xml:space="preserve">Elie ſe monte à vis dans une petite boëte percée au fond. </s> <s xml:id="echoid-s3865" xml:space="preserve">La <lb/>piece marquée 4, ſont deux reſlorts attachez enſemble par le milieu <lb/>avec un clou rond pour leur donner le mouvement qu'on ſouhai-<lb/>te. </s> <s xml:id="echoid-s3866" xml:space="preserve">Dans un des reſſorts on enſile la branche qui porte la lentille, <lb/>& </s> <s xml:id="echoid-s3867" xml:space="preserve">dans l'autre on enfile une petite branche qui porte par un de ſes <lb/>bouts une piece marquée 2, qui eſt blanche d'un côté & </s> <s xml:id="echoid-s3868" xml:space="preserve">noire de <lb/>l'autre, pour mettre les differens objets. </s> <s xml:id="echoid-s3869" xml:space="preserve">L'autre bout marqué 3, <lb/>eſt une petite pince qui s'ouvre en preſſant les deux petits boutons. <lb/></s> <s xml:id="echoid-s3870" xml:space="preserve">Elle ſert à tenir les petits animaux & </s> <s xml:id="echoid-s3871" xml:space="preserve">autres objets. </s> <s xml:id="echoid-s3872" xml:space="preserve">Le pied mar-<lb/>qué 5, a environ un pouce & </s> <s xml:id="echoid-s3873" xml:space="preserve">demi de diametre. </s> <s xml:id="echoid-s3874" xml:space="preserve">La branche s'y <lb/> <pb o="117" file="131" n="131" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> met à vis, afin de démonter l'inſtrument, pour qu'il ne tienne gué-<lb/>res de place.</s> <s xml:id="echoid-s3875" xml:space="preserve"/> </p> <div xml:id="echoid-div339" type="float" level="2" n="1"> <note position="right" xlink:label="note-130-01" xlink:href="note-130-01a" xml:space="preserve">Fig. L.</note> </div> <p> <s xml:id="echoid-s3876" xml:space="preserve">L'uſage en eſt fort facile. </s> <s xml:id="echoid-s3877" xml:space="preserve">On place les objets ſur la petite piece <lb/>ronde, ou au bout de la petite pince, & </s> <s xml:id="echoid-s3878" xml:space="preserve">on les approche de la len-<lb/>tille en faiſant couler le reſlort au long de la branche, juſqu'à ce <lb/>que l'on voye l'objet très-diſtinctement. </s> <s xml:id="echoid-s3879" xml:space="preserve">Alors on y remarquera <lb/>des choſes qui ſeront plaiſir.</s> <s xml:id="echoid-s3880" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3881" xml:space="preserve">On voit auſſi avec ce Microſcope, les animaux qui ſont dans les <lb/>liqueurs, en mettant un verre plat à la place de la petite piece <lb/>ronde marquée 2, qui ſe démonte à vis.</s> <s xml:id="echoid-s3882" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div341" type="section" level="1" n="154"> <head xml:id="echoid-head230" style="it" xml:space="preserve">Conſtruction d'un Microſcope à trois verres.</head> <p> <s xml:id="echoid-s3883" xml:space="preserve">CEt Inſtrument eſt compoſé de trois verres; </s> <s xml:id="echoid-s3884" xml:space="preserve">ſçavoir, le verre <lb/>oculaire marqué 3, le verre du milieu 4, & </s> <s xml:id="echoid-s3885" xml:space="preserve">la lentille ou verre <lb/>objectif marqué 5. </s> <s xml:id="echoid-s3886" xml:space="preserve">Il y a un couvercle pardeſſus pour garantir de <lb/> <anchor type="note" xlink:label="note-131-01a" xlink:href="note-131-01"/> la pouſſiere le verre oculaire. </s> <s xml:id="echoid-s3887" xml:space="preserve">Ces trois verres ſont enchaſſez dans <lb/>des cercles de bois & </s> <s xml:id="echoid-s3888" xml:space="preserve">à vis pour les maintenir en leur place & </s> <s xml:id="echoid-s3889" xml:space="preserve">pour <lb/>les démonter facilement, afin de les nétoyer ſans peine.</s> <s xml:id="echoid-s3890" xml:space="preserve"/> </p> <div xml:id="echoid-div341" type="float" level="2" n="1"> <note position="right" xlink:label="note-131-01" xlink:href="note-131-01a" xml:space="preserve">Fig. M.</note> </div> <p> <s xml:id="echoid-s3891" xml:space="preserve">L'oculaire & </s> <s xml:id="echoid-s3892" xml:space="preserve">le verre du milieu ſont ajuſtez aux extremitez d'un <lb/>tuïau de velin qui entre juſte dans le tuiau extérieur, afin d'al-<lb/>longer le Microſcope & </s> <s xml:id="echoid-s3893" xml:space="preserve">le mettre à ſon juſte point, ſuivant une <lb/>ligne qui eſt tracée autour dudit tuïau. </s> <s xml:id="echoid-s3894" xml:space="preserve">Pour que cet inſtrument <lb/>ſoit d'une grandeur raiſonnable, il faut que le verre oculaire ſoit <lb/>d'environ vingt lignes de foyer, & </s> <s xml:id="echoid-s3895" xml:space="preserve">le verre du milieu d'environ <lb/>trois pouces de foyer, & </s> <s xml:id="echoid-s3896" xml:space="preserve">placez à environ trois pouces trois lignes <lb/>l'un de l'autre.</s> <s xml:id="echoid-s3897" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3898" xml:space="preserve">La lentille eſt placée au bout d'un cul-de-lampe de bois qui eſt <lb/>collé à l'extremité du tuïau extérieur. </s> <s xml:id="echoid-s3899" xml:space="preserve">Ladite lentille eſt enfermée <lb/>dans une petite boëte percée au fond, & </s> <s xml:id="echoid-s3900" xml:space="preserve">qui ſe démonte à vis, a-<lb/>fin de changer de lentille, & </s> <s xml:id="echoid-s3901" xml:space="preserve">en mettre de different foyer. </s> <s xml:id="echoid-s3902" xml:space="preserve">Il y en <lb/>a ordinairement de 2, 3, 4 & </s> <s xml:id="echoid-s3903" xml:space="preserve">5 lignes de foyer, & </s> <s xml:id="echoid-s3904" xml:space="preserve">qui ſont plus <lb/>ou moins convexes. </s> <s xml:id="echoid-s3905" xml:space="preserve">La bonté de ces verres dépend d'avoir des baſ-<lb/>ſins de cuivre concaves tournez d'une juſte proportion aux verres <lb/>qu'on veut travailler; </s> <s xml:id="echoid-s3906" xml:space="preserve">comme auſſi du mouvement de la main, de <lb/>la bonté de la matiere que vous employez pour les conſtruire, & </s> <s xml:id="echoid-s3907" xml:space="preserve"><lb/>ſur tout de les bien polir: </s> <s xml:id="echoid-s3908" xml:space="preserve">on ſe ſert d'abord de grais pour les dé-<lb/>groſſir dans les baſſins, enſuite de ſable fin pour les adoucir, & </s> <s xml:id="echoid-s3909" xml:space="preserve">puis <lb/>de tripoli bien doux pour les polir. </s> <s xml:id="echoid-s3910" xml:space="preserve">Je ne m'arrêterai pas davantage <lb/>à la conſtruction de ces verres, le P. </s> <s xml:id="echoid-s3911" xml:space="preserve">Cherubin en ayant ſuffiſam-<lb/>ment parlé.</s> <s xml:id="echoid-s3912" xml:space="preserve"/> </p> <pb o="118" file="132" n="132" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s3913" xml:space="preserve">Le pied marqué 1 qui doit être un peu peſant à cauſe qu'il porte <lb/>le Microſcope en l'air, eſt fait de cuivre de 4 à 5 pouces de diame-<lb/>tre. </s> <s xml:id="echoid-s3914" xml:space="preserve">Il y a au milieu un creux, dans lequel on met une petite piece <lb/>qui eſt blanche d'un côté & </s> <s xml:id="echoid-s3915" xml:space="preserve">noire de l'autre, on met les objets noirs <lb/>ſur le côté blanc, & </s> <s xml:id="echoid-s3916" xml:space="preserve">les blancs ſur le côte noir.</s> <s xml:id="echoid-s3917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3918" xml:space="preserve">La branche eſt attachée au bord du pied, elle eſt de cuivre rond, <lb/>au long de laquelle le Microſcope ſe peut hauſſer, baiſſer & </s> <s xml:id="echoid-s3919" xml:space="preserve">tour-<lb/>ner par le moyen du ſupport fait en double équerre marqué 2. </s> <s xml:id="echoid-s3920" xml:space="preserve">Il <lb/>y a un cercle qui eſt fortement attaché à la double équerre, & </s> <s xml:id="echoid-s3921" xml:space="preserve">qui <lb/>embraſſe bien juſte le tuïau exterieur. </s> <s xml:id="echoid-s3922" xml:space="preserve">Il ya auſſi un reſſort d'acier <lb/>qui appuie contre la branche, & </s> <s xml:id="echoid-s3923" xml:space="preserve">fait tenir l'inſtrument à la hau-<lb/>teur & </s> <s xml:id="echoid-s3924" xml:space="preserve">dans la ſituaton qu'on a beſoin.</s> <s xml:id="echoid-s3925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3926" xml:space="preserve">La piece marquée 6, eſt un petit chaſſis de cuivre qui porte un <lb/>morceau de glace ou de verre blanc pour mettre deſſus les objets <lb/>tranſparens. </s> <s xml:id="echoid-s3927" xml:space="preserve">Il coule auſſi au long de la branche au-deſſous du Mi-<lb/>croſcope, & </s> <s xml:id="echoid-s3928" xml:space="preserve">eſt porté de même par une double équerre.</s> <s xml:id="echoid-s3929" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3930" xml:space="preserve">Enſin la piece marquée 7, eſt un verre convexe qui raſſemble <lb/>dans un petit eſpace les raïons de lumiere qu'il reçoit la nuit d'une <lb/>bougie allumée, & </s> <s xml:id="echoid-s3931" xml:space="preserve">qui la refléchit vivement ſous l'objet tranſpa-<lb/>rent qui eſt ſur la glace, & </s> <s xml:id="echoid-s3932" xml:space="preserve">le fait voir bien plus diſtinctement. </s> <s xml:id="echoid-s3933" xml:space="preserve">Ce <lb/>verre eſt enchaſſé dans un cercle de cuivre, & </s> <s xml:id="echoid-s3934" xml:space="preserve">hauſſe, baiſſe, allon-<lb/>ge & </s> <s xml:id="echoid-s3935" xml:space="preserve">racourcit par le moyen d'un petit bras qui le porte, comme la <lb/>figure le montre.</s> <s xml:id="echoid-s3936" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div343" type="section" level="1" n="155"> <head xml:id="echoid-head231" style="it" xml:space="preserve">Vſage de ce Microſcope.</head> <p> <s xml:id="echoid-s3937" xml:space="preserve">POur s'en ſervir, par exemple, à voir la circulation du ſang de <lb/>quelque animal, on met un très petit poiſſon vivant ſur la gla-<lb/>ce en telle maniere qu'une partie des nageoires de la queuë ſoit juſ-<lb/>te vis-à-vis du verre objectif & </s> <s xml:id="echoid-s3938" xml:space="preserve">au-deſſus du raïon du vorre con-<lb/>vexe au grand jour, ou à la lumiere de la bougie la nuit; </s> <s xml:id="echoid-s3939" xml:space="preserve">alors pla-<lb/>çant le Microſcope juſte à ſon point, vous verrez le ſang monter, <lb/>deſcendre ou circuler.</s> <s xml:id="echoid-s3940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3941" xml:space="preserve">La petite piece marquée 9, eſt un petit canal de plomb qu'il faut <lb/>mettre ſur le poiſſon, pour l'empêcher de ſauter hors de ſa place & </s> <s xml:id="echoid-s3942" xml:space="preserve"><lb/>de retirer ſa queuë du petit eſpace éclairé.</s> <s xml:id="echoid-s3943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3944" xml:space="preserve">Parce Microſcope on peut auſſi fort bien examiner les liqueurs; <lb/></s> <s xml:id="echoid-s3945" xml:space="preserve">car fi vous mettez une petite goute de vinaigre ſur le verre juſte-<lb/>ment dans le milieu de l'eſpace éclairé, vous verrez très-diſtnc-<lb/>tement les petits animaux qui y ſont. </s> <s xml:id="echoid-s3946" xml:space="preserve">Il en ſera de même de l'eau <lb/>où l'on aura fait infuſer du poivre, de l'orge, &</s> <s xml:id="echoid-s3947" xml:space="preserve">c. </s> <s xml:id="echoid-s3948" xml:space="preserve">comme auſſi <lb/> <pb o="119" file="133" n="133" rhead="DE DIFFERENS INSTRUMENS. Liv. III. Ch. II."/> les vers & </s> <s xml:id="echoid-s3949" xml:space="preserve">les autres petits inſectes qui ſont dans l'eau croupie.</s> <s xml:id="echoid-s3950" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3951" xml:space="preserve">Le ſang dont on veut obſerver ce qu'il contient de viſible, ſe <lb/>peut connoître en y en mettant une très-petite quantité & </s> <s xml:id="echoid-s3952" xml:space="preserve">tout <lb/>chaud vis-à vis le raïon de lumiere. </s> <s xml:id="echoid-s3953" xml:space="preserve">Alors on y remarquera très-<lb/>bien la ſeroſitê & </s> <s xml:id="echoid-s3954" xml:space="preserve">les petites boules qui paroiſſent d'une couleur <lb/>rougeâtre.</s> <s xml:id="echoid-s3955" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3956" xml:space="preserve">Il ſera facile d'avoir du ſang ſur le champ. </s> <s xml:id="echoid-s3957" xml:space="preserve">En ſe ſerrant le pouce <lb/>avec un cordon, & </s> <s xml:id="echoid-s3958" xml:space="preserve">ſe piquant avec une épingle, on en aura ſuffi-<lb/>ſamment.</s> <s xml:id="echoid-s3959" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3960" xml:space="preserve">Les liqueurs ſe mettent ſur la glace avec un petit bout de tuïau <lb/>de verre que l'on trempe dans la liqueur, & </s> <s xml:id="echoid-s3961" xml:space="preserve">on la fait deſcendre ſur <lb/>la glace, ſoit en ſoufflant doucement dans le tuïau, ou en preſſant <lb/>du pouce par le haut: </s> <s xml:id="echoid-s3962" xml:space="preserve">car l'air preſſé dans le tuïau, preſſe de mê-<lb/>me la liqueur, qui eſt contrainte d'en ſortir.</s> <s xml:id="echoid-s3963" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3964" xml:space="preserve">Pour retirer beaucoup d'anguilles dans une petite quantité de li-<lb/>queur, il faut mettre cette liqueur dans une petite bouteille fort <lb/>étroite par en haut & </s> <s xml:id="echoid-s3965" xml:space="preserve">l'entretenir toûjous pleine; </s> <s xml:id="echoid-s3966" xml:space="preserve">par ce moyen <lb/>les animaux qui montent en haut pour y reſpirer, ſeront pompez <lb/>avec le petit tuïau en plus grande quantité que ſi le vaiſſeau qui les <lb/>contient étoit plus large en haut.</s> <s xml:id="echoid-s3967" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3968" xml:space="preserve">Les yeux de mouche, les fourmis, les poux, les puces & </s> <s xml:id="echoid-s3969" xml:space="preserve">les mi-<lb/>tes de fromages ſe mettent au milieu du pied du Microſcope, auſli-<lb/>bien que le ſable, les ſels & </s> <s xml:id="echoid-s3970" xml:space="preserve">toute autre poudre, pour examiner <lb/>leurs couleurs & </s> <s xml:id="echoid-s3971" xml:space="preserve">leurs qualitez, en obſervant toûjours de mettre ſur <lb/>le côté blanc les objets noirs, & </s> <s xml:id="echoid-s3972" xml:space="preserve">ſur le côté noir les objets blancs.</s> <s xml:id="echoid-s3973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3974" xml:space="preserve">L'on ſuppoſe ici que les verres de ce Microſcope ſoient bien tra-<lb/>vaillez & </s> <s xml:id="echoid-s3975" xml:space="preserve">bien placez en leurs foyers. </s> <s xml:id="echoid-s3976" xml:space="preserve">Il eſt bon auſſi de ſçavoir que <lb/>l'image de l'objet & </s> <s xml:id="echoid-s3977" xml:space="preserve">ſa grandeur ſeront d'autant plus conſidera-<lb/>bles, que la lentille ſera d'un plus court foyer; </s> <s xml:id="echoid-s3978" xml:space="preserve">mais il ne ſera pas <lb/>tout-à-fait ſi net.</s> <s xml:id="echoid-s3979" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div344" type="section" level="1" n="156"> <head xml:id="echoid-head232" style="it" xml:space="preserve">Fin du troiſiéme Livre.</head> <pb file="134" n="134"/> </div> <div xml:id="echoid-div345" type="section" level="1" n="157"> <head xml:id="echoid-head233" xml:space="preserve">DE LA <lb/>CONSTRUCTION <lb/>ET DES USAGES <lb/>DES INSTRUMENS <lb/>DE MATHEMATIQUE</head> <p> <s xml:id="echoid-s3980" xml:space="preserve">Qui ſervent à travailler à la Campagne, pour arpenter <lb/>les Terres, lever les Plans, meſurer les diſtances & </s> <s xml:id="echoid-s3981" xml:space="preserve"><lb/>prendre les hauteurs. </s> <s xml:id="echoid-s3982" xml:space="preserve">Les plus uſitez ſont les Piquets, <lb/>les Cordeaux, la Toiſe, la Chaîne, les Equerres <lb/>d'Arpenteur, les Recipiangles ou Meſurangles, les <lb/>Planchettes, le quart de Cercle, le demi Cercle & </s> <s xml:id="echoid-s3983" xml:space="preserve"><lb/>la Bouſſole.</s> <s xml:id="echoid-s3984" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div346" type="section" level="1" n="158"> <head xml:id="echoid-head234" style="it" xml:space="preserve">LIVRE LU AT RIÉ ME.</head> <head xml:id="echoid-head235" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head236" style="it" xml:space="preserve">Contenant la Deſcription & les Vſages des Piquets, des <lb/>Cordeaux, de la Toiſe & de la Chaîne.</head> <p> <s xml:id="echoid-s3985" xml:space="preserve">LEs Piquets ſont de petits morceaux de bois de Cor-<lb/> <anchor type="note" xlink:label="note-134-01a" xlink:href="note-134-01"/> mier de deux à trois pieds de long, arrondis & </s> <s xml:id="echoid-s3986" xml:space="preserve">poin-<lb/>tus par un bout, que l'on garnit de fer, pour être <lb/>plus facilement enfoncez en terre. </s> <s xml:id="echoid-s3987" xml:space="preserve">On en fait quel-<lb/>ques-uns de plus longs, afin d'être vûs de loin, <lb/>comme on les voit repreſentez dans la Planche onziéme.</s> <s xml:id="echoid-s3988" xml:space="preserve"/> </p> <div xml:id="echoid-div346" type="float" level="2" n="1"> <note position="left" xlink:label="note-134-01" xlink:href="note-134-01a" xml:space="preserve">X1. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s3989" xml:space="preserve">Les Cordeaux doivent être de bonne ficelle bien torſe & </s> <s xml:id="echoid-s3990" xml:space="preserve">d'une <lb/>groſſeur convenable, pour ne pas s'allonger facilement, telle que <lb/>la figure B le marque.</s> <s xml:id="echoid-s3991" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s3992" xml:space="preserve">La Toiſe eſt une meſure de ſix pieds de long d'un bâton rond <lb/> <anchor type="note" xlink:label="note-134-02a" xlink:href="note-134-02"/> tout d'une piece, diviſé en ſes pieds marquez par de petits anneaux <lb/> <pb o="121" file="135" n="135" rhead="CONST. ET US. DESINST. POUR LEV.&c.L.IV.C.I."/> ou de petits clous de cuivre. </s> <s xml:id="echoid-s3993" xml:space="preserve">Le dernier pied ſe diviſe en 12 pouces, <lb/>qui ſe diſtînguent auſſi par de petits clous.</s> <s xml:id="echoid-s3994" xml:space="preserve"/> </p> <div xml:id="echoid-div347" type="float" level="2" n="2"> <note position="left" xlink:label="note-134-02" xlink:href="note-134-02a" xml:space="preserve">Fig. C.</note> </div> <p> <s xml:id="echoid-s3995" xml:space="preserve">Il y en a qui ſont briſées & </s> <s xml:id="echoid-s3996" xml:space="preserve">qui ſe montent à vis en 2, 3, ou 4 <lb/> <anchor type="note" xlink:label="note-135-01a" xlink:href="note-135-01"/> pieces par le moyen des viroles & </s> <s xml:id="echoid-s3997" xml:space="preserve">des vis de cuivre qui ſont atta-<lb/>chées à chaque bout: </s> <s xml:id="echoid-s3998" xml:space="preserve">& </s> <s xml:id="echoid-s3999" xml:space="preserve">on met auſſi aux deux bouts des Toiſes <lb/>une virole de cuivre ou d'acier pour la conſerver dans ſa longueur.</s> <s xml:id="echoid-s4000" xml:space="preserve"/> </p> <div xml:id="echoid-div348" type="float" level="2" n="3"> <note position="right" xlink:label="note-135-01" xlink:href="note-135-01a" xml:space="preserve">Fig. D.</note> </div> <p> <s xml:id="echoid-s4001" xml:space="preserve">La Chaine eſt compoſée de pluſieurs pieces de gros fil de fer ou <lb/> <anchor type="note" xlink:label="note-135-02a" xlink:href="note-135-02"/> de laiton recourbées par les 2 bouts. </s> <s xml:id="echoid-s4002" xml:space="preserve">Chacune de ces pieces a 1 pied <lb/>de long, y compris les petits anneaux qui les joignent enſemble.</s> <s xml:id="echoid-s4003" xml:space="preserve"/> </p> <div xml:id="echoid-div349" type="float" level="2" n="4"> <note position="right" xlink:label="note-135-02" xlink:href="note-135-02a" xml:space="preserve">Fig. E.</note> </div> <p> <s xml:id="echoid-s4004" xml:space="preserve">Les Chaînes ſe font ordinairement de la longueur de la Perche <lb/>du lieu où l'on veut s'en ſervir, ou bien de quatre à cinq toiſes de <lb/>long diſtinguées par un plus grand anneau de toiſe en toiſe. </s> <s xml:id="echoid-s4005" xml:space="preserve">Ces <lb/>ſortes de chaînes ſont fort commodes, en ce qu'elles ne ſe noüent <lb/>point comme celles qui ſont faites de petites mailles de fer.</s> <s xml:id="echoid-s4006" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4007" xml:space="preserve">En 1668 on a placé un nouvel Etalon de la toiſe fort juſte, au <lb/>bas de l'Eſcalier du Grand-Châtelet de Paris, pour y avoir recours <lb/>en cas de beſoin.</s> <s xml:id="echoid-s4008" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4009" xml:space="preserve">Nous avons dit que la toiſe en longueur contient ſix pieds, & </s> <s xml:id="echoid-s4010" xml:space="preserve"><lb/>chaque pied, douze pouces.</s> <s xml:id="echoid-s4011" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4012" xml:space="preserve">La toiſe quarrée contient 36 pieds quarrez, & </s> <s xml:id="echoid-s4013" xml:space="preserve">chaque pied 144 <lb/>pouces, parce qu'on multiplie 6 par 6.</s> <s xml:id="echoid-s4014" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4015" xml:space="preserve">La toiſe cube contient 216 pieds cubes, & </s> <s xml:id="echoid-s4016" xml:space="preserve">chaque pied 1721 <lb/>pouces cubes, parce qu'on multiplïe 36 par 9.</s> <s xml:id="echoid-s4017" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4018" xml:space="preserve">La Perche n'a point de longueur determinée.</s> <s xml:id="echoid-s4019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4020" xml:space="preserve">Celle de la Prévôté de Paris a trois toiſes ou dix-huit pieds. </s> <s xml:id="echoid-s4021" xml:space="preserve">En <lb/>d'autres Païs elle a vingt, vingt-deux & </s> <s xml:id="echoid-s4022" xml:space="preserve">vingt-quatre pieds.</s> <s xml:id="echoid-s4023" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4024" xml:space="preserve">La Perche dont on ſe ſert en France, pour arpenter les Eaux & </s> <s xml:id="echoid-s4025" xml:space="preserve"><lb/>Forêts, ſuivant les derniers Reglemens, a 22 pieds de longueur, & </s> <s xml:id="echoid-s4026" xml:space="preserve"><lb/>par conſequent la Perche quarrée contient 484 pieds quarrez.</s> <s xml:id="echoid-s4027" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4028" xml:space="preserve">L'Arpent eſt une meſure quarrée dont on ſe ſert pour la vente <lb/>des Terres & </s> <s xml:id="echoid-s4029" xml:space="preserve">de Bois.</s> <s xml:id="echoid-s4030" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4031" xml:space="preserve">L'Arpent des environs de Paris contient 100 Perches quarrées ou <lb/>300 toiſes, & </s> <s xml:id="echoid-s4032" xml:space="preserve">chaque côté eſt par conſequent de 10 Perches ou 30 <lb/>toiſes.</s> <s xml:id="echoid-s4033" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4034" xml:space="preserve">La Lieuë eſt un eſpace de Terre dont on ſe ſert pour meſurer <lb/>les Chemins. </s> <s xml:id="echoid-s4035" xml:space="preserve">Sa meſure n'eſt pas déterminée. </s> <s xml:id="echoid-s4036" xml:space="preserve">étant difſerente ſe-<lb/>lon les diſſerens Païs.</s> <s xml:id="echoid-s4037" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4038" xml:space="preserve">On compte depuisla Porte de Paris près le Grand Châtelet, juſ-<lb/>qu'à la Porte de l'Egliſe S. </s> <s xml:id="echoid-s4039" xml:space="preserve">Denys, deux lieuës, dont chacune eſt <lb/>de deux mille deux cens toiſes.</s> <s xml:id="echoid-s4040" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4041" xml:space="preserve">Meſſieurs de l'Academie des Sciences en travaillant à la meſure <lb/> <pb o="122" file="136" n="136" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> de la terre, ont obſervé qu'un degré d'un meridien terreſtre con-<lb/>tient 57060 toiſes, & </s> <s xml:id="echoid-s4042" xml:space="preserve">donnant 25 lieuës au degré, chaque lieuë <lb/>contiendra 2282 toiſes.</s> <s xml:id="echoid-s4043" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4044" xml:space="preserve">La lieuë Marine eſt un peu plus grande, puiſqu'on n'en compte <lb/>que 20 au degré; </s> <s xml:id="echoid-s4045" xml:space="preserve">c'eſt pourquoi elle contient près de 3000 toiſes.</s> <s xml:id="echoid-s4046" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4047" xml:space="preserve">Les Italiens comptent par mille, dont chacun contient mille pas <lb/>géométriques.</s> <s xml:id="echoid-s4048" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4049" xml:space="preserve">Le pas géométrique eſt de 5 pieds antiques, dont le palme eſt les 3 <lb/>quarts du pied ancien Romain, qu'on peut eſtimer environ 11 de <lb/>nos pouces. </s> <s xml:id="echoid-s4050" xml:space="preserve">Et par conſequent le mille d'Italie à Rome contient <lb/>769 de nos toiſes, à très-peu près.</s> <s xml:id="echoid-s4051" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4052" xml:space="preserve">Les Allemans comptent auſſi par mille, mais ils ſont bien plus <lb/>grands que ceux d'Italie; </s> <s xml:id="echoid-s4053" xml:space="preserve">ils contiennent 3626 toiſes.</s> <s xml:id="echoid-s4054" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4055" xml:space="preserve">On compte par lieuës en Eſpagne, qui contiennent 2863 toiſes, <lb/>& </s> <s xml:id="echoid-s4056" xml:space="preserve">reviennent juſtement à 20 lieuës par degré terreſtre.</s> <s xml:id="echoid-s4057" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4058" xml:space="preserve">Il en eſt de même en Angleterre & </s> <s xml:id="echoid-s4059" xml:space="preserve">en Hollande.</s> <s xml:id="echoid-s4060" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div351" type="section" level="1" n="159"> <head xml:id="echoid-head237" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head238" style="it" xml:space="preserve">Par deux points donnez ſnr la terre, tracer une ligne droite & <lb/>la prolonger tant qu'il eſt beſoin.</head> <p> <s xml:id="echoid-s4061" xml:space="preserve">PLantez un Piquet ſur chaque point donné, & </s> <s xml:id="echoid-s4062" xml:space="preserve">ayant tendu un <lb/>cordeau d'un piquet à l'autre, faites tracer un ſillon le long dud-<lb/>cordeau, faites en ſorte qu'ils ſoient bien à plomb ſur le terrain, & </s> <s xml:id="echoid-s4063" xml:space="preserve"><lb/>qu'en les bornaïant ou les regardant, le premier cache l'autre à l'œil.</s> <s xml:id="echoid-s4064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4065" xml:space="preserve">Ceſt de la même maniere que l'on peut prolonger une ligne droi-<lb/>te ſur la terre; </s> <s xml:id="echoid-s4066" xml:space="preserve">car ayant planté deux Piquets on en peut planter <lb/>tant d'autres qu'on voudra dans le même alignement, en bornaïant <lb/>comme nous venons de dire; </s> <s xml:id="echoid-s4067" xml:space="preserve">mais il faut qu'il y ait toûjours deux <lb/>Piquets bien plantez pour ſervir à aligner le troiſiéme.</s> <s xml:id="echoid-s4068" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div352" type="section" level="1" n="160"> <head xml:id="echoid-head239" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head240" style="it" xml:space="preserve">Meſurer une ligne droite ſur la Terre.</head> <p> <s xml:id="echoid-s4069" xml:space="preserve">LOrſqu'on a une longue ligne à meſurer ſur le terrain, il faut u-<lb/>ſer de précaution pour ne ſe pas tromper & </s> <s xml:id="echoid-s4070" xml:space="preserve">n'être pas obligé de <lb/>recommencer. </s> <s xml:id="echoid-s4071" xml:space="preserve">Pour ce faire, il faut deux hommes portants chacun <lb/>une toiſe; </s> <s xml:id="echoid-s4072" xml:space="preserve">le premier ayant étendu ſa toiſe ſur le terrain ne la doit pas <lb/>lever que le ſecond n'ait poſé la ſienne au bout de la premiere. </s> <s xml:id="echoid-s4073" xml:space="preserve">Le <lb/>premier homme ayant rélevé ſa toiſe, comptera tout haut, une; </s> <s xml:id="echoid-s4074" xml:space="preserve">& </s> <s xml:id="echoid-s4075" xml:space="preserve"><lb/>quand il l'aura remiſe au bout de la ſeconde, le ſecond homme rele-<lb/>vera la ſienne & </s> <s xml:id="echoid-s4076" xml:space="preserve">comptera 2, en continuant ainſi de ſuite juſqu'au <lb/>bout, & </s> <s xml:id="echoid-s4077" xml:space="preserve">afin de bien poſer les toiſes en ligne droite, il faut toûjours <lb/> <pb o="123" file="137" n="137" rhead="POUR LEVER LES PLANS. Liv. IV. Chap. I."/> avoir devant les yeux 2 piquets pour les bornayer, car s'il n'y en avoit <lb/>qu'un, les Toiſeurs iroient tout de travers & </s> <s xml:id="echoid-s4078" xml:space="preserve">ne feroient rien de juſte.</s> <s xml:id="echoid-s4079" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4080" xml:space="preserve">Pour abreger le tems & </s> <s xml:id="echoid-s4081" xml:space="preserve">la peine, on doit avoir une chaîne, laquel-<lb/>le eſt ſouvent compoſée de 30 pieds ou 5 toiſes, avec un anneau à <lb/>chaque bout. </s> <s xml:id="echoid-s4082" xml:space="preserve">Celui des deux hommes qui va devant, porte auſſi plu-<lb/>ſieurs piquets. </s> <s xml:id="echoid-s4083" xml:space="preserve">Lorſque la chaîne eſt bien étenduë en ligne droite, <lb/>bien allignée & </s> <s xml:id="echoid-s4084" xml:space="preserve">de niveau, il poſe un piquet au bout des 5 toiſes, a-<lb/>fin que celui qui va derriere puiſſe connoître où la chaíne a fini; </s> <s xml:id="echoid-s4085" xml:space="preserve">car <lb/>toute l'adreffe conſiſte à bien compter & </s> <s xml:id="echoid-s4086" xml:space="preserve">meſurer juſte.</s> <s xml:id="echoid-s4087" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div353" type="section" level="1" n="161"> <head xml:id="echoid-head241" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head242" style="it" xml:space="preserve">Sur une ligne droite, & d'un point donné en icelle, élever <lb/>une perpendiculaire.</head> <p> <s xml:id="echoid-s4088" xml:space="preserve">SOit la ligne donnée AB, & </s> <s xml:id="echoid-s4089" xml:space="preserve">le point donné C.</s> <s xml:id="echoid-s4090" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4091" xml:space="preserve">Plantez un piquet au point C, & </s> <s xml:id="echoid-s4092" xml:space="preserve">deux autres comme E, D, ſur <lb/> <anchor type="note" xlink:label="note-137-01a" xlink:href="note-137-01"/> la même ligne en diſtance égale dudit point C; </s> <s xml:id="echoid-s4093" xml:space="preserve">ayez un cordeau <lb/>dont chaque bout ſoit noüé de telle maniere qu'il y ait un petit an-<lb/>neau où l'on puiſſe faire entrer le haut des piquets; </s> <s xml:id="echoid-s4094" xml:space="preserve">pliez ce cordeau <lb/>en deux également, & </s> <s xml:id="echoid-s4095" xml:space="preserve">faites une marque au milieu; </s> <s xml:id="echoid-s4096" xml:space="preserve">paſſez enfin <lb/>les anneaux qui ſont à chaque bout du cordeau autour des piquets <lb/>E & </s> <s xml:id="echoid-s4097" xml:space="preserve">D, & </s> <s xml:id="echoid-s4098" xml:space="preserve">tenant en main le milieu dudit cordeau tendu également, <lb/>plantez en terre un piquet comme F, la ligne FC, ſera perpendi-<lb/>culaire fur A B.</s> <s xml:id="echoid-s4099" xml:space="preserve"/> </p> <div xml:id="echoid-div353" type="float" level="2" n="1"> <note position="right" xlink:label="note-137-01" xlink:href="note-137-01a" xml:space="preserve">Xi. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s4100" xml:space="preserve">Autrement: </s> <s xml:id="echoid-s4101" xml:space="preserve">du point donné C, meſurez ſur la ligne AB, de quel <lb/> <anchor type="note" xlink:label="note-137-02a" xlink:href="note-137-02"/> côté vous voudrez 4 pieds ou 4 toiſes, & </s> <s xml:id="echoid-s4102" xml:space="preserve">plantez-y le piquet G. <lb/></s> <s xml:id="echoid-s4103" xml:space="preserve">Ayez un cordeau qui contienne 8 pareilles meſures, c'eſt-à-dire, des <lb/>pieds ou des toiſes. </s> <s xml:id="echoid-s4104" xml:space="preserve">Mettez un des anneaux du cordeau autour du <lb/>piquet C, & </s> <s xml:id="echoid-s4105" xml:space="preserve">l'autre anneau autour du piquet G; </s> <s xml:id="echoid-s4106" xml:space="preserve">puis ayant tendu <lb/>ce cordeau en ſorte que 3 de ces parties ſoient du côté du point C, & </s> <s xml:id="echoid-s4107" xml:space="preserve"><lb/>les 5 autres du côté de G, plantez le piquet H, la ligne CH, ſera <lb/>perpendiculaire ſur AB.</s> <s xml:id="echoid-s4108" xml:space="preserve"/> </p> <div xml:id="echoid-div354" type="float" level="2" n="2"> <note position="right" xlink:label="note-137-02" xlink:href="note-137-02a" xml:space="preserve">Fig. 2.</note> </div> </div> <div xml:id="echoid-div356" type="section" level="1" n="162"> <head xml:id="echoid-head243" xml:space="preserve">USAGE IV.</head> <head xml:id="echoid-head244" style="it" xml:space="preserve">D'un point donné bors la ligne tirer une perpendiculaire.</head> <p> <s xml:id="echoid-s4109" xml:space="preserve">SOit la ligne donnée AB & </s> <s xml:id="echoid-s4110" xml:space="preserve">le point F donné hors la ligne. <lb/></s> <s xml:id="echoid-s4111" xml:space="preserve">Pliez le cordeau en deux parties égalez, arrêtez le milieu au <lb/> <anchor type="note" xlink:label="note-137-03a" xlink:href="note-137-03"/> piquet F; </s> <s xml:id="echoid-s4112" xml:space="preserve">étendez les deux moitiez que je ſuppoſe aſſez grandes <lb/>pour que les bouts puiſſent atteindre la ligne AB; </s> <s xml:id="echoid-s4113" xml:space="preserve">plantez deux pi-<lb/>quets, ſçavoir, un à chaque bout du cordeau, & </s> <s xml:id="echoid-s4114" xml:space="preserve">diviſez leur diſ-<lb/>tance en 2 également, ce qui ſe peut faire par le moyen d'un cordeau <lb/> <pb o="124" file="138" n="138" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> auſſi long que la diſtance AB, que l'on pliera en deux, plantez le <lb/>piquet C, au milieu, & </s> <s xml:id="echoid-s4115" xml:space="preserve">la ligne CF, ſera perpendiculaire ſur AB.</s> <s xml:id="echoid-s4116" xml:space="preserve"/> </p> <div xml:id="echoid-div356" type="float" level="2" n="1"> <note position="right" xlink:label="note-137-03" xlink:href="note-137-03a" xml:space="preserve">Fig. 3.</note> </div> </div> <div xml:id="echoid-div358" type="section" level="1" n="163"> <head xml:id="echoid-head245" xml:space="preserve">USAGE V.</head> <head xml:id="echoid-head246" style="it" xml:space="preserve">D'une diſtance donnée tracer une ligne parallele à une donnée.</head> <p> <s xml:id="echoid-s4117" xml:space="preserve"> <lb/> <anchor type="note" xlink:label="note-138-01a" xlink:href="note-138-01"/> SOit la ligne donnée AB, à laquelle on propoſe de tracer une <lb/>parallele diſtante de quatre toiſes.</s> <s xml:id="echoid-s4118" xml:space="preserve"/> </p> <div xml:id="echoid-div358" type="float" level="2" n="1"> <note position="left" xlink:label="note-138-01" xlink:href="note-138-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s4119" xml:space="preserve">Tracez par l'Uſage troiſiéme deux perpendiculaires de quatre <lb/>toiſes chacune, ſur les deux points A & </s> <s xml:id="echoid-s4120" xml:space="preserve">B plantez un piquet à cha-<lb/>cune de leurs extremitez C & </s> <s xml:id="echoid-s4121" xml:space="preserve">D, & </s> <s xml:id="echoid-s4122" xml:space="preserve">par ces deux piquets tracez la <lb/>droite CD, elle ſera parallele à AB.</s> <s xml:id="echoid-s4123" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div360" type="section" level="1" n="164"> <head xml:id="echoid-head247" xml:space="preserve">USAGE VI.</head> <head xml:id="echoid-head248" style="it" xml:space="preserve">D'un point donné ſur le bout d'une ligne tracer ſur le terrain un <lb/>angle ſemblable à celui d'un Plan propoſé.</head> <p> <s xml:id="echoid-s4124" xml:space="preserve"> <lb/> <anchor type="note" xlink:label="note-138-02a" xlink:href="note-138-02"/> SOit ABC, l'Angle d'un Plan propoſé auquel on en veut faire <lb/>un ſemblable ſur le terrain.</s> <s xml:id="echoid-s4125" xml:space="preserve"/> </p> <div xml:id="echoid-div360" type="float" level="2" n="1"> <note position="left" xlink:label="note-138-02" xlink:href="note-138-02a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s4126" xml:space="preserve">Du point B, comme centre, décrivez ſur le papier l'Arc AC, & </s> <s xml:id="echoid-s4127" xml:space="preserve"><lb/>tirez la droite AD, qui ſera ſoûtendante dudit Arc. </s> <s xml:id="echoid-s4128" xml:space="preserve">Meſurez ſur <lb/>une Echelle, ou ſur la lïgne des parties égales d'un compas de pro-<lb/>portion une des jambes egales dudit Angle AB ou BC. </s> <s xml:id="echoid-s4129" xml:space="preserve">Meſurez <lb/>auſſi ſur la même Echelle la ſoûtendante AC, laquelle je ſuppoſe <lb/>par exemple, contenir trente-ſix parties égales à celle dont la jam-<lb/>be AB en contient trente.</s> <s xml:id="echoid-s4130" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4131" xml:space="preserve">Soit ſur la terre une ligne droite comme BC, ſur laquelle il faut <lb/>tracer une autre ligne FB, qui faſſe un angle ſemblable au propo-<lb/>ſé. </s> <s xml:id="echoid-s4132" xml:space="preserve">Plantez un piquet au point B, & </s> <s xml:id="echoid-s4133" xml:space="preserve">ayant meſuré trente pieds ou <lb/>cinq toiſes le long de la ligne BC, plantez-y un autre piquet, <lb/>comme D; </s> <s xml:id="echoid-s4134" xml:space="preserve">ayez deux cordeaux, l'un de trente pieds de long que <lb/>vous attacherez par un anneau au piquet B, & </s> <s xml:id="echoid-s4135" xml:space="preserve">l'autre de trente-<lb/>ſix pieds, que vous attacherez auſſi par un anneau au piquet D. <lb/></s> <s xml:id="echoid-s4136" xml:space="preserve">Tendez ces deux cordeaux juſqu'à ce qu'ils ſe joignent par leurs <lb/>extremitez au point F, où vous planterez encore un piquet, d'où <lb/>vous tracerez la ligne FB, laquelle formera au point B, l'angle <lb/>ſemblable au propoſé avec la ligne BC; </s> <s xml:id="echoid-s4137" xml:space="preserve">& </s> <s xml:id="echoid-s4138" xml:space="preserve">ainſi de l'autre.</s> <s xml:id="echoid-s4139" xml:space="preserve"/> </p> <pb o="125" file="139" n="139" rhead="POUR LEVER LES PLANS. Liv. IV. Chap. I."/> </div> <div xml:id="echoid-div362" type="section" level="1" n="165"> <head xml:id="echoid-head249" xml:space="preserve">USAGE VII.</head> <head xml:id="echoid-head250" style="it" xml:space="preserve">Deſigner ſur le papier un Angle ſemblable à celui que font <lb/>deux lignes ſur la terre.</head> <p> <s xml:id="echoid-s4140" xml:space="preserve">CEtte propoſition eſt la converſe de la precedente.</s> <s xml:id="echoid-s4141" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4142" xml:space="preserve">Soit propoſé ſur la terre l'angle FBC, formé par les deux <lb/> <anchor type="note" xlink:label="note-139-01a" xlink:href="note-139-01"/> cotez d'une terre labourable, auquel on veut en faire un ſembla-<lb/>ble ſur le papier. </s> <s xml:id="echoid-s4143" xml:space="preserve">Meſurez de B vers C trente pieds ou cinq toiſes, <lb/>& </s> <s xml:id="echoid-s4144" xml:space="preserve">plantez un piquet D au bout; </s> <s xml:id="echoid-s4145" xml:space="preserve">meſurez pareillement de B vers <lb/>F trente pieds, & </s> <s xml:id="echoid-s4146" xml:space="preserve">plantez-y un autre piquet; </s> <s xml:id="echoid-s4147" xml:space="preserve">meſurez auſſi la li-<lb/>gne droite qui fait la diſtance des deux piquets FD, que je ſuppo-<lb/>ſerai de trente-ſix pieds, comme en l'exemple de l'uſage precedent.</s> <s xml:id="echoid-s4148" xml:space="preserve"/> </p> <div xml:id="echoid-div362" type="float" level="2" n="1"> <note position="right" xlink:label="note-139-01" xlink:href="note-139-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s4149" xml:space="preserve">Soit ſur le papier la ligne BC: </s> <s xml:id="echoid-s4150" xml:space="preserve">du point B comme centre & </s> <s xml:id="echoid-s4151" xml:space="preserve">d'une <lb/>ouverture de trente parties égales, priſes ſur une Echelle, décrivez <lb/>l'Arc AC; </s> <s xml:id="echoid-s4152" xml:space="preserve">prenez avec le compas ſur la même échelle trente-ſix <lb/>parties égales, portez cette ouverture ſur l'arc AC, en poſant une <lb/>des pointes du compas ſur le point C. </s> <s xml:id="echoid-s4153" xml:space="preserve">L'autre jambe marquera ſur <lb/>ledit Arc le point par lequel ſe doit tirer la ligne BA.</s> <s xml:id="echoid-s4154" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4155" xml:space="preserve">Si de plus on veut ſçavoir la valeur dudit angle, on connoîtra <lb/>par le moyen d'un rapporteur qu'il eſt peu moins de ſoixante & </s> <s xml:id="echoid-s4156" xml:space="preserve"><lb/>quatorze degrez.</s> <s xml:id="echoid-s4157" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4158" xml:space="preserve">On pourra connoître plus préciſément en degrez & </s> <s xml:id="echoid-s4159" xml:space="preserve">minutes la <lb/>valeur des angles dont on aura meſuré les baſes ou ſoûtendantes <lb/>par le table ſuivante. </s> <s xml:id="echoid-s4160" xml:space="preserve">Elle eſt calculée pour angles toûjours com-<lb/>pris par deux côtez égaux de trente pieds chacun.</s> <s xml:id="echoid-s4161" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4162" xml:space="preserve">L'uſage de cette Table eſt très-facile pour connoître la grandeur <lb/>de tous les Angles Plans ſur le terrain.</s> <s xml:id="echoid-s4163" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4164" xml:space="preserve">Meſurez trente pieds ſur chacune des lignes qui forment l'an-<lb/>gle, & </s> <s xml:id="echoid-s4165" xml:space="preserve">plantez un piquet ſur chaque ligne où finiſſent les trente <lb/>pieds; </s> <s xml:id="echoid-s4166" xml:space="preserve">meſurez enſuite la baſe de l'Angle qui eſt la ligne droite <lb/>étendue entre les deux piquets, que je ſuppoſe être de trente-ſix <lb/>pieds comme en l'exemple precedent, cherchez dans ladite Table <lb/>en la colonne des Baſes trente-ſix pieds, & </s> <s xml:id="echoid-s4167" xml:space="preserve">vous trouverez vis-à-<lb/>vis en la colonne des Angles ſoixante & </s> <s xml:id="echoid-s4168" xml:space="preserve">treize degrez, quarante-<lb/>quatre minutes pour la valeur dudit Angle.</s> <s xml:id="echoid-s4169" xml:space="preserve"/> </p> <pb file="140" n="140"/> </div> <div xml:id="echoid-div364" type="section" level="1" n="166"> <head xml:id="echoid-head251" xml:space="preserve">TABLE DES ANGLES PLANS</head> <p> <s xml:id="echoid-s4170" xml:space="preserve">toûjours compris par deux côtez de trente pieds.</s> <s xml:id="echoid-s4171" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. <lb/>2 # 0 # 19 # 2 # 6 # 3 # 2 # 11 # 48 # 2 # 17 # 34 # 2 # 23 # 24 <lb/>4 # 0 # 38 # 4 # 6 # 22 # 4 # 12 # 8 # 4 # 17 # 54 # 4 # 23 # 44 <lb/>6 # 7 # 57 # 6 # 6 # 41 # 6 # 12 # 27 # 6 # 18 # 13 # 6 # 24 # 3 <lb/>8 # 1 # 8 # 8 # 7 # 0 # 8 # 12 # 46 # 8 # 18 # 32 # 8 # 24 # 23 <lb/>10 # 1 # 36 # 10 # 7 # 20 # 10 # 13 # 5 # 10 # 18 # 52 # 10 # 24 # 42 <lb/>1 # 1 # 55 # 4 # 7 # 39 # 7 # 13 # 24 # 10 # 19 # 11 # 13 # 25 # 1 <lb/>2 # 2 # 14 # 2 # 7 # 58 # 2 # 13 # 43 # 2 # 19 # 30 # 2 # 25 # 21 <lb/>4 # 2 # 33 # 4 # 8 # 17 # 4 # 14 # 2 # 4 # 19 # 50 # 4 # 25 # 41 <lb/>6 # 2 # 52 # 6 # 8 # 36 # 6 # 14 # 22 # 6 # 20 # 19 # 6 # 26 # 1 <lb/>8 # 3 # 11 # 8 # 8 # 55 # 8 # 14 # 41 # 8 # 20 # 29 # 8 # 26 # 20 <lb/>10 # 3 # 30 # 10 # 9 # 14 # 10 # 15 # 0 # 10 # 20 # 48 # 10 # 26 # 40 <lb/>2 # 3 # 49 # 5 # 9 # 34 # 8 # 15 # 20 # 11 # 21 # 8 # 14 # 26 # 53 <lb/>2 # 4 # 8 # 2 # 9 # 53 # 2 # 15 # 39 # 2 # 21 # 27 # 2 # 27 # 18 <lb/>4 # 4 # 28 # 4 # 10 # 12 # 4 # 15 # 58 # 4 # 21 # 46 # 4 # 27 # 38 <lb/>6 # 4 # 47 # 6 # 10 # 31 # 6 # 16 # 18 # 6 # 22 # 6 # 6 # 27 # 58 <lb/>8 # 5 # 6 # 8 # 10 # 50 # 8 # 16 # 37 # 8 # 22 # 25 # 8 # 28 # 18 <lb/>10 # 5 # 25 # 10 # 11 # 9 # 10 # 16 # 56 # 10 # 22 # 45 # 10 # 28 # 38 <lb/>3 # 5 # 44 # 6 # 11 # 29 # 9 # 17 # 15 # 12 # 23 # 6 # 15 # 28 # 57 <lb/>B. # Angles. # B. # Angles. # B. # Angles. # B. # Angles. # B. # Angles. <lb/>2 # 29 # 17 # 2 # 35 # 15 # 2 # 41 # 19 # 2 # 47 # 30 # 2 # 53 # 51 <lb/>4 # 29 # 37 # 4 # 35 # 35 # 4 # 41 # 40 # 4 # 47 # 51 # 4 # 54 # 12 <lb/>6 # 29 # 56 # 6 # 35 # 55 # 6 # 41 # 0 # 6 # 48 # 12 # 6 # 54 # 34 <lb/>8 # 30 # 16 # 8 # 36 # 15 # 8 # 42 # 20 # 8 # 48 # 33 # 8 # 54 # 55 <lb/>10 # 30 # 36 # 10 # 46 # 35 # 10 # 44 # 40 # 10 # 48 # 54 # 10 # 55 # 16 <lb/>16 # 30 # 56 # 19 # 36 # 55 # 22 # 43 # 1 # 25 # 49 # 15 # 28 # 55 # 38 <lb/>2 # 31 # 16 # 2 # 37 # 15 # 2 # 43 # 22 # 2 # 49 # 36 # 2 # 56 # 0 <lb/>4 # 31 # 36 # 4 # 37 # 36 # 4 # 43 # 42 # 4 # 49 # 57 # 4 # 56 # 22 <lb/>6 # 31 # 56 # 6 # 37 # 56 # 6 # 44 # 3 # 6 # 50 # 18 # 6 # 56 # 43 <lb/>8 # 32 # 16 # 8 # 38 # 16 # 8 # 44 # 24 # 8 # 50 # 39 # 8 # 57 # 5 <lb/>10 # 32 # 35 # 10 # 38 # 36 # 20 # 44 # 44 # 10 # 51 # 0 # 10 # 57 # 26 <lb/>17 # 32 # 55 # 20 # 38 # 56 # 23 # 45 # 5 # 26 # 51 # 21 # 29 # 57 # 48 <lb/>2 # 33 # 16 # 2 # 39 # 17 # 2 # 45 # 26 # 2 # 51 # 42 # 2 # 58 # 10 <lb/>4 # 33 # 35 # 4 # 39 # 38 # 4 # 45 # 46 # 4 # 52 # 3 # 4 # 58 # 32 <lb/>6 # 33 # 55 # 6 # 39 # 58 # 6 # 46 # 7 # 6 # 52 # 24 # 6 # 58 # 54 <lb/>8 # 34 # 15 # 8 # 40 # 18 # 8 # 46 # 28 # 8 # 52 # 46 # 8 # 59 # 16 <lb/>10 # 34 # 35 # 10 # 40 # 38 # 10 # 46 # 48 # 10 # 53 # 8 # 10 # 59 # 38 <lb/>18 # 34 # 55 # 21 # 40 # 59 # 24 # 47 # 9 # 27 # 53 # 29 # 30 # 60 # 0 <lb/></note> <pb file="141" n="141"/> </div> <div xml:id="echoid-div365" type="section" level="1" n="167"> <head xml:id="echoid-head252" xml:space="preserve">TABLE DES ANGLES PLANS</head> <p> <s xml:id="echoid-s4172" xml:space="preserve">toûjours compris par deux côtez de trente pieds.</s> <s xml:id="echoid-s4173" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. # Baſes. # ## Angles. \\ D. M. <lb/>2 # 60 # 22 # 2 # 67 # 7 # 2 # 74 # 8 # 2 # 81 # 30 # 2 # 89 # 18 <lb/>4 # 60 # 44 # 4 # 67 # 30 # 4 # 74 # 32 # 4 # 81 # 55 # 4 # 89 # 45 <lb/>6 # 61 # 6 # 6 # 67 # 53 # 6 # 74 # 56 # 6 # 82 # 20 # 6 # 90 # 12 <lb/>8 # 61 # 28 # 8 # 68 # 16 # 8 # 75 # 20 # 8 # 82 # 46 # 8 # 90 # 39 <lb/>10 # 61 # 50 # 10 # 68 # 39 # 10 # 75 # 44 # 10 # 83 # 12 # 10 # 91 # 6 <lb/>31 # 62 # 13 # 34 # 69 # 2 # 37 # 76 # 9 # 40 # 83 # 37 # 43 # 91 # 33 <lb/>2 # 62 # 35 # 2 # 69 # 25 # 2 # 76 # 33 # 2 # 84 # 3 # 2 # 92 # 1 <lb/>4 # 62 # 58 # 4 # 69 # 48 # 4 # 76 # 57 # 4 # 84 # 29 # 4 # 92 # 29 <lb/>6 # 63 # 20 # 6 # 70 # 12 # 6 # 77 # 22 # 6 # 84 # 54 # 6 # 92 # 56 <lb/>8 # 63 # 43 # 8 # 70 # 35 # 8 # 77 # 46 # 8 # 85 # 20 # 8 # 93 # 24 <lb/>10 # 64 # 5 # 10 # 70 # 59 # 10 # 78 # 9 # 10 # 85 # 46 # 10 # 93 # 52 <lb/>32 # 64 # 28 # 35 # 71 # 22 # 38 # 78 # 35 # 41 # 86 # 12 # 44 # 94 # 20 <lb/>2 # 64 # 50 # 2 # 71 # 46 # 2 # 79 # 0 # 2 # 86 # 39 # 2 # 94 # 48 <lb/>4 # 65 # 13 # 4 # 72 # 10 # 4 # 79 # 25 # 4 # 87 # 5 # 4 # 95 # 16 <lb/>6 # 65 # 36 # 6 # 72 # 33 # 6 # 79 # 50 # 6 # 87 # 32 # 6 # 95 # 20 <lb/>8 # 65 # 58 # 8 # 72 # 56 # 8 # 80 # 15 # 8 # 87 # 58 # 8 # 96 # 13 <lb/>10 # 66 # 21 # 10 # 73 # 20 # 10 # 80 # 40 # 10 # 88 # 25 # 10 # 96 # 42 <lb/>33 # 66 # 44 # 36 # 73 # 44 # 39 # 81 # 5 # 42 # 88 # 51 # 45 # 97 # 11 <lb/>B. # ## Angles. B. # ## Angles. # B. # ## Angles. # B. # ## Angles. # B. ## Angles. <lb/>2 # 97 # 40 # 2 # 106 # 48 # 2 # 117 # 2 # 2 # 129 # 3 # 2 # 144 # 39 <lb/>4 # 98 # 9 # 4 # 107 # 20 # 4 # 117 # 39 # 4 # 129 # 48 # 4 # 145 # 43 <lb/>6 # 98 # 38 # 6 # 107 # 52 # 6 # 118 # 16 # 6 # 130 # 33 # 6 # 146 # 48 <lb/>8 # 99 # 8 # 8 # 108 # 25 # 8 # 118 # 53 # 8 # 131 # 19 # 8 # 147 # 57 <lb/>10 # 99 # 37 # 10 # 108 # 57 # 10 # 119 # 31 # 10 # 132 # 6 # 10 # 149 # 8 <lb/>46 # 100 # 6 # 49 # 109 # 30 # 52 # 120 # 9 # 55 # 132 # 53 # 58 # 150 # 20 <lb/>2 # 100 # 36 # 2 # 120 # 4 # 2 # 110 # 47 # 2 # 133 # 44 # 2 # 151 # 36 <lb/>4 # 101 # 6 # 4 # 121 # 37 # 4 # 111 # 26 # 4 # 134 # 30 # 4 # 152 # 55 <lb/>6 # 101 # 36 # 6 # 111 # 11 # 6 # 122 # 6 # 6 # 135 # 20 # 6 # 154 # 19 <lb/>8 # 102 # 7 # 8 # 111 # 44 # 8 # 122 # 45 # 8 # 136 # 11 # 8 # 155 # 48 <lb/>10 # 102 # 37 # 10 # 112 # 18 # 10 # 123 # 25 # 10 # 137 # 3 # 10 # 157 # 22 <lb/>47 # 103 # 8 # 50 # 112 # 53 # 53 # 124 # 6 # 56 # 137 # 57 # 59 # 159 # 3 <lb/>2 # 103 # 39 # 2 # 113 # 28 # 2 # 124 # 47 # 2 # 138 # 49 # 2 # 160 # 53 <lb/>4 # 104 # 10 # 4 # 114 # 3 # 4 # 125 # 28 # 4 # 139 # 44 # 4 # 162 # 54 <lb/>6 # 104 # 41 # 6 # 114 # 38 # 6 # 126 # 10 # 6 # 140 # 40 # 6 # 165 # 12 <lb/>8 # 105 # 12 # 8 # 115 # 14 # 8 # 126 # 52 # 8 # 141 # 38 # 8 # 167 # 48 <lb/>10 # 105 # 44 # 10 # 115 # 49 # 10 # 127 # 35 # 10 # 142 # 36 # 10 # 171 # 28 <lb/>48 # 106 # 16 # 51 # 116 # 26 # 54 # 128 # 19 # 57 # 143 # 36 # 60 # 180 # 0 <lb/></note> <pb o="128" file="142" n="142" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> <p> <s xml:id="echoid-s4174" xml:space="preserve">Il faut remarquer que dans la colonne des Baſes les pouces n'y <lb/>ſont marquez que de deux en deux, & </s> <s xml:id="echoid-s4175" xml:space="preserve">les pieds y ſont marquez d'un <lb/>en un. </s> <s xml:id="echoid-s4176" xml:space="preserve">L'on trouvera toûjours avec autant de facilité que de juſ-<lb/>teſſe l'ouverture & </s> <s xml:id="echoid-s4177" xml:space="preserve">la valeur de tous les Angeles; </s> <s xml:id="echoid-s4178" xml:space="preserve">car ſuppoſant, par <lb/>exemple, que vôtre baſe ſoit de la longueur de 50 toiſes 3 pouces, & </s> <s xml:id="echoid-s4179" xml:space="preserve"><lb/>les deux autres côtez toûjours de 30 pieds, vous chercherez dans la <lb/>colonne des baſes le nombre de 50 pieds 3 pouces, & </s> <s xml:id="echoid-s4180" xml:space="preserve">vous trouve-<lb/>rez vis-à-vis dans la colonne des Angles 113 degrez & </s> <s xml:id="echoid-s4181" xml:space="preserve">44 minutes <lb/>pour la valeur de l'Angle requis, en gardant les proportions des <lb/>minutes & </s> <s xml:id="echoid-s4182" xml:space="preserve">des pouces, comme on fait en cet exemple.</s> <s xml:id="echoid-s4183" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4184" xml:space="preserve">En réduiſant ce nombre de pieds par le moyen d'une Echelle <lb/>bien deviſée ſur du cuivre, l'on meſurera lesmêmes Angles ſur la <lb/>carte & </s> <s xml:id="echoid-s4185" xml:space="preserve">ſur le papier avec autant de juſteſſe que les cordeaux ſur la <lb/>terre; </s> <s xml:id="echoid-s4186" xml:space="preserve">d'autant qu'aux triangles équiangles les côtez ſont propor-<lb/>tionels entr'eux.</s> <s xml:id="echoid-s4187" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4188" xml:space="preserve">Cette methode de meſurer les Angles Plans peut auſſi ſervir à <lb/>conſtruire les deſſeins de Fortification des Places, tant regulieres que <lb/>irregulieres, pour en connoître l'ouverture des Angles, tant des Baſ-<lb/>tions que du Poligone formé par les rencontres des lignes des Ba-<lb/>ſes, ou côtez exterieurs, tant ſur le papier que ſur la terre.</s> <s xml:id="echoid-s4189" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4190" xml:space="preserve">Pour tracer les Angles, cherchez dansla Table le nombre des de-<lb/>grez & </s> <s xml:id="echoid-s4191" xml:space="preserve">minutes que vous aurez à tracer, par exemple, de 54 degrez <lb/>34 minutes, & </s> <s xml:id="echoid-s4192" xml:space="preserve">après l'avoir trouvé prenez à côté dans la colonne <lb/>des baſes, le nombre des pieds & </s> <s xml:id="echoid-s4193" xml:space="preserve">pouces qui lui répond, à ſçavoir, <lb/>27 pieds & </s> <s xml:id="echoid-s4194" xml:space="preserve">6 pouces pour la meſure de la longueur de la baſe de <lb/>l'Angle toûjours compris par les deux autres côtez du triangle de 30 <lb/>pieds chacun; </s> <s xml:id="echoid-s4195" xml:space="preserve">& </s> <s xml:id="echoid-s4196" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s4197" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div366" type="section" level="1" n="168"> <head xml:id="echoid-head253" xml:space="preserve">USAGE VIII.</head> <head xml:id="echoid-head254" style="it" xml:space="preserve">Pour lever le Plan d'une Place dans laquelle on peut entrer.</head> <p> <s xml:id="echoid-s4198" xml:space="preserve">Soit la place ABCDE, de laquelle on veut lever le Plan. <lb/></s> <s xml:id="echoid-s4199" xml:space="preserve"> <anchor type="note" xlink:label="note-142-01a" xlink:href="note-142-01"/> </s> </p> <div xml:id="echoid-div366" type="float" level="2" n="1"> <note position="left" xlink:label="note-142-01" xlink:href="note-142-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s4200" xml:space="preserve">Faites premierement ſur vôtre papier une figure à peu près <lb/>ſemblable à vôtre Plan, & </s> <s xml:id="echoid-s4201" xml:space="preserve">après avoir meſuré avec la toiſe ſur le <lb/>terrain les côtez AB, BC, CD & </s> <s xml:id="echoid-s4202" xml:space="preserve">DE, écrivez les meſures trouvées <lb/>ſur chacune des lignes qui leur correſpondent ſur le papier; </s> <s xml:id="echoid-s4203" xml:space="preserve">enſuite <lb/>au lieu de meſurer les Angles qui font les côtez de la Place, meſurez <lb/>les Diagonales comme ſont les lignes AD, BD, dont vous écrirez <lb/>la valeur en nombre ſur vôtre broüillon; </s> <s xml:id="echoid-s4204" xml:space="preserve">laquelle ſera reduite en <lb/>trois triangles dont tous les côtez ſont connus, puiſqu'ils ont éte <lb/>meſurez actuellement.</s> <s xml:id="echoid-s4205" xml:space="preserve"/> </p> <pb o="129" file="143" n="143" rhead="POUR LEVER LES PLANS Liv. IV. Chap. I."/> <p> <s xml:id="echoid-s4206" xml:space="preserve">Vous remettrez au net ce broüillon par le moyen d'une Echelle <lb/>de parties égales qui en contienne autant que la plus longue ligne <lb/>du Plan.</s> <s xml:id="echoid-s4207" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4208" xml:space="preserve">De toutes les methodes de lever un Plan, celle de le lever par de-<lb/>dans eſt la plus exacte & </s> <s xml:id="echoid-s4209" xml:space="preserve">la moins ſujete à erreur.</s> <s xml:id="echoid-s4210" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div368" type="section" level="1" n="169"> <head xml:id="echoid-head255" xml:space="preserve">USAGE IX.</head> <head xml:id="echoid-head256" style="it" xml:space="preserve">Pour lever le Plan d'une Place par dehors.</head> <p> <s xml:id="echoid-s4211" xml:space="preserve">SOit propoſé un Bois ou un Etang dont on veut lever le Plan, <lb/> <anchor type="note" xlink:label="note-143-01a" xlink:href="note-143-01"/> comme ſeroit EFGHI.</s> <s xml:id="echoid-s4212" xml:space="preserve"/> </p> <div xml:id="echoid-div368" type="float" level="2" n="1"> <note position="right" xlink:label="note-143-01" xlink:href="note-143-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s4213" xml:space="preserve">Faites-end'abord le broüillon en vous promenant tout autour, ſi <lb/>vous le pouvez faire ſans perdre beaucoup de tems.</s> <s xml:id="echoid-s4214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4215" xml:space="preserve">Meſurez avec la toiſe ou la chaîne tous les côtez qui font l'en-<lb/>ceinte du lieu propoſé, & </s> <s xml:id="echoid-s4216" xml:space="preserve">marquez-en les nombres ſur chacune des <lb/>lignes de vôtre broüillon; </s> <s xml:id="echoid-s4217" xml:space="preserve">mais pour les Angles, vous les meſure-<lb/>rez par la methode ci-jointe.</s> <s xml:id="echoid-s4218" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4219" xml:space="preserve">Pour meſurer, par exemple, l'Angle EFG, prolongez en bor-<lb/>naïant le côté E F, de 5 toiſes, & </s> <s xml:id="echoid-s4220" xml:space="preserve">plantez un piquet à l'extremité K; <lb/></s> <s xml:id="echoid-s4221" xml:space="preserve">prolongez également le côté GF, & </s> <s xml:id="echoid-s4222" xml:space="preserve">plantez un piquet à l'extremité <lb/>L. </s> <s xml:id="echoid-s4223" xml:space="preserve">meſurez avec la toiſe la diſtance LK, & </s> <s xml:id="echoid-s4224" xml:space="preserve">ſuppoſant qu'elle ſoit <lb/>de 6 toiſes 4 pieds, c'eſt-à dire, 40 pieds, marquez ce nombre ſur <lb/>la ligne L K de vôtre broüillon; </s> <s xml:id="echoid-s4225" xml:space="preserve">par ce moyen vous aurez les trois <lb/>côtez du triangle iſocele LFK, qui ſerviront à vous faire connoî-<lb/>tre l'ouverture de l'Angle LFK; </s> <s xml:id="echoid-s4226" xml:space="preserve">ſoit par la Table ci-devant ou au-<lb/>trement. </s> <s xml:id="echoid-s4227" xml:space="preserve">Or cet Angle eſt égal à ſon oppoſé par la pointe EFG, & </s> <s xml:id="echoid-s4228" xml:space="preserve"><lb/>ſi l'on cherche dans la Table 40 pieds en la colonne des Baſes, on <lb/>trouvera que cet Angle eſt de 8; </s> <s xml:id="echoid-s4229" xml:space="preserve">degrez 37 minutes.</s> <s xml:id="echoid-s4230" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4231" xml:space="preserve">Vous meſurerez de même l'Angle FGH, & </s> <s xml:id="echoid-s4232" xml:space="preserve">tous les autres de la <lb/>figure, ou bien de cette autre maniere; </s> <s xml:id="echoid-s4233" xml:space="preserve">prolongez en bornaïant le <lb/>côté HG, de 4 toiſes de G en N, où vous planterez un piquet; </s> <s xml:id="echoid-s4234" xml:space="preserve">me-<lb/>ſurez le long du côté GL, de G en M, 5 toiſes, au bout deſquelles <lb/>vous ferez une marque en y plantant un piquet ou autrement. </s> <s xml:id="echoid-s4235" xml:space="preserve">Me-<lb/>ſurez exactement la diſtance MN, laquelle je ſuppoſe pour exem-<lb/>ple de 6 toiſes 2 pieds, ou de 38 pieds, que vous écrirez ſur la ligne <lb/>MN de vôtre broüillon.</s> <s xml:id="echoid-s4236" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4237" xml:space="preserve">Ce nombre cherché dans la colonne des Baſes, qui correſpond a <lb/>78 degrez 35 min. </s> <s xml:id="echoid-s4238" xml:space="preserve">pour l'Angle exterieur MGH, dont le complé-<lb/>ment 101 degrez 25 min. </s> <s xml:id="echoid-s4239" xml:space="preserve">eſt la valeur de l'Angle de la figure FGH, <lb/>parce que deux Angles de ſuite valent autant que 2 Angles droits.</s> <s xml:id="echoid-s4240" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4241" xml:space="preserve">Vous remettrez enſuite vôtre broüillon au net avec une Echelle <lb/> <pb o="130" file="144" n="144" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> de parties égales, tant pour marquer la longueur des côtez quc cel-<lb/>le des Baſes de tous les Angles que l'on peut avoir exactement, ſans <lb/>ſe mettre en peine de leur valeur en degrez & </s> <s xml:id="echoid-s4242" xml:space="preserve">minutes.</s> <s xml:id="echoid-s4243" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div370" type="section" level="1" n="170"> <head xml:id="echoid-head257" xml:space="preserve">USAGE X.</head> <head xml:id="echoid-head258" style="it" xml:space="preserve">Pour tracer ſur la terre tout Polygone regulier ſur une Ligne <lb/>donnée.</head> <p> <s xml:id="echoid-s4244" xml:space="preserve">SOit pour exemple la ligne donnée AB, ſur laquelle on propoſe <lb/> <anchor type="note" xlink:label="note-144-01a" xlink:href="note-144-01"/> de tracer un triangle équilateral.</s> <s xml:id="echoid-s4245" xml:space="preserve"/> </p> <div xml:id="echoid-div370" type="float" level="2" n="1"> <note position="left" xlink:label="note-144-01" xlink:href="note-144-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s4246" xml:space="preserve">Meſurez ſur cette ligne du point A allant vers B, 30 pieds, & </s> <s xml:id="echoid-s4247" xml:space="preserve"><lb/>plantez-y un piquet D; </s> <s xml:id="echoid-s4248" xml:space="preserve">ayez deux cordeaux meſurez de 30 pieds <lb/>chacun dont vous en attacherez un au piquet D, & </s> <s xml:id="echoid-s4249" xml:space="preserve">l'autre au pi-<lb/>quet A, & </s> <s xml:id="echoid-s4250" xml:space="preserve">les tendez également juſqu'à ce qu'ils ſe joignent par les <lb/>deux autres bouts au point C, où vous planterez un autre piquet.</s> <s xml:id="echoid-s4251" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4252" xml:space="preserve">Faites la même choſe à l'auttre extremité B, de la ligne donnée, <lb/>& </s> <s xml:id="echoid-s4253" xml:space="preserve">prolongez les lignes juſqu'à ce qu'elles ſe joignent pour former <lb/>le triangle équilateral & </s> <s xml:id="echoid-s4254" xml:space="preserve">équiangle ABE.</s> <s xml:id="echoid-s4255" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4256" xml:space="preserve">S'il s'agit de tracer ſur la terre un quarré parfait ſur la ligne don-<lb/>née AB.</s> <s xml:id="echoid-s4257" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4258" xml:space="preserve">Elevez ſur chaque extemité A & </s> <s xml:id="echoid-s4259" xml:space="preserve">B une perpendiculaire par l'U-<lb/> <anchor type="note" xlink:label="note-144-02a" xlink:href="note-144-02"/> ſage troiſiéme.</s> <s xml:id="echoid-s4260" xml:space="preserve"/> </p> <div xml:id="echoid-div371" type="float" level="2" n="2"> <note position="left" xlink:label="note-144-02" xlink:href="note-144-02a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s4261" xml:space="preserve">Prolongez ces perpendiculaires pour les faire égales à la lignc <lb/>donnée, plantez des piquets à leurs extremitez C & </s> <s xml:id="echoid-s4262" xml:space="preserve">D, & </s> <s xml:id="echoid-s4263" xml:space="preserve">tracez la <lb/>ligne C D, qui achevera le quarré popoſé.</s> <s xml:id="echoid-s4264" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4265" xml:space="preserve">S'il faut tracer un Pentagone ſur la ligne donnée AB.</s> <s xml:id="echoid-s4266" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4267" xml:space="preserve">Souvenez-vous que les Angles formez par les côtez d'un Penta-<lb/>gone regulier ſont de 108 degrez chacun, comme nous l'avons ex-<lb/> <anchor type="note" xlink:label="note-144-03a" xlink:href="note-144-03"/> pliqué ci-devant en l'Uſage troiſiéme du Rapporteur, & </s> <s xml:id="echoid-s4268" xml:space="preserve">en la Sec-<lb/>tion troiſiéme de la ligne des Poligones du compas de proportion; <lb/></s> <s xml:id="echoid-s4269" xml:space="preserve">c'eſt pourquoi cherchez dans la Table des Angles Plans compris par <lb/>deux côtez de 30 pieds dans la colonne des Baſes, le nombre qui <lb/>correſpond à 108 degrez ou le plus approchant, vous trouverez 48 <lb/>pieds 6 pouces & </s> <s xml:id="echoid-s4270" xml:space="preserve">quelque peu plus; </s> <s xml:id="echoid-s4271" xml:space="preserve">car ce nombre correſpond à <lb/>107 degrez 52 minutes, qui eſt moindre de 8 minutes que 108 <lb/>degrez; </s> <s xml:id="echoid-s4272" xml:space="preserve">c'eſt pourquoi on peut prendre 48 pieds 6 pouces & </s> <s xml:id="echoid-s4273" xml:space="preserve">de-<lb/>mi pour ladite baſe.</s> <s xml:id="echoid-s4274" xml:space="preserve"/> </p> <div xml:id="echoid-div372" type="float" level="2" n="3"> <note position="left" xlink:label="note-144-03" xlink:href="note-144-03a" xml:space="preserve">Fig. 10.</note> </div> <p> <s xml:id="echoid-s4275" xml:space="preserve">Suivant cette methode, meſurez ſur la ligne donnée, du piquet A <lb/>vers B, 30 pieds, & </s> <s xml:id="echoid-s4276" xml:space="preserve">plantez un piquet au point C, où ſe termine la-<lb/>dite meſure. </s> <s xml:id="echoid-s4277" xml:space="preserve">A yez deux cordeaux meſurez, l'un de 30 pieds, que <lb/>vous attacherez par un de ſes bouts au piquet A, & </s> <s xml:id="echoid-s4278" xml:space="preserve">l'autre de 48 <lb/> <pb o="131" file="145" n="145" rhead="POUR LEVER LES PLANS. Liv. IV. Chap. I."/> pieds 6 pouces & </s> <s xml:id="echoid-s4279" xml:space="preserve">demi que vous attacherez de même au piquet C, <lb/>tendez également ces deux cordeaux juſqu'à ce qu'ils ſe joignent <lb/>au point E, où vous planterez un piquet, & </s> <s xml:id="echoid-s4280" xml:space="preserve">vous aurez par ce <lb/>moyen un Angle de 108 degrez; </s> <s xml:id="echoid-s4281" xml:space="preserve">prolongez la ligne AE, pourla <lb/>tracer égale à AB, faites la même choſe à l'autre extremité B de la <lb/>ligne donnée, & </s> <s xml:id="echoid-s4282" xml:space="preserve">par ce moyen vous aurez déja trois côtez du Penta-<lb/>gone AB, AG, BD, que vous acheverez par la même méthode.</s> <s xml:id="echoid-s4283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4284" xml:space="preserve">Si le Pentagone n'eſt pas trop grand, on peut l'achever par le <lb/>moyen de deux cordeaux égaux au côté donné, en attachant l'un au <lb/>piquet D, & </s> <s xml:id="echoid-s4285" xml:space="preserve">l'autre au piquet G; </s> <s xml:id="echoid-s4286" xml:space="preserve">car ſi vous les tendez également, <lb/>ils formeront les deux autres côtez du Pentagone en ſe joignant au <lb/>point H.</s> <s xml:id="echoid-s4287" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4288" xml:space="preserve">Vous pourrez par la même methode tracer ſur le terrain tout au-<lb/>tre Polygone regulier, ou irregulier, en cherchant dans la ſuſdite <lb/>Table le nombre des pieds & </s> <s xml:id="echoid-s4289" xml:space="preserve">pouces qui correſpond à l'Angle du <lb/>Polygone que l'on veut tracer.</s> <s xml:id="echoid-s4290" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div374" type="section" level="1" n="171"> <head xml:id="echoid-head259" xml:space="preserve">USAGE XI.</head> <head xml:id="echoid-head260" style="it" xml:space="preserve">Connoitre la diſtance de deux objets inacceſſibles de l'un à <lb/>l'autre, chacun étant acceſſible en particulier.</head> <p> <s xml:id="echoid-s4291" xml:space="preserve">ON demande, par exemple, la diſtance en ligne droite de la <lb/> <anchor type="note" xlink:label="note-145-01a" xlink:href="note-145-01"/> Tour A, au Moulin B.</s> <s xml:id="echoid-s4292" xml:space="preserve"/> </p> <div xml:id="echoid-div374" type="float" level="2" n="1"> <note position="right" xlink:label="note-145-01" xlink:href="note-145-01a" xml:space="preserve">Fig. 11.</note> </div> <p> <s xml:id="echoid-s4293" xml:space="preserve">Plantez le piquet C en une place d'où il ſoit ſacile de meſurer la <lb/>diſtance en ligne droite juſqu'aux lieux A & </s> <s xml:id="echoid-s4294" xml:space="preserve">B.</s> <s xml:id="echoid-s4295" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4296" xml:space="preserve">Meſurez exactement ces diſtances, comme par exemple de C en <lb/>A, que je ſuppoſe de 54 toiſes; </s> <s xml:id="echoid-s4297" xml:space="preserve">prolongez la ligne AC, juſqu'en <lb/>D, d'une quantité égale, c'eſt-à-dire de 54 toiſes; </s> <s xml:id="echoid-s4298" xml:space="preserve">meſurez pareil-<lb/>lement la ligne BC, que je ſuppoſe de 37 toiſes, & </s> <s xml:id="echoid-s4299" xml:space="preserve">la prolongez juſ-<lb/>qu'en E, d'une quantité égale, c'eſt-à-dire, de 37 toiſes, vous for-<lb/>merez par ce moyen le triangle CDE égal & </s> <s xml:id="echoid-s4300" xml:space="preserve">ſemblable au triangle <lb/>ABC, & </s> <s xml:id="echoid-s4301" xml:space="preserve">par conſequent la diſtance DE ſera égale à la diſtance <lb/>propoſée inacceſſible de A en B.</s> <s xml:id="echoid-s4302" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div376" type="section" level="1" n="172"> <head xml:id="echoid-head261" xml:space="preserve">USAGE XII.</head> <head xml:id="echoid-head262" style="it" xml:space="preserve">Connoître la diſtance de deux objets, dont un ſeulement <lb/>eſt acceſſible</head> <p> <s xml:id="echoid-s4303" xml:space="preserve">SOit propoſé pour exemple à trouver la largeur d'un Foſſe ou du <lb/> <anchor type="note" xlink:label="note-145-02a" xlink:href="note-145-02"/> lit d'une Riviere AB; </s> <s xml:id="echoid-s4304" xml:space="preserve">étant ſur un des bords au point A: </s> <s xml:id="echoid-s4305" xml:space="preserve">plan-<lb/>tez-y le piquet AC, de 4 à 5 pieds de haut & </s> <s xml:id="echoid-s4306" xml:space="preserve">bien perpendiculaire; <lb/></s> <s xml:id="echoid-s4307" xml:space="preserve">faites à l'extremité C du piquet une petite fente pour y faire entrer <lb/> <pb o="132" file="146" n="146" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> une lame d'un morccau de cuivre ou d'acier bien droit qui puiſſe <lb/>hauſſer ou baiſſer, long d'environ 3 pouces, que vous hauſſerez ou <lb/>baiſſerez juſqu'à ce que vous voyiez le point B, de l'autre côté de la <lb/>Riviere, en bornaïant le long de ladite lame; </s> <s xml:id="echoid-s4308" xml:space="preserve">enſuite tournez le pi-<lb/>quet toûjours perpendiculaire, en conſervant la lame dans la même <lb/>ſituation, & </s> <s xml:id="echoid-s4309" xml:space="preserve">bornaïez le long du bord de la Riviere ſur un terrain <lb/>de niveau, en remarquant le point comme D, où ſe termine le raïon <lb/>viſuel. </s> <s xml:id="echoid-s4310" xml:space="preserve">La diſtance AD, étant meſurée avec la chaîne, vous don-<lb/>nera la largeur de la Riviere ou du Foſlé à laquelle elle eſt égale, <lb/>comme il eſt facile de juger.</s> <s xml:id="echoid-s4311" xml:space="preserve"/> </p> <div xml:id="echoid-div376" type="float" level="2" n="1"> <note position="right" xlink:label="note-145-02" xlink:href="note-145-02a" xml:space="preserve">Fig. 12.</note> </div> <p> <s xml:id="echoid-s4312" xml:space="preserve">Cette propoſition, toute ſimple qu'elle eſt, peut ſervir à connoître <lb/>de quelle longueur on doit couper des branches d'arbres, pour faire <lb/>un pont ſur un foſſé ou ſur une Riviere que l'on veut traverſer.</s> <s xml:id="echoid-s4313" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div378" type="section" level="1" n="173"> <head xml:id="echoid-head263" xml:space="preserve">USAGE XIII.</head> <p> <s xml:id="echoid-s4314" xml:space="preserve">SOit propoſé de tracer ſur la terre uneligne droite du point A au <lb/> <anchor type="note" xlink:label="note-146-01a" xlink:href="note-146-01"/> point B, entre leſquels il y a un bâtiment ou autre obſtacle <lb/>qui empêche de continuer l'allignement.</s> <s xml:id="echoid-s4315" xml:space="preserve"/> </p> <div xml:id="echoid-div378" type="float" level="2" n="1"> <note position="left" xlink:label="note-146-01" xlink:href="note-146-01a" xml:space="preserve">Fig. 13.</note> </div> <p> <s xml:id="echoid-s4316" xml:space="preserve">Cherchez ſur un terrain bien de niveau un troiſiéme point com-<lb/>me C, duquel vous puiſſiez voir les piquets plantez aux points A & </s> <s xml:id="echoid-s4317" xml:space="preserve"><lb/>B; </s> <s xml:id="echoid-s4318" xml:space="preserve">meſurez exactement la diſtance de C en A, & </s> <s xml:id="echoid-s4319" xml:space="preserve">de C en B; </s> <s xml:id="echoid-s4320" xml:space="preserve">prenez <lb/>la moitié, le tiers ou toute autre partie égale de chacune de ces li-<lb/>gnes; </s> <s xml:id="echoid-s4321" xml:space="preserve">plantez-y des piquets comme en D, moitié de CB, & </s> <s xml:id="echoid-s4322" xml:space="preserve">en E <lb/>moitié de CA; </s> <s xml:id="echoid-s4323" xml:space="preserve">tirez une ligne droite de D en E, laquelle vous pro-<lb/>longerez tant qu'il ſera beſoin, & </s> <s xml:id="echoid-s4324" xml:space="preserve">tracez à cette ligne une parallele <lb/>qui paſſe par les points A & </s> <s xml:id="echoid-s4325" xml:space="preserve">B, par le moyen des piquets que vous <lb/>planterez entre le point A & </s> <s xml:id="echoid-s4326" xml:space="preserve">la Maiſon, de même qu'entre ladite <lb/>Maiſon & </s> <s xml:id="echoid-s4327" xml:space="preserve">le point B, tous en égale diſtance de la ligne LE, & </s> <s xml:id="echoid-s4328" xml:space="preserve"><lb/>ainſi vous continuerez l'allignement de A en B.</s> <s xml:id="echoid-s4329" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div380" type="section" level="1" n="174"> <head xml:id="echoid-head264" xml:space="preserve">USAGE XIV.</head> <p> <s xml:id="echoid-s4330" xml:space="preserve">SOit propoſé à percer une bute de terre pour y faire une gallerie <lb/> <anchor type="note" xlink:label="note-146-02a" xlink:href="note-146-02"/> qui communique de A en B.</s> <s xml:id="echoid-s4331" xml:space="preserve"/> </p> <div xml:id="echoid-div380" type="float" level="2" n="1"> <note position="left" xlink:label="note-146-02" xlink:href="note-146-02a" xml:space="preserve">Fig. 14.</note> </div> <p> <s xml:id="echoid-s4332" xml:space="preserve">Tracez d'un côté une ligne droite comme DC, & </s> <s xml:id="echoid-s4333" xml:space="preserve">de l'autre côté <lb/>de la bute uue autre ligne droite comme FE, parallele à CD; </s> <s xml:id="echoid-s4334" xml:space="preserve">du <lb/>point A, tirez ſur la ligne CD, la perpendiculaire AG, & </s> <s xml:id="echoid-s4335" xml:space="preserve">en quel-<lb/>que autre point par delà la bute, tirez une autre perpendiculaire <lb/>comme CH, égale à AG.</s> <s xml:id="echoid-s4336" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4337" xml:space="preserve">Du point B tirez ſur EF la perpendiculaire BI, & </s> <s xml:id="echoid-s4338" xml:space="preserve">en quelque au-<lb/>tre point par delà la bute, tirez une autre perpendiculaire ſur la même li-<lb/> <pb o="133" file="147" n="147" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. II."/> gne comme L M, égale à B I, en telle ſorte que la diſtance I L ſoit <lb/>égale à CG; </s> <s xml:id="echoid-s4339" xml:space="preserve">tracez enſuite une ligne droite du piquet H au piquet <lb/>M que vous prolongerez tant qu'il ſera beſoin, cette ligne ſera pa-<lb/>rallele à la gallerie propoſée à faire de A en B; </s> <s xml:id="echoid-s4340" xml:space="preserve">c'eſt pourquoi on <lb/>pourra planter en diſtance égale de cette parallele H M de côte & </s> <s xml:id="echoid-s4341" xml:space="preserve"><lb/>d'autre de la bute, tant de piquets que l'on voudra, comme O, P, <lb/>Q, qui ſerviront à percer la bute de A en B.</s> <s xml:id="echoid-s4342" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4343" xml:space="preserve">Je parlerai encore de l'uſage de ces Inſtrumens, dans le petit <lb/>Traité de Fortiſication, que je donnerai ci-après.</s> <s xml:id="echoid-s4344" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div382" type="section" level="1" n="175"> <head xml:id="echoid-head265" xml:space="preserve">CHAPITRE II.</head> <head xml:id="echoid-head266" style="it" xml:space="preserve">Contenant la deſcription & l'uſage de l'Equerre d'Arpenteur.</head> <note position="right" xml:space="preserve">Fig. A.</note> <p> <s xml:id="echoid-s4345" xml:space="preserve">L'Equerre d'Arpenteur eſt un cercle de cuivre d'une bonne épaiſ-<lb/> <anchor type="note" xlink:label="note-147-02a" xlink:href="note-147-02"/> ſeur & </s> <s xml:id="echoid-s4346" xml:space="preserve">de 4, 5 ou 6 pouces de diametre. </s> <s xml:id="echoid-s4347" xml:space="preserve">Ou le diviſe en qua-<lb/>tre parties égales par deux lignes qui s'entrecoupent à angles droits <lb/>au centre. </s> <s xml:id="echoid-s4348" xml:space="preserve">Aux quatre extremitez de ces lignes & </s> <s xml:id="echoid-s4349" xml:space="preserve">au milieu du lim-<lb/>be on y met quatre fortes pinules bien rivées dans des trous quar-<lb/>rez, & </s> <s xml:id="echoid-s4350" xml:space="preserve">très-perpendiculairement fenduës ſur leſdites lignes, avec des <lb/>trous au-deſſous de chaque fente pour mieux découvrir les objets <lb/>en campagne. </s> <s xml:id="echoid-s4351" xml:space="preserve">On évuide ce cercle pour le rendre plus leger.</s> <s xml:id="echoid-s4352" xml:space="preserve"/> </p> <div xml:id="echoid-div382" type="float" level="2" n="1"> <note position="right" xlink:label="note-147-02" xlink:href="note-147-02a" xml:space="preserve">XII. <lb/>Planche.</note> </div> <p> <s xml:id="echoid-s4353" xml:space="preserve">Au deſſous & </s> <s xml:id="echoid-s4354" xml:space="preserve">au centre de l'Inſtrument ſe doit monter à vis une <lb/>virole qui ſert à ſoûtenir l'Equerre ſur ſon bâton de 4 à 5 pieds ſui-<lb/>vant la hauteur de l'œil de l'Obſervateur. </s> <s xml:id="echoid-s4355" xml:space="preserve">Ce bâton doït être garni <lb/> <anchor type="note" xlink:label="note-147-03a" xlink:href="note-147-03"/> d'un fer pointu par le bout pui entre en terre, & </s> <s xml:id="echoid-s4356" xml:space="preserve">l'autre bout doit <lb/>être arrondi pour que la virole y reſte juſte.</s> <s xml:id="echoid-s4357" xml:space="preserve"/> </p> <div xml:id="echoid-div383" type="float" level="2" n="2"> <note position="right" xlink:label="note-147-03" xlink:href="note-147-03a" xml:space="preserve">Fig. B.</note> </div> <p> <s xml:id="echoid-s4358" xml:space="preserve">Toute la préciſion de cet Inſtrument conſiſte en ce que les pinu-<lb/>les ſoient bien exactement fenduës à angles droits; </s> <s xml:id="echoid-s4359" xml:space="preserve">ce que l'on con-<lb/>noîtra facilement en bornaïant un objet éloigné par deux pinules, <lb/>& </s> <s xml:id="echoid-s4360" xml:space="preserve">uu autre objet par les deux autres pinules. </s> <s xml:id="echoid-s4361" xml:space="preserve">Il faut enſuite tourner <lb/>l'Equerre bien juſte ſur ſon bâton, & </s> <s xml:id="echoid-s4362" xml:space="preserve">regarder les mêmes objets par <lb/>les pinules oppoſées; </s> <s xml:id="echoid-s4363" xml:space="preserve">s'ils ſe rencontrent bien exactement dans l'ali-<lb/>gnement des fentes, c'eſt une marque de la juſteſſe de l'inſtrument.</s> <s xml:id="echoid-s4364" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4365" xml:space="preserve">Pour éviter de fauſſer l'Equerre, il faut premierement enfoncer <lb/>en terre le bâton ſeul, & </s> <s xml:id="echoid-s4366" xml:space="preserve">quand il eſt bien affermi, placer ladite <lb/>Equerre ſur la virole par le moyen de ſa vis.</s> <s xml:id="echoid-s4367" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4368" xml:space="preserve">On fait auſſi de ces ſortes d'Equerres, où l'on met huit pinules de <lb/>la même maniere que celle décrite ci-deſſus; </s> <s xml:id="echoid-s4369" xml:space="preserve">elles ſervent pour avoir <lb/>lcs Angles de 45 degrez; </s> <s xml:id="echoid-s4370" xml:space="preserve">comme auſſi aux Jardiniers, pour aligner <lb/>& </s> <s xml:id="echoid-s4371" xml:space="preserve">planter les Allées d'Arbres en étoile.</s> <s xml:id="echoid-s4372" xml:space="preserve"/> </p> <pb o="134" file="148" n="148" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> </div> <div xml:id="echoid-div385" type="section" level="1" n="176"> <head xml:id="echoid-head267" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head268" style="it" xml:space="preserve">Pour lever le Plan & faire la meſure d'un Champ ou d'un <lb/>Pré dans lequel on peut entrer.</head> <p> <s xml:id="echoid-s4373" xml:space="preserve">SOit propoſé le champ A B C D E: </s> <s xml:id="echoid-s4374" xml:space="preserve">plantez à tous les angles des <lb/> <anchor type="note" xlink:label="note-148-01a" xlink:href="note-148-01"/> Piquets ou Jallons bien à plomb, meſurez exactement la ligne <lb/>A C, par parties, de la maniere que nous allons dire ci-après, ou <lb/>telle autre qu'il vous plaira, mais d'où l'on puiſſe découvrir tous les <lb/>piquets plantez aux angles.</s> <s xml:id="echoid-s4375" xml:space="preserve"/> </p> <div xml:id="echoid-div385" type="float" level="2" n="1"> <note position="left" xlink:label="note-148-01" xlink:href="note-148-01a" xml:space="preserve">Fig. 1.</note> </div> <p> <s xml:id="echoid-s4376" xml:space="preserve">Faites un broüillon oumémorial ſur une feüille de papier qui re-<lb/>preſente à peu près la figure du plan propoſé, ſur lequel vous écri-<lb/>rez toutes les meſures des parties de la ligne A C, & </s> <s xml:id="echoid-s4377" xml:space="preserve">des lignes per-<lb/>pendiculaires tirées des angles, à la rencontre de la ligne A C.</s> <s xml:id="echoid-s4378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4379" xml:space="preserve">Si, par exemple, vous commencez par le piquet A, cherchez le <lb/>long de la ligne A C le point F, ſur lequel tombe la perpendiculaire <lb/>E F, meſurez les lignes A F, F E, & </s> <s xml:id="echoid-s4380" xml:space="preserve">marquez leur longueur ſur les <lb/>lignes correſpondantes de vôtre mémorial.</s> <s xml:id="echoid-s4381" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4382" xml:space="preserve">Pour trouver ce point F plantez pluſieurs piquets à diſcretion le <lb/>long de la ligne A C; </s> <s xml:id="echoid-s4383" xml:space="preserve">plantez auſſi le pied de vôtre Equerre dans la <lb/>même ligne, en ſorte que par deux de ſes pinules opoſées, vous de-<lb/>couvriez deux de ces piquets, & </s> <s xml:id="echoid-s4384" xml:space="preserve">que par les fentes des deux autres <lb/>pinules, qui font angle droit avec les deux premiers, vous puiſſiez <lb/>voir le piquet E. </s> <s xml:id="echoid-s4385" xml:space="preserve">Que ſi du premier coup vous ne découvrez pas ce <lb/>piquet, aprochez ou reculez du point A le pied de l'Inſtrument juſ-<lb/>qu'à ce que les lignes bornaïées AF, E, faſſent angle droit au point F, <lb/>au moyen de quoi vous aurez le plan & </s> <s xml:id="echoid-s4386" xml:space="preserve">la ſurface du triangle AFE.</s> <s xml:id="echoid-s4387" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4388" xml:space="preserve">C'eſt de la même maniere que vous trouverez le point H où <lb/>tombe la perpendiculaire DH, laquelle vous meſurerez actuelle-<lb/>ment, auſſi-bien que GF, & </s> <s xml:id="echoid-s4389" xml:space="preserve">en marquerez les longueurs ſur vôtre <lb/>memorial afin d'avoir le plan & </s> <s xml:id="echoid-s4390" xml:space="preserve">la furface du trapeze E F H D.</s> <s xml:id="echoid-s4391" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4392" xml:space="preserve">Meſurez enſuite H C faiſant angle droit avec A D, vous aurez <lb/>le plan & </s> <s xml:id="echoid-s4393" xml:space="preserve">la ſurface du triangle D H C.</s> <s xml:id="echoid-s4394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4395" xml:space="preserve">Ayant ainſi meſuré toute la ligne H C, il ne s'agit plus que de <lb/>trouver ſur cette ligne le point G oú tombe la perpendiculiare BG, <lb/>& </s> <s xml:id="echoid-s4396" xml:space="preserve">de la meſurer afin d'avoir le plan & </s> <s xml:id="echoid-s4397" xml:space="preserve">la ſurface du triangle rectili-<lb/>gne A B C, au moyen de quoi vous aurez le plan du champ propoſé <lb/>A B C D E. </s> <s xml:id="echoid-s4398" xml:space="preserve">Vous aurez auſſi ſa ſurface totale en ajoûtant celles des <lb/>triangles & </s> <s xml:id="echoid-s4399" xml:space="preserve">trapezes qui en font les parties, & </s> <s xml:id="echoid-s4400" xml:space="preserve">qui ſe connoîtront fa-<lb/>cilement par les regles de la planimctrie, de la maniere qui ſuit.</s> <s xml:id="echoid-s4401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4402" xml:space="preserve">Suppoſons, par exemple, que A F ſoit de 7 toiſes, & </s> <s xml:id="echoid-s4403" xml:space="preserve">la perpen-<lb/> <pb o="135" file="149" n="149" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. II."/> diculaire EF de 10, multipliant 7 par 10, le produit eſt 70, dont <lb/>la moitié 35 ſera la ſurſace du triangle AFE.</s> <s xml:id="echoid-s4404" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4405" xml:space="preserve">Si de plus la ligne FH eſt de 14 toiſes, & </s> <s xml:id="echoid-s4406" xml:space="preserve">la perpendiculaire HD <lb/>de 12, ajoûtant 12 avec 10, que contient la parallele FE, on aura <lb/>22, dont la moitié 11 étant multipliée par 14, produit 154 toiſes <lb/>quarrées pour la ſurface du trapeze E F H D. </s> <s xml:id="echoid-s4407" xml:space="preserve">Et ſi la ligne HC eſt <lb/>de 8 toiſes, multipliant 8 par 12, le produit eſt 96, dont la moi-<lb/>tié 48 ſera la ſurface du triangle C H D.</s> <s xml:id="echoid-s4408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4409" xml:space="preserve">Toute la ligne entiere A C eſt de 29 toiſes, & </s> <s xml:id="echoid-s4410" xml:space="preserve">la perpendiculai-<lb/>re B G de 10; </s> <s xml:id="echoid-s4411" xml:space="preserve">le produit eſt 290, dont la moitié 145 eſt la ſurſa-<lb/>ce du triangle A B C. </s> <s xml:id="echoid-s4412" xml:space="preserve">Enſin ajoûtant les quatre ſurfaces partiales, <lb/>35, 154, 48 & </s> <s xml:id="echoid-s4413" xml:space="preserve">145, la ſomme 382 toiſes quarrées ſera la ſurface <lb/>totale du plan A B C D E, figure 1 de la planche 12.</s> <s xml:id="echoid-s4414" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div387" type="section" level="1" n="177"> <head xml:id="echoid-head269" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head270" style="it" xml:space="preserve">Pour lever le Plan d'un terrain dans lequel il n'eſt pas facile <lb/>d'entrer, comme pourroit être un Bois, un Etang, un <lb/>Marais, & autre choſe de cette nature.</head> <note position="right" xml:space="preserve">Fig. 2.</note> <p> <s xml:id="echoid-s4415" xml:space="preserve">SOit propoſé le Marais E F G H I: </s> <s xml:id="echoid-s4416" xml:space="preserve">plantez des piquets à tous les <lb/>angles, faites en ſorte de renfermer ſa figure dans un rectangle, <lb/>lequel vous meſurerez: </s> <s xml:id="echoid-s4417" xml:space="preserve">puis en ſouſtraïant les triangles & </s> <s xml:id="echoid-s4418" xml:space="preserve">trapezes <lb/>qui ſe trouverent ajoûtez autour de ſon plan, le reſte ſera la ſurface <lb/>du terrain propoſé.</s> <s xml:id="echoid-s4419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4420" xml:space="preserve">Si, par exemple, vous commencez par le piquet E, prolongez avec <lb/>vôtre Equerre la ligne E F, tant qu'il eſt beſoin, pour tracer ſur ſon <lb/>prolongement une perpendiculaire qui rencontre le piquet G, com-<lb/>me eſt ici la ligne K G; </s> <s xml:id="echoid-s4421" xml:space="preserve">plantez un piquet en K, & </s> <s xml:id="echoid-s4422" xml:space="preserve">prolongez cette li-<lb/>gne juſqu'en L, c'eſt-à-dire, tant qu'il ſera neceſſaire pour y tracer <lb/>une perpendiculaire qui paſſe par le point H, comme la ligne L H, <lb/>que vous prolongerez auſſi tant qu'il ſera beſoin; </s> <s xml:id="echoid-s4423" xml:space="preserve">retournez enſuite <lb/>au piquet E pour y tracer une autre perdiculaire ſur la ligne E F, <lb/>laquelle étant prolongée rencontrera au point M la perpendiculaire <lb/>LH, ce qui étant fait vous aurez le rectangle EMLK, dont vous <lb/>meſurerez les longueurs & </s> <s xml:id="echoid-s4424" xml:space="preserve">largeurs avec vôtre chaîne ou une toiſe.</s> <s xml:id="echoid-s4425" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4426" xml:space="preserve">Suppoſons pour exemple, que la longueur EK, ou ſa parallele M <lb/>L qui lui doit être égàle, ſoit de 34 toiſes, & </s> <s xml:id="echoid-s4427" xml:space="preserve">que la largeur EM ou <lb/>ſa parellele LK; </s> <s xml:id="echoid-s4428" xml:space="preserve">ſoit de 10 toiſes' multipliant ces deux nombres l'un <lb/>par l'autre, vous aurez 350 toiſes quarrées pour la ſurſace totale <lb/>dudit Rectangle.</s> <s xml:id="echoid-s4429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4430" xml:space="preserve">Mais ſi le prolongement FK eſt de 5 toiſes, & </s> <s xml:id="echoid-s4431" xml:space="preserve">K G de 4, multi-<lb/> <pb o="136" file="150" n="150" rhead="CONSTRUCTION ET USAGES DES INSTRUM."/> pliant 4 par 5 le produit eſt 20, dont la moitié 10 toiſes eſt la ſur-<lb/>face du triangle FKG. </s> <s xml:id="echoid-s4432" xml:space="preserve">La ligne GD, étant de 6 toiſes, & </s> <s xml:id="echoid-s4433" xml:space="preserve">LH de <lb/>quatre, le produit de 4 par 6 eſt 24, dont la moitié 12 eſt la ſurſace <lb/>du triangle GLH.</s> <s xml:id="echoid-s4434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4435" xml:space="preserve">Il faut enſuite trouver dans la ligne HM un point où tombe la <lb/>perpendiculaire qui part du piquet 1, laquelle formera un triangle <lb/>& </s> <s xml:id="echoid-s4436" xml:space="preserve">un trapeze: </s> <s xml:id="echoid-s4437" xml:space="preserve">de ſorte que ſi la diſtance HN eſt de 24 toiſes, & </s> <s xml:id="echoid-s4438" xml:space="preserve">la <lb/>perpendiculaire NI de 4 toiſes, le produit de 24 par 4 eſt 96, dont <lb/>la moitié 48 eſt la ſurface du triangle HNI. </s> <s xml:id="echoid-s4439" xml:space="preserve">Enſin NM étant de <lb/>7 toiſes, M E de 10, & </s> <s xml:id="echoid-s4440" xml:space="preserve">ſa parallele NI de 4 toiſes, ajoûtant 10 & </s> <s xml:id="echoid-s4441" xml:space="preserve"><lb/>4, la ſomme eſt 14, dont la moitié 7, multipliée par 7, fait 49 pour <lb/>la ſurface du trapeze E M N I.</s> <s xml:id="echoid-s4442" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4443" xml:space="preserve">C'eſt pourquoi ajoûtant enſemble les ſurſaces de ces trois trian-<lb/>gles & </s> <s xml:id="echoid-s4444" xml:space="preserve">celle du trapeze, on aura 119 toiſes, leſquelles étant ôtées <lb/>de 350, qui eſt la ſurſace totale du quarré long, reſtent 231 toiſes <lb/>pour la ſurface du Maris propoſé E F G H I. </s> <s xml:id="echoid-s4445" xml:space="preserve">On ſera la même <lb/>choſe de toute autre figure. </s> <s xml:id="echoid-s4446" xml:space="preserve">Ces deux Uſages font aſſez connoître <lb/>la maniere dont les Arpenteurs ſe ſervent de leur Inſtrumens pour <lb/>lever les Plans & </s> <s xml:id="echoid-s4447" xml:space="preserve">meſurer toutes ſortes de Pieces de Terre.</s> <s xml:id="echoid-s4448" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div388" type="section" level="1" n="178"> <head xml:id="echoid-head271" xml:space="preserve">CHAPITRE III.</head> <head xml:id="echoid-head272" style="it" xml:space="preserve">Contenant la conſtruction & uſages de differens Recipiangles.</head> <p> <s xml:id="echoid-s4449" xml:space="preserve">IL y a pluſieurs ſortes de Recipiangles ou Meſurangles, mais les <lb/> <anchor type="note" xlink:label="note-150-01a" xlink:href="note-150-01"/> meilleurs & </s> <s xml:id="echoid-s4450" xml:space="preserve">les plus en uſage ſont ceux dont nous allons faire la <lb/>deſcription.</s> <s xml:id="echoid-s4451" xml:space="preserve"/> </p> <div xml:id="echoid-div388" type="float" level="2" n="1"> <note position="left" xlink:label="note-150-01" xlink:href="note-150-01a" xml:space="preserve">XII. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s4452" xml:space="preserve">Le Recipiangle marqué A eſt compoſé de deux Regles parfaite-<lb/>ment égales en largeur: </s> <s xml:id="echoid-s4453" xml:space="preserve">car il faut que les côtez interieurs de chaque <lb/>Regle ſoient bien paralleles aux côtez exterieurs. </s> <s xml:id="echoid-s4454" xml:space="preserve">Leur largeur eſt <lb/>d'environ x pouce, & </s> <s xml:id="echoid-s4455" xml:space="preserve">leur longueur d'un pied ou plus. </s> <s xml:id="echoid-s4456" xml:space="preserve">Ces 2 Regles <lb/>ſont arrondies par la tête également, & </s> <s xml:id="echoid-s4457" xml:space="preserve">attachées l'une ſur l'autre <lb/>par le moyen d'un clou à tête artiſtement tourné, de ſorte que l'inſ-<lb/>trument ſe puiſſe ouvrir & </s> <s xml:id="echoid-s4458" xml:space="preserve">fermer facilement. </s> <s xml:id="echoid-s4459" xml:space="preserve">Lorſqu'on a pris l'ou-<lb/>verture d'un angle, on met le centre d'un rapporteur à l'endroit où <lb/>les 2 Regles ſejoignent, & </s> <s xml:id="echoid-s4460" xml:space="preserve">les degrez du bord marquent l'ouvertu-<lb/>re de l'angle, ou bien on trace ſur le papier l'ouverture que font les <lb/>Regles du Recipiangle, & </s> <s xml:id="echoid-s4461" xml:space="preserve">puis on la meſure avec un rapporteur.</s> <s xml:id="echoid-s4462" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4463" xml:space="preserve">Le Recipiangle marqué B eſt fait comme le precedent, excepté <lb/> <anchor type="note" xlink:label="note-150-02a" xlink:href="note-150-02"/> qu'il y a deux pointes d'acier aux extremitez, aſin qu'il puiſſe ſervir <lb/>de compas. </s> <s xml:id="echoid-s4464" xml:space="preserve">On le nomme ordinairement fauſſe Equerre.</s> <s xml:id="echoid-s4465" xml:space="preserve"/> </p> <div xml:id="echoid-div389" type="float" level="2" n="2"> <note position="left" xlink:label="note-150-02" xlink:href="note-150-02a" xml:space="preserve">Fig. B.</note> </div> <pb o="137" file="151" n="151" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. III."/> <p> <s xml:id="echoid-s4466" xml:space="preserve">Le Recipiangle marqué C eſt different des autres en ce qu'il <lb/> <anchor type="note" xlink:label="note-151-01a" xlink:href="note-151-01"/> marque l'ouverture des angles ſans rapporteur.</s> <s xml:id="echoid-s4467" xml:space="preserve"/> </p> <div xml:id="echoid-div390" type="float" level="2" n="3"> <note position="right" xlink:label="note-151-01" xlink:href="note-151-01a" xml:space="preserve">Fig. C.</note> </div> <p> <s xml:id="echoid-s4468" xml:space="preserve">Il eſt compoſé de deux regles de cuivre d'égale largeur & </s> <s xml:id="echoid-s4469" xml:space="preserve">bien <lb/>paralleles, longues de 2 pieds ou environ, larges de 2 ou 3 pouces & </s> <s xml:id="echoid-s4470" xml:space="preserve"><lb/>d'une ligne d'épaiſſeur jointes enſemble par un clou bien rond. </s> <s xml:id="echoid-s4471" xml:space="preserve">Il y <lb/>a de plus un cercle diviſé en 360 degrez au bout d'une des regles & </s> <s xml:id="echoid-s4472" xml:space="preserve"><lb/>un petit index attaché fortement au clou, lequel à meſure que l'on <lb/>ouvre ou ferme l'inſtrument, marque les degrez de ſon ouverture. <lb/></s> <s xml:id="echoid-s4473" xml:space="preserve">Nous nerepetons pas ici la maniere de diviſer le cercle, l'ayant ex-<lb/>pliquée ſuffiſamment en parlant du rapporteur. </s> <s xml:id="echoid-s4474" xml:space="preserve">On dira ſeulement <lb/>qu'on commence toûjours à compter les degrez du milieu de la re-<lb/>gle où eſt le centre.</s> <s xml:id="echoid-s4475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4476" xml:space="preserve">On fait encore de cette ſorte de Recipiangle en diviſant un cer-<lb/>cle ſur la regle inferieure, & </s> <s xml:id="echoid-s4477" xml:space="preserve">l'on lime la regle de deſſus comme la <lb/>tête d'un compas de proportion, de ſorte qu'en ouvrant l'inſtru-<lb/>ment les deux épaulieres marquent les degrez de ſon ouverture.</s> <s xml:id="echoid-s4478" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4479" xml:space="preserve">Pour meſurer un angle ſaillant avec quelqu'un de ccs trois Re-<lb/>cipiangles, on applique les côtez interieurs des deux regles ſur les <lb/>lignes qui ſorment l'angle. </s> <s xml:id="echoid-s4480" xml:space="preserve">Et pour meſurer un angle rentrant, on <lb/>applique les côtez exterieurs des mêmes regles le long des lignes <lb/>qui forment ledit angle.</s> <s xml:id="echoid-s4481" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4482" xml:space="preserve">Le Recipiangle marqué D eſt compoſé de quatre regles de cui-<lb/> <anchor type="note" xlink:label="note-151-02a" xlink:href="note-151-02"/> vre, de largeur parſaitement égale, jointes enſemble par quatre clous <lb/>ronds à tête tournée, leſquelles ſorment un parallelogramme équi-<lb/>lateral. </s> <s xml:id="echoid-s4483" xml:space="preserve">Au bout de l'une deſdites regles il y a un demi cercle de 3 à <lb/>4 pouces de diametre, diviſé en 180 degrez, & </s> <s xml:id="echoid-s4484" xml:space="preserve">même en demis, ſi <lb/>l'on veut, & </s> <s xml:id="echoid-s4485" xml:space="preserve">c'eſt ce qui doit faire preferer ce Recipiangle aux au-<lb/>tres. </s> <s xml:id="echoid-s4486" xml:space="preserve">L'autre branche qui paſſe ſur le demi-cercle eſt prolongée juſ-<lb/>ques ſur la diviſion, afin d'y marquer l'ouverture des angles.</s> <s xml:id="echoid-s4487" xml:space="preserve"/> </p> <div xml:id="echoid-div391" type="float" level="2" n="4"> <note position="right" xlink:label="note-151-02" xlink:href="note-151-02a" xml:space="preserve">Fig. D.</note> </div> <p> <s xml:id="echoid-s4488" xml:space="preserve">Ces Regles ſe font d'un pied ou deux de longueur, de 8 ou 10 li-<lb/>gnes de largeur & </s> <s xml:id="echoid-s4489" xml:space="preserve">d'épaiſſeur convenable. </s> <s xml:id="echoid-s4490" xml:space="preserve">Elles doivent être percées <lb/>très-également en longueur, ſçavoir celle où eſt le demi-cercle au <lb/>point 2, où eſt ſon centre, & </s> <s xml:id="echoid-s4491" xml:space="preserve">à l'autre bout au point marqué 1. </s> <s xml:id="echoid-s4492" xml:space="preserve">Celle <lb/>qui ſert d'alidade doit être percée aux points marquez 2 & </s> <s xml:id="echoid-s4493" xml:space="preserve">3, & </s> <s xml:id="echoid-s4494" xml:space="preserve">en-<lb/>fin les deux autres regles, chacune à leurs extremitez, au point mar-<lb/>qué 4. </s> <s xml:id="echoid-s4495" xml:space="preserve">La regle qui ſert d'alidade doit être attachée au centre & </s> <s xml:id="echoid-s4496" xml:space="preserve"><lb/>deſſus le demi-cercle; </s> <s xml:id="echoid-s4497" xml:space="preserve">les deux autres Regles, qui ſont d'une même <lb/>longueur, doivent être attachées par deſſous les deux autres; </s> <s xml:id="echoid-s4498" xml:space="preserve">le tout <lb/>de maniere que leur mouvement ſoit bien uniforme.</s> <s xml:id="echoid-s4499" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4500" xml:space="preserve">Quand on veut meſurer un angle ſaillant avec ce Recipiangle, <lb/> <pb o="138" file="152" n="152" rhead="CONSTRUCTION ET USAGES DES RECIPIANG."/> on fait paſſer les deux Regles égales par deſſous les deux autres, <lb/>afin que les quatre Regles n'en faſſent que deux, pour embraſſer <lb/>l'angle; </s> <s xml:id="echoid-s4501" xml:space="preserve">mais quand on veut meſurer un angle rentrant, on retire <lb/>ces deux Regles en dehors, comme elles ſont à preſent, & </s> <s xml:id="echoid-s4502" xml:space="preserve">on les <lb/>applique dans l'enfoncement de l'angle; </s> <s xml:id="echoid-s4503" xml:space="preserve">& </s> <s xml:id="echoid-s4504" xml:space="preserve">comme en tout paral-<lb/>lelogramme les angles oppoſez ſont égaux, on en connoît l'ou-<lb/>verture par les degrez du demi-cercle oppoſé.</s> <s xml:id="echoid-s4505" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div393" type="section" level="1" n="179"> <head xml:id="echoid-head273" style="it" xml:space="preserve">Uſage du Recipiangle.</head> <p> <s xml:id="echoid-s4506" xml:space="preserve">POur lever le plan d'un Baſtion, comme par exemple de celui <lb/>cotté ABCDE, tracez un broüillon ſur une feüille de papier, <lb/>meſurez avec le Recipiangle rentrant l'angle E, formé d'une courti-<lb/>ne de la place & </s> <s xml:id="echoid-s4507" xml:space="preserve">du flanc du Baſtion propoſé, en l'appliquant hori-<lb/> <anchor type="note" xlink:label="note-152-01a" xlink:href="note-152-01"/> zontalement, de ſorte qu'une des regles ſoit dans l'alignement de <lb/>ladite courtine, & </s> <s xml:id="echoid-s4508" xml:space="preserve">l'autre regle dans l'alignement du flanc; </s> <s xml:id="echoid-s4509" xml:space="preserve">& </s> <s xml:id="echoid-s4510" xml:space="preserve">ayant <lb/>reconnu ſa valeur en degrez, marquez-la ſur vôtre memorial dans <lb/>un petit are, pour faire connoître que c'eſt la cotte d'un angle. </s> <s xml:id="echoid-s4511" xml:space="preserve">Faites <lb/>enſuite meſurer la longueur du flanc ED, que vous marquerez le <lb/>long de la ligne e d, de vôtre broüillon; </s> <s xml:id="echoid-s4512" xml:space="preserve">embraſſez avec les regles de <lb/>vôtre Recipiangle l'angle ſaillant D, de l'épaule, & </s> <s xml:id="echoid-s4513" xml:space="preserve">cottez ſa valeur <lb/>dans un petit arc; </s> <s xml:id="echoid-s4514" xml:space="preserve">ſaites meſurer la longueur de la face gauche CD; <lb/></s> <s xml:id="echoid-s4515" xml:space="preserve">meſurezavec le Recipiangle l'ouverture de l'angle flan qué C, & </s> <s xml:id="echoid-s4516" xml:space="preserve">en-<lb/>fuite celle des autres angles du Baſtion, de même que la longueur de <lb/>ſes faces & </s> <s xml:id="echoid-s4517" xml:space="preserve">flances; </s> <s xml:id="echoid-s4518" xml:space="preserve">après quoi il ſera facile de le remettre au net par <lb/>le moyen d'une échelle de parties égales & </s> <s xml:id="echoid-s4519" xml:space="preserve">d'un rapporteur.</s> <s xml:id="echoid-s4520" xml:space="preserve"/> </p> <div xml:id="echoid-div393" type="float" level="2" n="1"> <note position="left" xlink:label="note-152-01" xlink:href="note-152-01a" xml:space="preserve">Fig. 1.</note> </div> <p> <s xml:id="echoid-s4521" xml:space="preserve">Mais comme il ſe rencontre ſouvent que les angles, qui d'ordi-<lb/>naire ſont de pierre de taille, ont été mal taillez par la negligence <lb/>des Ouvriers, qui les font ou trop aigus ou trop obtus, pour y re-<lb/>medier on applique une longue regle ſur chaque mur, dont l'ali-<lb/>gnemet peut être bon, quoique l'angle ſoit mauvais, & </s> <s xml:id="echoid-s4522" xml:space="preserve">poſant <lb/>de niveau ſur ces deux regles les jambes du Recipiangle, on aura <lb/>plus exactement l'ouverture de l'angle à meſurer.</s> <s xml:id="echoid-s4523" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div395" type="section" level="1" n="180"> <head xml:id="echoid-head274" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head275" style="it" xml:space="preserve">Lever le Plan d'un terrain dont l'enceinte ſoit de figure rectiligne.</head> <p> <s xml:id="echoid-s4524" xml:space="preserve">SOit propoſé le plan ABCDEFG. </s> <s xml:id="echoid-s4525" xml:space="preserve">Il faut d'abord en deſſiner la <lb/>figure à vûë ſur un memorial, meſurer exactement ſur le terrain <lb/>la longueur de tous les côtez, & </s> <s xml:id="echoid-s4526" xml:space="preserve">les marquer à meſure ſur les lignes <lb/> <anchor type="note" xlink:label="note-152-02a" xlink:href="note-152-02"/> relatives du memorial; </s> <s xml:id="echoid-s4527" xml:space="preserve">prenez enſuite avec tel Recipiangle que <lb/>vous voudrez choiſir l'ouverture de chaque angle, comme par ex-<lb/> <pb o="139" file="153" n="153" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. IV."/> emple de l'angle ſaillant AGF, l'enſermant avec les jambes du Re-<lb/>cipiangle, & </s> <s xml:id="echoid-s4528" xml:space="preserve">marquez les degrez de ſon ouverture ſur l'angle relatif <lb/>a g f du memorial; </s> <s xml:id="echoid-s4529" xml:space="preserve">meſurez auſſi l'angle rentrant FED, en mettant <lb/>la tête du Recipiangle dans le fond de cet angle, en ſorte que l'exte-<lb/>terieur des branches joigne exactement les côtez du terrain qui for-<lb/>ment l'angle, & </s> <s xml:id="echoid-s4530" xml:space="preserve">marquez-en la valeur ſur l'angle relatif du memo-<lb/>rial, & </s> <s xml:id="echoid-s4531" xml:space="preserve">ainſi de tous les autres angles, dont ayant marqué les degrez, <lb/>auſſi-bien que la longueur de toutes les lignes meſurées ſur le ter-<lb/>rain, on le remettra au net, & </s> <s xml:id="echoid-s4532" xml:space="preserve">par ce moyen on aura le plan ſem-<lb/>blable a b c d e f g. </s> <s xml:id="echoid-s4533" xml:space="preserve">Figure 2.</s> <s xml:id="echoid-s4534" xml:space="preserve"/> </p> <div xml:id="echoid-div395" type="float" level="2" n="1"> <note position="left" xlink:label="note-152-02" xlink:href="note-152-02a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s4535" xml:space="preserve">Sur la même planche on verra le plan d'un Pentagone regulier <lb/>fortiſié avec les noms des parties de ſa fortification.</s> <s xml:id="echoid-s4536" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div397" type="section" level="1" n="181"> <head xml:id="echoid-head276" xml:space="preserve">CHAPITRE IV.</head> <head xml:id="echoid-head277" style="it" xml:space="preserve">Contenant la conſtruction & l'uſage de la Planchete.</head> <p> <s xml:id="echoid-s4537" xml:space="preserve">CEt Inſtrument ſe fait de bois, de cuivre ou de toute autre ma-<lb/> <anchor type="note" xlink:label="note-153-01a" xlink:href="note-153-01"/> tiere ſolide. </s> <s xml:id="echoid-s4538" xml:space="preserve">Sa figure la plus ordinaire eſt la circulaire. </s> <s xml:id="echoid-s4539" xml:space="preserve">On lui <lb/>donne environ un pied de diametre. </s> <s xml:id="echoid-s4540" xml:space="preserve">En ſon centre il y a un petit cy-<lb/>lindre de cuivre élevé à plomb qui ſert de clou, autour duquel tour-<lb/>ne une regle ou alidade garnie de deux pinnules ou d'une lunete. <lb/></s> <s xml:id="echoid-s4541" xml:space="preserve">Cette regle doit avoir une ligne droite appellée Ligne de foi, qui ré-<lb/>ponde exactement au centre du clou, dont le haut doit être tour-<lb/>né en vis pour y recevoir un écrou qui ſerre la regle, à laquelle on <lb/>attache une petite bouſſole pour orienter les places.</s> <s xml:id="echoid-s4542" xml:space="preserve"/> </p> <div xml:id="echoid-div397" type="float" level="2" n="1"> <note position="right" xlink:label="note-153-01" xlink:href="note-153-01a" xml:space="preserve">XIII. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s4543" xml:space="preserve">Autour de la Planchete il y a un cercle d'une épaiſſeur à contenir <lb/>environ ſix cartons, & </s> <s xml:id="echoid-s4544" xml:space="preserve">d'une largeur convenable à recevoir les di-<lb/>viſions de 363 degrez, & </s> <s xml:id="echoid-s4545" xml:space="preserve">quelquefois les minutes de 5 en 5.</s> <s xml:id="echoid-s4546" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4547" xml:space="preserve">Il faut avoir pluſieurs cartons de la grandeur de la Planchete per <lb/>cez dans le milieu, d'un trou égal à la groſſeur du pivot, de ſorte <lb/>qu'on puiſſe enſiler tous ces cartons, & </s> <s xml:id="echoid-s4548" xml:space="preserve">mettre la regle par deſſus. </s> <s xml:id="echoid-s4549" xml:space="preserve">Il <lb/>faut auſſi que l'on puiſſe arrêter le carton de deſſus par le moyen <lb/>d'une petite pointe attachée au bord de la Planchete, & </s> <s xml:id="echoid-s4550" xml:space="preserve">qui entre <lb/>un peu dans le carton. </s> <s xml:id="echoid-s4551" xml:space="preserve">On marque ordinairemnt ſur chacun de ces <lb/>cartons un raïon ou demi-diametre à l'encre pour ſervir de ligne <lb/>de ſtation.</s> <s xml:id="echoid-s4552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4553" xml:space="preserve">Au-deſſous de la Planchete on attache un genoüil, comme celui <lb/>marqué D. </s> <s xml:id="echoid-s4554" xml:space="preserve">Il eſt compoſé d'une boule de cuivre renfermée entre <lb/>deux, coquilles de même métal, que l'on ſerre plus ou moins parle <lb/>moyend'une vis. </s> <s xml:id="echoid-s4555" xml:space="preserve">La tige de ce genoüil, qui eſt une virole, s'emboëte <lb/> <pb o="140" file="154" n="154" rhead="CONSTRUCT. ET USAGES DE LA PLANCHETE"/> autour d'un pied à trois branches, qui s'écartent & </s> <s xml:id="echoid-s4556" xml:space="preserve">ſe reſſerrent <lb/>ſuivant l'înégalité du terrain.</s> <s xml:id="echoid-s4557" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4558" xml:space="preserve">La figure A de la planche 14 repreſente l'inſtrument tout monté. <lb/></s> <s xml:id="echoid-s4559" xml:space="preserve">Nous allons donner la conſtruction des pieces qui le compoſent, en <lb/>commençant par la diviſion de ſon bord ou limbe.</s> <s xml:id="echoid-s4560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4561" xml:space="preserve">On y trace premierement 2 ou 3 circonferences pour y marquer <lb/>les degrez avec les chifres de 10 en 10. </s> <s xml:id="echoid-s4562" xml:space="preserve">On diviſe d'abord une de ces <lb/>circonferences en 4 parties bien égales, dont chacune eſt de 90 de-<lb/>grez, que l'on diviſeen 4, & </s> <s xml:id="echoid-s4563" xml:space="preserve">chacune encore en 3, & </s> <s xml:id="echoid-s4564" xml:space="preserve">par ce moyen <lb/>le cercle ſe trouve diviſé de 10 en 10 degrez. </s> <s xml:id="echoid-s4565" xml:space="preserve">On ſubdiviſe ces parties <lb/>en 2, & </s> <s xml:id="echoid-s4566" xml:space="preserve">enfin chacune en 5, & </s> <s xml:id="echoid-s4567" xml:space="preserve">toutle cercle ſe trouve diviſéen 360 <lb/>degrez. </s> <s xml:id="echoid-s4568" xml:space="preserve">On trace avec une regle à centre les lignes de ces diviſions <lb/>dans les circonferences qui leur conviennent, puis on y marque les <lb/>chifres de 10 en 10, en commençant par la ligne de foide l'inſtru-<lb/>ment, qui eſt celle où l'on attache les 2 pinnules fixes ou la lunete.</s> <s xml:id="echoid-s4569" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4570" xml:space="preserve">Une Planchete ainſi diviſée eſt d'un uſage plus étendu que les <lb/>ſimples Planchetes dont le limbe n'eſt pas diviſé, car elle peut ſer-<lb/>vir pour lever exactement les plans & </s> <s xml:id="echoid-s4571" xml:space="preserve">meſurer les diſtances inac-<lb/>ceſſibles, par la trigonométrie.</s> <s xml:id="echoid-s4572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4573" xml:space="preserve">Les figures marquées B repreſentent les pinnules qui ſe placent <lb/>ſur les differens inſtrumens. </s> <s xml:id="echoid-s4574" xml:space="preserve">Celle de laquelle on aproche l'œil a une <lb/>fente longue & </s> <s xml:id="echoid-s4575" xml:space="preserve">étroite, qui doit être bien perpendiculairement fen-<lb/>duë avec une ſcie mince, & </s> <s xml:id="echoid-s4576" xml:space="preserve">celle qui eſt tournée vers l'objet, a une <lb/>ouverture quarrée aſſez large, afin de donner un grand champ pour <lb/>apercevoir les environs de l'objet, & </s> <s xml:id="echoid-s4577" xml:space="preserve">au milieu de cette ouverture il <lb/>y a un filet de cuivre très-délié & </s> <s xml:id="echoid-s4578" xml:space="preserve">limé bien droit, afin de couper <lb/>verticalement l'objet & </s> <s xml:id="echoid-s4579" xml:space="preserve">répondre juſte à la fente de l'autre pinnule; <lb/></s> <s xml:id="echoid-s4580" xml:space="preserve">mais afin que l'on puiſſe indifferemment approcher l'œil de telle <lb/>pinnule que l'on veut, afin d'obſerver auſſi-bien d'un côté que de <lb/>l'autre avec l'inſtrument ſur lequel elle eſt poſée, on fait à chaque <lb/>pinnule une fente étroite & </s> <s xml:id="echoid-s4581" xml:space="preserve">un ſilet délicat, l'une au-deſſus & </s> <s xml:id="echoid-s4582" xml:space="preserve">l'au-<lb/>tre au-deſſous, comme les petites ſigures le montrent. </s> <s xml:id="echoid-s4583" xml:space="preserve">On fait auſſi <lb/>le plus ſouvent un petit trou entre le filet & </s> <s xml:id="echoid-s4584" xml:space="preserve">la fente. </s> <s xml:id="echoid-s4585" xml:space="preserve">Ces pinnules <lb/>doivent être exactement poſées aux extremitez & </s> <s xml:id="echoid-s4586" xml:space="preserve">dans la ligne de <lb/>ſoi auſſi-bien des inſtrumens que des alidades; </s> <s xml:id="echoid-s4587" xml:space="preserve">on les y attache, ſoit <lb/>dans des petits quarrez avec un écrou au-deſſous, ou bien par le <lb/>moyen de vis, ſuivant que la place le requiert.</s> <s xml:id="echoid-s4588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4589" xml:space="preserve">La petite figure marquée C repreſente le cilindre qui ſert de clou <lb/>avec ſon écrou pour joindre l'alidade à la Planchete: </s> <s xml:id="echoid-s4590" xml:space="preserve">ceux des demi-<lb/>cercles & </s> <s xml:id="echoid-s4591" xml:space="preserve">autres inſtrumens ſont ſaits à peu près de la même manie-<lb/>re, excepté qu'on les rive par deſſous.</s> <s xml:id="echoid-s4592" xml:space="preserve"/> </p> <pb o="141" file="155" n="155" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. IV."/> <p> <s xml:id="echoid-s4593" xml:space="preserve">La figure marquée D repreſente le genouil pour porter les inſtru-<lb/>mens. </s> <s xml:id="echoid-s4594" xml:space="preserve">Il eſt compoſé d'une boule de cuivre renfermée entré 2 co-<lb/>quilles de mëme mètal, qui ſont fraiſées, bien rondes, avec des bou-<lb/>les d'acier trempées & </s> <s xml:id="echoid-s4595" xml:space="preserve">taillées en maniere de lime; </s> <s xml:id="echoid-s4596" xml:space="preserve">ces coquilles ſont <lb/>ſerrées plus ou moins par le moyen d'une vis, & </s> <s xml:id="echoid-s4597" xml:space="preserve">preſſent auſſi par ce <lb/>moyen la boule qui eſt renfermée entre les 2 coquilles, & </s> <s xml:id="echoid-s4598" xml:space="preserve">dont une <lb/>eſt ſoudée à une virole tournée dans laquelle s'emboëte le pied de <lb/>l'inſtrument; </s> <s xml:id="echoid-s4599" xml:space="preserve">ce genoüil ſe ſait de differente groſſeur, ſuivant la <lb/>grandeur des inſtrumens; </s> <s xml:id="echoid-s4600" xml:space="preserve">& </s> <s xml:id="echoid-s4601" xml:space="preserve">on les y attache avec des vis & </s> <s xml:id="echoid-s4602" xml:space="preserve">une <lb/>plaque qui eſt rivée au haut de la boule.</s> <s xml:id="echoid-s4603" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div399" type="section" level="1" n="182"> <head xml:id="echoid-head278" style="it" xml:space="preserve">Conſtruction des pieds à poſer les Inſtrumens en campagne.</head> <p> <s xml:id="echoid-s4604" xml:space="preserve">NOus avons parlé du pied ſimple pour porter les Equerres d'Ar-<lb/>penteur; </s> <s xml:id="echoid-s4605" xml:space="preserve">ceux dont nous allons donner la deſcription ſont <lb/>faits pour n'être pas enſoncez en terre, mais s'étendre ou reſſerrer <lb/>ſelon que l'inégalité du terrain le requiert.</s> <s xml:id="echoid-s4606" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4607" xml:space="preserve">Le pied marqué E eſt compoſé d'une platine en triangle qui por-<lb/>te dans ſon milieu une tige qui entre dans la virole du genoüil.</s> <s xml:id="echoid-s4608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4609" xml:space="preserve">Au-deſſous de la platine ſont attachées trois viroles ou douilles à <lb/>charniere, comme des têtes de compas pour recevoir les troisbâtons <lb/>ronds, d'une longueur convenable pour que l'œil de l'Obſervateur <lb/>ſoit environ vis-a-vis des pinnules de l'inſtrument, quand il eſt <lb/>monté; </s> <s xml:id="echoid-s4610" xml:space="preserve">les extremitez de ces bâtons ſont garnies d'une virole & </s> <s xml:id="echoid-s4611" xml:space="preserve"><lb/>d'une pointe de fer, afin de tenir ferme ſur la terre & </s> <s xml:id="echoid-s4612" xml:space="preserve">de reſiſter au <lb/>mouvement que l'on donne aux Inſtrumens quand on les veut <lb/>tourner, élever ou abaiſſer.</s> <s xml:id="echoid-s4613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4614" xml:space="preserve">Le pied marqué F eſt fait de 4 bâtons de chêne ou de noïer d'en-<lb/>viron 2 pieds de long, & </s> <s xml:id="echoid-s4615" xml:space="preserve">dont celui du milieu, que l'on nommetige, <lb/>a ſon extremité arrondie pour entrer dans la virole du genoüil. </s> <s xml:id="echoid-s4616" xml:space="preserve">Le <lb/>reſte de ce bâton eſt taillé en figure triangulaire, afin de recevoir fur <lb/>ſes 3 faces les 3 autres bâtons qui y ſont attachez par le moyen d'u-<lb/>ne vis en 3 qui eſt attachée au bâton triangulaire, & </s> <s xml:id="echoid-s4617" xml:space="preserve">de 3 écrous <lb/>pour le tenir ferme quand on l'ouvre, & </s> <s xml:id="echoid-s4618" xml:space="preserve">s'en ſervir en campagne. <lb/></s> <s xml:id="echoid-s4619" xml:space="preserve">Ces 3 bâtons ſont garnis d'une virole & </s> <s xml:id="echoid-s4620" xml:space="preserve">d'une pointe de fer & </s> <s xml:id="echoid-s4621" xml:space="preserve">ſont <lb/>plats en dedans, & </s> <s xml:id="echoid-s4622" xml:space="preserve">à 3 faces en dehors.</s> <s xml:id="echoid-s4623" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4624" xml:space="preserve">Quand on veut porter ce pied on réunit tous les bâtons enſemble, <lb/>de ſorte qu'ils n'en font qu'un, & </s> <s xml:id="echoid-s4625" xml:space="preserve">ſont par ce moyen plus courts <lb/>d'environ la moitié que quand on s'en ſert.</s> <s xml:id="echoid-s4626" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4627" xml:space="preserve">A l'un & </s> <s xml:id="echoid-s4628" xml:space="preserve">à l'autre de ces pieds on acroche au milieu un ſil avec <lb/>ſon plomb qui tomde ſur le terrain, pour marquer le point de ſtation.</s> <s xml:id="echoid-s4629" xml:space="preserve"/> </p> <pb o="142" file="156" n="156" rhead="CONSTRUCT. ET USAGES DE LA PLANCHETE"/> </div> <div xml:id="echoid-div400" type="section" level="1" n="183"> <head xml:id="echoid-head279" style="it" xml:space="preserve">Vſage de la Planchete.</head> <p> <s xml:id="echoid-s4630" xml:space="preserve">POur lever la carte d'un Païs, choiſiſſez deux endroits éminens <lb/>comme ſont, par exemple, l'Obſervatoire & </s> <s xml:id="echoid-s4631" xml:space="preserve">la Salpetriere d'où <lb/>l'on puiſſe découvrir le Païs proche de Paris, dont on veut ſaire la <lb/>Carte; </s> <s xml:id="echoid-s4632" xml:space="preserve">marquez autour du centre d'un de vos cartons le nom du <lb/> <anchor type="note" xlink:label="note-156-01a" xlink:href="note-156-01"/> lieu où vous prétendez faire cette premiere ſtation, & </s> <s xml:id="echoid-s4633" xml:space="preserve">ce carton é-<lb/>tant arrêté par la point qui eſt au bord de la Planchete, mettez la <lb/>regle par deſſus en la ſerrant ſuffiſamment par le moyen de la vis & </s> <s xml:id="echoid-s4634" xml:space="preserve"><lb/>de ſon écrou.</s> <s xml:id="echoid-s4635" xml:space="preserve"/> </p> <div xml:id="echoid-div400" type="float" level="2" n="1"> <note position="left" xlink:label="note-156-01" xlink:href="note-156-01a" xml:space="preserve">Fig. I.</note> </div> <p> <s xml:id="echoid-s4636" xml:space="preserve">Poſez la Planchete ſur ſon pied en lui donnant une ſituation à peu <lb/>près horiſontale, en ſorte qu'elle demeure ferme quoiqu'on tourne <lb/>l'alidade, & </s> <s xml:id="echoid-s4637" xml:space="preserve">la ſuppoſant plantée à l'Obſervatoire, mirez par les <lb/>pinnules de la regle le clocher de la Salpetriere, & </s> <s xml:id="echoid-s4638" xml:space="preserve">marquez le long <lb/>de la ligne de foi depuis le centre, la ligne de ſtation.</s> <s xml:id="echoid-s4639" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4640" xml:space="preserve">Tournez enſuite la regle alidade, pour obſerver par ſes pinnules <lb/>quelque objet remarquable, comme par exemple, le clocher de <lb/>Vaugirard, vers lequel il faut tracer une ligne ſur le carton au long <lb/>du côté de la regle qui répond au centre de l'inſtrument, & </s> <s xml:id="echoid-s4641" xml:space="preserve">écrire <lb/>le long de cette ligne le nom du lieu où vous avez miré.</s> <s xml:id="echoid-s4642" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4643" xml:space="preserve">Tournez encore la regle vers un autre objet, comme vers Mont-<lb/>rouge, & </s> <s xml:id="echoid-s4644" xml:space="preserve">faites la même choſe vers tous les autres Lieux conſi-<lb/>derables que l'on peut appercevoir de l'Obſervatoire.</s> <s xml:id="echoid-s4645" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4646" xml:space="preserve">Levez la Planchete de la premiere ſtation ayant bien remarqué <lb/>ſa place, & </s> <s xml:id="echoid-s4647" xml:space="preserve">la tranſportez au lieu déſigne, comme à la Salpetiere <lb/>faites meſurer exactement la diſtance entre les deux ſtations ſur un <lb/>terrain de niveau, dont vous marquerez le nombre des toiſes ſur <lb/>vôtre carton, lequel vous tournerez pour en avoir un blanc ſous la <lb/>regle, car il en faut changer autant de fois que l'on fait de ſtations <lb/>differentes pour obſerver les angles de poſition des lieux. </s> <s xml:id="echoid-s4648" xml:space="preserve">Marquez <lb/>autour du centre de ce nouveau carton le nom du lieu de la ſecon-<lb/>de ſtation & </s> <s xml:id="echoid-s4649" xml:space="preserve">ſur la ligne de baſe, le nombre des toiſes meſurées, <lb/>afin de vous ſouvenir que cette ligne eſt la même que celle du pre-<lb/>cedent carton. </s> <s xml:id="echoid-s4650" xml:space="preserve">La Planchete étant placée en ce lieu, diſpoſez la <lb/>de maniere qu'en mettant la ligne de foi de la regle ſur la ligne de <lb/>ſtation, vous découvriez par ſes pinnules le lieu de l'Obſervatoire <lb/>où s'eſt faite la premiere ſtation.</s> <s xml:id="echoid-s4651" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4652" xml:space="preserve">L'Inſtrument demeurant ferme en cette ſituation, tournez la <lb/>regle pour mirer l'un après l'autre les mêmes objets qui ont été vûs <lb/>de l'Obſervatoire, & </s> <s xml:id="echoid-s4653" xml:space="preserve">tracez de même ſur le carton des lignes le <lb/> <pb o="143" file="157" n="157" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. V."/> long de la regle, depuis le centre vers les lieux que vous pourrez <lb/>voir, en écrivant leur nom ſur chaque ligne quileur correſpond.</s> <s xml:id="echoid-s4654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4655" xml:space="preserve">Si l'on ne peut voir tous les lieux que l'on veut placer ſur la car-<lb/>te, des deux ſtations precedentes, il faudra choiſir quelque autre <lb/>lieu d'où l'on puiſſe les obſerver & </s> <s xml:id="echoid-s4656" xml:space="preserve">faire autant de nouvelles ſta-<lb/>tions qu'il ſera neceſſaire pour voir chaque objet remarquable de <lb/>deux endroits ſuffiſamment éloignez l'un de l'autre.</s> <s xml:id="echoid-s4657" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4658" xml:space="preserve">Pour repreſenter cette carte ſur une feüille de papier, tracez-y <lb/>une ligne droite longue à volonté, pour ſervir de baſe commune, & </s> <s xml:id="echoid-s4659" xml:space="preserve"><lb/>la diviſez en autant de parties égales que vous avez meſuré de toi-<lb/>ſes ſur le terrain: </s> <s xml:id="echoid-s4660" xml:space="preserve">d'une extremité de la ligne comme centre, décrivez <lb/>des arc de cercle égaux à ceux qui ont été tracez ſur le premier <lb/>carton; </s> <s xml:id="echoid-s4661" xml:space="preserve">de l'autre extremité décrivez des arcs de cercle égaux à <lb/>ceux qui ont été tracez ſur le ſecond carton, & </s> <s xml:id="echoid-s4662" xml:space="preserve">prolongez leslignes <lb/>juſqu'à ce qu'elles ſe rencontrent; </s> <s xml:id="echoid-s4663" xml:space="preserve">les points où ces lignes ſe coupe-<lb/>ront ſeront les points de poſition des lieux qui auront été obſervez.</s> <s xml:id="echoid-s4664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4665" xml:space="preserve">On peut encore rapporter les ſtations plus facilement en poſant <lb/>le centre du carton ſur le point, & </s> <s xml:id="echoid-s4666" xml:space="preserve">marquer ſur le papier les extre-<lb/>mitez des lignes du carton & </s> <s xml:id="echoid-s4667" xml:space="preserve">tirer des lignes depuis leurs ſtations.</s> <s xml:id="echoid-s4668" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4669" xml:space="preserve">Par le moyen de cette Planchete on a tous les angles de poſition <lb/>des lieux où l'on peut pointer les pinnules ou lunetes, par rapport <lb/>aux lieux où l'on a placé l'inſtrument, quand même on ne connoî-<lb/>troit pas leur valeur en degrez.</s> <s xml:id="echoid-s4670" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4671" xml:space="preserve">Ce que nous venons de dire eſt ſuffiſant pour l'uſage de la Plan-<lb/>chete par rapport aux poſitions des lieux, pour la conſtruction des <lb/>Cartes de Géographie, parce que les operations ſont les mêmes pour <lb/>tous les differens endroits; </s> <s xml:id="echoid-s4672" xml:space="preserve">à l'égard de ſes uſages, par rapport à la <lb/>Trigonométrie, ce ſont les mêmes que ceux du demi-cercle & </s> <s xml:id="echoid-s4673" xml:space="preserve">du <lb/>quart de cercle dont nous allons parler.</s> <s xml:id="echoid-s4674" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div402" type="section" level="1" n="184"> <head xml:id="echoid-head280" xml:space="preserve">CHAPITRE V.</head> <head xml:id="echoid-head281" style="it" xml:space="preserve">Contenant la conſtruction & les uſages du quart de Cercle <lb/>& du quarré géométrique.</head> <p> <s xml:id="echoid-s4675" xml:space="preserve">LA figure marquée G, repreſente un quart de cercle & </s> <s xml:id="echoid-s4676" xml:space="preserve">un quarré <lb/>géométrique avec ſon alidade & </s> <s xml:id="echoid-s4677" xml:space="preserve">ſes pinnules.</s> <s xml:id="echoid-s4678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4679" xml:space="preserve">On le fait ordinairement de cuivre ou d'une autre matiere ſolide, <lb/>de 12 à 15 pouces de raïon, d'une épaiſſeur raiſonnable & </s> <s xml:id="echoid-s4680" xml:space="preserve">bien <lb/>dreſſée: </s> <s xml:id="echoid-s4681" xml:space="preserve">ſa círconference ſe diviſe premierement en 90 degrez, & </s> <s xml:id="echoid-s4682" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-157-01a" xlink:href="note-157-01"/> chaque degré ſe ſubdiviſe en autant de parties égales qu'il eſt poſſi-<lb/> <pb o="144" file="158" n="158" rhead="CONSTRUCTION ET USAGES DU QUART, &c."/> ble de le faire ſans conſuſion, & </s> <s xml:id="echoid-s4683" xml:space="preserve">de telle ſorte que les diviſions & </s> <s xml:id="echoid-s4684" xml:space="preserve"><lb/>ſubdiviſions des degrez puiſſent être juſtes & </s> <s xml:id="echoid-s4685" xml:space="preserve">bien diſtinctement <lb/>marquées ſur le bord de l'inſtrument.</s> <s xml:id="echoid-s4686" xml:space="preserve"/> </p> <div xml:id="echoid-div402" type="float" level="2" n="1"> <note position="right" xlink:label="note-157-01" xlink:href="note-157-01a" xml:space="preserve">Fig. G.</note> </div> <p> <s xml:id="echoid-s4687" xml:space="preserve">Pour cet eſſet on décrit premierement deux circonferences ſur <lb/>le bord du quart de cercle, l'une intérieure, & </s> <s xml:id="echoid-s4688" xml:space="preserve">l'autre extérieure, <lb/>éloignées l'une de l'autre d'environ 8'ou 6 lignes, & </s> <s xml:id="echoid-s4689" xml:space="preserve">après les avoir <lb/>diviſées en degrez, on tire des lignes tranſverſales entre ces deux <lb/>circonferences du premier degré au ſecond, du ſecond au troiſié-<lb/>me, & </s> <s xml:id="echoid-s4690" xml:space="preserve">ainſi de ſuite, juſqu'au dernier.</s> <s xml:id="echoid-s4691" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4692" xml:space="preserve">Enſuite dequoi, ſi l'on veut ſubdiviſer chaque degré de 10 en 10 <lb/>minutes, on décrit du centre de l'inſtrument 5 autres circonferen-<lb/>ces concentriques qui coupent toutes les tranſverſales; </s> <s xml:id="echoid-s4693" xml:space="preserve">mais ſi l'on <lb/>vouloit ſubdiviſer chaque degré de 5 en 5 minutes, il faudroit dé-<lb/>crire onze circonferences concentriques entre les deux extremitez.</s> <s xml:id="echoid-s4694" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4695" xml:space="preserve">Les diſtances entre ces circonferences ne doivent pas être tout-à-<lb/>fait égales, à cauſe que l'étenduë d'un degré priſe dans la largeur <lb/>du bord forme une eſpece de trapeze plus large vers la circonferen-<lb/>ce extérieure, & </s> <s xml:id="echoid-s4696" xml:space="preserve">plus étroite vers l intérieure, ce qui fait que la cir-<lb/>conference moyenne qui diviſe chaque degré en deux parties égales <lb/>doit être un peu plus près de la circonference intérieure que de l'ex-<lb/>térieure, & </s> <s xml:id="echoid-s4697" xml:space="preserve">les autres à proportion.</s> <s xml:id="echoid-s4698" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4699" xml:space="preserve">Pour faire exactement ces ſubdiviſions les tranſverſales doivent <lb/> <anchor type="note" xlink:label="note-158-01a" xlink:href="note-158-01"/> être des lignes courbes comme BCD, que l'on décrit en faiſant <lb/>paſſer une portion de circonference par le centre du quart de cercle <lb/>B, par le commencement du I<emph style="sub">r</emph> degré marqué D, ſur le bord en la cir-<lb/>conference intérieure, & </s> <s xml:id="echoid-s4700" xml:space="preserve">par la fin du même degré C, en la circon-<lb/>ference extérieure; </s> <s xml:id="echoid-s4701" xml:space="preserve">ce qui eſt facile à executer par l'uſage 18, du I<emph style="sub">r</emph>. <lb/></s> <s xml:id="echoid-s4702" xml:space="preserve">Liv. </s> <s xml:id="echoid-s4703" xml:space="preserve">qui enſeigne à ſaire paſſer la circonference d'un cercle par trois <lb/>point donnez, & </s> <s xml:id="echoid-s4704" xml:space="preserve">par ce moyen on trouvera le point F pour centre <lb/>de la tranſverſale courbe qui paſſe par le premier degré.</s> <s xml:id="echoid-s4705" xml:space="preserve"/> </p> <div xml:id="echoid-div403" type="float" level="2" n="2"> <note position="left" xlink:label="note-158-01" xlink:href="note-158-01a" xml:space="preserve">I.XIII. <lb/>Planche. <lb/>Fig. H.</note> </div> <p> <s xml:id="echoid-s4706" xml:space="preserve">On diviſe enſuite une de ces lignes courbes tranſverſales en parties <lb/>égales, & </s> <s xml:id="echoid-s4707" xml:space="preserve">du centre de l'inſtrument on trace autant de circonferen-<lb/>ces concentriques qu'il en faut pour ſnbdiviſer chaque degré en au-<lb/>tant de parties égales qu'il eſt poſſible de le faire ſans confuſion.</s> <s xml:id="echoid-s4708" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4709" xml:space="preserve">La raiſon de cette operation eſt que la tranſverſale courbe étant <lb/>diviſée en parties égales, ſi du centre de l'inſtrument vous menez <lb/>par tous les points de diviſion de cet arc des lignes droites, vous <lb/>aurez audit centre autant d'angles égaux entr'eux, puiſqu'ils ſeront <lb/>tous dans la circonference d'un même cercle, & </s> <s xml:id="echoid-s4710" xml:space="preserve">qu'ils s'appuïeront <lb/>tous ſur des arcs égaux; </s> <s xml:id="echoid-s4711" xml:space="preserve">& </s> <s xml:id="echoid-s4712" xml:space="preserve">les côtez de ces angles étant continuez, <lb/> <pb o="145" file="159" n="159" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. V."/> diviſeront le degré en autant de parties égales.</s> <s xml:id="echoid-s4713" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4714" xml:space="preserve">Mais comme ce n'eſt pas une petite peine de trouver les centres <lb/>de 90 arcs qui paſſent chacun par 3 points ſemblables à BDC, & </s> <s xml:id="echoid-s4715" xml:space="preserve"><lb/>que d'ailleurs il eſt évident que tous les centres de ces arcs doivent <lb/>être placez dans la circonference d'un cercle qui ait le point B pour <lb/>centre, puiſque tous ces arcs paſſent par le point B, il n'y a qu'à dé-<lb/>crire un cercle du centre B & </s> <s xml:id="echoid-s4716" xml:space="preserve">de l'intervale BF, & </s> <s xml:id="echoid-s4717" xml:space="preserve">diviſer ſa circon-<lb/>ference en 360 degrez, ſur leſquels poſant l'un après l'autre le pied <lb/>immobile du compas, vous décrirez avec la même ouverture FB <lb/>tous les arcs ſemblables à BDC entre les cercles AC, DE, & </s> <s xml:id="echoid-s4718" xml:space="preserve">les arcs <lb/>de cercle qui ſeront ſes tranſverſales diviſeront pareillement en de-<lb/>grez les circonferences qui ſont au bord de l'inſtrument. </s> <s xml:id="echoid-s4719" xml:space="preserve">Il eſt à re-<lb/>marquer que la figure n'eſt diviſée que de 5 en 5 degrez, étant trop <lb/>petite pour qu'elle pût être diviſée de degrez en degrez.</s> <s xml:id="echoid-s4720" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4721" xml:space="preserve">On peut encore tracer les tranſverſales courbes de cette autre ma-<lb/>niere, ſans transferer le pied immobile du compas ſur tous les degrez <lb/>l'un après l'autre: </s> <s xml:id="echoid-s4722" xml:space="preserve">Tenez la pointe du compas immobile dans un <lb/>ſeul & </s> <s xml:id="echoid-s4723" xml:space="preserve">même point, comme F; </s> <s xml:id="echoid-s4724" xml:space="preserve">mais en ce cas il faudra faire avan-<lb/>cer par degrez l'inſtrument que vous voulez diviſer autour du cen-<lb/>tre d'un grand cercle déja diviſé par degrez, par le moyen d'une re-<lb/>gle, laquelle lui ſera fortement attachée, & </s> <s xml:id="echoid-s4725" xml:space="preserve">qui s'étend juſques ſur <lb/>la diviſion du grand cercle.</s> <s xml:id="echoid-s4726" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4727" xml:space="preserve">Les ouvriers adroits pourront abreger leur travail en ajuſtant une <lb/>regle d'acier, mince ſuivant la courbure de la premiere tranſverſale <lb/>qu'ils auront tracée, & </s> <s xml:id="echoid-s4728" xml:space="preserve">par ce moyen ils pourront tracer toutes les <lb/>autres.</s> <s xml:id="echoid-s4729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4730" xml:space="preserve">Si l'on veut tirer les tranſverſales en lignes droites d'un degré à <lb/>l'autre, on peut trouver parle calcul de la Trigonométrie rectiligne <lb/>la longueur des raïons de chacune des circonferences qui coupent <lb/>les tranſverſales, dont voici un exemple.</s> <s xml:id="echoid-s4731" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4732" xml:space="preserve">Je ſuppoſe un quart de cercle ayant 6 pouces de raïon, quieſt un <lb/>des plus petits que l'on ait coûtume de diviſer par des tranſverſales. <lb/></s> <s xml:id="echoid-s4733" xml:space="preserve">Je ſuppoſe auſſi une échelle de mille parties égales, & </s> <s xml:id="echoid-s4734" xml:space="preserve">que la largeur <lb/>du bord de ce quart de cercle entre la circonference intérieure & </s> <s xml:id="echoid-s4735" xml:space="preserve"><lb/>l'extérieure ſoit de 9 lignes, leſquelles correſpondent à 125 des mê-<lb/>mes parties égales, dont le raïon en contient mille; </s> <s xml:id="echoid-s4736" xml:space="preserve">je trouve par <lb/>le calcul que la tranſverſale droite, tirée d'un degré à l'autre qui <lb/>ſuit, eſt de 126 des mêmes parties, & </s> <s xml:id="echoid-s4737" xml:space="preserve">que le raïon de la circonfe-<lb/>rence intérieure qui eſt de 5 pouces & </s> <s xml:id="echoid-s4738" xml:space="preserve">3 lignes, en contient 875.</s> <s xml:id="echoid-s4739" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4740" xml:space="preserve">L'Angle obtus fait de ce raïon & </s> <s xml:id="echoid-s4741" xml:space="preserve">la tranſverſale eſt de 172 d. </s> <s xml:id="echoid-s4742" xml:space="preserve">2 <lb/> <pb o="146" file="160" n="160" rhead="CONSTRUCT. ET USAGES DU QUART, &c."/> m. </s> <s xml:id="echoid-s4743" xml:space="preserve">& </s> <s xml:id="echoid-s4744" xml:space="preserve">calculant enſuite la longue ur de chaque raïon des circonfe-<lb/>rences qui coupent les tranſverſales & </s> <s xml:id="echoid-s4745" xml:space="preserve">qui les diviſent de 10 en 10 <lb/>m. </s> <s xml:id="echoid-s4746" xml:space="preserve">je trouve que le raïon de 10 m. </s> <s xml:id="echoid-s4747" xml:space="preserve">contient 894 des mêmes parties, <lb/>au lieu de 896 qu'il contiendroit ſi l'on diviſoit la largeur du bord <lb/>du quart de cercle en 6 parties égales. </s> <s xml:id="echoid-s4748" xml:space="preserve">Le raïon de 20 min. </s> <s xml:id="echoid-s4749" xml:space="preserve">en doit <lb/>contenir 913, au lieu qu'il en auroit 917. </s> <s xml:id="echoid-s4750" xml:space="preserve">Le raïon de 30 m. </s> <s xml:id="echoid-s4751" xml:space="preserve">en doit <lb/>contenir 933, au lieu de 938. </s> <s xml:id="echoid-s4752" xml:space="preserve">Le raïon de 40 m. </s> <s xml:id="echoid-s4753" xml:space="preserve">en doit contenir <lb/>954, au lieu de 959. </s> <s xml:id="echoid-s4754" xml:space="preserve">Enfin le raïon de 50 min. </s> <s xml:id="echoid-s4755" xml:space="preserve">en doit contenir <lb/>977, au lieu de 980 qu'il auroit ſi l'on diviſoit la largeur du bord <lb/>de ce quart de cercle en 6 parties égales.</s> <s xml:id="echoid-s4756" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4757" xml:space="preserve">La plus grande erreur qui eſt de 5 parties répond environ à 1 tiers <lb/>de ligne, ce qui pourroit cauſer erreur de 2 minutes. </s> <s xml:id="echoid-s4758" xml:space="preserve">Mais cette er-<lb/>reur diminuë à proportion que le raïon du quart de cercle a de lon-<lb/>gueur comparé aux tranſverſales, de ſorte que l'erreur eſt moindre <lb/>de moitié, ſi le raïon du quart de cercle étant d'un pied, la largeur <lb/>du bord entre les 2 circonferences extrêmes n'eſt que de 9 lignes.</s> <s xml:id="echoid-s4759" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4760" xml:space="preserve">Ce que nous venons de dire pour la diviſion du quart de cercle, ſe <lb/>doit entendre de même pour les Planchetes, le cercle, le demi-cer-<lb/>cle, & </s> <s xml:id="echoid-s4761" xml:space="preserve">toutes portions de cercle que l'on veut divifer en minutes.</s> <s xml:id="echoid-s4762" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4763" xml:space="preserve">A l'égard du quarré géométrique chaque côté ſe diviſe en cent <lb/>parties égales, commençant par les extremitez, afin que le centiéme <lb/>nombre finiſſe à l'angle de 45 degrez. </s> <s xml:id="echoid-s4764" xml:space="preserve">On diſtingue ces diviſions par <lb/>de petites lignes de 5 en 5 & </s> <s xml:id="echoid-s4765" xml:space="preserve">des chifres de 10 en 10. </s> <s xml:id="echoid-s4766" xml:space="preserve">Toutes ces di-<lb/>viſions étant prolongées de par & </s> <s xml:id="echoid-s4767" xml:space="preserve">d'autre, forment un petit treillis <lb/>qui contient en ſa ſurface dix mille petits quarrez égaux.</s> <s xml:id="echoid-s4768" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4769" xml:space="preserve">Ce quart de cercle eſt garni de deux pinules immobiles, atta-<lb/>chées à un de ſes demi-diametres, & </s> <s xml:id="echoid-s4770" xml:space="preserve">d'un fil avec ſon plomb, ſuſ-<lb/>pendu au centre, & </s> <s xml:id="echoid-s4771" xml:space="preserve">d'une alidade mobile, avec deux autres pinules, <lb/>laquelle eſt attachée au centre par le moyen d'un clou à tête, <lb/>tourné à peu près comme celui de la Planchete. </s> <s xml:id="echoid-s4772" xml:space="preserve">Les pinules ſont <lb/>preſque de la même façon que celle de la figure B.</s> <s xml:id="echoid-s4773" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4774" xml:space="preserve">Au lieu des pinules immobiles on attache quelquefois à un des <lb/>raïons du quart de cercle une Lunete de longue vûë, & </s> <s xml:id="echoid-s4775" xml:space="preserve">l'on cherche <lb/>enſuite le 1<emph style="sub">r</emph> point de diviſion de la circonference en la maniere qui <lb/>eſt expliquée ci-après dans le traité du quart de cercle Aſtronomi-<lb/>que: </s> <s xml:id="echoid-s4776" xml:space="preserve">car pour celui-ci nous le deſtinons principalement à meſurer <lb/>fur la terre les hauteurs & </s> <s xml:id="echoid-s4777" xml:space="preserve">diſtances tant acceſſibles qu'inacceſſibles.</s> <s xml:id="echoid-s4778" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4779" xml:space="preserve">A la ſurface inferieure de ce quart de cercle on attache avec <lb/>trois vis un genoüil, par le moyen duquel il peut être ſitué en <lb/>toutes les poſitions convenables à ſes differens uſages. </s> <s xml:id="echoid-s4780" xml:space="preserve">Ce genoüil <lb/>eſt le même que celui marqué D.</s> <s xml:id="echoid-s4781" xml:space="preserve"/> </p> <pb o="147" file="161" n="161" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. V."/> <p> <s xml:id="echoid-s4782" xml:space="preserve">Cet inſtrument ſe met en uſage en differentes ſituations; </s> <s xml:id="echoid-s4783" xml:space="preserve">car pre-<lb/>mierement il peut être diſpoſé en ſorte que ſon plan faſſe angles <lb/>droits avec l'horiſon, afin de pouvoir obſerver les hauteurs & </s> <s xml:id="echoid-s4784" xml:space="preserve">pro-<lb/>fondeurs; </s> <s xml:id="echoid-s4785" xml:space="preserve">ce qui ſe peut encore faire en deux manieres differentes, <lb/>ſçavoir, en ſe ſervant des pinnules immobiles & </s> <s xml:id="echoid-s4786" xml:space="preserve">du fil avec ſon <lb/>plomb, & </s> <s xml:id="echoid-s4787" xml:space="preserve">pour lors aucun de ſes demi-diametres ne ſe trouve paral-<lb/>lele au plan de l'horiſon: </s> <s xml:id="echoid-s4788" xml:space="preserve">ou bien en ſe fervant des pinules attachées <lb/>à l'alidade mobile, & </s> <s xml:id="echoid-s4789" xml:space="preserve">pour lors il faut toûjours qu'un des demi-dia-<lb/>metres du quart de cercle ſoit parallele à l'horiſon, & </s> <s xml:id="echoid-s4790" xml:space="preserve">que l'autre lui <lb/>ſoit perpendiculaire; </s> <s xml:id="echoid-s4791" xml:space="preserve">ce qui ſe peut faire par le moyen du plomb <lb/>ſuſpendu au centre, & </s> <s xml:id="echoid-s4792" xml:space="preserve">pour lors les pinules immobiles ſont inutiles.</s> <s xml:id="echoid-s4793" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4794" xml:space="preserve">Enfin, ce quart de cercle ſe peut placer de maniere que ſon plan <lb/>ſoit à peu près parallele à l'horiſon pour obſerver les diſtances hori-<lb/>ſontales avec l'alidade mobile & </s> <s xml:id="echoid-s4795" xml:space="preserve">les pinules immobiles, & </s> <s xml:id="echoid-s4796" xml:space="preserve">pour lors <lb/>le fil avec ſon plomb n'eſt pas d'uſage,</s> </p> </div> <div xml:id="echoid-div405" type="section" level="1" n="185"> <head xml:id="echoid-head282" style="it" xml:space="preserve">Vſage du quart de cercle avec deux pinules immobiles & un <lb/>plomb ſuſpendu au centre.</head> <head xml:id="echoid-head283" xml:space="preserve"><emph style="sc">Premierement par les</emph> <emph style="sc">Degrez</emph>.</head> <p> <s xml:id="echoid-s4797" xml:space="preserve">POur obſerver les hauteurs, comme celle d'un Aſtre au Ciel, oula <lb/>hauteur d'une Tour, placez le quart de cercle verticalement; <lb/></s> <s xml:id="echoid-s4798" xml:space="preserve">mettez l'œil ſous la pinule immobile qui eſt vers la circonference du <lb/>quart de cercle, & </s> <s xml:id="echoid-s4799" xml:space="preserve">dirigez l'inſtrument de maniere que le raïon vi-<lb/>ſuel paſſant par les ouvertures des 2 pinules tende au point de l'ob-<lb/>jet propoſé; </s> <s xml:id="echoid-s4800" xml:space="preserve">à l'égard du Soleil il ſuffit qu'un de ſes raïons paſſe par <lb/>les deux petits trous qui doivent être percez au bas des pinules.</s> <s xml:id="echoid-s4801" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4802" xml:space="preserve">L'Arc de la circonference compris entre le fil du plomb & </s> <s xml:id="echoid-s4803" xml:space="preserve">le de-<lb/>me-diametre où ſont attachées les pinules, marque le complément <lb/>de la hauteur del'Aſtre ſur l'horiſon ou ſa diſtance du Zénith: </s> <s xml:id="echoid-s4804" xml:space="preserve">l'arc <lb/>compris entre le fil & </s> <s xml:id="echoid-s4805" xml:space="preserve">l'autre demi-diametre qui eſt vers l'objet <lb/>marque ſa hauteur ſur l'horiſon.</s> <s xml:id="echoid-s4806" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4807" xml:space="preserve">Ce même Arc détermine auſſi l'ouverture de l'angle fait par le <lb/>raïon viſuel & </s> <s xml:id="echoid-s4808" xml:space="preserve">la ligne horiſontale parallele à la baſe de la Tour.</s> <s xml:id="echoid-s4809" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4810" xml:space="preserve">Mais pour obſerver des profondeurs, comme celle d'un foſſé ou <lb/>d'un puits, il faut mettre l'œil au-deſſus de la pinule qui eſt vers le <lb/>centre du quart de cercle.</s> <s xml:id="echoid-s4811" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4812" xml:space="preserve">Toute l'operation conſiſte à calculer des triangles par des regles <lb/>detrois, formées de la proportion des ſinus des angles à leurs côtez <lb/>oppoſez, ſuivant les preceptes de la Trigonometrie rectiligne, dont <lb/>nous allons donner ici quelques exemples.</s> <s xml:id="echoid-s4813" xml:space="preserve"/> </p> <pb o="148" file="162" n="162" rhead="CONSTRUCT. ET USAGES DU QUART, &c."/> </div> <div xml:id="echoid-div406" type="section" level="1" n="186"> <head xml:id="echoid-head284" xml:space="preserve">USAGE I.</head> <p> <s xml:id="echoid-s4814" xml:space="preserve">SOit propoſé à connoître la hauteur de la Tour AB, dontle pied <lb/> <anchor type="note" xlink:label="note-162-01a" xlink:href="note-162-01"/> eſt acceſſible.</s> <s xml:id="echoid-s4815" xml:space="preserve"/> </p> <div xml:id="echoid-div406" type="float" level="2" n="1"> <note position="left" xlink:label="note-162-01" xlink:href="note-162-01a" xml:space="preserve">XIII. <lb/>Planche. <lb/>Fig. 2.</note> </div> <p> <s xml:id="echoid-s4816" xml:space="preserve">Ayant planté le pied de vôtre inſtrument au point C, regardez le <lb/>ſommet de la Tour A par les deux pinules immobiles; </s> <s xml:id="echoid-s4817" xml:space="preserve">le fil du <lb/>plomb ſuſpendu librement s'arrêtera ſur le nombre de degrez qui <lb/>détermine la valeur de l'angle qui ſe fait au centre du quart de cer-<lb/>cle par le raïon viſuel & </s> <s xml:id="echoid-s4818" xml:space="preserve">la ligne horiſontale, parallele à la baſe de <lb/>la Tour; </s> <s xml:id="echoid-s4819" xml:space="preserve">comptantles degrez compris entre le fil & </s> <s xml:id="echoid-s4820" xml:space="preserve">le demi-diama-<lb/>tre qui eſt du côté de la Tour.</s> <s xml:id="echoid-s4821" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4822" xml:space="preserve">Suppoſé donc que ce fil ſoit arrêté ſur 35 deg. </s> <s xml:id="echoid-s4823" xml:space="preserve">35 m. </s> <s xml:id="echoid-s4824" xml:space="preserve">& </s> <s xml:id="echoid-s4825" xml:space="preserve">qu'ayant <lb/>meſuré exactement la diſtance du pied de la Tour ſur leterrain de <lb/>niveau, avec la chaîne, juſqu'au lieu où s'eſt faite l'obſervation, on <lb/>ait trouvé 47 pieds; </s> <s xml:id="echoid-s4826" xml:space="preserve">on aura trois choſes connuës, ſçavoir, le côté <lb/>meſuré BC, & </s> <s xml:id="echoid-s4827" xml:space="preserve">les angles du triangle ABC; </s> <s xml:id="echoid-s4828" xml:space="preserve">car comme on ſuppoſe <lb/>toûjours les murs bâtis à plomb, l'angle B eſt droit ou de 90 deg. </s> <s xml:id="echoid-s4829" xml:space="preserve">& </s> <s xml:id="echoid-s4830" xml:space="preserve"><lb/>par conſequent les 2 angles aigus A & </s> <s xml:id="echoid-s4831" xml:space="preserve">C valent enſemble 90 deg. <lb/></s> <s xml:id="echoid-s4832" xml:space="preserve">puiſque les 3 angles de tout triangle rectiligne ſont égaux à 2 droits.</s> <s xml:id="echoid-s4833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4834" xml:space="preserve">Or l'angle obſervé eſt de 35 d. </s> <s xml:id="echoid-s4835" xml:space="preserve">35 m. </s> <s xml:id="echoid-s4836" xml:space="preserve">donc l'angle A eſt de 54 d. <lb/></s> <s xml:id="echoid-s4837" xml:space="preserve">25 m. </s> <s xml:id="echoid-s4838" xml:space="preserve">enſuite dequoi vous formerez cette analogie; </s> <s xml:id="echoid-s4839" xml:space="preserve">le ſinus de 54 <lb/>d. </s> <s xml:id="echoid-s4840" xml:space="preserve">25 m. </s> <s xml:id="echoid-s4841" xml:space="preserve">donne 47, que donnera le ſinus de 35 d. </s> <s xml:id="echoid-s4842" xml:space="preserve">35 m.</s> <s xml:id="echoid-s4843" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4844" xml:space="preserve">Le calcul étant fait on trouvera 33 pieds & </s> <s xml:id="echoid-s4845" xml:space="preserve">demi, pour 4<emph style="sub">me</emph> terme <lb/>de la regle de trois, auquel nombre ajoûtant 5 pieds pour la hauteur <lb/>du centre du quart de cercle, & </s> <s xml:id="echoid-s4846" xml:space="preserve">qui eſt ordinairement la hauteur de <lb/>l'œil d'un homme qui obſerve au-deſſus du terrain, on aura 38 pieds <lb/>& </s> <s xml:id="echoid-s4847" xml:space="preserve">demi pour la hauteur de la Tour propoſée.</s> <s xml:id="echoid-s4848" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div408" type="section" level="1" n="187"> <head xml:id="echoid-head285" xml:space="preserve">USAGE II.</head> <p> <s xml:id="echoid-s4849" xml:space="preserve">SOit propoſé à connoître la hauteur de la Tour inacceſſible DE. <lb/></s> <s xml:id="echoid-s4850" xml:space="preserve">Il faut en ce cas faire deux Obſervations, comme je vais l'ex-<lb/>pliquer.</s> <s xml:id="echoid-s4851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4852" xml:space="preserve">Placez le pied de vôtre quart de cercle au point F, & </s> <s xml:id="echoid-s4853" xml:space="preserve">regardant le <lb/> <anchor type="note" xlink:label="note-162-02a" xlink:href="note-162-02"/> fommet de la Tour D par les 2 pinules immobiles, remarquez ſur <lb/>quel degré s'arrête le fil du plomb, que je ſuppoſe pour exemple êtro <lb/>arrêté ſur 34 degrez; </s> <s xml:id="echoid-s4854" xml:space="preserve">levez enſuite l'inſtrument avec ſon pied, à la <lb/>place duquel vous planterez un piquet; </s> <s xml:id="echoid-s4855" xml:space="preserve">reculez-vous ſur un terrain <lb/>de niveau pour placer une ſeconde fois le pied de l'inſtrument, com-<lb/>me au point G, en ſorte que le piquet laiſſé au point F, ſoit dansle <lb/>même alignement que la la Tour, & </s> <s xml:id="echoid-s4856" xml:space="preserve">regardant par les 2 pinules im-<lb/> <pb o="149" file="163" n="163" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. V."/> mobiles le ſommet de ladite Tour D, remarquez le point de la cir-<lb/>conference du quart de cercle marqué par le fil du plomb, lequel je <lb/>ſuppoſe par exemple, être 20 deg. </s> <s xml:id="echoid-s4857" xml:space="preserve">meſurez auſſi très exactement la <lb/>diſtance entre les 2 ſtations, laquelle je ſuppoſe 9 toiſes ou 54 pieds.</s> <s xml:id="echoid-s4858" xml:space="preserve"/> </p> <div xml:id="echoid-div408" type="float" level="2" n="1"> <note position="left" xlink:label="note-162-02" xlink:href="note-162-02a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s4859" xml:space="preserve">Cela étant fait vous connoîtrez tous les angles du triangle DG, <lb/>& </s> <s xml:id="echoid-s4860" xml:space="preserve">de plus le côté meſuré FG, & </s> <s xml:id="echoid-s4861" xml:space="preserve">par ce moyen il ſera facile de trou-<lb/>ver le côté DF, enſuite le côté DE en faiſant les analogies ſuivantes.</s> <s xml:id="echoid-s4862" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4863" xml:space="preserve">L'angle EFD étant trouvé de 34 deg. </s> <s xml:id="echoid-s4864" xml:space="preserve">l'angle de ſuite DFG ſera <lb/>de 146, & </s> <s xml:id="echoid-s4865" xml:space="preserve">l'angle G ayant été trouvé de 20 deg. </s> <s xml:id="echoid-s4866" xml:space="preserve">ils'enſuit que l'an-<lb/>gle FDG eſt de 14; </s> <s xml:id="echoid-s4867" xml:space="preserve">c'eſt pourquoi vous direz ſi le ſinus de 14 deg. <lb/></s> <s xml:id="echoid-s4868" xml:space="preserve">donne 54 pieds, que donnera le ſinus de 20 deg. </s> <s xml:id="echoid-s4869" xml:space="preserve">le calcul étant fait <lb/>on trouvera 76 pieds & </s> <s xml:id="echoid-s4870" xml:space="preserve">environ un tiers, pour le côté DF, après <lb/>quoi il faut calculer le triangle rectangle DEF, duquel on connoît <lb/>déja tous les angles & </s> <s xml:id="echoid-s4871" xml:space="preserve">l'hypotenuſe DF: </s> <s xml:id="echoid-s4872" xml:space="preserve">c'eſt pourquoi on dira ſi le <lb/>ſinus total donne 76 pieds & </s> <s xml:id="echoid-s4873" xml:space="preserve">un tiers, que donnera le ſinus de 34 <lb/>degrez; </s> <s xml:id="echoid-s4874" xml:space="preserve">le calcul étant fait on trouvera 42 pieds & </s> <s xml:id="echoid-s4875" xml:space="preserve">deux tiers pour <lb/>le côté DE, auquel ajoûtant 5 pieds pour la hauteur du centre du <lb/>quart de cercle au-deſſus du terrain, on aura 47 pieds & </s> <s xml:id="echoid-s4876" xml:space="preserve">deux tiers <lb/>pour la hauteur de la Tour propoſée.</s> <s xml:id="echoid-s4877" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4878" xml:space="preserve">Ces calculs ſe font bien plus promptement par les Logarithmes <lb/>que par les nombres ordinaires, puiſque le tout ſe réſout par addi-<lb/>tions & </s> <s xml:id="echoid-s4879" xml:space="preserve">ſouſtractions, comme il eſt expliqué plus amplement dans <lb/>les Livres quitraitent de la Trigonométrie.</s> <s xml:id="echoid-s4880" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4881" xml:space="preserve">Ces propoſitions & </s> <s xml:id="echoid-s4882" xml:space="preserve">toutes autres de même, ſe peuvent auſſi ré-<lb/>ſoudre ſans calcul, faiſant ſur le papier des triangles ſemblables à <lb/>ceux qui ſe forment ſur le terrain.</s> <s xml:id="echoid-s4883" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4884" xml:space="preserve">Ainſi pour réſoudre la preſente queſtion faites une Echelle de 10 <lb/>toiſes, c'eſt à-dire, tracez la ligne droite AB aſſez longue, afin que <lb/>la diviſion en ſoit exacte; </s> <s xml:id="echoid-s4885" xml:space="preserve">diviſez-la en 10 parties égales & </s> <s xml:id="echoid-s4886" xml:space="preserve">ſubdivi-<lb/>ſez une deſdites parties en 6 pour avoir une toiſe diviſée en pieds.</s> <s xml:id="echoid-s4887" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4888" xml:space="preserve">Tirez enſuite la ligne indéterminée EG; </s> <s xml:id="echoid-s4889" xml:space="preserve">faites avec un rappor-<lb/>teur au point G un angle de 20 degrez, & </s> <s xml:id="echoid-s4890" xml:space="preserve">tirez la ligne indétermi-<lb/>née GM; </s> <s xml:id="echoid-s4891" xml:space="preserve">portez de G en F 9 toiſes ou 54 pieds, priſes ſur vôtre E-<lb/>chelle; </s> <s xml:id="echoid-s4892" xml:space="preserve">faites au point F un angle de 34 degrez, & </s> <s xml:id="echoid-s4893" xml:space="preserve">tirez la ligne FD, <lb/>laquelle coupera la ligne GD en un point comme D, duquel vous <lb/>abaiſſerez la perpendiculaire DE, qui repreſentera la hauteur de <lb/>la Tour propoſée, & </s> <s xml:id="echoid-s4894" xml:space="preserve">meſurant cette ligne DE ſur l'Echelle, vous <lb/>trouverez qu'elle contient 47 pieds & </s> <s xml:id="echoid-s4895" xml:space="preserve">8 pouces.</s> <s xml:id="echoid-s4896" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4897" xml:space="preserve">Tous les autres côtez de ces triangles ſe meſureront ſur la même <lb/>Echelle.</s> <s xml:id="echoid-s4898" xml:space="preserve"/> </p> <pb o="150" file="164" n="164" rhead="CONSTRUCT. ET USAGES DU QUART, &c."/> </div> <div xml:id="echoid-div410" type="section" level="1" n="188"> <head xml:id="echoid-head286" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head287" style="it" xml:space="preserve">Connoitre la largeur d'un Puits ou d'un Foſſé dont on peut <lb/>meſurer la profondeur.</head> <p> <s xml:id="echoid-s4899" xml:space="preserve">SOit propoſé à meſurer la largeur du Foſſé CD, dont on peut <lb/>approcher.</s> <s xml:id="echoid-s4900" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4901" xml:space="preserve">Placez le quart de cercle ſur le bord au point A, en ſorte que par <lb/>les ouvertures des pinules immobiles vous puiſſiez voir le fonds du <lb/> <anchor type="note" xlink:label="note-164-01a" xlink:href="note-164-01"/> Foſſé au pied de l'autre bord D, Examinez quel angle eſt marqué par <lb/>le ſil du plomb, que je ſuppoſe en cet exemple de 63 deg. </s> <s xml:id="echoid-s4902" xml:space="preserve">Meſurez la <lb/>profondeur AC, depuis le centre du quart de cercle, laquelle je ſup-<lb/>poſe de 25 pieds & </s> <s xml:id="echoid-s4903" xml:space="preserve">perpendiculaire. </s> <s xml:id="echoid-s4904" xml:space="preserve">Faites enſuite un petit triangle <lb/>rectangle ſemblable, dont un des angles aigus ſoit de 63 deg. </s> <s xml:id="echoid-s4905" xml:space="preserve">& </s> <s xml:id="echoid-s4906" xml:space="preserve">par <lb/>conſequent l'autre ſera de 27, & </s> <s xml:id="echoid-s4907" xml:space="preserve">que le plus petit côté ſoit de 25 <lb/>parties égales priſes ſur une Echelle; </s> <s xml:id="echoid-s4908" xml:space="preserve">meſurez enfin ſur cette même <lb/>Echelle le côté CD du petit triangle; </s> <s xml:id="echoid-s4909" xml:space="preserve">il ſera d'environ 49 parties, <lb/>ce qui fait juger que la largeur du Foſſé propoſé eſt de 49 pieds.</s> <s xml:id="echoid-s4910" xml:space="preserve"/> </p> <div xml:id="echoid-div410" type="float" level="2" n="1"> <note position="left" xlink:label="note-164-01" xlink:href="note-164-01a" xml:space="preserve">Fig. 4.</note> </div> </div> <div xml:id="echoid-div412" type="section" level="1" n="189"> <head xml:id="echoid-head288" style="it" xml:space="preserve">Vſage du quarré géométrique.</head> <p> <s xml:id="echoid-s4911" xml:space="preserve">LE quart de cercle étant bien placé verticalement & </s> <s xml:id="echoid-s4912" xml:space="preserve">les pinules <lb/>dirigées vers le haut de la Tour propoſée à meſurer; </s> <s xml:id="echoid-s4913" xml:space="preserve">ſi le fil du <lb/>plomb coupe le côté du quarré où eſt marqué, ombre droite, la diſ-<lb/>tance du pied de la Tour au point de ſtation eſt moindre que ſa hau-<lb/>teur; </s> <s xml:id="echoid-s4914" xml:space="preserve">ſile fil tombe le long de la diagonale du quarré, la diſtance eſt <lb/> <anchor type="note" xlink:label="note-164-02a" xlink:href="note-164-02"/> égale à la hauteur, mais ſi le fil coupe le côté du quarré où eſt marqué <lb/>ombre verſe, la diſtance de la Tour eſt plus grande que ſa hauteur.</s> <s xml:id="echoid-s4915" xml:space="preserve"/> </p> <div xml:id="echoid-div412" type="float" level="2" n="1"> <note position="left" xlink:label="note-164-02" xlink:href="note-164-02a" xml:space="preserve">Fig. G.</note> </div> <p> <s xml:id="echoid-s4916" xml:space="preserve">Ayant donc meſuré la diſtance du pied de la Tour, au lieu où ſe <lb/>fait l'obſervation, on en trouvera la hauteur par le moyen de la regle <lb/>de proportion dont on aura 3 termes connus, mais leur diſpoſition <lb/>n'eſt pas toûjours la même; </s> <s xml:id="echoid-s4917" xml:space="preserve">car lorſque le fil coupe le côté du quarré <lb/>où eſt marqué, ombre droite, le premier terme de la regle de 3, doit <lb/>être la partie du dit côté coupée par le fil, le ſecond terme ſera le <lb/>nombre entier du côté du quarré géométrique, & </s> <s xml:id="echoid-s4918" xml:space="preserve">le troiſiéme ter-<lb/>me, la diſtance meſurée.</s> <s xml:id="echoid-s4919" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4920" xml:space="preserve">Et lorſque le fil coupe le côté du quarré où eſt marqué, ombre <lb/>verſe, le premier terme de la regle de trois doit être le côté entier du <lb/>quarre geometrique; </s> <s xml:id="echoid-s4921" xml:space="preserve">le ſecond terme, la partie du côté coupée par <lb/>le fil; </s> <s xml:id="echoid-s4922" xml:space="preserve">& </s> <s xml:id="echoid-s4923" xml:space="preserve">le troiſiéme, la diſtance meſurée.</s> <s xml:id="echoid-s4924" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4925" xml:space="preserve">Suppoſons, par exemple, qu'ayant obſervé le haut d'une Tour, le <lb/>fil du plomb ait coupé le côté d'ombre droite au point marqué 40, <lb/> <pb o="151" file="165" n="165" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. V."/> & </s> <s xml:id="echoid-s4926" xml:space="preserve">que lâ diſtance meſurée ſoit de 20 toiſes; </s> <s xml:id="echoid-s4927" xml:space="preserve">je diſpoſe la regle de <lb/>proportion en la maniere ſuivante. </s> <s xml:id="echoid-s4928" xml:space="preserve">[20. </s> <s xml:id="echoid-s4929" xml:space="preserve">100. </s> <s xml:id="echoid-s4930" xml:space="preserve">20.</s> <s xml:id="echoid-s4931" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4932" xml:space="preserve">Multipliant 20, par 100, & </s> <s xml:id="echoid-s4933" xml:space="preserve">diviſant le produit 2000 par 40, <lb/>on trouvera pour quatriéme terme de cette regle 50, qui ſignifie <lb/>que la hauteur de la Tour eſt de 50 toiſes.</s> <s xml:id="echoid-s4934" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4935" xml:space="preserve">Mais ſi le fil du plomp a coupé le côté d'ombre verſe, comme par <lb/>exemple, au point marqué 60, & </s> <s xml:id="echoid-s4936" xml:space="preserve">que la diſtance meſurée ſoit de <lb/>35 toiſes, diſpoſez les trois premiers termes de la regle de proprion <lb/>en cette autre maniere. </s> <s xml:id="echoid-s4937" xml:space="preserve">[100. </s> <s xml:id="echoid-s4938" xml:space="preserve">60. </s> <s xml:id="echoid-s4939" xml:space="preserve">35.</s> <s xml:id="echoid-s4940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4941" xml:space="preserve">Mult<unsure/>ipliez 35 par 60, & </s> <s xml:id="echoid-s4942" xml:space="preserve">le produit 2100, étant diviſé par 100; <lb/></s> <s xml:id="echoid-s4943" xml:space="preserve">le quotien 21 ſera la hauteur de la Tour.</s> <s xml:id="echoid-s4944" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div414" type="section" level="1" n="190"> <head xml:id="echoid-head289" style="it" xml:space="preserve">Vſage du Treillis ſans calcul.</head> <p> <s xml:id="echoid-s4945" xml:space="preserve">TOutes ces operations ſe peuvent réſoudre ſans calcul, comme <lb/>nous allons le faire voir par quelques exemples.</s> <s xml:id="echoid-s4946" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div415" type="section" level="1" n="191"> <head xml:id="echoid-head290" xml:space="preserve">USAGE I.</head> <p> <s xml:id="echoid-s4947" xml:space="preserve">SUppoſons, comme nous avons déja fait, que le fil du plomb <lb/> <anchor type="note" xlink:label="note-165-01a" xlink:href="note-165-01"/> coupe le côté d'ombre droite au point marqué 40, & </s> <s xml:id="echoid-s4948" xml:space="preserve">que la diſ-<lb/>tance meſurée ſoit de 20 toiſes, cherehez dans le treillis celle des <lb/>perpendiculaires au raïon, qui ſoit de 20 parties depuis le fil; </s> <s xml:id="echoid-s4949" xml:space="preserve">cette <lb/>perpendiculaire coupera le côté du quarré qui aboutit an centre au <lb/>point marqué 50; </s> <s xml:id="echoid-s4950" xml:space="preserve">c'eſt pourquoi en ce cas la hauteur de la Tour <lb/>ſera de 50 toiſes.</s> <s xml:id="echoid-s4951" xml:space="preserve"/> </p> <div xml:id="echoid-div415" type="float" level="2" n="1"> <note position="right" xlink:label="note-165-01" xlink:href="note-165-01a" xml:space="preserve">Fig. G.</note> </div> <p> <s xml:id="echoid-s4952" xml:space="preserve">On diviſe quelquefois l'alidade mobile en parties égales à celles <lb/>du Treillis, & </s> <s xml:id="echoid-s4953" xml:space="preserve">par ce moyen on peut connoître la longueur de l'hy-<lb/>potenuſe ou raïon viſuel, eu rapportant l'alidade diviſée à la place <lb/>du fil.</s> <s xml:id="echoid-s4954" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div417" type="section" level="1" n="192"> <head xml:id="echoid-head291" xml:space="preserve">USAGE II.</head> <p> <s xml:id="echoid-s4955" xml:space="preserve">MAis ſi le fil coupoit le côté d'ombre verſe au point marqué <lb/>60, & </s> <s xml:id="echoid-s4956" xml:space="preserve">que la diſtance meſurée fut de 35 toiſes, comptez ſur <lb/>le raïon pu quart du cercle depuis le centre, 35 parties; </s> <s xml:id="echoid-s4957" xml:space="preserve">comptez <lb/>auſſi les diviſions de la perpendiculaire depuis ce point 35 juſqu'au <lb/>fil, vous y trouverez 21 parties; </s> <s xml:id="echoid-s4958" xml:space="preserve">c'eſt pourquoi en ce cas la hau-<lb/>teur de la Tour ſeroit de 21 toiſes.</s> <s xml:id="echoid-s4959" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4960" xml:space="preserve">Souvenez-vous qu'en tous les cas il faut ajoûter la hauteur du <lb/>centre de l'Inſtrument au-deſſus du terrain. </s> <s xml:id="echoid-s4961" xml:space="preserve">Si, par exemple, cette <lb/>hauteur eſt 5 pieds, la hauteur de la Tour dans le dernier exem-<lb/>ple ſera de 21 toiſes 5 pieds.</s> <s xml:id="echoid-s4962" xml:space="preserve"/> </p> <pb o="152" file="166" n="166" rhead="CONSTRUCTION ET USAGES DU QUART, &c."/> </div> <div xml:id="echoid-div418" type="section" level="1" n="193"> <head xml:id="echoid-head292" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head293" style="it" xml:space="preserve">Connoitre avec le Treillis une hauteur inacceſſible.</head> <p> <s xml:id="echoid-s4963" xml:space="preserve">POur cet effet il faut faire deux ſtations & </s> <s xml:id="echoid-s4964" xml:space="preserve">meſurer la diſtance <lb/>entre les deux ſtations, mais il y a trois cas à obſerver.</s> <s xml:id="echoid-s4965" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div419" type="section" level="1" n="194"> <head xml:id="echoid-head294" xml:space="preserve">PREMIER CAS.</head> <head xml:id="echoid-head295" style="it" xml:space="preserve">Où le côté d'ombre droite eſt coupé toutes les <emph style="bf">2</emph> fois par le fil du plomb.</head> <p> <s xml:id="echoid-s4966" xml:space="preserve">SUppoſons, par exemple, qu'à la premiere obſervation le fil coupe <lb/>le côté d'ombre droite au point marqué 30, & </s> <s xml:id="echoid-s4967" xml:space="preserve">que s'étant recu-<lb/>lé de 20 toiſes en place bien de niveau, au premier point, ce fil <lb/>coupe le même côté d'ombre droite au point 70; </s> <s xml:id="echoid-s4968" xml:space="preserve">marquez la poſi-<lb/>tion du filen ces deux ſtations, en traçant ſur le treillis une ligne de <lb/>craïon depuis le centre juſqu'audit point 30, & </s> <s xml:id="echoid-s4969" xml:space="preserve">une autre juſqu'au <lb/>point marqué 70; </s> <s xml:id="echoid-s4970" xml:space="preserve">cherchez entre ces deux lignes une portion de <lb/>parallele qui ſoit d'autant de parties que la dîſtance meſurée con-<lb/>tient de toiſes, c'eſt-à-dire 20 en cet exemple, ladite parallele étant <lb/>continuée, conviendra au nombre 50, compté depuis le centre; <lb/></s> <s xml:id="echoid-s4971" xml:space="preserve">c'eſt pourquoi la hauteur de la Tour obſervée ſera de 50 toiſes; </s> <s xml:id="echoid-s4972" xml:space="preserve">on <lb/>connoîtra auſſi par le même moyen que la diſtance du pied de la <lb/>Tour juſqu'à la premiere ſtation qui n'avoit pû être meſurée, eſt de <lb/>15 toiſes; </s> <s xml:id="echoid-s4973" xml:space="preserve">parce qu'il y a 15 parties compriſes ſur la parallele entre <lb/>le nombre 50 & </s> <s xml:id="echoid-s4974" xml:space="preserve">la ligne de craïon de la premiere ſtation.</s> <s xml:id="echoid-s4975" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4976" xml:space="preserve">Au lieu de tirer des lignes de craïon on pourroit ſe ſervir de 2 fils <lb/>téndus depuis le centre, dont celui où eſt attaché le plomb en ſeroit <emph style="sc">I</emph>.</s> <s xml:id="echoid-s4977" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div420" type="section" level="1" n="195"> <head xml:id="echoid-head296" xml:space="preserve">SECOND CAS.</head> <head xml:id="echoid-head297" style="it" xml:space="preserve">Où le côté d'ombre verſe eſt coupé toutes les deux fois par le fil.</head> <p> <s xml:id="echoid-s4978" xml:space="preserve">SUppoſons qu'en la premiere ſtation le fil du plomb coupe le côtê <lb/>d'ombre verſe au point marqué 80; </s> <s xml:id="echoid-s4979" xml:space="preserve">& </s> <s xml:id="echoid-s4980" xml:space="preserve">que s'étant reculé en pla-<lb/>ce unie, de 15 toiſes, le fil coupe le même côté d'ombre verſe au point <lb/>50; </s> <s xml:id="echoid-s4981" xml:space="preserve">marquez ſur le treillis les 2 differentes poſitions du fil par 2 li-<lb/>gnes de craion ou autrement, & </s> <s xml:id="echoid-s4982" xml:space="preserve">cherchez entre ces deux lignes une <lb/>portion de parallele qui contienne autant de parties que la diſtance <lb/>meſurée contient de toiſes, comme en cet exemple 15 parties à cauſe <lb/>des 15 toiſes de diſtance ſuppoſée entre les 2 ſtations; </s> <s xml:id="echoid-s4983" xml:space="preserve">à ces 15 parties <lb/>ajoûtez-en 25, qui ſont la continuation de la même parallele juſ-<lb/>qu'au côté du quarré qui aboutit au centre, ce qui fait en tout 40 <lb/>parties, c'eſt pourquoi la diſtance de la Tour juſqu'au point de la ſe-<lb/>conde ſtation eſt de 40 toiſes; </s> <s xml:id="echoid-s4984" xml:space="preserve">& </s> <s xml:id="echoid-s4985" xml:space="preserve">pour avoir ſa hauteur, cherchez <lb/> <pb o="153" file="167" n="167" rhead="POUR LEVER LES PLANS. Liv. IV. Chap. V."/> ſur le côté du quarré qui aboutit au centre le nombre 40, qui eſt ce-<lb/>lui de ſa diſtance, & </s> <s xml:id="echoid-s4986" xml:space="preserve">comptez depuis ce nombre juſqu'à la premiere <lb/>ligne de craïon les parties de la parallele, qui en cet exemple ſe trou-<lb/>veront au nombre de 20; </s> <s xml:id="echoid-s4987" xml:space="preserve">c'eſt pourquoi la hauteur de ladite Tour <lb/>eſt de 20 toiſes, en y ajoûtant toûjours, comme nous avons déja <lb/>dit, la hauteur du centre du quart de cercle par-deſſus le terrain.</s> <s xml:id="echoid-s4988" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div421" type="section" level="1" n="196"> <head xml:id="echoid-head298" xml:space="preserve">TROISIEME CAS.</head> <p> <s xml:id="echoid-s4989" xml:space="preserve">SI dans une des ſtations le fil tombe le long de la diagonale du <lb/>quarré, & </s> <s xml:id="echoid-s4990" xml:space="preserve">que dans l'autre il coupe le côté d'ombre droite, il <lb/>faut faire la même choſe que ſile côté d'ombre droite avoit été cou-<lb/>pé toutes les deux fois par le fil du plomb.</s> <s xml:id="echoid-s4991" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4992" xml:space="preserve">Mais ſi le fil tombe le long de la diagonale à une des <emph style="bf">2</emph> ſtations, & </s> <s xml:id="echoid-s4993" xml:space="preserve"><lb/>qu'il coupe le côté d'ombre verſe en l'autre ſtation; </s> <s xml:id="echoid-s4994" xml:space="preserve">il faut faire com-<lb/>me ſi toutes les 2 fois le côté d'ombre verſe avoit été coupé par le fil.</s> <s xml:id="echoid-s4995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s4996" xml:space="preserve">La raiſon de tout ceci eſt qu'il ſe fait toûjours ſur le treillis un pe-<lb/>tit triangle ſemblable au grand, qui ſe fait ſur la terre, quoique di-<lb/>verſement poſé. </s> <s xml:id="echoid-s4997" xml:space="preserve">La ligne marquée par le fil du plomb repreſente <lb/>toûjours le raïon viſuel; </s> <s xml:id="echoid-s4998" xml:space="preserve">les 4 autres côtez du petit triangle qui font <lb/>angle droit, repreſentent la hauteur de la Tour & </s> <s xml:id="echoid-s4999" xml:space="preserve">ſa diſtance; </s> <s xml:id="echoid-s5000" xml:space="preserve">quand <lb/>le fil du plomb coupe le côté d'ombre droite, la hauteur eſt repreſen-<lb/>tée par les diviſions du côte qui part du centre; </s> <s xml:id="echoid-s5001" xml:space="preserve">mais quand le fil <lb/>coupe le côté d'ombre verſe, la diſtance eſt repreſentée par les divi-<lb/>ſions du côté du treillis qui part du centre, & </s> <s xml:id="echoid-s5002" xml:space="preserve">la hauteur par la per-<lb/>pendiculaire, qui convient au nombre de la diviſion dudit côté.</s> <s xml:id="echoid-s5003" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div422" type="section" level="1" n="197"> <head xml:id="echoid-head299" xml:space="preserve">USAGE IV.</head> <head xml:id="echoid-head300" style="it" xml:space="preserve">Pour connoitre une profondeur comme celle d'un Puits'ou d'un Foſſé.</head> <p> <s xml:id="echoid-s5004" xml:space="preserve">IL en faut meſurer la largeur & </s> <s xml:id="echoid-s5005" xml:space="preserve">voir le fond par les ouvertures des <lb/>deux pinules immobiles, mais de telle ſorte que d'une ſeule vûë <lb/>on voye le bord intérieur d'en haut de devers nous, & </s> <s xml:id="echoid-s5006" xml:space="preserve">l'oppoſite <lb/>d'en bas où touche l'eau. </s> <s xml:id="echoid-s5007" xml:space="preserve">Alors le fil coupera la parallele correſpon-<lb/>dante au nombre des pieds ou toiſes de la largeur du Puits, que l'on <lb/>ſuppoſe avoir été meſurée actuellement; </s> <s xml:id="echoid-s5008" xml:space="preserve">& </s> <s xml:id="echoid-s5009" xml:space="preserve">le nombre de la perpen-<lb/>didulaire où aboutira cette parallele, déterminera la profondeur, <lb/>dont il faudra ſouſtraire la hauteur du centre de l'inſtrument au-<lb/>deſſus du bord du Puits.</s> <s xml:id="echoid-s5010" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5011" xml:space="preserve">On trouvera de même la largeur d'un Foſſé dont on pourra me-<lb/>ſurer la profondeur.</s> <s xml:id="echoid-s5012" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5013" xml:space="preserve">Pour bien entendre tout ceci, il eſt bon d'avoir en main le quar-<lb/>ré geométrique avec ſon treillis.</s> <s xml:id="echoid-s5014" xml:space="preserve"/> </p> <pb o="154" file="168" n="168" rhead="CONSTRUCT. ET USAGES DU QUART, &c."/> </div> <div xml:id="echoid-div423" type="section" level="1" n="198"> <head xml:id="echoid-head301" style="it" xml:space="preserve">Vſage du quart de cercle, en ſe ſervant de l'alidade mobile avec <lb/>ſes pinules, pour meſurer les hauteurs & profondeurs.</head> <p> <s xml:id="echoid-s5015" xml:space="preserve">PLacez le quart de cercle, de ſorte que ſon plan faſſe angle droit <lb/>avec l'horiſon, & </s> <s xml:id="echoid-s5016" xml:space="preserve">qu'un de ſes raïons ou demi-diametres ſoit <lb/>exactement parallele audit horiſon, ce qui ſera lorſque le fil du plomb <lb/>librement ſuſpendu, tombera le long de l'autre demi-diametre.</s> <s xml:id="echoid-s5017" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5018" xml:space="preserve">En cette ſituation les 2 pinules immobiles neſont d'aucun uſage, <lb/>à moins que l'on ne voulut s'en ſervir pour obſerver la diſtance de <lb/>2 étoiles, & </s> <s xml:id="echoid-s5019" xml:space="preserve">pour lors il faut incliner le quart de cercle en dirigeant <lb/>les pinules immobiles vers un aſtre, & </s> <s xml:id="echoid-s5020" xml:space="preserve">les pinules mobiles vers l'au-<lb/>tre; </s> <s xml:id="echoid-s5021" xml:space="preserve">l'arc compris entre deux donnera leur diſtance, d'où l'on peut <lb/>conclure la diverſité de leurs aſpects.</s> <s xml:id="echoid-s5022" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5023" xml:space="preserve">S'il s'agit d'obſerver une hauteur, le centre de l'inſtrument doit <lb/>être au-deſſus de l'œil; </s> <s xml:id="echoid-s5024" xml:space="preserve">mais ſi l'on obſerve une profondeur, il faut <lb/>que l'œil ſoit au-deſſus du centre.</s> <s xml:id="echoid-s5025" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div424" type="section" level="1" n="199"> <head xml:id="echoid-head302" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head303" style="it" xml:space="preserve">Pour obſerver une hauteur comme celle d'une Tour, dont <lb/>le pied eſt acceſſible.</head> <p> <s xml:id="echoid-s5026" xml:space="preserve">AYant placé le quart de cercle de la maniere que nous venons <lb/>de dire, tournez l'alidade de telle ſorte que vous puiſſiez voir <lb/>le ſommet de la Tour par les ouvertures des pinules; </s> <s xml:id="echoid-s5027" xml:space="preserve">l'Arc de la cir-<lb/>conference du quart de cercle compris entre le demi-diametre, pa-<lb/>rallele à l'horiſon, & </s> <s xml:id="echoid-s5028" xml:space="preserve">la ligne de foy de l'alidade marquera l'ouver-<lb/>ture de l'angle qui ſe fait au centre de l'inſtrument. </s> <s xml:id="echoid-s5029" xml:space="preserve">Si enſuite on <lb/>meſure exactement la diſtance du pied de la Tour au lieu où eſt pla-<lb/>cé l'inſtrument, on aura 3 choſes connuës dans le triangle à meſu-<lb/>rer, ſçavoir, la baſe & </s> <s xml:id="echoid-s5030" xml:space="preserve">les 2 angles faits à ſes extremitez, dont l'un <lb/>eſt toûjours droit, puiſqu'on ſuppoſe la Tour bâtie & </s> <s xml:id="echoid-s5031" xml:space="preserve">dreſſée à <lb/>plomb, & </s> <s xml:id="echoid-s5032" xml:space="preserve">l'autre angle égal à celui que fait la ligne de foy de l'ali-<lb/>dade avec le demi-diametre, parallele à l'horiſon; </s> <s xml:id="echoid-s5033" xml:space="preserve">le reſte ſe trouve-<lb/>ra par les regles de la Trigonométrie rectiligne, comme nous avons <lb/>dit ci-devant; </s> <s xml:id="echoid-s5034" xml:space="preserve">ou bien ſans calcul en traçant ſur le papier des trian-<lb/>gles ſemblables à ceux qui ſe font ſur le terrain; </s> <s xml:id="echoid-s5035" xml:space="preserve">ou bien par le quar-<lb/>ré géométrique, en obſervant que dans cette poſition du quart de <lb/>cercle le côté d'ombre droite doit toûjours être parallele à l'hori-<lb/>ſon, & </s> <s xml:id="echoid-s5036" xml:space="preserve">que le côté d'ombre verſe lui doit être perpendiculaire.</s> <s xml:id="echoid-s5037" xml:space="preserve"/> </p> <pb o="155" file="169" n="169" rhead="POUR LEVER DES PLANS. Liv. IV. Chap. V."/> </div> <div xml:id="echoid-div425" type="section" level="1" n="200"> <head xml:id="echoid-head304" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head305" style="it" xml:space="preserve">Pour connoître la hauteur d'une Tour ſoit acceſſible ou inac-<lb/>ceſſible, par le moyen du Treillis.</head> <p> <s xml:id="echoid-s5038" xml:space="preserve">EN cette ſituation du quart de cercle, il ſe forme toûjours ſur le <lb/>Treillis de petits triangles ſemblables, dons les côtez homolo-<lb/>gues ſont paralleles & </s> <s xml:id="echoid-s5039" xml:space="preserve">ſemblablement poſez à ceux des grands <lb/>triangles qui ſe forment ſur la terre; </s> <s xml:id="echoid-s5040" xml:space="preserve">ce qui rend les operations plus <lb/>ſimples & </s> <s xml:id="echoid-s5041" xml:space="preserve">plus faciles que dans l'autre ſituation du quart de cercle; <lb/></s> <s xml:id="echoid-s5042" xml:space="preserve">comme nous allons l'expliquer en faiſant trois differentes ſuppoſi-<lb/>tions, ſelon les differens cas qui peuvent ſe rencontrer.</s> <s xml:id="echoid-s5043" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div426" type="section" level="1" n="201"> <head xml:id="echoid-head306" xml:space="preserve">PREMIER CAS</head> <p> <s xml:id="echoid-s5044" xml:space="preserve">SUppoſons, par exemple, qu'ayant obſervé le haut d'une Tour <lb/>dont le pied eſt acceſſible, par les ouvertures des pinules de l'ali-<lb/>dade mobile, la ligne de foy coupe le côté d'ombre droite au point <lb/>marqué 40, & </s> <s xml:id="echoid-s5045" xml:space="preserve">que la diſtance du pied de la Tour ſoit de 20 toiſes, <lb/>cherchez entre les paralleles à l'horiſon, depuis celle qui paſſe par le <lb/>centre juſqu'à l'alidade, la parallele qui eſt de 20 parties, à cauſe <lb/>des 20 toiſes de diſtance ſuppoſée, vous verrez qu'elle aboutit au <lb/>nombre 50, du côté perpendiculaire du quarré compté depuis le <lb/>centre, d'ou vous jugerez que la hauteur de cette Tour eſt de 50 <lb/>toiſes au-deſſus du centre du quart de cercle.</s> <s xml:id="echoid-s5046" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div427" type="section" level="1" n="202"> <head xml:id="echoid-head307" xml:space="preserve">SECOND CAS.</head> <p> <s xml:id="echoid-s5047" xml:space="preserve">SUppoſons que dans une autre obſervation l'alidade coupele cô-<lb/>té d'ombre verſe au point marqué 60, & </s> <s xml:id="echoid-s5048" xml:space="preserve">que la diſtance meſu-<lb/>rée ſoit de 35 toiſes; </s> <s xml:id="echoid-s5049" xml:space="preserve">comptez depuis le centre du quart de cercle le <lb/>long du côté parallele à l'horiſon 35 parties, pourles 35 toiſes de di-<lb/>ſtance, & </s> <s xml:id="echoid-s5050" xml:space="preserve">dece point, comptant les parties de la perpendiculaire juſ-<lb/>qu'à l'interſection de la ligne de foy, vons en trouverez 21; </s> <s xml:id="echoid-s5051" xml:space="preserve">ce qui <lb/>doit faire juger que la hauteur de la Tour propoſée à meſurer, eſt <lb/>de 21 toiſes.</s> <s xml:id="echoid-s5052" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div428" type="section" level="1" n="203"> <head xml:id="echoid-head308" xml:space="preserve">TROISIE'ME CAS.</head> <p> <s xml:id="echoid-s5053" xml:space="preserve">SUppoſons enfin que le pied de la Tour ſoit inacceſſible, & </s> <s xml:id="echoid-s5054" xml:space="preserve">qu'il <lb/>faille faire 2 ſtations, comme nous avons dit ci-devant, on peut <lb/>trouver la hauteur ſans aucune diſtinction d'ombre droite ou verſe; <lb/></s> <s xml:id="echoid-s5055" xml:space="preserve">car ayant meſuré la diſtance entre les 2 ſtations, & </s> <s xml:id="echoid-s5056" xml:space="preserve">marqué ſur le <lb/>treillis 2 lignes qui faſſent connoître la ſituation de l'alidade dans <lb/>ces 2 differentes poſitions, cherchez entre ces 2 lignes une portion <lb/>de parallele à l'horiſon, qui ſoit d'autant de parties que la diſtance <lb/>meſurée contient de toiſes: </s> <s xml:id="echoid-s5057" xml:space="preserve">Si vous la continuez juſqu'au côté per-<lb/> <pb o="156" file="170" n="170" rhead="CONSTRUCTION ET USAGES DU QUART, &c."/> pendiculaire du quarré géométrique qui part du centre, vous y trou-<lb/>verez un nombre qui exprimera la hauteur de la Tour, & </s> <s xml:id="echoid-s5058" xml:space="preserve">la conti-<lb/>nuation de cette parallele juſqu'à ce nombre vous fera connoître la <lb/>diſtance juſqu'au pied de la Tour, laquelle n'avoit pû être meſurée.</s> <s xml:id="echoid-s5059" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5060" xml:space="preserve">Remarquez qu'en cette ſituation du quart de cercle les diſtances <lb/>horiſontales ſont toûjours repreſentées ſur le treillis par des lignes <lb/>paralleles a l'horiſon, & </s> <s xml:id="echoid-s5061" xml:space="preserve">que les élevations ou hauteurs y ſont toûjours <lb/>repreſentées par des lignes perpendiculaires ſur ledit horiſon; </s> <s xml:id="echoid-s5062" xml:space="preserve">ce <lb/>qui rend, comme nous avons déja dit, les operations plus faciles à <lb/>connoître.</s> <s xml:id="echoid-s5063" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5064" xml:space="preserve">Il n'en eſt pas de même dans l'autre ſituation verticale du quart <lb/>de cercle où l'on ſe ſert des pinules immobiles; </s> <s xml:id="echoid-s5065" xml:space="preserve">car ſi en obſervant la <lb/>hauteur d'une Tour inacceſſible, le fil du plomb dans une des ſta-<lb/>tions coupe le côté d'ombre droite, & </s> <s xml:id="echoid-s5066" xml:space="preserve">dans l'autre ſtation le côté <lb/>d'ombre verſe la diſtance entre les 2 lignes de craïon qui marquent <lb/>les 2 differentes poſitions du fil, traverſe les quarrez du treillis par <lb/>leurs diagonales, leſquelles n'ont point de communes meſures avec <lb/>les côtez, & </s> <s xml:id="echoid-s5067" xml:space="preserve">ainſi on ne pourroit pas s'en ſervir pour trouver la <lb/>hauteur de la Tour propoſée.</s> <s xml:id="echoid-s5068" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div429" type="section" level="1" n="204"> <head xml:id="echoid-head309" style="it" xml:space="preserve">Vſage du quart de cercle pour meſurer les diſtances horiſontales.</head> <p> <s xml:id="echoid-s5069" xml:space="preserve">QUoique le quart de cercle ne ſoit pas ſi propre pour meſurer les <lb/>diſtances horiſontales que le demi-cercle ou le cercle entier, à <lb/>cauſe que l'on ne peut s'en ſervir à meſurer les angles obtus, nous <lb/>ne laiſſerons pourtant pas d'en donner ici quelques uſages, par rap-<lb/>port au quarré géométrique & </s> <s xml:id="echoid-s5070" xml:space="preserve">au treillis que nous ſuppoſons tracé <lb/>ſur le plan de cet inſtrument.</s> <s xml:id="echoid-s5071" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5072" xml:space="preserve">Placez ſur ſon píed la ſurface du quart de cercle horiſontalement, <lb/>de ſorte que ſa circonference ſoit à peu près parallele à l'horiſon; <lb/></s> <s xml:id="echoid-s5073" xml:space="preserve">car il n'eſt pas beſoin que ſon plan ſoit parfaitement de niveau, é-<lb/>tant quelquefois neceſſaire de l'incliner pour appercevoir les objets <lb/>par les ouvertures des pinules.</s> <s xml:id="echoid-s5074" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5075" xml:space="preserve">Mettez le pied de cet inſtrument dans la ligne que vous préten-<lb/>dez meſurer, & </s> <s xml:id="echoid-s5076" xml:space="preserve">faites deux obſervations en la maniere ſuivante, où <lb/>le plomb n'eſt plus d'uſage, mais on ſe ſert de quatre pinules tant <lb/>mobiles qu'immobles.</s> <s xml:id="echoid-s5077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5078" xml:space="preserve">Suppoſons, par exemple, qu'il faille meſurer la diſtance perpen-<lb/> <anchor type="note" xlink:label="note-170-01a" xlink:href="note-170-01"/> diculaire AB: </s> <s xml:id="echoid-s5079" xml:space="preserve">plantez pluſieurs piquets dans la ligne ACD, & </s> <s xml:id="echoid-s5080" xml:space="preserve">le <lb/>quart de cercle au point A, en ſorte que les 2 pinules immobiles <lb/>ſoient dans la ligne AC, & </s> <s xml:id="echoid-s5081" xml:space="preserve">que le point B ſoit vû par les ouvertures <lb/> <pb o="157" file="171" n="171" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. V."/> des 2 pinules de la regle mobile, placée à angle droit avec la ligne <lb/>AC; </s> <s xml:id="echoid-s5082" xml:space="preserve">ôtez enſuite le quart de cercle & </s> <s xml:id="echoid-s5083" xml:space="preserve">plantez un piquet au point A, <lb/>meſurez depuis A vers C telle quantité qu'il vous plaira, comme, <lb/>par exemple, 18 toiſes, au bout deſquelles ayant placé l'inſtrument <lb/>en ſorte que les deux pinules immobiles ſoient dans la ligne AC, <lb/>tournez l'alidade mobile juſqu'à ce que vous puiſſiez voir le point <lb/>B par les ouvertures de ſes 2 pinules, vous aurez ſur le treillis un pe-<lb/>tit triangle tout ſemblable au grand qui ſe fait ſur la terre; </s> <s xml:id="echoid-s5084" xml:space="preserve">c'eſt <lb/>pourquoi cherchez entre les paralleles coupées par l'alidade, celle <lb/>qui a autant de parties que la diſtance meſurée a de toiſes, c'eſt-à-<lb/>dire, 18 en cet exemple, elleaboutira ſur le demi-diametre du quart <lb/>de cercle, à un nombre, lequel compté depuis le centre de l'inſtru-<lb/>ment, contient autant de parties qu'il y a de toiſes dans la ligne <lb/>AB, propoſée à meſurer.</s> <s xml:id="echoid-s5085" xml:space="preserve"/> </p> <div xml:id="echoid-div429" type="float" level="2" n="1"> <note position="left" xlink:label="note-170-01" xlink:href="note-170-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s5086" xml:space="preserve"><emph style="sc">Autrement</emph>. </s> <s xml:id="echoid-s5087" xml:space="preserve">On pourra trouver encore la diſtance AB, <lb/>ſoit perpendiculaire ou non, d'une autre maniere, ſans s'aſſujetir <lb/>à faire une ſtation à angle droit au point A.</s> <s xml:id="echoid-s5088" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5089" xml:space="preserve">Suppoſons, par exemple, que la premiere ſtation ſefaſſe au point <lb/>C, & </s> <s xml:id="echoid-s5090" xml:space="preserve">la ſeconde au point D; </s> <s xml:id="echoid-s5091" xml:space="preserve">tracez ſur le treillis deux lignes droites <lb/>avec du craïon ou autrement, qui marquent les deux differentes <lb/>poſitions de l'alidade; </s> <s xml:id="echoid-s5092" xml:space="preserve">& </s> <s xml:id="echoid-s5093" xml:space="preserve">ayant meſuré la diſtance du point C au <lb/>point D, que je ſuppoſe ici 20 toiſes, cherchez entre les 2 lignes <lb/>de craïon une portion de parallele qui ſoit de 20 parties, elle correſ-<lb/>pondra ſur le demi-diametre du quarré géométr que à un nombre <lb/>lequel compté depuis le centre contiendra autant de parties qu'il y <lb/>a de toiſes ſur la terre en ligne droite, depuis A juſqu'en B.</s> <s xml:id="echoid-s5094" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5095" xml:space="preserve">On connoîtra auſſi la longueur des diſtances CB & </s> <s xml:id="echoid-s5096" xml:space="preserve">DB par les <lb/>diviſions de l'alidade; </s> <s xml:id="echoid-s5097" xml:space="preserve">car il ſe fait ſur le treillis un petit triangle <lb/>obliquangle ſemblable au grand CDB, qui ſe fait ſur la terre.</s> <s xml:id="echoid-s5098" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div431" type="section" level="1" n="205"> <head xml:id="echoid-head310" xml:space="preserve">CHAPITRE VI.</head> <head xml:id="echoid-head311" style="it" xml:space="preserve">Contenant la conſtruction & les uſages du demi-cercle.</head> <p> <s xml:id="echoid-s5099" xml:space="preserve">L'On nommeauſſices Inſtrumens, Graphometres. </s> <s xml:id="echoid-s5100" xml:space="preserve">On les fait de <lb/> <anchor type="note" xlink:label="note-171-01a" xlink:href="note-171-01"/> laiton battu ou de cuivre fondu en ſable, ſuivant les modeles <lb/>que l'on donne aux Fondeurs, depuis 7 pouces de diametre juſqu'à <lb/> <anchor type="note" xlink:label="note-171-02a" xlink:href="note-171-02"/> 15. </s> <s xml:id="echoid-s5101" xml:space="preserve">La diviſion ſe fait de la même maniere que celle de la Planche-<lb/>te, & </s> <s xml:id="echoid-s5102" xml:space="preserve">du quart du cercle, comme nousavons explique ci-devant. </s> <s xml:id="echoid-s5103" xml:space="preserve">Le <lb/>plus ſimple de ces Inſtrumens eſt celui marqué B. </s> <s xml:id="echoid-s5104" xml:space="preserve">Aux extremitez <lb/>de ſon diametre & </s> <s xml:id="echoid-s5105" xml:space="preserve">dans un petit trou quarré fait ſur la ligne de foy, <lb/> <pb o="158" file="172" n="172" rhead="CONSTRUCT. ET USAGES DU DEMI CERCLE"/> on ajuſte 2 piuules immobiles, qu'on arrête avec un écrou au-deſ-<lb/>ſous, & </s> <s xml:id="echoid-s5106" xml:space="preserve">à ſon centre une regle ou alidade mobile garnie de 2 autres <lb/>pinules faites de la même maniere que celle dont nous avons parlé <lb/>ci-devant, & </s> <s xml:id="echoid-s5107" xml:space="preserve">qu'on arrête avec une vis. </s> <s xml:id="echoid-s5108" xml:space="preserve">On emboëte une bouſſole <lb/>au milieu de ſa ſurface pour ſer vir à orienter les cartes & </s> <s xml:id="echoid-s5109" xml:space="preserve">les plans.</s> <s xml:id="echoid-s5110" xml:space="preserve"/> </p> <div xml:id="echoid-div431" type="float" level="2" n="1"> <note position="right" xlink:label="note-171-01" xlink:href="note-171-01a" xml:space="preserve">XIV. <lb/>Planche.</note> <note position="right" xlink:label="note-171-02" xlink:href="note-171-02a" xml:space="preserve">Fig. A. <lb/>& B.</note> </div> <p> <s xml:id="echoid-s5111" xml:space="preserve">Au-deſſous du demi-cercle il y a un genoüil qui eſt attaché au <lb/>centre, dont la virole entre autour d'un pied à 3 branches, comme <lb/>la figure le montre.</s> <s xml:id="echoid-s5112" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5113" xml:space="preserve">Ileſt neceſſaire de dire ici que ces Inſtrumens doivent être d'abord <lb/>bien dreſſez au marteau; </s> <s xml:id="echoid-s5114" xml:space="preserve">puis il faut les dégroſſir avec une lime ru-<lb/>de; </s> <s xml:id="echoid-s5115" xml:space="preserve">enſuite on les adoucit avec une lime bâtarde & </s> <s xml:id="echoid-s5116" xml:space="preserve">une douce. <lb/></s> <s xml:id="echoid-s5117" xml:space="preserve">Quand ces Inſtrumens ſont ainſi limez, il faut prendre garde ſi on <lb/>ne les a pas gauchis en limant. </s> <s xml:id="echoid-s5118" xml:space="preserve">En ce cas on les doit bien redreſſer à <lb/>la regle ſur une pierre ou un marbre bien droit, puis on paſſe une <lb/>pierre de ponce avec de l'eau pour ôter les traits de la lime. </s> <s xml:id="echoid-s5119" xml:space="preserve">Pour <lb/>bien polir les demi-cercles, comme tout autre Inſtrument, on ſe ſert <lb/>de pierre douce d'Allemagne, puis d'un charbon bien doux, en ſorte <lb/>qu'il ne raïe pas l'ouvrage; </s> <s xml:id="echoid-s5120" xml:space="preserve">enſuite pour le bien éclaircir on ſe ſert <lb/>de tripoli fin trempé dans de l'huile, & </s> <s xml:id="echoid-s5121" xml:space="preserve">qu'on paſſe fortement avec <lb/>un morceau de caſtor ou de chamois.</s> <s xml:id="echoid-s5122" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5123" xml:space="preserve">Le demi-cercle à lunetes marqué A ſert à prendre les diſtances <lb/>fort éloignées, & </s> <s xml:id="echoid-s5124" xml:space="preserve">a les degrez de ſon limbe diviſez en minutes par <lb/>des lignes tranſverſales droites ou courbes, comme il a été dit ci-<lb/>devant en parlant du quart de cercle.</s> <s xml:id="echoid-s5125" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5126" xml:space="preserve">Il y a une lunete d'approche attachée par deſſous au long de ſon <lb/>diametre, dont les bouts marquez B, excedent de part & </s> <s xml:id="echoid-s5127" xml:space="preserve">d'autre. <lb/></s> <s xml:id="echoid-s5128" xml:space="preserve">A l'alidade de ce demi-cercle eſt ajuſtée une autre lunete. </s> <s xml:id="echoid-s5129" xml:space="preserve">Lorſque la <lb/>ligne de foy coupe le milieu de l'alidade, il faut que la lunete qui y <lb/>eſt attachée ſoit un peu plus courte, afin que l'on puiſſe voir les de-<lb/>grez de la diviſion coupez par la ligne de foy; </s> <s xml:id="echoid-s5130" xml:space="preserve">mais pour le mieux il <lb/>eſt plus à propos que les 2 lunetes ſoient égales en longueur, & </s> <s xml:id="echoid-s5131" xml:space="preserve">pour <lb/>lors il faut que la ligne de foy de l'alidade ſoit tracée du bout mar-<lb/>qué C, & </s> <s xml:id="echoid-s5132" xml:space="preserve">que paſſant par le centre du demi-cercle, elle aille aboutir <lb/>à l'extremité oppoſée, marquée D. </s> <s xml:id="echoid-s5133" xml:space="preserve">On échancreles deux bouts de <lb/>l'alidade de maniere qu'ils conviennent aux diviſions des degrez du <lb/>limbe, comme on voit aux endroits marquez CF, GD, de telle ſorte <lb/>que la ligne GFEGD eſt la ligne de foi du demi-cercle.</s> <s xml:id="echoid-s5134" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5135" xml:space="preserve">Il eſt bon de remarquer que l'on ne commence pas à compter les <lb/>degrez de ce demi-cercle depuis le diametre, comme aux autres, <lb/>mais à l'endroit où ſe trouve l'échancrure de la ligne de foi, quand <lb/> <pb o="159" file="173" n="173" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. VI."/> les raïons viſuels des 2 lunetes étant l'une ſur l'autre ſont d'accord, <lb/>& </s> <s xml:id="echoid-s5136" xml:space="preserve">pour les faire convenir on avance ou recule le petie chaſſis qui <lb/>porte les filets par le moyen des vis. </s> <s xml:id="echoid-s5137" xml:space="preserve">La largeur depuis le centre des <lb/>lunetes juſqu'aux échancrures de l'alidade eſt ordinairement de 5 <lb/>degrez, ce qui fait que la diviſion avance d'autant de degrez plus <lb/>d'un côté que de l'autre, comme la figure le montre.</s> <s xml:id="echoid-s5138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5139" xml:space="preserve">Les lunetes ſont à 2 ou à 4 verres, & </s> <s xml:id="echoid-s5140" xml:space="preserve">ont toutes une ſoye très-<lb/>fine tenduëau foyer du verre objectif, pour ſervir de pinule.</s> <s xml:id="echoid-s5141" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5142" xml:space="preserve">Les lunetes à 4 verres font voir les objets dans leur veritable ſitua-<lb/>tion; </s> <s xml:id="echoid-s5143" xml:space="preserve">mais celles des 2 verres les renverſent en ſorte que ce qui eſt à <lb/>doit paroît à gauche, & </s> <s xml:id="echoid-s5144" xml:space="preserve">ce qui eſt en haut paroît en bas; </s> <s xml:id="echoid-s5145" xml:space="preserve">mais cela <lb/>n'ôte pas la juſteſſe de l'operation, parce qu'elles donnent toûjours <lb/>le point de direction.</s> <s xml:id="echoid-s5146" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5147" xml:space="preserve">Ces lunetes ſont faites de tuïaux de cuivre ſoudez & </s> <s xml:id="echoid-s5148" xml:space="preserve">tournez en <lb/>forme cylindrique, comme on voit par la figure D, qui repreſente u-<lb/>nelunete détachée. </s> <s xml:id="echoid-s5149" xml:space="preserve">Le verre oculaire, qui eſt celui dont on aproche <lb/>l'œil pour regarder les objets, eſt au bout marqué 1. </s> <s xml:id="echoid-s5150" xml:space="preserve">On le poſe dans <lb/>un autre petit tuïau qui eſt à part, auſſi marqué 1, que l'on avance <lb/>ou recule dans le tuïau de la lunete ſelon les difſerentes vûës. </s> <s xml:id="echoid-s5151" xml:space="preserve">Ce pe-<lb/>tit tuïau porte auſſi quelquefois au foyer du verre la ſoye fine qui <lb/>ſert de pinule; </s> <s xml:id="echoid-s5152" xml:space="preserve">mais pour le mieux cette ſoie eſt attachée ſur une peti-<lb/>te piece de cuivre, qu'on voit auſſi à part, ſur laquelle on trace bien <lb/>juſte un trait quarré marqué 2, ſur lequel on poſe cesſoies. </s> <s xml:id="echoid-s5153" xml:space="preserve">On place <lb/>cette piece dans un rainure faite dans un petit chaſſis de cuivre ſou-<lb/>dé au tuïau de la lunete à l'endroit marqué. </s> <s xml:id="echoid-s5154" xml:space="preserve">2. </s> <s xml:id="echoid-s5155" xml:space="preserve">La petite vis marquée <lb/>5, eſt faite pour avancer ou reculer la petite piece qui porte les ſoyes. <lb/></s> <s xml:id="echoid-s5156" xml:space="preserve">Le verre objectif eſt placé à l'autre bout de la lunete du côté de l'ob-<lb/>jet que l'on veut voir. </s> <s xml:id="echoid-s5157" xml:space="preserve">Il eſt auſſi placé dans un petittuïau marqué <lb/>3, & </s> <s xml:id="echoid-s5158" xml:space="preserve">qui entre à force dans le canal de la lunete, afin que ce verre ne <lb/>change pas facilement de place quand la lunete eſt ajuſtée. </s> <s xml:id="echoid-s5159" xml:space="preserve">Ces ver-<lb/>res ſont convexes, ce qui rend leur milieu plus épais que leurs bords. </s> <s xml:id="echoid-s5160" xml:space="preserve"><lb/>Mais l'oculaire doit avoir plus de convexité que l'objectif, afin que <lb/>les objets paroiſſent plus grands qu'à la vûë ſimple.</s> <s xml:id="echoid-s5161" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5162" xml:space="preserve">On appelle le foyer d'un verre convexe l'endroit où les raïons qui <lb/>viennent d'un objet lumineux ou coloré, lequel eſt dans une diſtan-<lb/>ce fort éloignée, vont ſe réunir après avoir paſſé au-delà du verre; <lb/></s> <s xml:id="echoid-s5163" xml:space="preserve">c'eſt pourquoi la peinture des objets qui ſont oppoſez au verre, ſe re-<lb/>preſente très-diſtinctement dans cet endroit. </s> <s xml:id="echoid-s5164" xml:space="preserve">Par exemple, le point <lb/>L, à l'extremite du côte de la figure H, eſt le foyer du verre S, à cau-<lb/>ſe que c'eſt le point où les raions, qui entrent par l'autre bout N du <lb/> <pb o="160" file="174" n="174" rhead="CONSTRUCT. ET USAGES DU DEMI CERCLE"/> tuïau, vont ſe réunir après avoir paſſé à travers le verre S.</s> <s xml:id="echoid-s5165" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5166" xml:space="preserve">Les lunetes les plus en uſage ſont celles à 2 verres, qui ſont pla-<lb/>cez de maniere que leurs foyers ſoient communs & </s> <s xml:id="echoid-s5167" xml:space="preserve">ſe réuniſſent à <lb/>un même point dans le tuïau de la lunete, & </s> <s xml:id="echoid-s5168" xml:space="preserve">c'eſt en ce point que <lb/>l'on place les filets; </s> <s xml:id="echoid-s5169" xml:space="preserve">ſi le foyer du verre objectif eſt 7 ou 8 fois plus <lb/>éloigné que celui du verre oculaire, l'objet paroîtra 7 ou 8 fois plus <lb/>grand que ſi les foyers de ces deux verres étoient égaux.</s> <s xml:id="echoid-s5170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5171" xml:space="preserve">Le foyer du verre oculaire étant commun avec celui de l'objectif <lb/>les raïons colorez, qui après s'être rompus en tombant ſur la ſurfa-<lb/>ce du verre objectif, ſe ſont réunis à ſon foyer, continuent leur che-<lb/>min en s'écartant, & </s> <s xml:id="echoid-s5172" xml:space="preserve">rencontrant le verre oculaire, ſe rompent de-<lb/>rechefen paſſant au travers, & </s> <s xml:id="echoid-s5173" xml:space="preserve">ſe dirigent de telle ſorte qu'en met-<lb/>tant l'œil derriere ce verre on apperçoit les objets, la peinture <lb/>ſe fait au foyer: </s> <s xml:id="echoid-s5174" xml:space="preserve">car c'eſt l'objet qui renvoye ſon eſpece à l'œil; </s> <s xml:id="echoid-s5175" xml:space="preserve">ce <lb/>qui ſe prouve encore très-manifeſtement par l'experience ſuivante. <lb/></s> <s xml:id="echoid-s5176" xml:space="preserve">On bouche entierement le jour d'une chambre, & </s> <s xml:id="echoid-s5177" xml:space="preserve">l'on fait un petit <lb/>trou rond à un volet de fenêtre expoſée à un lieu bien éclairé, on y <lb/>applique un verre convexe, & </s> <s xml:id="echoid-s5178" xml:space="preserve">l'on met un papier ou un linge blanc <lb/>à l'opoſite de ce verre, au dedans de la chambre, à la diſtance de ſon <lb/>foyer; </s> <s xml:id="echoid-s5179" xml:space="preserve">alors on voit ſur le papier une peinture très-nette & </s> <s xml:id="echoid-s5180" xml:space="preserve">très-diſ-<lb/>tincte des objets qui ſont oppoſez au verre par dehors, dans une ſi-<lb/>tuation renverſée, & </s> <s xml:id="echoid-s5181" xml:space="preserve">cette peinture ſe fait par les raïons de lumiere <lb/>qui rejailliſſent des objets. </s> <s xml:id="echoid-s5182" xml:space="preserve">On trouvera le foyer du verre en appro-<lb/>chant ou reculant le papier tant que l'on voïe la peinture bien nette <lb/>& </s> <s xml:id="echoid-s5183" xml:space="preserve">bien déterminée.</s> <s xml:id="echoid-s5184" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5185" xml:space="preserve">Il y a une bouſſole & </s> <s xml:id="echoid-s5186" xml:space="preserve">un genoüil à ce demi-cercle, qui étant bien <lb/>fait de cette maniere, eſt un des plus parfaits qu'on puiſſe faire.</s> <s xml:id="echoid-s5187" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5188" xml:space="preserve">L'Inſtrument marqué C eſt un rapporteur d'environ 8 ou 10 pou-<lb/> <anchor type="note" xlink:label="note-174-01a" xlink:href="note-174-01"/> ces de diametre avec ſon alidade ou regle mobile. </s> <s xml:id="echoid-s5189" xml:space="preserve">On le fait quel-<lb/>quefois auſſi grand que les Graphometres, dont on ſe ſert en campa-<lb/>gne, afin que l'on puiſſe marquer ſur ſon bord les minutes, & </s> <s xml:id="echoid-s5190" xml:space="preserve">qu'il <lb/>ſerve à rapporter ſur le papier les mêmes angles en degrez & </s> <s xml:id="echoid-s5191" xml:space="preserve">minu-<lb/>tes que ceux qui ont été obſervez en campagne.</s> <s xml:id="echoid-s5192" xml:space="preserve"/> </p> <div xml:id="echoid-div432" type="float" level="2" n="2"> <note position="left" xlink:label="note-174-01" xlink:href="note-174-01a" xml:space="preserve">Fig. C.</note> </div> <p> <s xml:id="echoid-s5193" xml:space="preserve">Ce rapporteur eſt évuidé, & </s> <s xml:id="echoid-s5194" xml:space="preserve">ſon alidade tourne autour d'un petit <lb/>cercle auſſi évuidé, au milieu duquel il y a une petite pointe qui <lb/>marque le centre du rapporteur, La diviſion ſe fait de même qu'au <lb/>demi-cercle, & </s> <s xml:id="echoid-s5195" xml:space="preserve">par la methode que nous avons marquée.</s> <s xml:id="echoid-s5196" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div434" type="section" level="1" n="206"> <head xml:id="echoid-head312" xml:space="preserve">USAGE I.</head> <p> <s xml:id="echoid-s5197" xml:space="preserve">POur lever le plan d'un champ propoſé, comme ABEDC, faites <lb/> <anchor type="note" xlink:label="note-174-02a" xlink:href="note-174-02"/> planter un piquet bien à plomb a chaque angle de la figure, & </s> <s xml:id="echoid-s5198" xml:space="preserve"><lb/> <pb o="161" file="175" n="175" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. VI."/> meſurez exactement avec la toiſe un de ſes longs côtez, comme <lb/>AB, lequel je ſuppoſe pour exemple de 40 toiſes 2 pieds: </s> <s xml:id="echoid-s5199" xml:space="preserve">faites un <lb/>memorial en craionnant ſur le papier une figure à peu près ſembla-<lb/>ble à celle du terrain; </s> <s xml:id="echoid-s5200" xml:space="preserve">mettez le demi cercle avec ſon pied à la place <lb/>du piquet A, en ſorte que bornaïant par les fentes des pinules im-<lb/>mobiles du diametre, vous voyiez le piquet B; </s> <s xml:id="echoid-s5201" xml:space="preserve">enſuite le demi-cer-<lb/>cle demeurant ferme en cette ſituation, tournez l'alidade mobile en <lb/>ſorte que par ſes pinules vous puiſſiez voir le piquet C; </s> <s xml:id="echoid-s5202" xml:space="preserve">remarquez <lb/>quel angle fait la ligne de foy de l'alidade avec le côté AB, & </s> <s xml:id="echoid-s5203" xml:space="preserve">mar-<lb/>quez ſur vôtre memorial le nombre des degrez de l'angle BAC; <lb/></s> <s xml:id="echoid-s5204" xml:space="preserve">tournez enſuite l'alidade de ſorte que par les pinules vous puiſſiez <lb/>voir le piquet D, & </s> <s xml:id="echoid-s5205" xml:space="preserve">marquez ſur vôtre memorial le nombre des de-<lb/>grez que contient l'angle BAD, tournez encore l'alidade de ſorte <lb/>que par les pinules on puiſſe voir le piquet E, & </s> <s xml:id="echoid-s5206" xml:space="preserve">marquez le nombre <lb/>des degrez que contient l'Angle BAE. </s> <s xml:id="echoid-s5207" xml:space="preserve">Mais toutes les fois que <lb/>vous bornaïez chacun des piquets par les pinules de l'alidade, ayez <lb/>ſoin de regarder ſi le piquet B eſt toûjours bien dans l'alignement <lb/>des pinules immobiles du diametre.</s> <s xml:id="echoid-s5208" xml:space="preserve"/> </p> <div xml:id="echoid-div434" type="float" level="2" n="1"> <note position="left" xlink:label="note-174-02" xlink:href="note-174-02a" xml:space="preserve">Fig. 1.</note> </div> <p> <s xml:id="echoid-s5209" xml:space="preserve">Ceci étant fait, levez le demi cercle avec ſon pied, & </s> <s xml:id="echoid-s5210" xml:space="preserve">ayant re-<lb/>planté le piquet A, allez poſer le demi-cercle avec ſon pied à la pla-<lb/>ce du piquet B, en ſorte que bornaïant par les ouvertures des pinu-<lb/>les immobiles du diametre, vous voyiez le piquet A, & </s> <s xml:id="echoid-s5211" xml:space="preserve">le demi-cercle <lb/>demeurant ferme en cette ſituation, tournez, comme vous avez dè-<lb/>ja fait, l'alidade mobile, en ſorte que par ſes pinules vous puiſſiez <lb/>voir l'un après l'autre les piquets C, D, E, & </s> <s xml:id="echoid-s5212" xml:space="preserve">marquez ſur le me-<lb/>morial la valeur de chaque angle ABC, ABD, ABE.</s> <s xml:id="echoid-s5213" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5214" xml:space="preserve">Enfin mettez au net la figure en traçant exactement avec un de-<lb/>mi-cercle ou rapporteur tous les angles dont la valeur eſt marquée <lb/>aux extremitez de la ligne AB, d'où vous tirerez autant de lignes <lb/>droites, & </s> <s xml:id="echoid-s5215" xml:space="preserve">de leurs interſections d'autres lignes qui formeront le <lb/>plan propoſé. </s> <s xml:id="echoid-s5216" xml:space="preserve">La longueur de tous les côtez qui n'ont pas été meſu-<lb/>rez ſe pourra connoître par le moyen d'une échelle de parties éga-<lb/>les, dont la ligne AB en contiendra 50 & </s> <s xml:id="echoid-s5217" xml:space="preserve">un tiers, & </s> <s xml:id="echoid-s5218" xml:space="preserve">l'on pourra <lb/>trouver la ſurface de ce champ en meſurant chacun des triangles <lb/>du plan ainſi reduit par les regles de la Planimétrie dont traitent <lb/>quantité de Livres.</s> <s xml:id="echoid-s5219" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5220" xml:space="preserve">Remarquez qu'il eſt à propos de meſurer actuellement une des <lb/>plus longues lignes du plan propoſé, pour la faire ſervir de baſe <lb/>commune, & </s> <s xml:id="echoid-s5221" xml:space="preserve">faire à chacune de ſes extremitez toutes les obſerva-<lb/>tions neceſſaires pour y former les angles des triangles qu'on eſt <lb/> <pb o="162" file="176" n="176" rhead="CONSTRUCT. ET USAGES DU DEMI CERCLE"/> obligé d'y faire: </s> <s xml:id="echoid-s5222" xml:space="preserve">car ſi l'on prenoit pour baſe commune de tous ces <lb/>triangles une des plus courtes lignes, les angles qui ſe forment par <lb/>les interſections des raïons viſuels en bornaïant les piquets, de-<lb/>viendroient trop aigus, & </s> <s xml:id="echoid-s5223" xml:space="preserve">l'interſection trop incertaine.</s> <s xml:id="echoid-s5224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5225" xml:space="preserve">On pourra orienter ce plan par le moyen de la bouſſole, dontla <lb/>ligne du Nord & </s> <s xml:id="echoid-s5226" xml:space="preserve">Sud ſe trace ordinairement parallele au diametre <lb/>du demi-cercle : </s> <s xml:id="echoid-s5227" xml:space="preserve">car comme la baſe commune de tous les triangles <lb/>obſervez eſt parallele à ce diametre, il n'y a qu'à remarquer l'angle <lb/>qu'elle fait avec l'éguille aimantée, ce qui ſe connoîtra facilement <lb/>en dirigeant la ligne de foi de l'alidade parallelement à lad. </s> <s xml:id="echoid-s5228" xml:space="preserve">aiguil-<lb/>le. </s> <s xml:id="echoid-s5229" xml:space="preserve">Enſuite dequoi on deſſigne ſur le plan une petite roſe des Rumbs <lb/>des Vents, où les principaux ſont marquez par leurs noms, & </s> <s xml:id="echoid-s5230" xml:space="preserve">pla-<lb/>cez conformément à l'obſervation qui en a été faite ſur le terrain.</s> <s xml:id="echoid-s5231" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div436" type="section" level="1" n="207"> <head xml:id="echoid-head313" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head314" style="it" xml:space="preserve">Pour ſçavoir la diſtance du Clocher A à la Tour C, que l'on <lb/>ſuppoſe être inacceſſible.</head> <p> <s xml:id="echoid-s5232" xml:space="preserve">A Yant choiſi deux endroits aux environs, d'où l'on puiſſe voir <lb/> <anchor type="note" xlink:label="note-176-01a" xlink:href="note-176-01"/> le Clocher & </s> <s xml:id="echoid-s5233" xml:space="preserve">la Tour, & </s> <s xml:id="echoid-s5234" xml:space="preserve">meſurer leur diſtance pour ſervir de <lb/>baſe, placez le demi-cercle à l'un de ces lieux, comme en D, & </s> <s xml:id="echoid-s5235" xml:space="preserve">un <lb/>piquet à l'autre, comme au point E, tournez le de maniere que par <lb/>les pinules fixes de ſon diametre, ou par la lunete, vous découvriez <lb/>le piquet E, faites mouvoir l'alidade en ſorte que par ſes pinules <lb/>vous puiſſiez voir le Clocher A, les degrez du demi-cercle compris <lb/>entre le diametre & </s> <s xml:id="echoid-s5236" xml:space="preserve">l'alidade, donneront l'ouverture de l'angle A <lb/>DE, quidans cet exemple eſt de 32 degrez, que vous marquerez ſur <lb/>le Memorial. </s> <s xml:id="echoid-s5237" xml:space="preserve">Tournez encore l'alidade juſqu'à ce que vous puiſſiez <lb/>voir la Tour C par les pinules ou lunete, en conſervant toûjours le <lb/>diametre dans la ligne DE, alors les degrez compris entre le diame-<lb/>tre & </s> <s xml:id="echoid-s5238" xml:space="preserve">l'alidade donneront l'ouverture de l'angle CDE, qui ſera de <lb/>123 degrez, & </s> <s xml:id="echoid-s5239" xml:space="preserve">que vous marquerez ſur le Memorial. </s> <s xml:id="echoid-s5240" xml:space="preserve">Vous ôterez <lb/>enſuite le demi cercle de la ſtation D, & </s> <s xml:id="echoid-s5241" xml:space="preserve">vous y laiſſerez un piquet; <lb/></s> <s xml:id="echoid-s5242" xml:space="preserve">meſurez exactement la diſtance du piquet D au piquet E, que jeſup-<lb/>poſe ici de 32 toiſes, que vous écrirez ſur le Memorial; </s> <s xml:id="echoid-s5243" xml:space="preserve">poſez le de-<lb/>mi cercle à la place du piquet E, de telle ſorte que les pinules fixes <lb/>du diametre, ou la lunete, ſoient directement ſur la ligne ED; </s> <s xml:id="echoid-s5244" xml:space="preserve">tour-<lb/>nez l'alidade, afin de voir par ſes pinules la Tour C, les degrez com-<lb/>pris entre le diametre & </s> <s xml:id="echoid-s5245" xml:space="preserve">l'alidade donneront l'ouverture de l'angle <lb/>CED, qui eſt en cet exemple de 26 degrez. </s> <s xml:id="echoid-s5246" xml:space="preserve">Tournez enfin l'alida-<lb/>de pour voir par ſes pinules le Clocher A, & </s> <s xml:id="echoid-s5247" xml:space="preserve">l'angle AED ſera de 125 <lb/> <pb o="163" file="177" n="177" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. VI."/> degrez, que vous chifrerez ſur le Memorial; </s> <s xml:id="echoid-s5248" xml:space="preserve">& </s> <s xml:id="echoid-s5249" xml:space="preserve">par le moyen d'une <lb/>Echelle & </s> <s xml:id="echoid-s5250" xml:space="preserve">d'un Rapporteur vous ferez une figure ſemblable pour <lb/>connoître la diſtance AC, propoſée à meſurer.</s> <s xml:id="echoid-s5251" xml:space="preserve"/> </p> <div xml:id="echoid-div436" type="float" level="2" n="1"> <note position="left" xlink:label="note-176-01" xlink:href="note-176-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s5252" xml:space="preserve">Pour reſoudre la même propoſition par le calcul de la Trigono-<lb/>métrie. </s> <s xml:id="echoid-s5253" xml:space="preserve">Premierement, on connoît par obſervation dans le triangle <lb/>DAE, l'angle aigu ADE de 32 degrez, & </s> <s xml:id="echoid-s5254" xml:space="preserve">l'obtus DEA de 125 deg. <lb/></s> <s xml:id="echoid-s5255" xml:space="preserve">d'où il ſuit que le troiſiéme angle DAE eſt de 23 deg. </s> <s xml:id="echoid-s5256" xml:space="preserve">puiſque les 3 <lb/>angles de tout triangle rectiligne ſont égaux à deux droits; </s> <s xml:id="echoid-s5257" xml:space="preserve">& </s> <s xml:id="echoid-s5258" xml:space="preserve">pour <lb/>connoître le côté AE, vous ferez cette analogie. </s> <s xml:id="echoid-s5259" xml:space="preserve">Le ſinus de 23 deg. </s> <s xml:id="echoid-s5260" xml:space="preserve"><lb/>auquel répond dans les Tables ce nombre 39073, eſt à 32 toiſes, <lb/>comme le ſinus de 32 deg. </s> <s xml:id="echoid-s5261" xml:space="preserve">52992 eſt à la ligne AE de 43 toiſes, <lb/>peu plus. </s> <s xml:id="echoid-s5262" xml:space="preserve">On connoît de même par obſervation dans le triangle C <lb/>DE l'angle aigu CED de 26 deg. </s> <s xml:id="echoid-s5263" xml:space="preserve">& </s> <s xml:id="echoid-s5264" xml:space="preserve">l'obtus EDC de 123 deg. </s> <s xml:id="echoid-s5265" xml:space="preserve"><lb/>d'où s'enſuit que le troiſiéme angle DCE eſt de 31 deg. </s> <s xml:id="echoid-s5266" xml:space="preserve">& </s> <s xml:id="echoid-s5267" xml:space="preserve">pour con-<lb/>noître le côté CE, faites cette ſeconde analogie: </s> <s xml:id="echoid-s5268" xml:space="preserve">comme le ſinus de <lb/>31 deg. </s> <s xml:id="echoid-s5269" xml:space="preserve">51504 eſt à 32 toiſes; </s> <s xml:id="echoid-s5270" xml:space="preserve">ainſi le ſinus de 123 d. </s> <s xml:id="echoid-s5271" xml:space="preserve">ou de ſon com-<lb/>plément 57, qui eſt le même, 83867 eſt à CE 52 toiſes. </s> <s xml:id="echoid-s5272" xml:space="preserve">Enſuite <lb/>pour connoître la diſtance CA, examinez le triangle CAE, duquel <lb/>vous connoiſſez les deux côtez CE & </s> <s xml:id="echoid-s5273" xml:space="preserve">AE, avec l'angle compris <lb/>ADC de 99 deg. </s> <s xml:id="echoid-s5274" xml:space="preserve">& </s> <s xml:id="echoid-s5275" xml:space="preserve">par conſequent les deux autres angles incon-<lb/>nus valent enſemble 81 deg. </s> <s xml:id="echoid-s5276" xml:space="preserve">& </s> <s xml:id="echoid-s5277" xml:space="preserve">pour les connoître chacun en parti-<lb/>culier, faites encore cette autre analogie: </s> <s xml:id="echoid-s5278" xml:space="preserve">comme la ſomme des deux <lb/>côtez connus 95 toiſes eſt à leur difference 9 toiſes, ainſi la tangen-<lb/>te de 40 d. </s> <s xml:id="echoid-s5279" xml:space="preserve">3ò m. </s> <s xml:id="echoid-s5280" xml:space="preserve">moitié des deux angles inconnus 85408 eſt à un <lb/>quatriéme nombre 8091, qui eſt tangente de la moitié de la diffe-<lb/>rence des 2 angles inconnus, ce quatriéme terme cherché dans la <lb/>colonne des tangentes répond à 4 d. </s> <s xml:id="echoid-s5281" xml:space="preserve">37, qu'il faut ajoûter à ladite <lb/>moitié 40 d. </s> <s xml:id="echoid-s5282" xml:space="preserve">3ò pour avoir le plus grand des 2 angles aigus CAE <lb/>45 d. </s> <s xml:id="echoid-s5283" xml:space="preserve">7, & </s> <s xml:id="echoid-s5284" xml:space="preserve">par conſequent le troiſiéme angle ACE ſera de 35 d. </s> <s xml:id="echoid-s5285" xml:space="preserve">53. </s> <s xml:id="echoid-s5286" xml:space="preserve"><lb/>Enfin pour avoir la longueur CA, dites: </s> <s xml:id="echoid-s5287" xml:space="preserve">comme le ſinus de 35 d. </s> <s xml:id="echoid-s5288" xml:space="preserve"><lb/>53, 58613 eſt à 43 toiſes, ainſi le ſinus de 66 d. </s> <s xml:id="echoid-s5289" xml:space="preserve">ou de ſon complé-<lb/>ment 81 d. </s> <s xml:id="echoid-s5290" xml:space="preserve">98768 eſt à la diſtance AC de 72 toiſes 2 pieds.</s> <s xml:id="echoid-s5291" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div438" type="section" level="1" n="208"> <head xml:id="echoid-head315" xml:space="preserve">USAGE III.</head> <p> <s xml:id="echoid-s5292" xml:space="preserve">POur avoir la hauteur de la Tour AB, du pied de laquelle on ne <lb/> <anchor type="note" xlink:label="note-177-01a" xlink:href="note-177-01"/> peut pas approcher à cauſe d'un ruiſſeau qui paſſe au bas de la-<lb/>dite Tour, cherchez un terrain à peu près de niveau, propre à y faire <lb/>2 ſtations, comme en cet exemple C & </s> <s xml:id="echoid-s5293" xml:space="preserve">D; </s> <s xml:id="echoid-s5294" xml:space="preserve">placez le demi-cercle <lb/>verticalement au point D, de ſorte que ſon diametre ſoit parallele <lb/>à l'horiſon, ce qui ſe fait par le moyen d'un fil avec ſon plomb, que <lb/> <pb o="164" file="178" n="178" rhead="CONSTRUCT. ET USAGES DU DEMI CERCLE"/> l'on accroche au haut d'une ligne perpendiculaire, qui eſt tracée <lb/>derriere le demi-cercle; </s> <s xml:id="echoid-s5295" xml:space="preserve">tournez l'alidade, afin de voir par ſes pinu-<lb/>les le ſommet de la Tour B, examinez de combien de degrez eſt l'an-<lb/>gle BDA, que nous ſuppoſons ici de 42 deg. </s> <s xml:id="echoid-s5296" xml:space="preserve">que vous marquerez <lb/>ſur le Memorial, puis ayant levé le demi-cercle & </s> <s xml:id="echoid-s5297" xml:space="preserve">placé à l'autre <lb/>ſtation C, meſurez la diſtance DC, que je ſuppoſe ici de 12 toiſes, <lb/>& </s> <s xml:id="echoid-s5298" xml:space="preserve">après avoir ajuſté le demi-cercle de maniere que ſon diametre ſoit <lb/>parallele à l'horiſon, tournez l'alidade juſqu'à ce que vous voyiez le <lb/>haut de la Tour B, remarquez l'angle BCD, pour l'écrire ſur le Me-<lb/>morial, que nous ſuppoſonsici de 22 degrez, faites enſuite une figu-<lb/>re ſemblable par le moyen d'une échelle & </s> <s xml:id="echoid-s5299" xml:space="preserve">d'un rapporteur, & </s> <s xml:id="echoid-s5300" xml:space="preserve">vous <lb/>connoîtrez la hauteur AB, laquelle ſe peut auſſi trouver par le cal-<lb/>cul de la Trigonométrie en cette maniere.</s> <s xml:id="echoid-s5301" xml:space="preserve"/> </p> <div xml:id="echoid-div438" type="float" level="2" n="1"> <note position="right" xlink:label="note-177-01" xlink:href="note-177-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s5302" xml:space="preserve">L'angle BDA de 42 degrez donne l'angle de ſuite BDC de 138 <lb/>deg. </s> <s xml:id="echoid-s5303" xml:space="preserve">& </s> <s xml:id="echoid-s5304" xml:space="preserve">parce que l'angle C a été meſuré de 22 deg. </s> <s xml:id="echoid-s5305" xml:space="preserve">le troiſiéme an-<lb/>gle du triangle CBD ſera de 20 deg. </s> <s xml:id="echoid-s5306" xml:space="preserve">Vous direz donc par une <lb/>regle de proportion: </s> <s xml:id="echoid-s5307" xml:space="preserve">comme le ſinus de 20 deg. </s> <s xml:id="echoid-s5308" xml:space="preserve">34202 eſt à 12 toi-<lb/>ſes, ainſi le ſinus de 22 a. </s> <s xml:id="echoid-s5309" xml:space="preserve">37461 eſt à la ligne BD 13 toiſes 10 pou-<lb/>ces: </s> <s xml:id="echoid-s5310" xml:space="preserve">or cette ligne BD eſt l'hypotenuſe du triangle rectangle BDA, <lb/>dont tous les angles ſont connus; </s> <s xml:id="echoid-s5311" xml:space="preserve">c'eſt pourquoi vous direz par une <lb/>ſeconde regle de 3, comme le ſinustotal 10000 eſt à 13 toiſes 10 pou-<lb/>ces, ainſi le ſinus de 42 degrez 66913 eſt à la hauteur AB 8 toiſes, <lb/>& </s> <s xml:id="echoid-s5312" xml:space="preserve">peu moins de 5 pieds.</s> <s xml:id="echoid-s5313" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div440" type="section" level="1" n="209"> <head xml:id="echoid-head316" xml:space="preserve">USAGE VI.</head> <head xml:id="echoid-head317" style="it" xml:space="preserve">Pour lever la Carte d'un Païs.</head> <p> <s xml:id="echoid-s5314" xml:space="preserve">CHoiſiſſez premierement 2 endroits éminens, d'où l'on puiſſe <lb/>découvrir une grande étenduë de Païs, leſquels ſoient aſſez é-<lb/>loignez l'un de l'autre pour ſervir de baſe commune à pluſieurs <lb/>triangles qu'il faut obſerver pour faire cette carte; </s> <s xml:id="echoid-s5315" xml:space="preserve">meſurez actuel-<lb/>lement avec la chaîne la diſtance de ces deux lieux.</s> <s xml:id="echoid-s5316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5317" xml:space="preserve">Ces 2 hauteurs étant ſuppoſées A & </s> <s xml:id="echoid-s5318" xml:space="preserve">B, éloignées l'une de l'autre <lb/>de 200 toiſes, placez horiſontalement le plan du demi-cercle avec <lb/>ſon pied au point A, en ſorte que par les pinules immobiles du dia-<lb/>metre, ou par la lunete, vous découvriez le point B; </s> <s xml:id="echoid-s5319" xml:space="preserve">l'inſtrument <lb/>reſtant ferme en cette ſituation, tournez l'alidade mobile pour dé-<lb/>couvrir l'un après l'autre les Tours, Clochers, Moulins, Arbres & </s> <s xml:id="echoid-s5320" xml:space="preserve"><lb/>autres lieux remarquables que vous ſouhaitez placer ſur vôtre Car-<lb/>te; </s> <s xml:id="echoid-s5321" xml:space="preserve">examinez quels angles ils font avec la baſe commune, & </s> <s xml:id="echoid-s5322" xml:space="preserve">les mar-<lb/>quez auſſi-tôt ſur le Memorial avec les noms propres de chaque <lb/> <pb o="165" file="179" n="179" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. VII."/> lieu bornaïé par les pinules ou lunete, par exemple, l'angle BAI de <lb/> <anchor type="note" xlink:label="note-179-01a" xlink:href="note-179-01"/> 14 deg. </s> <s xml:id="echoid-s5323" xml:space="preserve">BAG de 47, BAH de 53, BAF de 68, BAE de 83 BAD <lb/>de 107, & </s> <s xml:id="echoid-s5324" xml:space="preserve">enfin l'angle BAC de 130 deg. </s> <s xml:id="echoid-s5325" xml:space="preserve">ce qui étant fait, & </s> <s xml:id="echoid-s5326" xml:space="preserve">les <lb/>angles marquez ſur le Memorial avec la diſtance AB des deux ſta-<lb/>tions que nous avons ſuppoſée de 200 toiſes, poſez le demi-cercle <lb/>au point B, pour y faire la ſeconde ſtation.</s> <s xml:id="echoid-s5327" xml:space="preserve"/> </p> <div xml:id="echoid-div440" type="float" level="2" n="1"> <note position="right" xlink:label="note-179-01" xlink:href="note-179-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s5328" xml:space="preserve">L'Inſtrument étant placé de maniere que ſon diametre convien-<lb/>ne avec la ligne BA, tournez l'alidade mobile & </s> <s xml:id="echoid-s5329" xml:space="preserve">obſervez les angles <lb/>que ſont les mêmes objets qui ſont vûs du point A, comme par ex-<lb/>emple l'angle ABC de 20 deg. </s> <s xml:id="echoid-s5330" xml:space="preserve">ABF de 37, ABD de 44, ABE <lb/>de 56, ABG de 83, ABH de 96, & </s> <s xml:id="echoid-s5331" xml:space="preserve">l'angle ABI de 133 deg. </s> <s xml:id="echoid-s5332" xml:space="preserve">que vous <lb/>marquerez ſur le Memorial, comme vous avez fait les autres.</s> <s xml:id="echoid-s5333" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5334" xml:space="preserve">Si quelque objet a été vû du point A, & </s> <s xml:id="echoid-s5335" xml:space="preserve">que l'on ne puiſſe pas le <lb/>voir du point B, il faut changer de baſe en choiſiſſant un autre point <lb/>d'où l'on puiſſe le découvrir; </s> <s xml:id="echoid-s5336" xml:space="preserve">car il eſt abſolument neceſſaire qu'un <lb/>même objet ſoit vû de 2 lieux differens; </s> <s xml:id="echoid-s5337" xml:space="preserve">puiſqu'on ne peut avoir ſa <lb/>poſition que par le point d'interſection de 2 lignes, dont chacune <lb/>ſe tire des extremitez de la Baſe, avec laquelle ils forment un trian-<lb/>gle rectiligne.</s> <s xml:id="echoid-s5338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5339" xml:space="preserve">Il eſt à propos de ſe ſouvenir que l'étenduë de la Baſe que l'on me-<lb/>ſure doit être aſſez grande, à proportion des triangles auſquels elle <lb/>doit ſervir, & </s> <s xml:id="echoid-s5340" xml:space="preserve">de plus bien alignée & </s> <s xml:id="echoid-s5341" xml:space="preserve">nivelée, car ſi l'on ſuivoit les <lb/>inegalitez du terrain haut & </s> <s xml:id="echoid-s5342" xml:space="preserve">bas, on auroit des Baſes trop longues <lb/>à proportion des angles & </s> <s xml:id="echoid-s5343" xml:space="preserve">des raïons viſuels qui ſe tirent en bor-<lb/>naïant les objets.</s> <s xml:id="echoid-s5344" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5345" xml:space="preserve">Pour mettre cette Carte au net, réduiſez tous ces triangles obſer-<lb/>vez dans leur juſte proportion, par le moyen d'une Echelle & </s> <s xml:id="echoid-s5346" xml:space="preserve">d'un <lb/>Rapporteur, de la maniere que nous avons dit ci-devant.</s> <s xml:id="echoid-s5347" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div442" type="section" level="1" n="210"> <head xml:id="echoid-head318" xml:space="preserve">CHAPITRE VII.</head> <head xml:id="echoid-head319" style="it" xml:space="preserve">Contenant la conſtruction & les uſages de la Bouſſole.</head> <p> <s xml:id="echoid-s5348" xml:space="preserve">CEt Inſtrument ſe fait de Cuivre, d'Ivoire, de Bois, ou detoute <lb/> <anchor type="note" xlink:label="note-179-02a" xlink:href="note-179-02"/> autre matiere ſolide. </s> <s xml:id="echoid-s5349" xml:space="preserve">Il s'en fait depuis 2 pouces juſqu'à 6 de <lb/>diametre. </s> <s xml:id="echoid-s5350" xml:space="preserve">Son milieu eſt fait en cercle comme une boëte ronde, au <lb/> <anchor type="note" xlink:label="note-179-03a" xlink:href="note-179-03"/> fond de laquelle on décrit une roſe de vents & </s> <s xml:id="echoid-s5351" xml:space="preserve">une circonference <lb/>diviſée en 360 deg. </s> <s xml:id="echoid-s5352" xml:space="preserve">Ce cercle eſt appliqué ſur une plaque quarrée; <lb/></s> <s xml:id="echoid-s5353" xml:space="preserve">à ſon centre on place un petit pivot de cuivre ou d'acier bien poin-<lb/>tu, qui ſert à porter une éguille d'acier aimantée, poſée en équili-<lb/>bre afin qu'elle puiſſe tourner librement; </s> <s xml:id="echoid-s5354" xml:space="preserve">& </s> <s xml:id="echoid-s5355" xml:space="preserve">par deſſus on met un <lb/> <pb o="166" file="180" n="180" rhead="CONSTRUCT. ET USAGES DE LA BOUSSOLE"/> verre taillé en rond que l'on fait tenir dans une petite renure faite <lb/>exprès autour du cercle, pour empêcher que l'agitation de l'air <lb/>ne donne trop de mouvement à l'éguille.</s> <s xml:id="echoid-s5356" xml:space="preserve"/> </p> <div xml:id="echoid-div442" type="float" level="2" n="1"> <note position="right" xlink:label="note-179-02" xlink:href="note-179-02a" xml:space="preserve">XIV. <lb/>Planche.</note> <note position="right" xlink:label="note-179-03" xlink:href="note-179-03a" xml:space="preserve">Fig. E.</note> </div> <p> <s xml:id="echoid-s5357" xml:space="preserve">Un des bouts de l'éguille aimantée, ſçavoir celui qui a été froté <lb/>du Pole méridional de la pierre d'aiman, ſe tourne toûjours vers la <lb/>partie Septentrionale du Monde, non pas préciſément, mais avec <lb/>quelque déclinaiſon qui change de tems à autre.</s> <s xml:id="echoid-s5358" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5359" xml:space="preserve">Suivant les Obſervations faites au mois d'Octobre de l'année <lb/>1715, dans l'Obſervatoire Roïal, l'éguille aimantée déclinoit de <lb/>douze degrez quinze minutes du Nord à l'Oüeſt.</s> <s xml:id="echoid-s5360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5361" xml:space="preserve">Les éguilles ſont faites de lames d'acier, de la longueur du diame-<lb/>tre de la Bouſſole. </s> <s xml:id="echoid-s5362" xml:space="preserve">On y ſoude au milieu une petite chape de cuivre, <lb/>que l'on perce fort droit, en forme de cône, & </s> <s xml:id="echoid-s5363" xml:space="preserve">on donne un petit <lb/>coup de pointeau au fond, afin que l'éguille ait un mouvement bien <lb/>libre ſur ſon pivot. </s> <s xml:id="echoid-s5364" xml:space="preserve">On les lime fort délicatement en leur donnant <lb/>differentes figures; </s> <s xml:id="echoid-s5365" xml:space="preserve">les unes en dard par un bout, & </s> <s xml:id="echoid-s5366" xml:space="preserve">par l'autre une <lb/>flèche, ce ſont ordinairement les grandes qu'on lime de cette façon. <lb/></s> <s xml:id="echoid-s5367" xml:space="preserve">Aux moyenes & </s> <s xml:id="echoid-s5368" xml:space="preserve">aux petites on y fait un anneau vers l'extremité, <lb/>pour diſtinguer le côté qui doit tourner vers le Nord, telles que les <lb/>petites figures qui ſont auprès de la Bouſſole le montrent.</s> <s xml:id="echoid-s5369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5370" xml:space="preserve">Pour aimanter les éguilles il faut les faire paſſer ſur le Pole d'un <lb/>bon aiman ou ſur ſon armure, de maniere que le bout qui doit tour-<lb/>ner vers le Sud, touchele premier ſur la pierre, en coulant l'éguille <lb/>au long de l'aiman; </s> <s xml:id="echoid-s5371" xml:space="preserve">& </s> <s xml:id="echoid-s5372" xml:space="preserve">que le bout qui doit ſe diriger au Nord <lb/>y paſſe le dernier. </s> <s xml:id="echoid-s5373" xml:space="preserve">Il faut faire la même choſe trois ou quatre fois, <lb/>écartant la main en arc afin que la vertu y reſte mieux imprimée.</s> <s xml:id="echoid-s5374" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5375" xml:space="preserve">Cette admirable proprieté de l'aiman & </s> <s xml:id="echoid-s5376" xml:space="preserve">de l'éguille aimantée, <lb/>n'eſt connuë en Europe que depuis environ l'an 1260.</s> <s xml:id="echoid-s5377" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5378" xml:space="preserve">C'eſt par ſon moyen que l'on a oſé entreprendre de grands voïa-<lb/>ges par Mer, & </s> <s xml:id="echoid-s5379" xml:space="preserve">que l'on a découvert deux cens ans après, dester-<lb/>res fort riches vers l'Orient & </s> <s xml:id="echoid-s5380" xml:space="preserve">d'autre vers l'Occident.</s> <s xml:id="echoid-s5381" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5382" xml:space="preserve">On peut auſſi par ſon moïen ſe conduire par terre dans un voïage, <lb/>lorſqu'on ne trou ve perſonne pour enſeigner le chemin, ayant une <lb/>Carte géographique; </s> <s xml:id="echoid-s5383" xml:space="preserve">car pour cet effet il n'y a qu'à poſer le centre <lb/>de la Bouſlole ſur le lieu du départ, faire couvenirl éguille aiman-<lb/>tée avec le Méridien de ce lieu, & </s> <s xml:id="echoid-s5384" xml:space="preserve">remarquer quel angle fait ce Mé-<lb/>ridien avec la ligne de Route; </s> <s xml:id="echoid-s5385" xml:space="preserve">c'eſt-à-dire, qui conduit au lieu où <lb/>l'on veut aller. </s> <s xml:id="echoid-s5386" xml:space="preserve">Ainſi les Pilotes & </s> <s xml:id="echoid-s5387" xml:space="preserve">les Voïageurs connoiſſent par <lb/>la Bouſſole la ſituation dans laquelle ils ſe trouvent à l ègard des <lb/>Poles du Monde.</s> <s xml:id="echoid-s5388" xml:space="preserve"/> </p> <pb o="167" file="181" n="181" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. VII."/> <p> <s xml:id="echoid-s5389" xml:space="preserve">Elle eſt auſſi fort utile au gens qui travaillent ſous terre dans les <lb/>Carrieres & </s> <s xml:id="echoid-s5390" xml:space="preserve">dans les Mines; </s> <s xml:id="echoid-s5391" xml:space="preserve">car ayant remarqué ſur terre le point <lb/>où l'on veut aller, on poſe la Bouſlole à l'ouverture du trou pour <lb/>voir l'angle que fait la ligne de direction avec l'éguille; </s> <s xml:id="echoid-s5392" xml:space="preserve">& </s> <s xml:id="echoid-s5393" xml:space="preserve">quand <lb/>on eſt ſous terre on fait une tranchée qui faſſe le même angle avec <lb/>la Bouſſole, & </s> <s xml:id="echoid-s5394" xml:space="preserve">par ce moyen on arrive au lieu propoſé.</s> <s xml:id="echoid-s5395" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5396" xml:space="preserve">Il y a encore beaucoup d'autres uſages, dont nous allons ex-<lb/>pliquer les principaux.</s> <s xml:id="echoid-s5397" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div444" type="section" level="1" n="211"> <head xml:id="echoid-head320" xml:space="preserve">USAGE I.</head> <head xml:id="echoid-head321" style="it" xml:space="preserve">Rour trouver avec la Bouſſole la déclinaiſon d'un Mur.</head> <p> <s xml:id="echoid-s5398" xml:space="preserve">IL faut ſe ſouvenir qu'il y a quatre points que l'on appelle Car-<lb/>dinaux; </s> <s xml:id="echoid-s5399" xml:space="preserve">ſçavoir, le Septentrion, le Midi, l'Orient & </s> <s xml:id="echoid-s5400" xml:space="preserve">l'Occi-<lb/>dent, leſquels partagent l'horiſon en quatre parties égales, comme <lb/>il eſt marqué par la figure premiere.</s> <s xml:id="echoid-s5401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5402" xml:space="preserve">Quand on a trouvé un deces points, on a tous les autres; </s> <s xml:id="echoid-s5403" xml:space="preserve">car, par <lb/>exemple, ſivous avez le Septentrion devant les yeux, le Midi ſera <lb/>derriere vous, l'Orient à vôtre droite & </s> <s xml:id="echoid-s5404" xml:space="preserve">l'Occident à vôtre gauche.</s> <s xml:id="echoid-s5405" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5406" xml:space="preserve">Un Mur qui ſeroit élevé ſur une ligne qui tend du Septentrion au <lb/>Midi, ſeroit dans le plan du Méridien; </s> <s xml:id="echoid-s5407" xml:space="preserve">de maniere qu'une de ſes fa-<lb/>ces ſeroit tournée directement vers l'Orient, & </s> <s xml:id="echoid-s5408" xml:space="preserve">l'autre vers l'Oc-<lb/>cident.</s> <s xml:id="echoid-s5409" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5410" xml:space="preserve">Un autre Mur qui feroit angles droits avec ce premier, c'eſt-à-di-<lb/>re, qui ſeroit élevé ſur la ligne qui tend d'Orient en Occident, ſe-<lb/>roit parallele au premier vertical & </s> <s xml:id="echoid-s5411" xml:space="preserve">ne déclineroit point; </s> <s xml:id="echoid-s5412" xml:space="preserve">une de ſes <lb/>faces ſeroit tournée directement au Midi, & </s> <s xml:id="echoid-s5413" xml:space="preserve">l'autre au Septentrion.</s> <s xml:id="echoid-s5414" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5415" xml:space="preserve">Mais ſi l'on s'imagine un Mur élevé ſur la ligne CD, il ſera dit <lb/>décliner d'autant de degrez qu'en contient l'arc F; </s> <s xml:id="echoid-s5416" xml:space="preserve">c'eſt pourquoi, ſi <lb/>par exemple, cet arc eſt de 40 deg. </s> <s xml:id="echoid-s5417" xml:space="preserve">la face de ce Mur qui eſt tour-<lb/>née vers le Midi, décline du Midi vers Orient de 40 deg. </s> <s xml:id="echoid-s5418" xml:space="preserve">la face <lb/>oppoſée du même Mur décline du Septentrion à l'Occident de 40 <lb/>degrez, de ſorte que la déclinaiſon d'un Mur n'eſt autre choſe que <lb/>l'angle que fait ce Mur avec le premier vertical.</s> <s xml:id="echoid-s5419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5420" xml:space="preserve">Un autre Mur qui ſeroit parallele à la ligne GH, déclineroit <lb/>d'autant de degrez qu'en contient l'arc C; </s> <s xml:id="echoid-s5421" xml:space="preserve">c'eſt pourquoi ſi cet arc <lb/>eſt de 30 deg. </s> <s xml:id="echoid-s5422" xml:space="preserve">la face du Mur qui regarde le Midi déclineroit de 30 <lb/>deg. </s> <s xml:id="echoid-s5423" xml:space="preserve">du Midi à l'Occident, la face oppoſée déclineroit pareillement <lb/>de 30 deg du Septentriou à l'Orient.</s> <s xml:id="echoid-s5424" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5425" xml:space="preserve">En toutes les operations qui ſe font avec la Bouſſole, il ſaut avoir <lb/>grand ſoin d'éloigner toute ſorte de fer, & </s> <s xml:id="echoid-s5426" xml:space="preserve">prendre bien garde qu'il <lb/> <pb o="168" file="182" n="182" rhead="CONSTRUCT. ET USAGES DE LA BOUSSOLE"/> n'y en ait de caché, car le fer change entierement la direction de <lb/>l'Eguille aimantée.</s> <s xml:id="echoid-s5427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5428" xml:space="preserve">Je ſuppoſe que le Pivot ſur lequel eſt poſée la chape de l'Eguille <lb/>eſt au centre d'un cercle diviſé en 360 deg. </s> <s xml:id="echoid-s5429" xml:space="preserve">ou 4 fois 90, dont le <lb/>premier degré eſt dans la ligne qui tend du Septentrion au Midi, & </s> <s xml:id="echoid-s5430" xml:space="preserve"><lb/>que la Bouſſole eſt quarrée, comme elle eſt ici repreſentée.</s> <s xml:id="echoid-s5431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5432" xml:space="preserve">Appliquez le long du Mur le côté de la Bouſſole où eſt la marque <lb/>du Septentrion; </s> <s xml:id="echoid-s5433" xml:space="preserve">le nombre des degrez où s'arrêtera l'éguille aiman-<lb/>tée, marquera la déclinaiſon du Mur, & </s> <s xml:id="echoid-s5434" xml:space="preserve">dequel côté. </s> <s xml:id="echoid-s5435" xml:space="preserve">Si, par exem-<lb/>ple, la pointe de l'éguille qui marque le Septentrion tend vers le <lb/>Mur, c'eſt une marque qu'il peut être éclairé du Soleil à midi; </s> <s xml:id="echoid-s5436" xml:space="preserve">& </s> <s xml:id="echoid-s5437" xml:space="preserve">ſi <lb/>elle s'arrête ſur le 30 deg. </s> <s xml:id="echoid-s5438" xml:space="preserve">compté du Septentrion vers l'Orient, la <lb/>déclinaiſon eſt d'autant de degrez du Midi à l'Orient. </s> <s xml:id="echoid-s5439" xml:space="preserve">Si elle s'ar-<lb/>rête ſur le 30 degré compté du Septentrion vers l'Occident, la dé-<lb/>clinaiſon eſt d'autant de degrez du Midi à l'Occident.</s> <s xml:id="echoid-s5440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5441" xml:space="preserve">Mais comme l'Eguille aimantée décline preſentement à Paris <lb/>d'environ 12 deg & </s> <s xml:id="echoid-s5442" xml:space="preserve">15 min. </s> <s xml:id="echoid-s5443" xml:space="preserve">au Nord Oüeſt; </s> <s xml:id="echoid-s5444" xml:space="preserve">pour corriger ce dé-<lb/>faut on doit les ajoûter au nombre des degrez marquez par l'Eguil-<lb/>le lorſque la déclinaiſon eſt vers l'Orient. </s> <s xml:id="echoid-s5445" xml:space="preserve">Il faut au contraire les ô-<lb/>ter lorſque la déclinaiſon eſt du côté d'Occident.</s> <s xml:id="echoid-s5446" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5447" xml:space="preserve">Ainſi ſuppoſant, comme nous venons de faire, que l'Eguille ſoit <lb/>arrêtée ſur le 30<emph style="sub">me</emph> degré vers l'Orient; </s> <s xml:id="echoid-s5448" xml:space="preserve">la déclinaiſon du Mur ſera <lb/>de 42 deg. </s> <s xml:id="echoid-s5449" xml:space="preserve">15 min. </s> <s xml:id="echoid-s5450" xml:space="preserve">du Midi vers Orient. </s> <s xml:id="echoid-s5451" xml:space="preserve">Mais ſi l'Eguille s'arrête <lb/>du côté d'Occident ſur le 30<emph style="sub">me</emph> degré, la déclinaiſon du Mur ſera <lb/>de 17 deg. </s> <s xml:id="echoid-s5452" xml:space="preserve">45 min. </s> <s xml:id="echoid-s5453" xml:space="preserve">du Midivers l'Occident.</s> <s xml:id="echoid-s5454" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5455" xml:space="preserve">Que ſi la pointe de l'Eguille aimantée qui marque le Midi, <lb/>tend vers le Mur, c'eſt une marque que le Midi eſt de l'autre côté <lb/>du Mur, & </s> <s xml:id="echoid-s5456" xml:space="preserve">par conſequent que la face dont on veut trouver la dé-<lb/>clinaiſon, ne ſera point éclairée du Soleil à midi; </s> <s xml:id="echoid-s5457" xml:space="preserve">c'eſt pourquoi ſa <lb/>déclinaiſon ſera du Septentrion à l'Orient, ou à l'Occident ſelon <lb/>qu'il ſera tourné vers l'une ou l'autre de ces Parties du Monde. </s> <s xml:id="echoid-s5458" xml:space="preserve">Ceci <lb/>ſera plus amplement expliqué en parlant des Cadrans Solaires.</s> <s xml:id="echoid-s5459" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div445" type="section" level="1" n="212"> <head xml:id="echoid-head322" xml:space="preserve">USAGE II.</head> <head xml:id="echoid-head323" style="it" xml:space="preserve">Pour meſurer un angle ſur la terre avec la Bouſſole.</head> <p> <s xml:id="echoid-s5460" xml:space="preserve">SOit l'angle DAE propoſé à meſurer. </s> <s xml:id="echoid-s5461" xml:space="preserve">Appliquez le long d'une <lb/> <anchor type="note" xlink:label="note-182-01a" xlink:href="note-182-01"/> deslignes qui forment l'angle, comme lelong de la ligne AD, le <lb/>côté dela Bouſſole où eſt la marque du Septentrion; </s> <s xml:id="echoid-s5462" xml:space="preserve">faites en ſorte <lb/>quel' Eguille tourne librement ſur ſon pivot, & </s> <s xml:id="echoid-s5463" xml:space="preserve">quand elle ſera ar-<lb/>rêtée, prenez garde quel nombre de degrez répond à la pointe de l'é-<lb/> <pb o="169" file="183" n="183" rhead="POUR LEVER LES PLANS. Liv. IV. Ch. VII."/> guille qui indique le Septentrion; </s> <s xml:id="echoid-s5464" xml:space="preserve">& </s> <s xml:id="echoid-s5465" xml:space="preserve">le trouvant, par exemple, de <lb/>80 deg. </s> <s xml:id="echoid-s5466" xml:space="preserve">la déclinaiſon de ladite ligne ſera d'autant de degrez. </s> <s xml:id="echoid-s5467" xml:space="preserve">Pre-<lb/>nez enſuite de la même maniere la déclinaiſon de la ligne AE, que <lb/>je ſuppoſe de 215 deg. </s> <s xml:id="echoid-s5468" xml:space="preserve">ôtez le petit nombre 80, du plus grand 215, <lb/>reſtera 135, qu'il faut ſouſtraire de 180 ce dernier reſte ſera 45 d. <lb/></s> <s xml:id="echoid-s5469" xml:space="preserve">pour la valeur de l'angle propoſé à meſurer.</s> <s xml:id="echoid-s5470" xml:space="preserve"/> </p> <div xml:id="echoid-div445" type="float" level="2" n="1"> <note position="left" xlink:label="note-182-01" xlink:href="note-182-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s5471" xml:space="preserve">Mais ſi la déclinaiſon de la ligne AD n'étoit, par exemple, que <lb/>de 30 deg. </s> <s xml:id="echoid-s5472" xml:space="preserve">& </s> <s xml:id="echoid-s5473" xml:space="preserve">que celle de la ligne AE fût de 265, la difference de <lb/>ces deux déclinaiſons qui eſt de 235, ſeroit trop grande pour être <lb/>ôtée de 180; </s> <s xml:id="echoid-s5474" xml:space="preserve">c'eſt pourquoi en ce cas il faudroit ôter 180 du plus <lb/>grand nombre 235, le reſte 55 ſera la valeur de l'angle propoſé.</s> <s xml:id="echoid-s5475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5476" xml:space="preserve">Quand on meſure des angles avec la Bouſſole, il n'eſt pas neceſ-<lb/>ſaire d'avoir aucun égard à la variation de l éguille aimantée, puiſ-<lb/>que cette variation ſera toûjours la même en toutes les differentes <lb/>poſitions de l'éguille, pourvü toutefois qu'il n'y ait pas de fer qui la <lb/>faſſe dévoïer; </s> <s xml:id="echoid-s5477" xml:space="preserve">& </s> <s xml:id="echoid-s5478" xml:space="preserve">lorſqu'on ne peut poſer la Bouſſole proche du plan, <lb/>par quelque empêchement, il ſuffira de la placer bien parallelement, <lb/>comme la figure le montre, elle fera le même effet.</s> <s xml:id="echoid-s5479" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div447" type="section" level="1" n="213"> <head xml:id="echoid-head324" xml:space="preserve">USAGE III.</head> <head xml:id="echoid-head325" style="it" xml:space="preserve">Pour lever le Plan d'une Forêt, d'un Marais ou d'un Chemin <lb/>avec ſes détours.</head> <p> <s xml:id="echoid-s5480" xml:space="preserve">SOit propoſé à lever le Plan d'un Marais ou Etang ABCDE, <lb/> <anchor type="note" xlink:label="note-183-01a" xlink:href="note-183-01"/> dans lequel on ne peut entrer. </s> <s xml:id="echoid-s5481" xml:space="preserve">Pour ces ſortes d'operations il faut <lb/>qu'il y ait ſur la Bouſſole 2 pinules immobiles attachées ſur la li-<lb/>gne qui tend du Septentrion au Midi. </s> <s xml:id="echoid-s5482" xml:space="preserve">Faites planter des piquets aſ-<lb/>ſez longs & </s> <s xml:id="echoid-s5483" xml:space="preserve">bien à plomb, de maniere qu'ils ſoient dans les lignes <lb/>paralleles aux côtes qui ſont l'enceinte du Marais; </s> <s xml:id="echoid-s5484" xml:space="preserve">placez la Bouſſo-<lb/>le ſur ſon pied dans une ſituation horiſontale; </s> <s xml:id="echoid-s5485" xml:space="preserve">bornaiez deux de ces <lb/>piquets par les fentes des pinules, mettant toûjours auprès de l'œil <lb/>celle qui eſt ſur la partie méridionale de la Bouſſole; </s> <s xml:id="echoid-s5486" xml:space="preserve">puis ayant tra-<lb/>cé ſur du papier une figure qui repreſente à peu près le plan du Ma-<lb/>rais, écrivez ſur chaque ligne le nombre des degrez que marquera <lb/>l'éguille lorſqu'elle ſera arrêtée. </s> <s xml:id="echoid-s5487" xml:space="preserve">Faites en même tems meſurer avec <lb/>la toiſe la longueur exacte de chaque côté du Marais, & </s> <s xml:id="echoid-s5488" xml:space="preserve">marquez-en <lb/>la valeur ſur chaque ligne correſpondante de vôtre mémorial. </s> <s xml:id="echoid-s5489" xml:space="preserve">Lorſ-<lb/>que vous aurez fait tout le tour du Marais, les degrez marquez par <lb/>l'éguille de la Bouſſole ſerviront à former les angles de la figure, & </s> <s xml:id="echoid-s5490" xml:space="preserve">la <lb/>longueur de chaque ligne déterminera tout le plan du Marais pro-<lb/>poſé.</s> <s xml:id="echoid-s5491" xml:space="preserve"/> </p> <div xml:id="echoid-div447" type="float" level="2" n="1"> <note position="right" xlink:label="note-183-01" xlink:href="note-183-01a" xml:space="preserve">Fig. 3.</note> </div> <pb o="170" file="184" n="184" rhead="CONSTRUCT. ET USAGES DE LA BOUSSOLE"/> <p> <s xml:id="echoid-s5492" xml:space="preserve">Suppoſons pour exemple, qu'ayant placé la Bouſſole le long du <lb/>côté AB, ou ce qui eſt la même choſe, le long d'une ligne parailele <lb/>à ce côté, & </s> <s xml:id="echoid-s5493" xml:space="preserve">que mettant l'œil proche la pinule du midi, on décou-<lb/>vre deux piquets plantez dans ladite ligne; </s> <s xml:id="echoid-s5494" xml:space="preserve">ſi l'éguille s'arrête ſur le <lb/>30<emph style="sub">me</emph> degré vers l'Occident, j'écris ce nombre 30 deg. </s> <s xml:id="echoid-s5495" xml:space="preserve">le long de la <lb/>ligne AB du mémorial, & </s> <s xml:id="echoid-s5496" xml:space="preserve">en même tems la quantité de 50 toiſes <lb/>qui ont été meſurées du point A au point B. </s> <s xml:id="echoid-s5497" xml:space="preserve">Je tranſporte enſuite <lb/>la Bouſſole avec ſon pied, le long du côté BC, ou dans l'alignement <lb/>des piquets, plantez parallelement audit côté, mettant toûjours la <lb/>pinule du Sud ou Midi du côté de l'œil; </s> <s xml:id="echoid-s5498" xml:space="preserve">ſi l'éguille s'arrête ſur le <lb/>100 degré, j'écris ce nombre ſur la ligne BC, & </s> <s xml:id="echoid-s5499" xml:space="preserve">en même tems la <lb/>quantité de 70 toiſes qui ont été meſurées du point B au point C: <lb/></s> <s xml:id="echoid-s5500" xml:space="preserve">Faiſant ainſi tout le tour du Marais, on marquera ſur chaque ligne <lb/>correſpondante le nombre des degrez & </s> <s xml:id="echoid-s5501" xml:space="preserve">des toiſes, par le moïen deſ-<lb/>quels on mettra au net le plan propoſé en la maniere ſuivante, en fe <lb/>ſervant d'un Rapporteur, ou demi-cercle, & </s> <s xml:id="echoid-s5502" xml:space="preserve">d'une Regle diviſée <lb/>en parties égales, ou bien d'un Compas de Proportion.</s> <s xml:id="echoid-s5503" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Angles \\ obſervez # Angles \\ ſouſtraits. <lb/>30 degrez # Degrez. <lb/>100. . . . # 70 <lb/>130. . . . # 30 <lb/>240. . . . # 100 <lb/>300. . . . # 60 <lb/></note> <p> <s xml:id="echoid-s5504" xml:space="preserve">Marquez de ſuite tous les <lb/>Angles obſervez avec la Bouſ-<lb/>ſole, & </s> <s xml:id="echoid-s5505" xml:space="preserve">ſouſtraïez le moindre <lb/>du plus grand que vous mar-<lb/>querez entre deux, comme on <lb/>voit en cette Table.</s> <s xml:id="echoid-s5506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5507" xml:space="preserve">Commencez par tracer la ligne indéfinie AB, ſur laquelle vous <lb/>porterez 50 parties égales de vôtre Echellle, à cauſe des 50 toiſes, <lb/>meſurées ſur le terrain; </s> <s xml:id="echoid-s5508" xml:space="preserve">faites au point B avec un rapporteur l'angle <lb/>extérieur de 70 deg. </s> <s xml:id="echoid-s5509" xml:space="preserve">& </s> <s xml:id="echoid-s5510" xml:space="preserve">tirez la ligne indéfinie BC, ſur laquelle vous <lb/>marquerez de B en C 70 toiſes, qui ont été meſurées ſur le terrain: <lb/></s> <s xml:id="echoid-s5511" xml:space="preserve">faites au point C l'angle extérieur de 30 deg. </s> <s xml:id="echoid-s5512" xml:space="preserve">& </s> <s xml:id="echoid-s5513" xml:space="preserve">tirez la ligne indé-<lb/>finie CD, laquelle vous déterminerez de 65 toiſes de longueur, <lb/>conformément à la meſure qui en a été trouvée. </s> <s xml:id="echoid-s5514" xml:space="preserve">Faites pareillement <lb/>au point D l'angle extérieur de 110 deg. </s> <s xml:id="echoid-s5515" xml:space="preserve">& </s> <s xml:id="echoid-s5516" xml:space="preserve">tirez la ligne DE de 70 <lb/>toiſes. </s> <s xml:id="echoid-s5517" xml:space="preserve">Faites enfin au point E l'angle extérieur de 60 deg. </s> <s xml:id="echoid-s5518" xml:space="preserve">& </s> <s xml:id="echoid-s5519" xml:space="preserve">tirez <lb/>la derniere ligne AE de 94 toifes, & </s> <s xml:id="echoid-s5520" xml:space="preserve">le plan ſera achevé.</s> <s xml:id="echoid-s5521" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5522" xml:space="preserve">Enſuite il ſera facile de l'orienter, puiſque vous ſcavez quel an-<lb/>gle fait l'éguille avec chaque côté du plan.</s> <s xml:id="echoid-s5523" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5524" xml:space="preserve">Remarquez, que les angles ſouſtraits vous donnent les angles <lb/> <pb o="171" file="185" n="185" rhead="POUR LES FORTIFICATIONS. Liv. IV. Ch. VIII."/> extérieurs, & </s> <s xml:id="echoid-s5525" xml:space="preserve">que leurs complémens ſont les angles de la figure.</s> <s xml:id="echoid-s5526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5527" xml:space="preserve">Remarquez auſſi que tous les angles de la figure pris enſenble <lb/>doivent faire deux fois autant d'angles droits, moins quatre, qu'elle <lb/>a de côtez. </s> <s xml:id="echoid-s5528" xml:space="preserve">Ainſi, par exemple, la figure de cet uſage ayant 5 côtez, <lb/>tous ſes angles ajoûtez enſemble font 540 deg. </s> <s xml:id="echoid-s5529" xml:space="preserve">ou 6 fois 90, ce qui <lb/>peut ſervir à prouver les operations.</s> <s xml:id="echoid-s5530" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5531" xml:space="preserve">Cette maniere de lever un plan paroît aſſez expeditive, mais il <lb/>y a bien de la difficulté de faire avec la Bouſſole des operations <lb/>fort exactes, à cauſe du fer caché qui ſe peut rencontrer dans les <lb/>lieux où l'on eſt obligé de la placer.</s> <s xml:id="echoid-s5532" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div449" type="section" level="1" n="214"> <head xml:id="echoid-head326" xml:space="preserve">CHAPITRE VIII.</head> <head xml:id="echoid-head327" style="it" xml:space="preserve">Uſages des ſuſdits Inſtrumens de Mathematique, appliquez <lb/>à la Fortification des Places.</head> <p> <s xml:id="echoid-s5533" xml:space="preserve">LA Fortification eſt l'art de mettre un lieu en tel état, qu'un pe-<lb/>tit Corps de Troupes y puiſſe reſiſter avantageuſement à une <lb/>Armée conſiderable.</s> <s xml:id="echoid-s5534" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5535" xml:space="preserve">Les Maximes qui ſervent de fondement à l'art de fortifier, ſont <lb/>de certaines Regles generales établies par les Ingenieurs, fondées <lb/>ſur la raiſon & </s> <s xml:id="echoid-s5536" xml:space="preserve">ſur l'experience, dont nous parlerons ci-après.</s> <s xml:id="echoid-s5537" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5538" xml:space="preserve">L'Ingenieur principal ayant examineé l'étenduë & </s> <s xml:id="echoid-s5539" xml:space="preserve">la ſituation <lb/>du lieu que l'on veut fortifier, communique ſon deſſein par un <lb/>plan & </s> <s xml:id="echoid-s5540" xml:space="preserve">un profil, comme il paroît par la Planche (A); </s> <s xml:id="echoid-s5541" xml:space="preserve">à quoi il <lb/>ajoûte ordinairement un devis, c'eſt-à-dire, un diſcours qui ex-<lb/>plique l'ordre & </s> <s xml:id="echoid-s5542" xml:space="preserve">la qualité des Matériaux qui doivent y être em-<lb/>ployez par les Entrepreneurs; </s> <s xml:id="echoid-s5543" xml:space="preserve">leſquels ayant fait ſonder en pluſieurs <lb/>endroits du lieu propoſé, la nature du terrain, feront un Marché <lb/>de chaque toiſe d'ouvrage, par le moyen du quel l'ingenieur pour-<lb/>ra voir à peu près la depenſe de tout l'ouvrage, le nombre des <lb/>Oavriers neceſſaires pour l'execution, & </s> <s xml:id="echoid-s5544" xml:space="preserve">le tems qu'il conviendra <lb/>d'y employer pour le rendre parfait.</s> <s xml:id="echoid-s5545" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5546" xml:space="preserve">Le plan d'une fortification repreſente par pluſieurs lignes tra-<lb/>cées horiſontalement ou de niveau l'enceinte de la Place.</s> <s xml:id="echoid-s5547" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5548" xml:space="preserve">Ce deſſein contient pluſieurs lignes paralleles entr'elles, mais le <lb/>premier & </s> <s xml:id="echoid-s5549" xml:space="preserve">principal trait, qui doit être marqué par une ligne plus <lb/>apparente que les autres, repreſente la principale enceinte du corps <lb/>de la Place entre le Rempart & </s> <s xml:id="echoid-s5550" xml:space="preserve">le Foſſé: </s> <s xml:id="echoid-s5551" xml:space="preserve">de ſorte par le Plan & </s> <s xml:id="echoid-s5552" xml:space="preserve">ſon <lb/>Echelle on connoît les longueurs & </s> <s xml:id="echoid-s5553" xml:space="preserve">les largeurs de tous les Ou-<lb/> <pb o="172" file="186" n="186" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> vrages qui compoſent la Fortification. </s> <s xml:id="echoid-s5554" xml:space="preserve">Figure premiere.</s> <s xml:id="echoid-s5555" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5556" xml:space="preserve">Le profil repreſente les principaux traits qui paroîtroient ſur <lb/>une ſurface plane qui couperoit verticalement, & </s> <s xml:id="echoid-s5557" xml:space="preserve">ſepareroit par le <lb/>milieu tous ces mêmes ouvrages. </s> <s xml:id="echoid-s5558" xml:space="preserve">Pour le tracer on a coûtume de <lb/>ſe ſervir d'une plus grande Echelle que celle du Plan, afin d'y <lb/>pouvoir mieux diſtinguer leurs largeurs & </s> <s xml:id="echoid-s5559" xml:space="preserve">leurs hauteurs ou pro-<lb/>fondeurs, comme il paroît par la figure 3.</s> <s xml:id="echoid-s5560" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div450" type="section" level="1" n="215"> <head xml:id="echoid-head328" style="it" xml:space="preserve">Noms des principales lignes & des principaux angles qui <lb/>forment le Plan.</head> <p> <s xml:id="echoid-s5561" xml:space="preserve">LA ligne AB ſe nomme côté exterieur du Polygone. <lb/></s> <s xml:id="echoid-s5562" xml:space="preserve"> <anchor type="note" xlink:label="note-186-01a" xlink:href="note-186-01"/> </s> </p> <div xml:id="echoid-div450" type="float" level="2" n="1"> <note position="left" xlink:label="note-186-01" xlink:href="note-186-01a" xml:space="preserve">Planche <lb/>A. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s5563" xml:space="preserve">LE, côté interieur du Polygone.</s> <s xml:id="echoid-s5564" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5565" xml:space="preserve">LG, demie gorge du Baſtion, dont E G eſt le flanc, A E la fa-<lb/>ce, & </s> <s xml:id="echoid-s5566" xml:space="preserve">A L la capitale.</s> <s xml:id="echoid-s5567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5568" xml:space="preserve">G H eſt la courtine, & </s> <s xml:id="echoid-s5569" xml:space="preserve">A H, ligne de défenſe razante.</s> <s xml:id="echoid-s5570" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5571" xml:space="preserve">La ſigure A L G E repreſente un demi-Baſtion.</s> <s xml:id="echoid-s5572" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5573" xml:space="preserve">L'Angle ANB eſt l'angle du Centre.</s> <s xml:id="echoid-s5574" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5575" xml:space="preserve">L'Angle KAB, l'angle du Polygone.</s> <s xml:id="echoid-s5576" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5577" xml:space="preserve">L'Angle IAE fait des deux faces, s'appelle Angle flanqué, <lb/>ou Angle du Baſtion.</s> <s xml:id="echoid-s5578" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5579" xml:space="preserve">L'Angle AEG fait de la face & </s> <s xml:id="echoid-s5580" xml:space="preserve">du flanc, ſe nomme Angle <lb/>de l'Epaule.</s> <s xml:id="echoid-s5581" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5582" xml:space="preserve">L'Angle EGH fait du flanc & </s> <s xml:id="echoid-s5583" xml:space="preserve">de la courtine, ſe nomme An-<lb/>gle du flanc.</s> <s xml:id="echoid-s5584" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5585" xml:space="preserve">L'Angle EGB fait du flanc & </s> <s xml:id="echoid-s5586" xml:space="preserve">de la ligne de défenſe razante, <lb/>ſe nomme Angle flanquant intérieur.</s> <s xml:id="echoid-s5587" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5588" xml:space="preserve">L'Angle EDF fait par les deux Razantes qui s'entre-coupent <lb/>vers le milieu de la Courtine, s'appelle Angle flanquant extérieur, <lb/>ou Angle de Tenaille.</s> <s xml:id="echoid-s5589" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5590" xml:space="preserve">L'Angle EAG fait de la Courtine & </s> <s xml:id="echoid-s5591" xml:space="preserve">de la ligne de défenſe ra-<lb/>zante, s'appelle Angle diminuë. </s> <s xml:id="echoid-s5592" xml:space="preserve">Cet Angle eſt toûjours égal à <lb/>celui qui eſt fait de la face du Baſtion & </s> <s xml:id="echoid-s5593" xml:space="preserve">de la Baſe, ou du côté <lb/>extérieur.</s> <s xml:id="echoid-s5594" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div452" type="section" level="1" n="216"> <head xml:id="echoid-head329" style="it" xml:space="preserve">Maximes fondamentales de la Fortification</head> <p> <s xml:id="echoid-s5595" xml:space="preserve">CEs principales Maximes ſe peuvent reduire à ſix.</s> <s xml:id="echoid-s5596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5597" xml:space="preserve">La premiere eſt, qu'il n'y ait aucun endroit dans le contour <lb/>d'une Place qui ne ſoit flanqué ou défendu des flance; </s> <s xml:id="echoid-s5598" xml:space="preserve">parce que <lb/>s'il y avoit quelque endroit autour d'une Place, qui ne fut pas vû <lb/>& </s> <s xml:id="echoid-s5599" xml:space="preserve">défendu par les Aſſiegez, l'Ennemi pourroit s'y mettre à cou-<lb/> <pb o="173" file="187" n="187" rhead="POUR LES FORTIFICATIONS. Liv. IV. Ch. VIII."/> vert, & </s> <s xml:id="echoid-s5600" xml:space="preserve">ſe rendre maître de la Place en peu de tems.</s> <s xml:id="echoid-s5601" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5602" xml:space="preserve">Il s'enſuit de cette Maxime, que l'Angle flanqué, ou l'Angle <lb/>fait des deux faces du Baſtion trop aigu eſt défectueux, parce que <lb/>ſa pointe peut être facilement émouſſée ou rompuë par le canon <lb/>des Aſſiegeans, & </s> <s xml:id="echoid-s5603" xml:space="preserve">qu'enſuite le Mineur y peut travailler en ſûreté, <lb/>pour en agrandir la Breche.</s> <s xml:id="echoid-s5604" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5605" xml:space="preserve">C'eſt encore un pareil défaut d'arrondir la pointe des Baſtions, <lb/>par la même raiſon.</s> <s xml:id="echoid-s5606" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5607" xml:space="preserve">La ſeconde eſt, que la force ſoit, autant qu'il eſt poſſible, éga-<lb/>lement diſtribuée par tout; </s> <s xml:id="echoid-s5608" xml:space="preserve">parce que, s'il y a quelque endroit plus <lb/>foible, ce ſera par là que l'Ennemi l'attaquera: </s> <s xml:id="echoid-s5609" xml:space="preserve">ceſt pourquoi ſi <lb/>par la nature du terrain, un côté ſe trouve plus foible que les au-<lb/>tres, on y ajoûte quelque ouvrage, pour augmenter ſa force, en <lb/>multipliant ſa défenſe.</s> <s xml:id="echoid-s5610" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5611" xml:space="preserve">Latroiſiéme eſt, que les parties flanquées ne ſoient éloignées de <lb/>celles qui les flanquent, que de la portée du Mouſquet; </s> <s xml:id="echoid-s5612" xml:space="preserve">c'eſt pour-<lb/>quoi la ligne de défenſe, ou la diſtance de la pointe du Baſtion aux <lb/>flancs des Baſtions voiſins, ne doit guéres exceder 125 toiſes, qui <lb/>eſt la portée ordinaire des Mouſquets chargez à la hâte, comme <lb/>ſont ceux des Soldats dans un Siege.</s> <s xml:id="echoid-s5613" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5614" xml:space="preserve">La quatriéme Maxime eſt, que les flancs des Baſtions ſoient aſ-<lb/>ſez grands pour contenir du moins trente Mouſquetaires de front, <lb/>& </s> <s xml:id="echoid-s5615" xml:space="preserve">quatre ou cinq pieces de canon montées ſur leurs affuts, afin de <lb/>bien défendre toute la face du Baſtion, qui pourroit être attaquée <lb/>par l'ennemi: </s> <s xml:id="echoid-s5616" xml:space="preserve">& </s> <s xml:id="echoid-s5617" xml:space="preserve">comme la principale défenſe ſe tire des flancs, il <lb/>eſt plus à propos qu'ils ſoient perpendiculaires ſur la ligne de dé-<lb/>fenſe, que de toute autre ſituation. </s> <s xml:id="echoid-s5618" xml:space="preserve">Cette méthode a été enſeignée <lb/>par M. </s> <s xml:id="echoid-s5619" xml:space="preserve">le Comte de Pagan, & </s> <s xml:id="echoid-s5620" xml:space="preserve">ſuivie par les plus habiles Ingenieurs <lb/>qui ont paru depuis, & </s> <s xml:id="echoid-s5621" xml:space="preserve">particulierement par M. </s> <s xml:id="echoid-s5622" xml:space="preserve">le Marêchal de <lb/>Vauban, qui par ſes ſignalez ſervices, a merité l'eſtime de tous les <lb/>Gens de Guerre & </s> <s xml:id="echoid-s5623" xml:space="preserve">habiles Ingenieurs de ſon tems.</s> <s xml:id="echoid-s5624" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5625" xml:space="preserve">La cinquiéme eſt, que la Fortereſſe ne ſoit commandée d'aucun <lb/>endroit, qui ſoit à la portée des armes à feu, qui ſont le mouſquet <lb/>& </s> <s xml:id="echoid-s5626" xml:space="preserve">le canon; </s> <s xml:id="echoid-s5627" xml:space="preserve">car au contraire, elle doit commander ſur tous les <lb/>lieux d'alentour.</s> <s xml:id="echoid-s5628" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5629" xml:space="preserve">La ſixiéme eſt, que les ouvrages les plus proches du centre de la <lb/>Place, ſoient plus élevez & </s> <s xml:id="echoid-s5630" xml:space="preserve">commandent à ceux qui en ſont plus <lb/>éloignez, afin que ſi l'Ennemi vient à ſe rendre maître de quelque <lb/>partie des dehors, ou de quelque ouvrage éloigné, il puiſſe en être <lb/>repouſſé par ceux qui détendent le Corps de la Place.</s> <s xml:id="echoid-s5631" xml:space="preserve"/> </p> <pb o="174" file="188" n="188" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> </div> <div xml:id="echoid-div453" type="section" level="1" n="217"> <head xml:id="echoid-head330" style="it" xml:space="preserve">Pour tracer ſur le papier un Plan fortifié, ſuivant la métbode <lb/>du Comte de 'Pagan.</head> <p> <s xml:id="echoid-s5632" xml:space="preserve">SOit, par exemple, propoſé un Exagone: </s> <s xml:id="echoid-s5633" xml:space="preserve">tracez premierement <lb/> <anchor type="note" xlink:label="note-188-01a" xlink:href="note-188-01"/> la ligne AB de 120 toiſes, pour côté extericur dudit Exagone; <lb/></s> <s xml:id="echoid-s5634" xml:space="preserve">ſur le point du milieu C, tirez à angles droits la ligne CD, <lb/>de 30 toiſes; </s> <s xml:id="echoid-s5635" xml:space="preserve">tirez énſuite les lignes ADH, BDG, s'entre-cou-<lb/>pantes au point D, prenez ſur vôtre Echelle 55 toiſes, pour déter-<lb/>miner la longueur des faces AE, BF; </s> <s xml:id="echoid-s5636" xml:space="preserve">du point E tirez le flanc EG <lb/>faiſant angle droit au point G, à l'extremité de la ligne de défenſe <lb/>razante BG, & </s> <s xml:id="echoid-s5637" xml:space="preserve">pareillement l'autre flanc FH a angle droit ſur AH; </s> <s xml:id="echoid-s5638" xml:space="preserve"><lb/>tirez enfin la Courtine GH, & </s> <s xml:id="echoid-s5639" xml:space="preserve">vousaurez un côté dudit Exagone <lb/>fortifié: </s> <s xml:id="echoid-s5640" xml:space="preserve">les autres côtez ſe fortifieront de même. </s> <s xml:id="echoid-s5641" xml:space="preserve">Autour de ce côté <lb/>de Polygone ainſi fortifié, vous tracerez un Foſſé ici repreſenté par <lb/>les lignes AC, CB, paralleles aux faces des Baſtions, leſquelles <lb/>ſe rencontrent vers le milieu de la Courtine au point C: </s> <s xml:id="echoid-s5642" xml:space="preserve">ce Foſſé <lb/>doit avoir de largeur au moins 20 toiſes vis-à-vis les faces, & </s> <s xml:id="echoid-s5643" xml:space="preserve">3 <lb/>toiſes de profondeur. </s> <s xml:id="echoid-s5644" xml:space="preserve">Les terres qui ſe tireront du Foſſé, ſerviront <lb/>à former le Rempartavec ſon Parapet & </s> <s xml:id="echoid-s5645" xml:space="preserve">le Glacis du Chemin cou-<lb/>vert, ayant ſoin de conſerver les terres les plus fines pour le Parapet <lb/>du corps de la Place & </s> <s xml:id="echoid-s5646" xml:space="preserve">celui du Chemin couvert; </s> <s xml:id="echoid-s5647" xml:space="preserve">car ſi ces terres <lb/>étoient pierreuſes, les boulets de canon tirez par les Aſſiegeans con-<lb/>tre ces Parapets, feroient ſauter les pierres, & </s> <s xml:id="echoid-s5648" xml:space="preserve">accableroient les Sol-<lb/>dats qui défendentle corps de la Place: </s> <s xml:id="echoid-s5649" xml:space="preserve">au contraire, quand ces ter-<lb/>res ſont fines & </s> <s xml:id="echoid-s5650" xml:space="preserve">épurées de pierres, le boulet ne fait que ſon trou & </s> <s xml:id="echoid-s5651" xml:space="preserve">s'y <lb/>enterre, pourvû toutefois qu'il y ait aſſez d'épaiſſeur pour l'amortir. </s> <s xml:id="echoid-s5652" xml:space="preserve"><lb/>L'experience a ſait connoître qu'il faut environ 20 pieds d'épaiſſeur <lb/>de terre bien battuë, poùr mettre un parapet à l'épreuve du canon.</s> <s xml:id="echoid-s5653" xml:space="preserve"/> </p> <div xml:id="echoid-div453" type="float" level="2" n="1"> <note position="left" xlink:label="note-188-01" xlink:href="note-188-01a" xml:space="preserve">Planche <lb/>A. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s5654" xml:space="preserve">Le Parapet ſe conſtruit ſur le Rempart large de 4 toiſes, y com-<lb/>pris la Banquette, & </s> <s xml:id="echoid-s5655" xml:space="preserve">ſe trace parallele aux faces, flancs & </s> <s xml:id="echoid-s5656" xml:space="preserve">courtines <lb/>qui forment l'enceinte de la place.</s> <s xml:id="echoid-s5657" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5658" xml:space="preserve">Mais pour le Rempart on lui donne 15 toiſes de largeur par ſa <lb/>baſe, & </s> <s xml:id="echoid-s5659" xml:space="preserve">on le trace parallele aux Courtines ſeulement, afin que <lb/>les Baſtions ſoient pleins, & </s> <s xml:id="echoid-s5660" xml:space="preserve">que l'on y trouve de la terre quand on <lb/>en a beſoin pour faire quelque retranchement.</s> <s xml:id="echoid-s5661" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5662" xml:space="preserve">Quand on laiſſe quelque Baſtion vuide, on y conſtruit des ſous-<lb/>terrains bien voutez, à l'êpreuve de bombe, que l'on recouvre de <lb/>terre bien battuë, & </s> <s xml:id="echoid-s5663" xml:space="preserve">on tâche de faire en ſorte que l'eau de pluie <lb/>n'en penetre point les voutes, afin que les proviſions que l'on ſerrera <lb/>dans ces ſous-terrains s'y puiſſent conſerver en tout tems.</s> <s xml:id="echoid-s5664" xml:space="preserve"/> </p> <pb o="175" file="189" n="189" rhead="POUR LES FOR TIFICATIONS. Liv. IV. Ch. VIII."/> <p> <s xml:id="echoid-s5665" xml:space="preserve">Le Chemin couvert ſe trace parallele au-dehors du Foſſé, large <lb/>d'environ 5 toiſes; </s> <s xml:id="echoid-s5666" xml:space="preserve">on y fait un Parapet de 6 pieds de hauteur, & </s> <s xml:id="echoid-s5667" xml:space="preserve"><lb/>une Banquete au pied dudit Parapet, de 3 pieds de large, & </s> <s xml:id="echoid-s5668" xml:space="preserve">d'un <lb/>pied & </s> <s xml:id="echoid-s5669" xml:space="preserve">demide haut, afin que les Soldats puiſſent tirer commodé-<lb/>ment leurs armes à feu par-deſſus le Parapet, dont le deſſus doit <lb/>être en Glacis, c'eſt-à-dire, ayant une pente douce, qui ne ſe ter-<lb/>mine qu'à 20 ou 30 toiſes dans la campagne; </s> <s xml:id="echoid-s5670" xml:space="preserve">& </s> <s xml:id="echoid-s5671" xml:space="preserve">il faut faire en <lb/>ſorte qu'autour de ce Glacis, qui doit environner toute la Place, <lb/>& </s> <s xml:id="echoid-s5672" xml:space="preserve">loin par delà, s'il ſe peut, il n'y ait aucun lieu creux, où l'En-<lb/>nemi ſe puiſſe mettre à couvert. </s> <s xml:id="echoid-s5673" xml:space="preserve">C'eſt pourquoi quand un Inge-<lb/>nieur viſite les Fortifications d'une Place, il a grand ſoin d'en exa-<lb/>miner les environs, pour faire combler tout ce qui ſe trouve de <lb/>chemin creux, du moins à la portée du mouſquet au-delà du Che-<lb/>min couvert; </s> <s xml:id="echoid-s5674" xml:space="preserve">& </s> <s xml:id="echoid-s5675" xml:space="preserve">en même tems fait razer tout ce qui s'y trouve de <lb/>trop élevé, afin que ceux qui défendent la Place puiſſent décou-<lb/>vrir tous les environs.</s> <s xml:id="echoid-s5676" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div455" type="section" level="1" n="218"> <head xml:id="echoid-head331" style="it" xml:space="preserve">Pour tracer le Profil d'une Place fortifiée.</head> <p> <s xml:id="echoid-s5677" xml:space="preserve">IL faut premierement conſtruire une Echelle de 20 ou 30 toiſes, <lb/>aſſez étenduë, pour qu'une toiſe y ſoit d'une grandeur ſenſible.</s> <s xml:id="echoid-s5678" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5679" xml:space="preserve">Tirez enſuite la ligne indéfinie ON, repreſentant le niveau de <lb/> <anchor type="note" xlink:label="note-189-01a" xlink:href="note-189-01"/> la campagne, prenez ſur vôtre Echelle 15 toiſes, que vous porte-<lb/>rez de O en Q, pour marquer la Baſe du Rempart; </s> <s xml:id="echoid-s5680" xml:space="preserve">portez de Q <lb/>en R 20 toiſes, pour la largeur du Foſſé, vis-à-vis une des faces <lb/>de Baſtion, car il eſt plus large vis-à-vis la Courtine; </s> <s xml:id="echoid-s5681" xml:space="preserve">portez 5 <lb/>toiſes de R en P, pour la largeur du Chemin couvert; </s> <s xml:id="echoid-s5682" xml:space="preserve">& </s> <s xml:id="echoid-s5683" xml:space="preserve">enfin, <lb/>20 ou 30 toiſes de P en N, pour la baſe du Glacis; </s> <s xml:id="echoid-s5684" xml:space="preserve">les plus longs <lb/>ſont les meilleurs.</s> <s xml:id="echoid-s5685" xml:space="preserve"/> </p> <div xml:id="echoid-div455" type="float" level="2" n="1"> <note position="right" xlink:label="note-189-01" xlink:href="note-189-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s5686" xml:space="preserve">Après avoir déterminé les largeurs ou épaiſſeurs, il faut marquer <lb/>les élevations au deſſus du niveau de la campagne, & </s> <s xml:id="echoid-s5687" xml:space="preserve">les enfon-<lb/>cemens au-deſſous du même niveau, comme nous allons faire.</s> <s xml:id="echoid-s5688" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5689" xml:space="preserve">Prenez 3 toiſes ſur ladite Echelle, élevez ſur les points O & </s> <s xml:id="echoid-s5690" xml:space="preserve">Q <lb/>des perpendiculaires de cette hauteur, pour élever au-deſſus du ni-<lb/>veau, le Terre-plein du Rempart, dont O S eſt le talud intérieur, <lb/>ou la Rampe pour monter de la ville ſur le Terre-plein du Rem-<lb/>part ST, qui a 6 ou 7 toiſes de large, pour conduire & </s> <s xml:id="echoid-s5691" xml:space="preserve">voiturer <lb/>commodément les Canons ſur leurs affuts, & </s> <s xml:id="echoid-s5692" xml:space="preserve">toutes les Munitions <lb/>neceſſaires pour la défenſe de la Place. </s> <s xml:id="echoid-s5693" xml:space="preserve">La Rampe ou Montée du <lb/>Rempart, doit être fort aiſée vis-à-vis la gorge des Baſtions, de <lb/>ſorte que les Chariots y puiſſent monter & </s> <s xml:id="echoid-s5694" xml:space="preserve">deſcendre facilement.</s> <s xml:id="echoid-s5695" xml:space="preserve"/> </p> <pb o="176" file="190" n="190" rhead="CONSTRUT. ET USAGES DES INSTRUMENS"/> <p> <s xml:id="echoid-s5696" xml:space="preserve">Aux terres nouvellement remuées, on fait la Baſe du talud OZ <lb/>égale à la hauteur des terres, de ſorte que ſi la hauteur a 3 toiſes, <lb/>la baſe du talud a auſſi 3 toiſes; </s> <s xml:id="echoid-s5697" xml:space="preserve">c'eſt ce que l'on fait tout le long <lb/>des Courtines au talud intérieur du Rempart.</s> <s xml:id="echoid-s5698" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5699" xml:space="preserve">Mais à l'entrée des Baſtions, il faut du moins doubler la baſe du <lb/>talud; </s> <s xml:id="echoid-s5700" xml:space="preserve">c'eſt-à-dîre, que pour une hauteur de 3 toiſes, il faut faire <lb/>la baſe du talud, au moins de 6 ou 8 toiſes, pour qu'un chariot <lb/>y puiſſe monter.</s> <s xml:id="echoid-s5701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5702" xml:space="preserve">Lorſque le Rempart eſt formé, & </s> <s xml:id="echoid-s5703" xml:space="preserve">que les terres en ſont ſuffiſam-<lb/>ment raſſiſes, ce qui ne ſe peut faire qu'avec le tems & </s> <s xml:id="echoid-s5704" xml:space="preserve">la précau-<lb/>tion de les bien battre de deux pieds en deux pieds de hauteur, & </s> <s xml:id="echoid-s5705" xml:space="preserve"><lb/>afin que les terres ſe puiſſent lier enſemble, on y étend d'eſpace en <lb/>eſpace un lit de faſcines; </s> <s xml:id="echoid-s5706" xml:space="preserve">on conſtruit ſur les terres du Rempart un <lb/>Parapet, auquel on donne ſix pieds de hauteur intérieure, & </s> <s xml:id="echoid-s5707" xml:space="preserve">qua-<lb/>tre pieds de hauteur extérieure, afin que le deſſus des terres ait une <lb/>pente douce, auiſerve à découvrir tout ce qui eſt au-delà du Foſſé, <lb/>& </s> <s xml:id="echoid-s5708" xml:space="preserve">qu'étant monté ſur la Banquete, on puiſſe voir le Chemin cou-<lb/>vert, & </s> <s xml:id="echoid-s5709" xml:space="preserve">le défendre en cas d'attaque.</s> <s xml:id="echoid-s5710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5711" xml:space="preserve">La Baſe du Parapet X Y, doit avoir environ 4 toiſes de largeur, <lb/>afin que le haut diminué de ſes deux taluds, ait encore au moins <lb/>20 pieds de large. </s> <s xml:id="echoid-s5712" xml:space="preserve">Au bas du talud intérieur du Parapet, on fait une <lb/>Banquete de 2 pieds de largeur, & </s> <s xml:id="echoid-s5713" xml:space="preserve">d'un pied & </s> <s xml:id="echoid-s5714" xml:space="preserve">demi de haut, afin <lb/>que le Parapet ait 4 pieds & </s> <s xml:id="echoid-s5715" xml:space="preserve">demi de hauteur au-deſſus de la Ban-<lb/>quete, ce qui ſuffit pour que les Soldats puiſſent tirer commodé-<lb/>ment leurs armes à feu par-deſlus le Parapet.</s> <s xml:id="echoid-s5716" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5717" xml:space="preserve">Il faut avoir grand ſoin de battre les terres du Parapet de pied en <lb/>pied de hauteur avec des lits de faſcines; </s> <s xml:id="echoid-s5718" xml:space="preserve">& </s> <s xml:id="echoid-s5719" xml:space="preserve">afin de ne pas donner <lb/>un ſi grand talud aux terres du Parapet, on a coûtume de le revêtir <lb/>de bons gazons de terre graſſe, que l'on coupe avec une bêche de <lb/>Jardinier, tous égaux, ſur la ſuperficie d'un Pré, choiſie aux envi-<lb/>rons de la Place; </s> <s xml:id="echoid-s5720" xml:space="preserve">leur longueur eſt d'environ 15 pouces ſur 10 de <lb/>large. </s> <s xml:id="echoid-s5721" xml:space="preserve">Pour placer les gazons, il faut aſſeoir le premier lit bien de <lb/>niveau tout le long d'une étenduë de pluſieurs toiſes, & </s> <s xml:id="echoid-s5722" xml:space="preserve">poſer ceux <lb/>du ſecond en ſorte que tous les joints du premier ſoient recouverts <lb/>des gazons qui font le ſecond lit, & </s> <s xml:id="echoid-s5723" xml:space="preserve">les joints du ſecond pareille-<lb/>ment recouverts des gazons du troiſiéme lit, & </s> <s xml:id="echoid-s5724" xml:space="preserve">ainſi des autres, <lb/>afin que le tout faſle bonne liaiſon.</s> <s xml:id="echoid-s5725" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5726" xml:space="preserve">Il ſuffira de donner deux pouces de talud par pied de hauteur, à <lb/>l'intérieur du Parapet, & </s> <s xml:id="echoid-s5727" xml:space="preserve">environ 4 pouces par pied au talud ex-<lb/>térieur dudit Parapet. </s> <s xml:id="echoid-s5728" xml:space="preserve">Il faut un Jardinier adroit, pour conduire <lb/> <pb o="177" file="191" n="191" rhead="POUR LES FORTIFICATIONS. Liv. IV. Ch. VIII."/> cette ſorte d'ouvrage; </s> <s xml:id="echoid-s5729" xml:space="preserve">c'eſt-à-dire, pour couper les gazons, & </s> <s xml:id="echoid-s5730" xml:space="preserve"><lb/>les placer comme il convient.</s> <s xml:id="echoid-s5731" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5732" xml:space="preserve">Au bas ou pied du talud extérieur du Parapet & </s> <s xml:id="echoid-s5733" xml:space="preserve">du Rempart, <lb/>on laiſſe une petite Berme marquée Q, d'environ 4 pieds de lar-<lb/>ge, pour retenir les terres qui peuvent ſe détacher du talud.</s> <s xml:id="echoid-s5734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5735" xml:space="preserve">La pente QB repreſente le talud intérieur des terres du Foſſé, <lb/>qui a 3 toiſes de profondeur, BK en eſt le talud extérieur. </s> <s xml:id="echoid-s5736" xml:space="preserve">Si ces <lb/>terres ſont mouvantes, il faut leur donner aſſez de pente, pour <lb/>qu'elles reſtent ſans s'ébouler ou retomber dans le Foſſé. </s> <s xml:id="echoid-s5737" xml:space="preserve">Mais ſi <lb/>elles ſont fermes, & </s> <s xml:id="echoid-s5738" xml:space="preserve">qu'elles puiſſent facilement reſter ſans re-<lb/>tomber, on leur donne moins de talud. </s> <s xml:id="echoid-s5739" xml:space="preserve">La ligne K P repreſente <lb/>le Terre-plein du Chemin couvert, qui doit avoir 5 toiſes de lar-<lb/>geur. </s> <s xml:id="echoid-s5740" xml:space="preserve">P A repreſente le Parapet du Chemin couvert, avec ſa Ban-<lb/>quete au pied, le tout doit avoir 6 pieds de hauteur, pour mettre à <lb/>couvert ceux qui ſont ſur le Chemin couvert.</s> <s xml:id="echoid-s5741" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5742" xml:space="preserve">La pente ſupérieure du Glacis AN, doit être de terres douces, <lb/>dont on ôte les pierres, s'il y en a, avec un rateau de fer, & </s> <s xml:id="echoid-s5743" xml:space="preserve">on les <lb/>enterre au pied du Glacis, afin que quand l'Ennemi fera tirer le ca-<lb/>non ſur ledit Glacis, les boulets s'y enfoncent ſans faire réjaillir les <lb/>éclats de pierres dans le Chemin couvert.</s> <s xml:id="echoid-s5744" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div457" type="section" level="1" n="219"> <head xml:id="echoid-head332" style="it" xml:space="preserve">Pour tracer le plan d'une Fortification ſur la Terre.</head> <p> <s xml:id="echoid-s5745" xml:space="preserve">SOit propoſé, par exemple, le Plan de la figure premiere, à tra-<lb/> <anchor type="note" xlink:label="note-191-01a" xlink:href="note-191-01"/> cer ſur la Terre.</s> <s xml:id="echoid-s5746" xml:space="preserve"/> </p> <div xml:id="echoid-div457" type="float" level="2" n="1"> <note position="right" xlink:label="note-191-01" xlink:href="note-191-01a" xml:space="preserve">Planche <lb/>A.</note> </div> <p> <s xml:id="echoid-s5747" xml:space="preserve">Au lieu de Compas & </s> <s xml:id="echoid-s5748" xml:space="preserve">de Regle, il faut employer les Piquets, la <lb/> <anchor type="note" xlink:label="note-191-02a" xlink:href="note-191-02"/> Toiſe & </s> <s xml:id="echoid-s5749" xml:space="preserve">les Cordeaux: </s> <s xml:id="echoid-s5750" xml:space="preserve">c'eſt pourquoi, après avoir bien examiné <lb/>le terrain, & </s> <s xml:id="echoid-s5751" xml:space="preserve">conſideré où l'on doit placer les Baſtions & </s> <s xml:id="echoid-s5752" xml:space="preserve">les Por-<lb/>tes, qui ſe font pour l'ordinaire au milieu des Courtines, il faut <lb/>premierement planter de longs piquets aux endroits où l'on pré-<lb/>tend placer les Angles flanquez des Baſtions, & </s> <s xml:id="echoid-s5753" xml:space="preserve">il eſt à propos d'y <lb/>faire toute l'attention neceſſaire, avant que de commencer.</s> <s xml:id="echoid-s5754" xml:space="preserve"/> </p> <div xml:id="echoid-div458" type="float" level="2" n="2"> <note position="right" xlink:label="note-191-02" xlink:href="note-191-02a" xml:space="preserve">Fig. 1.</note> </div> <p> <s xml:id="echoid-s5755" xml:space="preserve">Ayant done planté perpendiculairement un long piquet ſur le <lb/>Terrain, à l'endroit où l'on a reſolu de placer la pointe du Baſtion, <lb/>marquée A, on fera meſurer bien exactement avec une toiſe, ou <lb/>avec une chaîne de 5 toiſes, juſqu'à 90 toiſes au bout deſquelles <lb/>on plantera un piquet marqué C, & </s> <s xml:id="echoid-s5756" xml:space="preserve">l'on continuëra vers le lieu <lb/>où l'on prétend placer la pointe du Baſtion B, en meſurant encore <lb/>90 toiſes, ou bout deſquelles on plantera un autre piquet, qui <lb/>marquera la pointe du Baſtion B.</s> <s xml:id="echoid-s5757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5758" xml:space="preserve">Pendant que l'on meſurera avec les Chaînes ou Cordeaux, il <lb/> <pb o="178" file="192" n="192" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> faut faire ſuivre quelque Ouvrier avec un Pic à la main, qui faſſe <lb/>ſur le terrain une trace ou ſillon, continué de Piquet en Piquet, <lb/>avant qu'on leve les Cordeaux.</s> <s xml:id="echoid-s5759" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5760" xml:space="preserve">Après quoi il faudra retourner au Piquet C, pour y faire une <lb/>perpendiculaire ſur la trace ACB.</s> <s xml:id="echoid-s5761" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5762" xml:space="preserve">Pour tracer ladite perpendiculaire, meſurez avec la toiſe de C en <lb/>A 2 ou 3 toiſes, & </s> <s xml:id="echoid-s5763" xml:space="preserve">au bout plantez-y un Piquet; </s> <s xml:id="echoid-s5764" xml:space="preserve">meſurez pareil-<lb/>lement de C vers B un nombre égal de toiſes, au bout deſquclles <lb/>vous planterez un ſecond Piquet: </s> <s xml:id="echoid-s5765" xml:space="preserve">ayez deux Cordeaux bien égaux, <lb/>qui ayent chacun un nœud à un de leurs bouts; </s> <s xml:id="echoid-s5766" xml:space="preserve">faites entrer un de <lb/>ces nœudsautour de chacun des Piquets, que vous venez de plan-<lb/>ter, & </s> <s xml:id="echoid-s5767" xml:space="preserve">tenant à vôtre main les deux autres bouts des Cordeaux <lb/>égaux, étendez-les juſqu'à ce qu'ils ſe joignent ſur le terrain, & </s> <s xml:id="echoid-s5768" xml:space="preserve"><lb/>au point de leur jonction plantez un troiſiéme Piquet; </s> <s xml:id="echoid-s5769" xml:space="preserve">mettez en-<lb/>fin un Cordeau au Piquet C, prolongez-le tant qu'il ſera beſoin, <lb/>le faiſant paſſer par ce troiſiéme Piquet: </s> <s xml:id="echoid-s5770" xml:space="preserve">& </s> <s xml:id="echoid-s5771" xml:space="preserve">faites tracer un fillon le <lb/>long du Cordeau, il ſera perpendiculaire ſur la ligne ACB.</s> <s xml:id="echoid-s5772" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5773" xml:space="preserve">Du point C faites meſurer 30 toiſes le long de ce ſillon, & </s> <s xml:id="echoid-s5774" xml:space="preserve">au <lb/>bout de ces 30 toiſes, plantez-y un long Piquet bien à plomb, qui <lb/>marquera le point D de vôtre Plan.</s> <s xml:id="echoid-s5775" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5776" xml:space="preserve">Retournez au Piquet A, d'où étant bien alligné au Piquet D, <lb/>faites tracer un ſillon le long de cet allignement, vous ſervant <lb/>pour cet effet d'un Piquet que vous ferez mettre à plomb entre A <lb/>& </s> <s xml:id="echoid-s5777" xml:space="preserve">D, devant les yeux de l'Ouvrier qui trace le ſillon; </s> <s xml:id="echoid-s5778" xml:space="preserve">faites meſu-<lb/>rer le long dudit ſillon 55 toiſes du Piquet A, allant vers D, pour <lb/>la longueur de la face du Baſtion AE; </s> <s xml:id="echoid-s5779" xml:space="preserve">faites planter un long Pi-<lb/>quet au point E, pour y marquer l'Angle de l'épaule.</s> <s xml:id="echoid-s5780" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5781" xml:space="preserve">Allez au Piquet B, & </s> <s xml:id="echoid-s5782" xml:space="preserve">faites-y les mêmes operations, pour tra-<lb/>cer la face BF, & </s> <s xml:id="echoid-s5783" xml:space="preserve">plantez un Piquet à l'Angle de l'épaule F.</s> <s xml:id="echoid-s5784" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5785" xml:space="preserve">Prolongez l'allignement BF de D, allant vers G; </s> <s xml:id="echoid-s5786" xml:space="preserve">& </s> <s xml:id="echoid-s5787" xml:space="preserve">de même <lb/>l'allignement AE de D vers H; </s> <s xml:id="echoid-s5788" xml:space="preserve">meſurez avec l'Echelle du Plan les <lb/>lignes DG, DH, portez ſur le terrain leurs juſtes longueurs de <lb/>E en G & </s> <s xml:id="echoid-s5789" xml:space="preserve">en H, où vous planterez des Piquets: </s> <s xml:id="echoid-s5790" xml:space="preserve">après quoi il ſera <lb/>facile de tracer ſur la terre les Flancs EG, FH, & </s> <s xml:id="echoid-s5791" xml:space="preserve">la Courtine GH.</s> <s xml:id="echoid-s5792" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5793" xml:space="preserve">Vous aurez par ce moyen un front de Place fortifiée, tracé ſur <lb/>le Terrain; </s> <s xml:id="echoid-s5794" xml:space="preserve">les autres ſe traceront de même avec les Piquets & </s> <s xml:id="echoid-s5795" xml:space="preserve">Cor-<lb/>deaux, il ne ſera pas hors de propos d'examiner avec un demi-cer-<lb/>cle ou un Recipiangle, fi les Angles du Plan tracé ſont égaux <lb/>à ceux du Plan deſtiné, & </s> <s xml:id="echoid-s5796" xml:space="preserve">de le rectifier avant que d'y mettre les <lb/>Ouvriers. </s> <s xml:id="echoid-s5797" xml:space="preserve">Il faut auſſi de tems en tems prendre garde ſi les traces <lb/> <pb o="179" file="193" n="193" rhead="POUR LES FORTIFICATIONS Liv. IV. Ch. VIII."/> ſont ſuivies exactement; </s> <s xml:id="echoid-s5798" xml:space="preserve">car ſans ces précautions, il s'y pourroit fai-<lb/>re beaucoup de difformitez, qu'il ſeroit très-difficile de corriger.</s> <s xml:id="echoid-s5799" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div460" type="section" level="1" n="220"> <head xml:id="echoid-head333" style="it" xml:space="preserve">De la Conſtruction des dehors.</head> <p> <s xml:id="echoid-s5800" xml:space="preserve">LEs dehors, en terme de Fortification, ſont des Ouvrages éle-<lb/> <anchor type="note" xlink:label="note-193-01a" xlink:href="note-193-01"/> vez, que l'on conſtruit au-delà du Foſſé d'une Place fortifiée, <lb/>pour la couvrir & </s> <s xml:id="echoid-s5801" xml:space="preserve">en augmenter la défenſe.</s> <s xml:id="echoid-s5802" xml:space="preserve"/> </p> <div xml:id="echoid-div460" type="float" level="2" n="1"> <note position="right" xlink:label="note-193-01" xlink:href="note-193-01a" xml:space="preserve">Fig P.</note> </div> <p> <s xml:id="echoid-s5803" xml:space="preserve">Les plus ordinaires & </s> <s xml:id="echoid-s5804" xml:space="preserve">les plus communs entre ces ſortes d'Ou-<lb/>vrages, ſont les Ravelins ou Demi-lunes qui ſe forment ſur l'An-<lb/>gle flanquant de la Contreſcarpe entre deux Baſtions, & </s> <s xml:id="echoid-s5805" xml:space="preserve">devant la <lb/>Courtine, pour couvrir les Portes & </s> <s xml:id="echoid-s5806" xml:space="preserve">les Ponts qui ſe font ordinaire-<lb/>ment au milieu des Courtines, comme les figures PP le montrent.</s> <s xml:id="echoid-s5807" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5808" xml:space="preserve">Les Ravelins ſont compoſez de deux faces, garnies d'une Ban-<lb/>quete ou deux, & </s> <s xml:id="echoid-s5809" xml:space="preserve">d'un bon Parapet élevé du côté de la campagne <lb/>& </s> <s xml:id="echoid-s5810" xml:space="preserve">de deux demies gorges, ſans Parapet, du côté de la Ville, avec <lb/>une ouverture & </s> <s xml:id="echoid-s5811" xml:space="preserve">un talud, pour monter du grand Foſſé ſur le <lb/>Terre-plein du Ravelin.</s> <s xml:id="echoid-s5812" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5813" xml:space="preserve">On bâtit en chaque Ravelin un Corps-de-Garde, pour mettre à <lb/>l'abri des injures du tems, les Soldats neceſſaires pour le garder & </s> <s xml:id="echoid-s5814" xml:space="preserve"><lb/>le défendre; </s> <s xml:id="echoid-s5815" xml:space="preserve">mais il eſt à propos que ce Corps-de-Garde ſoit en for-<lb/>me de reduit, avec des crenaux tout autour, pour que les Soldats, <lb/>en cas d'aſſauts, s'y puiſſent retirer & </s> <s xml:id="echoid-s5816" xml:space="preserve">obtenir quelque capitula-<lb/>tion, avant que de rendre les Armes.</s> <s xml:id="echoid-s5817" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5818" xml:space="preserve">Pour tracer un Ravelin devant une Courtine, ouvrez le Compas <lb/>de la grandeur du côté intérieur du Polygone; </s> <s xml:id="echoid-s5819" xml:space="preserve">arrêtez une des <lb/>pointes du Compas ainſi ouvert, ſur une des extremitez de ladite <lb/>ligne, & </s> <s xml:id="echoid-s5820" xml:space="preserve">de l'autre pointe décrivez un Arc au-delà de la Con-<lb/>treſcarpe; </s> <s xml:id="echoid-s5821" xml:space="preserve">arrêtez de même une pointe du Compas ſur l'autre <lb/>extremité du côté intérieur, & </s> <s xml:id="echoid-s5822" xml:space="preserve">de l'autre pointe tracez un ſecond <lb/>Arc, coupant le premier en un point qui marquera la pointe ou <lb/>l'angle flanqué du Ravelin; </s> <s xml:id="echoid-s5823" xml:space="preserve">mettez une regle ſur ce point d'inter-<lb/>ſection & </s> <s xml:id="echoid-s5824" xml:space="preserve">ſur chacune des extremitez dudit côté intérieur, pour <lb/>tracer les faces du Ravelin, qui ſe termineront à droite & </s> <s xml:id="echoid-s5825" xml:space="preserve">à <lb/>gauche ſur le bord de la Contreſcarpe. </s> <s xml:id="echoid-s5826" xml:space="preserve">Les deux demies-gorges <lb/>ſe tireront de l'extremitê de chaque face, juſqu'à l'angle rentrant <lb/>de ladite Contreſcarpe.</s> <s xml:id="echoid-s5827" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5828" xml:space="preserve">Mais pour quel'angle flanqué du Ravelin ne ſoit pas trop aigu, <lb/>ne donnez qu'environ 40 toiſes à ſa capitale RS; </s> <s xml:id="echoid-s5829" xml:space="preserve">& </s> <s xml:id="echoid-s5830" xml:space="preserve">faites le reſte, <lb/>comme nous venons de dire.</s> <s xml:id="echoid-s5831" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5832" xml:space="preserve">On place quelquefois un ſemblable Ouvrage devant la pointe <lb/> <pb o="180" file="194" n="194" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> d'un Baſtion; </s> <s xml:id="echoid-s5833" xml:space="preserve">& </s> <s xml:id="echoid-s5834" xml:space="preserve">comme ſa gorge eſt bâtie ſur le bord de la Con-<lb/>treſcarpe, que l'on arrondit ordinairement vis-à-vis la pointe des <lb/>Baſtions, donne à cet Ouvrage le nom de Demi-Lune, parce <lb/>que ſa gorge eſt en forme d'Arc: </s> <s xml:id="echoid-s5835" xml:space="preserve">l'on confond ſouvent l'un avec <lb/>l'autre, & </s> <s xml:id="echoid-s5836" xml:space="preserve">la plûpart des Soldats donnent, ſans diſtinction, le nom <lb/>de Demi. </s> <s xml:id="echoid-s5837" xml:space="preserve">Lune aux Ravelins qui ſe font devant les Courtines.</s> <s xml:id="echoid-s5838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5839" xml:space="preserve">Le défaut de cet Ouvrage eſt, qu'il eſt trop éloigné des flancs <lb/>des Baſtions, pour en être ſuffiſamment défendu; </s> <s xml:id="echoid-s5840" xml:space="preserve">c'eſt pourquoi <lb/>on ne fait point de Demi-Lune devant la pointe d'un Baſtion, à <lb/>moins qne l'on ne faſſe en même tems d'autres dehors à droite & </s> <s xml:id="echoid-s5841" xml:space="preserve">à <lb/>gauche devant les Courtines voiſines, qui la puiſſent déſendre.</s> <s xml:id="echoid-s5842" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5843" xml:space="preserve">Il eſt à propos que ces Ouvrages ſoient revêtus de murailles, <lb/>auſſi-bien que le Corps de la place; </s> <s xml:id="echoid-s5844" xml:space="preserve">car quand ils ne ſont pas revê-<lb/>tus, on eſt obligé de donner un ſi grand talud aux terres, qu'il eſt <lb/>facile de monter dans l'Ouvrage par ſon talud.</s> <s xml:id="echoid-s5845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5846" xml:space="preserve">Cependant il faut laiſſer raſſeoir du moins un an ou deux les ter-<lb/>res nouvellement remuées, avant que de les revêtir, afin qu'elles <lb/>s'affaiſſent peu à peu, & </s> <s xml:id="echoid-s5847" xml:space="preserve">que dans la ſuite elles ne renverſent pas <lb/>les Murailles qui leur ſervent de revêtement.</s> <s xml:id="echoid-s5848" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div462" type="section" level="1" n="221"> <head xml:id="echoid-head334" style="it" xml:space="preserve">Conſtruction des Ouvrages à Corne.</head> <p> <s xml:id="echoid-s5849" xml:space="preserve">CEs ſortes d'Ouvrages ſe font ordinairement devant les Cour-<lb/> <anchor type="note" xlink:label="note-194-01a" xlink:href="note-194-01"/> tines, & </s> <s xml:id="echoid-s5850" xml:space="preserve">comme ils ſont de plus grande depenſe que les Ra-<lb/>velins, ils ne ſe font pas fans neceſſité; </s> <s xml:id="echoid-s5851" xml:space="preserve">ſoit pour couvrir quelque <lb/>endroit de la Place, plus foible que les autres; </s> <s xml:id="echoid-s5852" xml:space="preserve">ſoit pour occuper <lb/>une hauteur, qu'on n'a pû renfermer dans le Corps de la Place.</s> <s xml:id="echoid-s5853" xml:space="preserve"/> </p> <div xml:id="echoid-div462" type="float" level="2" n="1"> <note position="left" xlink:label="note-194-01" xlink:href="note-194-01a" xml:space="preserve">Plam be <lb/>A. <lb/>Fig. 3.</note> </div> <p> <s xml:id="echoid-s5854" xml:space="preserve">Pour le tracer, tirez premierement ſur le milieu de la Courtine, <lb/>la perpendiculaire 1, 2, longue à diſcretion; </s> <s xml:id="echoid-s5855" xml:space="preserve">& </s> <s xml:id="echoid-s5856" xml:space="preserve">à cette ligne deux <lb/>paralleles ſur les Angles des épaules des Baſtions voiſins de la Cour-<lb/>tine 3, 4, 5, 6. </s> <s xml:id="echoid-s5857" xml:space="preserve">Ces 2 paralleles, que l'on appelle les aîles de l'Ou-<lb/>vrage à Corne, doivent tirer leurs défenſes des faces de ces Baſtions; <lb/></s> <s xml:id="echoid-s5858" xml:space="preserve">c'eſt pourquoi leur longueur ne doit guéres paſler 120 toiſes, à <lb/>compter des Epaules. </s> <s xml:id="echoid-s5859" xml:space="preserve">Par les extremitez des aîles, tirez la ligne 4, <lb/>6, qui ſera le côté extérieur de l'Ouvrage à Corne, & </s> <s xml:id="echoid-s5860" xml:space="preserve">qui ſe trou-<lb/>vera diviſé en 2 parties égales au point 7, par la perpendiculaire 1, <lb/>2: </s> <s xml:id="echoid-s5861" xml:space="preserve">prenez avec un Compas la moitié dudit côté extérieur, & </s> <s xml:id="echoid-s5862" xml:space="preserve">la <lb/>portez ſur les longs côtez de 4 en 8, & </s> <s xml:id="echoid-s5863" xml:space="preserve">de 6 en 9, tirez les lignes <lb/>4, 9, & </s> <s xml:id="echoid-s5864" xml:space="preserve">6, 8, qui ſe croiſant au point 10, forment l'Angle de te-<lb/>naille; </s> <s xml:id="echoid-s5865" xml:space="preserve">ce qui repreſente un Ouvrage, que l'on appelle Tenaille <lb/>ſimple, qui ſe place aſſez or dinairement devant les Courtines avec <lb/> <pb o="181" file="195" n="195" rhead="POUR LES FOR TIFICATIONS. Liv. IV. Chap. VIII."/> un petit Ravelin au-delà du Foſſé, entre les deux Angles ſaillans & </s> <s xml:id="echoid-s5866" xml:space="preserve"><lb/>vis-a-vis le milieu de l'Angle rentrant, ou de Tenaille.</s> <s xml:id="echoid-s5867" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5868" xml:space="preserve">Mais pour renforcer cet Ouvrage, on y ajoûte deux demi-Baſtions <lb/>& </s> <s xml:id="echoid-s5869" xml:space="preserve">une Courtine entre deux; </s> <s xml:id="echoid-s5870" xml:space="preserve">ce qui vaut mieux que deux ſimples <lb/>Angles rentrans.</s> <s xml:id="echoid-s5871" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5872" xml:space="preserve">Pour tracer les demi-Baſtions, diviſez la ligne 4, 10 en deux <lb/>parties égales au point 11; </s> <s xml:id="echoid-s5873" xml:space="preserve">& </s> <s xml:id="echoid-s5874" xml:space="preserve">de même la ligne 10, 6 au point 12; <lb/></s> <s xml:id="echoid-s5875" xml:space="preserve">des points 11 & </s> <s xml:id="echoid-s5876" xml:space="preserve">12, tirez juſqu'au milieu de la Courtine de la Pla-<lb/>ce, où eſt le point 1, les lignes occultes 12 1, 11 1, & </s> <s xml:id="echoid-s5877" xml:space="preserve">par ce moyen <lb/>vous aurez la petite Courtine 13 14 de l'Ouvrage à Corne, les deux <lb/>flancs 21 13, 12 14, & </s> <s xml:id="echoid-s5878" xml:space="preserve">les deux faces 11 4, 12 6.</s> <s xml:id="echoid-s5879" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5880" xml:space="preserve">Les côtez de ces Ouvrages qui ſont tournez du côté de la campa-<lb/>gne, comme ſont les demi-Baſtions, la Courtine & </s> <s xml:id="echoid-s5881" xml:space="preserve">les aîles de <lb/>l'Ouvrage à Corne, doivent être munis d'un bon Parapet de terre <lb/>douce bien batuë, de 18 à 20 pieds d'épaiſſeur, & </s> <s xml:id="echoid-s5882" xml:space="preserve">de 6 pieds de <lb/>hauteur par devant, y compris la Banquete, de même que celui du <lb/>Corps de la Place, en obſervant toutefois que les Parapets des Ou-<lb/>vrages les plus proches du centre de la Place doivent toûjours être <lb/>plus élevez au-deſſus du niveau de la campagne, que ceux des Ou-<lb/>vrages plus éloignez, afin que quand les Aſſiegeans ſe ſeront em-<lb/>parez de quelque dehors, les Aſſiegez, qui défendent le Corps de <lb/>la Place, les voyant tout à découvert, puiſſent les empêcher d'y <lb/>reſter & </s> <s xml:id="echoid-s5883" xml:space="preserve">de s'y loger.</s> <s xml:id="echoid-s5884" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5885" xml:space="preserve">Ces Parapets doivent être ſoûtenus d'un Rempart, dont le Terre-<lb/>plein, qui porte la Banquete, ait 3 ou 4 toiſes de largeur; </s> <s xml:id="echoid-s5886" xml:space="preserve">mais <lb/>quand la terre manque, on ſe contente de conſtruire pluſieurs Ban-<lb/>quetes l'une ſur l'autre de 18 pouces de haut & </s> <s xml:id="echoid-s5887" xml:space="preserve">de 3 ou 4 pieds de <lb/>large; </s> <s xml:id="echoid-s5888" xml:space="preserve">& </s> <s xml:id="echoid-s5889" xml:space="preserve">au-deſſus de la plus haute Banquete, le Parapet doit a-<lb/>voir environ 4 pieds & </s> <s xml:id="echoid-s5890" xml:space="preserve">demi de hauteur, pour couvrir les Soldats <lb/>juſqu'aux épaules; </s> <s xml:id="echoid-s5891" xml:space="preserve">le deſſus du Parapet doit être en Glacis, qui <lb/>baiſſe peu a peu vers la campagne, afin que les Aſſiegez puiſſent <lb/>voir l'Ennemi, & </s> <s xml:id="echoid-s5892" xml:space="preserve">tirer deſſus ſans être vûs.</s> <s xml:id="echoid-s5893" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5894" xml:space="preserve">Les parties de ces Ouvrages, qui ſont du côté de la Place, doi-<lb/>vent être ſans Parapet, mais ſeulement fermez d'un ſimple Mur, <lb/>ou d'une rangée de Paliſſades, pour éviter les ſurpriſes de l'Enne-<lb/>mi; </s> <s xml:id="echoid-s5895" xml:space="preserve">& </s> <s xml:id="echoid-s5896" xml:space="preserve">c'eſt de ce côté là que doit être la Porte, pour communiquer <lb/>du Corps de la Place dans l'Ouvrage, & </s> <s xml:id="echoid-s5897" xml:space="preserve">le Corps-de-Garde, pour <lb/>mettre à couvert les Soldats deſtinez pour la défenſe.</s> <s xml:id="echoid-s5898" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5899" xml:space="preserve">Tous ces Ouvrages doivent être environnez d'un Foſſé large de 10 <lb/>à 12 toiſes, qui communique avec le Foſſé du corps de la Place, & </s> <s xml:id="echoid-s5900" xml:space="preserve">qui <lb/>ſoit auſſi profond.</s> <s xml:id="echoid-s5901" xml:space="preserve"/> </p> <pb o="182" file="196" n="196" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> <p> <s xml:id="echoid-s5902" xml:space="preserve">Au-delà du Foſſé on fait un Chemin couvert large de 5 à 6 toiſes <lb/>avec un Parapet & </s> <s xml:id="echoid-s5903" xml:space="preserve">ſa Banquete, que l'on garnit ordinairement <lb/>d'une enceinte de fortes Paliſſades enſoncées dans la terre à 3 ou 4 <lb/>pieds de profondeur. </s> <s xml:id="echoid-s5904" xml:space="preserve">Le deſſus de ce Parapet, qui va en Glacis, ſe <lb/>doit terminer à la campagne; </s> <s xml:id="echoid-s5905" xml:space="preserve">& </s> <s xml:id="echoid-s5906" xml:space="preserve">ſi l'on peut le prolonger de 20 ou <lb/>30 toiſes, il n'en ſera que mieux; </s> <s xml:id="echoid-s5907" xml:space="preserve">car un Glacis ne peut pas être <lb/>trop long; </s> <s xml:id="echoid-s5908" xml:space="preserve">puiſque par ſon moyen l'Ennemi ne peut approcher de <lb/>la Place, qu'il ne ſoit entierement découvert.</s> <s xml:id="echoid-s5909" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5910" xml:space="preserve">Les Dehors, dont nous venons de parler, ſont les plus ordinaires; <lb/></s> <s xml:id="echoid-s5911" xml:space="preserve">il s'en fait néanmoins de pluſieurs autres ſortes, dont nous ne par-<lb/>lerons point ici; </s> <s xml:id="echoid-s5912" xml:space="preserve">cette Matiere demanderoit ſeule un gros Volume.</s> <s xml:id="echoid-s5913" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div464" type="section" level="1" n="222"> <head xml:id="echoid-head335" style="it" xml:space="preserve">Méthode pour toiſer les Ouvrages des Fortifications.</head> <p> <s xml:id="echoid-s5914" xml:space="preserve">LEs terres dont ſe forment les Remparts & </s> <s xml:id="echoid-s5915" xml:space="preserve">les Parapets, ſe ti-<lb/>rent ordinairement des Foſſez que l'on faits autour de la Pla-<lb/>ce; </s> <s xml:id="echoid-s5916" xml:space="preserve">& </s> <s xml:id="echoid-s5917" xml:space="preserve">pour en connoître la quantité, on meſure le vuide des Foſſez, <lb/>& </s> <s xml:id="echoid-s5918" xml:space="preserve">on le reduit en toiſes cubes, dont on paye l'excavation & </s> <s xml:id="echoid-s5919" xml:space="preserve">le <lb/>tranſport aux Entrepreneurs, ſuivant le prix convenu.</s> <s xml:id="echoid-s5920" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5921" xml:space="preserve">Comme, par exemple, ſi le Foſſé, vis-à-vis la face d'un Baſtion <lb/>à 50 toiſes de long, 20 toiſes de large, & </s> <s xml:id="echoid-s5922" xml:space="preserve">4 de profondeur; </s> <s xml:id="echoid-s5923" xml:space="preserve">on <lb/>multiplie la longueur 50 par la largeur 20, le produit ſera 1000 <lb/>toiſes quarrées, leſquelles on multiplie par 4 toiſes de profondeur, <lb/>ce qui fait 4000 toiſes cubes.</s> <s xml:id="echoid-s5924" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5925" xml:space="preserve">Il faut remarquer, que comme on eſt obligé de donner un grand <lb/>talud aux terres, afin qu'elles puiſſent reſter ſans s'écouler, ce F oſ-<lb/>ſé doit être bien plus large par le haut que le bas: </s> <s xml:id="echoid-s5926" xml:space="preserve">C'eſt pour-<lb/>quoi, ſi l'on veut que le Foſſé ait 20 toiſes de largeur par le mi-<lb/>lieu de la profondeur, il faut lui donner par le haut; </s> <s xml:id="echoid-s5927" xml:space="preserve">au moins 22 <lb/>toiſes de largeur, & </s> <s xml:id="echoid-s5928" xml:space="preserve">18 par le bas; </s> <s xml:id="echoid-s5929" xml:space="preserve">ces 22 toiſes ajoûtées à 18, font <lb/>40, dont la moitié 20 eſt la largeur réduite.</s> <s xml:id="echoid-s5930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5931" xml:space="preserve">A l'égard de la profondeur, comme il y a ſouvent des creux & </s> <s xml:id="echoid-s5932" xml:space="preserve"><lb/>& </s> <s xml:id="echoid-s5933" xml:space="preserve">des butes ſur la face de la terre, on oblige les Ouvriers de laiſſer <lb/>en creuſant au travers du Foſſé, quelques bandes de terre, pour <lb/>ſervir de témoins de la hauteur des terres, juſqu'à ce que le tout <lb/>ſoit meſuré; </s> <s xml:id="echoid-s5934" xml:space="preserve">& </s> <s xml:id="echoid-s5935" xml:space="preserve">quand il y a dans un Atelier pluſieurs témoins, <lb/>d'eſpace en eſpace, on prend les hauteurs perpendiculaires de cha-<lb/>cun, on les ajoûte enſemble, & </s> <s xml:id="echoid-s5936" xml:space="preserve">on diviſe la ſomme par le nombre <lb/>des témoins. </s> <s xml:id="echoid-s5937" xml:space="preserve">Si, par exemple, on a ajoûté enſemble ſix hauteurs, <lb/>on prend la ſixiéme partie de la ſomme pour la hauteur réduite.</s> <s xml:id="echoid-s5938" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5939" xml:space="preserve">La Maſſonnerie qui ſoûtient les terres, doit avoit de l'épaiſſeur <lb/> <pb o="183" file="197" n="197" rhead="POUR LES FOR TIFICATIONS. Liv. IV. Chap. VIII."/> à proportion de ſa hauteur, on lui donne auſſi un talud d'environ <lb/>un pied par toiſe de hauteur.</s> <s xml:id="echoid-s5940" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5941" xml:space="preserve">Si, par exemple, on bâtit un Mur pour ſoûtenir les terres du <lb/>Rempart de la Place, & </s> <s xml:id="echoid-s5942" xml:space="preserve">que ce Mur ait ſix toiſes de hauteur, la <lb/>moindre épaiſſeur que l'on puiſſe donner par le haut, eſt trois <lb/>pieds, & </s> <s xml:id="echoid-s5943" xml:space="preserve">par le bas neuf pieds d'épaiſſeur, au-deſſus de la fonda-<lb/>tion, à cauſe de ſon talud, qui eſt d'un pied par toiſe: </s> <s xml:id="echoid-s5944" xml:space="preserve">or ces deux <lb/>épaiſſeurs, 9 & </s> <s xml:id="echoid-s5945" xml:space="preserve">3 font 12, dont la moitié 6 pieds, ſera l'épaiſſeur <lb/>réduite de ce Mur: </s> <s xml:id="echoid-s5946" xml:space="preserve">& </s> <s xml:id="echoid-s5947" xml:space="preserve">par conſequent, pour revetir la face d'un <lb/>Baſtion, qui a 50 toiſes de long, 6 toiſes de haut, & </s> <s xml:id="echoid-s5948" xml:space="preserve">une toiſe d'é-<lb/>paiſſeur réduite, il faut 300 toiſes cubes de Maſſonnerie, ſans y <lb/>comprendre la fondation, que l'on ne peut pas déterminer ſans <lb/>connoître le terrain, Outre cela, on a coûtume de faire des Con-<lb/>treforts, pour ſoûtenir les terres, & </s> <s xml:id="echoid-s5949" xml:space="preserve">les empêcher de trop peſer <lb/>contre le Mur du Revêtement: </s> <s xml:id="echoid-s5950" xml:space="preserve">Ces Contreforts doivent être fon-<lb/>dez ſur la terre ferme, & </s> <s xml:id="echoid-s5951" xml:space="preserve">entrer dans les terres rémuées, au moins <lb/>d'une toiſe de long, on leur donne 7 à 8 pieds de large à la racine, <lb/>c'eſt-à-dire, du côté où ils ſont attachez au Mur du Revêtement, <lb/>& </s> <s xml:id="echoid-s5952" xml:space="preserve">4à 5 pieds à la queuë qui s'avance dans les terres du Rempart, <lb/>ce qui revient à une toiſe de ſurface, en ſuppoſant, comme nous <lb/>venons de dire, 7 pieds à la racine, & </s> <s xml:id="echoid-s5953" xml:space="preserve">5 pieds à la queuë; </s> <s xml:id="echoid-s5954" xml:space="preserve">qui font <lb/>12 pieds, dont la moitié 6 pieds eſt l'épaiſſeur reduite; </s> <s xml:id="echoid-s5955" xml:space="preserve">& </s> <s xml:id="echoid-s5956" xml:space="preserve">ſuppo-<lb/>ſant 4 toiſes de hauteur l'un portant l'autre, chaque Contrefort <lb/>aura 3 toiſes cubes. </s> <s xml:id="echoid-s5957" xml:space="preserve">Et comme on n'en doit pas faire moins de dix <lb/>dans une étenduë de 50 toiſes, la Maſſonnerie de dix Contreforts <lb/>reviendra à 40 toiſes cubes: </s> <s xml:id="echoid-s5958" xml:space="preserve">de telle ſorte que pour revêtir de Mu-<lb/>railles les 2 faces & </s> <s xml:id="echoid-s5959" xml:space="preserve">les 2 flance d'un Baſtion, on peut compter en-<lb/>viron mille toiſes cubes de Maſſonnerie: </s> <s xml:id="echoid-s5960" xml:space="preserve">& </s> <s xml:id="echoid-s5961" xml:space="preserve">pour revêtir une Cour-<lb/>tine, qui a 80 toiſes de longueur, il faut compter environ 900 <lb/>toiſes cubes de Maſſonnerie: </s> <s xml:id="echoid-s5962" xml:space="preserve">de là on pourra facilement eſtimer ce <lb/>qu'il en faut pour le Revêtement de toute une Place. </s> <s xml:id="echoid-s5963" xml:space="preserve">Remarquez <lb/>qu'il vaut mieux faire l'eſtimation plus forte que trop foible; </s> <s xml:id="echoid-s5964" xml:space="preserve">car ſi <lb/>on a trop de fonds, il ſert pour ſubvenir aux dépenſes imprévûës.</s> <s xml:id="echoid-s5965" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5966" xml:space="preserve">Il nous reſte encore à parler du toiſé de le Charpente, dont on a <lb/>beſoin pour conſtruire les Ponts & </s> <s xml:id="echoid-s5967" xml:space="preserve">les Portes, & </s> <s xml:id="echoid-s5968" xml:space="preserve">autres Ouvrages <lb/>de cette nature.</s> <s xml:id="echoid-s5969" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5970" xml:space="preserve">Pour meſurer les Bois de Charpente, on les reduit en Solives.</s> <s xml:id="echoid-s5971" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5972" xml:space="preserve">La Solive eſt une piece de Bois ayant 12 pieds de longueur & </s> <s xml:id="echoid-s5973" xml:space="preserve">36 <lb/>pouces quarrez de ſurface, ceſt-à-dire, 6 pouces de largeur ſur 6 <lb/>de groſſeur, ce qui revient à 3 pieds cubes de Bois, qui font la 72<emph style="sub">me</emph> <lb/>partie d'une toiſe cube.</s> <s xml:id="echoid-s5974" xml:space="preserve"/> </p> <pb o="184" file="198" n="198" rhead="CONSTRUCT. ET USAGES DES INSTRUM. &c."/> <p> <s xml:id="echoid-s5975" xml:space="preserve">Dans les Ouvrages de Fortification on compte les longueurs des <lb/>pieces de Bois miſes en œuvre, comme elles ſont, y compris les <lb/>tenons.</s> <s xml:id="echoid-s5976" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5977" xml:space="preserve">Nous donnerons ici deux manieres d'en faire le calcul, afin que <lb/>l'une puiſſe ſervir de preuve à l'autre.</s> <s xml:id="echoid-s5978" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5979" xml:space="preserve">La premiere, eſt de réduire en pouces la groſſeur de la piece de <lb/>Bois, c'eſt-à-dire, les pouces de ſa largeur & </s> <s xml:id="echoid-s5980" xml:space="preserve">de ſon épaiſſeur & </s> <s xml:id="echoid-s5981" xml:space="preserve"><lb/>après avoir multiplié ces deux quantitez, l'une par l'autre pour <lb/>en faire des pouces quarrez, on multiplie le produit par les toiſes, <lb/>pieds & </s> <s xml:id="echoid-s5982" xml:space="preserve">pouces de la longueur, on diviſe ce der nier produit par 72, le <lb/>quotien donne le nombre des Solives que contient la piece de Bois.</s> <s xml:id="echoid-s5983" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5984" xml:space="preserve">La raiſon de cette pratique, eſt que 72 chevilles d'un pouce de <lb/>gros ſur une toiſe de long, font une Solive.</s> <s xml:id="echoid-s5985" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5986" xml:space="preserve">Suppoſons, par exemple, qu'il faille réduire en Solives une pou-<lb/>tre ayant de longueur 2 toiſes 4 pieds 6 pouces, & </s> <s xml:id="echoid-s5987" xml:space="preserve">12 à 15 pou-<lb/>ces de gros; </s> <s xml:id="echoid-s5988" xml:space="preserve">il faut multiplier 15 par 12, le produit eſt 180 pou-<lb/>ces quarrez, leſquels il faut encore multiplier par 2 toiſes 4 pieds <lb/>6 pouces, le produit eſt 495, lequel diviſé par 72, donne pour <lb/>quotien 6 Solives & </s> <s xml:id="echoid-s5989" xml:space="preserve">{7/8}.</s> <s xml:id="echoid-s5990" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5991" xml:space="preserve">La ſeconde méthode, pour réduire les Bois de Charpente en So-<lb/>lives, eſt fondée ſur ce que la Solive contient 3 pieds cubes, ou <lb/>la 72<emph style="sub">me</emph> partie de la toiſe.</s> <s xml:id="echoid-s5992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5993" xml:space="preserve">Elle ſe pratique de la maniere ſuivante: </s> <s xml:id="echoid-s5994" xml:space="preserve">multipliez les pouces <lb/>de ſon équarriſſage, les uns par les autres, c'eſt-à-dire, les pou-<lb/>ces de ſa largeur par ceux de ſon épaiſleur, & </s> <s xml:id="echoid-s5995" xml:space="preserve">du produit prenez-<lb/>en le douziéme, que vous multiplierez par la longueur de la piece; <lb/></s> <s xml:id="echoid-s5996" xml:space="preserve">ce dernier produit ſera le nombre des Solives, & </s> <s xml:id="echoid-s5997" xml:space="preserve">parties de Solive.</s> <s xml:id="echoid-s5998" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s5999" xml:space="preserve">Soit pour exemple, la même piece de Bois ayant de longueur <lb/>2 toiſes 4 pieds 9 pouces, & </s> <s xml:id="echoid-s6000" xml:space="preserve">12 à 15 pouces de gros, en multi-<lb/>pliant 15 par 12, le produit eſt 180 pouces quarrez.</s> <s xml:id="echoid-s6001" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6002" xml:space="preserve">La douziéme partie de ce nombre eſt 15, qui étant conſide-<lb/>rez comme des pieds font 2 toiſes 3 pieds, leſquels multipliez <lb/>par la longueur 2 toiſes 4 pieds 6 pouces, font enfin 6 Solives 5 <lb/>pieds & </s> <s xml:id="echoid-s6003" xml:space="preserve">3 pouces; </s> <s xml:id="echoid-s6004" xml:space="preserve">de ſorte qu'il ne s'en manque que neuf pouces <lb/>ou la huitiéme partie d'une toiſe pour faire ſept Solives, comme <lb/>dans le calcul de la premiere méthode.</s> <s xml:id="echoid-s6005" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div465" type="section" level="1" n="223"> <head xml:id="echoid-head336" style="it" xml:space="preserve">Fin du quatriéme Livre.</head> <pb file="199" n="199"/> </div> <div xml:id="echoid-div466" type="section" level="1" n="224"> <head xml:id="echoid-head337" xml:space="preserve">Planche A. # Page 184.</head> <figure> <caption xml:id="echoid-caption2" style="it" xml:space="preserve">Fig. 3<emph style="sub">e</emph>.</caption> <variables xml:id="echoid-variables1" xml:space="preserve">2 4 7 0 11 12 13 10 14 8 9</variables> </figure> <figure> <caption xml:id="echoid-caption3" style="it" xml:space="preserve">Fig. 1<emph style="sub">e</emph>.</caption> <description xml:id="echoid-description1" style="it" xml:space="preserve">Echelle du Plan</description> <variables xml:id="echoid-variables2" xml:space="preserve">Z 5 A C B E F D G 1 H L R P I S S P R K N 30 60 90 120 150 180 P P P</variables> </figure> <figure> <caption xml:id="echoid-caption4" style="it" xml:space="preserve">Fig. 2<emph style="sub">e</emph>.</caption> <description xml:id="echoid-description2" style="it" xml:space="preserve">Batterie enterrées</description> <description xml:id="echoid-description3" style="it" xml:space="preserve">Batterie de Ilireau</description> <description xml:id="echoid-description4" style="it" xml:space="preserve">Tranchée</description> <description xml:id="echoid-description5" style="it" xml:space="preserve">Batteries de</description> <description xml:id="echoid-description6" style="it" xml:space="preserve">Canons</description> <description xml:id="echoid-description7" style="it" xml:space="preserve">Echelle du Profil</description> <variables xml:id="echoid-variables3" xml:space="preserve">S T X Y O Q K A R P N B B 5 10 15 20 25 30</variables> </figure> <pb file="200" n="200"/> <figure> <image file="200-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/200-01"/> </figure> </div> <div xml:id="echoid-div467" type="section" level="1" n="225"> <head xml:id="echoid-head338" xml:space="preserve">DE LA <lb/>CONSTRUCTION <lb/>ET DES USAGES <lb/>DE PLUSIEURS DIFFERENS <lb/>NIVEAUX <lb/>POUR LA CONDUITE DES EAUX.</head> <p> <s xml:id="echoid-s6006" xml:space="preserve">Comme auſſi des Inſtrumens ſervans à l'Artillerie.</s> <s xml:id="echoid-s6007" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div468" type="section" level="1" n="226"> <head xml:id="echoid-head339" style="it" xml:space="preserve">LIVRE CIN 2 UIÉME.</head> <head xml:id="echoid-head340" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head341" style="it" xml:space="preserve">De la Conſtruction & des Vſages de pluſieurs Niveaux. <lb/>Conſiruction du Niveau à l'Eau.</head> <p> <s xml:id="echoid-s6008" xml:space="preserve">JE premier de ces Inſtrumens eſt un Niveau d'Eau. </s> <s xml:id="echoid-s6009" xml:space="preserve">Il eſt <lb/> <anchor type="note" xlink:label="note-200-01a" xlink:href="note-200-01"/> compoſé d'un tuïau rond de cuivre ou autre matiere, <lb/>long d'environ 3 pieds, ſur 12 à 15 lignes de diametre: <lb/></s> <s xml:id="echoid-s6010" xml:space="preserve">Il eſt recourbé par les bouts à l'équerre pour y recevoir <lb/>2 tuïaux de verre de 3 ou 4 pouces, que l'on fait tenir avec de la <lb/>cire ou du maſtic. </s> <s xml:id="echoid-s6011" xml:space="preserve">Il y a par deſſous une virole attachée au mi-<lb/>lieu, pour le placer ſur ſon pied.</s> <s xml:id="echoid-s6012" xml:space="preserve"/> </p> <div xml:id="echoid-div468" type="float" level="2" n="1"> <note position="right" xlink:label="note-200-01" xlink:href="note-200-01a" xml:space="preserve">XV. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s6013" xml:space="preserve">On y verſe de l'eau ordinaire ou colorée par un des bouts juſqu'à <lb/>ce qu'il y en ait aſſez pour paroître dans les deux tuïaux de verre.</s> <s xml:id="echoid-s6014" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6015" xml:space="preserve">Ce Niveau, quoique fort ſimple, eſt très-commode pour niveler <lb/>de moyennes diſtances.</s> <s xml:id="echoid-s6016" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6017" xml:space="preserve">Il eſt fondé ſur ce que l'eau ſe place toûjours naturellement <lb/>de niveau; </s> <s xml:id="echoid-s6018" xml:space="preserve">c'eft pourquoi il n'eſt pas neceſſaire qu'elle ſoit éga-<lb/>lement éloignée des extremitez des 2 tuîaux de verre, car elle s'y <lb/> <pb o="186" file="201" n="201" rhead="CONSTRUCTION ET USAGES"/> mettra toûjours d'égale hauteur, par rapport au centre de la terre.</s> <s xml:id="echoid-s6019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6020" xml:space="preserve">Le Niveau d'air marqué B, eſt un tuïau de verre bien droit, d'é-<lb/> <anchor type="note" xlink:label="note-201-01a" xlink:href="note-201-01"/> gale groſſeur & </s> <s xml:id="echoid-s6021" xml:space="preserve">épaiſſeur par tout.</s> <s xml:id="echoid-s6022" xml:space="preserve"/> </p> <div xml:id="echoid-div469" type="float" level="2" n="2"> <note position="left" xlink:label="note-201-01" xlink:href="note-201-01a" xml:space="preserve">Fig. B.</note> </div> <p> <s xml:id="echoid-s6023" xml:space="preserve">Il s'en fait de differente 'longueur & </s> <s xml:id="echoid-s6024" xml:space="preserve">groſſeur à proportion; </s> <s xml:id="echoid-s6025" xml:space="preserve">on le <lb/>remplit à quelque goute près, d'eſprit-de-vin ou d'autre liqueur qui <lb/>n'eſt point ſujette à ſe geler. </s> <s xml:id="echoid-s6026" xml:space="preserve">Les bouts de ce tuïau ſont terminez <lb/>en pointe & </s> <s xml:id="echoid-s6027" xml:space="preserve">fermez hermétiquement; </s> <s xml:id="echoid-s6028" xml:space="preserve">c'eſt-à-dire, que le bout par <lb/>lequel on a verſé l'eſprit de vin, à été enſuite bouché avec le verre <lb/>même, en le tortillant au raïon du feu vif d'une lampe que l'on ſou-<lb/>fle pour le rendre bien ardent, par le moyen d'un chalumeau.</s> <s xml:id="echoid-s6029" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6030" xml:space="preserve">On connoît que cet inſtrument eſt parfaitement de niveau, lorſ-<lb/>que la goute d'air s'arrête juſtement au milieu; </s> <s xml:id="echoid-s6031" xml:space="preserve">car quand il n'eſt <lb/>pas de niveau, la goute d'air, comme plus legere, court vers le haut, <lb/>pour remplir le vuide.</s> <s xml:id="echoid-s6032" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div471" type="section" level="1" n="227"> <head xml:id="echoid-head342" style="it" xml:space="preserve">Conſtruction du Niveau d'air monté.</head> <p> <s xml:id="echoid-s6033" xml:space="preserve">CEt inſtrument eſt compoſé d'un Niveau d'air d'environ 8 pou-<lb/>ces de long ſur 7 à 8 lignes de diametre, marquez 1. </s> <s xml:id="echoid-s6034" xml:space="preserve">Il eſt en-<lb/>châſſé dans un tuïau de cuivre, marqué 2, qui eſt évuidé dans ſon <lb/>milieu, afin que l'on puiſſe voir au-deſſus la bulle d'air.</s> <s xml:id="echoid-s6035" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6036" xml:space="preserve">Il eſt porté ſur une forte regle bien droite d'environ un pied de <lb/> <anchor type="note" xlink:label="note-201-02a" xlink:href="note-201-02"/> long, aux extremitez de laquelle ſont placées 2. </s> <s xml:id="echoid-s6037" xml:space="preserve">pinules juſtement <lb/>de même hauteur & </s> <s xml:id="echoid-s6038" xml:space="preserve">ſemblables à celle marquée 3, qui eſt vûë de <lb/>front; </s> <s xml:id="echoid-s6039" xml:space="preserve">elle a une ouverture quarrée, dans laquelle il y a deux filets <lb/>de cuivre très-délicatement limez, qui ſe croiſent à angles droits. <lb/></s> <s xml:id="echoid-s6040" xml:space="preserve">On y perce un petit trou au milîeu, & </s> <s xml:id="echoid-s6041" xml:space="preserve">on y attache une petite piece <lb/>de cuivre mince, avec un petit clou à tête, afin de boucher l'ouver-<lb/>ture quarrée, quand il eſt beſoin. </s> <s xml:id="echoid-s6042" xml:space="preserve">Cette piece eſt percée d'un petit <lb/>trou qui répond à celui qui eſt au milieu des filets. </s> <s xml:id="echoid-s6043" xml:space="preserve">Le tuiau de cui-<lb/>vre eſt attaché ſur la regle par le moyen de 2 vis, dont l'une mar-<lb/>quée 4, ſert à lever ou baiſſer le tuïau, tant & </s> <s xml:id="echoid-s6044" xml:space="preserve">ſi peu que l'on veut <lb/>pour le placer de niveau & </s> <s xml:id="echoid-s6045" xml:space="preserve">le faire accorder avec les pinules.</s> <s xml:id="echoid-s6046" xml:space="preserve"/> </p> <div xml:id="echoid-div471" type="float" level="2" n="1"> <note position="left" xlink:label="note-201-02" xlink:href="note-201-02a" xml:space="preserve">Fig. C.</note> </div> <p> <s xml:id="echoid-s6047" xml:space="preserve">La boule du genoüil eſt rivée à une petite regle, qui fait reſſort, & </s> <s xml:id="echoid-s6048" xml:space="preserve"><lb/>eſt attachée par un de ſes bouts avec 2 vis à la grande regle, & </s> <s xml:id="echoid-s6049" xml:space="preserve">à l'au-<lb/>tre bout il y a une vis à oreille, marquée 5, qui ſert à hauſſer ou baiſ-<lb/>ſer tout l'inſtrument quand il y a peu de choſe à changer.</s> <s xml:id="echoid-s6050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6051" xml:space="preserve">La maniere d'ajuſter ce Niveau eſt facile. </s> <s xml:id="echoid-s6052" xml:space="preserve">Il n'y a qu'à le placer ſur <lb/>ſon pied, de maniere que la goute d'air ſoit juſtement au milieu du <lb/>tu@au, alors fermant la pinule du côté de l'œil, & </s> <s xml:id="echoid-s6053" xml:space="preserve">ouvrant l'autre, <lb/>le point de l'objet qui eſt coupé par le filet horiſontal eſt de niveau <lb/> <pb o="187" file="202" n="202" rhead="DE DIFFERENS NIVEAUX. Liv. V. Chap. I."/> avec l'œil; </s> <s xml:id="echoid-s6054" xml:space="preserve">& </s> <s xml:id="echoid-s6055" xml:space="preserve">pour connoître ſi le niveau d'air eſt bien d'accord avec <lb/>les pinules, il n'y a qu'à retourner l'inſtrument bout pour bout, <lb/>fermer la pinule qui étoit ouverte & </s> <s xml:id="echoid-s6056" xml:space="preserve">ouvrir l'autre, puis regardant <lb/>par le petit trou, ſi le même point de l'objet eſt coupé par le filct <lb/>horiſontal, c'eſt une marque que le niveau eſt juſte; </s> <s xml:id="echoid-s6057" xml:space="preserve">& </s> <s xml:id="echoid-s6058" xml:space="preserve">s'il s'y trouve <lb/>quelque difference, il faut tant ſoit peu hauſler ou baiſſer le tuïau <lb/>par le moyen de la vis marquée 4, & </s> <s xml:id="echoid-s6059" xml:space="preserve">repeter cette operation juſ-<lb/>qu'à ce que les pinules ſoient d'accord avcc le niveau; </s> <s xml:id="echoid-s6060" xml:space="preserve">c'eſt-à-dire, <lb/>que regardant un objet, la bulle d'air étant au milieu & </s> <s xml:id="echoid-s6061" xml:space="preserve">enſuitere-<lb/>tournant l'inſtrument, on voye le même objet.</s> <s xml:id="echoid-s6062" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6063" xml:space="preserve">Le Niveau marqué D, eſt compoſé d'un petit tuïau de verre en-<lb/> <anchor type="note" xlink:label="note-202-01a" xlink:href="note-202-01"/> châſſé dans un autre tuîau de cuivre attaché ſur une regle parfaite-<lb/>ment égale d'épaiſſeur. </s> <s xml:id="echoid-s6064" xml:space="preserve">Il ſert à connoître ſi un plan, comme une <lb/>table, pendule, ou autre choſe ſemblable, eſt de niveau.</s> <s xml:id="echoid-s6065" xml:space="preserve"/> </p> <div xml:id="echoid-div472" type="float" level="2" n="2"> <note position="right" xlink:label="note-202-01" xlink:href="note-202-01a" xml:space="preserve">Fig. D.</note> </div> </div> <div xml:id="echoid-div474" type="section" level="1" n="228"> <head xml:id="echoid-head343" style="it" xml:space="preserve">Conſtruction du Niveau d'air à lunete.</head> <p> <s xml:id="echoid-s6066" xml:space="preserve">CE Niveau eſt ſemblable à celui marqué C, excepté qu'au lieu <lb/>de pinules, il y a une Lunete d'approche afin de découvrir de <lb/>plus loin. </s> <s xml:id="echoid-s6067" xml:space="preserve">Cette Lunete eſt dans un tuïau de cuivre, d'environ 15 <lb/>pouces de long, attaché ſur la même regle que le Niveau, laquelle <lb/>doit être d'une bonne épaiſſeur & </s> <s xml:id="echoid-s6068" xml:space="preserve">fort droite.</s> <s xml:id="echoid-s6069" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6070" xml:space="preserve">A l'extremité du tuïau de la Lunete marquée 1, entre le petit <lb/> <anchor type="note" xlink:label="note-202-02a" xlink:href="note-202-02"/> tuïau, auſſi marqué 1, qui porte le verre oculaire & </s> <s xml:id="echoid-s6071" xml:space="preserve">une ſoie très-<lb/>déliée, placée horiſontalement au foyer de l'objectif marqué 2, on <lb/>avance ou recule ce petit tuïau dans le grand, pour ajuſter la Lu-<lb/>nete aux difſerentes vûës.</s> <s xml:id="echoid-s6072" xml:space="preserve"/> </p> <div xml:id="echoid-div474" type="float" level="2" n="1"> <note position="right" xlink:label="note-202-02" xlink:href="note-202-02a" xml:space="preserve">Fig. E.</note> </div> <p> <s xml:id="echoid-s6073" xml:space="preserve">A l'autre bout de la Lunete eſt placé le verre objectif, dont la <lb/>conſtruction eſt la même que celle que nous avons donnée pour le <lb/>demi-cercle. </s> <s xml:id="echoid-s6074" xml:space="preserve">Tout le corps de cette Lunete eſt attaché à la regle, <lb/>auſſi-bien que le Niveau, avec des vis, ſur 2 petites plaques quar-<lb/>rées qui ſont ſoudées vers les extremitez de chaque tuïau, & </s> <s xml:id="echoid-s6075" xml:space="preserve">qui <lb/>doivent être d'épaiſſeur parfaitement égale.</s> <s xml:id="echoid-s6076" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6077" xml:space="preserve">Il y a une vis à la petite figure marquée 3, qui doit traverſer la <lb/>regle & </s> <s xml:id="echoid-s6078" xml:space="preserve">le tuïau de la Lunete, afin de pouvoir haſſer ou baiſſer la <lb/>petite fourchete qui porte la ſoie, & </s> <s xml:id="echoid-s6079" xml:space="preserve">la faire accorder avec la bulle <lb/>d'air, quand l'Inſtrument eſt de niveau. </s> <s xml:id="echoid-s6080" xml:space="preserve">La vis marquée 4, eſt pour <lb/>faire auſſi accorder la bulle d'air avec la Lunete.</s> <s xml:id="echoid-s6081" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6082" xml:space="preserve">Au-deſſous de la regle il y a une plaque de cuivre qui fait reſſort <lb/>& </s> <s xml:id="echoid-s6083" xml:space="preserve">qui porte le genoüil, comme au Niveau à pinules.</s> <s xml:id="echoid-s6084" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6085" xml:space="preserve">Le Niveau marqué F, eſt en forme d'Equerre, ayant ſes 2 bran-<lb/> <anchor type="note" xlink:label="note-202-03a" xlink:href="note-202-03"/> <pb o="188" file="203" n="203" rhead="CONSTRUCTION ET USAGES"/> ches parfaitement égales en longueur: </s> <s xml:id="echoid-s6086" xml:space="preserve">à la jonction de ſes 2 bran-<lb/>ches on fait un petit trou d'où pend une ſoie chargée d'un plomb, <lb/>qui bat fur une ligne penpendiculaire, au milieu du quart de cer-<lb/>cle, quile plus ſouvent eſt diviſé en 90 degrez. </s> <s xml:id="echoid-s6087" xml:space="preserve">Son uſage eſt fort <lb/>facile, car les extremitez de ſes 2 branches étant poſées ſur un plan, <lb/>on connoît qu'il eſt de niveau lorſque la ſoie bat juſte ſur la ligne <lb/>qui eſt au milieu du quart de cercle.</s> <s xml:id="echoid-s6088" xml:space="preserve"/> </p> <div xml:id="echoid-div475" type="float" level="2" n="2"> <note position="right" xlink:label="note-202-03" xlink:href="note-202-03a" xml:space="preserve">Fig. F.</note> </div> </div> <div xml:id="echoid-div477" type="section" level="1" n="229"> <head xml:id="echoid-head344" style="it" xml:space="preserve">Conſtruction d'un Niveau à plomb & à lunete.</head> <p> <s xml:id="echoid-s6089" xml:space="preserve">CEt Inſtrument eſt compoſé de deux regles attachées enſemble, <lb/>faiſant angles droits; </s> <s xml:id="echoid-s6090" xml:space="preserve">celle qui porte le filet avec ſon plomb a <lb/>environ un pied & </s> <s xml:id="echoid-s6091" xml:space="preserve">demi, ou deux pieds.</s> <s xml:id="echoid-s6092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6093" xml:space="preserve">On attache le filet vers le haut, à un petit clou qui eſt au point <lb/> <anchor type="note" xlink:label="note-203-01a" xlink:href="note-203-01"/> marqué 2. </s> <s xml:id="echoid-s6094" xml:space="preserve">Le milieu de la regle, où paſſe la ſoie, eſt évuidé, afin <lb/>qu'elle ne touche en aucun endroit que vers le bas, à l'endroit mar-<lb/>qué 3, où eſt une petite lame d'argent, ſur laquelle on a tracé dé-<lb/>licatement une ligne perpendiculaire à la lunete.</s> <s xml:id="echoid-s6095" xml:space="preserve"/> </p> <div xml:id="echoid-div477" type="float" level="2" n="1"> <note position="left" xlink:label="note-203-01" xlink:href="note-203-01a" xml:space="preserve">Fig. G.</note> </div> <p> <s xml:id="echoid-s6096" xml:space="preserve">On recouvre le vuide par deux pieces de cuivre, pour empêcher <lb/>quele vent n'agite la ſoie, & </s> <s xml:id="echoid-s6097" xml:space="preserve">qui forment une eſpece de boëte; </s> <s xml:id="echoid-s6098" xml:space="preserve">pour <lb/>la même raiſon il y a un criſtal qui couvre la lame d'argent, afin que <lb/>l'on puiſſe voir à travers, quand la ſoie avec ſon plomb eſt ſur la <lb/>perpendiculaire. </s> <s xml:id="echoid-s6099" xml:space="preserve">La lunete marquée 1, eſt attachée ſur l'autre re-<lb/>gle qui a environ deux pieds de long; </s> <s xml:id="echoid-s6100" xml:space="preserve">elle eſt conſtruite comme les <lb/>autres lunetes, dont nous avons parlé ci-devant. </s> <s xml:id="echoid-s6101" xml:space="preserve">Toute la juſteſſe <lb/>de cet Inſtrument conſiſte en ce que cette lunete ſoit parfaitement <lb/>à angle droit à la perpendiculaire.</s> <s xml:id="echoid-s6102" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6103" xml:space="preserve">Il y a un genoüil de la maniere ordinaire, attaché derriere cette <lb/>regle, pour placer tout l'inſtrument ſur ſon pied.</s> <s xml:id="echoid-s6104" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6105" xml:space="preserve">Nous faiſons auſſi de ces Niveaux à plomb & </s> <s xml:id="echoid-s6106" xml:space="preserve">à lunete, ſoit de <lb/>cuivre ou de fer; </s> <s xml:id="echoid-s6107" xml:space="preserve">dont la lunete & </s> <s xml:id="echoid-s6108" xml:space="preserve">le canal où eſt enfermé le filet <lb/>qui porte le plomb, ontenviron 4 à 5 pieds de longueur, afin de don-<lb/>ner de plus grands coups de niveau. </s> <s xml:id="echoid-s6109" xml:space="preserve">La lunete a environ un pouce <lb/>& </s> <s xml:id="echoid-s6110" xml:space="preserve">demi de diametre, & </s> <s xml:id="echoid-s6111" xml:space="preserve">la boëte du filet, qui porte le plomb, a <lb/>environ deux pouces de largeur ſur un & </s> <s xml:id="echoid-s6112" xml:space="preserve">demi d'épaiſſeur: </s> <s xml:id="echoid-s6113" xml:space="preserve">on at-<lb/>tache la boëte avec des vis par le milieu, à la lunete, de maniere <lb/>qu'elles ſoient parfaitement à angles di oits l'une à l'autre: </s> <s xml:id="echoid-s6114" xml:space="preserve">aux deux <lb/>extremitez de la lunete ſont ajuſtez deux larges cercles, dans leſ-<lb/>quels la lunete tourne juſte: </s> <s xml:id="echoid-s6115" xml:space="preserve">ces cercles qui ſont plats par deſſous <lb/>ſont attachez ſur uue forte regle de fer, afin qu'elle ſoit plus ſolide. <lb/></s> <s xml:id="echoid-s6116" xml:space="preserve">Ce Niveau eſt porté par 2 pieds, à peu près pareils à celui quej'ai <lb/>dé-<lb/> <pb o="189" file="204" n="204" rhead="DE DIFFERENS NIVEAUX. Liv. V. Chap. I."/> décrit à la Planche 13, figure E; </s> <s xml:id="echoid-s6117" xml:space="preserve">ces pieces ſont attachées avec des <lb/>vis aux extremitez de la regle de fer. </s> <s xml:id="echoid-s6118" xml:space="preserve">Il y a deux ouvertures, & </s> <s xml:id="echoid-s6119" xml:space="preserve">re-<lb/>couvertes d'un criſtal qui s'ouvre par le moyen d'un petit chaffis <lb/>de cuivre, afin de pouvoir accrocher le filet qui porte le plomb, au <lb/>haut de la boëte, de maniere que le filet batte ſur deux petites la-<lb/>mes d'argent, & </s> <s xml:id="echoid-s6120" xml:space="preserve">vis à-vis une ligne perpendiculaire à la lunete, <lb/>qu'on a tracée délicatement ſur leſdites lames. </s> <s xml:id="echoid-s6121" xml:space="preserve">Ces lames ſont <lb/>placées vis-à-vis les ouvertures de la boëte. </s> <s xml:id="echoid-s6122" xml:space="preserve">Le filet qui porte le <lb/>plomb, eſt un cheveu ou bien une ſoie très-fine, & </s> <s xml:id="echoid-s6123" xml:space="preserve">la lunete eſt <lb/>pareille à celle que j'ai décrite ci-devant, en parlant du demi-<lb/>cercle.</s> <s xml:id="echoid-s6124" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6125" xml:space="preserve">Toute la juſteſſe de cet Inſtrument conſiſte en ce que la lunete <lb/>ſoit parfaitement à angles droits avec les perpendiculaires qui ſont <lb/>tracées ſur les lames d'argent.</s> <s xml:id="echoid-s6126" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6127" xml:space="preserve">Pour éprouver ce Niveau, on le place ſur ſon pied, en ſorte que <lb/>le filet tombe juſte ſur la ligne perpendiculaire, & </s> <s xml:id="echoid-s6128" xml:space="preserve">l'on remarque <lb/>l'objet qui eſt coupépar la ſoie, qui eſt au foyer de la lunete; </s> <s xml:id="echoid-s6129" xml:space="preserve">puis <lb/>vous décrochez le filet qui porte le plomb, & </s> <s xml:id="echoid-s6130" xml:space="preserve">vous retournez la lu-<lb/>nete ſens deſſus deſſous; </s> <s xml:id="echoid-s6131" xml:space="preserve">enſuite vous racrochez le filet au crochet <lb/>qui ſe trouve an haut de la boëte, & </s> <s xml:id="echoid-s6132" xml:space="preserve">vous regardez par la lunete le <lb/>même objet; </s> <s xml:id="echoid-s6133" xml:space="preserve">ſi le filet tombe juſte ſur la ligne perpendiculaire, <lb/>c'eſt une marque que l'Inſtrument eſt juſte; </s> <s xml:id="echoid-s6134" xml:space="preserve">mais s'il ne s'y ren-<lb/>controit pas, il faudroit pouſſer à droite ou à gauche le p@tit cro-<lb/>chet, juſqu'à ce que le tout convienne de côté & </s> <s xml:id="echoid-s6135" xml:space="preserve">d'autre; </s> <s xml:id="echoid-s6136" xml:space="preserve">on peut <lb/>auſſi lever ou baiſſer la lunete par le moyen d'une vis. </s> <s xml:id="echoid-s6137" xml:space="preserve">Les Ou-<lb/>vriers intelligens ſuppléeront ſans peine à l'abregé de cette Deſ-<lb/>cription.</s> <s xml:id="echoid-s6138" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6139" xml:space="preserve">L'Inſtrument marqué H, eſt un petit Niveau ſimple, fondé ſur <lb/> <anchor type="note" xlink:label="note-204-01a" xlink:href="note-204-01"/> le même principe que les trois precedens. </s> <s xml:id="echoid-s6140" xml:space="preserve">Sa figure fait aſſez con-<lb/>noître ſon uſage & </s> <s xml:id="echoid-s6141" xml:space="preserve">ſa conſtruction.</s> <s xml:id="echoid-s6142" xml:space="preserve"/> </p> <div xml:id="echoid-div478" type="float" level="2" n="2"> <note position="right" xlink:label="note-204-01" xlink:href="note-204-01a" xml:space="preserve">Fig. H.</note> </div> <p> <s xml:id="echoid-s6143" xml:space="preserve">Le Niveau marqué I, ſe place de lui même. </s> <s xml:id="echoid-s6144" xml:space="preserve">Il eſt compoſé d'une <lb/> <anchor type="note" xlink:label="note-204-02a" xlink:href="note-204-02"/> regle de cuivre, d'une forte épaiſſeur, d'environ un pied de long, <lb/>ſur un pouce de large. </s> <s xml:id="echoid-s6145" xml:space="preserve">Il y a deux pinules de même hauteur, pla-<lb/>cées aux extremitez de la regle, & </s> <s xml:id="echoid-s6146" xml:space="preserve">au milieu une eſpece de fleau, <lb/>à peu près comme aux balances ordinaires pour ſuſpendre libre-<lb/>ment le niveau; </s> <s xml:id="echoid-s6147" xml:space="preserve">au-deſſous de ladite regle eſt attachée avec des <lb/>vis une piece de cuivre qui porte une boule auſſi de cuivre, un peu <lb/>groſſe, afin de lui donner plus de poids. </s> <s xml:id="echoid-s6148" xml:space="preserve">Toute la juſteſſe de cet <lb/>Inſtrument conſiſte dans un parfait équilibre. </s> <s xml:id="echoid-s6149" xml:space="preserve">Il eſt facile de le con-<lb/>noître, car en tenant l'Inſtrument ſuſpendu par ſon anneau, & </s> <s xml:id="echoid-s6150" xml:space="preserve">ayant <lb/> <pb o="190" file="205" n="205" rhead="CONSTRUCTION ET USAGES"/> remarqué un objet par les pinules, il ne faut que retourner l'inſ-<lb/>trument pour approcher l'œil de l'autre pinule, & </s> <s xml:id="echoid-s6151" xml:space="preserve">voir ſi le même <lb/>objet paroît à même hauteur, c'eſt une marque que l'inſtrument <lb/>eſt en parfait équilibre, mais ſi l'objet paroît un peu plus haut ou <lb/>plus bas, on pourra y remedier en pouſſant un peu la piece qui por-<lb/>te la boule, juſqu'à ce qu'elle ſoit juſtement au milieu du point de <lb/>ſuſpenſion, & </s> <s xml:id="echoid-s6152" xml:space="preserve">l'arrêter avec la vis, lorſque par les experiences on <lb/>aura reconnu que l'Inſtrument ſera de niveau.</s> <s xml:id="echoid-s6153" xml:space="preserve"/> </p> <div xml:id="echoid-div479" type="float" level="2" n="3"> <note position="right" xlink:label="note-204-02" xlink:href="note-204-02a" xml:space="preserve">Fig. I.</note> </div> </div> <div xml:id="echoid-div481" type="section" level="1" n="230"> <head xml:id="echoid-head345" style="it" xml:space="preserve">Conſtruction du Niveau de Monſieur Hugens.</head> <p> <s xml:id="echoid-s6154" xml:space="preserve">LA principale partie de cet Inſtrument eſt une lunete d'approche <lb/> <anchor type="note" xlink:label="note-205-01a" xlink:href="note-205-01"/> de 15 à 18 pouces de long, marquée 1, & </s> <s xml:id="echoid-s6155" xml:space="preserve">compoſée de la même <lb/>maniere que celle que nous avons décrite ci-devant, la lunete qui <lb/>eſt de forme cylindrique, paſſe par une virole où elle eſt arrêtée par <lb/>le milieu. </s> <s xml:id="echoid-s6156" xml:space="preserve">Cette virole a 2 branches plates pareilles, l'une en haut <lb/>& </s> <s xml:id="echoid-s6157" xml:space="preserve">l'autre en bas, marquée 2, chacune d'environ le quart de la lu-<lb/>nete; </s> <s xml:id="echoid-s6158" xml:space="preserve">de ſorte que le tout fait une maniere de croix. </s> <s xml:id="echoid-s6159" xml:space="preserve">Au bout de <lb/>chacune de ces deux branches eſt attachée une petite piece mou-<lb/>vante en forme de pince, dans laquelle eſt arrêrée une ſoie aſſez <lb/>forte, qui eſt paſſée en pluſieurs doubles dans un anneau.</s> <s xml:id="echoid-s6160" xml:space="preserve"/> </p> <div xml:id="echoid-div481" type="float" level="2" n="1"> <note position="left" xlink:label="note-205-01" xlink:href="note-205-01a" xml:space="preserve">Fig. K.</note> </div> <p> <s xml:id="echoid-s6161" xml:space="preserve">Par l'un de ces anneaux on ſuſpend la croix à un crochet qui eſt <lb/>au bout de la vis marquée 3, & </s> <s xml:id="echoid-s6162" xml:space="preserve">par en bas on attache à l'autre an-<lb/>neau un poids qui égale au moins la peſanteur de la croix, afin de <lb/>la maintenir en ſon équilibre; </s> <s xml:id="echoid-s6163" xml:space="preserve">ce poids eſt enfermé dans la boëte <lb/>marquée 5, dont il ne ſort que ſon crochet; </s> <s xml:id="echoid-s6164" xml:space="preserve">ce qui reſte d'eſpace <lb/>dans cette boëte, eſt remplide quelque huile de noix, ou de lin, ou <lb/>autre qui ne ſe fige point, pour arrêter plus promptement les ba-<lb/>lancemens du poids & </s> <s xml:id="echoid-s6165" xml:space="preserve">de la lunete.</s> <s xml:id="echoid-s6166" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6167" xml:space="preserve">On met quelquefois 2 lunetes à cet Inſtrument, l'une à côté de <lb/>l'autre & </s> <s xml:id="echoid-s6168" xml:space="preserve">bien paralleles; </s> <s xml:id="echoid-s6169" xml:space="preserve">l'oculaire d'une de ces lunetes eſt d'un <lb/>côté, & </s> <s xml:id="echoid-s6170" xml:space="preserve">l'oculaire de l'autre eſt du côté oppoſé, afin de pouvoir voir <lb/>des deux côtez ſans tourner le niveau. </s> <s xml:id="echoid-s6171" xml:space="preserve">Si le tuïau de la lunete étant <lb/>fuſpendu ne ſe trouve pas de niveau, comme il arrive ſouvent, on y <lb/>mettra une virole ou anneau marqué 4, que l'on pourra faire cou-<lb/>ler le long du tuïau de la lunete pour la placer de niveau & </s> <s xml:id="echoid-s6172" xml:space="preserve">la main-<lb/>tenir parallele à l'horiſon, ſoit qu'il y en ait une ou deux.</s> <s xml:id="echoid-s6173" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6174" xml:space="preserve">Il y a un filet tendu horiſontalement, attaché à une petite four-<lb/>chete au foyer du verre objectif de chaque lunete, que l'on peut <lb/>hauſſer ou baiſſer par le moyen d'une petite vis, comme nousavons <lb/>dit ci-devant.</s> <s xml:id="echoid-s6175" xml:space="preserve"/> </p> <pb o="191" file="206" n="206" rhead="DE DIFFERENS NIVEAUX. Liv. V. Ch. I."/> <p> <s xml:id="echoid-s6176" xml:space="preserve">Pour verifier ce niveau, l'ayant ſuſpendu par une de ſes branches, <lb/>on viſe à quelque objet éloigné, ſans que le plomb y ſoit attaché, & </s> <s xml:id="echoid-s6177" xml:space="preserve"><lb/>l'on remarque préciſément le point de l'objet qui eſt coupé par le fil <lb/>de la lunete, puis on y ajouté le plomb l'accrochant à l'anneau d'en <lb/>bas; </s> <s xml:id="echoid-s6178" xml:space="preserve">& </s> <s xml:id="echoid-s6179" xml:space="preserve">ſi alors le fil horiſontal répond au même point de l'objet, <lb/>c'eſt une marque que le centre de gravité de la croix eſt préciſé-<lb/>ment dans la ligne droite qui joint les deux points de ſuſpenſion, <lb/>& </s> <s xml:id="echoid-s6180" xml:space="preserve">répond au centre de la terre.</s> <s xml:id="echoid-s6181" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6182" xml:space="preserve">Mais ſi cela ne ſe trouve point, il faut y remedier en faiſant couler <lb/>la petite virole de côté ou d'autre. </s> <s xml:id="echoid-s6183" xml:space="preserve">L'ayant ainſi réduit à viſer au <lb/>même point, ſans plomb & </s> <s xml:id="echoid-s6184" xml:space="preserve">avec le plomb, on la retourne ſens deſſus <lb/>deſſous, en la ſuſpendant par la branche qui étoit en bas, & </s> <s xml:id="echoid-s6185" xml:space="preserve">atta-<lb/>chant le plomb par l'autre. </s> <s xml:id="echoid-s6186" xml:space="preserve">Que ſi alors le fil qui eſt dans la lunete <lb/>coupe le même point de l'objet, on eſt aſſuré que ce point eſt préci-<lb/>ſément dans le plan horiſontal du centre du tuïau de la lunete. </s> <s xml:id="echoid-s6187" xml:space="preserve">Mais <lb/>ſi le fil ne viſe pas au même point, on l'y reduira en le hauſſant ou <lb/>baiſſant par le moyen de la vis. </s> <s xml:id="echoid-s6188" xml:space="preserve">Il faut de tems en tems faire la verifi-<lb/>cation de l'inſtument, de crainte qu'il n'y arrive quelque chan-<lb/>gement.</s> <s xml:id="echoid-s6189" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6190" xml:space="preserve">Le crochet d'où eſt ſuſpendu cet inſtrument eſt attaché à une <lb/>croix faite de bandes de bois mince, & </s> <s xml:id="echoid-s6191" xml:space="preserve">qui excede un peu de part & </s> <s xml:id="echoid-s6192" xml:space="preserve"><lb/>d'autre la lunete & </s> <s xml:id="echoid-s6193" xml:space="preserve">ſes 2 branches; </s> <s xml:id="echoid-s6194" xml:space="preserve">aux extremitez de chaque bras <lb/>de cette croix, il y a un crochet qui ſert pour garantir la lunete de <lb/>trop d'agitation, quand on ſe ſert de l'inſtrument, ou pour la main-<lb/>tenir en repos quand on le tranſporte, en faiſant deſcendre la lu-<lb/>nete par le moyen de la vis qui la porte.</s> <s xml:id="echoid-s6195" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6196" xml:space="preserve">On applique à cette croix plate une autre croix creuſe que l'on at-<lb/>tache avec des crochets, qui ſert comme d'étui à l'inſtrument; </s> <s xml:id="echoid-s6197" xml:space="preserve">les 2 <lb/>bouts de la croix reſtent ouverts, & </s> <s xml:id="echoid-s6198" xml:space="preserve">par ce moyen la lunete étant à <lb/>couvert du vent & </s> <s xml:id="echoid-s6199" xml:space="preserve">de la pluie, elle ſe trouve toûjours en état de <lb/>ſervir.</s> <s xml:id="echoid-s6200" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6201" xml:space="preserve">Le pied pour porter cet Inſtrument eſt une plaque ronde de lai-<lb/>ton un peu concave, à laquelle ſont attachées trois viroles en <lb/>charniere, dans leſquelles on met des bâtons de longueur conve-<lb/>nable; </s> <s xml:id="echoid-s6202" xml:space="preserve">la boëte qui eſt au bas du niveau eſt poſée ſur cette plaque <lb/>& </s> <s xml:id="echoid-s6203" xml:space="preserve">ſe peut tourner du côté que l'on veut, de maniere que le plomb <lb/>ait ſon mouvement libre dans ſa boëte, qui doit être de cuivre, & </s> <s xml:id="echoid-s6204" xml:space="preserve"><lb/>que l'on bouche par le moyen d'une vis, pour conſerver l'huile <lb/>dans les voyages.</s> <s xml:id="echoid-s6205" xml:space="preserve"/> </p> <pb o="192" file="207" n="207" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div483" type="section" level="1" n="231"> <head xml:id="echoid-head346" style="it" xml:space="preserve">Conſtruction d'un autre Niveau.</head> <p> <s xml:id="echoid-s6206" xml:space="preserve">CEt Inſtrument eſt un niveau à peu près ſemblable a celui dont <lb/>nous venons de donner la deſcription; </s> <s xml:id="echoid-s6207" xml:space="preserve">mais il eſt plus facile à <lb/>tranſporter en campagne.</s> <s xml:id="echoid-s6208" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6209" xml:space="preserve">1. </s> <s xml:id="echoid-s6210" xml:space="preserve">Eſt la boëte dans laquelle eſt enfermée la lunete.</s> <s xml:id="echoid-s6211" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6212" xml:space="preserve">2. </s> <s xml:id="echoid-s6213" xml:space="preserve">Eſt une eſpece d'étrier où paſſe la vis qui ſert de point de ſuſ-<lb/> <anchor type="note" xlink:label="note-207-01a" xlink:href="note-207-01"/> penſion, au bout de laquelle il y a un crochet où s'accroche l'an-<lb/>neau qui eſt au bout de la plaque qui porte la lunete.</s> <s xml:id="echoid-s6214" xml:space="preserve"/> </p> <div xml:id="echoid-div483" type="float" level="2" n="1"> <note position="left" xlink:label="note-207-01" xlink:href="note-207-01a" xml:space="preserve">Fig. L.</note> </div> <p> <s xml:id="echoid-s6215" xml:space="preserve">3. </s> <s xml:id="echoid-s6216" xml:space="preserve">Sont des vis deſſus & </s> <s xml:id="echoid-s6217" xml:space="preserve">deſſous pour arrêter fixement la lunete, <lb/>lorſqu'on tranſporte l'Inſtrument.</s> <s xml:id="echoid-s6218" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6219" xml:space="preserve">4. </s> <s xml:id="echoid-s6220" xml:space="preserve">Sont des crochets pour tenir la boëte fermée.</s> <s xml:id="echoid-s6221" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6222" xml:space="preserve">5. </s> <s xml:id="echoid-s6223" xml:space="preserve">Eſt un bout de la lunete.</s> <s xml:id="echoid-s6224" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6225" xml:space="preserve">6. </s> <s xml:id="echoid-s6226" xml:space="preserve">Eſt le bout de la plaque où eſt accrochée une groſſe boule de <lb/>plomb qui ſert à maintenir la lunete de niveau.</s> <s xml:id="echoid-s6227" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6228" xml:space="preserve">Il y a trois viroles marquées 8, attachées fortement au-deſſous <lb/>de l'étrier, qui ſervent de pied pour porter tout l'Inſtrument, le-<lb/>quel doit être fort libre dans ſa boëte lorſqu'on s'en ſert. </s> <s xml:id="echoid-s6229" xml:space="preserve">Il eſt à re-<lb/>marquer que l'on met quelquefois deux lunetes dans ce niveau, <lb/>auſſi-bien que dans l'autre dont nous venons de parler.</s> <s xml:id="echoid-s6230" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div485" type="section" level="1" n="232"> <head xml:id="echoid-head347" xml:space="preserve">CHAPITRE II.</head> <head xml:id="echoid-head348" style="it" xml:space="preserve">Des Vſages des ſudïts Inſtrumens pour niveler.</head> <p> <s xml:id="echoid-s6231" xml:space="preserve">LE nivellement eſt une operation qui nous fait connoître la <lb/>hauteur d'un lieu à l'égard d'un autre. </s> <s xml:id="echoid-s6232" xml:space="preserve">On dit qu'un lieu eſt <lb/>plus élevé qu'un autre lorſqu'il eſt plus éloigné du centre de la ter-<lb/>re. </s> <s xml:id="echoid-s6233" xml:space="preserve">Une ligne qui eſt également éloignée du centre de la terre dans <lb/>tous ſes points, eſt appellée de niveau; </s> <s xml:id="echoid-s6234" xml:space="preserve">c'eſt pourquoi comme la <lb/>Terre eſt ronde, cette ligne doit être courbe & </s> <s xml:id="echoid-s6235" xml:space="preserve">faire partie de ſa <lb/> <anchor type="note" xlink:label="note-207-02a" xlink:href="note-207-02"/> circonference, comme on voit ici la ligne BDFG, dont tous les <lb/>points ſont également éloignez du centre de la Terre, marqué A. <lb/></s> <s xml:id="echoid-s6236" xml:space="preserve">Mais la ligne de viſée, que donnent les operations des Niveaux, <lb/>eſt une ligne droite perpendiculaire au demi-diametre de la Terre <lb/>AB, la quelle s'éleve au-deſſus du vrai Niveau marqué par la cour-<lb/>bure de la Terre, à proportion qu'elle eſt plus étenduë, c'eſt pour-<lb/>quoi toutes les operations ne nous donnent que le niveau apparent, <lb/> <pb o="193" file="208" n="208" rhead="DE DIFFERENS NIVEAUX. Liv. V. Ch. II."/> que l'on doit corriger pour avoir le vrai Niveau, lorſque la ligne <lb/>de viſée paſſe cinquante toiſes.</s> <s xml:id="echoid-s6237" xml:space="preserve"/> </p> <div xml:id="echoid-div485" type="float" level="2" n="1"> <note position="left" xlink:label="note-207-02" xlink:href="note-207-02a" xml:space="preserve">Fig. T.</note> </div> <p> <s xml:id="echoid-s6238" xml:space="preserve">La Table ſuivante où ſont marquées les corrections des points <lb/>du Niveau apparent pour les réduire au vrai Niveau, a été cal-<lb/>culée, par le moyen du demi-diametre de la terre dont on a connu <lb/>la grandeur après avoir meſuré un degré de ſa circonference. </s> <s xml:id="echoid-s6239" xml:space="preserve">Meſ-<lb/>ſieurs de l'Academie Roïale des Sciences ont trouvé par des Ob-<lb/>ſervations bien exactes, qu'un degré de la circonference de là Ter-<lb/>re dans un grand cercle, comme le Méridien, contient 5 7 0 6 0 <lb/>toiſes, & </s> <s xml:id="echoid-s6240" xml:space="preserve">donnant 25 lieuës au degré qui ſont les moyenes entre <lb/>les grandes & </s> <s xml:id="echoid-s6241" xml:space="preserve">les petites, il y aura 2282 toiſes & </s> <s xml:id="echoid-s6242" xml:space="preserve">deux cinquiémes <lb/>dans la longueur d'une lieuë.</s> <s xml:id="echoid-s6243" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6244" xml:space="preserve">Toute la circonference de la Terre ſera de 9000 de ces mémes <lb/>lieuës, & </s> <s xml:id="echoid-s6245" xml:space="preserve">ſon diametre en contiendra 2865, d'où il s'enſuit qu'il <lb/>y a de chaque endroit de la ſuperficie de la Terre à ſon centre <lb/>1432 lieuës & </s> <s xml:id="echoid-s6246" xml:space="preserve">demie.</s> <s xml:id="echoid-s6247" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6248" xml:space="preserve">La ligne A B repreſente le demi-diametre de la Terre, ſous les <lb/>pieds de l'Obſervateur. </s> <s xml:id="echoid-s6249" xml:space="preserve">La droite B D E, repreſente le raïon vi-<lb/>ſuel dont les points D E ſont dans le Niveau apparent du point <lb/>B. </s> <s xml:id="echoid-s6250" xml:space="preserve">On ſe ſert de cette ligne du Niveau apparent, pour en déter-<lb/>miner une qui ſoit de vrai Niveau; </s> <s xml:id="echoid-s6251" xml:space="preserve">ce qui ſe fait en ôtant des points <lb/>de la ligne du Niveau apparent, la hauteur dont ils s'élevent au-<lb/>deſſus du vrai Niveau à l'égard de certain point, comme B. </s> <s xml:id="echoid-s6252" xml:space="preserve">Car <lb/>il eſt facile à voir par cette figure que tous les points du Niveau <lb/>apparent D E, ſont plus éloignez du centre de la Terre que le <lb/>point B; </s> <s xml:id="echoid-s6253" xml:space="preserve">& </s> <s xml:id="echoid-s6254" xml:space="preserve">pour en connoître la difference, il n'y a qu'à conſi-<lb/>derer le triangle rectangle A B D, duquel ayant connu les deux <lb/>côtez AB, BD, on trouvera l'hypotenuſe AD, & </s> <s xml:id="echoid-s6255" xml:space="preserve">en ôtant le <lb/>raïon ou demi-diametre de la Terre AC, le reſte CD repreſente <lb/>l'élevation du point de Niveau apparent D par-deſſus le point du <lb/>vrai Niveau C.</s> <s xml:id="echoid-s6256" xml:space="preserve"/> </p> <figure> <image file="208-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/208-01"/> </figure> <pb o="194" file="209" n="209" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div487" type="section" level="1" n="233"> <head xml:id="echoid-head349" style="it" xml:space="preserve">Tai@@e qui montre les corrections des points de Niveau appa-<lb/>rent. ponr les reduire au vrai Niveau, ſuivant les diffe-<lb/>rentes diſtances de cinquante en cinquante toiſes.</head> <note position="right" xml:space="preserve"> <lb/>Diſtances des \\ points du Ni- \\ veau apparent. # ##### Corrections, ou \\ abaiſſemens. <lb/> # ##### Pouces. Lignes. <lb/>50 toiſes. # 0 # # 0 # # 1 tiers. <lb/>100 # 0 # # 1 # # 1 tiers. <lb/>150 # 0 # # 3 # Lignes. # 0 <lb/>200 # 0 # # 5 # # 1 tiers. <lb/>250 # 0 # Pouces. # 8 # # 1 tiers. <lb/>300 # 1 # # 0 # # 0 <lb/>350 # 1 # # 4 # # 1 tiers. <lb/>400 # 1 # # 9 # Lignes. # 1 tiers. <lb/>450 # 2 # # 3 # # 0 <lb/>500 # 2 # Pouces. # 9 # # 0 <lb/>550 # 3 # # 6 # # 0 <lb/>600 # 4 # # 0 # # 0 <lb/>650 # 4 # # 8 # # 0 <lb/>700 # 6 # # 4 # # 0 <lb/>750 # 5 # # 3 # Lignes. # 0 <lb/>800 # 7 # Pouces. # 1 # # 0 <lb/>850 # 7 # # 11 # # 1 demie. <lb/>900 # 8 # # 11 # # 0 <lb/>950 # 10 # # 0 # # 0 <lb/>1000 # 11 # # 0 # # 0 <lb/></note> <p> <s xml:id="echoid-s6257" xml:space="preserve">La Regle qui a ſervi à <lb/>calculer cette Table, eſt <lb/>de diviſer le quarré de <lb/>la diſtance par le diame-<lb/>tre de la Terre, qui eſt <lb/>6538694 toiſes, & </s> <s xml:id="echoid-s6258" xml:space="preserve">c'eſt <lb/>pour cette raiſon que les <lb/>corrections ou abaiſſe-<lb/>mens ſont entr'eux com-<lb/>me les quarrez des diſ-<lb/>tances. </s> <s xml:id="echoid-s6259" xml:space="preserve">Quoique le ſon-<lb/>dement de ce calcul ne <lb/>ſoit pas tout-à-fait géo-<lb/>métrique, il en approche <lb/>ſi fort, que dans la prati-<lb/>que il ne peut s'enſuivre <lb/>aucune erreur ſenſible.</s> <s xml:id="echoid-s6260" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6261" xml:space="preserve">Si l'on prenoit les points du Niveau apparent, au lieu de ceux du <lb/>vrai Niveau, on ſe tromperoit dans la conduite de l'eau d'une ſour-<lb/>ce, qui ſeroit, par exemple, au point B: </s> <s xml:id="echoid-s6262" xml:space="preserve">car cette ſource ne coule-<lb/>roit pas au long de la ligne BDE, mais elle demeureroit en B: </s> <s xml:id="echoid-s6263" xml:space="preserve">de <lb/>ſorte que pour s'étendre au long de ladite ligne, il faudroit qu'elle <lb/>remontât plus haut qu'elle n'eſt; </s> <s xml:id="echoid-s6264" xml:space="preserve">ce qui n'eſt pas poſſible, puisqu'el-<lb/>le ne peut prendre d'autre figure extérieure que la circulaire, qui eſt <lb/>également éloignée du centre de la terre. </s> <s xml:id="echoid-s6265" xml:space="preserve">Au contraire une ſource <lb/>qui ſeroit en D, auroit beaucoup de pente pour deſcendre en B, mais <lb/>elle ne pourroit pas paſſer outre, à cauſe qu'il faudroit qu'elle s'éle-<lb/>vât plus haut que ſa ſource, ſi elle continuoit ſon chemin au long <lb/>de la même ligne droite; </s> <s xml:id="echoid-s6266" xml:space="preserve">ce qu'elle ne peut pas faire à moins qu'elle <lb/> <pb o="195" file="210" n="210" rhead="DE DIFFERENS NIVEAUX. Liv. V. Chap. II."/> ne ſoit forcée par quelque machine. </s> <s xml:id="echoid-s6267" xml:space="preserve">Je pourrai donner à la fin de <lb/>cet Ouvrage, la deſcription d'une machine qui pourra faire con-<lb/>noître la maniere de faire monter l'eau plus haut que le niveau.</s> <s xml:id="echoid-s6268" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div488" type="section" level="1" n="234"> <head xml:id="echoid-head350" style="it" xml:space="preserve">Maniere de rectifier les Niveaux, ou verifier s'ils ſont juſtes.</head> <p> <s xml:id="echoid-s6269" xml:space="preserve">POur rectifier les Niveaux, comme, par exemple, celui d'air, il <lb/> <anchor type="note" xlink:label="note-210-01a" xlink:href="note-210-01"/> faut planter 2 piquets, comme AB, qui ſoient eloignez l'un <lb/>de l'autre d'environ 50 toiſes, à cauſe de la rondeur de la Terre; <lb/></s> <s xml:id="echoid-s6270" xml:space="preserve">car paſſé ce nombre @e toiſes, il faudroit y avoir égard; </s> <s xml:id="echoid-s6271" xml:space="preserve">puis en bor-<lb/>naïant de la ſituation A le piquet B, le Niveau étant poſé horiſonta-<lb/>lement, lorſque la bulle d'air ſera dans le milieu du tuïau, on fera <lb/>lever ou baiſſer le long dudit piquet B un carton, ſur le milieu du-<lb/>quel on aura tracé une ligne noire horiſontalement, juſqu'à ce que <lb/>le raïon viſuel de l Obſervateur rencontre cette ligne, après quoi il <lb/>faudra attacher contre le piquet A un autre carton pareil, dont le <lb/>milieu ſoit à la hauteur de l'œil, quand on a bornaïé le carton B; </s> <s xml:id="echoid-s6272" xml:space="preserve"><lb/>puis on tranſportera le Niveau au piquet B; </s> <s xml:id="echoid-s6273" xml:space="preserve">& </s> <s xml:id="echoid-s6274" xml:space="preserve">on le diſpoſera à <lb/>la hauteur du centre dudit carton, & </s> <s xml:id="echoid-s6275" xml:space="preserve">le Niveau étant poſé horiſon-<lb/>talement pour bornaïer le milieu du carton A, ſi pour lors le raïon <lb/>viſuel donnoit au milieu dudit carton, c'eſt une marque que ce Ni-<lb/>veau eſt bien juſte; </s> <s xml:id="echoid-s6276" xml:space="preserve">mais ſi le raïon viſuel donne au-deſſous ou au-<lb/>deſſus, comme par exemple au point C; </s> <s xml:id="echoid-s6277" xml:space="preserve">il faut, en conſervant toû-<lb/>jours la même hauteur de l'œil, baiſſer la lunete ou la pinule juſ-<lb/>qu'à ce que le raïon viſuel donne dansle milieu de la difference, <lb/>comme en D, & </s> <s xml:id="echoid-s6278" xml:space="preserve">la lunete reſtant ainſi, il faut ajuſter le tuïau de <lb/>niveau juſqu'à ce que la bulle d'air s'arrête dans le milieu, ce qui ſe <lb/>fait par le moyen de la vis marquée 4.</s> <s xml:id="echoid-s6279" xml:space="preserve"/> </p> <div xml:id="echoid-div488" type="float" level="2" n="1"> <note position="right" xlink:label="note-210-01" xlink:href="note-210-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s6280" xml:space="preserve">Enſuite on retournera au piquet A, remettre le Niveau à la hau-<lb/>teur du point D, pour bornaïer le carton B; </s> <s xml:id="echoid-s6281" xml:space="preserve">& </s> <s xml:id="echoid-s6282" xml:space="preserve">ſi le raïon viſuel don-<lb/>ne dans le centre de ce carton, c'eſt une marque que la lunete s'ac-<lb/>corde avec le niveau: </s> <s xml:id="echoid-s6283" xml:space="preserve">ſinon il faudra recommencer les mêmes opera-<lb/>tions juſqu'à ce qu'on vienne à rencontrer les centres des 2 cartons.</s> <s xml:id="echoid-s6284" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div490" type="section" level="1" n="235"> <head xml:id="echoid-head351" style="it" xml:space="preserve">Autre maniere de rectifier les Niveaux.</head> <p> <s xml:id="echoid-s6285" xml:space="preserve">COnnoiſſant deux points, qui ſoient parfaitement de niveau, é-<lb/>loignez l'un de l'autre, on mettra le bout qui porte l'oculaire <lb/>de la lunete à la hauteur juſte d'un de ces deux points, la bulle d'air <lb/>étant arrêtée au milieu de ſon tuïau, alors en bornaïant, s'il arrive <lb/>que la ſoie ou le filet de la lunete donne dans le ſecond point, c'eſt <lb/>une marque que le Niveau eſt juſte; </s> <s xml:id="echoid-s6286" xml:space="preserve">mais ſi le filet donnoit au-deſ-<lb/> <pb o="196" file="211" n="211" rhead="CONSTRUCTION ET USAGES"/> ſus ou au-deſſous du point de niveau, il faudroit, en conſervant <lb/>toûjours la même hauteur de l'œil, hauſſer ou baiſſer le bout du ni-<lb/>veau où eſt le verre objectif, juſqu'à ce que le raïon viſuel de la lu-<lb/>nete donne juſte au point de niveau, & </s> <s xml:id="echoid-s6287" xml:space="preserve">le laiſſant en cet état hauſ-<lb/>ſer ou baiſſer le tuïau qui porte le niveau, en ſorte que la bulle d'air <lb/>reſte dans le milieu.</s> <s xml:id="echoid-s6288" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6289" xml:space="preserve">Ce que l'on vient de dire pour ce Niveau, peut ſervir auſſi pour <lb/>rectifier les autres. </s> <s xml:id="echoid-s6290" xml:space="preserve">La difference n'eſt que de changer les plombs & </s> <s xml:id="echoid-s6291" xml:space="preserve"><lb/>filets des lunetes, ſuivant leurs conſtructions.</s> <s xml:id="echoid-s6292" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div491" type="section" level="1" n="236"> <head xml:id="echoid-head352" style="it" xml:space="preserve">Pratique du Nivellement.</head> <p> <s xml:id="echoid-s6293" xml:space="preserve">POur ſçavoir, par exemple, la difference de hauteur ou la pents <lb/>du haut de la montagne au point marqué A, juſqu'au bas de la-<lb/>dite montagne au point B, poſez vôtre Niveau environ au milieu <lb/> <anchor type="note" xlink:label="note-211-01a" xlink:href="note-211-01"/> de vos 2 points, comme en D, ayez des piquets plantez en A & </s> <s xml:id="echoid-s6294" xml:space="preserve">en B <lb/>avec des perſonnes inſtruites des ſignaux pour hauſſer ou baiſſer le <lb/>long defdits piquets des bâtons fendus, au bout deſquels on at-<lb/>tache les cartons, vôtre Niveau étant placé ſur ſon pied, bornaïez <lb/>vers le piquet AE, en faiſant le ſignal dont on eſt convenu avec des <lb/>perſonnes intelligentes pour cela de hauſſer ou baiſſer le carton, juſ-<lb/>qu'à ce que la partie de deſſus, ou la ligne du milieu, paroiſſe dans le <lb/>raïon viſuel; </s> <s xml:id="echoid-s6295" xml:space="preserve">faites meſurer exactement la hautcur perpendiculaire <lb/>du point A au point E, que nous ſuppoſons en cet exemple de 6 <lb/>pieds 4 pouces, que l'on écrira au memorial. </s> <s xml:id="echoid-s6296" xml:space="preserve">Tournez enſuite vô-<lb/>tre Niveau horiſontalement ſur ſon genoüil, en ſorte qu'il ſoit toû-<lb/>jours à même hauteur, & </s> <s xml:id="echoid-s6297" xml:space="preserve">donne droit au piquet B, afin que l'ocu-<lb/>laire de la lunete ſoit du côté de l'œil; </s> <s xml:id="echoid-s6298" xml:space="preserve">car ſi c'eſt un niveau à pinu-<lb/>le, il n'eſt pas neceſſaire de le retourner; </s> <s xml:id="echoid-s6299" xml:space="preserve">faites ſignal que l'on hauſſe <lb/>ou baiſſe le carton C, juſqu'à ce que ſon bout ſupérieur ſoit dans la <lb/>ligne de mire; </s> <s xml:id="echoid-s6300" xml:space="preserve">faites meſurer la hauteur du point B au point C, que <lb/>l'on ſuppoſe ici être de 16 pieds 6 pouces, que l'on chifrera au me-<lb/>morial au-deſſus de l'autre nombre de la premiere ſtation, & </s> <s xml:id="echoid-s6301" xml:space="preserve">pour <lb/>ſçavoir la pente dù point B au point A, ſouſtraiez 6 pieds 4 pouces <lb/>de 16 pieds 6 pouces, reſtent 10 pieds 2 pouces de pente, qui eſt <lb/>ce que l'on cherchoit.</s> <s xml:id="echoid-s6302" xml:space="preserve"/> </p> <div xml:id="echoid-div491" type="float" level="2" n="1"> <note position="left" xlink:label="note-211-01" xlink:href="note-211-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s6303" xml:space="preserve">Il eſt remarquer, que ſile point D, où eſt placé l'Obſervateur, eſt <lb/>au milieu entre le point A & </s> <s xml:id="echoid-s6304" xml:space="preserve">le point B, quelque diſtance qu'il puiſ-<lb/>ſe y avoir, il ne ſera pas neceſſaire d'avoir égard au hauſſement du <lb/>Niveau apparent par deſſus le vrai, parce que ces 2 points étans éga-<lb/>lement éloignez de l'œil de l'Obſervateur, le raïon viſuel s'élevera <lb/> <pb o="197" file="212" n="212" rhead="DE DIFFERENS NIVEAUX. Liv. V. Chap. II."/> également au-deſſus du vrai niveau, & </s> <s xml:id="echoid-s6305" xml:space="preserve">par conſequent il n'y aura <lb/>aucune correction à faire pour connoître la pente du point A au <lb/>point B.</s> <s xml:id="echoid-s6306" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div493" type="section" level="1" n="237"> <head xml:id="echoid-head353" style="it" xml:space="preserve">Autre exemple du Nivellement.</head> <p> <s xml:id="echoid-s6307" xml:space="preserve">ON veut ſçavoir s'il y a ſuffiſamment de la pente pour conduire <lb/> <anchor type="note" xlink:label="note-212-01a" xlink:href="note-212-01"/> l'eau depuis la ſource marquée A juſqu'au baſſin marqué B. <lb/></s> <s xml:id="echoid-s6308" xml:space="preserve">Comme la diſtance du point A au point B eſt grande, on eſt obligé <lb/>de faire pluſieurs operations. </s> <s xml:id="echoid-s6309" xml:space="preserve">A yant choiſi une hauteur commode <lb/>pour y placer le niveau, comme au point I, faites planter perpendi-<lb/>culairement au point A proche de la ſource, une perche au long de <lb/>laquelle on fera couler une autre perche fenduë qui porte le carton <lb/>L, faites meſurer la diſtance depuis A juſqu'en I, que nous ſuppo-<lb/>ſons icide 1000 toiſes; </s> <s xml:id="echoid-s6310" xml:space="preserve">le niveau étant ajuſté au point K, bornaïez <lb/>le haut du carton L, en le ſaiſant hauſſer ou baiſſer commenous a-<lb/>vons dit ci-devant, faites meſurer la hauteur AL, que nous ſuppo-<lb/>ſons 2 toiſes 1 pied 5 pouces; </s> <s xml:id="echoid-s6311" xml:space="preserve">mais à cauſe de la diſtance de 1000 <lb/>toiſes, ſuivant la table des hauſſemens du Niveau apparent par-deſ-<lb/>ſus le vrai niveau, il faut en ſouſtraire 11 pouces, & </s> <s xml:id="echoid-s6312" xml:space="preserve">la hauteur AL <lb/>ne ſcra plus par conſequent que de 2 toiſes 6 pouces, que vous mar-<lb/>querez ſur le memorial.</s> <s xml:id="echoid-s6313" xml:space="preserve"/> </p> <div xml:id="echoid-div493" type="float" level="2" n="1"> <note position="right" xlink:label="note-212-01" xlink:href="note-212-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s6314" xml:space="preserve">Tournez enſuite le Niveau du côté de la perche plantée au point <lb/>H, en ſorte que l'oculaire ſoit du côté de l'œil de l'obſervateur, & </s> <s xml:id="echoid-s6315" xml:space="preserve"><lb/>le niveau é@ant ajuſté, bornaïez le carton G, l'ayant fait hauſſer le <lb/>long de la perche juſqu'à ce que ſon bord ſuperieur ſoit dans le <lb/>raïon viſucl de la lunete, faites meſurer la hauteur HG, que l'on <lb/>ſuppoſe 3 toiſes 4 pieds 2 pouces.</s> <s xml:id="echoid-s6316" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6317" xml:space="preserve">Faites auſſi meſurer la diſtance du point I au point H, que nous <lb/>ſuppoſons ici de 650 toiſes, pour laquelle diſtance, ſuivant la ta-<lb/>ble, il faudra ſouſtraire 4 pouces 8 lignes de la hauteur HG, la-<lb/>quelle par conſequent ne ſera plus que de 3 toiſes 3 pieds 9 pouces <lb/>4 lignes, que vous marquerez ſur vôtre memorial.</s> <s xml:id="echoid-s6318" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6319" xml:space="preserve">Cela fait, tranſportez le Niveau fur quelqu'autre hauteur d'où <lb/>l'on puiſſe découvrir la perche HG, & </s> <s xml:id="echoid-s6320" xml:space="preserve">l'angle de la maiſon D, <lb/>dont le rez de chauſſée eſt de niveau avec le Baſſin B, quieſt le ter-<lb/>me du nivellement.</s> <s xml:id="echoid-s6321" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6322" xml:space="preserve">Le Niveau étant ajuſtê au point E, bornaïez la perche H; </s> <s xml:id="echoid-s6323" xml:space="preserve">le raïon <lb/>viſuel donnera au point F, faites meſurer la hauteur HF, que nous <lb/>ſuppoſons être de 11 pieds 6 pouces; </s> <s xml:id="echoid-s6324" xml:space="preserve">faites auſſi meſurer la diſtance <lb/>HB, que nous ſuppoſons de 50 toiſes, pour laquelle diſtance la <lb/> <pb o="198" file="213" n="213" rhead="CONSTRUCTION ET USAGES"/> table marque 2 pouſes 9 lignes de hauſſement, leſquels étant ôtez <lb/>de la hauteur HF, reſtera 11 pieds 3 pouces 3 lignes que l'on écrira <lb/>au memorial. </s> <s xml:id="echoid-s6325" xml:space="preserve">Ayant enſin tourné le Niveau pour bornaïer l'angle <lb/>de la maiſon D, faites meſurer la hauteur depuis le point D où s'eſt <lb/>terminé le raïon viſuel juſqu'au rez de chauſſée, laquelle nous ſup-<lb/>poſons de 8 pieds 3 pouces. </s> <s xml:id="echoid-s6326" xml:space="preserve">Faites auſſi meſurer la diſtance du point <lb/>E, juſqu'à ladite maiſon, laquelle ſe trouve de 450 toiſes, pour la-<lb/>quelle diſtance la table marque 2 pouſes 3 lignes de hauſſement, <lb/>leſquels étant ôtez de ladite hauteur reſteront 8 pieds 9 lignes, que <lb/>l'on écrira au memorial.</s> <s xml:id="echoid-s6327" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6328" xml:space="preserve">Ces deux exemples ſuffiront pour tout les cas du Nivellement, <lb/>ſinon on pourra avoir recours aux Livres qui en traitent.</s> <s xml:id="echoid-s6329" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div495" type="section" level="1" n="238"> <head xml:id="echoid-head354" style="it" xml:space="preserve">Maniere d'écrire toutes ces differentes bauteurs ſur le Mémorial.</head> <p> <s xml:id="echoid-s6330" xml:space="preserve">AYant trouvé des lieux commodes, comme nous venons de <lb/>ſuppoſer, pour placer le niveau entre 2 points, il faudra écrire <lb/>ſur le memorial en 2 differentes colonnes les hauteurs obſervées; </s> <s xml:id="echoid-s6331" xml:space="preserve">ſça-<lb/>voir, ſous la premiere colonne celles que l'on a miré, l'œil étant tour-<lb/>né du côte de la ſource A; </s> <s xml:id="echoid-s6332" xml:space="preserve">& </s> <s xml:id="echoid-s6333" xml:space="preserve">ſous la ſeconde colonne, celles qui ont <lb/>été obſervées du côté du Baſſin B, en la maniere ſuivante.</s> <s xml:id="echoid-s6334" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/> ##### Premiere colonne. <lb/>Premiere \\ hauteur # toiſes. # pieds. # pouc. # lig. <lb/>corrigée # 2 # 0 # 6 <lb/>Troiſiéme <lb/>hauteur # 1 # 5 # 3 # 3 <lb/> # 3 # 5 # 9 # 3 <lb/> ##### Seconde colonne. <lb/>Seconde # toiſes. # pieds. # pouc. # lig. <lb/>hauteur # 3 # 3 # 9 # 4 <lb/>Quatriéme <lb/>hauteur # 1 # 2 # 0 # 9 <lb/> # 4 # 5 # 10 # 1 <lb/></note> <p> <s xml:id="echoid-s6335" xml:space="preserve">Ayant ajoûté enſemble les hauteurs de la premiere colonne, & </s> <s xml:id="echoid-s6336" xml:space="preserve"><lb/>enſuite celles de la ſeconde, ſouſtraïez la premiere addition de la <lb/>ſeconde,</s> </p> <note position="right" xml:space="preserve"> <lb/> # toiſes. # pieds. # pouces. # lignes. <lb/>c'eſt-à-dire, de # 4 # 5 # 10 # 1 <lb/>ôtez # 3 # 5 # 9 # 3 <lb/> # 1 # 0 # 0 # 10 <lb/></note> <p> <s xml:id="echoid-s6337" xml:space="preserve">Il y a donc une toiſe & </s> <s xml:id="echoid-s6338" xml:space="preserve">dix lignes de pente depuis la ſource A, <lb/>juſqu'au baſſin B.</s> <s xml:id="echoid-s6339" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6340" xml:space="preserve">Si l'on v@ut en ſçavoir la diſtance, il n'y aura qu'à ajoûter en-<lb/> <pb o="199" file="214" n="214" rhead="DE LA JAUGE. Liv. V. Chap. III."/> ſemble toutes celles qui ont été meſurées; </s> <s xml:id="echoid-s6341" xml:space="preserve">ſçavoir,</s> </p> <note position="right" xml:space="preserve"> <lb/>La premiere de # 1000 toiſes. <lb/>La ſeconde de # 650 <lb/>La troiſiéme de # 500 <lb/>La quatriéme de # 450 <lb/>Total des diſtances # 2600 # toiſes. <lb/></note> <p> <s xml:id="echoid-s6342" xml:space="preserve">Enfin diviſant la pente par le nombre des toiſes de diſtance, <lb/>on trouvera qu'il y a pour chaque centaine de toiſes deux pouces <lb/>neuf lignes de pente, peu plus.</s> <s xml:id="echoid-s6343" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div496" type="section" level="1" n="239"> <head xml:id="echoid-head355" xml:space="preserve">CHAPITRE III.</head> <head xml:id="echoid-head356" style="it" xml:space="preserve">De la Conſtruction & Vſage de la fauge, pour le partage <lb/>des Eaux.</head> <p> <s xml:id="echoid-s6344" xml:space="preserve">CEtte Jauge ſert à connoítre la quantité d'eau que fournit un <lb/> <anchor type="note" xlink:label="note-214-02a" xlink:href="note-214-02"/> ſource. </s> <s xml:id="echoid-s6345" xml:space="preserve">On la fait ordinairement d'un Vaiſſeau parallelipipe-<lb/>de rectangle de cuivre, bien ſoudé, d'environ un pied de long, 8 <lb/>pouces de large & </s> <s xml:id="echoid-s6346" xml:space="preserve">autant de hauteur, plus ou moins, ſuivant la <lb/>quantité d'eau qu'on veut meſurer. </s> <s xml:id="echoid-s6347" xml:space="preserve">On y perce pluſieurs trous cir-<lb/>culaires très-exactement, d'un pouce de diametre, & </s> <s xml:id="echoid-s6348" xml:space="preserve">d'autres pour <lb/>qu'il paſſe un demipouce d'eau, & </s> <s xml:id="echoid-s6349" xml:space="preserve">d'autres pour qu'il en en paſſe un <lb/>quart de pouce. </s> <s xml:id="echoid-s6350" xml:space="preserve">Tous ces trous doivent être percez de maniere que <lb/>leurs centres ſoient à même hauteur. </s> <s xml:id="echoid-s6351" xml:space="preserve">Les extrémitez ſupérieures <lb/>des trous d'un pouce doivent être à 2 lignes près du haut de la Jau-<lb/>ge; </s> <s xml:id="echoid-s6352" xml:space="preserve">on bouche ces trous avec de petites plaques de cuivre quar-<lb/>rées, & </s> <s xml:id="echoid-s6353" xml:space="preserve">qui ſont ajuſtées dans des couliſſes marquées 1, 2, & </s> <s xml:id="echoid-s6354" xml:space="preserve">3. </s> <s xml:id="echoid-s6355" xml:space="preserve">Il <lb/>y a une bande de cuivre mince, qui traverſe le Vaiſſeau à l'endroit <lb/>marqué 4 Elle eſt arrêtée environ à un pouce du fond & </s> <s xml:id="echoid-s6356" xml:space="preserve">percée de <lb/>pluſieurs trous, afin que l'eau y paſſe plus librement. </s> <s xml:id="echoid-s6357" xml:space="preserve">Elle eſt faite <lb/>pour recevoir le choc de l'eau qui tombe de la ſource dans ladite <lb/>Jauge, & </s> <s xml:id="echoid-s6358" xml:space="preserve">empêcher qu'elle ne faſſe des vagues, & </s> <s xml:id="echoid-s6359" xml:space="preserve">faire qu'elle ſorte <lb/>plus naturellement par les ouvertures.</s> <s xml:id="echoid-s6360" xml:space="preserve"/> </p> <div xml:id="echoid-div496" type="float" level="2" n="1"> <note position="right" xlink:label="note-214-02" xlink:href="note-214-02a" xml:space="preserve">Fig. M.</note> </div> <p> <s xml:id="echoid-s6361" xml:space="preserve">Il eſt à remarquer que les trous qui donnent un pouce cylindri-<lb/>que d'eau, doivent avoir 12 lignes juſte de diametre; </s> <s xml:id="echoid-s6362" xml:space="preserve">celui d'unde-<lb/>mi pouce doit avoir 8 lignes & </s> <s xml:id="echoid-s6363" xml:space="preserve">demi, & </s> <s xml:id="echoid-s6364" xml:space="preserve">celui d'un quart de pouce <lb/>doit être de 6 lignes juſte. </s> <s xml:id="echoid-s6365" xml:space="preserve">Cela ſe trouve facilement par le calcul.</s> <s xml:id="echoid-s6366" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6367" xml:space="preserve">Pour ſe ſervir de cet inſtrument, il faut le placer de maniere que <lb/>ſon fonds ſoit horiſontal & </s> <s xml:id="echoid-s6368" xml:space="preserve">ſes côtez bien perpendiculaires, puis fai-<lb/> <pb o="200" file="215" n="215" rhead="CONSTRUCTION ET USAGES"/> re entrer dans la Jauge l'eau de la ſource par le moyen d'un tuïau, <lb/>comme la figure le marque, & </s> <s xml:id="echoid-s6369" xml:space="preserve">lorſqu'elle ſera pleine environ une <lb/>ligne près du bord, on ouvrira une des ouvertures, par exemple, d'un <lb/>pouce; </s> <s xml:id="echoid-s6370" xml:space="preserve">ſi l'eau reſte toûjours à même hauteur dans la Jauge, c'eſt une <lb/>marque qu'il y entre autant d'eau qu'il en ſort, & </s> <s xml:id="echoid-s6371" xml:space="preserve">que la ſource four-<lb/>nit un pouce d'eau. </s> <s xml:id="echoid-s6372" xml:space="preserve">Mais ſi l'eau augment oit dans le Vaiſſeau, il fau-<lb/>droit ouv rir une autre ouverture, ſoit d'un pouce, d'un demi ou d'un <lb/>quart; </s> <s xml:id="echoid-s6373" xml:space="preserve">de telle ſorte que l'eau reſte toûjours à même hauteur dans la <lb/>Jauge, c'eſt, à-dire, à une ligne au-deſſus des trous d'un pouce, alors <lb/>le nombre des trous ouverts donnera la quantité d'eau que fournit <lb/>la ſource.</s> <s xml:id="echoid-s6374" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6375" xml:space="preserve">Le petit vaſe qui reçoit l'eau qui ſort de la Jauge, eſt fait pour <lb/> <anchor type="note" xlink:label="note-215-01a" xlink:href="note-215-01"/> ſçavoir combien la ſource en fournit dans un eſpace de tems déter-<lb/>miné, car ayant une pendule à ſecondes bien reglée, & </s> <s xml:id="echoid-s6376" xml:space="preserve">remarquant <lb/>le nombre de ſecondes qu'elle marque lorſque vous placerez le vaiſ-<lb/>ſeau ſous le canal d'un pouce d'eau, & </s> <s xml:id="echoid-s6377" xml:space="preserve">voyant combien il s'eſt paſſé <lb/>de ſecondes ou de minutes dans le tems qu'il a été à s'emplir, & </s> <s xml:id="echoid-s6378" xml:space="preserve">en-<lb/>ſuite meſurant exactement la quantité d'eau qu'il contient, on di-<lb/>ra: </s> <s xml:id="echoid-s6379" xml:space="preserve">Cette ſource fournit tant d'eau par heure.</s> <s xml:id="echoid-s6380" xml:space="preserve"/> </p> <div xml:id="echoid-div497" type="float" level="2" n="2"> <note position="left" xlink:label="note-215-01" xlink:href="note-215-01a" xml:space="preserve">Fig. N.</note> </div> <p> <s xml:id="echoid-s6381" xml:space="preserve">On a fait plu ſieurs experiences bien juſtes à ce ſujet, & </s> <s xml:id="echoid-s6382" xml:space="preserve">on a trou-<lb/>vé qu'une ſource qui donnoit 1 pouce d'eau, en fourniſſoit 14 pintes <lb/>meſure de Paris, en une minute de tems, de celle qui peſe 2 livres <lb/>la pinte.</s> <s xml:id="echoid-s6383" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6384" xml:space="preserve">Il s'enſuit de là qu'un pouce d'eau donnera dans l'eſpace d'une <lb/>heure 3 muids meſure de Paris, & </s> <s xml:id="echoid-s6385" xml:space="preserve">en 24 heures 72 muids.</s> <s xml:id="echoid-s6386" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6387" xml:space="preserve">Si, par exemple, on plaçoit ſous la Jauge un Viſſeau cubique, <lb/>contenant un pied cube, & </s> <s xml:id="echoid-s6388" xml:space="preserve">qu'on y fit couler l'eau par l'ouverture <lb/>d'un pouce, on verroit que ce Vaiſſeau ſeroit rempli dans l'eſpace <lb/>de 2 minutes & </s> <s xml:id="echoid-s6389" xml:space="preserve">demie, d'où s'enſuit que c'eſt 14 pintes par minute, <lb/>puiſqu'elle a fourni 35 pintes en 2 minutes & </s> <s xml:id="echoid-s6390" xml:space="preserve">demie.</s> <s xml:id="echoid-s6391" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6392" xml:space="preserve">On ſçaura par ce moyen les pouces d'eau que donne une Fontaine <lb/>ou Ruiſſeau coulant; </s> <s xml:id="echoid-s6393" xml:space="preserve">car ſi, par exemple, on a reçû 7 pintes d'eau <lb/>en une ſeconde, on dira que cette eau coulante eſt d'un pouce. </s> <s xml:id="echoid-s6394" xml:space="preserve">Si <lb/>elle en fourniſſoit 21 pintes, on diroit qu'elle eſt de trois pouces, & </s> <s xml:id="echoid-s6395" xml:space="preserve"><lb/>ainſi des autres.</s> <s xml:id="echoid-s6396" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6397" xml:space="preserve">Pour meſurer l'eau courante dans un Aqueduc ou Riviere, <lb/>qu'on ne peut recev oir dans une Jauge, on mettra ſur l'eau une bou-<lb/>le de cire chargée de matiere un peu plus péſante, en ſorte qu'il ne <lb/>paſſe que fort peu de cire au-deſſus de la ſurface de l'eau, de peur <lb/>du vent: </s> <s xml:id="echoid-s6398" xml:space="preserve">& </s> <s xml:id="echoid-s6399" xml:space="preserve">après avoir meſuré une longueur de 15 ou 20 pieds de <lb/> <pb o="201" file="216" n="216" rhead="DE LA JAUGE. Liv. V. Chap. III."/> l'Aqueduc, on connoîtra avec une pendule à ſeconde, en com-<lb/>bien de tems la boule de cire, emportée par le cours de l'eau, paſ-<lb/>ſera cette diſtance; </s> <s xml:id="echoid-s6400" xml:space="preserve">enſuite on multipliera la largeur de l'A queduc <lb/>ou Riviere par la hauteur de l'eau, & </s> <s xml:id="echoid-s6401" xml:space="preserve">le produit multiplié par l'eſ-<lb/>pace qu'aura parcouru la boule de cire, le dernier produit marquera <lb/>toute l'eau qui aura paſſé pendant le tems qu'on aura remarqué, <lb/>par une ſection de l'Aqueduc. </s> <s xml:id="echoid-s6402" xml:space="preserve">Exemple, on ſuppoſe un Aqueduc <lb/>large de deux pieds, haut d'eau d'un pied, qu'en 20 ſecondes la <lb/>cire ait parcouru 30 pieds, ce ſera un pied & </s> <s xml:id="echoid-s6403" xml:space="preserve">demi par ſeconde: <lb/></s> <s xml:id="echoid-s6404" xml:space="preserve">mais com me l'eau va plus vite au haut qu'au fond, il ne faut pren-<lb/>dre que 20 pieds parcourus, ce ſera un pied par ſeconde, le pro-<lb/>duit d'un pied de haut par deux de large, eſt deux, qui multipliez <lb/>par 20 de longueur font 40 pieds cubes, ou 40 fois 35 pintes d'eau <lb/>qui font 1400 pintes en 20 ſecondes, & </s> <s xml:id="echoid-s6405" xml:space="preserve">ſi 20 ſecondes donnent <lb/>1400 pintes, 60 ſecondes en donneront trois fois autant, ſçavoir <lb/>4200 pintes; </s> <s xml:id="echoid-s6406" xml:space="preserve">& </s> <s xml:id="echoid-s6407" xml:space="preserve">diviſant 4200 par 14, qui eſt le nombre de <lb/>pintes qu'un pouce d'eau donne en une minute ou en 60 ſecondes, <lb/>on trouvera le quotien de 300, qui ſera le nombre des pouces que <lb/>donnera l'eau de l'A queduc.</s> <s xml:id="echoid-s6408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6409" xml:space="preserve">M. </s> <s xml:id="echoid-s6410" xml:space="preserve">Mariotte, qui a ſçavamment écrit ſur le mouvement des Eaux, <lb/>eſt du ſentiment que les Fontaines ne ſont autre choſe que l'eau de <lb/>la pluie, qui paſſant à travers de la terre, rencontre un tuf ou ter-<lb/>re glaiſe, qu'elle ne ſçauroit pénétrer, & </s> <s xml:id="echoid-s6411" xml:space="preserve">eſt obligé de ſe faire paſ-<lb/>ſage par les côtez, & </s> <s xml:id="echoid-s6412" xml:space="preserve">forme une Fontaine. </s> <s xml:id="echoid-s6413" xml:space="preserve">Pour prouver ce ſyſtê-<lb/>me, il rapporte l'experience ſuivante.</s> <s xml:id="echoid-s6414" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6415" xml:space="preserve">A yant fait faire un vaſe quarré de deux pieds, qu'il expoſa à la <lb/>pluie pendant pluſieurs années, il remarqua que l'eau montoit <lb/>dans ce vaſe chaque année l'une portant l'autre, à 18 pouces; </s> <s xml:id="echoid-s6416" xml:space="preserve">mais <lb/>il veut bien ne la prendre qu'à 15 pouces: </s> <s xml:id="echoid-s6417" xml:space="preserve">ſur ce pied une toiſe re-<lb/>cevroit en un an 45 pieds cubes d'eau; </s> <s xml:id="echoid-s6418" xml:space="preserve">car en multipliant 36 pieds <lb/>par 15 pouces, cela fait 45 pieds cubes.</s> <s xml:id="echoid-s6419" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6420" xml:space="preserve">Cet Auteur ſuppute auſſi l'étenduë du terrain qu'il prétend four-<lb/>nir l'eau à la Seine; </s> <s xml:id="echoid-s6421" xml:space="preserve">& </s> <s xml:id="echoid-s6422" xml:space="preserve">il trouve que la Seine n'eſt pas la ſixiéme <lb/>partie ſi groſſe qu'elle le devroit être: </s> <s xml:id="echoid-s6423" xml:space="preserve">il a encore obſervé, qu'elle <lb/>n'avoit que 10 pouces de pente par 1000 toiſes vis-à-vis les In-<lb/>valides. </s> <s xml:id="echoid-s6424" xml:space="preserve">Il prouve encore que la plus grande Fontaine de Mont-<lb/>martre, ſur ce pied, ne fournit pas même, quand elle eſt plus abon-<lb/>dante, ce que la terre qui la ſurmonte devroit lui envoyer d'eau. <lb/></s> <s xml:id="echoid-s6425" xml:space="preserve">Il conclud de là, qu'il faut qu'il s'en perde beaucoup dans les terres.</s> <s xml:id="echoid-s6426" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6427" xml:space="preserve">Pour ſçavoir le choc que doit produire l'eau, l'experience fait <lb/> <pb o="202" file="217" n="217" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> connoître que l'eau accelere ſon mouvement, ſelon les nombres 1, <lb/>3, 5, 7, c'eſt-à-dire, que ſi en un quart de ſeconde elle deſcend d'un <lb/>pied dans un tuïau, elle deſcendra de trois pieds pendant l'autre <lb/>quart de ſeconde.</s> <s xml:id="echoid-s6428" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6429" xml:space="preserve">Les quantitez d'eau qui ſortent par des ouvertures égales faites <lb/>audeſſous des Reſervoirs, de differentes hauteurs, ſont entr'elles <lb/>en la raiſon ſouſdaillée des hauteurs. </s> <s xml:id="echoid-s6430" xml:space="preserve">Les Tables ci-après feront <lb/>connoître les dépenſes d'eau à differentes élevations.</s> <s xml:id="echoid-s6431" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/> #### Table des dépen- \\ ſes d'Eau en une \\ minute à 3 lignes \\ de diamettre d'A- \\ jutoir à differente \\ hauteur de Reſer- \\ voir. # #### Table des dépen- \\ ſes d'Eau en une \\ minute par diffe- \\ rent Ajutoir à une \\ même hauteur de \\ Refervoir. # ##### Table des hau- \\ teurs des Jets d'Eau \\ aux differentes hau- \\ teurs des Reſervoirs. <lb/> ## Pieds. # ## Pintes. # ## Lignes. # ## Pintes. # ## Pieds. # Pint. # ## Pouc. <lb/> # 6 # 9 # Dépence d'Eau à 3 lig. d'Ajutoir. # Diametre de differens Ajutoirs. # 1 # 1 # # # 6 # 5 # 1 <lb/>Hauteurs des Reſervoirs. # 9 # 11 # # # 2 # 6 # # Hauteurs des @ets d'Eau. # 10 # 10 # 4 # Hauteurs des Reſervoirs. <lb/> # 12 # 14 # # # 3 # 14 # Dépenſe d'Eau. # # 20 # 21 # 4 <lb/> # 18 # 16 # # # 4 # 25 # # # 30 # 33 <lb/> # 25 # 19 # # # 5 # 39 # # # 40 # 45 # 4 <lb/> # 30 # 21 # # # 6 # 56 # # # 50 # 58 # 4 <lb/> # 40 # 24 # # # 7 # 76 # # # 60 # 72 <lb/> # 52 # 28 # # # 8 # 110 # # # 70 # 86 # 4 <lb/></note> <p> <s xml:id="echoid-s6432" xml:space="preserve">L'on voit par ces Tables qu'un Ajutoir une fois plus grand, dé-<lb/>penſe le quadruple d'un autre une fois plus petit. </s> <s xml:id="echoid-s6433" xml:space="preserve">Exemple, celui <lb/>de 3 lignes dépenſe en une minute 14 pintes, & </s> <s xml:id="echoid-s6434" xml:space="preserve">celui de 6 lignes <lb/>dépenſe 56 pintes. </s> <s xml:id="echoid-s6435" xml:space="preserve">Il eſt auſſi à remarquer qu'il ne faut pas faire les <lb/>Ajutoirs en cône, mais en cylindre; </s> <s xml:id="echoid-s6436" xml:space="preserve">& </s> <s xml:id="echoid-s6437" xml:space="preserve">qu'il ne faut pas que les con-<lb/>duits excedent de beaucoup le lieu de l'Ajutoir.</s> <s xml:id="echoid-s6438" xml:space="preserve"/> </p> <pb o="203" file="218" n="218" rhead="POUR L'ARTILLERIE. Liv. V. Ch. IV."/> </div> <div xml:id="echoid-div499" type="section" level="1" n="240"> <head xml:id="echoid-head357" xml:space="preserve">CHAPITRE IV.</head> <head xml:id="echoid-head358" style="it" xml:space="preserve">Contenant la Conſtruction & les V ſages des Inſtrumens <lb/>ſervans à l' Artillerie.</head> <head xml:id="echoid-head359" style="it" xml:space="preserve">Conſtruction du Compas de calibre.</head> <p> <s xml:id="echoid-s6439" xml:space="preserve">CEt Inſtrument eſt fait de 2 branches de cuivre, d'environ 6 à <lb/> <anchor type="note" xlink:label="note-218-01a" xlink:href="note-218-01"/> 7 pouces de long étant fermé. </s> <s xml:id="echoid-s6440" xml:space="preserve">Chaque branche a 4 lignes de <lb/>largeur ſur 3 d'épaiſleur.</s> <s xml:id="echoid-s6441" xml:space="preserve"/> </p> <div xml:id="echoid-div499" type="float" level="2" n="1"> <note position="right" xlink:label="note-218-01" xlink:href="note-218-01a" xml:space="preserve">XVI. <lb/>Planche. <lb/>Fig. A.</note> </div> <p> <s xml:id="echoid-s6442" xml:space="preserve">Le mouvement de la tête eſt ſemblable à celui des pieds de Roi; <lb/></s> <s xml:id="echoid-s6443" xml:space="preserve">ſes bouts ſont recourbez & </s> <s xml:id="echoid-s6444" xml:space="preserve">garnis d'acier aux extremitez.</s> <s xml:id="echoid-s6445" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6446" xml:space="preserve">Il y a une eſpece de languete attachée à une des branches dont <lb/>le mouvement eſt comme celui de la tête, pour la hauſſer ou baiſſer, <lb/>aſin que le bout qui doit être mince puiſſe entrer & </s> <s xml:id="echoid-s6447" xml:space="preserve">s'arrêter à des <lb/>crans que l'on fait dans l'épaiſſeur de l'autre branche. </s> <s xml:id="echoid-s6448" xml:space="preserve">On marque <lb/>au dedans de cette branche les diametres qui conviennent au poids <lb/>des boulets de fer en cette façon. </s> <s xml:id="echoid-s6449" xml:space="preserve">Il faut avoir une regle ſur laquelle <lb/>ſont marquées les diviſions des poids des boulets & </s> <s xml:id="echoid-s6450" xml:space="preserve">du calibre des <lb/>pieces, dont la méthode ſera expliquée en parlant de l'inſtrument <lb/>qui ſuit. </s> <s xml:id="echoid-s6451" xml:space="preserve">Ayant donc une regle preparée, on ou vre le compas de ca-<lb/>libre, en ſorte que ſes bouts intérieurs conviennent à l'ouverture d@ <lb/>chaque point de diviſion qui marque le poids des boulets; </s> <s xml:id="echoid-s6452" xml:space="preserve">alors on <lb/>fait un cran à chaque ouverture avec une lime triangulaire, afin <lb/>que le bout de la languete entrant dans chacun de ces crans, arrête <lb/>l'ouverture à chaque nombre juſte des poids des boulets On les <lb/>marque ordinairement depuis {1/4} de livre juſqu'à 48 1. </s> <s xml:id="echoid-s6453" xml:space="preserve">& </s> <s xml:id="echoid-s6454" xml:space="preserve">même ſou-<lb/>vent juſqu'à 64. </s> <s xml:id="echoid-s6455" xml:space="preserve">On trace des lignes ſur la ſurſace de cette bran-<lb/>che, vis-à-vis des crans, afin de marquer par des chifres le nom-<lb/>bre des livres qui leur conviennent.</s> <s xml:id="echoid-s6456" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6457" xml:space="preserve">L'uſage de cet inſtrument eſt facile, car il n'y a qu'à faire paſſer <lb/>les boulets qu'on veut meſurer, en ſorte que les 2 bouts intérieurs <lb/>embraſſent juſtement ſon diametre; </s> <s xml:id="echoid-s6458" xml:space="preserve">pour lors la languete étant mi-<lb/>ſe dans le cran convenable, marquera le poids du boulet.</s> <s xml:id="echoid-s6459" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6460" xml:space="preserve">Il doit toûjours y avoir une certaine proportion dans la largeur <lb/>des pointes de ce compas, de ſorte que faiſant un angle, comme la <lb/>figure le montre à chaque ouverture, l'intérieure donne le poids du <lb/>boulet, & </s> <s xml:id="echoid-s6461" xml:space="preserve">l'extérieure donne le calibre des pieces, c'eſt-à-dire, que <lb/>portant les bouts extérieurs de ces pointes au diametre de l'embou-<lb/> <pb o="204" file="219" n="219" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> chure d'un canon, la languete étant placée au cran neceſſaire, <lb/>fera connoître le poids du boulet qui lui convient. </s> <s xml:id="echoid-s6462" xml:space="preserve">On ſçait aſſez, <lb/>qu'il faut qu'il y ait un peu de jeu autour du boulet dans l'ame du <lb/>canon, & </s> <s xml:id="echoid-s6463" xml:space="preserve">c'eſt ce qu'on nom me calibre des pieces, qui excedetoû-<lb/>jours un peu le calibre des boulets à proportion de ſa groſſeur.</s> <s xml:id="echoid-s6464" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div501" type="section" level="1" n="241"> <head xml:id="echoid-head360" style="it" xml:space="preserve">Conſtruction de l'Equerre des Canoniers.</head> <note position="right" xml:space="preserve">Fig. B.</note> <p> <s xml:id="echoid-s6465" xml:space="preserve">CEtte Equerre ſert à élever ou baiſſer les Canons & </s> <s xml:id="echoid-s6466" xml:space="preserve">Mortiers, <lb/>ſuivant les lieux où l'on veut les pointer; </s> <s xml:id="echoid-s6467" xml:space="preserve">elle eſt faite de cuivre <lb/>& </s> <s xml:id="echoid-s6468" xml:space="preserve">a une branche d'environ un pied de longueur, de 8 lignes de lar-<lb/>geur & </s> <s xml:id="echoid-s6469" xml:space="preserve">d'une ligne d'épaiſſeur. </s> <s xml:id="echoid-s6470" xml:space="preserve">L'autre branche a 4 pouces de long, <lb/>de la même largeur & </s> <s xml:id="echoid-s6471" xml:space="preserve">épaiſſeur que l'autre branche. </s> <s xml:id="echoid-s6472" xml:space="preserve">Entre ces 2 <lb/>branches il y a un quart de cercle diviſé en 90 deg. </s> <s xml:id="echoid-s6473" xml:space="preserve">à commencer <lb/>du bras le plus court, avec une ſoie chargée d'un plomb & </s> <s xml:id="echoid-s6474" xml:space="preserve">attachée <lb/>à ſon centre.</s> <s xml:id="echoid-s6475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6476" xml:space="preserve">L'uſage de cet inſtrument eſt facile, il n'y a qu'à placer la grande <lb/>branche dans l'embouchure du Canon ou du Mortier & </s> <s xml:id="echoid-s6477" xml:space="preserve">l'élever ou <lb/>le baiſſer, juſqu'à ce que la ſoie qui porte le plomb coupe le degré <lb/>nece ſſaire pour tirer au licu propoſé.</s> <s xml:id="echoid-s6478" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6479" xml:space="preserve">On met auſſi le plus ſouvent ſur une des ſurfaces de la grande <lb/>branche la diviſion des diametres & </s> <s xml:id="echoid-s6480" xml:space="preserve">poids des boulets de fer, auſſi-<lb/>bien que celle du calibre des pieces.</s> <s xml:id="echoid-s6481" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6482" xml:space="preserve">Pour faire cette diviſion, il faut premierement être fondé ſur une <lb/>experience ou deux, en examinant avec toute l'exactitude poſſible <lb/>le diametre d'un boulet, dont on connoiſſe le poids bien juſte. </s> <s xml:id="echoid-s6483" xml:space="preserve">A yant <lb/>trouvé, par exemple, qu'un boulet peſant 4 livres, a 3 pouces de dia-<lb/>metre, il ſera facile de faire une Table qui contienne les poids & </s> <s xml:id="echoid-s6484" xml:space="preserve">dia-<lb/>metres de tels autres boulets qu'on voudra, puiſque par la 18<emph style="super">me</emph> pro-<lb/>poſition du 12<emph style="super">me</emph> Livre d'Euclide, les boulets ſont entr'eux comme <lb/>les cubes de leurs diametres, d'où s'enſuit que les diametres ſont en-<lb/>tr'eux comme les racines cubiques des nombres qui expriment leurs <lb/>poids.</s> <s xml:id="echoid-s6485" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6486" xml:space="preserve">A yant donc connu par l'experience qu'un boulet de fer peſant 4 <lb/>livres, a 3 pouces de diametre; </s> <s xml:id="echoid-s6487" xml:space="preserve">ſi on veut ſçavoir le diametre d'un <lb/>boulet de 32 livres, on dira par une regle de proportion, 4 eſt à 32, <lb/>comme 27 cube de 3 eſt à un 4<emph style="sub">me</emph> nombre, qui ſera 216, dont la <lb/>racine cubique 6 pouces ſera le diametre d'un boulet de 32 livres.</s> <s xml:id="echoid-s6488" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6489" xml:space="preserve">Ou bien on cherchera la racine cubique de ces 2 nombres 4 & </s> <s xml:id="echoid-s6490" xml:space="preserve"><lb/>32, ou plûtôt de 1 & </s> <s xml:id="echoid-s6491" xml:space="preserve">de 8, qui ſont en même proportion, & </s> <s xml:id="echoid-s6492" xml:space="preserve">on trou-<lb/>vera 1 eſt à 2, comme 3 eft à 6 ce qui revient au même.</s> <s xml:id="echoid-s6493" xml:space="preserve"/> </p> <pb o="205" file="220" n="220" rhead="POUR L'ARTILLERIE Liv. V. Ch. IV."/> <p> <s xml:id="echoid-s6494" xml:space="preserve">Mais comme tous les nombres n'ont pas des racines juſtes on pour-<lb/>ra ſe ſervir de la table des côtez homologues des ſolides ſemblables, <lb/>rapportée ci-devant au Traité du Compas de Proportion; </s> <s xml:id="echoid-s6495" xml:space="preserve">ſi donc <lb/>par ce moyen on veut avoir le diametre d'un boulet de 64 1. </s> <s xml:id="echoid-s6496" xml:space="preserve">on for-<lb/>mera une regle de 3, dont le premier terme ſera 397, côté du 4<emph style="sub">e</emph> ſo-<lb/>lide; </s> <s xml:id="echoid-s6497" xml:space="preserve">le ſecond ſera 3 pouces ou plûtôt 36 lignes diametre du boulet <lb/>de 4 1. </s> <s xml:id="echoid-s6498" xml:space="preserve">le 4<emph style="sub">me</emph> terme ſera 1000, côté du 64<emph style="sub">me</emph> ſolide; </s> <s xml:id="echoid-s6499" xml:space="preserve">la regle étant <lb/>achevée on aura 20 lig. </s> <s xml:id="echoid-s6500" xml:space="preserve">& </s> <s xml:id="echoid-s6501" xml:space="preserve">{1/4} pour le diametre d'un boulet de 64 1. <lb/></s> <s xml:id="echoid-s6502" xml:space="preserve">enſuite pour faciliter les operations des autres regles de 3, on pren-<lb/>dra toûjours pour premier terme le nombre 1000, pour ſecond 60 <lb/>lig. </s> <s xml:id="echoid-s6503" xml:space="preserve">{3/4}, & </s> <s xml:id="echoid-s6504" xml:space="preserve">pour le 3<emph style="sub">me</emph> le nombre qui ſe trouvera dans ladite table vis-<lb/>à-vis celui qui exprime le poids du boulet: </s> <s xml:id="echoid-s6505" xml:space="preserve">ainſi pout trouver par <lb/>exemple, le diametre d'un boulet de 24 liv. </s> <s xml:id="echoid-s6506" xml:space="preserve">on dira comme 1000 <lb/>ſont à 60 lignes {3/4}, ainſi 721. </s> <s xml:id="echoid-s6507" xml:space="preserve">La regle étant faite on trouvera 65 <lb/>lignes, qui font 5 pouces & </s> <s xml:id="echoid-s6508" xml:space="preserve">5 lignes; </s> <s xml:id="echoid-s6509" xml:space="preserve">c'eſt par cette méthode qu'on <lb/>a calculé la Table ſuivante.</s> <s xml:id="echoid-s6510" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div502" type="section" level="1" n="242"> <head xml:id="echoid-head361" style="it" xml:space="preserve">Table contenant les Poids & Diametres des Boulets de fer, & des Ca-<lb/>libres des Pieces les plus en uſage dans l'Artillerie.</head> <note position="right" xml:space="preserve"> <lb/> <lb/> ### Poids \\ du Boulet. # ## Pouces. # # ## Lignes. <lb/> ### 1 quart de liv. # 1 # # # 2 # 1 quart. <lb/> ### une demie li. # 1 # # # 6 # 0 <lb/> ### une livre # 1 # # # 10 # 5 huitiém. <lb/> # 2 # # 2 # # # 4 # 1 demie. <lb/> # 3 # # 2 # # # 8 # 2 tiers. <lb/> # 4 # # 3 # # # 0 # 0 <lb/> # 5 # # 3 # Pouces. # Lignes. # 2 # 3 quarts. <lb/> # 6 # # 3 # # # 5 # 0 <lb/>Livres. # 7 # # 3 # # # 7 # 1 quart. <lb/> # 8 # Poids des Boulets. # 3 # # # 9 # 3 huitiém. <lb/> # 9 # # 3 # # # 11 # 0 <lb/> # 10 # # 4 # # # 0 # 3 quarts: <lb/> # 12 # # 4 # # # 3 # 3 quarts. <lb/> # 16 # # 4 # # # 9 # 0 <lb/> # 18 # # 4 # # # 11 # 1 tiers. <lb/> # 20 # # 5 # Pouces. # # 1 # 1 demie. <lb/> # 24 # # 5 # # Lignes. # 5 # 0 <lb/> # 27 # # 5 # # 8 # 7 huitiém. <lb/>Livres. # 30 # # 5 # # # 10 # 1 demie. <lb/> # 33 # # 6 # # # 0 # 3 quarts. <lb/> # 36 # # 6 # # # 2 # 3 quarts. <lb/> # 40 # # 6 # # # 5 # 1 demie. <lb/> # 48 # # 6 # # # 10 # 0 <lb/> # 50 # # 6 # # # 11 # 1 demie. <lb/> # 64 # # 7 # # # 6 # 3 quarts. <lb/>Calibres <lb/>des pieces. # Po. # Lignes. <lb/>1 quart de liv. # 1 # 3 # 0 <lb/>une demie li. # 1 # 6 # 3 quarts. <lb/>une livre # 1 # 11 # 6 huitiém. <lb/>2 # 2 # 5 # 3 quarts. <lb/>3 # 2 # 10 # 0 <lb/>4 # 3 # 1 # 1 quart. <lb/>5 # 3 # 4 # 1 quart. <lb/>6 # 3 # 6 # 7 huitiém. <lb/>7 # 3 # 9 # 1 huitiém. <lb/>8 # 3 # 11 # 1 huitiém. <lb/>9 # 4 # 1 # 1 quart. <lb/>10 # 4 # 2 # 3 quarts. <lb/>12 # 4 # 5 # 3 quarts. <lb/>16 # 4 # 11 # 1 demie. <lb/>18 # 5 # 1 # 2 tiers. <lb/>20 # 5 # 4 # 0 <lb/>24 # 5 # 8 # 0 <lb/>27 # 5 # 10 # 2 tiers. <lb/>30 # 6 # 1 # 1 tiers. <lb/>33 # 6 # 3 # 1 demie. <lb/>36 # 6 # 5 # 3 quarts. <lb/>40 # 6 # 8 # 1 demie. <lb/>48 # 7 # 1 # 3 quarts. <lb/>50 # 7 # 2 # 3 quarts. <lb/>64 # 7 # 10 # 1 quart. <lb/></note> <pb o="206" file="221" n="221" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> </div> <div xml:id="echoid-div503" type="section" level="1" n="243"> <head xml:id="echoid-head362" style="it" xml:space="preserve">Du Compas à pointes courbes.</head> <p> <s xml:id="echoid-s6511" xml:space="preserve">CE Compas ne differe point pour la conſtruction des autres com-<lb/> <anchor type="note" xlink:label="note-221-01a" xlink:href="note-221-01"/> pas dont nous avons parlé ci-devant, ſinon que l'on démonte <lb/>les pointes des 2 côtez pour en placer de courbes, qui ſervent à <lb/>prendre la groſſeur des boulets & </s> <s xml:id="echoid-s6512" xml:space="preserve">à les rapporter ſur la regle de ca-<lb/>libre, afin d'en connoître le poids. </s> <s xml:id="echoid-s6513" xml:space="preserve">Mais quand on veut connoître <lb/>le calibre des pieces, on démonte les pointes courbes pour y en met-<lb/>tre de droites, avec leſquelles on prend les diametres des bouches <lb/>des canons, & </s> <s xml:id="echoid-s6514" xml:space="preserve">enſuite on les rapporte ſur la ligne du calibre des <lb/>pieces, qui eſt auſſi marquée ſur la regle, & </s> <s xml:id="echoid-s6515" xml:space="preserve">par ce moyen on con-<lb/>noîtra le poids du boulet convenable à la piece de canon.</s> <s xml:id="echoid-s6516" xml:space="preserve"/> </p> <div xml:id="echoid-div503" type="float" level="2" n="1"> <note position="left" xlink:label="note-221-01" xlink:href="note-221-01a" xml:space="preserve">Fig. C.</note> </div> </div> <div xml:id="echoid-div505" type="section" level="1" n="244"> <head xml:id="echoid-head363" style="it" xml:space="preserve">Conſtruction de l' Inſtrument à pointer les Canons & les Mortiers.</head> <p> <s xml:id="echoid-s6517" xml:space="preserve">CEt inſtrument eſt compoſé d'une plaque de cuivre triangulaire <lb/> <anchor type="note" xlink:label="note-221-02a" xlink:href="note-221-02"/> d'environ 4 pouces de hauteur, au bas de laquelle eſt une por-<lb/>tion de cercle, diviſée en 45 deg. </s> <s xml:id="echoid-s6518" xml:space="preserve">ce nombre étant ſuffiſant pour ti-<lb/>rer une piece à toute volée, & </s> <s xml:id="echoid-s6519" xml:space="preserve">donner au boulet la plus longue por-<lb/>tée, comme nous expliquerons ci-après. </s> <s xml:id="echoid-s6520" xml:space="preserve">Il y a une piece de cuivre <lb/>attachée au centre de la portion de cercle avec une vis pour la reſ-<lb/>ſerrer ou lui donner un mouvement libre ſelon les beſoins.</s> <s xml:id="echoid-s6521" xml:space="preserve"/> </p> <div xml:id="echoid-div505" type="float" level="2" n="1"> <note position="left" xlink:label="note-221-02" xlink:href="note-221-02a" xml:space="preserve">Fig. D.</note> </div> <p> <s xml:id="echoid-s6522" xml:space="preserve">Cette piece eſt renforcée par le bas pour ſervir de plomb, elle eſt <lb/>pointuë par le bout, afin de marquer ſur les deg. </s> <s xml:id="echoid-s6523" xml:space="preserve">les differentes ele-<lb/>vations des pieces d'Artillerie. </s> <s xml:id="echoid-s6524" xml:space="preserve">Il y a auſſi une eſpece de pied de cui-<lb/>vre quis'a puie ſur les Mortiers & </s> <s xml:id="echoid-s6525" xml:space="preserve">Canons, en ſorte que tout l'inſtru-<lb/>ment ſe tient perpendiculaire quand la piece eſt placée horiſontale-<lb/>ment.</s> <s xml:id="echoid-s6526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6527" xml:space="preserve">Son uſage eſt fort facile, il n'y a qu'à poſer le pied ſur la piece <lb/>qu'on éleve, de telle ſorte que la pointe du plomb donne ſur le degré <lb/>convenable, & </s> <s xml:id="echoid-s6528" xml:space="preserve">c'eſt ce qu'on nomme pointer une piece.</s> <s xml:id="echoid-s6529" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div507" type="section" level="1" n="245"> <head xml:id="echoid-head364" style="it" xml:space="preserve">Dupied à Niveau pour l' Artillerie.</head> <p> <s xml:id="echoid-s6530" xml:space="preserve">L'Inſtrument marqué E, eſt nommé pied à Niveau. </s> <s xml:id="echoid-s6531" xml:space="preserve">Nous en a-<lb/> <anchor type="note" xlink:label="note-221-03a" xlink:href="note-221-03"/> vons donné la conſtruction en parlant des pieds & </s> <s xml:id="echoid-s6532" xml:space="preserve">des équer-<lb/>res; </s> <s xml:id="echoid-s6533" xml:space="preserve">quand on veut s'en ſervir pour l'artillerie, on diviſe la languete <lb/>qui ſert à le maintenir à angles droits, en 90 d. </s> <s xml:id="echoid-s6534" xml:space="preserve">ou plûtôt en 2 fois <lb/>45, dont le commencement ſe compte du milieu. </s> <s xml:id="echoid-s6535" xml:space="preserve">La ſoie qui porte <lb/>le plombeſt attachée au centre de cette diviſion. </s> <s xml:id="echoid-s6536" xml:space="preserve">Les 2 bouts desre-<lb/>gles de cet inſtrument ſont échancrez, de maniere que le plomb <lb/>tombe perpendiculairement ſur le milieu de la languete, lorſqu'il <lb/>eſt poſe de niveau.</s> <s xml:id="echoid-s6537" xml:space="preserve"/> </p> <div xml:id="echoid-div507" type="float" level="2" n="1"> <note position="left" xlink:label="note-221-03" xlink:href="note-221-03a" xml:space="preserve">Fig. E.</note> </div> <p> <s xml:id="echoid-s6538" xml:space="preserve">Pour s'en ſervir on poſe les deux bouts ſur les pieces d'artillerie, <lb/>que l'on éleve à la hauteur propoſée, par le moyen du plomb dont <lb/>la ſoie marque les degrez.</s> <s xml:id="echoid-s6539" xml:space="preserve"/> </p> <pb o="207" file="222" n="222" rhead="POUR L'AR TIL LERIE. Liv. V. Ch. IV."/> <p> <s xml:id="echoid-s6540" xml:space="preserve">Sur la ſurface des branches de cette Equerre, qui s'ouvre toute droi-<lb/>te comme une regle, on marque les poids & </s> <s xml:id="echoid-s6541" xml:space="preserve">diametres des Boulets, <lb/>auſſi-bien que les Calibres des pieces, comme nous l'avons expliqué <lb/>en parlant de l'Equerre des Canoniers, pour s'en ſervir de même.</s> <s xml:id="echoid-s6542" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6543" xml:space="preserve">L'lnſtrument marqué F, eſt encore pour pointer les Canons & </s> <s xml:id="echoid-s6544" xml:space="preserve">les <lb/> <anchor type="note" xlink:label="note-222-01a" xlink:href="note-222-01"/> Mortiers. </s> <s xml:id="echoid-s6545" xml:space="preserve">Il eſt à peu près ſemblable à celui marqué D, excepté que <lb/>la piece où eſt la diviſion des degrez, eſt mobile par le moyen d'un <lb/>clou rond, c'eſt-à-dire, qu'elle s'ouvre en portion de cercle & </s> <s xml:id="echoid-s6546" xml:space="preserve">s'a-<lb/>juſte au long de l'autre branche, afin que l'inſtrument tienne moins <lb/>de place & </s> <s xml:id="echoid-s6547" xml:space="preserve">ſe mette plus facilement dans un étui. </s> <s xml:id="echoid-s6548" xml:space="preserve">Safigure fait aſſez <lb/>connoître ſa conſtruction, & </s> <s xml:id="echoid-s6549" xml:space="preserve">ſes uſages ſont les mêmes que ceux <lb/>des precedens Inſtrumens.</s> <s xml:id="echoid-s6550" xml:space="preserve"/> </p> <div xml:id="echoid-div508" type="float" level="2" n="2"> <note position="right" xlink:label="note-222-01" xlink:href="note-222-01a" xml:space="preserve">Fig. F.</note> </div> </div> <div xml:id="echoid-div510" type="section" level="1" n="246"> <head xml:id="echoid-head365" style="it" xml:space="preserve">Explication ſur l'effet du Mortier & du Canon.</head> <p> <s xml:id="echoid-s6551" xml:space="preserve">LA figure G repreſente un Mortier ſur ſon affût, élevé & </s> <s xml:id="echoid-s6552" xml:space="preserve">diſpoſé <lb/> <anchor type="note" xlink:label="note-222-02a" xlink:href="note-222-02"/> pour jetter une Bombe dans une Citadelle; </s> <s xml:id="echoid-s6553" xml:space="preserve">& </s> <s xml:id="echoid-s6554" xml:space="preserve">la ligne courbe re-<lb/>preſente la trace que fait en l'air la Bombe depuis la ſortie du Mor-<lb/>tier juſqu'à ſa chûte. </s> <s xml:id="echoid-s6555" xml:space="preserve">Cette courbe eſt ſelon les Géometres, une ligne <lb/>parabolique, parce que les proprietez de la parabole lui conviennent. <lb/></s> <s xml:id="echoid-s6556" xml:space="preserve">Car le mouvement de cette Bombe eſt compoſé de 2 mouvemens, <lb/>dont l'un eſt égal & </s> <s xml:id="echoid-s6557" xml:space="preserve">uniforme, qui lui vient du feu de la poudre, qui <lb/>l'a pouſſée, & </s> <s xml:id="echoid-s6558" xml:space="preserve">l'autre eſt uniformément acceleré, qui lui eſt commu-<lb/>niqué par ſa propre peſanteur. </s> <s xml:id="echoid-s6559" xml:space="preserve">Il naît de la compoſition de ces 2 <lb/>mouvemens la même proportion qui ſe rencontre entre les portions <lb/>de l'axe & </s> <s xml:id="echoid-s6560" xml:space="preserve">les ordonnées de la parabole, comme l'a très-bien dé-<lb/>montré M. </s> <s xml:id="echoid-s6561" xml:space="preserve">Blondel dans ſon Livre intitulé: </s> <s xml:id="echoid-s6562" xml:space="preserve">l'Art de jetter les Bombes.</s> <s xml:id="echoid-s6563" xml:space="preserve"/> </p> <div xml:id="echoid-div510" type="float" level="2" n="1"> <note position="right" xlink:label="note-222-02" xlink:href="note-222-02a" xml:space="preserve">Fig. G.</note> </div> <p> <s xml:id="echoid-s6564" xml:space="preserve">Maltus Ingenieur Anglois a été le premier qui a mis les Bombes <lb/>en uſage en France l'an 1634. </s> <s xml:id="echoid-s6565" xml:space="preserve">Toute ſa ſcience étoit purement d'ex-<lb/>perience; </s> <s xml:id="echoid-s6566" xml:space="preserve">il ne connoiſſoit point la nature de la ligne courbe qu'elles <lb/>décrivent dans l'air par leur paſſage, ni la diſtance de leurs portées, <lb/>ſuivant les differentes élevations du Mortier, qu'il ne pointoit qu'en <lb/>tâtonnant, ou pour mieux dire, par l'eſtime qu'il faiſoit de l'éloigne-<lb/>ment du lieu où il vouloit jetter la Bombe, ſuivant lequel il lui don-<lb/>noit plus ou moins d'élevation, prenant garde ſi les premiers coups <lb/>étoient juſtes ou non, aſin de baiſſer ſon Mortier ſi ſa portée étoit <lb/>trop courte, ou le hauſſer ſi elle alloit au-delà de ſon but, ſe ſervant à <lb/>cet effet d'une Equerre avec ſon plomb à peu près comme celle dont <lb/>nous avons parlé ci-devant.</s> <s xml:id="echoid-s6567" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6568" xml:space="preserve">La plûpart des Officiers qui ont ſervi depuis aux Batteries des <lb/>Bombes, ſont des Eleves de Maltus. </s> <s xml:id="echoid-s6569" xml:space="preserve">Ils ſçavent à peu près par expe-<lb/>rience l'élevation qu'on doit donner au Mortier pour le faire porter <lb/>à la diſtance qu'ils ſouhaitent, & </s> <s xml:id="echoid-s6570" xml:space="preserve">ont ſoin d'augmenter ou de dimi-<lb/> <pb o="208" file="223" n="223" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> nuer cette élevation à proportion que la Bombe ſe trouve plus ou <lb/>moins éloignée ou en deçà ou en delà du but.</s> <s xml:id="echoid-s6571" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6572" xml:space="preserve">Il y a cependant des regles certaines fondécs ſur la Géométrie, <lb/>pour connnoître la differente étenduë des portées, non ſeulement <lb/>des Bombes, mais auſſi du Canon en toutes ſortes d'élevations. </s> <s xml:id="echoid-s6573" xml:space="preserve">Car <lb/>la ligne tracée en l'air par le Boulet ſorti du Canon eſt auſſi parabo-<lb/>lique en toutes ſortes de projections, non ſeulement obliques, mais <lb/>même horiſontales, comme le montre la figure H.</s> <s xml:id="echoid-s6574" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6575" xml:space="preserve">Le boulet au ſortir de la piece ne va jamais droit au but vers le-<lb/>quel elle eſt pointée, mais il ſe détourne de la ligne de direction en <lb/>montant dès le moment qu'il ſort de la bouche, parce que les grains <lb/>de poudre qui ſont les plus proches de la Culaſſe, s'allumans les pre-<lb/> <anchor type="note" xlink:label="note-223-01a" xlink:href="note-223-01"/> miers, pouſl<unsure/>ent par leur mouvement précipité, non ſeulement le bou-<lb/>let, mais même les autres grains de la poudre qui ſuivent le boulet <lb/>au long du fond de l'ame, où s'allumans l'un après l'autre, ils fra-<lb/>pent quaſi tous les boulets vers le deſſous, qui n'étant pas de cali-<lb/>bre, à cauſe du jeu qu'il doit néceſſairement avoir dans la piece, eſt <lb/>élevé inſenſiblement vers le bord ſupérieur de la bouche, contre le-<lb/>quel ils frotent tellement en ſortant, qu'aux pieces qui ont beau-<lb/>coup ſervi, & </s> <s xml:id="echoid-s6576" xml:space="preserve">dont le métal eſt doux, l'on remarque un canal conſi-<lb/>derable que le boulet en ſortant y a creuſé peu à peu par ce frote-<lb/>ment. </s> <s xml:id="echoid-s6577" xml:space="preserve">Ainſi le boulet ſortant du Canon, comme par le point E, s'é-<lb/>leve en s'écartant juſqu'au ſommet de la parabole, comme au point <lb/>G, après quoi il deſcend par un mouvement mixte comme vers B.</s> <s xml:id="echoid-s6578" xml:space="preserve"/> </p> <div xml:id="echoid-div511" type="float" level="2" n="2"> <note position="left" xlink:label="note-223-01" xlink:href="note-223-01a" xml:space="preserve">Fig. H.</note> </div> <p> <s xml:id="echoid-s6579" xml:space="preserve">Les coups tirez à l'élevation du 44 deg. </s> <s xml:id="echoid-s6580" xml:space="preserve">ont les plus longues por-<lb/>tées, & </s> <s xml:id="echoid-s6581" xml:space="preserve">c'eſt ce que les Canoniers appellent tirer à toute volée, & </s> <s xml:id="echoid-s6582" xml:space="preserve">les <lb/>coups tirez ſous l'élevation des points également éloignez de 45 d. <lb/></s> <s xml:id="echoid-s6583" xml:space="preserve">ont des portées égales; </s> <s xml:id="echoid-s6584" xml:space="preserve">c'eſt-à-dire, qu'une piece de Canon ou un <lb/>Mortier pointé au 40<emph style="sub">me</emph> degré, chaſſe juſtement auſſi loin que s'il <lb/>étoit pointé à 50 deg. </s> <s xml:id="echoid-s6585" xml:space="preserve">& </s> <s xml:id="echoid-s6586" xml:space="preserve">au 30 autant qu'au 60, & </s> <s xml:id="echoid-s6587" xml:space="preserve">ainſi des au-<lb/>tres, comme il paroît par la figure I<unsure/>, au bas de la planche 16. </s> <s xml:id="echoid-s6588" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-223-02a" xlink:href="note-223-02"/> </s> </p> <div xml:id="echoid-div512" type="float" level="2" n="3"> <note position="left" xlink:label="note-223-02" xlink:href="note-223-02a" xml:space="preserve">Fig.I.</note> </div> <p> <s xml:id="echoid-s6589" xml:space="preserve">Le premier qui a bien raiſonné ſur cette matiere, eſt Galilée, <lb/>premier & </s> <s xml:id="echoid-s6590" xml:space="preserve">principal Ingenieur du Grand Duc de Toſcane, & </s> <s xml:id="echoid-s6591" xml:space="preserve">après <lb/>lui Toricelli ſon ſucceſſeur.</s> <s xml:id="echoid-s6592" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6593" xml:space="preserve">Ils ont expliqué, que pour connoître les differentes portées des <lb/>coups de volée d'une piece d'Artillerie ou d'un Mortier en toutes <lb/>ſortes d'élevations, il falloit avant toutes choſes en faire une épreu-<lb/>ve bien exacte en tirant la piece de Canon ou le Mortier, ſous un <lb/>angle bien connu, & </s> <s xml:id="echoid-s6594" xml:space="preserve">meſurant l'étenduë de la portée avec toute la <lb/>préciſion poſſible, car d'une ſeule experience ſûre & </s> <s xml:id="echoid-s6595" xml:space="preserve">fidele, on vient <lb/> <pb o="209" file="224" n="224" rhead="POUR L'AR TILLERIE. Liv. V. Ch. IV."/> à la connoiſſance de tous les autres effets par la mét hode ſuivante.</s> <s xml:id="echoid-s6596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6597" xml:space="preserve">Pour ſçavoir l'étenduë de la portée de vôtre piece à telle autre éle-<lb/>vation qu'il vous plaira, faites que comme le Sinus du double de <lb/>l'angle de l'élevation ſous laquelle l'experience a été faite, eſt au Si-<lb/>nus du double de l'angle de l'élévation propoſée, ainſi l'étenduë de <lb/>la portée connuê par l'experience ſoit à une autre.</s> <s xml:id="echoid-s6598" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6599" xml:space="preserve">Comme ſi ayant fait l'experience de vötre piece élevée de 30 deg. <lb/></s> <s xml:id="echoid-s6600" xml:space="preserve">vous avez trouvé qu'elle ait chaſſé préciſément à la longueur de mil-<lb/>le toiſes, pour ſçavoir quelle ſera la portée de la même piece avec la <lb/>même charge, lorfqu'elle ſera élevée à l'angle de 45 deg. </s> <s xml:id="echoid-s6601" xml:space="preserve">il faut <lb/>prendre le Sinus de 60 deg. </s> <s xml:id="echoid-s6602" xml:space="preserve">double de 30, qui eſt 8660, & </s> <s xml:id="echoid-s6603" xml:space="preserve">en faire <lb/>le premier terme d'une regle de 3, dont le ſecond ſera le Sinus de 60 <lb/>deg. </s> <s xml:id="echoid-s6604" xml:space="preserve">double de 45, que l'on propoſe, qui eſt 10000; </s> <s xml:id="echoid-s6605" xml:space="preserve">le troiſiéme <lb/>terme doit être le nombre des meſures de l'experience qui eſt ici mil-<lb/>le toiſes, le quatriéme terme de la regle ſetrouvera 1155 toiſes pour <lb/>la portée de la piece élevée de 35 degrez.</s> <s xml:id="echoid-s6606" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6607" xml:space="preserve">Que ſi l'angle dé l'élevation propoſée eſt plus grand que 45 d. </s> <s xml:id="echoid-s6608" xml:space="preserve">il <lb/>ne faut pas le doubler pour avoir le Sinus que la regle demande; </s> <s xml:id="echoid-s6609" xml:space="preserve">mais <lb/>il faut en ſa place prendre le Sinus du double de ſon complément à <lb/>l'angle droit, comme ſi l'on propoſe l'élevation de la piece à l'angle <lb/>de 50 deg. </s> <s xml:id="echoid-s6610" xml:space="preserve">il faut prendre le Sinus de 80 deg. </s> <s xml:id="echoid-s6611" xml:space="preserve">double de 40, qui <lb/>fait le complément à l'angle droit du propoſé de 50 deg.</s> <s xml:id="echoid-s6612" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6613" xml:space="preserve">Mais ſi l'on vous propoſe une étenduë déterminée à laquelle on <lb/>veut que la piece chaſſe, pourvû que cette étenduë ne ſoit pas plus <lb/>grande que celle de l'élevation de 35 deg. </s> <s xml:id="echoid-s6614" xml:space="preserve">pour trouver l'angle de <lb/>l'élevation qu'il faut donner à la piece pour qu'elle faſſe l'effet pro <lb/>poſé, comme ſi l'on veut que le Canon ou le Mortier porte à la diſ-<lb/>tance de 800 toiſes, ou telle autre meſure qu'il vous plaira, il faut <lb/>que l'étenduë trouvée par l'experience, comme par exemple 1000 t. <lb/></s> <s xml:id="echoid-s6615" xml:space="preserve">ſoit le premier terme de la regle de 3; </s> <s xml:id="echoid-s6616" xml:space="preserve">la portée propoſée de 800 t. </s> <s xml:id="echoid-s6617" xml:space="preserve"><lb/>le 2, & </s> <s xml:id="echoid-s6618" xml:space="preserve">que le 3<emph style="sub">me</emph> terme ſoit 8660 Sinus de 60 deg. </s> <s xml:id="echoid-s6619" xml:space="preserve">double de 30, <lb/>ſuppoſé l'experience. </s> <s xml:id="echoid-s6620" xml:space="preserve">La regle étant faite on trouvera pour 4 <lb/>terme 6928, qui eſt le Sinus de 43 d. </s> <s xml:id="echoid-s6621" xml:space="preserve">52 m. </s> <s xml:id="echoid-s6622" xml:space="preserve">dont la moitié 21 d. </s> <s xml:id="echoid-s6623" xml:space="preserve">56 <lb/>m. </s> <s xml:id="echoid-s6624" xml:space="preserve">eſt l'angle de l'élevation qu'il faut donner à la piece, pour faire <lb/>l'effet propoſé; </s> <s xml:id="echoid-s6625" xml:space="preserve">& </s> <s xml:id="echoid-s6626" xml:space="preserve">ſi vous ôtez le 21 d. </s> <s xml:id="echoid-s6627" xml:space="preserve">56 min. </s> <s xml:id="echoid-s6628" xml:space="preserve">de 90 d. </s> <s xml:id="echoid-s6629" xml:space="preserve">vous aurez <lb/>l'angle de complément 68 d. </s> <s xml:id="echoid-s6630" xml:space="preserve">4 m. </s> <s xml:id="echoid-s6631" xml:space="preserve">que vous pourrez prendre pour <lb/>l'élevation de vôtre piece, car elle chaſſera également loin, l'élevant <lb/>de 21 d. </s> <s xml:id="echoid-s6632" xml:space="preserve">56 m. </s> <s xml:id="echoid-s6633" xml:space="preserve">ou à celui de ſon complément 68 deg. </s> <s xml:id="echoid-s6634" xml:space="preserve">4 min.</s> <s xml:id="echoid-s6635" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6636" xml:space="preserve">Pour plus grande facilité, & </s> <s xml:id="echoid-s6637" xml:space="preserve">pour ôter l'embarras de chercher <lb/>les Sinus du double des angles des élevations propoſées, Galilée & </s> <s xml:id="echoid-s6638" xml:space="preserve"><lb/> <pb o="210" file="225" n="225" rhead="CONSTRUCT. ET USAGES DES INSTRUM. & c."/> Torricelli ont fait la Table ſuivante, dans laquelle on voit tout <lb/>d'un coup les Sinus des angles que l'on cherche.</s> <s xml:id="echoid-s6639" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/> ###### Table des Sinus ſervans au jet des Bombes. <lb/>Degrez. # Degrez. # Portées. # Degrez. # Degrez. # Pottées. <lb/>90 # 0 # 0 # 0 # 0 # 0 <lb/>89 # 1 # 349 # 66 # 24 # 7431 <lb/>88 # 2 # 698 # 65 # 25 # 7660 <lb/>87 # 3 # 1045 # 64 # 26 # 7880 <lb/>86 # 4 # 1392 # 63 # 27 # 8090 <lb/>85 # 5 # 1736 # 62 # 28 # 8290 <lb/>84 # 6 # 1709 # 61 # 29 # 8480 <lb/>83 # 7 # 2419 # 60 # 30 # 8660 <lb/>82 # 8 # 2556 # 59 # 31 # 8829 <lb/>81 # 9 # 3090 # 58 # 32 # 8988 <lb/>80 # 10 # 3420 # 57 # 33 # 9135 <lb/>79 # 11 # 3745 # 56 # 34 # 9272 <lb/>78 # 12 # 4067 # 55 # 35 # 9397 <lb/>77 # 13 # 4384 # 54 # 36 # 9511 <lb/>76 # 14 # 4695 # 53 # 37 # 9613 <lb/>75 # 15 # 5000 # 52 # 38 # 9703 <lb/>74 # 16 # 5299 # 51 # 39 # 9781 <lb/>73 # 17 # 5592 # 50 # 40 # 9848 <lb/>72 # 18 # 5870 # 49 # 41 # 9903 <lb/>71 # 19 # 6157 # 48 # 42 # 9945 <lb/>70 # 20 # 6428 # 47 # 43 # 9976 <lb/>69 # 21 # 6691 # 46 # 44 # 9994 <lb/>68 # 22 # 6947 # 45 # 45 # 10000 <lb/>67 # 23 # 7193 <lb/></note> <p> <s xml:id="echoid-s6640" xml:space="preserve">L'uſage de cette Table eſt facile, il ne faut que ſçavoir faire une <lb/>regle de 3. </s> <s xml:id="echoid-s6641" xml:space="preserve">Suppoſons, par exemple, qu'on ait reconnu par experien-<lb/>ce qu'un Mortier élevé de 15 d. </s> <s xml:id="echoid-s6642" xml:space="preserve">chargé de 3 l. </s> <s xml:id="echoid-s6643" xml:space="preserve">de poudre menuë, ait <lb/>chaſſé une Bombe à 350 t. </s> <s xml:id="echoid-s6644" xml:space="preserve">de diſtance, & </s> <s xml:id="echoid-s6645" xml:space="preserve">que l'on veüille avec la <lb/>même charge jetter une pareille Bombe à 100 t. </s> <s xml:id="echoid-s6646" xml:space="preserve">plusloin cherchez <lb/>dans la Table le nombre qui eſt à côté de 15 d. </s> <s xml:id="echoid-s6647" xml:space="preserve">vous trouverez 5000. <lb/></s> <s xml:id="echoid-s6648" xml:space="preserve">Formez enſuite cette regle de 3, comme 350 ſont à 450, ainſi 5000 <lb/>à un 4<emph style="sub">me</emph> nombre, qui ſe trouvera 6428. </s> <s xml:id="echoid-s6649" xml:space="preserve">Cherchez ce nombre ou <lb/>le plus approchant dans la Table, vous le trouverez à côté de 20 & </s> <s xml:id="echoid-s6650" xml:space="preserve"><lb/>de 70, qui ſigniſie, qu'élevant vôtre Mortier à 20 deg. </s> <s xml:id="echoid-s6651" xml:space="preserve">ou à 70, il <lb/>fera l'effet propoſé, & </s> <s xml:id="echoid-s6652" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s6653" xml:space="preserve"/> </p> <pb file="226" n="226"/> </div> <div xml:id="echoid-div514" type="section" level="1" n="247"> <head xml:id="echoid-head366" xml:space="preserve">DE LA <lb/>CONSTRUCTION <lb/>ET DES USAGES <lb/>DES INSTRUMENS <lb/>QUI SERVENT <lb/>A L'ASTR ON OMIE,</head> <p> <s xml:id="echoid-s6654" xml:space="preserve">Tirez des Tables Aſtronomiques de M. </s> <s xml:id="echoid-s6655" xml:space="preserve">de la Hire, & </s> <s xml:id="echoid-s6656" xml:space="preserve">des <lb/>Obſervations de l'Academie Roïale des Sciences.</s> <s xml:id="echoid-s6657" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div515" type="section" level="1" n="248"> <head xml:id="echoid-head367" style="it" xml:space="preserve">LIVRE SIXIÉME.</head> <head xml:id="echoid-head368" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head369" style="it" xml:space="preserve">De la Conſtruction & des Vſages du Luart de cercle <lb/>Aſtronomique.</head> <p> <s xml:id="echoid-s6658" xml:space="preserve">LE Quart de cercle, dont les Aſtronomes ſe ſervent dans <lb/> <anchor type="note" xlink:label="note-226-01a" xlink:href="note-226-01"/> leurs Obſervations, a pour l'ordinaire 3 pieds ou 3 pieds <lb/>& </s> <s xml:id="echoid-s6659" xml:space="preserve">demi de raïon meſure de Paris, pour qu'il puiſſe être <lb/>facilement manié & </s> <s xml:id="echoid-s6660" xml:space="preserve">tranſporté; </s> <s xml:id="echoid-s6661" xml:space="preserve">ſon bord eſt diviſé en <lb/>degrez & </s> <s xml:id="echoid-s6662" xml:space="preserve">minutes, aſin que les obſervations ſe puiſſent faire avec <lb/>exactitude.</s> <s xml:id="echoid-s6663" xml:space="preserve"/> </p> <div xml:id="echoid-div515" type="float" level="2" n="1"> <note position="right" xlink:label="note-226-01" xlink:href="note-226-01a" xml:space="preserve">XVII. <lb/>planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s6664" xml:space="preserve">Cet inſtrument eſt compoſé de pluſieurs regles de cuivre ou de fer <lb/>bien écroüi au marteau & </s> <s xml:id="echoid-s6665" xml:space="preserve">de mediocre épaiſſeur, dont la largeur <lb/>doit être parallele à ſon plan. </s> <s xml:id="echoid-s6666" xml:space="preserve">Il y a de plus d'autres regles de fer ou <lb/>de cuivre tellement ajuſtées & </s> <s xml:id="echoid-s6667" xml:space="preserve">jointes derriere les premieres, que <lb/>leur largeur ſoit perpendiculaire au plan du quart de cercle. </s> <s xml:id="echoid-s6668" xml:space="preserve">Ces re-<lb/>gles ſont jointes enſemble par de petites oreilles & </s> <s xml:id="echoid-s6669" xml:space="preserve">des vis, par le <lb/> <pb o="212" file="227" n="227" rhead="CONSTRUCT. ET USAGES DU QUART, & c."/> moyen deſquelles ſe fait tout l'aſſemblage de cet Inſtrument qui <lb/>doit être bien droit en tout ſens, ferme & </s> <s xml:id="echoid-s6670" xml:space="preserve">de mediocre peſanteur. </s> <s xml:id="echoid-s6671" xml:space="preserve">Le <lb/>derriere du bord doit être renforcé d'une regle courbe, auſſi de mê-<lb/>me métal. </s> <s xml:id="echoid-s6672" xml:space="preserve">On ajoûte au centre une lame circulaire épaiſſe & </s> <s xml:id="echoid-s6673" xml:space="preserve">ſoli-<lb/>de, pour ſervir aux uſages que nous expoſerons ci-après. </s> <s xml:id="echoid-s6674" xml:space="preserve">Le bord & </s> <s xml:id="echoid-s6675" xml:space="preserve"><lb/>la lame du centre ſont un peu élevez au-deſſus du plan de l'inſtru-<lb/>ment & </s> <s xml:id="echoid-s6676" xml:space="preserve">ſont recouverts de lames de cuivre bien polies. </s> <s xml:id="echoid-s6677" xml:space="preserve">Sur toutes <lb/>choſes il faut avoir grand ſoin en cette conſtruction que la lame du <lb/>centre & </s> <s xml:id="echoid-s6678" xml:space="preserve">le bord circulaire ſoient exactement en une même ſurface <lb/>plane.</s> <s xml:id="echoid-s6679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6680" xml:space="preserve">La lame de fer circulaire qui eſt au centre & </s> <s xml:id="echoid-s6681" xml:space="preserve">qui eſt recouverte <lb/>d'une autre de cuivre, doit avoir en ſon milieu un trou rond, dont <lb/>le diametre ſoit en viron d'un tiers de pouce.</s> <s xml:id="echoid-s6682" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6683" xml:space="preserve">Dans ce trou on met un Cylindre de cuivre bien tourné, lequel <lb/>s'éleve tant ſoit peu au-deſſus de ladite lame centrale.</s> <s xml:id="echoid-s6684" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6685" xml:space="preserve">Ce Cylindre eſt repreſenté en la figure 2; </s> <s xml:id="echoid-s6686" xml:space="preserve">au centre de la baſe du-<lb/> <anchor type="note" xlink:label="note-227-01a" xlink:href="note-227-01"/> dit Cylindre on ajuſte la pointe d'une éguille très-deliée, dont la <lb/>longueur eſt inſerée dans un petit canal demi-circulaire, & </s> <s xml:id="echoid-s6687" xml:space="preserve">y <lb/>eſt retenuë par le moyen d'un petit reſſort, qui la preſſant la tient le <lb/>long de ce canal, afin que quand on ôtera l'éguille & </s> <s xml:id="echoid-s6688" xml:space="preserve">qu'on vou-<lb/>dra la reméttre, elle ſe place juſte dans le petit trou qui eſt au centre <lb/>dudit Cylindre; </s> <s xml:id="echoid-s6689" xml:space="preserve">ce trou ne doit être que de la groſſeur d'uu cheveu, <lb/>mais il doit être un peu proſond, afin que la pointe de l'éguille en-<lb/>tre aſſez, pour qu'elle ne s'échape pas par les ſecouſſes qu'on pourra <lb/>donner au quart de cercle: </s> <s xml:id="echoid-s6690" xml:space="preserve">à la pointe de l'éguille eſt ſuſpendu un <lb/>cheveu, par le moyen d'un anneau fait du cheveu même, aſſez am-<lb/>ple, de crainte que le nœud de l'anneau ne rencontre la lame du <lb/>centre, & </s> <s xml:id="echoid-s6691" xml:space="preserve">que ſon mouvement n'en ſoit détourné. </s> <s xml:id="echoid-s6692" xml:space="preserve">Il faut remar-<lb/>quer que la baſe du Cylindre central A, repreſenté en cette figure, <lb/>doit être un peu convexe, afin qne l'anneau du cheveu ſuſpendu <lb/>à la pointe de l'éguille ne joigne point ladite baſe ailleurs qu'en <lb/>ſon centre, ayant attaché au bout du cheveu un poids de plomb <lb/>d'environ demie once.</s> <s xml:id="echoid-s6693" xml:space="preserve"/> </p> <div xml:id="echoid-div516" type="float" level="2" n="2"> <note position="left" xlink:label="note-227-01" xlink:href="note-227-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s6694" xml:space="preserve">La conſtruction de ce Cylindre central doit être de telle maniere <lb/>que l on puiſſe l'ôter & </s> <s xml:id="echoid-s6695" xml:space="preserve">le conſerver quand il ſera beſoin, pour met-<lb/>tre en ſa place un autre Cylindre central de même groſſeur, mais un <lb/>peu plus long, lequel ſurpaſſant la lame du centre ſoûtienne la regle <lb/>de l'inſtrument, telle que nous la décrirons ci-après.</s> <s xml:id="echoid-s6696" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6697" xml:space="preserve">On ajoûte de plus à la lame centrale de cuivre qui eſt ſur celle <lb/>de fer un anneau plan A, tournant autour du centre, lequel ne ren-<lb/> <pb o="213" file="228" n="228" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> contre pourtant pas le Cylindre central; </s> <s xml:id="echoid-s6698" xml:space="preserve">de telle ſorte que la ſurface <lb/>extérieure ne ſurpaſſe point la ſurſace de ladite lame de cuivre. </s> <s xml:id="echoid-s6699" xml:space="preserve">On <lb/>attache à cet anneau, par le moyen de deux vis, un tuïau applati <lb/>tout le long de la partie qui joint le plan de l'inſtrument, auquel il <lb/>s'ajuſte de telle ſorte, que ſon côté applati étant plus enſoncé que le <lb/>plan du bord & </s> <s xml:id="echoid-s6700" xml:space="preserve">de la lame centrale de cuivre, le mouvement du fil <lb/>avec ſon plomb pendant du centre, ſoit toûjours libre & </s> <s xml:id="echoid-s6701" xml:space="preserve">ſe puiſſe <lb/>mouvoir de toutes parts avec ledit tuïau qui ſert pour le garantir <lb/>de toute agitation de l'air.</s> <s xml:id="echoid-s6702" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6703" xml:space="preserve">On voit cette piece par derriere à l'endroit marqué M. </s> <s xml:id="echoid-s6704" xml:space="preserve">de la figu-<lb/> <anchor type="note" xlink:label="note-228-01a" xlink:href="note-228-01"/> re 3, On met auſſi une glace à ladite piece, vis-à-vis du limbe du <lb/>Quart de cercle, afin de voir ſur quel point de diviſion paſſe le che-<lb/>veu où eſt attaché le plomb. </s> <s xml:id="echoid-s6705" xml:space="preserve">Au-deſſous & </s> <s xml:id="echoid-s6706" xml:space="preserve">aux environs du centre <lb/>de gravité de toute cette machine, on attache ſermement aux re-<lb/>gles, par le moyen de 3 ou 4 vis un Cylindre de fer marqué I<unsure/>, au <lb/>derriere de l'inſtrument, que la figure repreſente tout monté.</s> <s xml:id="echoid-s6707" xml:space="preserve"/> </p> <div xml:id="echoid-div517" type="float" level="2" n="3"> <note position="right" xlink:label="note-228-01" xlink:href="note-228-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s6708" xml:space="preserve">La longueur de ce Cylindre doit être de 8 pouces, & </s> <s xml:id="echoid-s6709" xml:space="preserve">le diametre <lb/>de ſa baſe d'environ 2 pouces Ce Cylindre étant perpendiculaire <lb/>au plan du quart de cercle, ſe peut appeller ſon Axe.</s> <s xml:id="echoid-s6710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6711" xml:space="preserve">Or comme le principal uſage de cet Inſtrument eſt pour prendre <lb/>les hauteurs des Aſtres, il faut que ſon plan ſe puiſſe facilement pla-<lb/>cer dans une ſituation verticale; </s> <s xml:id="echoid-s6712" xml:space="preserve">c'eſt pourquoi on prepare une regle <lb/>de fer, comme MN, dont l'épaiſſeur ſoit de 3 lignes, la longueur de <lb/>8 pouces & </s> <s xml:id="echoid-s6713" xml:space="preserve">la largeur d'un pouce ou environ. </s> <s xml:id="echoid-s6714" xml:space="preserve">D'un côté de cette re-<lb/>gle, on ajuſte 2 anneaux de fer marquez Z, ouverts par en haut a-<lb/> <anchor type="note" xlink:label="note-228-02a" xlink:href="note-228-02"/> vec des oreilles, dans leſquelles on paſſe à chacune une vis propre à <lb/>reſſerrer les anneaux qui par ce moyen font reſſort. </s> <s xml:id="echoid-s6715" xml:space="preserve">La grandeur de <lb/>ces anneaux eſt à peu près égale à la groſſeur du Cylindre I, ou de <lb/>l'axe du quart de cercle, & </s> <s xml:id="echoid-s6716" xml:space="preserve">ces anneaux ayant joint l'axe ſe reſſer-<lb/>rent par le moyen des vis, de telle ſorte que l'axe & </s> <s xml:id="echoid-s6717" xml:space="preserve">le quart de cer-<lb/>cle qui y eſt attaché, demeure ferme & </s> <s xml:id="echoid-s6718" xml:space="preserve">immobile en quelque ſitua-<lb/>tion qu'on le mette.</s> <s xml:id="echoid-s6719" xml:space="preserve"/> </p> <div xml:id="echoid-div518" type="float" level="2" n="4"> <note position="right" xlink:label="note-228-02" xlink:href="note-228-02a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s6720" xml:space="preserve">De l'autre côté de ladite regle MN eſt ſoudé & </s> <s xml:id="echoid-s6721" xml:space="preserve">attaché à angles <lb/>droits le Cylindre de fer O, dont la longueur & </s> <s xml:id="echoid-s6722" xml:space="preserve">la groſſeur ſont éga-<lb/>les au tuîau marqué Q, dont nous allons parler.</s> <s xml:id="echoid-s6723" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6724" xml:space="preserve">Cette partie ſe nomme le genoüil de l'inſtrument. </s> <s xml:id="echoid-s6725" xml:space="preserve">Ce genoüil eſt <lb/>repreſenté tout monté en la figure 3.</s> <s xml:id="echoid-s6726" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6727" xml:space="preserve">Lorſque l'on veut placer l'inſtrument de maniere que ſon plan <lb/>ſoit horiſontal, pour ſe ſervir de la regle mobile, dont nous parle-<lb/>rons ci-après, pour prendre les diſtances des Aſtres ou des lieux de la <lb/> <pb o="214" file="229" n="229" rhead="CONSTRUCT. ET USAGES DU QUART, & c."/> terre, on fait entrer le Cylindre I dans le tuïau Q, & </s> <s xml:id="echoid-s6728" xml:space="preserve">par ce moyen <lb/>on tourne facilement le plan du quart de cercle vers telle partie que <lb/>l'on veut. </s> <s xml:id="echoid-s6729" xml:space="preserve">Cela ſe peut faire auſſi par le moyen d'un double genoüil, <lb/>pareil à celui que nous venons de décrire, que l'on joint enſemble.</s> <s xml:id="echoid-s6730" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6731" xml:space="preserve">Il nous reſte à marquer la conſtruction du pied ou ſupport de tout <lb/>l'inſtrument. </s> <s xml:id="echoid-s6732" xml:space="preserve">Il eſt compoſé pour l'ordinaire d'un tuïau de fer, dont <lb/>la partie ſupérieure ſoit capable de contenir le genoüil ou Cylindre <lb/>O. </s> <s xml:id="echoid-s6733" xml:space="preserve">La partie in férieure de ce tuïau traverſe le milieu d'une croix de <lb/>fer, & </s> <s xml:id="echoid-s6734" xml:space="preserve">y eſt attachée par 4 bras ou liens de fer; </s> <s xml:id="echoid-s6735" xml:space="preserve">il y a 4 groſſes vis <lb/>aux 4 bouts de la croix pour hauſſer ou baiſſer le quart de cercle, & </s> <s xml:id="echoid-s6736" xml:space="preserve"><lb/>le mettre dans la ſituation convenable. </s> <s xml:id="echoid-s6737" xml:space="preserve">M.</s> <s xml:id="echoid-s6738" xml:space="preserve">de la Hire propoſe un pied <lb/>triangulaire dans ſes Tables, dont nousallons donner la deſcription.</s> <s xml:id="echoid-s6739" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6740" xml:space="preserve">Il eſt compoſé d'un tuïau de fer ou de cuivre, aſſez ample & </s> <s xml:id="echoid-s6741" xml:space="preserve"><lb/>aſſez long pour contenir le Gylindre O. </s> <s xml:id="echoid-s6742" xml:space="preserve">Ledit tuïau eſt attaché <lb/> <anchor type="note" xlink:label="note-229-01a" xlink:href="note-229-01"/> avec 2 vis à 3 regles de fer courbées par le haut, leſquelles ſont de <lb/>l'épaiſſeur convenable pour affermir le pied ou ſupport de l'Inſtru-<lb/>ment. </s> <s xml:id="echoid-s6743" xml:space="preserve">Les regles R, S, ſon ajuſtées vers le bas à une double Equerre <lb/>TXY, & </s> <s xml:id="echoid-s6744" xml:space="preserve">attachées fermement aux 3 regles en deſſous par le moyen <lb/>d'une clavete. </s> <s xml:id="echoid-s6745" xml:space="preserve">La vis V, qui penetre le milieu du tuïau Q, ſert pour <lb/>affermir le Cylindre O, comme on le veut.</s> <s xml:id="echoid-s6746" xml:space="preserve"/> </p> <div xml:id="echoid-div519" type="float" level="2" n="5"> <note position="left" xlink:label="note-229-01" xlink:href="note-229-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s6747" xml:space="preserve">Lorſque l'on obſerve les hauteurs méridiennes des Aſtres, la re-<lb/>gle TY doit être placée dans la ligne méridienne, & </s> <s xml:id="echoid-s6748" xml:space="preserve">des 3 vis TXY, <lb/>qui ſoûtiennent le poids de tout l'Inſtrument, celle qui eſt en X, ſert <lb/>à baiſſer le plan de l'inſtrument juſqu'a ce qu'il convienne avec le <lb/>plan du méridien, à la commodité de l'obſervateur qui eſt aſſis vers <lb/>X, & </s> <s xml:id="echoid-s6749" xml:space="preserve">les deux autres ſervent a le hauſſer ou baîſſer peu à peu, juſ-<lb/>qu'à ce que le fil du plomb marque la hauteur requiſe. </s> <s xml:id="echoid-s6750" xml:space="preserve">Mais il ar-<lb/>rive ſouvent qu'en tournant les vis qui ſont en T & </s> <s xml:id="echoid-s6751" xml:space="preserve">en Y, le Quart <lb/>de cercle ſe détourne de ſa veritable poſition; </s> <s xml:id="echoid-s6752" xml:space="preserve">c'eſt pourquoi ſi le dé-<lb/>faut eſt de quelques minutes, on y peut remedier en ſuſpendant au <lb/>derriere des branches de l'inſtrument un poids mobile, lequel fai-<lb/>ſant changer le centre de gravité, fera auſſi changer l'inclinaiſon <lb/>du quart de cercle, car les regles qui compoſent le pied ne ſont pas <lb/>entierement exemptes du reſſort. </s> <s xml:id="echoid-s6753" xml:space="preserve">Or plus le lieu de ſuſpenſion du <lb/>poids ſera proche du pied, moins il aura de force pour faire pancher <lb/>l'Inſtrument.</s> <s xml:id="echoid-s6754" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6755" xml:space="preserve">La hauteur du pied eſt ordinairement de 4 pieds & </s> <s xml:id="echoid-s6756" xml:space="preserve">demi ou en-<lb/>viron, le même uſage ſe fait également avec le pied à 4 branches.</s> <s xml:id="echoid-s6757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6758" xml:space="preserve">La diviſion du quart de cercle doit être faite avec grand ſoin, afin <lb/>que les obſervations ſe puiſſent faire exactement. </s> <s xml:id="echoid-s6759" xml:space="preserve">Chaque degré de <lb/> <pb o="215" file="230" n="230" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> la diviſion du bord ſe diviſe en 60 minutes, par le moyen d'onze <lb/>cercles concentriques, & </s> <s xml:id="echoid-s6760" xml:space="preserve">de 6 lignes droites tranſverſales, comme <lb/>la figure 6 le marque. </s> <s xml:id="echoid-s6761" xml:space="preserve">Les diſtances tranſverſales ſon égales entr'-<lb/> <anchor type="note" xlink:label="note-230-01a" xlink:href="note-230-01"/> elles, mais celles des cercles ſont inégales. </s> <s xml:id="echoid-s6762" xml:space="preserve">Néanmoins cette iné-<lb/>galité n'eſt preſque pas ſenſible ſi nous ſuppoſons le raïon du quart <lb/>de cercle de 3 pieds, & </s> <s xml:id="echoid-s6763" xml:space="preserve">la diſtance entre les 2 cercles extérieurs, d'un <lb/>pouce. </s> <s xml:id="echoid-s6764" xml:space="preserve">Car ſi nous prenons l'arc AE du cercle extérieur de 10 m. </s> <s xml:id="echoid-s6765" xml:space="preserve">& </s> <s xml:id="echoid-s6766" xml:space="preserve"><lb/>que l'on tire au centre C du quart de cercle les raïons ADC, EBC, <lb/>leſquels rencontrent le cercle intérieur aux points D & </s> <s xml:id="echoid-s6767" xml:space="preserve">B, l'arc DB <lb/>ſera auſſi de 10 minutes: </s> <s xml:id="echoid-s6768" xml:space="preserve">(l'on ſuppoſe ici que la figure 6 eſt po-<lb/>ſée ſur le Limbe de l'inſtrument, figure 1.)</s> <s xml:id="echoid-s6769" xml:space="preserve"/> </p> <div xml:id="echoid-div520" type="float" level="2" n="6"> <note position="right" xlink:label="note-230-01" xlink:href="note-230-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s6770" xml:space="preserve">Mais ſi on tire les droites tranſverſales AB, LE, leſquelles s'entre-<lb/>coupent au point F, je dis que F eſt le point milieu de la diviſion par <lb/>lequel doit paſſer le cercle du milieu, car il y a même raiſon de l'arc <lb/>AE, à l'arc BD, que l'on peut confiderer comme lignes droites, que <lb/>de AF à FB. </s> <s xml:id="echoid-s6771" xml:space="preserve">Or le raïon qui partant du centre C diviſe en 2 par-<lb/>ties égales l'angle au centre, compris par les raïons CDA, CBE, <lb/>rencontrera la tranſverſale AB au même point F: </s> <s xml:id="echoid-s6772" xml:space="preserve">car il eſt évident <lb/>que CA eſt à CB, comme les diviſions de la baſe AB du triangle <lb/>rectiligne ACB; </s> <s xml:id="echoid-s6773" xml:space="preserve">mais comme CA eſt à C B, ainſi AE eſt à D B, <lb/>c'eſt pourquoi AE eſt à DB, comme les diviſions de la baſe AB, <lb/>faites par le raïon qui diviſe en 2 l'angle ACB, & </s> <s xml:id="echoid-s6774" xml:space="preserve">par couſequent <lb/>le point F ci-devant trouvé dans la droite tranſverſale AB, ſera le <lb/>poins milieu de la diviſion.</s> <s xml:id="echoid-s6775" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6776" xml:space="preserve">Or nous avons ſuppoſé que AC eſt à CB, comme 36 pouces ſont <lb/>a 34; </s> <s xml:id="echoid-s6777" xml:space="preserve">donc AB eſt à AF, comme 71 à 36. </s> <s xml:id="echoid-s6778" xml:space="preserve">C'eſt pourquoi ſi la lar-<lb/>geur d'un pouce ou de 12 lignes, qui eſt la meſure ſuppoſée de AB, <lb/>eſt diviſée en 71 parties égales, la partie AF en aura 36, laquelle ſe-<lb/>ra plus grande d'un demi ou d'environ un douziéme de ligne, que <lb/>la moitié de AB, qui n'eſt que 35 & </s> <s xml:id="echoid-s6779" xml:space="preserve">demi. </s> <s xml:id="echoid-s6780" xml:space="preserve">Cette difference n'eſt <lb/>d'aucune conſequence, & </s> <s xml:id="echoid-s6781" xml:space="preserve">peut ſans aucune erreur ſenſible, ſe ne-<lb/>gliger dans la diviſion du milieu, & </s> <s xml:id="echoid-s6782" xml:space="preserve">à plus forte raiſon dans les <lb/>autres, où elle eſt moindre.</s> <s xml:id="echoid-s6783" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6784" xml:space="preserve">On peut, au lieu de faire les tranſverſales en ligne droites, les <lb/>faire en portion d'un cercle qui paſſeroit par le centre de l'Inſtru-<lb/>ment, & </s> <s xml:id="echoid-s6785" xml:space="preserve">par le le premier point & </s> <s xml:id="echoid-s6786" xml:space="preserve">le dernier de la même tranſver-<lb/>fale; </s> <s xml:id="echoid-s6787" xml:space="preserve">alors il n'y auroit qu'à diviſer cette portion de circonference <lb/>circulaire en 10 parties égales, & </s> <s xml:id="echoid-s6788" xml:space="preserve">l'on auroit les points exacts par <lb/>où doivent paſſer les onze cercles concentriques.</s> <s xml:id="echoid-s6789" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6790" xml:space="preserve">Il eſt facile de calculer le raïon de ce cercle, & </s> <s xml:id="echoid-s6791" xml:space="preserve">de donner cette fi-<lb/> <pb o="216" file="231" n="231" rhead="CONSTRUCT. ET USAGES DU QUART, & c."/> gure à la regle qui ſervira à diviſer l'inſtrument, comme nous avons <lb/>dit ci-devant, en parlant de la diviſion des cercles & </s> <s xml:id="echoid-s6792" xml:space="preserve">demi-cer-<lb/>cles, & </s> <s xml:id="echoid-s6793" xml:space="preserve">c.</s> <s xml:id="echoid-s6794" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6795" xml:space="preserve">Il ſera bon de laiſſer au bas du Limbe, au-deſſous des diviſions, <lb/>les points qui auront ſervi à faire la diviſion de 10 en 10 min. </s> <s xml:id="echoid-s6796" xml:space="preserve">car <lb/>cela donnera moyen de reprendre les hauteurs correſpondantes du <lb/>Soleil le matin & </s> <s xml:id="echoid-s6797" xml:space="preserve">le ſoir, avec beaucoup plus de préciſion qu'on ne <lb/>peut faire en ſe ſervant des tranſverſales, à cauſe de l'eſtime que <lb/>l'on évite par là, outre qu'il peut y avoir quelque erreur dans les <lb/>tranſverſales, qui ne ſera pas dans les points; </s> <s xml:id="echoid-s6798" xml:space="preserve">car il eſt aſſez diffici-<lb/>le de faire paſſer des lignes toûjours préciſément par où l'on vent, <lb/>& </s> <s xml:id="echoid-s6799" xml:space="preserve">il eſt rare que les diviſions répondent toûjours exactement <lb/>au milieu du point par lequel on avoit eu intention de les faire paſ-<lb/>ſer; </s> <s xml:id="echoid-s6800" xml:space="preserve">& </s> <s xml:id="echoid-s6801" xml:space="preserve">ſi l'on joignoit au quart de cercle un Micrometre attaché a <lb/>la lunete ſixe de l'Inſtrument, on pourroit ſe paſſer des diviſions <lb/>par tranſverſales, & </s> <s xml:id="echoid-s6802" xml:space="preserve">les points ſuffiroient, puiſque le Micrometre <lb/>donneroit, par le moyen d'un fil mobile, l'intervale qu'il y auroit <lb/>depuis le point le plus proche juſqu'à l'endroit où ſe trouveroit le <lb/>fil, ſans qu'on fût ſujet à l'eſtime, toûjours incertaine, à cauſe <lb/>qu'on n'eſt pas toûjours ſûr de l'endroit que coupe préciſément le <lb/>cheveu ſur la tranſverſale comme ſur le point; </s> <s xml:id="echoid-s6803" xml:space="preserve">il ſuffiroit pour cela <lb/>que le filet mobile pût hauſſer ou baiſſer au-deſſus & </s> <s xml:id="echoid-s6804" xml:space="preserve">au-deſſous du <lb/>filet horiſontal fixe de 10 minutes de degrez, ou un peu plus.</s> <s xml:id="echoid-s6805" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6806" xml:space="preserve">M. </s> <s xml:id="echoid-s6807" xml:space="preserve">le Chevalier De Louville, de l'Academie des Sciences, ſe <lb/>ſert avec ſatisfaction, pour ſes Obſervations, d'un Quart de cercle <lb/>conſtruit de cette façon.</s> <s xml:id="echoid-s6808" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6809" xml:space="preserve">Il nous faut maintenant parler de lunetes de longue vûë, & </s> <s xml:id="echoid-s6810" xml:space="preserve">par <lb/>quel moyen on peut trouver le premier point de la diviſion du bord. <lb/></s> <s xml:id="echoid-s6811" xml:space="preserve">Je ne crois pas qu'on ait jamais rien inventé de plus induſtrieux & </s> <s xml:id="echoid-s6812" xml:space="preserve"><lb/>de plus utile en toute l'Aſtronomie pratique; </s> <s xml:id="echoid-s6813" xml:space="preserve">ceux qui ont la vûë <lb/>baſſe, & </s> <s xml:id="echoid-s6814" xml:space="preserve">les vieillards qui ne peuvent diſtinguer les objets qu'à cer-<lb/>taine diſtance, peuvent par le ſecours des lunetes & </s> <s xml:id="echoid-s6815" xml:space="preserve">des fils de ſoie <lb/>trés-déliez, voir auſſi diſtinctement les objets éloignez, que ceux <lb/>qui ont la vûë très-fine; </s> <s xml:id="echoid-s6816" xml:space="preserve">ils peuvent auſſi contempler les Aſtres, <lb/>comme s'ils étoient proches & </s> <s xml:id="echoid-s6817" xml:space="preserve">tres grands, & </s> <s xml:id="echoid-s6818" xml:space="preserve">déſigner leurs vrais <lb/>lieux. </s> <s xml:id="echoid-s6819" xml:space="preserve">Ces lunetes ontdeux verres, dont l'un eſt l'objectif poſé vers <lb/>l'objet viſible & </s> <s xml:id="echoid-s6820" xml:space="preserve">proche le centre du quart de cercle; </s> <s xml:id="echoid-s6821" xml:space="preserve">l'autre eſt <lb/>l'oculaire, lequel doit être placé à l'autre bout de la lunete, vers <lb/>l'œil de l'Obſervateur.</s> <s xml:id="echoid-s6822" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6823" xml:space="preserve">L'objectif eſt unelentille de verre immobile, fermement attachée <lb/> <pb o="217" file="232" n="232" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> dansun cadre de fer, lequel eſt arrêté avec desvis autour du centre <lb/>de l'inſtrument. </s> <s xml:id="echoid-s6824" xml:space="preserve">Du côté de l'oculaire on met deux fils de ſoie ſe ren-<lb/>contrans à angles droits, dans un cadre de fer, auquel on les atta-<lb/>che avec de la cire ſur une petite piece de cuivre, de telle ſorte que <lb/>l'un ſoit perpendiculaire au plan de l'inſtrument, & </s> <s xml:id="echoid-s6825" xml:space="preserve">que l'autre <lb/>lui ſoit parallele.</s> <s xml:id="echoid-s6826" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6827" xml:space="preserve">Le verre oculaire doit être mis dans un tuïau pour pouvoir l'a-<lb/>vancer ou reculer ſuivant les differentes vuës; </s> <s xml:id="echoid-s6828" xml:space="preserve">la diſtance entre la <lb/>lentille objective & </s> <s xml:id="echoid-s6829" xml:space="preserve">les fils de ſoie, doit, autant que faire ſe peut, être <lb/>bien égale à la longueur du foyer de ladite lentille. </s> <s xml:id="echoid-s6830" xml:space="preserve">Ces lunetes doi-<lb/>vent être diſpoſées de telle ſorte que la ſurſace de la lentille de verre <lb/>comme plane, & </s> <s xml:id="echoid-s6831" xml:space="preserve">le plan dans lequel ſont les fils de ſoie ſoient pa-<lb/>ralleles & </s> <s xml:id="echoid-s6832" xml:space="preserve">équidiſtans entr'eux & </s> <s xml:id="echoid-s6833" xml:space="preserve">perpendiculaires à la ligne droi-<lb/>te, conduite par le centre de la lentille & </s> <s xml:id="echoid-s6834" xml:space="preserve">par le point où ſe croiſent <lb/>les fils. </s> <s xml:id="echoid-s6835" xml:space="preserve">Ceslunetes s'ajuſtent derriere l'inſtrument, afin que le bord <lb/>de cuivre diviſé n'en ſoit aucunement embarraſſé.</s> <s xml:id="echoid-s6836" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6837" xml:space="preserve">Entre les cadres qui ſoûtiennent les lunetes, on met un tuïau <lb/>de cuivre ou de fer, compoſé de deux parties, dont l'une s'enchâſſe <lb/>dans l'autre, afin que l'on puiſſe facilement l'ôter des cadres par le <lb/>moyen des viroles qui les tiennent enſemble.</s> <s xml:id="echoid-s6838" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6839" xml:space="preserve">La lentille convexe oculaire doit s'approcher des fils de ſoie ou <lb/>s'en reculer, ſelon la diverſe conſtitution de l'œil de l'Obſervateur, <lb/>afin qu'il puiſſe voir diſtinctement l'objet éloigné & </s> <s xml:id="echoid-s6840" xml:space="preserve">les fils de ſoie.</s> <s xml:id="echoid-s6841" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6842" xml:space="preserve">Ce Verre oculaire ſe place dans un petit tuïau mobile, dont la <lb/>plus grande partie eſt cachée dans un autre tuïau, comme on le <lb/>voit par la figure 7.</s> <s xml:id="echoid-s6843" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6844" xml:space="preserve">Toutes les fois que l'on veut nettoïer le dedans de la lentille ob-<lb/>jective ou remettre des fils de ſoie à la place de ceux qui ſe rompent, <lb/>on détache de ces cadres le tuiau compoſé de lames de cuivre.</s> <s xml:id="echoid-s6845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6846" xml:space="preserve">Mais la conſtruction de la lunete oculaire ſera bien plus commo-<lb/> <anchor type="note" xlink:label="note-232-01a" xlink:href="note-232-01"/> de ſi au lieu d'un cadre ſimple on ſe ſert d'une petite boëte quarrée, <lb/>épaiſſe d'environ 4 lignes, dont les 2 côtez oppoſez qui ſont paral-<lb/>Jeles au bord du quart de cercle ayent une renure ſelon leur lon-<lb/>gueur, dans laquelle ſe puiſſe mouvoir une petite platine de medio-<lb/>cre épaiſſeur, percée par le milieu d'une ouverture ronde aſſez <lb/>grande.</s> <s xml:id="echoid-s6847" xml:space="preserve"/> </p> <div xml:id="echoid-div521" type="float" level="2" n="7"> <note position="right" xlink:label="note-232-01" xlink:href="note-232-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s6848" xml:space="preserve">Sur la ſurſace de cette platine repreſentée par la figure a, on tra-<lb/>cera de part & </s> <s xml:id="echoid-s6849" xml:space="preserve">d'autre les deux diametres de ladite ouverture, dont <lb/>l'un eſt parallele au bord, & </s> <s xml:id="echoid-s6850" xml:space="preserve">l'autre lui eſt perpendiculaire, afin d'y <lb/>pouvoir appliquer les fils de ſoie & </s> <s xml:id="echoid-s6851" xml:space="preserve">les bien remettre en leur place <lb/> <pb o="218" file="233" n="233" rhead="CONSTRUCT. ET USAGES DU QUART, & c."/> toutes les fois qu'on les renouvelle. </s> <s xml:id="echoid-s6852" xml:space="preserve">Cette platine eſt fort utile pour <lb/>approcher ou reculer les fils de ſoie autant qu'il eſt beſoin; </s> <s xml:id="echoid-s6853" xml:space="preserve">& </s> <s xml:id="echoid-s6854" xml:space="preserve">quand <lb/>ils ſeront bien placez on ſera tenir avec de la cire ladite platine à la <lb/>petite boëte, laquelle doit être garnie de ſon couvercle a couliſſe, <lb/>pour garantir les fils de ſoie de l'injure du tems & </s> <s xml:id="echoid-s6855" xml:space="preserve">de tout autre <lb/>accident.</s> <s xml:id="echoid-s6856" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6857" xml:space="preserve">Le dedans du tuïau doit être noirci avec de la ſumée de réſine, <lb/>afin de garantir l'œil des raîons trop forts qui partent de l'objet lu-<lb/>mineux, & </s> <s xml:id="echoid-s6858" xml:space="preserve">que par ce moyen la viſion en ſoit plus parfaite. </s> <s xml:id="echoid-s6859" xml:space="preserve">La figu-<lb/>re 7<emph style="super">me</emph> fait voir auſſi la conſtruction de la boëte ou porte-filets dans <lb/>laquelle on peut mettre au lieu des filets de ſoie une petite gla-<lb/>ce, ſur laquelle on a tracé deux lignes fines à angles droits, telle que <lb/>nous le verrons en parlant du Micrometre.</s> <s xml:id="echoid-s6860" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6861" xml:space="preserve">La lunete étant preparée & </s> <s xml:id="echoid-s6862" xml:space="preserve">placée dans une ſituation commode, <lb/>parallele au raïon du quart de cercle, il faut chercher par la métho-<lb/>de qui ſuît, le premier point de la divifion du bord, lequel ſoit éloi-<lb/>gné de 60 deg. </s> <s xml:id="echoid-s6863" xml:space="preserve">de la ligne de foi des lunetes, ou d'une ligne qui lui <lb/>ſoit parallele, paſſant par le centre dudit quart de cercle. </s> <s xml:id="echoid-s6864" xml:space="preserve">Maisau-<lb/>paravant il nous faut parler de cette ligne de foi, au ſujet de la-<lb/>quelle M. </s> <s xml:id="echoid-s6865" xml:space="preserve">de la Hire dit, qu'il eut autrefois une longue controverſe <lb/>avec des perſonnes ſort celebres & </s> <s xml:id="echoid-s6866" xml:space="preserve">grands Aſtronomes, leſquels <lb/>prétendoient qu'il étoit impoſſible de trouver une ligne de foiſta-<lb/>ble & </s> <s xml:id="echoid-s6867" xml:space="preserve">conſtante dans ces ſortes de lunetes, ne ſaiſant pas ſuffiſam-<lb/>ment attention aux regles de la Dioptrique.</s> <s xml:id="echoid-s6868" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6869" xml:space="preserve">Il eſt évident par la Dioptrique que tous les raïons, qui partans <lb/>d'un même point paſſent par une lentille de verre, concourent après <lb/>leur ſortie tous à un même point, que l'on appelle Foyer, pourvû <lb/>touteſois que la diſtance du point raïonant à la lentille, ſoit plus <lb/>grande que le demi-diametre de l'une & </s> <s xml:id="echoid-s6870" xml:space="preserve">l'autre convexité que nous <lb/>ſuppoſons ici égales; </s> <s xml:id="echoid-s6871" xml:space="preserve">que de plus entre les raïons qui du point raïo-<lb/>nant tombent ſur la ſurface antérieure de la lentille, celui qui con-<lb/>court avec la ligne droite qui conjoint les centres des convexitez, <lb/>ne ſouffre aucune refraction à l'entrée non plus qu'à la ſortie de la <lb/>lentille; </s> <s xml:id="echoid-s6872" xml:space="preserve">c'eſt pourquoi les points des objets qui ſont dans cette li-<lb/>gne droite, ſe repreſentent dans la même ligne que l'on nomme <lb/>l'Axe du tuïau optique, & </s> <s xml:id="echoid-s6873" xml:space="preserve">le point de cet Axe qui eſt dans le milieu <lb/>de l'épaîſſeur de la lentille, s'appelle le centre de ladite lentille.</s> <s xml:id="echoid-s6874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6875" xml:space="preserve">Si la ligne droite qui paſſe par le centre de la lentille, & </s> <s xml:id="echoid-s6876" xml:space="preserve">par le <lb/>point où ſe croiſent les fils, convient avec l'Axe dudit tuïau opti-<lb/>que, elle ſera la ligne de foi des lunetes, & </s> <s xml:id="echoid-s6877" xml:space="preserve">un objet fort éloigné, <lb/> <pb o="219" file="234" n="234" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> poſé dans l'Axe prolongé, paroîtra dans le point même où ſe croi-<lb/>ſent les fils ni plus ni moins que dans les alidades communes où <lb/>l'on prend pour ligne de foi la ligne droite, qui paſſant par les fentes <lb/>des pinules, eſt conduite juſqu'à l'objet. </s> <s xml:id="echoid-s6878" xml:space="preserve">Mais quoiqu'il n'arrive <lb/>preſque jamais dans la poſition des lunetes que nous avons éta-<lb/>blie, que la ligne droite conduite de l'objet au point où ſe croiſent <lb/>les fils & </s> <s xml:id="echoid-s6879" xml:space="preserve">où ſe repreſente ledit objet, convienne avec l'Axe opti-<lb/>que, nous ne laiſſerons pas cependant de trouver cette ligne de ſoi <lb/>des lunetes qui s'étend en ligne droite depuis l'objet juſqu'à la re-<lb/>preſentation qui ſe ſait au point où ſe croiſent les fils; </s> <s xml:id="echoid-s6880" xml:space="preserve">ce qui ſe dé-<lb/>montre par le diſcours ſuivant.</s> <s xml:id="echoid-s6881" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6882" xml:space="preserve">Soit la lentille de verre XV, ſon axe ACB, & </s> <s xml:id="echoid-s6883" xml:space="preserve">ſon centre C; </s> <s xml:id="echoid-s6884" xml:space="preserve">ſoit <lb/> <anchor type="note" xlink:label="note-234-01a" xlink:href="note-234-01"/> en outre F, le point où ſe croiſent les fils de ſoie hors de l'Axe ACB. <lb/></s> <s xml:id="echoid-s6885" xml:space="preserve">Si du point F, qui par la conſtruction eſt éloigné de la lentille, de la <lb/>longueur de ſon foyer, quelques raïons paſſent & </s> <s xml:id="echoid-s6886" xml:space="preserve">ſortent juſqu'à la <lb/>ſurface oppoſée de ladite lentille; </s> <s xml:id="echoid-s6887" xml:space="preserve">ils ſouffriront une reſraction à leur <lb/>entrée dans ladite lentille, & </s> <s xml:id="echoid-s6888" xml:space="preserve">une ſeconde reſraction à leur ſortie, <lb/>après quoi ils ſe continuëront paralleles entr'eux. </s> <s xml:id="echoid-s6889" xml:space="preserve">Or ces raions pa-<lb/>ralleles entr'eux le ſont auſſi à un des raïons qui du point F tombent <lb/>dans la lentille, ſçavoir FE, lequel après la premiere refraction au <lb/>point E, paſſe par le centre C, car après une ſeconde refraction à ſa <lb/>ſortie, au point D, il ſe continuë de D en O, parallele au même FE, <lb/>ſuivant la regle de la Dioptrique. </s> <s xml:id="echoid-s6890" xml:space="preserve">Mais tous les raïons briſez apres <lb/>la ſortie de la lentille ſont comme paralleles entr'eux, s'ils appar-<lb/>tiennent à un point O, fort éloigné, c'eſt pourquoi ils ſont auſſi pa-<lb/>ralleles au raïon FEO, qui de l'objet eſt prolongé directement au <lb/>point O, & </s> <s xml:id="echoid-s6891" xml:space="preserve">c'eſt cette ligne dr oite FEO, que nous appellons ligne <lb/>de foi dans la ſuſdite poſition des lunetes, & </s> <s xml:id="echoid-s6892" xml:space="preserve">elle demeurera toû-<lb/>jours la même, ſi l'on ne change point la ſituation deſdites lunetes, <lb/>c'eſt-à-dire; </s> <s xml:id="echoid-s6893" xml:space="preserve">que la lentille de verre & </s> <s xml:id="echoid-s6894" xml:space="preserve">lez fils croiſez ſoient en la <lb/>même poſition & </s> <s xml:id="echoid-s6895" xml:space="preserve">diſtance. </s> <s xml:id="echoid-s6896" xml:space="preserve">L'objet O étant en un des points extrê-<lb/>mes de la droite FEO, ſe preſentera au point F.</s> <s xml:id="echoid-s6897" xml:space="preserve"/> </p> <div xml:id="echoid-div522" type="float" level="2" n="8"> <note position="right" xlink:label="note-234-01" xlink:href="note-234-01a" xml:space="preserve">XVII. <lb/>Planche. <lb/>Fig. 8.</note> </div> <p> <s xml:id="echoid-s6898" xml:space="preserve">Il eſt à remarquer que la diſtance entre le raïon principal OD, qui <lb/>du point O de l'objet tom beſur la lentille, & </s> <s xml:id="echoid-s6899" xml:space="preserve">ſon raïon briſé EF, eſt <lb/>toûjours moindre que l'épaiſſeur de ladite lentille DE, laquelle eſt <lb/>inſenſible & </s> <s xml:id="echoid-s6900" xml:space="preserve">de nulle importance dans la diſtance d'un objet fort é-<lb/>loigné, & </s> <s xml:id="echoid-s6901" xml:space="preserve">que cette diſtance des raïons paralleles OD, OEF, eſt <lb/>d'autant moindre que la lentille ſera plus directement tournée vers <lb/>la poſition des fils, comme nous avons averti en la conſtruction.</s> <s xml:id="echoid-s6902" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6903" xml:space="preserve">Touteſois il pourroit ſe faire que le point F ſe rencontreroit dans <lb/> <pb o="220" file="235" n="235" rhead="CONSTRUCT. ET USAGES DU QUART, & c."/> l'Axe même; </s> <s xml:id="echoid-s6904" xml:space="preserve">mais il n'eſt pas beſoin de nous arrêter day<unsure/>antage ſur <lb/>cette Matiere.</s> <s xml:id="echoid-s6905" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6906" xml:space="preserve">Il nous faut preſentement expliquer de quelle maniere on peut <lb/> <anchor type="note" xlink:label="note-235-01a" xlink:href="note-235-01"/> trouver le premier point de la diviſion du bord du Quart de cercle. <lb/></s> <s xml:id="echoid-s6907" xml:space="preserve">Ayant affermi le plan du Quart de cercle en une ſituation verticale, <lb/>par le moyen du fil & </s> <s xml:id="echoid-s6908" xml:space="preserve">de ſon plomb CD, dirigez la lunete vers un <lb/>point viſible fort éloigné, poſé proche l'horiſon ſenſible, eu égard au <lb/>lieu où eſt placée la lunete de l'inſtrument; </s> <s xml:id="echoid-s6909" xml:space="preserve">ce que l'on pourra pre-<lb/>mierement connoître en marquant ſur le bord le point B, dans le <lb/>raïon CB, parallele à l'axe du tuïau, que l'on peut connoître à peu <lb/>près, & </s> <s xml:id="echoid-s6910" xml:space="preserve">en prenant le point D, éloigné dudit point B, de 90 de-<lb/>grez; </s> <s xml:id="echoid-s6911" xml:space="preserve">carlorſque le fil du pendule touchera le point D, l'objet qui <lb/>paroît au point où ſe croiſent les fils de ſoie, ou qui ſe voit par la lu-<lb/>nete, ſera proche l'horiſon, car l'horiſon ſenſible doit faire angle <lb/>droit avec le fil du plomb CD. </s> <s xml:id="echoid-s6912" xml:space="preserve">Mais comme nous ne ſommes point <lb/>encore certains que la lunete ſoit parfaitement horiſontale & </s> <s xml:id="echoid-s6913" xml:space="preserve">de ni-<lb/>veau, on renverſera l'inſtrument en ſorte que le point D ſoit en haut <lb/>& </s> <s xml:id="echoid-s6914" xml:space="preserve">le centre C en bas; </s> <s xml:id="echoid-s6915" xml:space="preserve">mais en cette tranſpoſition il faut avoir ſoin <lb/>que la ligne de foi des lunetes ſoit à la même hauteur qu'elle étoit <lb/>en la premiere poſition. </s> <s xml:id="echoid-s6916" xml:space="preserve">Ayant derechef dirigé les lunetes vers le <lb/>point premierement obſervé, en ſorte qu'il paroiſſe au point où ſe <lb/>croiſent les fils, & </s> <s xml:id="echoid-s6917" xml:space="preserve">ayant ajuſté au centre de l'inſtrument le cylindre <lb/>ſur lequel le centre C du quart de cercle avoit déja été marqué, on <lb/>attache le cheveu avec de la cire ſur le bord au point D, qui porte le <lb/>plomb, & </s> <s xml:id="echoid-s6918" xml:space="preserve">s'il paſſe juſteau centre C, il eſt certain que la ligne de foi <lb/>des lunetes eſt exactement de niveau & </s> <s xml:id="echoid-s6919" xml:space="preserve">dans l'horiſon ſenſible avec <lb/>l'objet viſible. </s> <s xml:id="echoid-s6920" xml:space="preserve">Car cette ligne de foi demeurant la même dans l'une <lb/>& </s> <s xml:id="echoid-s6921" xml:space="preserve">l'autre ſituation du quart de cercle & </s> <s xml:id="echoid-s6922" xml:space="preserve">prolongée avec la vertica-<lb/>le CD, le point D ſera le commencement de la diviſion du bord, é-<lb/>tant dans la ligne verticale & </s> <s xml:id="echoid-s6923" xml:space="preserve">ſous le Zénit à l'égard de la ligne de <lb/>foi de la lunete ou d'une autre ligne qui lui eſt parallele, avec leſ-<lb/>quelles la verticale DC, fait angles droits.</s> <s xml:id="echoid-s6924" xml:space="preserve"/> </p> <div xml:id="echoid-div523" type="float" level="2" n="9"> <note position="left" xlink:label="note-235-01" xlink:href="note-235-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s6925" xml:space="preserve">Mais ſi après avoir renverſé l'inſtrument, le cheveu du plomb ſuſ-<lb/>pendu du point D ne rencontre pas préciſément le centre C, il fau-<lb/>dra mouvoir le fil ou le cheveu juſqu'à ce qu'il paſſe par ledit cen-<lb/>tre C, ſans changer aucunement la ſituation du quart de cercle, ni <lb/>des lunetes qui doivent toûjours, comme auparavant, être dreſſées <lb/>vers l'objet; </s> <s xml:id="echoid-s6926" xml:space="preserve">pour lors on marquera dans l'arc de cercle D E, décrit <lb/>du centre C, paſlant par le point D, le point E qui ſe trouve ſous <lb/>le fil.</s> <s xml:id="echoid-s6927" xml:space="preserve"/> </p> <pb o="221" file="236" n="236" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> <p> <s xml:id="echoid-s6928" xml:space="preserve">Je dis que ſi l'on diviſe en deux parties égales l'arc D E au point <lb/>O, ce même point O ſera le premier point de la diviſion & </s> <s xml:id="echoid-s6929" xml:space="preserve">que le <lb/>raïon CO fera un angle droit avec la ligne de foi des lunetes. </s> <s xml:id="echoid-s6930" xml:space="preserve">Cet-<lb/>te operation eſt claire par elle-même, car la ligne de foi, ou le raïon <lb/>C B qui lui eſt parallele, ne changeant point en l'une & </s> <s xml:id="echoid-s6931" xml:space="preserve">en l'autre <lb/>poſition du quart de cercle, ſi l'angle BCD en la ſituation naturelle <lb/>de l'inſtrument eſt plus grand qu'un droit, c'eſt-à-dire, ſi le pointde <lb/>l'objet miré eſt au-deſſous de l'horiſon, il eſt évident que la vertica-<lb/>le C D prolongée, correſpendante au fil du plomb, fait avec la ligne <lb/>de foi un angle plus petit qu'un droit, à ſçavoir, le ſupplement de <lb/>l'angle BCD qui eſt égal à l'angle BCE; </s> <s xml:id="echoid-s6932" xml:space="preserve">c'eſt pourquoi l'angle <lb/>PCO, qui eſt moyen entre le plus grand & </s> <s xml:id="echoid-s6933" xml:space="preserve">le plus petit qu'un droit, <lb/>lequel eſt fait par le raïon CO, & </s> <s xml:id="echoid-s6934" xml:space="preserve">la ligne de foi, ſera droit, ce qu'il <lb/>falloit démontrer.</s> <s xml:id="echoid-s6935" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6936" xml:space="preserve">On pourra encore avoir le premier point de diviſion en con-<lb/>noiſſant un point parfaitement de niveau avec vôtre œil, & </s> <s xml:id="echoid-s6937" xml:space="preserve">pla-<lb/>çant la lunete dans ce point, l'endroit où tombera le cheveu ſera <lb/>le premier point de diviſion.</s> <s xml:id="echoid-s6938" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6939" xml:space="preserve">On peut faire la preuve de cette operation, ſi le fil du plomb paſ-<lb/>ſant par le point O, l'objet fort éloigné paroît au point où ſe croi-<lb/>ſent les fils. </s> <s xml:id="echoid-s6940" xml:space="preserve">Carayant renverſé l'inſtrument, & </s> <s xml:id="echoid-s6941" xml:space="preserve">la lunete étant toû-<lb/>jours dirigée vers le même objet, le fil du plomb paſſera par les <lb/>points O & </s> <s xml:id="echoid-s6942" xml:space="preserve">C, autrement il y aura de l'erreur dans les Obſervations.</s> <s xml:id="echoid-s6943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6944" xml:space="preserve">Etant bien aſſuré du premier point de la diviſion, on tracera du <lb/>centre C deux portions de cercle à 1 pouce de diſtance l'une de l'au-<lb/>tre pour renſermer les diviſions. </s> <s xml:id="echoid-s6945" xml:space="preserve">On ſe ſervira pour cela d'un Com-<lb/>pas à couliſſe, dont les pointes ſoient bien fines, & </s> <s xml:id="echoid-s6946" xml:space="preserve">dont celle du bout <lb/>puiſſe avancer ou reculer petit à petit par le moyen d'une vis & </s> <s xml:id="echoid-s6947" xml:space="preserve">d'un <lb/>écrou qui eſt ajuſté au bout de la branche du Compas; </s> <s xml:id="echoid-s6948" xml:space="preserve">enſuite du <lb/>point O, premier point de diviſion, & </s> <s xml:id="echoid-s6949" xml:space="preserve">de la même ouverture d'un <lb/>de cesarcs, on marquera une ſection, puis on diviſera cette diſtance <lb/>en deux juſte, quel'on tranſportera au-delà de la ſection qui don-<lb/>nera le point B, & </s> <s xml:id="echoid-s6950" xml:space="preserve">qui diviſera le quart de cercle en trois également, <lb/>qui vaudront chacun 30 degrez.</s> <s xml:id="echoid-s6951" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6952" xml:space="preserve">Ces diſtances ſeront encore partagées en 3, puis en 2; </s> <s xml:id="echoid-s6953" xml:space="preserve">enſin cha-<lb/>cune de ces parties ſera diviſée en 5, & </s> <s xml:id="echoid-s6954" xml:space="preserve">le quart de cercle ſera diviſé <lb/>en 90 deg. </s> <s xml:id="echoid-s6955" xml:space="preserve">on diviſera enſuite chaque dégré en ſix parties égales, <lb/>qui vaudront dix minutes.</s> <s xml:id="echoid-s6956" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6957" xml:space="preserve">Les circonferences intérieure & </s> <s xml:id="echoid-s6958" xml:space="preserve">extérieure étant très-parfaite-<lb/>ment diviſées de la maniere que nous venons de dire, on tracera des <lb/> <pb o="222" file="237" n="237" rhead="CONSTRUCT. ET USAGES DU QUART, & c."/> lignes très-ſines en tranſverſales, c'eſt-à-dire, du premier point de <lb/>diviſion de l'arc d'en haut, & </s> <s xml:id="echoid-s6959" xml:space="preserve">du ſecond d'en bas, & </s> <s xml:id="echoid-s6960" xml:space="preserve">ainſi de ſuite de <lb/>diviſions en diviſions, telle que la figure 6 le montre; </s> <s xml:id="echoid-s6961" xml:space="preserve">puis on parta-<lb/>gera la diſtance des 2 arcs de cercles en 10 également, & </s> <s xml:id="echoid-s6962" xml:space="preserve">du centre <lb/>Con tracera par ces points de diviſions 9 arcs de cercles, qui parta-<lb/>geront les tranſverſales en 10, & </s> <s xml:id="echoid-s6963" xml:space="preserve">par ce moyen le quart de cercle ſe <lb/>trouvera diviſé de minute en minute. </s> <s xml:id="echoid-s6964" xml:space="preserve">Il faut bien prendre garde ſur <lb/>toute choſe, que les diviſions ſoient bien égales. </s> <s xml:id="echoid-s6965" xml:space="preserve">Il faut ſe ſervir <lb/>pour cela de bons Compas bien fins, & </s> <s xml:id="echoid-s6966" xml:space="preserve">tracer les lignes & </s> <s xml:id="echoid-s6967" xml:space="preserve">les cercles <lb/>bien délicatement; </s> <s xml:id="echoid-s6968" xml:space="preserve">& </s> <s xml:id="echoid-s6969" xml:space="preserve">pour les petites diviſions, on doit avoir de pe-<lb/>tits Compas à reſſort, dont les pointes ne ſoient pas plus groſſes <lb/>qu'une éguille, & </s> <s xml:id="echoid-s6970" xml:space="preserve">un bon trace-ligne.</s> <s xml:id="echoid-s6971" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6972" xml:space="preserve">Outre les 90 deg. </s> <s xml:id="echoid-s6973" xml:space="preserve">du quart de cercle, on continuë pour certains <lb/>uſages la diviſion d'environ 5 deg. </s> <s xml:id="echoid-s6974" xml:space="preserve">au-delà du point O.</s> <s xml:id="echoid-s6975" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6976" xml:space="preserve">Toutes les fois que l'on tranſportera cet inſtrument par chariots <lb/>ou ſur des chevaux, il faudra le rectifier de crainte que les lunetes ne <lb/>ſoient ébranlées, ce qui arrive ſouvent aux fils de ſoie, encore bien <lb/>même que l'inſtrument ne change pas de place, principalement lorſ-<lb/>que le Soleil échaufe le tuïau de la lunete; </s> <s xml:id="echoid-s6977" xml:space="preserve">car pour lors les fils ſe ban-<lb/>dent, & </s> <s xml:id="echoid-s6978" xml:space="preserve">puis à l'abſence du Soleil ils ſe relâchent & </s> <s xml:id="echoid-s6979" xml:space="preserve">diviennent crê-<lb/>pus, ainſi ils ne ſont plus propres à faire des obſervations. </s> <s xml:id="echoid-s6980" xml:space="preserve">On peut <lb/>néanmoins ſe paſſer de faire la preuve de la lunete, lorſque l'on croi-<lb/>ra qu'il ne ſera arrivé aucun changement aux fils de ſoie, puiſque le <lb/>verre objectif demeure immobile & </s> <s xml:id="echoid-s6981" xml:space="preserve">toûjours le même, & </s> <s xml:id="echoid-s6982" xml:space="preserve">que la-<lb/>courbure des fils cauſée de tems en tems par l'humidité de l'air, ſe <lb/>rétablit le plus ſouvent au premier beau tems.</s> <s xml:id="echoid-s6983" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s6984" xml:space="preserve">Il faut remarquer que ſi l'on remet de nouvelles lunetes à un inſ-<lb/>trument déja diviſé, il ſera très-difficile de les faire convenir avec la <lb/>diviſion; </s> <s xml:id="echoid-s6985" xml:space="preserve">c'eſt pourquoi en ayant fait l'épreuve, comme nous avons <lb/>dit ci-devant, on connoîtra de combien les lunetes font l'angle plus <lb/>petit ou plus grand qu'un droit avec le raion qui paſſe par le pre-<lb/>mier point de la diviſion, & </s> <s xml:id="echoid-s6986" xml:space="preserve">il faudra avoir égard à cette difference <lb/>en toutes les obſervations; </s> <s xml:id="echoid-s6987" xml:space="preserve">car ſi cet angle eſt plus grand qu'un droit, <lb/>toutes les hauteurs obſervées ſeront plus grandes que les veritables <lb/>de la quantité de cette difference; </s> <s xml:id="echoid-s6988" xml:space="preserve">& </s> <s xml:id="echoid-s6989" xml:space="preserve">au contraire ſi cet angle eſt plus <lb/>petit qu'un droit, les veritables hauteurs ſeront plus grandes queles <lb/>obſervées; </s> <s xml:id="echoid-s6990" xml:space="preserve">cependant on pourroit placer les fils de ſoie de telle ma-<lb/>niere que la ligne de foi des lunetes feroit un angle droit avec le <lb/>raïon qui paſſe par le premier point de la divifion, en appliquant <lb/>les fils ſur une platine mobile, comme nous avons dit en la conſtru-<lb/> <pb o="223" file="238" n="238" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> ction. </s> <s xml:id="echoid-s6991" xml:space="preserve">Mais comme dans les voïages il faut ſouvent faire la preuve <lb/>de cet inſtrument, & </s> <s xml:id="echoid-s6992" xml:space="preserve">que la ſuſdite méthode eſt ſujete à beaucoup <lb/>d'incommoditez, tant parce qu'il eſt difficile de renverſer l'inſtru-<lb/>ment de maniere que le tuïau de la lunete reſte à même hauteur, <lb/>qu'à cauſe des differentes refractions de l'Atmoſphere autour de <lb/>l'horiſon à differentes heures du jour comme auſſi pour l'agi-<lb/>tation & </s> <s xml:id="echoid-s6993" xml:space="preserve">l'ondulation de l'air, & </s> <s xml:id="echoid-s6994" xml:space="preserve">autres choſes ſemblables, nous <lb/>ajoûtons ici deux autres méthodes propres à rectifier ces ſortes <lb/>d'inſtrumens, afin que chacun puiſſe choiſir celle qui lui paroîtra <lb/>plus commode ſelon les tems & </s> <s xml:id="echoid-s6995" xml:space="preserve">les lieux.</s> <s xml:id="echoid-s6996" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div525" type="section" level="1" n="249"> <head xml:id="echoid-head370" style="it" xml:space="preserve">Seconde méthode pour éprouver la poſition des Lunetes <lb/>de longue vûë.</head> <p> <s xml:id="echoid-s6997" xml:space="preserve">POur cette operation nous choiſiſſons un lieu d'où l'on puiſſe <lb/>voir diſtinctement un objet éloigné du moins de mille toiſes, <lb/>& </s> <s xml:id="echoid-s6998" xml:space="preserve">dont l'élevation ſur l'horiſon ne ſurpaſſe point le nombre des de-<lb/>grez que l'on marque ſur le bord au-delà du commencement de la <lb/>diviſion. </s> <s xml:id="echoid-s6999" xml:space="preserve">Ayant donc obſervé la hauteur de cet objet telle qu'elle <lb/>paroît par les degrez du bord, on mettra devant le quart de cercle, & </s> <s xml:id="echoid-s7000" xml:space="preserve"><lb/>le plus près qu'il ſe pourra, un vaſe de large embouchure, qu'on <lb/>remplira entierement d'eau juſqu'au ſommet des bords, le plus à <lb/>comble que faire ſe pourra. </s> <s xml:id="echoid-s7001" xml:space="preserve">Enſuite il faut hauſſer ou baiſſer le vaſe <lb/>juſqu'à ce que par la lunete on voïe ledit objet ſur la ſurface de l'eau <lb/>comme dans un miroir, ce qui ne ſera pas difficile, pourvû que la <lb/>ſurface de l'cau ne ſoit pas troublée par l'agitation de l'air; </s> <s xml:id="echoid-s7002" xml:space="preserve">nous au-<lb/>rons donc l'abaiſſement de cet objet par reflexion, & </s> <s xml:id="echoid-s7003" xml:space="preserve">on le verra <lb/>dans la ſituation droite, car nous nous ſervons de lunetes compo-<lb/>ſées de deux lentilles de verre convexe qui repreſentent les objets <lb/>renverſez; </s> <s xml:id="echoid-s7004" xml:space="preserve">mais par la reflexion, un objet renverſé ſe renverſe en-<lb/>core une fois; </s> <s xml:id="echoid-s7005" xml:space="preserve">c'eſt pourquoi il paroît droit.</s> <s xml:id="echoid-s7006" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7007" xml:space="preserve">Il faut remarquer cependant que l'abaiſſement de l'objet peut <lb/>quelquefois ſe voir ſur les degrez du bord comme la hauteur, ce qui <lb/>arrivera ſi l'angle fait de la ligne de foi & </s> <s xml:id="echoid-s7008" xml:space="preserve">du raïon qui paſſe par le <lb/>premier point de la diviſion eſt plus grand qu'un droit, & </s> <s xml:id="echoid-s7009" xml:space="preserve">au con-<lb/>traire, en d'autres cas la hauteur paroîtra comme l'abaiſſement, ſi <lb/>l'angle de la ligne de foi avec le raîon qui paſſe par le premier point <lb/>de la diviſion eſt plus petit qu'un droit. </s> <s xml:id="echoid-s7010" xml:space="preserve">Mais en tous les cas, ſans <lb/>avoir égard à l'élevation ou l'abaiſſement marqué ſur le bord, le <lb/>point milieu marqué exactement entre les deux obſervations, ſera <lb/>vertical & </s> <s xml:id="echoid-s7011" xml:space="preserve">répondra au Zénith, par rapport à la ligne de foi des lu-<lb/>netes.</s> <s xml:id="echoid-s7012" xml:space="preserve"/> </p> <pb o="224" file="239" n="239" rhead="CONSTRUCTION ET USAGES DU QUART, & c."/> <p> <s xml:id="echoid-s7013" xml:space="preserve">Ayant donctrouvé l'erreur de l'inſtrument, c'eſt-à-dire, la diffe-<lb/>rence entre le premier point de la diviſion marqué ſur le bord & </s> <s xml:id="echoid-s7014" xml:space="preserve">le <lb/>point qui répond au Zénith, on tachera de remettre les fils de ſoie <lb/>en leur vraie poſition, ſi cela ſe peut faire commodément, ſinon il <lb/>faudra avoir égard à l'erreur que l'on a reconnu en toutes les obſer-<lb/>vations, ſoit d'élevation, ſoit d'abaiſſement.</s> <s xml:id="echoid-s7015" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7016" xml:space="preserve">Mais il faut remarquer que ſi l'objet eſt proche & </s> <s xml:id="echoid-s7017" xml:space="preserve">élevé ſur l'ho-<lb/>riſon de pluſieurs minutes, il faudra trouver la veritable erreur de <lb/>l'inſtrument, par le calcul en la maniere ſuivante.</s> <s xml:id="echoid-s7018" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7019" xml:space="preserve">Dans un triangle dont un côté ſoit la diſtance connuë entre le <lb/>lieu de l'obſervation & </s> <s xml:id="echoid-s7020" xml:space="preserve">l'objet, l'autre côté ſoit la diſtance entre le <lb/>point milieu de la longueur de la lunete, & </s> <s xml:id="echoid-s7021" xml:space="preserve">le point de la ſurface de <lb/>l'eau où elle eſt rencontrée par le raïon refféchi avec l'angle com-<lb/>pris de ces deux côtez, à ſçavoir l'angle ou l'arc compris entre les <lb/>obſervations de l'élevation & </s> <s xml:id="echoid-s7022" xml:space="preserve">de l'abaiſſement de l'objet, on trou-<lb/>vera par le calcul l'angle oppoſé au plus petit côté; </s> <s xml:id="echoid-s7023" xml:space="preserve">de la quantité <lb/>de cet angle, il faut diminuer l'arc entre les obſervations du côté <lb/>du quart de cercle prolongé, & </s> <s xml:id="echoid-s7024" xml:space="preserve">le point milieu de l'arc reſtant ſe-<lb/>ra le vrai commencement de la diviſion.</s> <s xml:id="echoid-s7025" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7026" xml:space="preserve">Ainſi on peut trouver la diſtance entre le point milieu du tuïau <lb/>de la lunete & </s> <s xml:id="echoid-s7027" xml:space="preserve">le point de la ſurface de l'eau rencontrée par le raïon <lb/>refléchi, par le moyen d'une regle ou d'un fil tendu & </s> <s xml:id="echoid-s7028" xml:space="preserve">prolongé de-<lb/>puis ledit tuïau juſqu'à la ſurface de l'eau.</s> <s xml:id="echoid-s7029" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div526" type="section" level="1" n="250"> <head xml:id="echoid-head371" style="it" xml:space="preserve">Troiſiéme Méthode.</head> <p> <s xml:id="echoid-s7030" xml:space="preserve">CEtte operation eſt ſimple, mais les obſervations ne ſont pas fa-<lb/>ciles à faire. </s> <s xml:id="echoid-s7031" xml:space="preserve">Nous ſuppoſons en cette méthode, comme en la <lb/>precedente, qu'il y a ſur le bord du quart de cercle quelques degrez <lb/>marquez & </s> <s xml:id="echoid-s7032" xml:space="preserve">diviſez au-delà du point de 90 de hauteur, qui répond <lb/>au Zénith. </s> <s xml:id="echoid-s7033" xml:space="preserve">Nous obſervons pendant une belle nuit, le tems étant <lb/>ſerein & </s> <s xml:id="echoid-s7034" xml:space="preserve">ttanquille, la hauteur méridiene de quelque étoile qui ap-<lb/>proche de nôtre Zénith, ayant tourné vers l'Orient la face diviſéé <lb/>du bord de l'inſtrument. </s> <s xml:id="echoid-s7035" xml:space="preserve">La nuit ſuivante, ou peu de tems après, <lb/>nous obſervons ſem blablement la hauteur méridiene de la même <lb/>étoile, mais la face diviſée du bord étant tournée vers l'Occident: <lb/></s> <s xml:id="echoid-s7036" xml:space="preserve">je dis que le point milieu de l'arc entre les obſervations eſt le point <lb/>de 90 deg. </s> <s xml:id="echoid-s7037" xml:space="preserve">c'eſt à dire, par où paſſe le raïon parallele de la ligne <lb/>de foi de la lunete.</s> <s xml:id="echoid-s7038" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7039" xml:space="preserve">Cette troiſiéme méthode eſt fort utile pour prouver la poſition <lb/>des lunetes, que l'on ajuſte non ſeulement aux quarts de cercle, <lb/> <pb o="225" file="240" n="240" rhead="ASTRONOMIQUE. Liv. VI. Chap. I."/> mais principalement aux inſtrumens qui contiennent la huitiéme <lb/>ou ſixiéme partie, ou toute autre portîon de cercle; </s> <s xml:id="echoid-s7040" xml:space="preserve">car par ſon <lb/>moyen on connoîtra auquel des raïons de l'inſtrument ſera paral-<lb/>lele la ligne de foi deſdites lunetes.</s> <s xml:id="echoid-s7041" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7042" xml:space="preserve">Nous parlerons ci-après de la maniere d'obſerver les Aſtres dans <lb/>le méridien, ou la médiation du Ciel, & </s> <s xml:id="echoid-s7043" xml:space="preserve">de la maniere d'obſer-<lb/>yer les étoiles avec les lunetes de longue vûë.</s> <s xml:id="echoid-s7044" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div527" type="section" level="1" n="251"> <head xml:id="echoid-head372" style="it" xml:space="preserve">De la Regle mobile du Luart de cercle.</head> <p> <s xml:id="echoid-s7045" xml:space="preserve">IL ne nous reſte plus qu'à parler de la conſtruction & </s> <s xml:id="echoid-s7046" xml:space="preserve">uſage de la <lb/> <anchor type="note" xlink:label="note-240-01a" xlink:href="note-240-01"/> regle du Quart de cercle. </s> <s xml:id="echoid-s7047" xml:space="preserve">Cette regle n'eſt autre choſe qu'une a-<lb/>lidade mobile avec une lunete qui fait le même effet que les alida-<lb/>des des autres inſtrumens pour faire tel angle que l'on veut avec la <lb/>lunete immobile & </s> <s xml:id="echoid-s7048" xml:space="preserve">attachée au Quart de cercle. </s> <s xml:id="echoid-s7049" xml:space="preserve">On l'appelle Re-<lb/>gle, parce que la principale partie eſt une regle de fer ou de cuivre <lb/>percée par un bout, & </s> <s xml:id="echoid-s7050" xml:space="preserve">tellement ajuſtée au Cylindre central, dont <lb/>nous avons qarlé ci-devant, qu'elle ne peut ſe mouvoir que d'un <lb/>mouvement circulaire.</s> <s xml:id="echoid-s7051" xml:space="preserve"/> </p> <div xml:id="echoid-div527" type="float" level="2" n="1"> <note position="right" xlink:label="note-240-01" xlink:href="note-240-01a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s7052" xml:space="preserve">Sur cette Regle on attache deux cadres de fer ou de cuivre; </s> <s xml:id="echoid-s7053" xml:space="preserve">dans <lb/>le cadre qui eſt vers le centre de l'inſtrument on met la lentille ob-<lb/>jective, & </s> <s xml:id="echoid-s7054" xml:space="preserve">dans l'autre l'oculaire avec les fils de ſoie qui ſe croiſent, <lb/>leſquels compoſent enſemble une lunete de longue vûë, ſembla-<lb/>ble en toutes ſes parties à l'autre lunete, dont nous avons ci-devant <lb/>parlé, laquelle eſt attachée au Quart de cercle.</s> <s xml:id="echoid-s7055" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7056" xml:space="preserve">A l'extremité de la regle qui joint le bord du Quart de cercle on <lb/>fera une petite fenêtre de la grandeur environ d'un degré, comme <lb/>ils ſont marquez en la diviſion du bord. </s> <s xml:id="echoid-s7057" xml:space="preserve">On met à cette petite ou-<lb/>verture un cheveu tendu, lequel paſſant par le milieu eſt coutinué <lb/>au centre du Quart de cercle.</s> <s xml:id="echoid-s7058" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7059" xml:space="preserve">Mais comme dans l'uſage de cette Regle un cheveu eſt ſujet aux <lb/>diverſes inconſtances de l'air, nous mettrons à ſa place une lame <lb/>de corne bien claire, ou un verre blanc & </s> <s xml:id="echoid-s7060" xml:space="preserve">uni, ajuſté dans un petit <lb/>chaſſis. </s> <s xml:id="echoid-s7061" xml:space="preserve">Sur ſa ſurface qui regarde le bord de l'inſtrument nous y <lb/>traçons une ligne droite, laquelle ſera dirigée au contre de l'inſtru-<lb/>ment. </s> <s xml:id="echoid-s7062" xml:space="preserve">On fera tenir ce chaſſis à la petite fenêtre qui eſt au bas de la <lb/>Regle, par le moyen de quelques vis.</s> <s xml:id="echoid-s7063" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7064" xml:space="preserve">Avant que d'en venir à l'uſage, il faut éprouver la lunete, afin <lb/>de connoître ſi celle qui eſt immobile & </s> <s xml:id="echoid-s7065" xml:space="preserve">attachée à l'inſtrument <lb/>convient avec celle qui eſt mobile. </s> <s xml:id="echoid-s7066" xml:space="preserve">Pour cet effet ayant placé hori-<lb/>ſontalement le plan de l'inſtrument, & </s> <s xml:id="echoid-s7067" xml:space="preserve">ayant dirigé la lunete immo-<lb/> <pb o="226" file="241" n="241" rhead="CONSTRUCTION ET USAGES"/> bile vers un point de quelque objet viſible, éloigné au moins de <lb/>500 toiſes, on tournera la regle juſqu'à ce que l'on appercoive le <lb/>même objet par la lunete de ladite regle mobile, ou du moins qu'il <lb/>paroiſſe dans le fil de ſoie perpendiculaire au plan du quart de cer-<lb/>cle: </s> <s xml:id="echoid-s7068" xml:space="preserve">car il importe peu que l'objet ſoit au point où ſe croiſent les fils <lb/>en chaque lunete, ou dans le fil perpendiculaire. </s> <s xml:id="echoid-s7069" xml:space="preserve">Regardez pour <lb/>lors le point de la diviſion auquel convient la ligne de foi de la re-<lb/>gle; </s> <s xml:id="echoid-s7070" xml:space="preserve">que ſi la ligne marquée ſur la feuille de corne tombe juſtement <lb/>ſur le point de 90 deg. </s> <s xml:id="echoid-s7071" xml:space="preserve">de la diviſion, c'eſt une marque que leſdites <lb/>lunetes conviennent enſemble, ſinon, ou il faudra replacer ladite <lb/>feüille de corne pour la faire convenir, ou bien dans les obſervations <lb/>des angles il faudra toûjours avoir égard à la difſerence qui ſe trou-<lb/>ve entre le premier point de la diviſion & </s> <s xml:id="echoid-s7072" xml:space="preserve">la ligne tracée ſur ladite <lb/>corne ou verre.</s> <s xml:id="echoid-s7073" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7074" xml:space="preserve">Pour ce qui regarde les diſtances entre deux objets, ſoit au Ciel, <lb/>ſoit ſur la Terre, le plan de l'inſtrument étant ſitué de maniere que <lb/>les objets y conviennent, on obſervera les angles de la même ma-<lb/>niere que l'on fait avec des alidades ordinaires, c'eſt à-dire, celles <lb/>qui ſont au demi-cercle ou autres inſtrumens, dont nous avons <lb/>parlé au Livre IV.</s> <s xml:id="echoid-s7075" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div529" type="section" level="1" n="252"> <head xml:id="echoid-head373" xml:space="preserve">CHAPITRE II.</head> <head xml:id="echoid-head374" style="it" xml:space="preserve">De la Conſtruction & Vſage du Micrometre.</head> <p> <s xml:id="echoid-s7076" xml:space="preserve">LE Micrometre eſt un inſtrument de grand uſage en A ſtronomie, <lb/> <anchor type="note" xlink:label="note-241-01a" xlink:href="note-241-01"/> mais principalement pour meſurer les diametres des A ſtres, & </s> <s xml:id="echoid-s7077" xml:space="preserve"><lb/>les moindres diſtances qui ne ſurpaſſent point un degré ou un de-<lb/>gré & </s> <s xml:id="echoid-s7078" xml:space="preserve">demi. </s> <s xml:id="echoid-s7079" xml:space="preserve">Il eſt compoſé de deux cadres de cuivre rectangles, <lb/>dont celui ABCD a ordinairement 2 pouces & </s> <s xml:id="echoid-s7080" xml:space="preserve">demi de long & </s> <s xml:id="echoid-s7081" xml:space="preserve">I <lb/>pouce & </s> <s xml:id="echoid-s7082" xml:space="preserve">demi de large. </s> <s xml:id="echoid-s7083" xml:space="preserve">Les côtez AB, CD ſont diviſez en parties <lb/>égales & </s> <s xml:id="echoid-s7084" xml:space="preserve">éloignées entr'elles de 4 lignes ou environ, car c'eſt ſui-<lb/>vant les tours de vis, comme nous dirons ci-après; </s> <s xml:id="echoid-s7085" xml:space="preserve">mais de telle <lb/>ſorte queles lignes tirées par chaque diviſion, ſoient perpendiculai-<lb/>res aux côtez AB, CD. </s> <s xml:id="echoid-s7086" xml:space="preserve">On applique à ces diviſions des fils de ſoie <lb/>bien tendus avec de la cire que l'on y attache aux endroits mar-<lb/>quez 2.</s> <s xml:id="echoid-s7087" xml:space="preserve"/> </p> <div xml:id="echoid-div529" type="float" level="2" n="1"> <note position="left" xlink:label="note-241-01" xlink:href="note-241-01a" xml:space="preserve">XV III. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s7088" xml:space="preserve">L'autre cadre E F G H, dont la longueur E F eſt d'un pouce & </s> <s xml:id="echoid-s7089" xml:space="preserve">de-<lb/>mi, s'ajuſte de telle maniere avec le premier cadre, que les côtez <lb/>EF, GH de l'un peuvent ſe mouvoir le long des côtez AB, CD de <lb/>l'autre, ſans qu'ils s'en puiſſent ſeparer, ce qui ſe fait en les aſſem-<lb/> <pb o="235" file="242" n="242" rhead="DU MICROMETRE. Liv. VI. Chap. II."/><!-- <wrong/> --> blant en queuë d'éronde ou biſeau & </s> <s xml:id="echoid-s7090" xml:space="preserve">à couliſſe: </s> <s xml:id="echoid-s7091" xml:space="preserve">la face de ce ſe-<lb/>eond cadre qui regarde la face diviſée du premier, eſt auſſi garnie <lb/>d'un fil de ſoie fort déliétendu à l'endroit marqué 4, lequel dans le <lb/>mouvement du cadre demeure toûjours parallele aux fils du pre-<lb/>mier cadre, en les approchant de fort près au-deſſus l'un de lautre, <lb/>fans pourtant ſe toucher. </s> <s xml:id="echoid-s7092" xml:space="preserve">On place au côté B D une vis marquée I, <lb/>dont le Cylindre qui doit avoir 4 à 5 lignes de diametre entre & </s> <s xml:id="echoid-s7093" xml:space="preserve"><lb/>tourne dans un trou tarodè d'un pas fin, fait dans l'épaiſſeur du ca-<lb/>dre, & </s> <s xml:id="echoid-s7094" xml:space="preserve">qui eſt renſorcé en cet endroit la vis eſt entaillée par le bout <lb/>qui entre dans le trou du petit cadre, & </s> <s xml:id="echoid-s7095" xml:space="preserve">qui eſt auſſi renforcé à l'en-<lb/>droit marqué K. </s> <s xml:id="echoid-s7096" xml:space="preserve">Il y a une petite goupille qui entre dans un trou fait <lb/>au bout de la vis, pour que le cadre ne puiſſe aucunement mouvoir <lb/>qu'en faiſant tourner la vis à droite ou à gauche, ſuivant qu'on veut <lb/>faire avancer ou reculer ledit cadre.</s> <s xml:id="echoid-s7097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7098" xml:space="preserve">On met auſſi une plaque ronde d'environ un pouce de diametre, <lb/>qu'on attache avec deux vis ſur l'épaiſſeur du cadre aux endroits <lb/>marquez N. </s> <s xml:id="echoid-s7099" xml:space="preserve">On la diviſe ordinairement en 20 ou en 60 parties é-<lb/>gales qui ſervent à compter les tours de la vis dans les uſages qu'on <lb/>en fait, & </s> <s xml:id="echoid-s7100" xml:space="preserve">ce par le moyen de l'index M, qui eſt a juſté ſous le colet <lb/>de ladite vis, & </s> <s xml:id="echoid-s7101" xml:space="preserve">qui tourne avec elle: </s> <s xml:id="echoid-s7102" xml:space="preserve">la diviſion des côtez du cadre <lb/>ABCD, ſe fait ſuivant la groſſeur du pas de ladite vis; </s> <s xml:id="echoid-s7103" xml:space="preserve">car, par <lb/>exemple, ſi on veut que les diviſions ſoient éloignées l'une de l'au-<lb/>tre de 10 tours de vis, on fait faire 10 tours à ladite vis, & </s> <s xml:id="echoid-s7104" xml:space="preserve">on re-<lb/>marque combien le petit cadre a fait de chemin; </s> <s xml:id="echoid-s7105" xml:space="preserve">ſi c'eſt 4 lignes, on <lb/>fait les diviſions diſtantes l'une de l'autre de 4 lignes, & </s> <s xml:id="echoid-s7106" xml:space="preserve">on place les <lb/>filets bien juſte deſſus, & </s> <s xml:id="echoid-s7107" xml:space="preserve">on les fait tenir avec de la cire.</s> <s xml:id="echoid-s7108" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7109" xml:space="preserve">Pour obvier aux changemens qui arrivent facilement aux fils de <lb/>ſoie par la chaleur ou autrement, M. </s> <s xml:id="echoid-s7110" xml:space="preserve">de la Hire propoſe une choſe <lb/>fort commode; </s> <s xml:id="echoid-s7111" xml:space="preserve">c'eſt de placer au lieu de ſoie une plaque de verre <lb/>blanc, ou un morceau de glace mince, bien uni, qu'on ajuſte dans <lb/>une rénure faite au long du cadre. </s> <s xml:id="echoid-s7112" xml:space="preserve">On trace ſur ce verre des traits <lb/>paralleles & </s> <s xml:id="echoid-s7113" xml:space="preserve">très-déliez qui font le même effet que la ſoie. </s> <s xml:id="echoid-s7114" xml:space="preserve">Toute la <lb/>difficulté conſiſte à tracer ces lignes bien délicatement, & </s> <s xml:id="echoid-s7115" xml:space="preserve">a choi-<lb/>ſir une glace bien nette & </s> <s xml:id="echoid-s7116" xml:space="preserve">bien polie, car les défauts ſe groſſiſſent <lb/>extrêmement quand on les voit dans les lunetes. </s> <s xml:id="echoid-s7117" xml:space="preserve">On ſe ſert d'un <lb/>petit diaman, dont la pointe ſoit fort fine, pour tracer très-legere-<lb/>ment ſur le verre ces lignes. </s> <s xml:id="echoid-s7118" xml:space="preserve">La figure 1 de la Planche 18, fait <lb/>connoître la conſtruction de ce Micrometre, qui eſt fort commode <lb/>pour tous les uſages que nous allons expliquer.</s> <s xml:id="echoid-s7119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7120" xml:space="preserve">Toute la machine ſe joint aux grandes lunetes à obſerver, par le <lb/> <pb o="228" file="243" n="243" rhead="CONSTRUCTION ET USAGES"/> moyen des pieces marquées L, qui débordent le cadre & </s> <s xml:id="echoid-s7121" xml:space="preserve">qui entrent <lb/>à couliſſe dans une eſpece de boëte de fer blanc parallelograme, aux <lb/>deux côtez de laquelle il y a deux ouvertures circulaires où ſont ſou-<lb/>dez deux bouts de tuïau, l'un pour recevoir d'un côté le tuïau qui <lb/>porte le verre oculaire l'autre pour recevoir le tuïau qui porte le <lb/>verre objectif, de maniere que le Micrometre doit être placé juſ-<lb/>te au foyer de ce verre.</s> <s xml:id="echoid-s7122" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div531" type="section" level="1" n="253"> <head xml:id="echoid-head375" style="it" xml:space="preserve">Vſage du Micrometre.</head> <p> <s xml:id="echoid-s7123" xml:space="preserve">IL ſe fait au foyer de la lentille ou du verre objectif un vive re-<lb/>preſentation des objets au point où ſont poſez les fils du Micro-<lb/>metre; </s> <s xml:id="echoid-s7124" xml:space="preserve">c'eſt pourquoi ſi on ajoûte au devant du Micrometre la len-<lb/>tille oculaire qui en ſoit éloignée de l'étenduë de ſon foyer plus ou <lb/>moins, ſelon la nature & </s> <s xml:id="echoid-s7125" xml:space="preserve">conſtitution des yeux de l'obſervateur, les <lb/>objets & </s> <s xml:id="echoid-s7126" xml:space="preserve">les fils de ſoie y paroîtront diſtinctement.</s> <s xml:id="echoid-s7127" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7128" xml:space="preserve">Si donc on meſure en lignes ou 12<emph style="sub">me</emph> de pouce la longueur du <lb/>foyer de la lentille objective, ou ce qui eſt la même choſe, la diſtance <lb/>depuis le milieu de l'épaiſſeur de ladite lentille juſqu'aux fils de ſoie <lb/>du Micrometre, cette longueur ſera à la diſtance de 4 lignes, qui <lb/>font l'intervale des fils, comme le raïon ou ſinus total à la tangente <lb/>de l'angle compris entre les fils paralleles, ce qui eſt évident par la <lb/>Dioptrique. </s> <s xml:id="echoid-s7129" xml:space="preserve">Car nous ſuppoſons que la diſtance entre l'objet & </s> <s xml:id="echoid-s7130" xml:space="preserve">l'œil <lb/>de l'obſervateur eſt ſi grande, que la longueur du foyer de la lentille <lb/>n'eſt d'aucune conſequence à l'égard de cette diſtance; </s> <s xml:id="echoid-s7131" xml:space="preserve">de ſorre que <lb/>les raïons qui partent des points de l'objet paſſent directement par <lb/>le centre de la lentille juſqu'aux fils, ni plus ni moins que ſi l'œil de <lb/>l'obſervateur étoit placé dans la lentille même objective. </s> <s xml:id="echoid-s7132" xml:space="preserve">L'expe-<lb/>rience pourra nous confirmer cette invention, & </s> <s xml:id="echoid-s7133" xml:space="preserve">nous ſervir à trou-<lb/>ver la même choſe.</s> <s xml:id="echoid-s7134" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7135" xml:space="preserve">Car ſi ſur une petite table blanche & </s> <s xml:id="echoid-s7136" xml:space="preserve">bien unie on tire 2 lignes droi-<lb/>tes noires & </s> <s xml:id="echoid-s7137" xml:space="preserve">paralleles entr'elles, dont l'intervale ſoit tel que d'en-<lb/>viron 2 ou 300 toiſes, elles ſoient contenues entre 2 fils paralleles <lb/>du Micrometre dans un lieu commode & </s> <s xml:id="echoid-s7138" xml:space="preserve">pendant un tems ſérein, <lb/>ſans agitation ſenſible de l'air, éloignez la table de la lunete du Mi-<lb/>crometre, juſqu'à ce que les lignes de ladite table, qui doit être per-<lb/>pendiculaire à la ligne droite tirée de ladite table au Micrometre, <lb/>ſoient cachées par les fils paralleles dudit Micrometre; </s> <s xml:id="echoid-s7139" xml:space="preserve">pour lors la <lb/>diſtance entre la table & </s> <s xml:id="echoid-s7140" xml:space="preserve">le verre objectif du Micrometre ſera en <lb/>même raiſon à l'intervale des lignes de la table, comme le Sinus to-<lb/>tal à la tangente de l'angle compris entre deux fils paralleles du Mi-<lb/>crometre.</s> <s xml:id="echoid-s7141" xml:space="preserve"/> </p> <pb o="229" file="244" n="244" rhead="DU MICROMETRE. Liv. VI. Chap. II."/> <p> <s xml:id="echoid-s7142" xml:space="preserve">Faites enſuite mouvoir le cadre EFGH par le moyen de la vis, <lb/>juſqu'à ce que ſon fil de ſoie convienne exactement à un des fils pa-<lb/>ralleles de l'autre cadre, & </s> <s xml:id="echoid-s7143" xml:space="preserve">remarquez la ſituation de l'index de la <lb/>vis; </s> <s xml:id="echoid-s7144" xml:space="preserve">faites la tourner juſqu'à ce que le même fil du cadre EFGH con-<lb/>vienne avec le fil prochain de l'autre cadre, ou ce qui eſt la même <lb/>choſe, faites mouvoir le cadre EFG par l'eſpace de 4 lignes ou <lb/>d'un tiers de pouce, ce qui ſe connoîtra facilement par le moyen de <lb/>la lentille ou verre oculaire de la lunete, laquelle multiplie les ob-<lb/>jets, & </s> <s xml:id="echoid-s7145" xml:space="preserve">comptez les tours de la vis & </s> <s xml:id="echoid-s7146" xml:space="preserve">les parties d'une révolution <lb/>qui conviennent à l'intervale des fils. </s> <s xml:id="echoid-s7147" xml:space="preserve">Conſtruiſez enfin une table <lb/>des révolutions de la vis & </s> <s xml:id="echoid-s7148" xml:space="preserve">de ſes parties qui conviennent à cha-<lb/>que minute & </s> <s xml:id="echoid-s7149" xml:space="preserve">à chaque ſeconde, ayant, comme nous venons de <lb/>dire, connu l'angle qui convient à l'intervale entier.</s> <s xml:id="echoid-s7150" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7151" xml:space="preserve">Lorſque l'on voudra obſerver le diametre des Planetes, ayant di-<lb/>rigé vers une Planete la lunete de longue vûë & </s> <s xml:id="echoid-s7152" xml:space="preserve">ſon Micrometre, <lb/>diſpoſezles fils par le mouvement de la lunete, en telle ſorte qu'un <lb/>bord de l'Aſtre atteigne un des fils paralleles, immobiles, & </s> <s xml:id="echoid-s7153" xml:space="preserve">tournez <lb/>l'écrou ou la vis juſqu'à ce que le fil mobile joigne l'autre bord de <lb/>la Planete. </s> <s xml:id="echoid-s7154" xml:space="preserve">Il eſt évident que l'on connoîtra le diametre de la Pla-<lb/>nete par la diſtance connuë entre les fils du Micrometre qui con-<lb/>tiennent la Planete.</s> <s xml:id="echoid-s7155" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7156" xml:space="preserve">Nous avons dit qu'il y a un index au-deſſous du colet de la vis, <lb/>lequel marque ſur le bord d'un petit cercle diviſé en 60 parties é-<lb/>gales les fractions d'une révolution entiere dudit écrou.</s> <s xml:id="echoid-s7157" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7158" xml:space="preserve">Cette méthode eſt commode pour meſurer les diametres appa-<lb/>rens des planetes, ſi le corps de la Planete ſe meut entre 2 fils pa-<lb/>ralleles. </s> <s xml:id="echoid-s7159" xml:space="preserve">Cependant il faut remarquer qu'à l'égard du Soleil & </s> <s xml:id="echoid-s7160" xml:space="preserve">de <lb/>la Lune leurs diametres paroiſſent fort inégaux à cauſe des re-<lb/>fractions; </s> <s xml:id="echoid-s7161" xml:space="preserve">dans les moindres élevations ſur l'horiſon par l'eſpace de <lb/>30 minutes, le diametre vertical paroít un peu moindre qu'il n'eſt <lb/>en effet aux environs de l'horiſon, & </s> <s xml:id="echoid-s7162" xml:space="preserve">le diametre horiſontal ne ſe <lb/>peut reconnoître qu'avec bien de la peine, & </s> <s xml:id="echoid-s7163" xml:space="preserve">par des obſervations <lb/>pluſieurs fois repetées, non plus que la diſtance entre deux Aſtres <lb/>ou entre les cornes de la Lune, à cauſe de ſon mouvement diurne <lb/>qui paroît fort vîte par le Teleſcope ou Lunete.</s> <s xml:id="echoid-s7164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7165" xml:space="preserve">Par la même méthode on peut obſerver ſur la terre les petites <lb/>diſtances, & </s> <s xml:id="echoid-s7166" xml:space="preserve">plus facilement que les corps celeſtes, à cauſe de l'im-<lb/>mobilité de l'objet.</s> <s xml:id="echoid-s7167" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7168" xml:space="preserve">Si les deux Aſtres paſſent par le même méridien à differentes hau-<lb/>teurs & </s> <s xml:id="echoid-s7169" xml:space="preserve">en differens tems, la difference de leur hauteur donne le <lb/> <pb o="230" file="245" n="245" rhead="CONSTRUCTION ET USAGES"/> different éloignement où ils ſont de l'équateur vers l'un ou vers <lb/>l'autre pole, ce qu'on appelle leur difference de déclinaiſon, & </s> <s xml:id="echoid-s7170" xml:space="preserve">l'on <lb/>voit par la difference du tems où ils viennent au méridien, le difſe-<lb/>rent éloignement où ils ſont d'un point déterminé de l'équateur qui <lb/>eſt le premier degré d'Ariés, c'eſt-à-dire, qu'on a leur difference en <lb/>aſcenſion droite.</s> <s xml:id="echoid-s7171" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7172" xml:space="preserve">Si les 2 Aſtres ſont éloignez l'un de l'autre, on a dans l'intervale <lb/>de leur paſſage par le Méridien & </s> <s xml:id="echoid-s7173" xml:space="preserve">par le Micrometre, aſſez de loiſir <lb/>pour avoir entierement fini les operations qui regardent le premier <lb/>avant que d'aller au ſecond; </s> <s xml:id="echoid-s7174" xml:space="preserve">mais s'ils ſont fort proches l'un de l'au-<lb/>tre, il eſt trés difficile de faire en même tems les deux obſervations, <lb/>ſans compter qu'on ne peut pas toûjours prendre les deux Aſtres <lb/>aſſez préciſément dans le Méridien.</s> <s xml:id="echoid-s7175" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7176" xml:space="preserve">M. </s> <s xml:id="echoid-s7177" xml:space="preserve">de la Hire donne le moyen de remedier à cet inconvenient en <lb/>ne ſe ſervant que du Micrometre ordinaire. </s> <s xml:id="echoid-s7178" xml:space="preserve">La ſeule obſervation du <lb/>paſſage des Aſtres entre les filets, ou ſur les filets, du Micrometre <lb/>donnera par des conſequences faciles la difference de déclinaiſon <lb/>& </s> <s xml:id="echoid-s7179" xml:space="preserve">d'aſcenſion droite, ſans ſuppoſer même aucun Méridien connu <lb/>ni tracé.</s> <s xml:id="echoid-s7180" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7181" xml:space="preserve">Que ſi l'on veut avoir la difference de déclinaiſon & </s> <s xml:id="echoid-s7182" xml:space="preserve">d'aſcenſion <lb/>droite de deux Aſtres qui ne peuvent pas être compris entre les fils <lb/>du Micrometre, on pourra la trouver par la méthode ſuivante.</s> <s xml:id="echoid-s7183" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7184" xml:space="preserve">Nous ajuſtons au Micrometre un fil de ſoie, que l'on appelle <lb/>tranſverſal, parce qu'il coupe à angles droits les fils paralleles; </s> <s xml:id="echoid-s7185" xml:space="preserve">on <lb/>l'attache avec de la cire au milieu des côtez AC, BD. </s> <s xml:id="echoid-s7186" xml:space="preserve">A yant donc <lb/>affermi la lunete & </s> <s xml:id="echoid-s7187" xml:space="preserve">le Micrometre en telle poſition que l'on juge à <lb/>propos, pourvû que les Aſtres que l'on veut obſerver puiſſent paſſer <lb/>l'un après l'autre par les fils croiſez, comme on voit en la figure 2, <lb/>les Aſtres A & </s> <s xml:id="echoid-s7188" xml:space="preserve">S. </s> <s xml:id="echoid-s7189" xml:space="preserve">On obſervera par le moyen d'une pendule à ſe-<lb/> <anchor type="note" xlink:label="note-245-01a" xlink:href="note-245-01"/> condes le tems que le premier Aſtre A touchera le point où le fil <lb/>tranſverſal AS croiſe quelqu'un des fils paralleles, comme A d. </s> <s xml:id="echoid-s7190" xml:space="preserve">Le <lb/>Micrometre étant diſpoſé pour cette obſervation, ce qui n'eſt d'au-<lb/>cune difficulté, on comptera les ſecondes de tems qui s'écouleront <lb/>entre l'obſervation faite au point A, & </s> <s xml:id="echoid-s7191" xml:space="preserve">l'arrivée du même Aſtre au <lb/>point B, à la rencontre d'un autre fil parallele BD. </s> <s xml:id="echoid-s7192" xml:space="preserve">Nous obſerve-<lb/>rons de même le tems que l'autre Aſtre S rencontrera le fil tranſver-<lb/>ſal au point S, & </s> <s xml:id="echoid-s7193" xml:space="preserve">enſuite au point D du fil parallele BD.</s> <s xml:id="echoid-s7194" xml:space="preserve"/> </p> <div xml:id="echoid-div531" type="float" level="2" n="1"> <note position="left" xlink:label="note-245-01" xlink:href="note-245-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s7195" xml:space="preserve">Ce ſera la même choſe ſi l'Aſtre S rencontre premierement le fil <lb/>parallele en D, & </s> <s xml:id="echoid-s7196" xml:space="preserve">enſuite le fil tranſverſal en S.</s> <s xml:id="echoid-s7197" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7198" xml:space="preserve">Comme le nombre des ſecondes de tems du mouvement de l'Aſ-<lb/> <pb o="231" file="246" n="246" rhead="DU MICROMETRE. Liv. VI. Chap. II."/> tre A par l'eſpace AB eſt au nombre des ſecondes du mouvement <lb/>de l'Aſtre S par l'eſpace SD, ainſi la diſtance AC, laquelle eſt con-<lb/>nuë en minutes & </s> <s xml:id="echoid-s7199" xml:space="preserve">ſecondes de degré dans le Micrometre, eſt à la diſ-<lb/>tance CS en même eſpece & </s> <s xml:id="echoid-s7200" xml:space="preserve">ſecondes.</s> <s xml:id="echoid-s7201" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7202" xml:space="preserve">Mais il faut convertir les ſecondes horaires du mouvement par <lb/>l'eſpace AB, en minutes & </s> <s xml:id="echoid-s7203" xml:space="preserve">ſecondes de grand cercle, tels que ſont <lb/>ceux de la diſtance CA au Micrometre, ce qui ſe fait par la regle <lb/>ordinaire de proportion.</s> <s xml:id="echoid-s7204" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7205" xml:space="preserve">A yant premierement converti les ſecondes du tems dudit mou-<lb/>vement d'A en B, que nous regardons icicomme une ligne droite, <lb/>ou comme un arc de grand cercle, en minutes & </s> <s xml:id="echoid-s7206" xml:space="preserve">ſecondes de cercle <lb/>en prenant 15 minutes de cercle pour chaque minute d'heure, & </s> <s xml:id="echoid-s7207" xml:space="preserve">de <lb/>même des ſecondes, enſuite on fera par une regle de proportion, <lb/>comme le raïon ou Sinus total, au Sinus de complément de la dé-<lb/>clinaiſon de l'aſtre connuë; </s> <s xml:id="echoid-s7208" xml:space="preserve">ainſi le nombre des ſecondes de l'Arc <lb/>AB auſſi connu, au nombre des ſecondes de la même eſpece conte-<lb/>nues en CA, comme Arc de grand cercle.</s> <s xml:id="echoid-s7209" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7210" xml:space="preserve">De plus au triangle & </s> <s xml:id="echoid-s7211" xml:space="preserve">rectangle rectiligne CAB, les côtez CA. <lb/></s> <s xml:id="echoid-s7212" xml:space="preserve">AB étant donnez avec l'angle droit en C, nous trouverons l'angle <lb/>CAB, & </s> <s xml:id="echoid-s7213" xml:space="preserve">ſuppoſant la perpendiculaire CPR du point C ſur AB, <lb/>AB ſera à CA, comme CA eſt à AP.</s> <s xml:id="echoid-s7214" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7215" xml:space="preserve">Mais au triangle rectangle CAP, outre l'angle droit nous avons <lb/>l'angle A avec le côté CA, c'eſt pourquoi comme le raïon ou Sinus <lb/>total eſt à CA, ainſi le Sinus de l'angle CAP eſt à CP, & </s> <s xml:id="echoid-s7216" xml:space="preserve">comme le <lb/>nombre des ſecondes horaires du mouvement d'A en B eſt au nom-<lb/>bre des ſecondes horaires du mouvement d'S en D, ainſi CP eſt à <lb/>CR; </s> <s xml:id="echoid-s7217" xml:space="preserve">donc en ôtant CR de CP, ou bien les ajoûtant enſemble, ſi <lb/>AB & </s> <s xml:id="echoid-s7218" xml:space="preserve">SD ſont de l'un & </s> <s xml:id="echoid-s7219" xml:space="preserve">l'autre côté du point C, nous aurons la <lb/>valeur de PR en parties de grand cercle, qui ſera la difference de dé-<lb/>clinaiſon de l'un & </s> <s xml:id="echoid-s7220" xml:space="preserve">de l'autre Aſtre obſervé. </s> <s xml:id="echoid-s7221" xml:space="preserve">Nous n'avons aucun <lb/>égard à la difference du mouvement par les eſpaces AB & </s> <s xml:id="echoid-s7222" xml:space="preserve">SD cau-<lb/>ſée par la difference de déclinaiſon, parce qu'elle n'eſt d'aucune con-<lb/>ſequence dans les differences de déclinaiſon, telles qu'on peut les <lb/>obſerver par le Micrometre.</s> <s xml:id="echoid-s7223" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7224" xml:space="preserve">Enfin, comme AB eſt à AP, ainſi le nombre des ſecondes horai-<lb/>res du mouvement de l'aſtre A obſerve par l'eſpace AB, au nombre <lb/>des ſecondes du mouvement du même Aſtre pàr l'eſpace AP. </s> <s xml:id="echoid-s7225" xml:space="preserve">On <lb/>connnoîtra donc le tems que l'Aſtre A parvient en P. </s> <s xml:id="echoid-s7226" xml:space="preserve">Mais comme <lb/>le nombre des ſecondes horaires par l'eſpace AB eſt au nombre des <lb/>ſecondes horaires par l'eſpace SD; </s> <s xml:id="echoid-s7227" xml:space="preserve">ainſi le nombre des ſecondes ho-<lb/> <pb o="232" file="247" n="247" rhead="CONSTRUCTION ET USAGES"/> raires par l'eſpace AP, au nombre des ſecondes horaires par SR. <lb/></s> <s xml:id="echoid-s7228" xml:space="preserve">On connoît de plus le tems que l'Aſtre S eſt parvenu en S, à quoi <lb/>l'on ajoûte le temps par SR, ſi les rencontres A & </s> <s xml:id="echoid-s7229" xml:space="preserve">S ſont du même <lb/>côté du point C, ſinon il faut ſouſtraire letems par SR du tems de <lb/>l'obſervation en S, pour avoir le tems que l'Aſtre S eſt parvenu en <lb/>R. </s> <s xml:id="echoid-s7230" xml:space="preserve">Or la difference de l'arrivée des Aſtres en P & </s> <s xml:id="echoid-s7231" xml:space="preserve">R, c'eſt-à-dire, <lb/>à un même cercle Méridien, ſera leur difſerence d'aſcenſion droi-<lb/>te, laquelle ſe pourra réduire en degrez & </s> <s xml:id="echoid-s7232" xml:space="preserve">minutes par les regles <lb/>de proportion. </s> <s xml:id="echoid-s7233" xml:space="preserve">Il faut remarquer que nous n'avons ici aucun égard <lb/>au mouvement propre des Aſtres, pour la difference du tems en-<lb/>tre leur rencontre ſur le Méridien CP.</s> <s xml:id="echoid-s7234" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7235" xml:space="preserve">De cette méthode il eſt facile de reconnoître comment, au lieu <lb/>du fil parallele CBD, on peut ſe ſervir d'un autre parallele qui paſ-<lb/>ſe par A, ou de tout autre, comme auſſi du parallele mobile, pourvû <lb/>qu'il s'y forme des triang les ſemblables, ce qui s'entend par ce que <lb/>nous avons dit ci-devant.</s> <s xml:id="echoid-s7236" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7237" xml:space="preserve">Nous pouvons encore faire le même par une autre méthode. </s> <s xml:id="echoid-s7238" xml:space="preserve">Car <lb/>ayant diſpoſé les fils paralleles de maniere que le mouvement du <lb/>premier Aſtre ſe faſſe ſur un deſdits fils; </s> <s xml:id="echoid-s7239" xml:space="preserve">que l'on marque le tems <lb/>auquel le même Aſtre rencontre le fil tranſverſal; </s> <s xml:id="echoid-s7240" xml:space="preserve">que l'on obſerve <lb/>de même le tems que l'autre Aſtre arrive au même fil tranſverſal; </s> <s xml:id="echoid-s7241" xml:space="preserve">ſi <lb/>cependant on ajuſte le fil parallele mobile au ſecond Aſtre ſans chan-<lb/>ger aucunement le Micrometre, on trouvera par le moyen de la diſ-<lb/>tance des fils paralleles dudit Micrometre, la diſtance entre les pa-<lb/>ralleles de l'équateur qui paſſent par les lieux deſdits Aſtres, qui eſt <lb/>la difference de leur déclinaiſon. </s> <s xml:id="echoid-s7242" xml:space="preserve">Que ſi de plus, la difference du <lb/>tems entre le paſſage de l'un & </s> <s xml:id="echoid-s7243" xml:space="preserve">de l'autre Aſtre par le fil tranſverſal, <lb/>eſt convertie en minutes & </s> <s xml:id="echoid-s7244" xml:space="preserve">ſecondes de degrez, on aura leur diffe-<lb/>rence aſcenſionelle; </s> <s xml:id="echoid-s7245" xml:space="preserve">ce qui n'a pas beſoin d'exemple.</s> <s xml:id="echoid-s7246" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7247" xml:space="preserve">Mais ſi l'on cherche la même choſe entre quelque Aſtrc & </s> <s xml:id="echoid-s7248" xml:space="preserve">la <lb/>Lune ou le Soleil, comme par exemple, Mercure paſſant ſous le <lb/>diſque du Soleil.</s> <s xml:id="echoid-s7249" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7250" xml:space="preserve">Ayant premierement placé le Micrometre de telle ſorte que le <lb/>bord du Soleil parcourre un des fils paralleles, on obſervera le tems <lb/>que les bords du Soleil & </s> <s xml:id="echoid-s7251" xml:space="preserve">le centre de Mercure toucheront le fil <lb/>tranſverſal, & </s> <s xml:id="echoid-s7252" xml:space="preserve">par ce tems on connoîtra la difference de déclinai-<lb/>ſon entre Mercure & </s> <s xml:id="echoid-s7253" xml:space="preserve">le bord du Soleil par le moyen du fil parallele <lb/>mobile, le Micrometre demeurant immobile.</s> <s xml:id="echoid-s7254" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7255" xml:space="preserve">Que ſi au tems de l'obſervation du premier bord du Soleil on a-<lb/>joûte la moitié du tems écoulé entre les paſſages de l'un & </s> <s xml:id="echoid-s7256" xml:space="preserve">l'autre <lb/> <pb o="233" file="248" n="248" rhead="DU MICROMETRE. Liv. VI. Chap. II."/> bord, on aura le tems du paſſage du centre du Soleil par le même fil <lb/>tranſverſal: </s> <s xml:id="echoid-s7257" xml:space="preserve">& </s> <s xml:id="echoid-s7258" xml:space="preserve">par ce moyen on aura la difference du tems entre le <lb/>paſſage du centre du Soleil & </s> <s xml:id="echoid-s7259" xml:space="preserve">de Mercure par le fil tranſverſal, c'eſt-<lb/>à-dire, par le cercle Méridien. </s> <s xml:id="echoid-s7260" xml:space="preserve">Cette difference de tems étant con-<lb/>vertie en degrez & </s> <s xml:id="echoid-s7261" xml:space="preserve">minutes donnera la difference de leur aſcenſion <lb/>droite.</s> <s xml:id="echoid-s7262" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7263" xml:space="preserve">De plus, comme le centre du Soleil eſt dans l'écliptique, ſi dans <lb/>le même tems que ledit centre paſſera par le fil tranſverſal, connoiſ-<lb/>ſant d'ailleurs le vrail lieu du Soleil, vous cherchez dans la Table fai-<lb/>te exprès, l'angle de l'écliptique avec le cercle Méridien, vous aurez <lb/>auſſi l'angle que ſait l'écliptique avec le parallele du Soleil, comme <lb/>dans la figure ci-jointe, l'angle OCR, de l'écliptique OCB, & </s> <s xml:id="echoid-s7264" xml:space="preserve">du <lb/>parallele del'équateur RC. </s> <s xml:id="echoid-s7265" xml:space="preserve">PC eſt le Méridien, & </s> <s xml:id="echoid-s7266" xml:space="preserve">Mercure en M, <lb/> <anchor type="note" xlink:label="note-248-01a" xlink:href="note-248-01"/> le centre du Soleil étant en C, ſoit MR parallele à PC, & </s> <s xml:id="echoid-s7267" xml:space="preserve">CR la <lb/>diſſerence d'aſcenſion droite entre le centre du Soleil C & </s> <s xml:id="echoid-s7268" xml:space="preserve">Mercure <lb/>en M. </s> <s xml:id="echoid-s7269" xml:space="preserve">Mais les minutes de difference d'aſcenſion droite CR dans <lb/>le parallele, étant réduites en minutes de grand cercle, ſi on fait une <lb/>regle de proportion, en diſant, comme le raïon ou Sinustotal au Si-<lb/>nus de complément de la déclinaiſon du Soleil ou de Mercure, ainſi <lb/>le nombre des ſecondes de la difference d'aſcenſion droite, au nom-<lb/>bre des ſecondes CR, comme portion de grand cercle. </s> <s xml:id="echoid-s7270" xml:space="preserve">Pour lors <lb/>au triangle CRT, rectangle en R, nous avons le côté CR que l'on <lb/>vient de trouver avec l'angle RCT; </s> <s xml:id="echoid-s7271" xml:space="preserve">ſçavoir, la difference entre <lb/>l'angle droit & </s> <s xml:id="echoid-s7272" xml:space="preserve">l'angle de l'écliptique avec le Méridien; </s> <s xml:id="echoid-s7273" xml:space="preserve">c'eſt pour-<lb/>quoi on trouvera l'hypotenuſe CT, & </s> <s xml:id="echoid-s7274" xml:space="preserve">le côté RT. </s> <s xml:id="echoid-s7275" xml:space="preserve">Mais ſi on ôte <lb/>RT de MR, qui eſt la difference de déclinaiſon de Mercure en M <lb/>& </s> <s xml:id="echoid-s7276" xml:space="preserve">du centre du Soleil C, reſtera TM. </s> <s xml:id="echoid-s7277" xml:space="preserve">On dira enſuite par la regle <lb/>de proportion, comme CT eſt à TR, ainſi TM eſt à TO. </s> <s xml:id="echoid-s7278" xml:space="preserve">Et com-<lb/>me CT eſt à CR, ainſi TM à MO. </s> <s xml:id="echoid-s7279" xml:space="preserve">MO ſera la latitude de Mer-<lb/>cure au tems de l'obſervation. </s> <s xml:id="echoid-s7280" xml:space="preserve">Mais ajoûtant TO au côté CT, on <lb/>aura CO pour difference de longitude entre Mercure & </s> <s xml:id="echoid-s7281" xml:space="preserve">le centre <lb/>du Soleil. </s> <s xml:id="echoid-s7282" xml:space="preserve">C'eſt pourquoi connoiſſant la longitude du Soleil, on <lb/>trouvera celle de Mercure.</s> <s xml:id="echoid-s7283" xml:space="preserve"/> </p> <div xml:id="echoid-div532" type="float" level="2" n="2"> <note position="right" xlink:label="note-248-01" xlink:href="note-248-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s7284" xml:space="preserve">De plus, ſi 2 ou 3 heures après la premiere obſervation de Mer-<lb/>cure en M, on obſerve encore une fois la difference de déclinaiſon <lb/>& </s> <s xml:id="echoid-s7285" xml:space="preserve">d'aſcenſion droite de Mercure avancé en N, nous trouverons <lb/>comme ci-devant la latitude de Mercure NQ & </s> <s xml:id="echoid-s7286" xml:space="preserve">CQ, difference <lb/>de longitude du centre du Soleil C; </s> <s xml:id="echoid-s7287" xml:space="preserve">c'eſt pourquoi nous trouverons <lb/>le lieu du nœud apparent de Mercure. </s> <s xml:id="echoid-s7288" xml:space="preserve">Mais il faut remarquer que <lb/>le point de rencontre A dans la droite MN, avec l'écliptique CB, <lb/> <pb o="234" file="249" n="249" rhead="CONSTRUCTION ET USAGES"/> n'eſt point le lieu dudit noeud, eu égard au point C, parce qu'entre <lb/>les obſervations faites aux points M & </s> <s xml:id="echoid-s7289" xml:space="preserve">N, le Soleil par ſon mouve-<lb/>ment propre s'eſt avancé de quelques minutes, ſelon l'ordre des Si-<lb/>gnes, à quoi cependant on n'a pas d'égard dans les obſervations. <lb/></s> <s xml:id="echoid-s7290" xml:space="preserve">C'eſt pourquoi on dira par la regle de proportion, comme la diffe-<lb/>rence des latitudes MO, NQ à OQ, moins le mouvement propre <lb/>du Soleil, entre les obſervations faites en M & </s> <s xml:id="echoid-s7291" xml:space="preserve">N; </s> <s xml:id="echoid-s7292" xml:space="preserve">ainſi MO à la <lb/>diſtance OA, d'oùl'on trouvera la vraie diſtance CA du centre du <lb/>Soleil C au nœud de Mercure A. </s> <s xml:id="echoid-s7293" xml:space="preserve">Nous ôtons de OQ le mouve-<lb/>ment propre du Soleil entre les obſervations, parce que pendant ce <lb/>tems-là Mercure eſt retrograde. </s> <s xml:id="echoid-s7294" xml:space="preserve">Mais ſi ſon mouvement étoit di-<lb/>rect, il faudroit ajoûter le mouvement du Soleil à la droite OQ.</s> <s xml:id="echoid-s7295" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7296" xml:space="preserve">Dans les obſervations de Mercure en ſon paſſage entre les <lb/>bords du Soleil, nous n'avons eu aucun égard au mouvement pro-<lb/>pre du Soleil, comme étant de petite conſequence; </s> <s xml:id="echoid-s7297" xml:space="preserve">mais ſi nous vou-<lb/>lons y avoir ɔgard, il faudra diminuer CO & </s> <s xml:id="echoid-s7298" xml:space="preserve">CQ de la quantité du <lb/>mouvement propre du Soleil a raiſon du tems écoulé entre le paſſa-<lb/>ge du centre du Soleil & </s> <s xml:id="echoid-s7299" xml:space="preserve">de Mercure par le cercle Méridien.</s> <s xml:id="echoid-s7300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7301" xml:space="preserve">Par la même méthode on obſervera les diſtances des Planetes en-<lb/>tr'elles, ou avecles étoiles fixes aux environs de l'écliptique, excep-<lb/>té néanmoins quelques minutes, non ſeulement à cauſe du mouve-<lb/>ment propre des Planetes, ſoit vers les mêmes parties, ſoit vers les <lb/>parties oppoſées, comme nous avons dit du Soleil & </s> <s xml:id="echoid-s7302" xml:space="preserve">de Mercure; <lb/></s> <s xml:id="echoid-s7303" xml:space="preserve">mais auſſi à cauſe de leur éloignement de l'écliptique ou de leur <lb/>trop grande latitude, dont il nous ſuffit d'avoir ici averti.</s> <s xml:id="echoid-s7304" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7305" xml:space="preserve">Il eſt à remarquer que cette ſeconde méthode pour trouver la dif-<lb/>ference de déclinaiſon & </s> <s xml:id="echoid-s7306" xml:space="preserve">d'aſcenſion droite, n'eſt pas plus exacte <lb/>que la premiere, quoiqu'elle ſe faſſe avec moins de calcul, car il eſt <lb/>aſſez difficile de diſpoſer les fils du Micrometre ſelon le parallele du <lb/>mouvement diurne, ne le pouvant faire que par pluſieurs épreu-<lb/>ves incertaines.</s> <s xml:id="echoid-s7307" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7308" xml:space="preserve">M. </s> <s xml:id="echoid-s7309" xml:space="preserve">de la Hire a inventé encore un autre Micrometre, dont la conſ-<lb/>truction eſt facile, car ce n'eſt autre choſe qu'un double Compas, <lb/>comme il eſt ici repreſenté, dont les jambes d'une part, ſont par ex-<lb/> <anchor type="note" xlink:label="note-249-01a" xlink:href="note-249-01"/> emple, dix ſois plus grandes que les autres. </s> <s xml:id="echoid-s7310" xml:space="preserve">Il doit être fait de telle <lb/>maniere que les plus courtes jambes ſe puiſſent introduire par une <lb/>fente dans le tuïau de la lunete & </s> <s xml:id="echoid-s7311" xml:space="preserve">ſe placer à l'endroit du foyer de la <lb/>lentille objective, en ſorte que les pointes très-fines deſdites plus <lb/>courtes jambes ſe puiſlent appliquer à tous les objets dépeints au <lb/>foyer. </s> <s xml:id="echoid-s7312" xml:space="preserve">Car de la même ouverture du compas les pointes des plus <lb/> <pb o="235" file="250" n="250" rhead="DE LA MAN. D'OBSERV. LES ASTRES. L. VI. C.III."/> longues jambes s'appliqueront ſur une échelle diviſée en parties, qui <lb/>marqueront les minutes & </s> <s xml:id="echoid-s7313" xml:space="preserve">ſecondes telles qu'elles conviennent au <lb/>foyer de la lentille objective; </s> <s xml:id="echoid-s7314" xml:space="preserve">la diviſion de cette échelle ſe pourra <lb/>faire par la même méthode, dont nous nous ſommes ſervis à con-<lb/>noître les diſtances des fils paralleles de l'autre Micrometre, en di-<lb/>ſant par la regle de 3, comme le nombre des lignes contenuës en la <lb/>longueur du foyer de la lentille objective de la lunete, a une ligne, <lb/>ainſi le raïon ou Sinus total, à la tangente de l'angle meſuré au foyer <lb/>ſous une ligne. </s> <s xml:id="echoid-s7315" xml:space="preserve">C'eſt pourquoi ſi les plus longues jambes contien-<lb/>nent lès autres dix fois, dix lignes de l'échelle meſureront le même <lb/>angle, ce qui étant connu, il ſera facile de diviſer l'échelle en mi-<lb/>nutes & </s> <s xml:id="echoid-s7316" xml:space="preserve">ſecondes. </s> <s xml:id="echoid-s7317" xml:space="preserve">L'on pourra ſe ſervir de ce Micrometre pour ob-<lb/>ſerver les diametres des Planetes, comme auſſi les moindres diſtan-<lb/>ces des Aſtres & </s> <s xml:id="echoid-s7318" xml:space="preserve">des Lieux de la Terre.</s> <s xml:id="echoid-s7319" xml:space="preserve"/> </p> <div xml:id="echoid-div533" type="float" level="2" n="3"> <note position="left" xlink:label="note-249-01" xlink:href="note-249-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s7320" xml:space="preserve">La conſtruction de ce Micrometre eſt la même que cellc que <lb/>nous avons donnée pour les Compas de réduction.</s> <s xml:id="echoid-s7321" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div535" type="section" level="1" n="254"> <head xml:id="echoid-head376" xml:space="preserve">CHAPITRE III.</head> <head xml:id="echoid-head377" style="it" xml:space="preserve">Maniere d'obſerver les Aſtres.</head> <p> <s xml:id="echoid-s7322" xml:space="preserve">LES obſervations des Aſtres qui ſe font de jour par les lunetes de <lb/>longue vûë, ſont faciles, parce que les fils de ſoie ſe voyent diſ-<lb/>tinctement; </s> <s xml:id="echoid-s7323" xml:space="preserve">mais pendant la nuit il faut éclairer les fils avec un <lb/>flambeau ou une bougie, en ſorte que l'on puiſſe les voir avec les <lb/>Aſtres par la lunete, ce qui ſe fait en deux manieres.</s> <s xml:id="echoid-s7324" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7325" xml:space="preserve">Premierement, nous éclairons la lentille ou verre objectif de la <lb/>lunete, en approchant de ladite lentille une chandelle, mais obli-<lb/>quement, afin que ſon corps ou ſa fumée n'empêchent point les <lb/>raïons de l'Aſtre. </s> <s xml:id="echoid-s7326" xml:space="preserve">Mais ſi la lentille objective eſt un peu enfoncée <lb/>dans le tuïau, elle ne pourra point être éclairée à moins que la <lb/>chandelle ne ſoit fort proche, ce qui empêche de voir l'Aſtre; </s> <s xml:id="echoid-s7327" xml:space="preserve">& </s> <s xml:id="echoid-s7328" xml:space="preserve">ſi <lb/>la lunete a plus de ſix pieds, il ſera difficile d'éclairer ſuffiſamment <lb/>le verre objectif, en ſorte que les fils paroiſſent bien diſtinctement.</s> <s xml:id="echoid-s7329" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7330" xml:space="preserve">Secondement, on fait une ouverture aſſez ample au bout du <lb/>tuïau proche du cadre où ſont attachez les fils, & </s> <s xml:id="echoid-s7331" xml:space="preserve">approchant la <lb/>bougie, les fils & </s> <s xml:id="echoid-s7332" xml:space="preserve">les Aſtres paroîtront.</s> <s xml:id="echoid-s7333" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7334" xml:space="preserve">Mais cette méthode eſt ſujette à plufieurs inconveniens, car la <lb/>lumiere eſt ſi proche des yeux de l'obſervateur, que ſouvent ils en <lb/>ſont incommodez. </s> <s xml:id="echoid-s7335" xml:space="preserve">Et de plus, comme les fils ſont découverts & </s> <s xml:id="echoid-s7336" xml:space="preserve"><lb/>expoſez à l'air, ils perdent leur ſituation, ou ils ſe détendent, ou <lb/>même ſe peuvent rompre.</s> <s xml:id="echoid-s7337" xml:space="preserve"/> </p> <pb o="236" file="251" n="251" rhead="DE LA MANIERE"/> <p> <s xml:id="echoid-s7338" xml:space="preserve">Cette méthode eſt outre cela ſujette à un inconvenient qui la <lb/>doit faire rejetter abſolument, c'eſt qu'elle eſt ſujette à erreur, en <lb/>ce que ſelon la poſition de la lumiere qui éclaire les fils, ils paroî-<lb/>tront en differentes ſituations, à cauſe que lorſque le filet horiſon-<lb/>tal, par exemple, ſera éclairé par deſſus, on verra une ligne lumi-<lb/>neuſe, qu'on prendra pour le filet, qui ſera à ſa ſuperficie ſupérieu-<lb/>re: </s> <s xml:id="echoid-s7339" xml:space="preserve">& </s> <s xml:id="echoid-s7340" xml:space="preserve">au contraire, quand le même filet ſera éclairé par-deſſous, <lb/>la ligne limineuſe paroîtra à ſa ſuperficie inférieure, ſans que le fi-<lb/>let change de place, & </s> <s xml:id="echoid-s7341" xml:space="preserve">l'erreur ſera du diametre du filet, qui vaut <lb/>ſouvent plus de ſix ſecondes.</s> <s xml:id="echoid-s7342" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7343" xml:space="preserve">M. </s> <s xml:id="echoid-s7344" xml:space="preserve">de la Hire a trouvé un expedient pour y remedier: </s> <s xml:id="echoid-s7345" xml:space="preserve">comme il <lb/>avoit ſouvent experimenté dans les obſervations, qu'au clair de la <lb/>Lune, dans un tems un peu broüillé, les fils paroiſſoient diſtincte-<lb/>ment, & </s> <s xml:id="echoid-s7346" xml:space="preserve">qu'à peine pouvoit-on les voir lorſque le Ciel étoit ſerein, <lb/>il lui vint en penſée de couvrir le bout du tuïau de la lunete, du cô-<lb/>té du verre objectif, d'un morceau de gaze ou crêpe blanc très-fin, <lb/>c'eſt-à-dire, fait de fils de ſoie très-déliez, comme les toiles de ſoie <lb/>dont on ſe ſert pour faire des tamis. </s> <s xml:id="echoid-s7347" xml:space="preserve">Cetteinvention lui a réuſſi, car <lb/>la bougie placée loin de la lunete, éclairoit aſlez le crêpe pour ſaire <lb/>voir diſtinctement les fils, ſans empêcher de voir les Aſtres.</s> <s xml:id="echoid-s7348" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7349" xml:space="preserve">Les obſervations du Soleil ne ſe peuvent faire à moins que l'on <lb/>ne mette entre la lunete & </s> <s xml:id="echoid-s7350" xml:space="preserve">l'oeil un verre bruni ou enfumé, ce qui <lb/>ſe prépare ainſi. </s> <s xml:id="echoid-s7351" xml:space="preserve">Prenez deux morceaux de verre égaux & </s> <s xml:id="echoid-s7352" xml:space="preserve">bien po-<lb/>lis; </s> <s xml:id="echoid-s7353" xml:space="preserve">ſur la ſurface d'un de ces verres & </s> <s xml:id="echoid-s7354" xml:space="preserve">autour de ſes bords collez une <lb/>bande de carton; </s> <s xml:id="echoid-s7355" xml:space="preserve">mettez ſur la fumée d'un flambeau l'autre mor-<lb/>ceau de verre, en le remuant ſouvent & </s> <s xml:id="echoid-s7356" xml:space="preserve">le retirant de tems à autre, <lb/>de crainte que la trop grande chaleur ne le faſſe caſſer juſqu'à ce <lb/>que la ſumée y ſoit ſi épaiſſe, qu'à peine on puiſſe voir le flambcau; <lb/></s> <s xml:id="echoid-s7357" xml:space="preserve">mais il ne faut pas que le noir de fumée y ſoit par tout d'égale épaiſ-<lb/>ſeur, afin que l'on puiſſe choiſir celle qui convient à la ſplendeur du <lb/>Soleil. </s> <s xml:id="echoid-s7358" xml:space="preserve">Et afin que ce noir ne s'efface pas, il le faut appliquer ſur <lb/>l'autre morceau de verre, dont la ſurface ne touchera point ladite <lb/>fumée, à cauſe des bandes de carton qui ſont entre les deux verres, <lb/>dont enfin on joindra les bords avec une bande de papier collé.</s> <s xml:id="echoid-s7359" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7360" xml:space="preserve">Il faut ſe ſouvenir qu'obſervant la hauteur du Soleil avec une lu-<lb/>nete à deux verres, le bord ſupérieur paroît inferieur.</s> <s xml:id="echoid-s7361" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7362" xml:space="preserve">Il y a deux principales ſortes d'obſervations des Aſtres, l'une dans <lb/>le Méridien, & </s> <s xml:id="echoid-s7363" xml:space="preserve">l'autre dans les Cercles verticaux.</s> <s xml:id="echoid-s7364" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7365" xml:space="preserve">Si l'on connoît la poſition du Cercle Méridien en plaçant le plan <lb/>du quart de cercle dans le plan du Méridien par le mo yen du plomb <lb/> <pb o="237" file="252" n="252" rhead="D'OBSERVER LES ASTRES. Liv. VI. Ch. III."/> attachéau centre, on pourra trouver la hauteur méridienne de l'Aſ-<lb/>tre, qui eſt une des principales operations, & </s> <s xml:id="echoid-s7366" xml:space="preserve">qui ſert de fondement <lb/>à preſque toute l'Aſtronomie.</s> <s xml:id="echoid-s7367" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7368" xml:space="preserve">On peut auſſi avoir des obſervations méridiennes par le moyen <lb/>d'un Horloge a pendule, ſi l'on ſçait le tems précis du paſſage de <lb/>l'Aſtre par le Méridien.</s> <s xml:id="echoid-s7369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7370" xml:space="preserve">Il faut remarquer que les Aſtres ſont à même hauteur pendant <lb/>une minute, devant ou après leur paſſage par le Méridien, pourvû <lb/>néanmoins que l'Aſtre ne paſſe point par le Zénith ou aux envi-<lb/>rons; </s> <s xml:id="echoid-s7371" xml:space="preserve">mais à ce défaut on obſervera les hauteurs d'un Aſtre à cha-<lb/>que minute, plus ou moins, autour du Méridien, que l'on ſuppoſe <lb/>déja connu, & </s> <s xml:id="echoid-s7372" xml:space="preserve">ſa plus grande ou moindre hauteur, ſera ſa hauteur <lb/>Méridienne que l'on cherche.</s> <s xml:id="echoid-s7373" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7374" xml:space="preserve">Pour ce qui eſt des obſervations qui ſe font hors du Méridien <lb/>dans les cercles verticaux, il faudra connoître la poſition du verti-<lb/>cal, ou la chercher par la méthode ſuivante.</s> <s xml:id="echoid-s7375" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7376" xml:space="preserve">Premierement, le quart de cercle & </s> <s xml:id="echoid-s7377" xml:space="preserve">ſa lunete demeurant dans la <lb/>même ſituation verticale où il étoit quand on a obſervé la hauteur <lb/>de l'Aſtre avec l'heure de ſon paſſage par le point où ſe croiſent les <lb/>fils de l'oculaire, on remarque le tems que le Soleil ou quelque E-<lb/>toile fixe, dont la longitude & </s> <s xml:id="echoid-s7378" xml:space="preserve">latitude ſont connuës, arriveront au <lb/>fil vertical de la lunete, c'eſt-à dire, au cercle vertical qui paroît par <lb/>l'Aſtre & </s> <s xml:id="echoid-s7379" xml:space="preserve">par la ligne de foi au tems de l'obſervation; </s> <s xml:id="echoid-s7380" xml:space="preserve">d'oú l'on con-<lb/>noîtra la poſition dudit cercle vertical, & </s> <s xml:id="echoid-s7381" xml:space="preserve">on trouvera le vrai lieu <lb/>de l'Aſtre obſervé.</s> <s xml:id="echoid-s7382" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7383" xml:space="preserve">Mais ſi le Soleil ou un autre Aſtre ne paſſe point par l'ouverture <lb/>du tuïau, & </s> <s xml:id="echoid-s7384" xml:space="preserve">que d'ailleurs on ait une ligne Meridiene bien tracée <lb/>ſur un terrain bien de niveau dans le lieu de l'obſervation, il faut <lb/>abaiſſer un plomb d'un pignon ou de quelque autre corps ferme & </s> <s xml:id="echoid-s7385" xml:space="preserve"><lb/>immobile, éloigné du quart de cercle de 3 ou 4 toiſes, ſous lequel <lb/>plomb il y ait une pointe de fer en l'allignement du fil, laquelle puiſ-<lb/>ſe mar quer la rencontre du fil perpendiculaire. </s> <s xml:id="echoid-s7386" xml:space="preserve">Pour lors il faut met-<lb/>tre tout près de la lentille objective une platine de cuivre ou de car-<lb/>te, au milieu de laquelle il y ait une petite fente, laquelle étant poſée <lb/>verticalement, paſſe par le centre de la ſigure circulaire de la lentil-<lb/>le, qui nous tient lieu de vrai centre. </s> <s xml:id="echoid-s7387" xml:space="preserve">Cela fait voir diſtinctement le <lb/>fil du perpendicule, lequel ne pouvoit ſe voir auparavant par la lu-<lb/>nete à cauſe de la trop grande proximité. </s> <s xml:id="echoid-s7388" xml:space="preserve">C'eſt pourquoi on remuë-<lb/>ra le perpendicule juſqu'à ce que ſon fil convienne avec le fil verti-<lb/>cal de la lunete; </s> <s xml:id="echoid-s7389" xml:space="preserve">& </s> <s xml:id="echoid-s7390" xml:space="preserve">par ce moyen on marquera ſur le plancher le <lb/> <pb o="238" file="253" n="253" rhead="DE LA MANIERE"/> point où tombera ladite pointe de fer qui cſt ſous le plomb, & </s> <s xml:id="echoid-s7391" xml:space="preserve">ceſe-<lb/>ra un point du plan vertical que l'on cherche. </s> <s xml:id="echoid-s7392" xml:space="preserve">Enſuite on ſuſpendra <lb/>un perpendicule devant le centre de la lentille objective, ou vis-à-vis <lb/>le point où les fils ſe croiſent, & </s> <s xml:id="echoid-s7393" xml:space="preserve">l'on marquera comme ci-devant, <lb/>un point ſur le plancher, lequel ſera auſſi dans le même vertical, <lb/>c'eſt pourquoi ſi par ces 2 points verticaux on tire une ligne droite <lb/>qui rencontre la ligne Méridienne, on aura la poſition du cercle verti-<lb/>cal de l'Aſtre obſervé, par rapport à la ligne Méridiene, dont l'an-<lb/>gle ſe meſurera en prenant des grandeurs connuës ſur chacune de <lb/>ces 2 lignes du point où elles ſe rencontrent, & </s> <s xml:id="echoid-s7394" xml:space="preserve">par leurs extremitez <lb/>tirant une baſe on aura un triangle, dont les trois côtez étant con-<lb/>nus, on trouvera l'angle du ſommet, qui ſera la diſtance dudit <lb/>vertical au Méridien.</s> <s xml:id="echoid-s7395" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div536" type="section" level="1" n="255"> <head xml:id="echoid-head378" xml:space="preserve">Maniere d'obſerver la bauteur Méridienne des Aſtres.</head> <p> <s xml:id="echoid-s7396" xml:space="preserve">IL y a trop de difficulté à bien placer le quart de cercle dans le <lb/>plan du Méridien pour pouvoir exactement trouver la hauteur <lb/>Méridienne d'un Aſtre; </s> <s xml:id="echoid-s7397" xml:space="preserve">car a moins de trouver un lieu & </s> <s xml:id="echoid-s7398" xml:space="preserve">un mur <lb/>commode, où l'on puiſſe attacher fermement le quart Aſtronomi-<lb/>que dans le plan du Méridien, ce qui eſt tres-difficile à faire on n'au-<lb/>ra point la veritable poſition du cercle Méridien propre à obſerver <lb/>tous les Aſtres, comme nous avons dit ci-devant. </s> <s xml:id="echoid-s7399" xml:space="preserve">C'eſt pourquoi il <lb/>ſera beaucoup plus facile, principalement dans les Voïages, de ſe ſer-<lb/>vir d'un quart portatif, par le moyen duquel on obſervera la hau-<lb/>teur de l'Aſtre un peu avant ſon paſſage par le Méridien, à chaque <lb/>minute de tems, ſi l'on peut, juſqu'à ce qu'on trouve ſa plus grande <lb/>ou ſa moindre hauteur ſur l'horiſon. </s> <s xml:id="echoid-s7400" xml:space="preserve">Ainſi quoique l'on n'ait pas <lb/>la veritable poſition du Méridien, on ne laiſſera pas d'avoir la hau-<lb/>teur Méridiene apparente de l'Aſtre.</s> <s xml:id="echoid-s7401" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7402" xml:space="preserve">Quoique cette méthode ſoit ſort bonne & </s> <s xml:id="echoid-s7403" xml:space="preserve">exemte d'erreur ſenſi-<lb/>ble, néanmoins ſi l'Aſtre paſſe par le Méridien proche du Zénith, <lb/>on ne pourra avoir ſa veritable hauteur Méridiene que par hazard, <lb/>par les obſervations repetées de minute en minute, puiſqu'à chaque <lb/>minute d'heure la hauteur augmente environ de 15 min. </s> <s xml:id="echoid-s7404" xml:space="preserve">de degré; <lb/></s> <s xml:id="echoid-s7405" xml:space="preserve">& </s> <s xml:id="echoid-s7406" xml:space="preserve">en ces ſortes d'obſervations, la ſituation incommode de l'obſer-<lb/>vateur, la variation de l'azimut de l'Aſtre, de pluſieurs degrez en <lb/>peu detems, le changement qu'il faut faire à l'inſtrument & </s> <s xml:id="echoid-s7407" xml:space="preserve">la dif-<lb/>ficulté de le bien replacer verticalement, empêchent de faire les ob-<lb/>ſervations plus frequentes que de 4 en 4 minutes d'heures, pen-<lb/>dant lequel tems la difference de hauteur eſt un degré. </s> <s xml:id="echoid-s7408" xml:space="preserve">C'eſt pour-<lb/> <pb o="239" file="254" n="254" rhead="D'OBSERVER LES ASTRES. Liv. VI. Ch. III."/> quoi en ce cas il ſera plus ſur de chercher à connoître d'ailleurs la <lb/>poſition de cercle Méridien, ou le tems précis que l'Aſtre paſſe au <lb/>Méridien, afin de placer l'inſtrument dans le plan dudit Méridien, <lb/>ou de le mouvoir en ſorte que l'on puiſſe obſerver la hauteur de <lb/>l'Aſtre au moment qu'il paſſe par le Méridien.</s> <s xml:id="echoid-s7409" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div537" type="section" level="1" n="256"> <head xml:id="echoid-head379" xml:space="preserve">Des Refractions.</head> <p> <s xml:id="echoid-s7410" xml:space="preserve">AYant obſervé la hauteur Méridiene de deux Etoiles fixes, la-<lb/>quelle ſoit égale ou peu differente, dontl'une ſoit vers le Sep-<lb/>tentrion & </s> <s xml:id="echoid-s7411" xml:space="preserve">l'autre versle Midi, & </s> <s xml:id="echoid-s7412" xml:space="preserve">connoiſſant d'ailleurs leur décli-<lb/>naiſon, trouver la Refraction qui convient au degré de hauteur deſ-<lb/>dites Etoiles fixes, & </s> <s xml:id="echoid-s7413" xml:space="preserve">la vraie hauteur du Pole ou de l'Equateur dans <lb/>le lieu de l'obſervation.</s> <s xml:id="echoid-s7414" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7415" xml:space="preserve">Ayant trouvé par le précepte precedent la hauteur Méridiene <lb/>apparente d'une Etoile aux environs du Pole, ſi on y ajoûte ou que <lb/>l'on en ôte le complément de la déclinaiſon de ladite Etoile, on au-<lb/>ra la hauteur apparente du Pole; </s> <s xml:id="echoid-s7416" xml:space="preserve">on aura auſſi par la même raiſon <lb/>la hauteur apparente de l'Equateur, par le moyen de la hauteur Mé-<lb/>ridiéne d'une Etoile aux environs de l'Equateur, en ajoûtant ou <lb/>ſouſtraïant la déclinaiſon.</s> <s xml:id="echoid-s7417" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7418" xml:space="preserve">Enſuite ayant ajoûté enſemble les hauteurs trouvées de l'Equa-<lb/>teur & </s> <s xml:id="echoid-s7419" xml:space="preserve">du Pole, la ſomme en ſera toûjours plus grande qu'un quart <lb/>de cercle; </s> <s xml:id="echoid-s7420" xml:space="preserve">mais en ôtant 90 deg. </s> <s xml:id="echoid-s7421" xml:space="preserve">de cette ſomme, le reſte ſera double <lb/>de la Refraction de l'une & </s> <s xml:id="echoid-s7422" xml:space="preserve">l'autre Etoile obſervée à même hauteur; <lb/></s> <s xml:id="echoid-s7423" xml:space="preserve">c'eſt pourquoi ôtant cette Refraction de ladite hauteur apparente <lb/>du Pole ou de l'Equateur, on aura leur vraie hauteur.</s> <s xml:id="echoid-s7424" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div538" type="section" level="1" n="257"> <head xml:id="echoid-head380" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s7425" xml:space="preserve">La hauteur Méridiene obſervée d'une Etoile au-deſſous du Pole <lb/>borealſoit de 30d. </s> <s xml:id="echoid-s7426" xml:space="preserve">15 m. </s> <s xml:id="echoid-s7427" xml:space="preserve">& </s> <s xml:id="echoid-s7428" xml:space="preserve">le complément de la déclinaiſon de cet-<lb/>te Etoile ſoit de 5 deg. </s> <s xml:id="echoid-s7429" xml:space="preserve">donc la hauteur apparente du Pole ſera de 35 <lb/>d. </s> <s xml:id="echoid-s7430" xml:space="preserve">15 m. </s> <s xml:id="echoid-s7431" xml:space="preserve">Semblablement ſoit la hauteur Méridiene apparente, d'u-<lb/>ne autre Etoile obſervée aux environs de l'Equateur de 30 d. </s> <s xml:id="echoid-s7432" xml:space="preserve">40 <lb/>m. </s> <s xml:id="echoid-s7433" xml:space="preserve">& </s> <s xml:id="echoid-s7434" xml:space="preserve">ſa déclinaiſon méridionale de 24 d. </s> <s xml:id="echoid-s7435" xml:space="preserve">9 m. </s> <s xml:id="echoid-s7436" xml:space="preserve">d'où l'on connoîtra <lb/>la hauteur apparente de l'Equateur de 54 d. </s> <s xml:id="echoid-s7437" xml:space="preserve">49 m. </s> <s xml:id="echoid-s7438" xml:space="preserve">C'eſt pourquoi <lb/>la ſomme des hauteurs trouvées du Pole & </s> <s xml:id="echoid-s7439" xml:space="preserve">de l'Equateur ſera de <lb/>90 d. </s> <s xml:id="echoid-s7440" xml:space="preserve">4 m. </s> <s xml:id="echoid-s7441" xml:space="preserve">dont ayant ôté 90 d. </s> <s xml:id="echoid-s7442" xml:space="preserve">reſtera 4 m. </s> <s xml:id="echoid-s7443" xml:space="preserve">qui ſera le double de <lb/>la Refraction à la hauteur de 30 d. </s> <s xml:id="echoid-s7444" xml:space="preserve">28 m. </s> <s xml:id="echoid-s7445" xml:space="preserve">qui eſt eſt environ le milieu <lb/>entre les hauteurs trouvées; </s> <s xml:id="echoid-s7446" xml:space="preserve">c'eſt pourquoi à la hauteur de 30 d. </s> <s xml:id="echoid-s7447" xml:space="preserve">15 <lb/>m. </s> <s xml:id="echoid-s7448" xml:space="preserve">la Refraction ſera un peu plus de 2 m. </s> <s xml:id="echoid-s7449" xml:space="preserve">comme de 2 m. </s> <s xml:id="echoid-s7450" xml:space="preserve">1 ſecon-<lb/>de, & </s> <s xml:id="echoid-s7451" xml:space="preserve">à la hauteur de 30 d. </s> <s xml:id="echoid-s7452" xml:space="preserve">40 m. </s> <s xml:id="echoid-s7453" xml:space="preserve">la Refractionfera d'une minute <lb/>59 ſecondes.</s> <s xml:id="echoid-s7454" xml:space="preserve"/> </p> <pb o="240" file="255" n="255" rhead="DE LA MANIERE"/> <p> <s xml:id="echoid-s7455" xml:space="preserve">Enfin ſion ôte 2m. </s> <s xml:id="echoid-s7456" xml:space="preserve">une ſeconde de la hauteur apparente du Po-<lb/>le trouvée 35. </s> <s xml:id="echoid-s7457" xml:space="preserve">d. </s> <s xml:id="echoid-s7458" xml:space="preserve">15. </s> <s xml:id="echoid-s7459" xml:space="preserve">m. </s> <s xml:id="echoid-s7460" xml:space="preserve">reſtera la vraie hauteur du Pole 35. </s> <s xml:id="echoid-s7461" xml:space="preserve">d. </s> <s xml:id="echoid-s7462" xml:space="preserve">12. </s> <s xml:id="echoid-s7463" xml:space="preserve">m. <lb/></s> <s xml:id="echoid-s7464" xml:space="preserve">59 ſecondes, & </s> <s xml:id="echoid-s7465" xml:space="preserve">par la même raiſon la vraie hauteur de l'Equateur <lb/>ſera de 54 d. </s> <s xml:id="echoid-s7466" xml:space="preserve">47 m. </s> <s xml:id="echoid-s7467" xml:space="preserve">une ſeconde, qui eſt le complément de la hau-<lb/>teur du Pole.</s> <s xml:id="echoid-s7468" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7469" xml:space="preserve">Il faut remarquer que la Refraction & </s> <s xml:id="echoid-s7470" xml:space="preserve">la hauteur trouvée par <lb/>cette méthode ſera d'autant plus exacte que la hauteur des Aſtres <lb/>ſera grande; </s> <s xml:id="echoid-s7471" xml:space="preserve">car encore bien que la difference des hauteurs de cha-<lb/>que Etoile fût de 2 d. </s> <s xml:id="echoid-s7472" xml:space="preserve">cela n'empêcheroit pas d'avoir la refraction <lb/>& </s> <s xml:id="echoid-s7473" xml:space="preserve">la vraie hauteur du Pole, puiſqu'au-deſſus du 30<emph style="sub">me</emph> deg. </s> <s xml:id="echoid-s7474" xml:space="preserve">de hau-<lb/>teur, la difference de refraction entre 2 deg. </s> <s xml:id="echoid-s7475" xml:space="preserve">n'eſt point ſenſible.</s> <s xml:id="echoid-s7476" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div539" type="section" level="1" n="258"> <head xml:id="echoid-head381" xml:space="preserve">Autre métbode pour obſerver les Refractions.</head> <p> <s xml:id="echoid-s7477" xml:space="preserve">L'On peut encore reconnoître la quantité de la Refraction par <lb/>l'obſervation d'une même Etoile, dont la hauteur Méridiene <lb/>ſoit de 90 deg. </s> <s xml:id="echoid-s7478" xml:space="preserve">ou un peu moindre; </s> <s xml:id="echoid-s7479" xml:space="preserve">car connoiſſant d'ailleurs la <lb/>hauteur du Pole ou de l'Equateur dans le lieu de l'obſervation, par <lb/>la hauteur Méridiene de l'Etoile, on connoîtra ſa vraie déclinaiſon, <lb/>puiſque les Refractions ſont inſenſibles proche du Zénith.</s> <s xml:id="echoid-s7480" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7481" xml:space="preserve">Mais ſi à chaque degré de hauteur de l'Etoile on obſerve le tems <lb/>marqué par une pendule exacte, comme auſſi le tems de ſon paſſa-<lb/>ge par le Méridien que l'on connoitra par les hauteurs égales de la-<lb/>dite Etoile vers l'Orient & </s> <s xml:id="echoid-s7482" xml:space="preserve">vers l'Occident, nous aurons dans un <lb/>triangle ſpherique 3 choſes connuës; </s> <s xml:id="echoid-s7483" xml:space="preserve">à ſçavoir, l'arc de la diſtance <lb/>entre le Pole & </s> <s xml:id="echoid-s7484" xml:space="preserve">le Zénith, le complément de la déclinaiſon de l'E-<lb/>toile, & </s> <s xml:id="echoid-s7485" xml:space="preserve">l'angle compris par ces arcs; </s> <s xml:id="echoid-s7486" xml:space="preserve">ſçavoir, la difference du tems <lb/>moyen entre le paſſage de l'Etoile par le Méridien & </s> <s xml:id="echoid-s7487" xml:space="preserve">ſon lieu, pour <lb/>lequel ſe fait le calcul, convertie en degrez & </s> <s xml:id="echoid-s7488" xml:space="preserve">minutes; </s> <s xml:id="echoid-s7489" xml:space="preserve">à quoi il faut <lb/>ajoûter la partie proportionnelle convenable du moyen mouve-<lb/>ment du Soleil à raiſon de 59 m. </s> <s xml:id="echoid-s7490" xml:space="preserve">8 ſec. </s> <s xml:id="echoid-s7491" xml:space="preserve">par jour; </s> <s xml:id="echoid-s7492" xml:space="preserve">c'eſt pourquoi on <lb/>trouvera le vrai arc du vertical entre le Zénith & </s> <s xml:id="echoid-s7493" xml:space="preserve">le vrai lieu de <lb/>l'Etoile.</s> <s xml:id="echoid-s7494" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7495" xml:space="preserve">Mais par l'obſervation on a l'arc apparent de la hauteur de ladi-<lb/>te Etoile; </s> <s xml:id="echoid-s7496" xml:space="preserve">& </s> <s xml:id="echoid-s7497" xml:space="preserve">la difference de ces arcs ſera la quantité de la Refrac-<lb/>tion à la hauteur de l'Etoile. </s> <s xml:id="echoid-s7498" xml:space="preserve">Par uu ſemblable calcul on aura la <lb/>Refraction de chaque degré de hauteur.</s> <s xml:id="echoid-s7499" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7500" xml:space="preserve">On peut faire le même par le moyen du Soleil ou de quelque E-<lb/>toile que ce ſoit, pourvû que l'on connoiſſe ſa déclinaiſon, afin <lb/>qu'au tems de l'obſervation on puiſſe trouver la vraie diſtance du <lb/>Soleil ou de l'Etoile au Zénith.</s> <s xml:id="echoid-s7501" xml:space="preserve"/> </p> <pb o="241" file="256" n="256" rhead="D'OBSERVER LES ASTRES. Liv. VI. Ch. III."/> <p> <s xml:id="echoid-s7502" xml:space="preserve">Ayant connu la Refraction des Aſtres il ſera facile de trouver la <lb/>hauteur du Pole: </s> <s xml:id="echoid-s7503" xml:space="preserve">car ayant obſervé la hauteur Méridiene de l'Etoi-<lb/>le polaire, tant au-deſſus qu'au-deſſous du Pole, le même jour, à <lb/>peu de diſtance l'un de l'autre, ayant diminué de chaque hauteur la <lb/>Refraction convenable, la moitié de la difference des hauteurs cor-<lb/>rigées, ajoûtée à la moindre hauteur corrigée, ou ſouſtraite de la <lb/>plus grande auſſi corrigée, on aura la vraie hauteur du Pole.</s> <s xml:id="echoid-s7504" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7505" xml:space="preserve">M. </s> <s xml:id="echoid-s7506" xml:space="preserve">de la Hire a obſervé avec grand ſoin pendant pluſieurs an-<lb/>nées la hauteur Méridienne des Etoiles fixes, & </s> <s xml:id="echoid-s7507" xml:space="preserve">principalement de <lb/>Sirius & </s> <s xml:id="echoid-s7508" xml:space="preserve">de la Claire de la Lyre avec des Quarts de cercles Aſtrono-<lb/>miques très-bien diviſez & </s> <s xml:id="echoid-s7509" xml:space="preserve">des Lunetes tres-excellentes à differen-<lb/>tes heures du jour & </s> <s xml:id="echoid-s7510" xml:space="preserve">de la nuit, & </s> <s xml:id="echoid-s7511" xml:space="preserve">même pendant le milieu du jour, <lb/>& </s> <s xml:id="echoid-s7512" xml:space="preserve">en differentes ſaiſons de l'année. </s> <s xml:id="echoid-s7513" xml:space="preserve">Il aſſûre n'avoir remarqué au-<lb/>cune difference dans les hauteurs deſdites Etoiles, que celle qui pro-<lb/>vient de leur mouvement propre.</s> <s xml:id="echoid-s7514" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7515" xml:space="preserve">Et comme l'Etoile de Sirius monte environ juſqu'au 26<emph style="sub">me</emph> degré <lb/>du Méridien, on pourroit douter ſi dans les moindres hauteurs les <lb/>Reſractions d'Hyver ſeroient plus grandes que celles d'Eté; </s> <s xml:id="echoid-s7516" xml:space="preserve">c'eſt <lb/>pourquoi il a auſſi obſervé avec ſeu M. </s> <s xml:id="echoid-s7517" xml:space="preserve">Picard les hauteurs Méri-<lb/>dienes de l'Etoile nommée Capella, dans ſa moindre hauteur Méri-<lb/>diene, qui eſt environ de 4 degrez & </s> <s xml:id="echoid-s7518" xml:space="preserve">demi en pluſieurs differentes <lb/>ſaiſons de l'année.</s> <s xml:id="echoid-s7519" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7520" xml:space="preserve">Ayant comparé enſemble les diverſes obſervations & </s> <s xml:id="echoid-s7521" xml:space="preserve">fait les ré-<lb/>ductions néceſſaires à cauſe du mouvement propre de cette Etoile, <lb/>à peine a-t-il trouvé une minute de difference, laquelle pouvoit <lb/>provenir d'une autre cauſe que des Refractions. </s> <s xml:id="echoid-s7522" xml:space="preserve">C'eſt pourquoi il <lb/>n'a conſtruit qu'une ſeule table de Refraction du Soleil, de la Lune <lb/>& </s> <s xml:id="echoid-s7523" xml:space="preserve">des autres Aſtres pour toutes les ſaiſons de l'année, conformé-<lb/>ment aux obſervations qu'il en a faites.</s> <s xml:id="echoid-s7524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7525" xml:space="preserve">Cependant on peut croire que les Refractions ſont ſujetes à di-<lb/>verſes inconſtances autour de l'horiſon, ſelon la differente conſtitu-<lb/>tion de l'air & </s> <s xml:id="echoid-s7526" xml:space="preserve">la nature du terrain haut ou bas, comme M. </s> <s xml:id="echoid-s7527" xml:space="preserve">de la <lb/>Hire l'a ſouvent experimenté; </s> <s xml:id="echoid-s7528" xml:space="preserve">car obſervant au pied des Monta-<lb/>gnes la hauteur des Aſtres qui ſembloient en raſer le ſommet, elles <lb/>lui ont paru un peu plus hautes que s'il les avoit obſervées du ſom-<lb/>met même; </s> <s xml:id="echoid-s7529" xml:space="preserve">maîs ſi on veut ajoûtér foi aux obſervations des autres, <lb/>les Refractions ſont plus grandes, même en Eté dans les Païs Sep-<lb/>tentrionaux que dans les Zones temperées.</s> <s xml:id="echoid-s7530" xml:space="preserve"/> </p> <pb o="242" file="257" n="257" rhead="DE LA MANIERE"/> </div> <div xml:id="echoid-div540" type="section" level="1" n="259"> <head xml:id="echoid-head382" xml:space="preserve">Maniere de trouver par obſervation le tems de l'Equinoxe <lb/>& du Solſtice.</head> <p> <s xml:id="echoid-s7531" xml:space="preserve">AYant connu la hauteur de l'Equateur, la Refraction & </s> <s xml:id="echoid-s7532" xml:space="preserve">la pa-<lb/>rallaxe du Soleil à une même hauteur, il ne ſera pas difficile <lb/>de trouver le tems que le centre du Soleil ſera dans l'Equateur; </s> <s xml:id="echoid-s7533" xml:space="preserve">car <lb/>ſi de la hauteur Méridiene apparente du centre du Soleil, le jour <lb/>même qu'arrive l'Equinoxe, on ôte la Refraction convenable, & </s> <s xml:id="echoid-s7534" xml:space="preserve"><lb/>qu'on y ajoûte la parallaxe, reſtera la vraie hauteur Méridiene du <lb/>centre du Soleil. </s> <s xml:id="echoid-s7535" xml:space="preserve">Or la difference de cette hauteur & </s> <s xml:id="echoid-s7536" xml:space="preserve">de celle de l'E-<lb/>quateur, marquera le tems du vrai Equinoxe de vant ou après midi, <lb/>& </s> <s xml:id="echoid-s7537" xml:space="preserve">ſi l'on diviſe par 59 la ſomme des ſecondes de cette difference <lb/>trouvée, le quotien marquera les heures & </s> <s xml:id="echoid-s7538" xml:space="preserve">les fractions d'heures <lb/>qu'il faut ajoûter ou ſouſtraire du vrai midi pour avoir le tems du <lb/>vrai Equinoxe.</s> <s xml:id="echoid-s7539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7540" xml:space="preserve">Les heures du quotien s'ajoûtent au tems du midi ſi la hauteur <lb/>Méridienne du Soleil s'eſt trouvée moindre que celle de l'Equateur <lb/>vers l'Equinoxe du Printems, mais on les en ſouſtrait ſi eile s'eſt trou-<lb/>vée plus grande. </s> <s xml:id="echoid-s7541" xml:space="preserve">Il faut faire le contraire vers l'Equinoxe d'Automne.</s> <s xml:id="echoid-s7542" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div541" type="section" level="1" n="260"> <head xml:id="echoid-head383" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s7543" xml:space="preserve">Etant donnée la vraie hauteur de l'Equateur 41 d. </s> <s xml:id="echoid-s7544" xml:space="preserve">10 m. </s> <s xml:id="echoid-s7545" xml:space="preserve">& </s> <s xml:id="echoid-s7546" xml:space="preserve">ayant <lb/>obſervé la vraie hauteur Méridiene du centre du Soleil 41 d. </s> <s xml:id="echoid-s7547" xml:space="preserve">5 m. <lb/></s> <s xml:id="echoid-s7548" xml:space="preserve">15 ſec. </s> <s xml:id="echoid-s7549" xml:space="preserve">laquelle ſe connoît par la hauteur apparente du bord ſupé-<lb/>rieur ou inférieur du Soleil corrigée par ſon demi-diamette, refrac-<lb/>tion & </s> <s xml:id="echoid-s7550" xml:space="preserve">parallaxe, la difference ſera de 4 m. </s> <s xml:id="echoid-s7551" xml:space="preserve">45 ſec. </s> <s xml:id="echoid-s7552" xml:space="preserve">ou 285 ſec. </s> <s xml:id="echoid-s7553" xml:space="preserve">le-<lb/>quel nombre étant diviſé par 59, le quotien ſera 4{49/59} c'eſt-à dire, <lb/>4 heures 48 m. </s> <s xml:id="echoid-s7554" xml:space="preserve">qu'il faut ajoûter à midi, ſi le Soleil eſt en l'Equino-<lb/>xe du Printems, & </s> <s xml:id="echoid-s7555" xml:space="preserve">par conſequent l'Equinoxe arrivera à 4 h. </s> <s xml:id="echoid-s7556" xml:space="preserve">48 <lb/>m. </s> <s xml:id="echoid-s7557" xml:space="preserve">après midi. </s> <s xml:id="echoid-s7558" xml:space="preserve">Mais ſi le Soleil étoit en l'Equinoxe d'Automne, ledit <lb/>Equinoxe ſeroit arrivé 4 heures 48 m. </s> <s xml:id="echoid-s7559" xml:space="preserve">avant midi, c'eſt-à dire à 7 <lb/>heures 12 minutes du matin.</s> <s xml:id="echoid-s7560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7561" xml:space="preserve">A l'égard des Solſtices, il y a bien plus de difficulté à les détermi-<lb/>ner que les Equinoxes, car il ne ſuffit pas d'une ſeule obſervation, <lb/>parce qu'en ces tems la difference entre les hauteurs Méridienes <lb/>d'un jour à l'autre eſt preſque imperceptible. </s> <s xml:id="echoid-s7562" xml:space="preserve">Il faudra donc pren-<lb/>dre exactement la hauteur Méridiene du Soleil, 12 ou 15 jours avant <lb/>le Solſtice, & </s> <s xml:id="echoid-s7563" xml:space="preserve">autant de tems après, tâcher de retrouver à peu près <lb/>la même hauteur Méridiene du Soleil, afin que par les parties pro-<lb/>portionelles du changement de hauteur Méridiene du Soleil, on <lb/>puiſſe exactement déterminer le tems que le Soleil s'eſt trouvé à <lb/> <pb o="243" file="258" n="258" rhead="D'OBSERVER LES ASTRES. Liv. VI. Chap. III."/> même hauteur, devant & </s> <s xml:id="echoid-s7564" xml:space="preserve">après le Solſtice, étant dans le même <lb/>cercle parallele à l'Equateur.</s> <s xml:id="echoid-s7565" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7566" xml:space="preserve">Ayant donc connu le tems écoulé entre l'une & </s> <s xml:id="echoid-s7567" xml:space="preserve">l'autre ſituation <lb/>du Soleil, il en faut prendre le milieu, & </s> <s xml:id="echoid-s7568" xml:space="preserve">chercher dans les Tables le <lb/>vrai lieu du Soleil qui convient à ces trois tems. </s> <s xml:id="echoid-s7569" xml:space="preserve">Le milieu de la dif-<lb/>ference des lieux extrêmes du Soleil s'ajoûtera au moindre, afin d'en <lb/>faire un lieu moyen par la comparaiſon des extrêmes; </s> <s xml:id="echoid-s7570" xml:space="preserve">mais ſi le lieu <lb/>moyen trouvé par le calcul ne convient pas au lieu moyen trouvé <lb/>par ladite comparaiſon, il faut en prendre la difference & </s> <s xml:id="echoid-s7571" xml:space="preserve">ajoûter au <lb/>tems moyen le tems qui répond à cette difference, ſi le tems moyen <lb/>trouvé par le calcul eſt le plus petit, & </s> <s xml:id="echoid-s7572" xml:space="preserve">au contraire le ſouſtraire s'il <lb/>eſt plus grand, afin d'avoir le tems du Solſtice.</s> <s xml:id="echoid-s7573" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div542" type="section" level="1" n="261"> <head xml:id="echoid-head384" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s7574" xml:space="preserve">Le dixiéme jour du mois de Juin la hauteur Méridienc apparen-<lb/>te du Soleil a été trouvée dans l'Obſervatoire Roïal de 94d. </s> <s xml:id="echoid-s7575" xml:space="preserve">27 m. <lb/></s> <s xml:id="echoid-s7576" xml:space="preserve">25 ſec. </s> <s xml:id="echoid-s7577" xml:space="preserve">& </s> <s xml:id="echoid-s7578" xml:space="preserve">le 3<emph style="sub">me</emph> jour de Juillet enſuite, ladite hauteur Méridiene <lb/>apparente s'eſt trouvée de 64d. </s> <s xml:id="echoid-s7579" xml:space="preserve">28 m. </s> <s xml:id="echoid-s7580" xml:space="preserve">15 ſec. </s> <s xml:id="echoid-s7581" xml:space="preserve">d'où l'on connoît <lb/>par la difference de déclinaiſon en ce tems, que le Soleil eſt arrivéau <lb/>parallele de la premiere obſervation le 3<emph style="sub">me</emph> jour de Juillet à 4 h. </s> <s xml:id="echoid-s7582" xml:space="preserve">12 <lb/>min. </s> <s xml:id="echoid-s7583" xml:space="preserve">& </s> <s xml:id="echoid-s7584" xml:space="preserve">par conſequent le tems moyen entre les obſervations ſera <lb/>le 22 Juin à 2 h. </s> <s xml:id="echoid-s7585" xml:space="preserve">& </s> <s xml:id="echoid-s7586" xml:space="preserve">6 m. </s> <s xml:id="echoid-s7587" xml:space="preserve">du matin.</s> <s xml:id="echoid-s7588" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7589" xml:space="preserve">Or par les Tables, le vrai lieu du Soleil au tems de la premiere <lb/>obſervation eſt 2 ſignes, 58 m. </s> <s xml:id="echoid-s7590" xml:space="preserve">23 ſec. </s> <s xml:id="echoid-s7591" xml:space="preserve">& </s> <s xml:id="echoid-s7592" xml:space="preserve">au tems de la dernie-<lb/>re il eſt 3 ſig 11 d. </s> <s xml:id="echoid-s7593" xml:space="preserve">4 m. </s> <s xml:id="echoid-s7594" xml:space="preserve">52 ſec. </s> <s xml:id="echoid-s7595" xml:space="preserve">& </s> <s xml:id="echoid-s7596" xml:space="preserve">au milieu il eſt 3 ſig. </s> <s xml:id="echoid-s7597" xml:space="preserve">od. </s> <s xml:id="echoid-s7598" xml:space="preserve">1 m. </s> <s xml:id="echoid-s7599" xml:space="preserve">56 ſec.</s> <s xml:id="echoid-s7600" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7601" xml:space="preserve">Mais la difference des lieux extrêmes eſt 22 d. </s> <s xml:id="echoid-s7602" xml:space="preserve">6 m. </s> <s xml:id="echoid-s7603" xml:space="preserve">29 ſec. </s> <s xml:id="echoid-s7604" xml:space="preserve">dont <lb/>la moitié eſt 11 d. </s> <s xml:id="echoid-s7605" xml:space="preserve">3 m. </s> <s xml:id="echoid-s7606" xml:space="preserve">15 ſec. </s> <s xml:id="echoid-s7607" xml:space="preserve">leſquels ajoûtez au moindre lieu font <lb/>3 ſig. </s> <s xml:id="echoid-s7608" xml:space="preserve">od. </s> <s xml:id="echoid-s7609" xml:space="preserve">1 m. </s> <s xml:id="echoid-s7610" xml:space="preserve">38 ſec. </s> <s xml:id="echoid-s7611" xml:space="preserve">lequel eſt le lieu moyen par la comparaiſon <lb/>des extrêmes.</s> <s xml:id="echoid-s7612" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7613" xml:space="preserve">Entre le lieu moyen par le calcul 3 ſig. </s> <s xml:id="echoid-s7614" xml:space="preserve">o d. </s> <s xml:id="echoid-s7615" xml:space="preserve">1 m. </s> <s xml:id="echoid-s7616" xml:space="preserve">56 ſec. </s> <s xml:id="echoid-s7617" xml:space="preserve">& </s> <s xml:id="echoid-s7618" xml:space="preserve">le lieu <lb/>moyen par comparaiſon, la difference eſt 18 ſec. </s> <s xml:id="echoid-s7619" xml:space="preserve">qui correſpondent <lb/>à 7 m. </s> <s xml:id="echoid-s7620" xml:space="preserve">18 ſec. </s> <s xml:id="echoid-s7621" xml:space="preserve">de tems qu'il faut ôter du tems moyen, parce que le <lb/>lieu moyen par le calcul eſt plus grand que le lieu moyen par com-<lb/>paraiſon. </s> <s xml:id="echoid-s7622" xml:space="preserve">C'eſt pourquoi le tems du Solſtice ſera le 22 Juin à une <lb/>heure 58 min. </s> <s xml:id="echoid-s7623" xml:space="preserve">18 ſec. </s> <s xml:id="echoid-s7624" xml:space="preserve">du matin. </s> <s xml:id="echoid-s7625" xml:space="preserve">Ce qui peut ſe confirmer par plu-<lb/>ſieurs autres obſervations.</s> <s xml:id="echoid-s7626" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7627" xml:space="preserve">Il eſt à remarquer que l'erreur de peu de ſecondes, plus ou moins <lb/>dans la hauteur du Soleil obſervée, peut éloigner d'une heure le Sol-<lb/>ſtice de ſon vrai tems, comme en l'exemple propoſé 10 ſec. </s> <s xml:id="echoid-s7628" xml:space="preserve">de hau-<lb/>teur ou environ répondent à une heure detems; </s> <s xml:id="echoid-s7629" xml:space="preserve">c'eſt pourquoi cela <lb/>ne ſe peut faire qu'avec des Inſtrumens bien diviſez & </s> <s xml:id="echoid-s7630" xml:space="preserve">pluſieurs ob-<lb/>ſervations très-exactes.</s> <s xml:id="echoid-s7631" xml:space="preserve"/> </p> <pb o="244" file="259" n="259" rhead="DE LA MANIERE"/> </div> <div xml:id="echoid-div543" type="section" level="1" n="262"> <head xml:id="echoid-head385" xml:space="preserve">Obſervations faites dans l'Obſervatoire Roïal aux environs <lb/>des Solſtices pour avoir la bauteur du Pole de Paris dans <lb/>l'Obſervatoire, & de la plus grande déclinaiſon du Soleil <lb/>ou obliquité de l'Ecliptique.</head> <p> <s xml:id="echoid-s7632" xml:space="preserve">AU Solſtice d'Eté la hauteur Méridiene apparente du bord ſu-<lb/>périeur du Soleil, recueillie de pluſieurs Obſervations, s'eſt</s> </p> <note position="right" xml:space="preserve"> <lb/>trouvée de # 64d. # 55 m. # 24 ſec. <lb/>Refraction à ſouſtraire # # # 33 <lb/>Parallaxe à ajoûter # # # 1 <lb/>Vraie hauteur du bord ſupérieur # 64 # 54 # 52 <lb/>Demi-diametre du Soleil # # 15 # 49 <lb/>Vraie hauteur Méridiene du centre # 64 # 39 # 3 <lb/></note> <p> <s xml:id="echoid-s7633" xml:space="preserve">Au Solſtice d'Hyver, la hauteur Méridiene apparente du bord</s> </p> <note position="right" xml:space="preserve"> <lb/>ſupérieur du Soleil # 18d. # o m. # 24 ſec. <lb/>Refraction à ſouſtraire # # 3 # 12 <lb/>Parallaxe à ajoûter # # # 5 <lb/>Vraie hauteur du bord ſupérieur # 17 # 57 # 17 <lb/>Demi-diametre du Soleil # # 16 # 21 <lb/>Vraie hauteur Méridiene du centre # 17 # 40 # 56 <lb/>Donc la vraie diſtance des Tropiques eſt # 46 d. # 58 m. # 7 ſec. <lb/>La moitié qui eſt la plus grande déclinaiſ. du Sol. # 23 # 29 # 3{1/2} <lb/>La hauteur de l'Equateur à l'Obſervatoire, # 41 # 9 # 59{1/2} <lb/>Son complément qui eſt la hauteur du Pole, # 48 # 50 # 0 <lb/></note> </div> <div xml:id="echoid-div544" type="section" level="1" n="263"> <head xml:id="echoid-head386" xml:space="preserve">Obſervations de l'Etoile Polaire.</head> <p> <s xml:id="echoid-s7634" xml:space="preserve">PAr diverſes obſervations de la plus grande & </s> <s xml:id="echoid-s7635" xml:space="preserve">de la moindre <lb/>hauteur Méridiene apparente de l'Etoile polaire, qui eſt à l'ex-<lb/>trémité de la queuë de la petite Ourſe, on conclut la hauteur appa-<lb/>rente du Pole, comme l'a marqué M. </s> <s xml:id="echoid-s7636" xml:space="preserve">Picard dans ſon Livre de la <lb/>Meſure de la Terre, entre les Portes de S. </s> <s xml:id="echoid-s7637" xml:space="preserve">Jacques & </s> <s xml:id="echoid-s7638" xml:space="preserve">de S. </s> <s xml:id="echoid-s7639" xml:space="preserve">Martin, <lb/>aux en virons de S. </s> <s xml:id="echoid-s7640" xml:space="preserve">Jacques de la Boucherie, 48 d. </s> <s xml:id="echoid-s7641" xml:space="preserve">52 m. </s> <s xml:id="echoid-s7642" xml:space="preserve">20 ſec.</s> <s xml:id="echoid-s7643" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7644" xml:space="preserve">La réduction étant faite ſelon la diſtance des lieux, la hau-<lb/>teur Méridiene apparente du Pole à l'Obſervatoire Roïal, ſera</s> </p> <note position="right" xml:space="preserve"> <lb/>de # 48 # 51 # 2 <lb/>La Refraction qni convient à cette hauteur # # 1 # 4 <lb/>Donc la vraie hauteur du Pole à l'Obſervatoire # 48 # 49 # 58 <lb/>Pour laquelle nous prenons, # 48 # 50 # 0 <lb/>Et par conſequent la hauteur de l'Equateur, # 41 # 10 # 0 <lb/></note> <pb o="245" file="260" n="260" rhead="D'OBSERVER LES ASTRES. Liv. VI. Ch. III."/> </div> <div xml:id="echoid-div545" type="section" level="1" n="264"> <head xml:id="echoid-head387" style="it" xml:space="preserve">Connoiſſant l'beure ou le tems vrai ou apparent qu'une Etoile <lb/>fixe ou une Planete paſſe par le Cercle Meridien, trouver <lb/>la difference d'aſcenſion droite entre l'Etoile fixe ou la Pla-<lb/>nete & le Soleil.</head> <p> <s xml:id="echoid-s7645" xml:space="preserve">IL faut convertir en degrez de l'Equateur le tems donné dépuis <lb/>midi juſqu'au paſſage de l'Etoile fixe ou de la Planete, ou bien <lb/>le tems depuis leur paſſage juſqu'a midi, & </s> <s xml:id="echoid-s7646" xml:space="preserve">l'on aura ce que l'on <lb/>cherche.</s> <s xml:id="echoid-s7647" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div546" type="section" level="1" n="265"> <head xml:id="echoid-head388" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s7648" xml:space="preserve">La Planete de Jupiter a paſſé par le Méridien à 10 h. </s> <s xml:id="echoid-s7649" xml:space="preserve">du matin, <lb/>23 m. </s> <s xml:id="echoid-s7650" xml:space="preserve">& </s> <s xml:id="echoid-s7651" xml:space="preserve">15 ſec. </s> <s xml:id="echoid-s7652" xml:space="preserve">dont la diſtance juſqu'à midi, qui eſt 1 h. </s> <s xml:id="echoid-s7653" xml:space="preserve">46 m. </s> <s xml:id="echoid-s7654" xml:space="preserve">45 <lb/>ſec. </s> <s xml:id="echoid-s7655" xml:space="preserve">étant convertie en degrez de l'Equateur, nous aurons 24 d. </s> <s xml:id="echoid-s7656" xml:space="preserve">11 <lb/>m. </s> <s xml:id="echoid-s7657" xml:space="preserve">15 ſec. </s> <s xml:id="echoid-s7658" xml:space="preserve">pour la difference d'aſcenſion droite entre le Soleil & </s> <s xml:id="echoid-s7659" xml:space="preserve">Ju-<lb/>piter, au moment que le centre de Jupiter a paſſé par le Méridien.</s> <s xml:id="echoid-s7660" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7661" xml:space="preserve">Dans ce problême & </s> <s xml:id="echoid-s7662" xml:space="preserve">le ſuivant nous propoſons le tems vrai ou <lb/>apparent, & </s> <s xml:id="echoid-s7663" xml:space="preserve">non pas le tems moyen; </s> <s xml:id="echoid-s7664" xml:space="preserve">parce que le tems vrai eſt plus <lb/>aiſé à connoître par les obſervations du Soleil, que le tems moyen. <lb/></s> <s xml:id="echoid-s7665" xml:space="preserve">Nous expliquerons ce que c'eſt que le tems moyen auſſi-bien que le <lb/>tems vrai ou apparent, dans le 4<emph style="sub">me</emph> Chapitre de ce Livre, en parlant <lb/>de la Machine pour les Eclipſes.</s> <s xml:id="echoid-s7666" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div547" type="section" level="1" n="266"> <head xml:id="echoid-head389" style="it" xml:space="preserve">Connoiſſant le tems vrai entre le paſſage de deux Etoiles fixes <lb/>par le Méridien, ou bien d'une Etoile fixe & d'une Pla-<lb/>nete, trouver leur difference d'aſcenſion droite.</head> <p> <s xml:id="echoid-s7667" xml:space="preserve">IL faut convertir en degrez de l'Equateur le tems donné entre <lb/>leurs paſſages, & </s> <s xml:id="echoid-s7668" xml:space="preserve">y ajoûtez l'aſcenſion droite du vrai mouvement <lb/>du Soleil qui convient à ce tems; </s> <s xml:id="echoid-s7669" xml:space="preserve">la ſomme ſera la difference que <lb/>l'on cherche.</s> <s xml:id="echoid-s7670" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div548" type="section" level="1" n="267"> <head xml:id="echoid-head390" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s7671" xml:space="preserve">Entre les paſſages par le Méridien de l'Etoile du Grand-Chien <lb/>nommé Sirius, & </s> <s xml:id="echoid-s7672" xml:space="preserve">du cœur du Lion nommé Regulus, il s'eſt écoulé 3 <lb/>h. </s> <s xml:id="echoid-s7673" xml:space="preserve">20 m. </s> <s xml:id="echoid-s7674" xml:space="preserve">o ſec. </s> <s xml:id="echoid-s7675" xml:space="preserve">de tems, l aſcenſion droite du vrai mouvement du <lb/>Soleil qui convient à ce tems, ſoit ſuppoſée de 7 m. </s> <s xml:id="echoid-s7676" xml:space="preserve">35 ſec.</s> <s xml:id="echoid-s7677" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7678" xml:space="preserve">C'eſt pourquoi convertiſſant en degrez de l'Equateur leſdites 3 h. <lb/></s> <s xml:id="echoid-s7679" xml:space="preserve">20 m. </s> <s xml:id="echoid-s7680" xml:space="preserve">nous aurons 50 d. </s> <s xml:id="echoid-s7681" xml:space="preserve">auſquels ajoûtant 7 m. </s> <s xml:id="echoid-s7682" xml:space="preserve">35 ſec. </s> <s xml:id="echoid-s7683" xml:space="preserve">la ſomme <lb/>50 d. </s> <s xml:id="echoid-s7684" xml:space="preserve">7 m. </s> <s xml:id="echoid-s7685" xml:space="preserve">35 ſec. </s> <s xml:id="echoid-s7686" xml:space="preserve">ſera la difference d'aſcenſion droite entre Sirius <lb/>& </s> <s xml:id="echoid-s7687" xml:space="preserve">Regulus.</s> <s xml:id="echoid-s7688" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7689" xml:space="preserve">Il en eſt de même d'une Etoile fixe & </s> <s xml:id="echoid-s7690" xml:space="preserve">d'une Planete, ou de deux <lb/>Planetes; </s> <s xml:id="echoid-s7691" xml:space="preserve">cependant il faut remarquer que ſi le mouvement pro-<lb/> <pb o="246" file="261" n="261" rhead="DE LA MANIERE"/> pre de la Planete ou des Planetes eſt conſiderable entre le paſſage <lb/>de l'une & </s> <s xml:id="echoid-s7692" xml:space="preserve">de l'autre par le Méridien, il ſaut y avoir égard.</s> <s xml:id="echoid-s7693" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div549" type="section" level="1" n="268"> <head xml:id="echoid-head391" style="it" xml:space="preserve">Maniere d'obſerver les Eclipſes.</head> <p> <s xml:id="echoid-s7694" xml:space="preserve">ENtre les obſervations des Eclipſes nous avons le commence-<lb/>ment & </s> <s xml:id="echoid-s7695" xml:space="preserve">la fin, l'immerſion totale & </s> <s xml:id="echoid-s7696" xml:space="preserve">l'émerſion qui ſe peuvent <lb/>eſtimer aſſez exactement par les yeux ſeuls, ſans lunetes de longue <lb/>vûë, excepté néanmoins le commencement & </s> <s xml:id="echoid-s7697" xml:space="preserve">la fin des Eclipſes de <lb/>Lune où l'on peut faire erreur d'une minute ou 2, à cauſe qu'il eſt <lb/>difficile de déterminer certainement l'extremité de l'ombre. </s> <s xml:id="echoid-s7698" xml:space="preserve">Mais <lb/>la quantité de l'Eclipſe, c'eſt-à-dire, la portion éclipſée du diſque <lb/>du Soleil & </s> <s xml:id="echoid-s7699" xml:space="preserve">de la Lune, laquelle ſe meſure par doigts ou 12<emph style="sub">me</emph> partie <lb/>de tout le diametre du Soleil & </s> <s xml:id="echoid-s7700" xml:space="preserve">de la Lune, & </s> <s xml:id="echoid-s7701" xml:space="preserve">par minutes ou 60<emph style="sub">me</emph> <lb/>partie deſdits doigts, ne ſe peut bien connoître ſans une lune. <lb/></s> <s xml:id="echoid-s7702" xml:space="preserve">te de longue vûë jointe à quelque inſtrument. </s> <s xml:id="echoid-s7703" xml:space="preserve">Car l'eſtimation que <lb/>l'on en peut faire avec les yeux eſt fort ſujete à erreur, comme il eſt <lb/>aiſé de réconnoître dans l'Hiſtoire des anciennes Eclipſes, quoique <lb/>les obſervations en ayent étéfaites par de très habiles Aſtronomes.</s> <s xml:id="echoid-s7704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7705" xml:space="preserve">Les premiers Aſtronomes qui ſe ſont ſervis de lunetes de longue <lb/>vûë, garnies de 2 verres, ſçavoir, l'objectif convexe & </s> <s xml:id="echoid-s7706" xml:space="preserve">l'oculaire <lb/>concave dans les obſervations des Eclipſes, obſervoient celles de So-<lb/>leil par la méthode ſuivante. </s> <s xml:id="echoid-s7707" xml:space="preserve">On faiſoit un trou aux volets d'une <lb/>chambre bien fermée, on y mettoit le tuiau d'une lunete, comme <lb/>celleque nous venons de décrire; </s> <s xml:id="echoid-s7708" xml:space="preserve">de ſorte que les raïons du Soleil <lb/>paſſant par ladite lunete, étoient reçûs ſur un carton ou tablete blan-<lb/>che, ſur laquelle on avoit premierement décrit un cercle d'une gran-<lb/>deur convenable, avec 5 autres concentriques & </s> <s xml:id="echoid-s7709" xml:space="preserve">également éloi-<lb/>gnez l'un de l'autre. </s> <s xml:id="echoid-s7710" xml:space="preserve">Ces cercles avec le centre partageoient en 12 <lb/>parties égales tout le diametre du cercle extérieur. </s> <s xml:id="echoid-s7711" xml:space="preserve">Ayant doncaju-<lb/>ſté ladite tablete perpendiculaire à la ſituation du tuïau de la lune-<lb/>te, on y voyoit l image lumineuſe du Soleil d'autant plus grande que <lb/>cette tablete étoit éloignée de la lentille oculaire vers la partie inté-<lb/>rieure de la chambre; </s> <s xml:id="echoid-s7712" xml:space="preserve">c'eſt pourquoi en l'approchant ou reculant <lb/>dudit tuiau, on cherchoit le lieu où l'image du Soleil paroiſſoit exa-<lb/>ctement égale à la circonference du cercle extérieur, & </s> <s xml:id="echoid-s7713" xml:space="preserve">en cette diſ-<lb/>tance on arrêtoit la tablete avec le tuïau de la lunete qui compoſoit <lb/>la machine pour ladite obſervation. </s> <s xml:id="echoid-s7714" xml:space="preserve">Enſuite on faiſoit mouvoir le <lb/>tuïau ſelon le mouvement du Soleil, afin que le bord luminieux de <lb/>ſon diſque touchât partout la circonference du cercle extérieur dé-<lb/>crit ſur la tablete, & </s> <s xml:id="echoid-s7715" xml:space="preserve">par ce moïen on voyoit la quantité de la portion <lb/> <pb o="247" file="262" n="262" rhead="D'OBSERVER LES ASTRES. Liv. VI. Ch. III."/> éclipſée, & </s> <s xml:id="echoid-s7716" xml:space="preserve">de ſa plus grande obſcurité, qui ſe meſuroit par le moyen <lb/>des cercles concentriques; </s> <s xml:id="echoid-s7717" xml:space="preserve">on marquoit l'heure de chaque Phaſe <lb/>par une Horloge à ſecondes rectifiée & </s> <s xml:id="echoid-s7718" xml:space="preserve">preparée pour cette obſer-<lb/>vation. </s> <s xml:id="echoid-s7719" xml:space="preserve">La même méthode s'obſerve encore par pluſieurs Aſtrono-<lb/>mes, qui ſe ſervent auſſi d'un Reticule circulaire fait par 6 cercles <lb/>concentriques ſur du papier très-fin qu'on peut huiler pour rendre <lb/>l'image du Soleil plus ſenſible. </s> <s xml:id="echoid-s7720" xml:space="preserve">Le plus grand des cercles doit <lb/>contenir exactement l'image du Soleil au foyer du verre objectif <lb/>d'une lunete de 40 à 60 pieds, ces 6 cercles ſont à diſtance égale <lb/>& </s> <s xml:id="echoid-s7721" xml:space="preserve">diviſent avecle cercle le diametre du Soleil en 12 doigts égaux; <lb/></s> <s xml:id="echoid-s7722" xml:space="preserve">lorſque ce papier eſt placé au foyer d'une grande lunete, on diſtin-<lb/>gue nettement la partie du Soleil qui reſte éclairée; </s> <s xml:id="echoid-s7723" xml:space="preserve">on ne ſe ſert <lb/>point alors de verre oculaire.</s> <s xml:id="echoid-s7724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7725" xml:space="preserve">Il y en a d'autres qui ſe ſervent d'un Teleſcope garni de 2 lentil-<lb/>les convexes, d'où s'enſuit le même effet. </s> <s xml:id="echoid-s7726" xml:space="preserve">Mais quoique cet uſage <lb/>du Teleſcope ſoit très-propre pour obſerver les Eclipſes du Soleil, <lb/>il eſt cependant inutile pour les Eclipſes de Lune, à cauſe de ſon peu <lb/>de lumiere. </s> <s xml:id="echoid-s7727" xml:space="preserve">D'autres enfin ſe ſervent d'un Micrometre placéau foier <lb/>commun deslentilles convexes. </s> <s xml:id="echoid-s7728" xml:space="preserve">Outre la quantité des Phaſes des E-<lb/>clipſes de Soleil & </s> <s xml:id="echoid-s7729" xml:space="preserve">de Lune, que l'on connoît facilement par ledit <lb/>Micrometre, on peut de plus connoître les diametres des Luminai-<lb/>res, & </s> <s xml:id="echoid-s7730" xml:space="preserve">la proportion du diametre de la Terre à celui de la Lune, tant <lb/>par la portion obſcurcie de ſon diſque, que par la portion lumineuſe <lb/>avcc la diſtance entre ſes cornes.</s> <s xml:id="echoid-s7731" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7732" xml:space="preserve">Cette méthode d'obſerver les Eclipſes par le moyen du Micro-<lb/>metre ſera beaucoup plus utile, ſi les diviſions auſquelles s'appli-<lb/>quent les fils de ſoie, ſont faites de ſorte que ſix intervales de fils con-<lb/>tiennent le diametre du Soleil ou de la Lune. </s> <s xml:id="echoid-s7733" xml:space="preserve">Car le fil mobile poſé <lb/>au milieu de la diſtance entre les immobiles, ce qui n'eſt point diffi-<lb/>cile à faire, marquera chacun des doigts de l'Eclipſe.</s> <s xml:id="echoid-s7734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7735" xml:space="preserve">La même lunete du Micrometre pourra ſervir à toutes les autres <lb/>obſer vations & </s> <s xml:id="echoid-s7736" xml:space="preserve">meſures des Eclipſes, comme dans les Eclipſes de Lu-<lb/>ne pour obſerver l'ombre de la terre, laquelle couvre & </s> <s xml:id="echoid-s7737" xml:space="preserve">abandon-<lb/>ne les taches.</s> <s xml:id="echoid-s7738" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7739" xml:space="preserve">Il reſte pourtant une difficulté aſſez conſiderable, c'eſt de faire <lb/>pour chaque Eclipſe une diviſion nouvelle du Micrometre qui puiſ-<lb/>ſe ſervir d'un raiſeau commun à toutes les obſervations, car à peine <lb/>trouve t-on deux Eclipſes en tout un ſiecle, auſquelles le diametre <lb/>apparent du Soleil ou de la Lune ſoit le même.</s> <s xml:id="echoid-s7740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7741" xml:space="preserve">C'eſt pourquoi M. </s> <s xml:id="echoid-s7742" xml:space="preserve">de la Hire a inventé un nouveau Reticule ou <lb/> <pb o="248" file="263" n="263" rhead="DE LA MANIERE"/> Raiſeau, lequel àyant tous les uſages du Micrometre ordinaire, <lb/>peut ſervir à obſerver toutes ſortes d'Eclipſes, s'accommodant à <lb/>tousles diametres apparens du Soleil & </s> <s xml:id="echoid-s7743" xml:space="preserve">de la Lune, & </s> <s xml:id="echoid-s7744" xml:space="preserve">dont les divi-<lb/>ſions ou fils ſont aſſez fermes & </s> <s xml:id="echoid-s7745" xml:space="preserve">ſolides pour reſiſter à tous les chan-<lb/>gemens & </s> <s xml:id="echoid-s7746" xml:space="preserve">inconſtances de l'air, quoiqu'ils ſoient auſſi déliez que <lb/>des fils de ſoie.</s> <s xml:id="echoid-s7747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7748" xml:space="preserve">La conſtruction & </s> <s xml:id="echoid-s7749" xml:space="preserve">uſage de ce Reticule eſt telle. </s> <s xml:id="echoid-s7750" xml:space="preserve">Premierement, <lb/>il faut choiſir deux lentilles objectives de lunetes de même foyer, ou <lb/>à peu près, leſquelles on joint enſemble; </s> <s xml:id="echoid-s7751" xml:space="preserve">comme par exemple, lefoïer <lb/>de deux, lentilles enſemble de 8 pieds, qui eſt la longueur d'une lu-<lb/>nete, commode pour obſerver toutes ſortes d'Eclipſes, excepté néan-<lb/>moins le commencement & </s> <s xml:id="echoid-s7752" xml:space="preserve">la fin des Eclipſes de Soleil, où il faut <lb/>de plus longues lunetes pour les déterminer exactement.</s> <s xml:id="echoid-s7753" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7754" xml:space="preserve">Secondement, il eſt marqué dans les tables que le plus grand dia-<lb/>metre de la Lune à la hauteur de 90 d. </s> <s xml:id="echoid-s7755" xml:space="preserve">eſt de 34 m. </s> <s xml:id="echoid-s7756" xml:space="preserve">6 ſec. </s> <s xml:id="echoid-s7757" xml:space="preserve">auquel <lb/>ajoûtant 10 ſec. </s> <s xml:id="echoid-s7758" xml:space="preserve">on aura 34 m. </s> <s xml:id="echoid-s7759" xml:space="preserve">16 ſec. </s> <s xml:id="echoid-s7760" xml:space="preserve">C'eſt pourquoi il faut dire par <lb/>la regle de proportion, comme le raïon ou Sinus total, a la tangente <lb/>de 17 m. </s> <s xml:id="echoid-s7761" xml:space="preserve">8 ſec. </s> <s xml:id="echoid-s7762" xml:space="preserve">qui eſt moitié de 34 m. </s> <s xml:id="echoid-s7763" xml:space="preserve">16 ſec. </s> <s xml:id="echoid-s7764" xml:space="preserve">ainſi 8 pieds, ou la <lb/>longueur du foyer des deux lentilles, aux parties du pied, leſquelles <lb/>doublées au foyer de la lunete, contiendront un angle de 34 m. </s> <s xml:id="echoid-s7765" xml:space="preserve">16 ſ. <lb/></s> <s xml:id="echoid-s7766" xml:space="preserve">& </s> <s xml:id="echoid-s7767" xml:space="preserve">ce 4<emph style="sub">me</emph> nombre doublé ſera le diametre dudit raiſeau circulaire.</s> <s xml:id="echoid-s7768" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7769" xml:space="preserve">Troiſiémement, ſur un verre bien applani, clair & </s> <s xml:id="echoid-s7770" xml:space="preserve">poli on décrira <lb/>legerement avec une pointe de diaman, attachée à une des jambes <lb/>du compas ſix cercles concentriques & </s> <s xml:id="echoid-s7771" xml:space="preserve">également éloignez l'un de <lb/>l'autre, dont le plus grand & </s> <s xml:id="echoid-s7772" xml:space="preserve">dernier ait le demi-diametre égal au <lb/>4<emph style="sub">me</emph> terme ci-devant trouvé. </s> <s xml:id="echoid-s7773" xml:space="preserve">On tire auſſi ſur tous ces cercles deux <lb/>diametres, ſe croiſans à angles droits. </s> <s xml:id="echoid-s7774" xml:space="preserve">Cette petite platine de verre <lb/>ainſi préparée étant miſe dans le tuïau, dont nous avons ci devant <lb/>parlé, & </s> <s xml:id="echoid-s7775" xml:space="preserve">au foyer de la lunete, ſera un raiſeau fort commode pour <lb/>obſerver toutes les Eclipſes de Soleil & </s> <s xml:id="echoid-s7776" xml:space="preserve">de Lune, & </s> <s xml:id="echoid-s7777" xml:space="preserve">il diviſera en 12 <lb/>doigts ou parties égales tous les diametres apparens du Soleil & </s> <s xml:id="echoid-s7778" xml:space="preserve">de <lb/>la Lune, de la maniere que nous allons expliquer.</s> <s xml:id="echoid-s7779" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7780" xml:space="preserve">Il eſt évident par la dioptrique que tous les raions qui partent des <lb/>points d'un objet éloigné après leur refraction, par deux lentilles <lb/>convexes ou jointes ou peu éloignées, dépeindront au foyer com-<lb/>mun deſdites lentilles leur image, laquelle ſera d'autant plus grande <lb/>à proportion que les lentilles ſeront éloignées l'une de l'autre, & </s> <s xml:id="echoid-s7781" xml:space="preserve"><lb/>que la plus petite ſera lorſque les lentilles ſeront jointes enſem-<lb/>ble. </s> <s xml:id="echoid-s7782" xml:space="preserve">C'eſt pourquoi ſi les lentilles objectives, dont on ſe ſert <lb/>dans cette conſtruction, ſont miſes chacune en un tuïau, & </s> <s xml:id="echoid-s7783" xml:space="preserve">que ces <lb/> <pb o="249" file="264" n="264" rhead="D'OBSERVER LES ASTRES. Liv VI. Ch. III."/> deux tuïaux conviennent ſi bien qu'ils ſe puiſſent emboëter l'un <lb/>dans l'autre; </s> <s xml:id="echoid-s7784" xml:space="preserve">les lentilles étant conjointes, l'image de l'objet éloi-<lb/>gné, dont les raïons partans des extremitez tomberont dans les len-<lb/>tilles ſous un angle de 34. </s> <s xml:id="echoid-s7785" xml:space="preserve">m. </s> <s xml:id="echoid-s7786" xml:space="preserve">16 ſec. </s> <s xml:id="echoid-s7787" xml:space="preserve">ſurpaſſera de 10 ſec. </s> <s xml:id="echoid-s7788" xml:space="preserve">le plus <lb/>grand diametre apparent de la Lune; </s> <s xml:id="echoid-s7789" xml:space="preserve">c'eſt pourquoi en éloignant <lb/>peu à peu les lentilles, on trouvera la poſition en laquelle le plus <lb/>grand cercle du raiſeau poſé au foyer, répond à un angle de 34 m. <lb/></s> <s xml:id="echoid-s7790" xml:space="preserve">6 ſec. </s> <s xml:id="echoid-s7791" xml:space="preserve">Car l'image d'un objet vû ſous un moindre angle, pourra <lb/>être égale à l'image du même objet vû ſous un plus grand angle, ſe-<lb/>lon la differente longueur des foyers. </s> <s xml:id="echoid-s7792" xml:space="preserve">Mais le raiſeau a ſon tuïau par-<lb/>ticulier, ce qui fait qu'on le peut éloigner autant qu'on voudra des <lb/>lentilles objectives. </s> <s xml:id="echoid-s7793" xml:space="preserve">Nous allons ici rapporter deux méthodes pour <lb/>trouver les poſitions des lentilles & </s> <s xml:id="echoid-s7794" xml:space="preserve">du raiſeau propres à recevoir les <lb/>differens diametres du Soleil & </s> <s xml:id="echoid-s7795" xml:space="preserve">de la Lune.</s> <s xml:id="echoid-s7796" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7797" xml:space="preserve">Premierement, dans un lieu bien uni & </s> <s xml:id="echoid-s7798" xml:space="preserve">propre à faire des obſer-<lb/>vations avec des lunetes, mettez une table blanche à 2 ou 300 toi-<lb/>ſes de la lunete, & </s> <s xml:id="echoid-s7799" xml:space="preserve">directement oppoſée à la longueur du tuïau, ſur <lb/>laquelle table vous aurez tracé deux lignes droites, noires & </s> <s xml:id="echoid-s7800" xml:space="preserve">paral-<lb/>leles, l'intervale deſd. </s> <s xml:id="echoid-s7801" xml:space="preserve">lignes, à l'égard de la diſtance qu'il y a entre <lb/>lad. </s> <s xml:id="echoid-s7802" xml:space="preserve">table & </s> <s xml:id="echoid-s7803" xml:space="preserve">la lunete, ſoit tel que le requiert un angle de 34 m 6 <lb/>ſec. </s> <s xml:id="echoid-s7804" xml:space="preserve">de ſorte que ledit intervale des lignes noires repreſenté au foyer <lb/>des lentilles objectives y faſſe un angle de 34 m. </s> <s xml:id="echoid-s7805" xml:space="preserve">6 ſec. </s> <s xml:id="echoid-s7806" xml:space="preserve">ce que l'on <lb/>aura par une regle de proportion en diſant de même que nous a-<lb/>vons dit pour le Micrométre. </s> <s xml:id="echoid-s7807" xml:space="preserve">Comme le Sinus total eſt à la tan-<lb/>gente de 17 m. </s> <s xml:id="echoid-s7808" xml:space="preserve">3 ſec. </s> <s xml:id="echoid-s7809" xml:space="preserve">ainſi la diſtance de la table au tuïau des lentil-<lb/>les objectives eſt à la moitié de l'intervale des lignes noires. </s> <s xml:id="echoid-s7810" xml:space="preserve">Ainſi on <lb/>cherchera par l'experience le lieu de chaque lentille objective & </s> <s xml:id="echoid-s7811" xml:space="preserve">du <lb/>raiſeau poſé en leur foyer commun; </s> <s xml:id="echoid-s7812" xml:space="preserve">en ſorte qne la repreſentation <lb/>des lignes noires embraſſe tout le diametre du plus grand cercle du-<lb/>dit raiſeau. </s> <s xml:id="echoid-s7813" xml:space="preserve">L'on marquera ſur les tuïaux le nombre 34 m. </s> <s xml:id="echoid-s7814" xml:space="preserve">6 ſec. </s> <s xml:id="echoid-s7815" xml:space="preserve">en <lb/>chaque poſition des lentilles & </s> <s xml:id="echoid-s7816" xml:space="preserve">de leur foyer ou du raiſeau, afin de <lb/>pouvoir ajuſter les lentilles & </s> <s xml:id="echoid-s7817" xml:space="preserve">le raiſeau en leur juſte diſtance tou-<lb/>tes les fois qu'il s'agira d'un angle de 34 m. </s> <s xml:id="echoid-s7818" xml:space="preserve">6 ſec.</s> <s xml:id="echoid-s7819" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7820" xml:space="preserve">Enſuite ſi on éloigne davantage ladite table du tuïau, & </s> <s xml:id="echoid-s7821" xml:space="preserve">que ſa diſ-<lb/>tance ſoit telle que l'intervale des lignes noires ſoit la baſe d'un an-<lb/>gle de 33 m. </s> <s xml:id="echoid-s7822" xml:space="preserve">par exemple, dont le ſommet ſoit aux lentilles de la lu-<lb/>nete, ce que l'on connoîtra par le calcul, en diſant, comme la tan-<lb/>gente de 16 m. </s> <s xml:id="echoid-s7823" xml:space="preserve">30 ſec. </s> <s xml:id="echoid-s7824" xml:space="preserve">eſt au Sinus total, ainſi la moitié de l'inter-<lb/>vale des lignes noires eſt à la diſtance de la Table aux lentilles. </s> <s xml:id="echoid-s7825" xml:space="preserve">Or <lb/>dans cette poſition de la lunete & </s> <s xml:id="echoid-s7826" xml:space="preserve">de la table il faudra chercher la <lb/> <pb o="250" file="265" n="265" rhead="DE LA MANIERE"/> poſition des lentilles entr'elles & </s> <s xml:id="echoid-s7827" xml:space="preserve">du raiſeau, en ſorte que la repre-<lb/>ſentation des lignes noires qui ſe fait bien diſtincte au foyer des len-<lb/>tilles, occupe tout le diametre du plus grand cercle du raiſeau; </s> <s xml:id="echoid-s7828" xml:space="preserve">puis <lb/>l'on marquera le nombre 33 m. </s> <s xml:id="echoid-s7829" xml:space="preserve">ſur les tuïaux à la place où ſe doit <lb/>mettre chacune des lentilles & </s> <s xml:id="echoid-s7830" xml:space="preserve">le raiſeau. </s> <s xml:id="echoid-s7831" xml:space="preserve">Faites enſuite la même <lb/>operation pour les angles 32 m. </s> <s xml:id="echoid-s7832" xml:space="preserve">31 m. </s> <s xml:id="echoid-s7833" xml:space="preserve">30 & </s> <s xml:id="echoid-s7834" xml:space="preserve">29 m.</s> <s xml:id="echoid-s7835" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7836" xml:space="preserve">Que ſi l'on diviſe en 60 parties égales les diſtances marquées ſur <lb/>les tuïaux entre les differentes poſitions des lentilles & </s> <s xml:id="echoid-s7837" xml:space="preserve">du raiſeau <lb/>qui conviennent a une minute, on aura leurs poſitions pour chaque <lb/>ſeconde, & </s> <s xml:id="echoid-s7838" xml:space="preserve">par ce moyen le même cercle de vôtre raiſeau pourra <lb/>s'accommoder à tous les differens diametres apparens du Soleil & </s> <s xml:id="echoid-s7839" xml:space="preserve"><lb/>de la Lune, & </s> <s xml:id="echoid-s7840" xml:space="preserve">le diametre du plus grand cercle étant diviſé en 12 <lb/>parties égales, il ſervira à connoître la quantité de toutes les Eclip-<lb/>ſes de Soleil & </s> <s xml:id="echoid-s7841" xml:space="preserve">de Lune.</s> <s xml:id="echoid-s7842" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7843" xml:space="preserve">La ſeconde méthode tirée de l'optique, n'étant point fondée ſur <lb/>un ſi grand nombre d'experiences, paroîtra peut-être plus facile à <lb/>quelques-uns; </s> <s xml:id="echoid-s7844" xml:space="preserve">car connoiſſant les foyers de chacune des lentilles <lb/>objectives, on dira:</s> <s xml:id="echoid-s7845" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7846" xml:space="preserve">Comme la ſomme de la longueur des foyers des lentilles (ſoit de <lb/>même, ſoit de different foyer) moins la diſtance entre les lentilles <lb/>eſt à la longueur du foyer de la lentille extérieure, moins la diſtan-<lb/>ce entre les lentilles; </s> <s xml:id="echoid-s7847" xml:space="preserve">ainſi le même terme eſt à un quatriéme, lequel <lb/>étant ôté de la longueur du foyer de la lentille extérieure, reſtera la <lb/>diſtance de la lentille extérieure au foyer commun des lentilles, qui <lb/>eſt le lieu du raiſeau.</s> <s xml:id="echoid-s7848" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7849" xml:space="preserve">On connoîtra auſſi par la même méthode la poſition du foyer <lb/>commun des lentilles, ſi elles ſont jointes, par le moyen des mêmes <lb/>termes de la regle ci-deſſus, & </s> <s xml:id="echoid-s7850" xml:space="preserve">ſans avoir aucun égard à la diſtance <lb/>entre les lentilles, mais pour faire un calcul plus exact il faut comp-<lb/>ter le lieu des lentilles au milieu de leur épaiſſeur.</s> <s xml:id="echoid-s7851" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7852" xml:space="preserve">C'eſt pourquoi en ſuppoſant pluſieurs diſtances differentes entre <lb/>les lentilles objectives, on trouvera la longueur de leur foyer, c'eſt-<lb/>à-dire, le lieu du raiſeau correſpondant à chaque diſtance.</s> <s xml:id="echoid-s7853" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7854" xml:space="preserve">Enſuite on dira, comme la longueur du foyer connu, au demi-<lb/>diametre du raiſeau tel qu'il ſoit; </s> <s xml:id="echoid-s7855" xml:space="preserve">ainſi le raïon à la tangente de <lb/>l'angle qui convient au demi-diametre du raiſeau.</s> <s xml:id="echoid-s7856" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7857" xml:space="preserve">Par la même méthode on aura auſſi la grandeur du cercle exté-<lb/>rieur dudit raiſeau, en diſant, comme le raïon à la tangente d'un <lb/>angle de 17 m. </s> <s xml:id="echoid-s7858" xml:space="preserve">3 ſec. </s> <s xml:id="echoid-s7859" xml:space="preserve">ainſi la longueur du foyer des lentilles jointes <lb/>qui a été trouvée ci-devant, eſt au demi-diametre du plus grand <lb/>cercle extérieur.</s> <s xml:id="echoid-s7860" xml:space="preserve"/> </p> <pb o="251" file="266" n="266" rhead="D'OBSERVER LES ASTRES. Liv. VI. Ch. III."/> <p> <s xml:id="echoid-s7861" xml:space="preserve">Ayant donc ainſi connu le nombre des minutes & </s> <s xml:id="echoid-s7862" xml:space="preserve">ſecondes com-<lb/>priſes dans le plus grand cercle du raiſeau, ſelon les differens inter-<lb/>vales des lentilles, on les écrira ſur chaque tuïau des lentilles & </s> <s xml:id="echoid-s7863" xml:space="preserve">du <lb/>raiſeau, & </s> <s xml:id="echoid-s7864" xml:space="preserve">de plus on diviſera en ſecondes les diſtances entre les ter-<lb/>mes trouvez, comme nous avons dit en la premiere méthode. </s> <s xml:id="echoid-s7865" xml:space="preserve">C'eſt <lb/>pourquoi on trouvera auſſi-tôt les poſitions des lentilles & </s> <s xml:id="echoid-s7866" xml:space="preserve">du rai-<lb/>ſeau, qui contiendront les diametres apparens du Soleil & </s> <s xml:id="echoid-s7867" xml:space="preserve">de là <lb/>Lune tels qu'ils ſeront propoſez.</s> <s xml:id="echoid-s7868" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7869" xml:space="preserve">Que ſi l'on trouve trop de difficulté pour tracer exactement ſur le <lb/>verre les cercles concentriques, on n'aura qu'à tracer ſur ce verre <lb/>avec la pointe du diaman 13 lignes droites, parallleles entr'elles & </s> <s xml:id="echoid-s7870" xml:space="preserve"><lb/>d'égale diſtance, avec une autre ligne droite qui leur ſoit perpen-<lb/>diculaire; </s> <s xml:id="echoid-s7871" xml:space="preserve">mais la longueur de cette perpendiculaire entre les paral-<lb/>leles extrêmes doit êrre égale au diametre trouvé du plus grand cer-<lb/>cle du raiſeau, comme nous avons dit ci-devant. </s> <s xml:id="echoid-s7872" xml:space="preserve">On pourra ſe ſer-<lb/>vir de ce raiſeau au lieu de celui qui eſt compoſé de fils de ſoie.</s> <s xml:id="echoid-s7873" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7874" xml:space="preserve">On pourra auſſi ſe ſervir d'un verre ſur lequel on aura tracé des <lb/>lignes avec une pointe très-fine de diaman, dans le même ordre que <lb/>ſeroient les fils de ſoie, ſoit pour le Micrometre, ſoit pour la lunete <lb/>de longue vûë du quart dc cercle Aſtronomique ou du Niveau; </s> <s xml:id="echoid-s7875" xml:space="preserve">car <lb/>cette petite platine de verre étant ajuſtée dans ſon propre cadre; </s> <s xml:id="echoid-s7876" xml:space="preserve">ain-<lb/>ſi qu'il a été dit en parlant de la conſtruction du Micrometre, ſervi-<lb/>ra aux mêmes uſages que les fils de ſoie. </s> <s xml:id="echoid-s7877" xml:space="preserve">Je crois qu'on n'a encore <lb/>rien découvert juſqu'ici de plus utile en toute l'Aſtronomie prati-<lb/>que, puiſque de pareils raiſeaux ne ſont points ſujets aux inconſ-<lb/>ances de l'air; </s> <s xml:id="echoid-s7878" xml:space="preserve">ni à être rongez par des inſectes, ni aux mouvemens <lb/>de l'inſtrument, qui font que très-ſouvent les fils ſe rompent ou ſe <lb/>dérangent de leur vraie poſition; </s> <s xml:id="echoid-s7879" xml:space="preserve">ce qui ſera très-commode à tous <lb/>les Obſervateurs, mais principalement dans les lieux découverts & </s> <s xml:id="echoid-s7880" xml:space="preserve"><lb/>dans les longs voyages.</s> <s xml:id="echoid-s7881" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7882" xml:space="preserve">L'on peut auſſi ſe ſervir dans l'obſervation des angles, d'un verre <lb/>avec une ligne tracée dans le milieu, laquelle ſoit un peu plus large <lb/>que celles que l'on trace pour ſervir de fils de ſoie. </s> <s xml:id="echoid-s7883" xml:space="preserve">On ajuſtera un <lb/> <anchor type="note" xlink:label="note-266-01a" xlink:href="note-266-01"/> verre ainſi preparé dans la petite fenêtre qui eſt au bout de la regle <lb/>ou alidade mobile du Quart A ſtronomique, en ſorte que la ligne tra-<lb/>cée ſur la ſurface du verre touche le bord de l'inſtrument & </s> <s xml:id="echoid-s7884" xml:space="preserve">qu'elle <lb/>ſoit dirigée vers ſon centre, & </s> <s xml:id="echoid-s7885" xml:space="preserve">on s'en ſervira au lieu de cheveu que <lb/>l'on met ordinairement en cet endroit, lequel eſt ſujet à beaucoup <lb/>d'incom moditez.</s> <s xml:id="echoid-s7886" xml:space="preserve"/> </p> <div xml:id="echoid-div549" type="float" level="2" n="1"> <note position="right" xlink:label="note-266-01" xlink:href="note-266-01a" xml:space="preserve">XV II. <lb/>Planche. <lb/>Fig. 9.</note> </div> <p> <s xml:id="echoid-s7887" xml:space="preserve">Il y a des gens qui préferent les fils de ſoie aux lignes tracées ſur <lb/> <pb o="252" file="267" n="267" rhead="DE LA MANIERE"/> le verre, dontla ſurface peut cauſer quelque obſcurité aux objets, <lb/>ou qui peut faire quelque erreur, s'il n'eſt pas bien applani; </s> <s xml:id="echoid-s7888" xml:space="preserve">mais ſi <lb/>ces difficultez, qui ne ſont d'aucune conſequence, comme on con-<lb/>noîtra par l'uſage, leur font peine, ils pourront ſe ſervir de fils de <lb/>verre bien droits & </s> <s xml:id="echoid-s7889" xml:space="preserve">bien tendus, au lieu de fils de ſoie, car on en <lb/>trouve d'auſſi déliez que de la ſoie, & </s> <s xml:id="echoid-s7890" xml:space="preserve">qui ſont aſſez fermes pour re-<lb/>ſiſter aux inconſtances de l'air.</s> <s xml:id="echoid-s7891" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7892" xml:space="preserve">Ces filets de verre ſe font en tirant du creuſet qui eſt dans le Four-<lb/>neau aux Verreries; </s> <s xml:id="echoid-s7893" xml:space="preserve">on prend pour cela avec le bout de la verge de <lb/>fer dont on ſe ſef<unsure/>t, un peu de verre fondu qu'on attache promtement <lb/>à un grand Devidoir, il ſuit un filet très délié qui tient par un bout <lb/>au Devidoir, & </s> <s xml:id="echoid-s7894" xml:space="preserve">par l'autre au verre fondu qui eſt dans le creuſet. <lb/></s> <s xml:id="echoid-s7895" xml:space="preserve">On tourne avec une grande viteſſe auſſi-tôt le Devidoir, & </s> <s xml:id="echoid-s7896" xml:space="preserve">il ſe for-<lb/>me un filet de verre plus délié que les cheveux, qui ſe ploye & </s> <s xml:id="echoid-s7897" xml:space="preserve">re-<lb/>dreſſe ſans ſe caſſer; </s> <s xml:id="echoid-s7898" xml:space="preserve">on s'en ſert ordinairement pour faire desaigre-<lb/>tes. </s> <s xml:id="echoid-s7899" xml:space="preserve">On les attache aux lunetes comme les fils de ſoie.</s> <s xml:id="echoid-s7900" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7901" xml:space="preserve">Quoique les phaſes ou apparences des Eclipſes de Lune, dont les <lb/>A ſtronomes ſe ſervoient dans les uſages Aſtronomiques & </s> <s xml:id="echoid-s7902" xml:space="preserve">Géogra-<lb/>phiques, ſe puiſſent obſerver bien plus facilement & </s> <s xml:id="echoid-s7903" xml:space="preserve">plus exacte-<lb/>ment parle moyen de nôtre raiſeau que par les anciennes méthodes; <lb/></s> <s xml:id="echoid-s7904" xml:space="preserve">il faut cependant avoüer que l'on obſerve plus commodément l'im-<lb/>merſion & </s> <s xml:id="echoid-s7905" xml:space="preserve">l'émerſion des taches de la Lune dans l'ombre de la terre <lb/>queles phaſes, à cauſe de leur multitude, & </s> <s xml:id="echoid-s7906" xml:space="preserve">qu'il faut moins d'appa-<lb/>reil en ſe ſervant d'une lunete longue ſeulement de 6 pieds, car pour <lb/>cela il ne faut que la planche qui repreſente le diſque de la Lune <lb/>dans ſon plein, où ſont marquez les noms propres des taches & </s> <s xml:id="echoid-s7907" xml:space="preserve">des <lb/>principaux lieux qui paroiſſent ſur le diſque de la Lune, comme on <lb/>les trouve dans l'Aſtronomie reformée du R. </s> <s xml:id="echoid-s7908" xml:space="preserve">P. </s> <s xml:id="echoid-s7909" xml:space="preserve">Ricioly, & </s> <s xml:id="echoid-s7910" xml:space="preserve">dans le <lb/>Livre de la Connoiſſance des Tems.</s> <s xml:id="echoid-s7911" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7912" xml:space="preserve">On pourra marquer le tems que les principales taches commen-<lb/>ceront d'entrer dans l'ombre, & </s> <s xml:id="echoid-s7913" xml:space="preserve">le tems qu'elles y ſeront toutes <lb/>plongées, ou bien le tems du commencement & </s> <s xml:id="echoid-s7914" xml:space="preserve">de la fin de leur ſor-<lb/>tie, d'où l'on connoîtra le tems de l'immerſion & </s> <s xml:id="echoid-s7915" xml:space="preserve">de l'émerſion de <lb/>leur centre.</s> <s xml:id="echoid-s7916" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7917" xml:space="preserve">Cette figure de la Lune ſe trouve gravée à l'envers telle qu'elle <lb/>paroît avec une lunete garnie de deux verres convexes, ce qui a été <lb/>fait, afin que l'on puiſſe plus facilement rapporter à ladite figure le <lb/>paſſage de l'ombre de la Terre par les taches de la Lune.</s> <s xml:id="echoid-s7918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7919" xml:space="preserve">On tire de grands a vantages des obſervations des Eclipſes, car ſi <lb/>l'on marque exactement le tems du commencement d'une Eclipſe <lb/> <pb o="253" file="268" n="268" rhead="D'OBSERVER LES ASTRE Liv. VI. Ch. III."/> de Lune, de ſon immerſion totale dans bmbre, de ſon émerſion & </s> <s xml:id="echoid-s7920" xml:space="preserve"><lb/>de ſa fin, comme auſſi du paſſage de l'mbre de la Terre par les ta-<lb/>ches dépeintes ſur ſa figure, on aura la ifference des longitudes des <lb/>lieux où ſe feront les obſervations, come ſçavent tous les Aſtro-<lb/>nomes. </s> <s xml:id="echoid-s7921" xml:space="preserve">Mais parce qu'il arrive raremat des Eclipſes de Lune que <lb/>l'on puiſſe obſerver en differens païs, our en conclure la difference <lb/>de leur longitude, on peut à leur placeobſerver les Eclipſes des Sa-<lb/>tellites de Jupiter; </s> <s xml:id="echoid-s7922" xml:space="preserve">c'eſt-à-dire, leurs nmerſions & </s> <s xml:id="echoid-s7923" xml:space="preserve">émerſions dans <lb/>ſon ombre, mais principalement du remier, dont le mouvement <lb/>étant très-vîte autour de Jupiter, orpeut en faire commodément <lb/>pluſieurs obſervations pendant le cors d'une année, & </s> <s xml:id="echoid-s7924" xml:space="preserve">de-la on <lb/>peut connoître exactement la differnce des longitudes des lieux <lb/>où ſe font leſdites obſervations.</s> <s xml:id="echoid-s7925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7926" xml:space="preserve">Il faut pourtant remarquer, que Is Eclipſes de Lune n'ont pas <lb/>beſoin d'un ſi grand appareil que les Eclipſes des Satellites de Jupi-<lb/>ter, leſquelles on ne peut obſerver failement & </s> <s xml:id="echoid-s7927" xml:space="preserve">exactement à moins <lb/>que d'avoir une lunete de 12 pieds<unsure/>e long, au lieu que les Eclipſes <lb/>de Lune ſe peuvent obſerver ſant linete, s'il ne s'agit que des pha-<lb/>ſes du commencement & </s> <s xml:id="echoid-s7928" xml:space="preserve">de la fin, ou de l'immerſion & </s> <s xml:id="echoid-s7929" xml:space="preserve">de l'émer-<lb/>ſion, ou bien avec une lunete de mdiocre longueur, on peut obſer-<lb/>ver les immerſions & </s> <s xml:id="echoid-s7930" xml:space="preserve">émerſions de<unsure/>ſes taches.</s> <s xml:id="echoid-s7931" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7932" xml:space="preserve">M. </s> <s xml:id="echoid-s7933" xml:space="preserve">de Caſſini très-habile Aſtron<unsure/>ome de l'Academie Roïale des <lb/>Sciences, a mis au jour l'an 1693, des Tables exactes des mouve-<lb/>mens des Satellites de Jupiter. </s> <s xml:id="echoid-s7934" xml:space="preserve">C'eſtpourquoi en comparant le tems <lb/>de l'immerſion ou de l'émerſion d@ premier Satellite de Jupiter <lb/>trouvé par les Tables dreſſées pour l'Obſervatoire, avec les obſer-<lb/>vations faites en tous autres lieux, p<unsure/>r la difference du tems on con-<lb/>noîtra la difference des longitudes e<unsure/>tre l'Obſervatoire & </s> <s xml:id="echoid-s7935" xml:space="preserve">le lieu de <lb/>l'obſervation. </s> <s xml:id="echoid-s7936" xml:space="preserve">Ce qui ſe pourra con<unsure/>firmer en obſervant le même <lb/>phénomene en l'un & </s> <s xml:id="echoid-s7937" xml:space="preserve">l'autre lieu.</s> <s xml:id="echoid-s7938" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7939" xml:space="preserve">Il eſt à propos d'avertir ici les Obſervateurs d'un cas qui empê-<lb/>che ſouvent d'obſerver exactement les Satellites de Jupiter. </s> <s xml:id="echoid-s7940" xml:space="preserve">Dans <lb/>un tems ſerein on remarque ſouvent que la ſplendeur de Jupiter & </s> <s xml:id="echoid-s7941" xml:space="preserve"><lb/>de ſes Satellites s'éteint peu, de ſorte qu'il eſt impoſſible de dé-<lb/>terminer exactement le vrai tems de l'immerſion ou émerſion. </s> <s xml:id="echoid-s7942" xml:space="preserve">La <lb/>cauſe de cet accident vient de la lentille objective, laquelle ſe cou-<lb/>vre toute de goutes de roſée, qui détournent les raïons de lumiere, <lb/>ce qui fait qu'il y en a très-peu qui parviennent juſqu'à l'œil.</s> <s xml:id="echoid-s7943" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7944" xml:space="preserve">Un remede très-ſûr à cette incommodité, eſt qu'en faiſant un <lb/>tuïau de papier brouillard, c'eſt-à-dire, tournant 2 ou 3 feüilles <lb/> <pb o="254" file="269" n="269" rhead="CONSTRUCT. ETUSAGES D'UNE MACHINE"/> l'une ſur l'autre, on fera un @ïau long d'environ 2 pieds aſſez am-<lb/>ple pour embraſſer le bout d<unsure/> tuïau de la lunete du côté du verre ob-<lb/>jectif. </s> <s xml:id="echoid-s7945" xml:space="preserve">Ce tuïau ainſi ajuſté bi<unsure/>ra la roſée de la nuit, & </s> <s xml:id="echoid-s7946" xml:space="preserve">empêchera <lb/>quelle ne parvienne juſqu'au e<unsure/>rre; </s> <s xml:id="echoid-s7947" xml:space="preserve">& </s> <s xml:id="echoid-s7948" xml:space="preserve">par ce moyen on pourra com-<lb/>modément faire les obſervatins.</s> <s xml:id="echoid-s7949" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7950" xml:space="preserve">La difficulté dans les obſerations des Eclipſes du Soleil & </s> <s xml:id="echoid-s7951" xml:space="preserve">de la <lb/>Lune, eſt d'obſerver exactem<unsure/>nt les doigts éclipſez. </s> <s xml:id="echoid-s7952" xml:space="preserve">M. </s> <s xml:id="echoid-s7953" xml:space="preserve">le Cheva-<lb/>lier de Louville de l'Academ<unsure/> des Sciences, a dans l'idée une Ma-<lb/>chine pour pouvoir faire ſuiv<unsure/> le Micrometre à l'Aſtre qu'on ob-<lb/>ſerve; </s> <s xml:id="echoid-s7954" xml:space="preserve">car comme l'Aſtre va o<unsure/>ns un ſens, pendant que l'ombre va <lb/>dans un autre, l'Obſervateur l<unsure/>a pas le tems de meſurer la quantité <lb/>du diſque qui reſte illuminé. </s> <s xml:id="echoid-s7955" xml:space="preserve">M<unsure/>. </s> <s xml:id="echoid-s7956" xml:space="preserve">de Louville propoſe une Machine <lb/>paſſallatique, qui étant jointe à<unsure/>un horloge de fer qui feroit tourner <lb/>une manivelle attachée à une vi<unsure/> ſans fin, par le moyen de laquelle <lb/>ce mouvement d'horloge ſeroi tellement diſpoſé, qu'il feroit tour-<lb/>ner ladite Machine, avec la viteſ<unsure/>e du mouvement diurne du Soleil; <lb/></s> <s xml:id="echoid-s7957" xml:space="preserve">par ce moyen on pourroit faire<unsure/>n ſorte qu'un des fils du Microme-<lb/>tre ſeroit toûjours vis-à-vis ou b<unsure/>rd du Limbe de l'Aſtre oppoſé à <lb/>l'endroit le plus éclipſé; </s> <s xml:id="echoid-s7958" xml:space="preserve">& </s> <s xml:id="echoid-s7959" xml:space="preserve">l'O<unsure/>bſervateur n'ayant pour lors qu'à <lb/>ſonger à prendre cette quantité par le moyen de la vis du Micro-<lb/>metre, il en pourroit aiſément t<unsure/>enir à bout; </s> <s xml:id="echoid-s7960" xml:space="preserve">ce qu'on ne ſçauroit <lb/>faire par toute autre Machine q@on ait inventée juſqu'à preſent.</s> <s xml:id="echoid-s7961" xml:space="preserve"/> </p> <head xml:id="echoid-head392" xml:space="preserve">CHAPITRE IV.</head> </div> <div xml:id="echoid-div551" type="section" level="1" n="269"> <head xml:id="echoid-head393" style="it" xml:space="preserve">De la Conſtruction & Vſag<unsure/> d'une Machine qui montre les <lb/>Eclipſes, tant du Soleil que de la Lune, les mois & les <lb/>années lunaires<unsure/>, avec les Epactes.</head> <p> <s xml:id="echoid-s7962" xml:space="preserve">CEtte Machine eſt inventée par M. </s> <s xml:id="echoid-s7963" xml:space="preserve">de la Hire, & </s> <s xml:id="echoid-s7964" xml:space="preserve">eſt compoſée <lb/> <anchor type="note" xlink:label="note-269-01a" xlink:href="note-269-01"/> de trois platines rondes decuivre ou de carte, & </s> <s xml:id="echoid-s7965" xml:space="preserve">d'une regle ou <lb/>alidade qui tourne autour d'un centre commun vers le bord de la <lb/>platine ſupérieure qui eſt la plus petite. </s> <s xml:id="echoid-s7966" xml:space="preserve">Il y a deux bandes circulai-<lb/>res, dans leſquelles on a fait de petites ouvertures rondes, dont les <lb/>extérieures marquent les nouvel<unsure/>es Lunes, & </s> <s xml:id="echoid-s7967" xml:space="preserve">l'image du Soleil, & </s> <s xml:id="echoid-s7968" xml:space="preserve"><lb/>les intérieures marquent les pleines Lunes, & </s> <s xml:id="echoid-s7969" xml:space="preserve">l'image de la Lune. <lb/></s> <s xml:id="echoid-s7970" xml:space="preserve">Le bord de cette platine eſt diviſé en 12 mois lunaires qui contien-<lb/>nent chacun 29 jours 12 heures 44 min. </s> <s xml:id="echoid-s7971" xml:space="preserve">mais de telle ſorte que la <lb/>fin du 12<emph style="sub">me</emph> mois, qui fait le commencement de la ſeconde année lu-<lb/>naire, ſurpaſſe la premiere nouvelle Lune de la quantité de 4, des <lb/>179 diviſions marquées ſur la platine du milieu.</s> <s xml:id="echoid-s7972" xml:space="preserve"/> </p> <div xml:id="echoid-div551" type="float" level="2" n="1"> <note position="left" xlink:label="note-269-01" xlink:href="note-269-01a" xml:space="preserve">XVIII. <lb/>Planche. <lb/>Fig. 5.</note> </div> <pb o="255" file="270" n="270" rhead="POUR LES ECLIPSES. Liv. VI. Ch. IV."/> <p> <s xml:id="echoid-s7973" xml:space="preserve">Au bord de cette platineil y a un index attaché, dont l'un des cô-<lb/>tez, qui eſt en la ligne de foi, fait partied une ligne droite qui tend au <lb/>centre de la Machine; </s> <s xml:id="echoid-s7974" xml:space="preserve">laquelle ligne paſſe auſſi par le milieu de l'u-<lb/>ne des ouvertures extérieures qui montre la premiere nouvelle Lu-<lb/>ne de l'année Lunaire. </s> <s xml:id="echoid-s7975" xml:space="preserve">Le diametre des ouvertures eſt égal à l'éten-<lb/>duë de quatre degrez ou environ.</s> <s xml:id="echoid-s7976" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7977" xml:space="preserve">Le bord de la ſeconde platine eſt diviſé en 179 parties égales, qui <lb/>ſervent pour autant d'années lunaires, dont chacune eſt de 354 <lb/>jours & </s> <s xml:id="echoid-s7978" xml:space="preserve">9 heures on environ. </s> <s xml:id="echoid-s7979" xml:space="preserve">La premiere année commence au chi-<lb/>fre 179, auquel finit la derniere.</s> <s xml:id="echoid-s7980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7981" xml:space="preserve">Les années accomplies ſont marquées chacune par leurs chifres <lb/>1, 2, 3, 4, &</s> <s xml:id="echoid-s7982" xml:space="preserve">c. </s> <s xml:id="echoid-s7983" xml:space="preserve">qui vont de 4 en 4 diviſions, & </s> <s xml:id="echoid-s7984" xml:space="preserve">quifont 4 fois le tour <lb/>pour achever le nombre 179, comme on le voit en la figure de cette <lb/>platine. </s> <s xml:id="echoid-s7985" xml:space="preserve">Chacune des années lunaires comprend 4 deſdites divi-<lb/>ſions, de ſorte qu'en cette figure elles anticipent l'une ſur l'autre de <lb/>4 deſdites 179 diviſions du bord.</s> <s xml:id="echoid-s7986" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7987" xml:space="preserve">Sur cette même platine au-deſſous des ouvertures de la premiere, <lb/>il y a aux deux extremitez d'un même diametre un eſpace coloré <lb/>de noir, quirépond aux ouvertures extérieures, & </s> <s xml:id="echoid-s7988" xml:space="preserve">qui marque les E-<lb/>clipſes de Soleil, & </s> <s xml:id="echoid-s7989" xml:space="preserve">un autre eſpace rouge qui répond aux ouvertu-<lb/>res intérieures, qui marque les Eclipſes de la Lune. </s> <s xml:id="echoid-s7990" xml:space="preserve">La quantité de <lb/>chaque couleur qui paroît par les ouvertures fait voir la grandeur de <lb/>l'Eclipſe. </s> <s xml:id="echoid-s7991" xml:space="preserve">Le milieu des deux couleurs, qui eſt le lieu du nœud de la <lb/>Lune, répond d'un côté à la diviſion marquée 4, & </s> <s xml:id="echoid-s7992" xml:space="preserve"><unsure/> de degré de <lb/>plus; </s> <s xml:id="echoid-s7993" xml:space="preserve">& </s> <s xml:id="echoid-s7994" xml:space="preserve">d'autre côte il répond au nombre oppoſé.</s> <s xml:id="echoid-s7995" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7996" xml:space="preserve">La figure de l'eſpace coloré ſe voit ſur cette ſeconde platine, & </s> <s xml:id="echoid-s7997" xml:space="preserve"><lb/>ſon amplitude ou étenduë marque les termes des Eclipſes.</s> <s xml:id="echoid-s7998" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s7999" xml:space="preserve">La troiſiéme & </s> <s xml:id="echoid-s8000" xml:space="preserve">la plus grande des platines qui eſt au-deſſous des <lb/>autres, contient les jours & </s> <s xml:id="echoid-s8001" xml:space="preserve">les mois des années communes. </s> <s xml:id="echoid-s8002" xml:space="preserve">La divi-<lb/>ſion commence au premier jour de Mars, afin de pouvoir ajoûter un <lb/>jour au mois de Février, quand l'année eſt biſſextille. </s> <s xml:id="echoid-s8003" xml:space="preserve">Les jours de <lb/>l'année ſont décrits en ſorme de ſpirale, & </s> <s xml:id="echoid-s8004" xml:space="preserve">le mois de Février paſſe <lb/>au-delà du mois de Mars, à cauſe que l'année lunaire eſt plus courte <lb/>que l'année ſolaire, de ſorte que la 15<emph style="sub">e</emph> heure du 10<emph style="sub">e</emph> jour de Février <lb/>répond au commencement du mois de Mars. </s> <s xml:id="echoid-s8005" xml:space="preserve">Mais après avoir <lb/>compté le dernier jour de Février, il faut retrograder avecles deux <lb/>platines ſupérieures dans l'état où elles ſe trouvent pour reprendre <lb/>le premier jour de Mars. </s> <s xml:id="echoid-s8006" xml:space="preserve">Il y a 30 jours marquez au-deuant du mois <lb/>de Mars qui ſervent à trouver les Epactes.</s> <s xml:id="echoid-s8007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8008" xml:space="preserve">Il faut remarquer que les jours, comme nous les prenonsici, ne <lb/> <pb o="256" file="271" n="271" rhead="CONSTRUCT. ET USAGES D'UNE MACHINE"/> ſont point accomplis ſuivant l'uſage des Aſtronomes, mais comme <lb/>le vulgaire les compte, commençant à une minuit & </s> <s xml:id="echoid-s8009" xml:space="preserve">finiſſant à mi-<lb/>nuit du jour ſuivant. </s> <s xml:id="echoid-s8010" xml:space="preserve">C'eſt pourquoi toutes les fois qu'il s'agit du <lb/>premier jour d'un mois, ou de tout autre, nous entendons l'eſpace <lb/>de ce jour marqué dans la diviſion; </s> <s xml:id="echoid-s8011" xml:space="preserve">car nous comptons ici les jours <lb/>courans, ſuivant l'uſage vulgaire.</s> <s xml:id="echoid-s8012" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8013" xml:space="preserve">Dans le milieu de la platine ſupérieure on a décrit des Epoques <lb/>qui marquent le commencement des années lunaires, par rapport <lb/>aux années ſolaires, ſelon le Calendrier Grégorien & </s> <s xml:id="echoid-s8014" xml:space="preserve">pour le Méri-<lb/>dien de Paris. </s> <s xml:id="echoid-s8015" xml:space="preserve">Le commencement de la premiere année, dont la <lb/>marque doit être zero, & </s> <s xml:id="echoid-s8016" xml:space="preserve">qui répond à la diviſion 179, eſt arrivée à <lb/>Paris le 29 Fevrier à 14 heures & </s> <s xml:id="echoid-s8017" xml:space="preserve">demie de l'année 1680.</s> <s xml:id="echoid-s8018" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8019" xml:space="preserve">La fin de la premiere année lunaire, qui eſt le commencement de <lb/>la ſeconde, répond à la diviſion marquée 1, & </s> <s xml:id="echoid-s8020" xml:space="preserve">elle eſt arrivée à Pa-<lb/>ris l'an 1681, le 17 Février a 23 h. </s> <s xml:id="echoid-s8021" xml:space="preserve">& </s> <s xml:id="echoid-s8022" xml:space="preserve">{1/2}, en comptant comme nous <lb/>avons dit, 24 h. </s> <s xml:id="echoid-s8023" xml:space="preserve">de ſuite d'une minuit à l'autre.</s> <s xml:id="echoid-s8024" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8025" xml:space="preserve">Et de crainte qu'il n'y eût quelque erreur en rapportant les divi-<lb/>ſions du bord de la ſeconde platine avec celles des Epoques des an-<lb/>nées lunaires qui leur correſpondent, nous avons mis les mêmes <lb/>nombres aux unes & </s> <s xml:id="echoid-s8026" xml:space="preserve">aux autres.</s> <s xml:id="echoid-s8027" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8028" xml:space="preserve">Nous avons marqué les Epoques de ſuite de toutes les années lu-<lb/>naires, depuis l'année 1700 juſqu'à l'année 1750, afin que l'uſa-<lb/>ge de cette Machine fût plus facile pour accorder enſemble chacu-<lb/>ne deſdites années lunaires & </s> <s xml:id="echoid-s8029" xml:space="preserve">ſolaires. </s> <s xml:id="echoid-s8030" xml:space="preserve">Quant aux autres années <lb/>de nôtre Cycle de 179 ans, il ne ſera pas difficile de le rendre com-<lb/>plet en ajoûtant 354 jours 8 heures 48 minutes & </s> <s xml:id="echoid-s8031" xml:space="preserve">deux tiers pour <lb/>chaque année lunaire.</s> <s xml:id="echoid-s8032" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8033" xml:space="preserve">La regle ou alidade qui s'étend du centre de l'inſtrument juſqu'au <lb/>bord de la plus grande platine, ſert à rapporter les diviſions d'une <lb/>platine avec celles des deux autres. </s> <s xml:id="echoid-s8034" xml:space="preserve">Que ſi l'on applique cette Ma-<lb/>chine à un Horloge, on aura un inſtrument parfait & </s> <s xml:id="echoid-s8035" xml:space="preserve">accompli en <lb/>toutes ſes parties.</s> <s xml:id="echoid-s8036" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8037" xml:space="preserve">La Table des Epoques qui eſt dreſſée pour le Méridien de Paris <lb/>pourra facilement ſe réduire aux autres Méridiens, ſi pour les <lb/>lieux plus Orientaux que Paris, on ajoûte le tems de la differen-<lb/>ce des Méridiens, & </s> <s xml:id="echoid-s8038" xml:space="preserve">au contraire ſi on l'ôte pour les lieux plus <lb/>Occidentaux.</s> <s xml:id="echoid-s8039" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8040" xml:space="preserve">Il eſt à propos de mettre la Table des Epoques au milieu de la <lb/>platine ſupérieure, afin qu'elle ſe puiſſe voir avec cette Machine.</s> <s xml:id="echoid-s8041" xml:space="preserve"/> </p> <pb o="257" file="272" n="272" rhead="POUR LES ECLIPSES. Liv. VI. Ch. IV."/> </div> <div xml:id="echoid-div553" type="section" level="1" n="270"> <head xml:id="echoid-head394" style="it" xml:space="preserve">Maniere de faire les diviſions ſur les Platines.</head> <p> <s xml:id="echoid-s8042" xml:space="preserve">LE cercle de la plus grande Platine eſt diviſé de telle façon que <lb/>368 d. </s> <s xml:id="echoid-s8043" xml:space="preserve">2. </s> <s xml:id="echoid-s8044" xml:space="preserve">m. </s> <s xml:id="echoid-s8045" xml:space="preserve">42 ſec. </s> <s xml:id="echoid-s8046" xml:space="preserve">comprennent 354 jours 9 heures un peu <lb/>moins; </s> <s xml:id="echoid-s8047" xml:space="preserve">d'où il s'enſuit que ce cercle doit contenir 346 jours 15 h. <lb/></s> <s xml:id="echoid-s8048" xml:space="preserve">leſquelles on peut prendre ſans erreur ſenſible pour deux tiers de <lb/>jour. </s> <s xml:id="echoid-s8049" xml:space="preserve">Or pour diviſer un cercle en 346 parties égales & </s> <s xml:id="echoid-s8050" xml:space="preserve">deux tiers, <lb/>réduiſezle tout en tiers qui font en cet exemple 1040 tiers; </s> <s xml:id="echoid-s8051" xml:space="preserve">cher-<lb/>chez enſuite le plus grand nombre multiple de 3, qui ſe puiſſe faci-<lb/>lement diviſer par moitié & </s> <s xml:id="echoid-s8052" xml:space="preserve">qui ſoit contenu en 1040. </s> <s xml:id="echoid-s8053" xml:space="preserve">Ce nombre <lb/>ſe trou vera dans une progreſſion géométrique double, dont le pre-<lb/>mier & </s> <s xml:id="echoid-s8054" xml:space="preserve">moindre terme ſoit 3, comme par exemple, 3, 6, 12, 24, <lb/>48, 96, 192, 384, 768.</s> <s xml:id="echoid-s8055" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8056" xml:space="preserve">Le 9<emph style="sub">me</emph> nombre de cette progreſſion eſt celui qu'on cherche. </s> <s xml:id="echoid-s8057" xml:space="preserve">Il <lb/>faut donc ſouſtraire 768 de 1040, reſtera 272, & </s> <s xml:id="echoid-s8058" xml:space="preserve">chercher com-<lb/>bien ce nombre reſtant fait de degrez, minutes & </s> <s xml:id="echoid-s8059" xml:space="preserve">ſecondes par la <lb/>regle de 3, en diſant:</s> <s xml:id="echoid-s8060" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8061" xml:space="preserve">1040 tiers, 360 deg. </s> <s xml:id="echoid-s8062" xml:space="preserve">272 tiers, 94 deg. </s> <s xml:id="echoid-s8063" xml:space="preserve">9 min. </s> <s xml:id="echoid-s8064" xml:space="preserve">23 ſec.</s> <s xml:id="echoid-s8065" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8066" xml:space="preserve">C'eſt pourquoi retranchez dudit cercle un angle de 94 d. </s> <s xml:id="echoid-s8067" xml:space="preserve">9. </s> <s xml:id="echoid-s8068" xml:space="preserve">m. <lb/></s> <s xml:id="echoid-s8069" xml:space="preserve">23 ſec. </s> <s xml:id="echoid-s8070" xml:space="preserve">& </s> <s xml:id="echoid-s8071" xml:space="preserve">diviſez le reſte du cercle toûjours par moitié, après avoir <lb/>fait huit ſubdiviſions vous parviendrez au nombre 3, qui ſera l'arc <lb/>d'un jour, par lequel diviſant auſſi l'arc de 94 d. </s> <s xml:id="echoid-s8072" xml:space="preserve">9 m. </s> <s xml:id="echoid-s8073" xml:space="preserve">23 ſec. </s> <s xml:id="echoid-s8074" xml:space="preserve">tout <lb/>le cercle ſe trouvera diviſé en 346 jours & </s> <s xml:id="echoid-s8075" xml:space="preserve">2 tiers; </s> <s xml:id="echoid-s8076" xml:space="preserve">car il y aura 256 <lb/>jours dans le plus grand arc, & </s> <s xml:id="echoid-s8077" xml:space="preserve">90 jours 2 tiers dans l'autre. </s> <s xml:id="echoid-s8078" xml:space="preserve">Cha-<lb/>cun de ces eſpaces répond à 1 d. </s> <s xml:id="echoid-s8079" xml:space="preserve">2 m. </s> <s xml:id="echoid-s8080" xml:space="preserve">& </s> <s xml:id="echoid-s8081" xml:space="preserve">18 ſec. </s> <s xml:id="echoid-s8082" xml:space="preserve">comme on voit en <lb/>diviſant 360, par 346, 2 tiers, & </s> <s xml:id="echoid-s8083" xml:space="preserve">10 jours, répondent à 10 d. </s> <s xml:id="echoid-s8084" xml:space="preserve">23 <lb/>m. </s> <s xml:id="echoid-s8085" xml:space="preserve">& </s> <s xml:id="echoid-s8086" xml:space="preserve">par ce moyen on pourroît faire une Table qui ſerviroit à di-<lb/>viſer cette platine.</s> <s xml:id="echoid-s8087" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8088" xml:space="preserve">Ces jours ſeront enſuite diſtribuez à chacun des mois de l'an-<lb/>née, ſuivant le nombre qui leur convient, en commençant par le <lb/>mois de Mars, & </s> <s xml:id="echoid-s8089" xml:space="preserve">continuant juſqu'à la 15<emph style="sub">me</emph> heure du 10 de Fé-<lb/>vrier, qui répond au commencement de Mars, & </s> <s xml:id="echoid-s8090" xml:space="preserve">le reſte dudit <lb/>mois de Fevrier paſſe au-delà & </s> <s xml:id="echoid-s8091" xml:space="preserve">par deſſus.</s> <s xml:id="echoid-s8092" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8093" xml:space="preserve">Le cercle de la ſeconde Platine doit être diviſé en 179 parties é-<lb/>gales; </s> <s xml:id="echoid-s8094" xml:space="preserve">pour cet effet cherchez le plus grand nombre qui ſe puiſſe toû-<lb/>jours diviſer par moitié juſqu'à l'unité, & </s> <s xml:id="echoid-s8095" xml:space="preserve">qui ſoit contenu en 179; <lb/></s> <s xml:id="echoid-s8096" xml:space="preserve">vous trouverez 128, lequel ôté de 179, reſte 51. </s> <s xml:id="echoid-s8097" xml:space="preserve">Cherchez quelle <lb/>partie de la circonference du cercle fait ledit reſte par la regle de 3, <lb/>en diſant 179 part. </s> <s xml:id="echoid-s8098" xml:space="preserve">360 d. </s> <s xml:id="echoid-s8099" xml:space="preserve">51 part. </s> <s xml:id="echoid-s8100" xml:space="preserve">102 d. </s> <s xml:id="echoid-s8101" xml:space="preserve">34 m. </s> <s xml:id="echoid-s8102" xml:space="preserve">11 ſec.</s> <s xml:id="echoid-s8103" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8104" xml:space="preserve">C'eſt pourquoi ayant retranché du cercle un arc de 102 d. </s> <s xml:id="echoid-s8105" xml:space="preserve">34 <lb/> <pb o="258" file="273" n="273" rhead="CONSTRUCT. ET USAGES D'UNE MACHINE"/> m. </s> <s xml:id="echoid-s8106" xml:space="preserve">11 ſec. </s> <s xml:id="echoid-s8107" xml:space="preserve">diviſez le reſte dudit cercle toûjours par moitié, & </s> <s xml:id="echoid-s8108" xml:space="preserve">après <lb/>avoir fait 7 ſubdiviſions vous parviendrez à l'unité; </s> <s xml:id="echoid-s8109" xml:space="preserve">ainſi cette par-<lb/>tie de cercle ſera diviſée en 128 parties égales; </s> <s xml:id="echoid-s8110" xml:space="preserve">& </s> <s xml:id="echoid-s8111" xml:space="preserve">puis avec la mê-<lb/>me derniere ouverture de compas vous diviſerez l'arc reſtant en 51 <lb/>parties, & </s> <s xml:id="echoid-s8112" xml:space="preserve">tout le cercle ſe trouvera diviſé en 179 parties égales, <lb/>dont chacune répond à 2 deg. </s> <s xml:id="echoid-s8113" xml:space="preserve">& </s> <s xml:id="echoid-s8114" xml:space="preserve">40 ſec. </s> <s xml:id="echoid-s8115" xml:space="preserve">comme il eſt aiſé de voir <lb/>en diviſant 360 deg. </s> <s xml:id="echoid-s8116" xml:space="preserve">par 179; </s> <s xml:id="echoid-s8117" xml:space="preserve">& </s> <s xml:id="echoid-s8118" xml:space="preserve">c'eſt un ſecond moyen pour di-<lb/>yiſer ladite Platine.</s> <s xml:id="echoid-s8119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8120" xml:space="preserve">Enfin, pour diviſer le cercle de la Platine ſupérieure, prenez le <lb/>quart de ſa circonference, & </s> <s xml:id="echoid-s8121" xml:space="preserve">y ajoûtez une des 179 parties ou divi-<lb/>ſions du bord de la Platine du milieu; </s> <s xml:id="echoid-s8122" xml:space="preserve">le compas ouvert du quart <lb/>ainſiaugmenté, ayant tourné 4 fois, diviſera ledit cercle de la ma-<lb/>niere qu'il doit être; </s> <s xml:id="echoid-s8123" xml:space="preserve">car en ſubdiviſant chacun deſdits quarts en <lb/>3 parties égales, on aura 12 eſpaces pour les 11 mois lunaires, de tel-<lb/>le ſorte que la fin du 12<emph style="sub">me</emph> mois, qui fait le commencement de la <lb/>ſeconde année lunaire, ſurpaſſe la premiere nouvelle Lune de 4 des <lb/>179 diviſions marquées ſur la Platine du milieu.</s> <s xml:id="echoid-s8124" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div554" type="section" level="1" n="271"> <head xml:id="echoid-head395" style="it" xml:space="preserve">Vſage de cette Machine.</head> <p> <s xml:id="echoid-s8125" xml:space="preserve">UNe année lunaire étant propoſée, trouver les jours de l'an-<lb/>née ſolaire qui lui répondent, dans leſquels doivent arriver <lb/>les nouvelles & </s> <s xml:id="echoid-s8126" xml:space="preserve">pleines Lunes & </s> <s xml:id="echoid-s8127" xml:space="preserve">les Eclipſes.</s> <s xml:id="echoid-s8128" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8129" xml:space="preserve">Soit propoſée, par exemple, la 24<emph style="sub">me</emph> année lunaire de la Table <lb/>des Epoques, qui répond à la diviſion de la Platine du milieu mar-<lb/>quée (24.) </s> <s xml:id="echoid-s8130" xml:space="preserve">Arrêtez la ligne de foi de l'index à la Platine ſupérieu-<lb/>re ſur la diviſion marquée 24, en la Platine du milieu où eſt le com-<lb/>mencement de la 25<emph style="sub">me</emph> année lunaire. </s> <s xml:id="echoid-s8131" xml:space="preserve">Et voyant par la Table des <lb/>Epoques que ce commencement tombe ſur le 14<emph style="sub">me</emph> jour de Juin de <lb/>l'année 1703. </s> <s xml:id="echoid-s8132" xml:space="preserve">à 9 heures 52 min. </s> <s xml:id="echoid-s8133" xml:space="preserve">tournez enſemble les deux Pla-<lb/>tines ſupérieures en cet état, juſqu'à ce que la ligne de foi de l'in-<lb/>dex attaché à la Platine ſupérieure convienne avec la 10<emph style="sub">me</emph> heure <lb/>ou environ du 14<emph style="sub">me</emph> Juin, marquée ſur la Platine inférieure, auquel <lb/>tems arrive la premiere nouvelle Lune de l'année lunaire propoſée, <lb/>car la ligne de foi de l'index paſſe par le milieu de l'ouverture de la <lb/>premiere nouvelle Lune de ladite année lunaire.</s> <s xml:id="echoid-s8134" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8135" xml:space="preserve">Enſuite, ſans changer la ſituation des trois Platines, étendez de-<lb/>puis le centre de l'inſtrument un fil où la regle mobile la faiſant paſ-<lb/>ſer par le milieu de l'ouverture de la premiere pleine Lune, la ligne <lb/>de foi de cette regle répondra au commencement du 29<emph style="sub">me</emph> jour du-<lb/>dit mois de Juin à 4 h. </s> <s xml:id="echoid-s8136" xml:space="preserve">un quart, qui eſt le tems de cette pleine Lu-<lb/> <pb o="259" file="274" n="274" rhead="POUR LES ECLIPSES. Liv. VI. Ch. IV."/> ne, laquelle ſera totalement éclipſée, comme il paroît par la cou-<lb/>leur rouge qui remplit toute l'ouverture de cette pleine Lune.</s> <s xml:id="echoid-s8137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8138" xml:space="preserve">Nous connoîtrons par un ſemblable moyen qu'à la nouvèlle <lb/>Lune qui doit arriver environ les trois heures du matin du 14<emph style="sub">me</emph> <lb/>Juillet, il y aura une Eclipſe partiale de Soleil.</s> <s xml:id="echoid-s8139" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8140" xml:space="preserve">Si l'on pourſuit plus avant, on remarquera les Eclipſes qui doi-<lb/>vent arrriver pendant le mois de Decembre de la même année 1703, <lb/>& </s> <s xml:id="echoid-s8141" xml:space="preserve">vers le commencement de l'année ſuivante. </s> <s xml:id="echoid-s8142" xml:space="preserve">Mais comme la 10<emph style="sub">me</emph> <lb/>nouvelle Lune paſſe au-delà du 28<emph style="sub">me</emph> jour de Fevrier, ayant con-<lb/>duit l'alidade juſqu'au dit jour 28<emph style="sub">me</emph> Fevrier, faites retrograder les <lb/>deux Platines ſupérieures conjointement avec l'alidade, en l'état <lb/>où elles ſe trouvent, juſqu'à ce que la ligne de foi ſe rencontre ſur le <lb/>commencement de Mars par où nous avons commencé la diviſion <lb/>de l'année; </s> <s xml:id="echoid-s8143" xml:space="preserve">d'où conduiſant la Regle par toutes les ouvertures des <lb/>nouvelles & </s> <s xml:id="echoid-s8144" xml:space="preserve">pleines Lunes, vous connoîtrez ſur la derniere Platine <lb/>les tems qu'elles doivent arriver.</s> <s xml:id="echoid-s8145" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8146" xml:space="preserve">Mais comme la treiziéme nouvelle Lune eſt la premiere de l'an-<lb/>née lunaire ſuivante, laquelle répond au nombre 25 des diviſions <lb/>de la Platine du milieu, on laiſſera les deux Platines inſérieures en <lb/>l'état où elles ſe trouvent, & </s> <s xml:id="echoid-s8147" xml:space="preserve">on avancera celle de deſlus juſqu'à <lb/>ce que la ligne de foi de ſon index convienne avec le nombre 25 de <lb/>la Platine du milieu, auquel point elle marquera ſur la derniere & </s> <s xml:id="echoid-s8148" xml:space="preserve"><lb/>plus grande Platine le jour de la premiere nouvelle Lune de la 26<emph style="sub">me</emph> <lb/>année lunaire, ſelon l'ordre de nôtre Epoque, laquelle arrivera le ſe-<lb/>cond jour de Juin, 18 h. </s> <s xml:id="echoid-s8149" xml:space="preserve">40 m. </s> <s xml:id="echoid-s8150" xml:space="preserve">de l'an 1704, & </s> <s xml:id="echoid-s8151" xml:space="preserve">enſuite condui-<lb/>ſant la regle mobile ſur le milieu des ouvertures des nouvelles & </s> <s xml:id="echoid-s8152" xml:space="preserve"><lb/>pleines Lunes, elle marquera ſur la derniere Platine les jours qu'-<lb/>elles doivent arriver auſſi-bien que les Eclipſes juſqu'à la fin de Fe-<lb/>vrier, après quoi il faudra faire le même que pour l'année prece-<lb/>dente, c'eſt-à dire, qu'après être parvenu à la fin de Fevrier, il fau-<lb/>dra retrograder juſqu'au premier jour de Mars.</s> <s xml:id="echoid-s8153" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8154" xml:space="preserve">On pourroit ainſi trouver les commencemens de toutes les années <lb/>lunaires ſans ſe ſervir de la Table des Epoques; </s> <s xml:id="echoid-s8155" xml:space="preserve">mais d'autant qu'il <lb/>n'eſt pas poſſible d'ajuſter ſi exactement les Platines & </s> <s xml:id="echoid-s8156" xml:space="preserve">l'alidade les <lb/>unes ſur les autres qu'il ne ſe gliſſe quelque erreur, qui s'augmen-<lb/>teroit d'année en année, ladite Table des Epoques ſervira pour rec-<lb/>tifier l'uſage de cette Machine.</s> <s xml:id="echoid-s8157" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8158" xml:space="preserve">En poſant la ligne de foi de la regle mobile ſur l'âge de la Lune, <lb/>entre les jours des mois lunaires marquez ſur le bord de la Platine <lb/>ſupérieure, on verra les jours des mois communs correſpondans, & </s> <s xml:id="echoid-s8159" xml:space="preserve"><lb/> <pb o="260" file="275" n="275" rhead="CONSTRUCT. ET USAGES D'UNE MACHINE"/> à peu près les heures, ſur le bord de la Platine inférieure.</s> <s xml:id="echoid-s8160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8161" xml:space="preserve">Il eſt a remarquer que les calculs de la Table des Epoques ſont <lb/>faits pour les tems moyens des nouvelles Lunes, qui ſuppoſent les <lb/>mouvemens du Soleil & </s> <s xml:id="echoid-s8162" xml:space="preserve">de la Lune toûjours égaux; </s> <s xml:id="echoid-s8163" xml:space="preserve">c'eſt pourquoi <lb/>il ſe trouve quelque difference d'avec les tems apparens des nouvel-<lb/>les & </s> <s xml:id="echoid-s8164" xml:space="preserve">pleines Lunes & </s> <s xml:id="echoid-s8165" xml:space="preserve">des Eclipſes, telles que nous les voyons de <lb/>la Terre, comme elles ſont marquées dans les Ephemerides.</s> <s xml:id="echoid-s8166" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8167" xml:space="preserve">Les mouvemens propres du Soleil & </s> <s xml:id="echoid-s8168" xml:space="preserve">de la Lune, auſſi-bien que <lb/>ceux des autres Planetes nous paroiſſent tantôt plus vîtes, & </s> <s xml:id="echoid-s8169" xml:space="preserve">tan-<lb/>tôt plus lents: </s> <s xml:id="echoid-s8170" xml:space="preserve">Cette inégalité apparente vient en partie de ce que <lb/>leurs orbites ne ſont pas concentriques à la terre, & </s> <s xml:id="echoid-s8171" xml:space="preserve">en partie de <lb/>ce que les arcs égaux de l'écliptique qui eſt oblique à l'équateur, ne <lb/>paſſent pas toûjours par le Méridien avec des parties égales de l'é-<lb/>quateur. </s> <s xml:id="echoid-s8172" xml:space="preserve">Les Aſtronomes, pour la facilité de leurs calculs ont ima-<lb/>giné un mouvement qu'ils appellent moyen ou égal, ſuppoſans que <lb/>les Planetes décrivent en des tems égaux, des arcs égaux de leurs <lb/>orbites. </s> <s xml:id="echoid-s8173" xml:space="preserve">Le tems qu'ils appellent vrai ou apparent eſt la meſure du <lb/>mouvement vrai ou apparent, & </s> <s xml:id="echoid-s8174" xml:space="preserve">le tems moyen eſt la meſure du <lb/>moyen mouvement. </s> <s xml:id="echoid-s8175" xml:space="preserve">Ils ont auſſi inventé des regles pour réduire <lb/>les tems moyens en tems vrais ou apparens, (ces deux mots ſigni-<lb/>fians en cette occaſion la même choſe,) & </s> <s xml:id="echoid-s8176" xml:space="preserve">au contraire pour ré-<lb/>duire les tems vrais ou apparens en tems moyens.</s> <s xml:id="echoid-s8177" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div555" type="section" level="1" n="272"> <head xml:id="echoid-head396" style="it" xml:space="preserve">Pour trouver par le calcul ſi une nouvelle ou pleine Lune <lb/>ſera Ecliptique.</head> <p> <s xml:id="echoid-s8178" xml:space="preserve">POur les nouvelles Lunes, multipliez par 7361 le nombre des <lb/>mois lunaires accomplis depuis celui qui a commencé le 8<emph style="sub">me</emph> <lb/>Janvier 1701, ſuivant le Calendrier Grégorien, juſqu'à celui qu'on <lb/>examine; </s> <s xml:id="echoid-s8179" xml:space="preserve">ajoûtez au produit le nombre 33890, & </s> <s xml:id="echoid-s8180" xml:space="preserve">diviſez la ſom-<lb/>me par 43200, après la diviſion, ſans avoir égard au quotien, <lb/>examinez le reſte, ou la difference entre le diviſeur & </s> <s xml:id="echoid-s8181" xml:space="preserve">le reſte, car <lb/>ſi l'un ou l'autre eſt moindre que le nombre 4060, il y aura E-<lb/>clipſe de Soleil.</s> <s xml:id="echoid-s8182" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8183" xml:space="preserve">Mais s'il s'agit d'une pleine Lune, multipliez ſemblablement <lb/>par 7361, le nombre des mois lunaires accomplis depuis celui qui <lb/>a commencé le 8<emph style="sub">me</emph> Janvier 1701, juſqu'à la nouvelle Lune qui a <lb/>precedé la pleine Lune qu'on examine; </s> <s xml:id="echoid-s8184" xml:space="preserve">ajoûtez au produit 37326. <lb/></s> <s xml:id="echoid-s8185" xml:space="preserve">& </s> <s xml:id="echoid-s8186" xml:space="preserve">diviſez la ſomme par 43200; </s> <s xml:id="echoid-s8187" xml:space="preserve">la diviſion étant faite ſi le reſte <lb/>ou la difference entre, le reſte & </s> <s xml:id="echoid-s8188" xml:space="preserve">le diviſeur eſt moindre que le nom-<lb/>bre 2800, il y aura Eclipſe de Lune.</s> <s xml:id="echoid-s8189" xml:space="preserve"/> </p> <pb o="261" file="276" n="276" rhead="POUR LES ECLIPSES. Liv. VI. Ch. IV."/> <p> <s xml:id="echoid-s8190" xml:space="preserve">L'Eclipſe de Soleil ou de Lune ſera d'autant plus grande que le <lb/>reſte, ou la difference ſera petite; </s> <s xml:id="echoid-s8191" xml:space="preserve">& </s> <s xml:id="echoid-s8192" xml:space="preserve">au contraire.</s> <s xml:id="echoid-s8193" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div556" type="section" level="1" n="273"> <head xml:id="echoid-head397" style="it" xml:space="preserve">Exemple d'une nouvelle Lune.</head> <p> <s xml:id="echoid-s8194" xml:space="preserve">ON demande ſi la nouvelle Lune du 22 May de l'année 1705, <lb/>a été écliptique.</s> <s xml:id="echoid-s8195" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8196" xml:space="preserve">Depuis le 8 Janvier 1701, juſqu'au 22 May 1705, il y a 54 <lb/>lunaiſons accomplies. </s> <s xml:id="echoid-s8197" xml:space="preserve">Multipliez, ſelon la regle, ce nombre 54, <lb/>par 7361, & </s> <s xml:id="echoid-s8198" xml:space="preserve">au produit ajoûtez 33890; </s> <s xml:id="echoid-s8199" xml:space="preserve">la ſomme étant diviſée par <lb/>43200, reſtera 42584, qui eſt plus grand que 4060, & </s> <s xml:id="echoid-s8200" xml:space="preserve">la diffe-<lb/>rence entre le reſte 42584, & </s> <s xml:id="echoid-s8201" xml:space="preserve">le diviſeur 43200 eſt 616, laquelle <lb/>eſt moindre que 4060; </s> <s xml:id="echoid-s8202" xml:space="preserve">c'eſt pourquoi il y aura Eclipſe de Soleil.</s> <s xml:id="echoid-s8203" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div557" type="section" level="1" n="274"> <head xml:id="echoid-head398" style="it" xml:space="preserve">Exemple d'une pleine Lune.</head> <p> <s xml:id="echoid-s8204" xml:space="preserve">S'Il eſt queſtion de la plcine Lune du 27 d'Avril de l'année 1706, <lb/>nous trouvons 65 lunaiſons accomplies depuis la nouvelle Lu-<lb/>ne du 8 Janvier 1701, juſqu'à celle qui a precedé la pleine Lune <lb/>en queſtion: </s> <s xml:id="echoid-s8205" xml:space="preserve">c'eſt pourquoi ayant multiplié ſelon la regle, ledit <lb/>nombre 65 par 7361, & </s> <s xml:id="echoid-s8206" xml:space="preserve">ajouté au produit 37326, la ſomme ſera <lb/>515791, laquelle étant diviſée par 43200, ſans avoir égard au <lb/>quotien, le reſte ſera 40591, plus grand que 2800 la difference <lb/>entre le diviſeur & </s> <s xml:id="echoid-s8207" xml:space="preserve">ce reſte eſt 609, qui eſt moindre que 2800 <lb/>c'eſt pourquoi il y a eu Eclipſé de Lune ledit jour 27 Avril 1706.</s> <s xml:id="echoid-s8208" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8209" xml:space="preserve">J'ai diviſé & </s> <s xml:id="echoid-s8210" xml:space="preserve">fait graver des Planches d'une bon grandeur, <lb/>pour monter cet Inſtrument en cartons. </s> <s xml:id="echoid-s8211" xml:space="preserve">J'ai fait auſſi imprimer ſé-<lb/>parérement un petit Livre pour expliquer ſon uſage.</s> <s xml:id="echoid-s8212" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8213" xml:space="preserve">Les Spheres des differens ſyſtêmes & </s> <s xml:id="echoid-s8214" xml:space="preserve">les Globes celeſtes ſont auſſi <lb/>des Inſtrumens qui ſervent à l'Aſtronomie, auſſi-bien que les Aſ-<lb/>trolabes. </s> <s xml:id="echoid-s8215" xml:space="preserve">Nous n'en diſons rien ici, en ayant ſuffiſamment parlé <lb/>dans deux Traitez ſéparez, qui expliquent aſſez bien leurs conſtruc-<lb/>tions & </s> <s xml:id="echoid-s8216" xml:space="preserve">leurs uſages.</s> <s xml:id="echoid-s8217" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8218" xml:space="preserve">Celui des Globes & </s> <s xml:id="echoid-s8219" xml:space="preserve">Spheres eſt ſous la Preſſe pour la quatriéme <lb/>Edition, avec quelques augmentations qui feront plaiſir.</s> <s xml:id="echoid-s8220" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8221" xml:space="preserve">J'ai fait graver depuis peu des Spheres ſuivant les differens ſyſtê-<lb/>mes, & </s> <s xml:id="echoid-s8222" xml:space="preserve">des Globes qui ſont d'une grande beauté & </s> <s xml:id="echoid-s8223" xml:space="preserve">faits avec tou-<lb/>te la juſteſſe poſſible; </s> <s xml:id="echoid-s8224" xml:space="preserve">comme auſſi un Planiſphere celeſte d'une <lb/>grandeur convenable & </s> <s xml:id="echoid-s8225" xml:space="preserve">tres-commode pour connoître à tout mo-<lb/>ment l'état du Ciel, dont la conſtruction & </s> <s xml:id="echoid-s8226" xml:space="preserve">les uſages ſont expli-<lb/>quez dans un petit Traité que j'ai fait auſſi imprimer dant le mê-<lb/>me tems.</s> <s xml:id="echoid-s8227" xml:space="preserve"/> </p> <pb o="262" file="277" n="277" rhead="CONSTRUCT. ET USAGES D'UN HORLOGE"/> </div> <div xml:id="echoid-div558" type="section" level="1" n="275"> <head xml:id="echoid-head399" xml:space="preserve">CHAPITRE V.</head> <head xml:id="echoid-head400" style="it" xml:space="preserve">Diſeription d'un Horloge à pendule, à Secondes, & à Contre-<lb/>poids, pour les Obſervations Aſtronomiques.</head> <p> <s xml:id="echoid-s8228" xml:space="preserve">LA Figure ci-jointe fait voir la compoſition d'une pendule à <lb/> <anchor type="note" xlink:label="note-277-01a" xlink:href="note-277-01"/> ſecondes, dont les deux Platines AA, BB, ont environ un <lb/>demi-pied de long & </s> <s xml:id="echoid-s8229" xml:space="preserve">deux pouces & </s> <s xml:id="echoid-s8230" xml:space="preserve">demi de large; </s> <s xml:id="echoid-s8231" xml:space="preserve">ces Platines <lb/>ont aux quatre coins quatre petits baluſtres, afin qu'elles ſoient <lb/>éloignées l'une de l'autre d'un pouce & </s> <s xml:id="echoid-s8232" xml:space="preserve">demi. </s> <s xml:id="echoid-s8233" xml:space="preserve">Ces Platines ſervent <lb/>à tenir les axes des principales rouës: </s> <s xml:id="echoid-s8234" xml:space="preserve">la premiere de ces rouës, qui <lb/>eſt la plus baſſe, & </s> <s xml:id="echoid-s8235" xml:space="preserve">qui eſt marquée C, à 80 dents: </s> <s xml:id="echoid-s8236" xml:space="preserve">a l'axe de cette <lb/>rouë eſt attachée une petite poulie, qui a des pointes de fer DD, <lb/>afin de tenir la corde à laquelle les poids ſont attachez, de la ma-<lb/>niere que nous le dirons dans la ſuite; </s> <s xml:id="echoid-s8237" xml:space="preserve">la rouë C, par le moyen du <lb/>poids tourne & </s> <s xml:id="echoid-s8238" xml:space="preserve">s'engraine des le pignon E, qui a 8 dents, & </s> <s xml:id="echoid-s8239" xml:space="preserve">ainſi <lb/>fait mouvoir la rouë F, qui eſt attachée à l'axe du pig non E; </s> <s xml:id="echoid-s8240" xml:space="preserve">cette <lb/>rouë F a 48 dents, & </s> <s xml:id="echoid-s8241" xml:space="preserve">s'engraine dans le pignon G, qui a 8 dents, <lb/>dont l'axe porte la rouë H, qui a autant de dents que la rouë pre-<lb/>cedente F, ſçavoir 48; </s> <s xml:id="echoid-s8242" xml:space="preserve">mais cette rouë n'eſt pas faite comme les <lb/>autres, elle eſt en maniere de couronne; </s> <s xml:id="echoid-s8243" xml:space="preserve">les dents de cette derniere <lb/>rouë s'engrainent dans le pignon 1, dont l'axe qui eſt à plomb, <lb/>porte la rouë K, ce pignon I a 24 dents, & </s> <s xml:id="echoid-s8244" xml:space="preserve">la rouë K en a 15, dont <lb/>les dents ſont faites en forme de ſcie; </s> <s xml:id="echoid-s8245" xml:space="preserve">ſur cette rouë il y a un axe en <lb/>travers, qui a deux paletes LM, & </s> <s xml:id="echoid-s8246" xml:space="preserve">qui eſt ſoûtenu par les tenons N <lb/>Q & </s> <s xml:id="echoid-s8247" xml:space="preserve">P; </s> <s xml:id="echoid-s8248" xml:space="preserve">ces tenons ſont attachez à la Platine B B: </s> <s xml:id="echoid-s8249" xml:space="preserve">il eſt à remar-<lb/>quer qu'aux tenons N Q, la partie Q d'en bas qui paroît, eſt per-<lb/>cée d'un grand trou, pour laiſſer paſſer l'axe L M; </s> <s xml:id="echoid-s8250" xml:space="preserve">cette partie Q, <lb/>qui eſt attachée à la partie inférieure du tenon N, tient auſſi la <lb/>rouë K & </s> <s xml:id="echoid-s8251" xml:space="preserve">le pignon I. </s> <s xml:id="echoid-s8252" xml:space="preserve">Dans la platine BB, il y a une grande ouver-<lb/>ture, afin de laiſſer paſſer par delà cette Platine, l'axe & </s> <s xml:id="echoid-s8253" xml:space="preserve">les paletes <lb/>L M; </s> <s xml:id="echoid-s8254" xml:space="preserve">cet axe qui eſt en pointe, s'inſere dans le tenon P, & </s> <s xml:id="echoid-s8255" xml:space="preserve">ſe meut <lb/>ainſi plus facilement que s'il étoit ſoutenu par la Platine B B, & </s> <s xml:id="echoid-s8256" xml:space="preserve"><lb/>paſſe par-delà cette platine; </s> <s xml:id="echoid-s8257" xml:space="preserve">ce qui ſe doit faire ainſi néceſſairement <lb/>afin d'y pouvoir mettre le petit gouvernail S, qui puiſſe faire avec <lb/>l'axe les mêmes mouvemens ou vibrations, ce mouvement eſt reci-<lb/>proque, ſe faiſant tantôt d'une côté & </s> <s xml:id="echoid-s8258" xml:space="preserve">tantôt de l'autre; </s> <s xml:id="echoid-s8259" xml:space="preserve">les dents de <lb/>la rouê K rencontrent alternativement les paletes L L, comme dans <lb/>les Horloges ordinaires; </s> <s xml:id="echoid-s8260" xml:space="preserve">ce qui n'a pas beſoin d'une plus grande <lb/>explication.</s> <s xml:id="echoid-s8261" xml:space="preserve"/> </p> <div xml:id="echoid-div558" type="float" level="2" n="1"> <note position="left" xlink:label="note-277-01" xlink:href="note-277-01a" xml:space="preserve">planche <lb/>B. <lb/>Fig. 1.</note> </div> <pb o="263" file="278" n="278" rhead="A PENDULE A SECONDES, &c. Liv. VI. Ch. V."/> <p> <s xml:id="echoid-s8262" xml:space="preserve">Le petit gouvernail S eſt récour bé en ſa partie inférieure & </s> <s xml:id="echoid-s8263" xml:space="preserve">percée <lb/>dans le milieu par une fente, par laquelle paſſe la verge de fer, qui <lb/>ſert de pendule, à laquelle eſt attaché le plomb X; </s> <s xml:id="echoid-s8264" xml:space="preserve">cette verge eſt <lb/>ſuſpenduë par le haut avec un fil double entre deux lames, dont on <lb/>ne voit dans cette premiere figure que celle marquée T; </s> <s xml:id="echoid-s8265" xml:space="preserve">la figure 2 <lb/> <anchor type="note" xlink:label="note-278-01a" xlink:href="note-278-01"/> fait voir la maniere dont le pendule eſt attaché, & </s> <s xml:id="echoid-s8266" xml:space="preserve">la courbure des <lb/>deux lames, qu'on appelle cycloïde, dont on parlera dans la ſuite.</s> <s xml:id="echoid-s8267" xml:space="preserve"/> </p> <div xml:id="echoid-div559" type="float" level="2" n="2"> <note position="right" xlink:label="note-278-01" xlink:href="note-278-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s8268" xml:space="preserve">Il eſt facile de voir de quelle maniere cet Horloge ſe meut par la <lb/>force des rouës qui ſont tirées par le poids; </s> <s xml:id="echoid-s8269" xml:space="preserve">car pour ce qui eſt des <lb/>autres figures on en parlera dans la ſuite. </s> <s xml:id="echoid-s8270" xml:space="preserve">Le mouvement eſt conti-<lb/>nué par le pendule V X, lorſqu'on l'a mis une fois en branle, qui fait <lb/>aller tout l'Horloge, parce que le petit gouvernail S, quoiqu'il ſoit <lb/>fort leger étant en mouvement, non ſeulement va comme le pen-<lb/>dule, mais il aide encore tant ſoit peu le mouvement par ſes vibra-<lb/>tions, & </s> <s xml:id="echoid-s8271" xml:space="preserve">le rend ainſi perpetuel, lequel ſans cela, par la reſiſtance de <lb/>l'air, deviendroit à rien, & </s> <s xml:id="echoid-s8272" xml:space="preserve">demeureroit enfin en repos: </s> <s xml:id="echoid-s8273" xml:space="preserve">mais comme <lb/>le propre de ce pendule eſt de ſe mouvoir toûjours également, tant <lb/>que ſa longueur ne change point, étant ſuſpendu entre les deux la-<lb/>mes, cela fait que la rouë K ne peut aller ni plus vîte ni plus lente-<lb/>ment, commeil arrive dans les autres Horloges ordinaires ſans pen-<lb/>dule, mais chaque dent eſt contrainte de paſſer néceſſairement en <lb/>des tems égaux; </s> <s xml:id="echoid-s8274" xml:space="preserve">ce qui fait que les autres rouës & </s> <s xml:id="echoid-s8275" xml:space="preserve">l'éguille du ca-<lb/>dran ſont obligées defaire leurs revolutions égales, le tout ſe mou-<lb/>vant proportionnellement. </s> <s xml:id="echoid-s8276" xml:space="preserve">C'eſt pourquoi s'il y avoit quelque dé-<lb/>faut dans la conſtruction de l'Horloge, ou que les axes des rouës <lb/>euſſent de la peine à ſe mouvoir, à cauſe de l'intemperie de l'air, <lb/>pourvû qu'elle ne s'arrête point, il n'y a rien à craindre de ces iné-<lb/>galitez, & </s> <s xml:id="echoid-s8277" xml:space="preserve">elle ira toûjours bien ſi ſon mouvement ne ceſſe point.</s> <s xml:id="echoid-s8278" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8279" xml:space="preserve">Pour ce qui eſt des éguilles pour marquer les heures, minutes & </s> <s xml:id="echoid-s8280" xml:space="preserve"><lb/>ſecondes, ou les diſpoſera de la maniere ſuivante. </s> <s xml:id="echoid-s8281" xml:space="preserve">La troiſiéme Pla-<lb/>tine Y Y, eſt paralle le aux deux precedentes, & </s> <s xml:id="echoid-s8282" xml:space="preserve">eſt éloignée de trois <lb/>lignes de celle qui eſt marquée AA. </s> <s xml:id="echoid-s8283" xml:space="preserve">Dans cette Platine on décrira <lb/>intérieurement du centre a, qui ſort en dehors, & </s> <s xml:id="echoid-s8284" xml:space="preserve">qui eſt la partie <lb/>de l'axe, qui porte la rouëC, le cercle horaire, qui ſera diviſé en <lb/>12: </s> <s xml:id="echoid-s8285" xml:space="preserve">on décrira encore un autre cercle, qu'on diviſera en 60 parties, <lb/>qui ſeront les miuutes d'heure. </s> <s xml:id="echoid-s8286" xml:space="preserve">On mettra ſur l'axe R, par-delà la <lb/>Platine AA, la roue b, qui ſera attachée à un petit tuïau, qui ira <lb/>juſqu'en c, par-delà la Platine YY, & </s> <s xml:id="echoid-s8287" xml:space="preserve">ſera juſtement attachée à <lb/>l'axe qu'il tournera avec lui; </s> <s xml:id="echoid-s8288" xml:space="preserve">en ſorte cependant qu'on pourra le fai-<lb/>ze tourner ſeul, lorſqu'il en ſera beſoin. </s> <s xml:id="echoid-s8289" xml:space="preserve">On mettra en e l'éguille, <lb/> <pb o="264" file="279" n="279" rhead="CONSTRUCT. ET USAGES D'UN HORLOGE"/> qui marquera les minutes, & </s> <s xml:id="echoid-s8290" xml:space="preserve">qui fera ſon tour en une heure. </s> <s xml:id="echoid-s8291" xml:space="preserve">La <lb/>rouë b, dont on a parlé, fera mouvoir la rouë n, qui a autant de <lb/>dents qu'elle, ſçavoir 30, & </s> <s xml:id="echoid-s8292" xml:space="preserve">la rouë f s'engrainera dans le pignon h, <lb/>qui a 6 dents, ayant un petit axe qui leur eſt commun, qui ſera ſoûte-<lb/>nu par le tenon l; </s> <s xml:id="echoid-s8293" xml:space="preserve">ce pignon fera mouvoir la rouëf, qui aura 72 dents, <lb/>qui ſera attaché à un petit tube ou tuïau, qui paſſera par-delà la <lb/>Platine Y, & </s> <s xml:id="echoid-s8294" xml:space="preserve">s'étendra juſqu'a g, un peu en deçà du petit tube, qui <lb/>eſt attaché à la rouë b, & </s> <s xml:id="echoid-s8295" xml:space="preserve">qui l'environnera. </s> <s xml:id="echoid-s8296" xml:space="preserve">A l'extremité du petit <lb/>tuïau g on mettra l'éguille qui montrera les heures, qui ſera plus <lb/>petite que celle qui doit marquer les minutes, devant faire ſon tour <lb/>intérieurement : </s> <s xml:id="echoid-s8297" xml:space="preserve">mais afin qu'on ne puiſſe ſe tromper lorſqu'on vou-<lb/>dra voir les ſecondes, on mettra à l'extremité de l'axe de la rouë H, <lb/>une Platine ronde m, qui ira juſqu'en Y; </s> <s xml:id="echoid-s8298" xml:space="preserve">cette Platine ſera diviſée <lb/>en 60 parties, on fera une ouverture Z en la Platine Y, & </s> <s xml:id="echoid-s8299" xml:space="preserve">en la partie <lb/>ſupérieure on mettra une petite pointe O, pour marquer les ſecon-<lb/>des 3 on verra plus facilement la diſpoſition de toutes ces éguilles & </s> <s xml:id="echoid-s8300" xml:space="preserve"><lb/>de ces cercles en la figure 3, qui repreſente l'extérieur de l'Horloge.</s> <s xml:id="echoid-s8301" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8302" xml:space="preserve">A yant parlé de la diſpoſition des rouës, il faut déterminer la lon-<lb/>gueur du Pendule, qui doit être telle qu'il puiſſe marquer les ſe-<lb/>condes à chaque vibration ou battement; </s> <s xml:id="echoid-s8303" xml:space="preserve">cette longueur doit être <lb/>de 3 pieds 8 lignes {1/2} du pied de Paris, à commencer du point de ſuſ-<lb/>penſion T, qui eſt le commencement de la courbure du Cycloïde, <lb/>juſqu'au centre du poids X.</s> <s xml:id="echoid-s8304" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8305" xml:space="preserve">Nous allons dire quelque choſe du tems de la revolution des <lb/>rouës, & </s> <s xml:id="echoid-s8306" xml:space="preserve">de celle des éguilles, afin qu'on voye que tout ce qu'on a <lb/>dit ci-devant du nombre des dents convient enſemble. </s> <s xml:id="echoid-s8307" xml:space="preserve">Ainſi une <lb/>revolution de la rouë C en fera faire 10 à la rouë F 60 à la rouë H, <lb/>& </s> <s xml:id="echoid-s8308" xml:space="preserve">100 à la rouë ſupérieure K, laquelle ayant 15 dents & </s> <s xml:id="echoid-s8309" xml:space="preserve">pouſſant <lb/>alternativement les paletes LL, fera 30 vibrations, qui ſeront autant <lb/>d'allées & </s> <s xml:id="echoid-s8310" xml:space="preserve">venuës du Pendule VX; </s> <s xml:id="echoid-s8311" xml:space="preserve">ainſi 120 converſions répon-<lb/>dront à 3600 vibrations, qui eſt la quantité de ſecondes contenuës <lb/>en une heure de tems; </s> <s xml:id="echoid-s8312" xml:space="preserve">ainſi la rouë C fait ſa révolution en une heu-<lb/>re de tems, & </s> <s xml:id="echoid-s8313" xml:space="preserve">l'éguille e qui y eſt attachée, montrera les minutes; <lb/></s> <s xml:id="echoid-s8314" xml:space="preserve">& </s> <s xml:id="echoid-s8315" xml:space="preserve">comme dans le même eſpace de tems la rouë b fait ſa révolution <lb/>ainſi que la rouë f, avec ſon pignon b, qui a 6 dents; </s> <s xml:id="echoid-s8316" xml:space="preserve">& </s> <s xml:id="echoid-s8317" xml:space="preserve">comme le <lb/>nombre des dents de la rouë f eſt 12 fois plus grand, il doit faire un <lb/>tour en 12 heures, auſſi-bien que l'éguille g, qui y eſt attachée. </s> <s xml:id="echoid-s8318" xml:space="preserve"><lb/>Enfin, la rouë H faiſant 60 révolutions, pendant que la rouë C <lb/>en fait une, cela fait que le cercle Z, où ſont les ſecondes, fait 60 <lb/>révolutions en une heure, c'eſt-à-dire, un tour en une minute de <lb/> <pb o="265" file="280" n="280" rhead="A PENDULE, A SECONDES, &c. Liv. VI. Ch. V."/> tems, ainſi chaque 60<emph style="sub">me</emph> partie du cercle Y montrera une ſeconde: <lb/></s> <s xml:id="echoid-s8319" xml:space="preserve">le tout étant ainſi diſpoſé, il eſt manifeſte que toute la Pendule ſe-<lb/>ra dans l'état qu'elle doit être pour bien aller. </s> <s xml:id="echoid-s8320" xml:space="preserve">Le poids X qui eſt <lb/>attaché à l'extremitédu pendule, ſera de 3 liv. </s> <s xml:id="echoid-s8321" xml:space="preserve">& </s> <s xml:id="echoid-s8322" xml:space="preserve">de plomb couvert <lb/>de cuivre; </s> <s xml:id="echoid-s8323" xml:space="preserve">il ne faut pas ſeulement avoir égard à ſa peſanteur, mais <lb/>auſſi à ſa figure, ce qui eſt de conſequence, parce que la moindre <lb/>reſiſtance de l'air peut y nuire; </s> <s xml:id="echoid-s8324" xml:space="preserve">c'eſt pourquoi on le fait en forme <lb/>de cylindre convexe, ayant les extremitez pointuês, comme on le <lb/>peut voir en la figure 3, qui repreſente en petit la Pendule, quoi-<lb/>que les Pendules que l'on fait pour les Vaiſſeaux ayent le poids de la <lb/>forme X, fait en maniere de lentille, cette figure ayant été trouvée <lb/>plus propre.</s> <s xml:id="echoid-s8325" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8326" xml:space="preserve">On voit dans la même 3<emph style="sub">me</emph> figure, de quelle maniere il faut diſpo-<lb/>ſer le poids b, aſin de faire toûjours mouvoir l'Horloge; </s> <s xml:id="echoid-s8327" xml:space="preserve">de maniere <lb/>que relevant le poids, le mouvement de l'Horloge ne ceſſe point; <lb/></s> <s xml:id="echoid-s8328" xml:space="preserve">& </s> <s xml:id="echoid-s8329" xml:space="preserve">c'eſt à quoi il faut bien prendre garde. </s> <s xml:id="echoid-s8330" xml:space="preserve">C'eſt pourquoi on prendra <lb/>un cordon, qu'on attachera par les deuxbouts, comme un chapelet; </s> <s xml:id="echoid-s8331" xml:space="preserve"><lb/>on fera d'abord paſſer ce cordon ſur la rouë d, enſuite dans la pou-<lb/>lie c, à laquelle eſt attaché le poids b, qui monte vers la poulie d, <lb/>qui eſt attachée par dehors à la Pendule; </s> <s xml:id="echoid-s8332" xml:space="preserve">cette rouë a des pointes de <lb/>fer, faites en forme de ſcie, afin qu'en tournant & </s> <s xml:id="echoid-s8333" xml:space="preserve">en tirant la cor-<lb/>de e, elle l'empêche d'aller d'autre côté, la corde deſcend de cette <lb/>poulie vers l'autre poulie f, à laquelle eſt attaché le poids g, qui <lb/>doit être d'une peſanteur telle qu'il puiſſe tenir le poids b; </s> <s xml:id="echoid-s8334" xml:space="preserve">le <lb/>cordon ayant paſſé par la poulie f, remonte à la poulie d, d'où il <lb/>étoit deſcendu. </s> <s xml:id="echoid-s8335" xml:space="preserve">Les choſes étant ainſi diſpoſées, il eſt manifeſte <lb/> <anchor type="note" xlink:label="note-280-01a" xlink:href="note-280-01"/> que la moitié du poids b, fait mouvoir les rouës, & </s> <s xml:id="echoid-s8336" xml:space="preserve">que le mouve-<lb/>ment ne ceſſe point lorſqu'on tire avec la main la corde e, ainſi le <lb/>mouvement de la Pendule n'eſt jamais interrompu, & </s> <s xml:id="echoid-s8337" xml:space="preserve">ne perd pas <lb/>un moment de tems.</s> <s xml:id="echoid-s8338" xml:space="preserve"/> </p> <div xml:id="echoid-div560" type="float" level="2" n="3"> <note position="right" xlink:label="note-280-01" xlink:href="note-280-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s8339" xml:space="preserve">On ne peut pas certainement déterminer la peſanteur du poids <lb/>b, mais moins il ſera peſant, pourvû qu'il faſſe aller la Pendule, & </s> <s xml:id="echoid-s8340" xml:space="preserve"><lb/>mieux il ſera; </s> <s xml:id="echoid-s8341" xml:space="preserve">dans celles qui ſe font ordinairement, & </s> <s xml:id="echoid-s8342" xml:space="preserve">qui ſont <lb/>les meilleures qu'on ait à preſent, ce poids eſt de 6 livres, faiſant le <lb/>diametre de la poulie d, d'un pouce, comme il a été dit, & </s> <s xml:id="echoid-s8343" xml:space="preserve">le poids <lb/>du pendule X, de 3 liv. </s> <s xml:id="echoid-s8344" xml:space="preserve">& </s> <s xml:id="echoid-s8345" xml:space="preserve">long de 3 pieds 8 lig. </s> <s xml:id="echoid-s8346" xml:space="preserve">{1/2}, qui doit paſſer <lb/>par-delà la boëte, par une ouverture, & </s> <s xml:id="echoid-s8347" xml:space="preserve">autant qu'il ſera neceſſai-<lb/>re pour faire les vibrations; </s> <s xml:id="echoid-s8348" xml:space="preserve">on doit ſuſpendre cette Pendule à la <lb/>hauteur d'un homme, & </s> <s xml:id="echoid-s8349" xml:space="preserve">elle ira 30 heures.</s> <s xml:id="echoid-s8350" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8351" xml:space="preserve">Il faut preſentement donner la maniere de faire la courbure des <lb/> <pb o="266" file="281" n="281" rhead="CONSTRUCT. ET USAGES D'UN HORLOGE, &c."/> lames, qu'on appelle Cycloïde, auſquelles eſt attaché le Pendule, <lb/>en quoi conſiſte toute la juſteſſe de l'Horloge. </s> <s xml:id="echoid-s8352" xml:space="preserve">Décrivez le cercle <lb/>AFBK, dont le diametre AB ſoit égal à la moitié du pendule; </s> <s xml:id="echoid-s8353" xml:space="preserve">on <lb/>prendra ſur la circonference de ce cercle les parties AC, CD, DE, <lb/>DF & </s> <s xml:id="echoid-s8354" xml:space="preserve">AG, GH, HI, IK, égales entr'elles,& </s> <s xml:id="echoid-s8355" xml:space="preserve">on tirera les lignes CG, <lb/>DH, EI, FK, d'une diviſion à l'autre, & </s> <s xml:id="echoid-s8356" xml:space="preserve">elles ſeront paralleles: </s> <s xml:id="echoid-s8357" xml:space="preserve">on <lb/> <anchor type="note" xlink:label="note-281-01a" xlink:href="note-281-01"/> fera la ligne LM égale à l'arc AF, qu'on diviſera en autant de par-<lb/>ties que l'arc AF; </s> <s xml:id="echoid-s8358" xml:space="preserve">on prendra une de ces parties qu'on portera de C <lb/>en M & </s> <s xml:id="echoid-s8359" xml:space="preserve">de G en O, ſur la ligne CG; </s> <s xml:id="echoid-s8360" xml:space="preserve">on prendra enſuite ſur la li-<lb/>gne LM deux parties qu'on portera de D en P & </s> <s xml:id="echoid-s8361" xml:space="preserve">de H en Q ſurla <lb/>ligne DH; </s> <s xml:id="echoid-s8362" xml:space="preserve">on prendra encore trois parties ſur la ligne LM qu'on <lb/>portera ſur la ligne EI, de E en R & </s> <s xml:id="echoid-s8363" xml:space="preserve">de I en S: </s> <s xml:id="echoid-s8364" xml:space="preserve">enfin on prendra 4 <lb/>parties, qui eſt toute la longueur de la ligne LM, qu'on portera <lb/>ſur la ligne FK, de F en T, & </s> <s xml:id="echoid-s8365" xml:space="preserve">de C en V; </s> <s xml:id="echoid-s8366" xml:space="preserve">& </s> <s xml:id="echoid-s8367" xml:space="preserve">ainſi desautres parties, <lb/>ſi on avoit pris davantage de points ſur le cercle AFBK. </s> <s xml:id="echoid-s8368" xml:space="preserve">Par les <lb/>points trouvez NPRT & </s> <s xml:id="echoid-s8369" xml:space="preserve">OQSV, on tracera les lignes courbes <lb/>AT, AV, qui ſormeront la figure de la Cycloïde, ſur leſquelles on <lb/>formera leslames de cuivre qu'on veut avoir, entre leſquelles on ſuſ-<lb/>pend le pendule: </s> <s xml:id="echoid-s8370" xml:space="preserve">il ſuffit d'avoir une petite partie desarcs AT, AV; <lb/></s> <s xml:id="echoid-s8371" xml:space="preserve">une plus grande partie ſeroit inutile, le fil n'y pouvant atteindre; </s> <s xml:id="echoid-s8372" xml:space="preserve"><lb/>la figure 2 fait voir la maniere dont eſt ajuſté le pendule & </s> <s xml:id="echoid-s8373" xml:space="preserve">les 2 la-<lb/>mes. </s> <s xml:id="echoid-s8374" xml:space="preserve">Pour trouver la ligne LM égale à l'arc AF, on prendra les deux <lb/>demi-cordes de l'arc AF qu'on portera de X en Y ſur la ligne XV; </s> <s xml:id="echoid-s8375" xml:space="preserve"><lb/>on prendra enſuite toute la corde de l'arc AF qu'on portera de X en <lb/>Z; </s> <s xml:id="echoid-s8376" xml:space="preserve">on diviſera la grandeur YZ en trois, & </s> <s xml:id="echoid-s8377" xml:space="preserve">on prendra une partie <lb/>qu'on portera de Z en V; </s> <s xml:id="echoid-s8378" xml:space="preserve">toute la ligne XV ſera preſque égale à <lb/>l'arc AF.</s> <s xml:id="echoid-s8379" xml:space="preserve"/> </p> <div xml:id="echoid-div561" type="float" level="2" n="4"> <note position="left" xlink:label="note-281-01" xlink:href="note-281-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s8380" xml:space="preserve">L'uſage de cet Inſtrument eſt facile: </s> <s xml:id="echoid-s8381" xml:space="preserve">ayant remarqué au Cadran <lb/>l'heure, la minute & </s> <s xml:id="echoid-s8382" xml:space="preserve">la ſeconde, on compte enſuite les vibrations <lb/>ou battemens du pendule, pour déterminer l'heure préciſe des ob-<lb/>ſervations; </s> <s xml:id="echoid-s8383" xml:space="preserve">mais il faut que ledit Inſtrument ſoit bien reglé ſur le <lb/>mouvement des Aſtres.</s> <s xml:id="echoid-s8384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8385" xml:space="preserve">Les principaux Inſtrumens qu'un Aſtronome doit avoir après <lb/>un bon Quart de cercle, une Pendule, eſt une Lunete de 7 à 8 pieds, <lb/>où un Micrometre ſoit ajuſté, pour obſerver les doigts des Eclipſes <lb/>de Soleil ou de Lune, une Lunete de 15 ou 16 pieds pour obſer-<lb/>ver les immerſions & </s> <s xml:id="echoid-s8386" xml:space="preserve">émerſions des Satellites de Jupiter; </s> <s xml:id="echoid-s8387" xml:space="preserve">& </s> <s xml:id="echoid-s8388" xml:space="preserve">ſi cela <lb/>ſe peut une Machine parallactique, pour prendre la parallaxe 'des <lb/>Aſtres, telle que M. </s> <s xml:id="echoid-s8389" xml:space="preserve">de Louville l'a propoſée, & </s> <s xml:id="echoid-s8390" xml:space="preserve">dont nousavons parlé <lb/>ci-devant.</s> <s xml:id="echoid-s8391" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div563" type="section" level="1" n="276"> <head xml:id="echoid-head401" style="it" xml:space="preserve">Fin du ſixiéme Livre.</head> <pb file="282" n="282"/> </div> <div xml:id="echoid-div564" type="section" level="1" n="277"> <head xml:id="echoid-head402" xml:space="preserve">Planche B # Page 266.</head> <figure> <caption xml:id="echoid-caption5" style="it" xml:space="preserve">Fig. 1.<emph style="sub">e</emph></caption> <variables xml:id="echoid-variables4" xml:space="preserve">Y Z m Y m 7 2 f b 30 g a e 6 30 h n d A A B N A P L L M T K 15 I 24 H S G 8 48.Dents F 48 8.Dents E C D 80.Dents R D C B V X</variables> </figure> <figure> <caption xml:id="echoid-caption6" style="it" xml:space="preserve">Fig. 2.</caption> </figure> <figure> <caption xml:id="echoid-caption7" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables5" xml:space="preserve">e c b f g</variables> </figure> <figure> <caption xml:id="echoid-caption8" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables6" xml:space="preserve">G A C N O H P Q D I R S E K T V F B L 1 2 3 4 M X Y Z V</variables> </figure> <pb file="283" n="283"/> <figure> <image file="283-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/283-01"/> </figure> </div> <div xml:id="echoid-div565" type="section" level="1" n="278"> <head xml:id="echoid-head403" xml:space="preserve">DE LA <lb/>CONSTRUCTION <lb/>ET DES USAGES <lb/>DES INSTRUMENS <lb/>QUI SERVENT <lb/>A LA NAVIGATION. <lb/>LIVRE SEPTIÉME.</head> <head xml:id="echoid-head404" xml:space="preserve">CHAPTRE PREMIER.</head> <head xml:id="echoid-head405" style="it" xml:space="preserve">Di la Conſtruction & des Uſages de la Bouſſole Marine.</head> <p> <s xml:id="echoid-s8392" xml:space="preserve">LA figure premiere repreſente une roſe de Bouſſole que <lb/> <anchor type="note" xlink:label="note-283-01a" xlink:href="note-283-01"/> les Marins nomment auſſi Compas de Route. </s> <s xml:id="echoid-s8393" xml:space="preserve">Son <lb/>bord extérieur repréſente l'horiſon du Monde. </s> <s xml:id="echoid-s8394" xml:space="preserve">ll <lb/>ſe diviſé quelquefois en 360 deg. </s> <s xml:id="echoid-s8395" xml:space="preserve">& </s> <s xml:id="echoid-s8396" xml:space="preserve">le plus ſouvent <lb/>n'eſt diviſé qu'en 32 parties égales comme celle-ci, <lb/>pour les 32 airs de vent, dont les quatre principaux & </s> <s xml:id="echoid-s8397" xml:space="preserve">qui ſe <lb/>nomment vents cardinaux, ſe croiſent à angles droits; </s> <s xml:id="echoid-s8398" xml:space="preserve">ſavoir, le <lb/>Nord ou Septentrion, lequel ſe diſtingue par une Fleur-de-L ys, le <lb/>Sud ou Midi qui lui eſt oppoſé; </s> <s xml:id="echoid-s8399" xml:space="preserve">l'Eſt ou l'Orient, & </s> <s xml:id="echoid-s8400" xml:space="preserve">l'Oüeſt ou Oc-<lb/>cident. </s> <s xml:id="echoid-s8401" xml:space="preserve">Diviſant enſuite chacun de ces eſpaces en deux parties éga-<lb/>les, on a les 8 rumbs de vent; </s> <s xml:id="echoid-s8402" xml:space="preserve">diviſant encore chaque eſpace en 2, <lb/>on a les 8 demi-rumbs; </s> <s xml:id="echoid-s8403" xml:space="preserve">& </s> <s xml:id="echoid-s8404" xml:space="preserve">enſin ſubdiviſant chacune de ces 8 par-<lb/>ties en 2, on a les 16 quarts de vent. </s> <s xml:id="echoid-s8405" xml:space="preserve">Les 4 rumbs collateraux em-<lb/>pruntent leurs noms des 4 principaux, chacun prenant pour nom <lb/>les deux noms de ceux qui leur ſont plus proches; </s> <s xml:id="echoid-s8406" xml:space="preserve">ainſi le rumb qui <lb/>eſt au milieu entre le Nord & </s> <s xml:id="echoid-s8407" xml:space="preserve">l'Eſt, s'appelle Nord-Eſt; </s> <s xml:id="echoid-s8408" xml:space="preserve">celui quieſt <lb/>entre le Sud & </s> <s xml:id="echoid-s8409" xml:space="preserve">l'Eſt, ſe nomme Sud-Eſt; </s> <s xml:id="echoid-s8410" xml:space="preserve">celui quieſt entre le Sud & </s> <s xml:id="echoid-s8411" xml:space="preserve"><lb/> <pb o="268" file="284" n="284" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> l'Oüeſt,s'appelle Sud-Oueſt, & </s> <s xml:id="echoid-s8412" xml:space="preserve">celui qui eſt entre le Nord & </s> <s xml:id="echoid-s8413" xml:space="preserve">l'Oüeſt <lb/>ſe nomme Nord-Oüeſt.</s> <s xml:id="echoid-s8414" xml:space="preserve"/> </p> <div xml:id="echoid-div565" type="float" level="2" n="1"> <note position="right" xlink:label="note-283-01" xlink:href="note-283-01a" xml:space="preserve">XIX. <lb/>Planche. <lb/>Fig. 12</note> </div> <p> <s xml:id="echoid-s8415" xml:space="preserve">Pareillement chacun des huit demi-rumbs de vent porte le nom <lb/>des deux rumbs qui lui ſont les plus proches; </s> <s xml:id="echoid-s8416" xml:space="preserve">ainſi celui qui eſt entre <lb/>le Nord & </s> <s xml:id="echoid-s8417" xml:space="preserve">le Nord-Eſt, s'appelle Nord Nord Eſt; </s> <s xml:id="echoid-s8418" xml:space="preserve">celui qui eſt en-<lb/>tre l'Eſt & </s> <s xml:id="echoid-s8419" xml:space="preserve">le Nord-Eſt ſe nomme Eſt Nord-Eſt; </s> <s xml:id="echoid-s8420" xml:space="preserve">celui d'entre l'Eſt <lb/>& </s> <s xml:id="echoid-s8421" xml:space="preserve">le Sud-Eſt, s'appelle Eſt Sud-Eſt; </s> <s xml:id="echoid-s8422" xml:space="preserve">& </s> <s xml:id="echoid-s8423" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s8424" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8425" xml:space="preserve">Enfin chacun des quarts de vents a ſon nom compoſé des rumbs <lb/>ou demi-rumbs qui lui ſont les plus proches, en ajoûtant le mot de <lb/>quart après le nom de rumb qui lui eſt le plus proche. </s> <s xml:id="echoid-s8426" xml:space="preserve">Par exemple, <lb/>le quart le plus proche du Nord du côté du Nord-Eſt, ſe nomme <lb/>Nord-Quart, Nord-Eſt; </s> <s xml:id="echoid-s8427" xml:space="preserve">celui qui eſt plus proche du Nord-Eſt vers <lb/>le Nord, ſe nomme Nord-Eſt, Quart-Nord, & </s> <s xml:id="echoid-s8428" xml:space="preserve">ainſi des autres, <lb/>comme ils ſont marquez en abregé autour de la roſe.</s> <s xml:id="echoid-s8429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8430" xml:space="preserve">Chaque quart de rumb contient 11 deg. </s> <s xml:id="echoid-s8431" xml:space="preserve">15 m. </s> <s xml:id="echoid-s8432" xml:space="preserve">les demi-rumbs <lb/>22 deg. </s> <s xml:id="echoid-s8433" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8434" xml:space="preserve">& </s> <s xml:id="echoid-s8435" xml:space="preserve">les rumbs entiers 45 deg.</s> <s xml:id="echoid-s8436" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8437" xml:space="preserve">L'intérieur de cette roſe, qui eſt ſuppoſée double, eſt pareillement <lb/>diviſé en 32 parties égales par autant de raïons qui marquent les <lb/>mêmes vents, & </s> <s xml:id="echoid-s8438" xml:space="preserve">ſon milieu qui eſt colé ſur un carton, a un mouve-<lb/>ment libre ſur ſon pivot, pours'en ſervir lorſqu'on a reconnu la dé-<lb/>clinaiſon ou la variation de l'éguille aimantée. </s> <s xml:id="echoid-s8439" xml:space="preserve">L'on remarquera <lb/>que l'exterieur de cette roſe ſe place ſur le bord de la boëte.</s> <s xml:id="echoid-s8440" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8441" xml:space="preserve">La figure 2<emph style="sub">me</emph> repreſente une piece d'acier en lozange qui ſert d'é-<lb/> <anchor type="note" xlink:label="note-284-01a" xlink:href="note-284-01"/> guille aimantée, & </s> <s xml:id="echoid-s8442" xml:space="preserve">que l'on attache ſous la roſe mobile avec 2 pe-<lb/>tits clous. </s> <s xml:id="echoid-s8443" xml:space="preserve">Il ne faut pas la coller, comme font quelques-uns, parce <lb/>que cela cauſe une roüille qui eſt fort contraire à la vertu de l'ai-<lb/>man; </s> <s xml:id="echoid-s8444" xml:space="preserve">un des bouts du grand diametre doit être préciſément ſous la <lb/>Fleur-de-Lys, & </s> <s xml:id="echoid-s8445" xml:space="preserve">doit être touché par une bonne pierre d'aiman; <lb/></s> <s xml:id="echoid-s8446" xml:space="preserve">de ſorte que ce bout là ſe dirige vers le Nord du monde. </s> <s xml:id="echoid-s8447" xml:space="preserve">Nous a-<lb/>vons expliqué la maniere de toucher les éguilles, en parlant des <lb/>pierres d'aiman, & </s> <s xml:id="echoid-s8448" xml:space="preserve">de la Bouſſole.</s> <s xml:id="echoid-s8449" xml:space="preserve"/> </p> <div xml:id="echoid-div566" type="float" level="2" n="2"> <note position="left" xlink:label="note-284-01" xlink:href="note-284-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s8450" xml:space="preserve">La petite piece qui eſt au milieu du lozange à l'endroit marqué <lb/>B, eſt ce qu'on appelle la chape de l'éguille. </s> <s xml:id="echoid-s8451" xml:space="preserve">Elle eſt faite de cuivre <lb/>& </s> <s xml:id="echoid-s8452" xml:space="preserve">creuſée en forme de cône; </s> <s xml:id="echoid-s8453" xml:space="preserve">on l'applique au centre de la roſe, & </s> <s xml:id="echoid-s8454" xml:space="preserve"><lb/>on la fait tenir avec de la colle.</s> <s xml:id="echoid-s8455" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8456" xml:space="preserve">La figure 3<emph style="sub">me</emph> repreſente la Bouſſole entiere. </s> <s xml:id="echoid-s8457" xml:space="preserve">C'eſt une boëte ron-<lb/>de de bois d'environ 6 à 7 pouces de diametre & </s> <s xml:id="echoid-s8458" xml:space="preserve">4 de profondeur; <lb/></s> <s xml:id="echoid-s8459" xml:space="preserve">on la fait quelqueſois quarrée.</s> <s xml:id="echoid-s8460" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8461" xml:space="preserve">Il y a deux cercles de cuivre, dont le plus grand eſt attaché à la <lb/>Boëté par deux pivots, aux endroits marquez B.</s> <s xml:id="echoid-s8462" xml:space="preserve"/> </p> <pb o="269" file="285" n="285" rhead="POUR LA NAVIGATION. Liv. VII. Chap. I."/> <p> <s xml:id="echoid-s8463" xml:space="preserve">L'autre cercle eſt attaché par deux autres pivots qui traverſent <lb/>leſdits cercles diametralement aux en droits marquez C, & </s> <s xml:id="echoid-s8464" xml:space="preserve">ces 2 pi-<lb/> <anchor type="note" xlink:label="note-285-01a" xlink:href="note-285-01"/> vots vont aboutir dans 2 trous qui ſont percez au milieu & </s> <s xml:id="echoid-s8465" xml:space="preserve">vcrs le <lb/>haut d'une autre eſpece de boëte de bois, concave en dedans & </s> <s xml:id="echoid-s8466" xml:space="preserve">con-<lb/>vexe en dehors, comme une calote dans laquelle on met la roſe. </s> <s xml:id="echoid-s8467" xml:space="preserve">Il <lb/>faut que cette boëte & </s> <s xml:id="echoid-s8468" xml:space="preserve">les 2 cercles ayent un mouvement fort li-<lb/>bre, en telle ſorte que la grande boëte marquée A, étant poſée à <lb/>plat, tel mouvement que faſſe le Vaiſſeau, la boëte intérieure ſoit <lb/>toûjours horiſontale & </s> <s xml:id="echoid-s8469" xml:space="preserve">en équilibre. </s> <s xml:id="echoid-s8470" xml:space="preserve">Au milieu du ſonds de cette boë-<lb/>te eſt placé un pivot de cuivre bien droit & </s> <s xml:id="echoid-s8471" xml:space="preserve">bien pointu, ſur lequel <lb/>on poſe la chape qui porte la roſe, laquelle doit avoir un mouvement <lb/>très-libre, & </s> <s xml:id="echoid-s8472" xml:space="preserve">l'éguille étant frotée d'aiman, comme nousavons dit, <lb/>la Fleur de Lys tendra vers le Nord, & </s> <s xml:id="echoid-s8473" xml:space="preserve">tous les autres rumbs de vent <lb/>ſeront tournez vers les autres parties du Monde. </s> <s xml:id="echoid-s8474" xml:space="preserve">On poſe un verre qui <lb/>couvre la roſe, aſin que le vent ne l'agite point.</s> <s xml:id="echoid-s8475" xml:space="preserve"/> </p> <div xml:id="echoid-div567" type="float" level="2" n="3"> <note position="right" xlink:label="note-285-01" xlink:href="note-285-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s8476" xml:space="preserve">Il y a auſſi dans chaque Vaiſſeau une Bouſſole qui ſert à connoî-<lb/>tre la déclinaiſon ou variation de l'éguillle aimantée. </s> <s xml:id="echoid-s8477" xml:space="preserve">Elle eſt faite <lb/>comme celle dont nous venons de parler; </s> <s xml:id="echoid-s8478" xml:space="preserve">mais le bord extérieur de <lb/>la roſe doit être diviſé en 4 fois 90 deg. </s> <s xml:id="echoid-s8479" xml:space="preserve">en commençant du Nord <lb/>& </s> <s xml:id="echoid-s8480" xml:space="preserve">Sud à droite & </s> <s xml:id="echoid-s8481" xml:space="preserve">à gauche. </s> <s xml:id="echoid-s8482" xml:space="preserve">Il doit y avoit 2 pinules mobiles autour <lb/>de la boëte pour regarder les Aſtres, & </s> <s xml:id="echoid-s8483" xml:space="preserve">on tend un ſil d'une pinule à <lb/>l'autre qui paſſe par deſſus le centre de la roſe, de ſorte que quand <lb/>on regarde un Aſtre par les deux pinules, le ſil qui traverſe la roſe <lb/>repreſente le raïon de l'Aſtre. </s> <s xml:id="echoid-s8484" xml:space="preserve">Ces ſortes de Bouſſoles s'appellent <lb/>auſſi Compas de variation.</s> <s xml:id="echoid-s8485" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div569" type="section" level="1" n="279"> <head xml:id="echoid-head406" style="it" xml:space="preserve">Vſage de la Bouſſole.</head> <p> <s xml:id="echoid-s8486" xml:space="preserve">AY ant reconnu ſur une Carte Marine la route que doit tenir le <lb/>Vaiſſeau pour aller au lieu propoſé, & </s> <s xml:id="echoid-s8487" xml:space="preserve">la Bouſſole étant affer-<lb/>mie dans la Chambre du Pilote, de telle maniere que les 2 côtez pa-<lb/>ralleles de la boëte quarrée ſoient arrêtez ſelon la longueur du Na-<lb/>vire, c'eſt-à-dire, parallelement à la ligne qui s'étend de la poupe à la <lb/>prouë, on marquera d'une croix ou autre marque le milieu du côté <lb/>de la boëte perpendiculaire à la longueur du Vaiſſeau & </s> <s xml:id="echoid-s8488" xml:space="preserve">le plus éloi-<lb/>gné de la poupe, afin que par ce moïen on puiſſe diriger ſon gouver-<lb/>nail.</s> <s xml:id="echoid-s8489" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div570" type="section" level="1" n="280"> <head xml:id="echoid-head407" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s8490" xml:space="preserve">Nous partons de l'Iſle Oüeſſant, ſur les conſins de la Bretagne, à <lb/>l'Occident de Breſt, & </s> <s xml:id="echoid-s8491" xml:space="preserve">nous voulons naviger vers le Cap de Finiſterre <lb/>en Galice. </s> <s xml:id="echoid-s8492" xml:space="preserve">Nous cherchons premierement dans une Carte Marine <lb/> <pb o="270" file="286" n="286" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> réduite de la maniere que nous dirons ci-après, quelle doit être la <lb/>direction du Navire, & </s> <s xml:id="echoid-s8493" xml:space="preserve">nous remarquons que la route ſe doit faire <lb/>entre le Sud-Oüeſt & </s> <s xml:id="echoid-s8494" xml:space="preserve">le Sud Sud-Oüeſt, c'eſt-à-dire, ſelon la ligne <lb/>qui tend au Sud-Oüeſt quart au Sud; </s> <s xml:id="echoid-s8495" xml:space="preserve">c'eſt pourquoi ayant le vent <lb/>propre on tournera le gouvernail du Navire de maniere que la ligne <lb/>du Sud-Oüeſt quart au Sud, réponde exactement à la croix marquée <lb/>ſur le bord du cadre de la Bouſſole; </s> <s xml:id="echoid-s8496" xml:space="preserve">& </s> <s xml:id="echoid-s8497" xml:space="preserve">ce qui eſt admirable, c'eſt que <lb/>par ce moïen on peut diriger la route du Vaiſſeau de nuit comme de <lb/>jour; </s> <s xml:id="echoid-s8498" xml:space="preserve">dans une chambre fermée comme ſi on étoit à l'air; </s> <s xml:id="echoid-s8499" xml:space="preserve">dans un <lb/>tems obſcur, comme dans un tems ſerein; </s> <s xml:id="echoid-s8500" xml:space="preserve">de telle ſorte que l'on <lb/>pourra toûjours reconnoître ſi le Navire s'écarte de la route qu'il <lb/>doit tenir.</s> <s xml:id="echoid-s8501" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div571" type="section" level="1" n="281"> <head xml:id="echoid-head408" style="it" xml:space="preserve">De la variation ou déclinaiſon de l'Aiman.</head> <p> <s xml:id="echoid-s8502" xml:space="preserve">L'Experience nous a fait connoître que l'éguille aimantée décli-<lb/>ne du vrai Septentrion, c'eſt-à-dire, que la Fleur-de-Lys ne <lb/>tend pas exactement au Nord du Monde; </s> <s xml:id="echoid-s8503" xml:space="preserve">mais qu'elle s'en écarte <lb/>quelquefois vers l'Orient, d'autrefois vers l'Occident, plus ou <lb/>moins, ſelon les tems & </s> <s xml:id="echoid-s8504" xml:space="preserve">les lieux differens.</s> <s xml:id="echoid-s8505" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8506" xml:space="preserve">Environ l'an 1665, elle n'av oit aucune déclinaiſon à Paris, au <lb/>lieu qu'à preſent ſa déclinaiſon y eſt de plus de 12 d. </s> <s xml:id="echoid-s8507" xml:space="preserve">du Septentrion <lb/>vers l'Occident. </s> <s xml:id="echoid-s8508" xml:space="preserve">C'eſt pourquoi il ſaut tâcher d'obſerver avec ſoin <lb/>la déclinaiſon de l'éguille aimantée toutes les fois qu'on en trouve <lb/>l'occaſion favorable, afin d'y avoir égard dans la conduite de la <lb/>Navigation.</s> <s xml:id="echoid-s8509" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8510" xml:space="preserve">Car ſi, par exemple, la déclinaiſon de l'éguille aimantée étoit de <lb/>10 d. </s> <s xml:id="echoid-s8511" xml:space="preserve">du Nord à l'Oüeſt dans l'Iſle d'Oüeſſant, que nous avons ſup-<lb/>poſée le lieu du départ du Navire, & </s> <s xml:id="echoid-s8512" xml:space="preserve">que l'on ſuivît exactement la li-<lb/>gne de Sud-Oüeſt quart au Sud, au lieu d'aller au Cap de Finiſterre <lb/>on iroit vers une autre contrée plus Orientale de 10 deg.</s> <s xml:id="echoid-s8513" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8514" xml:space="preserve">Pour y remedier, il n'y a qu'à changer de place ſur le cadre de la <lb/>Bouſſole, la croix qui marque le rumb de direction, & </s> <s xml:id="echoid-s8515" xml:space="preserve">la reculer vers <lb/>Eſt d'autant de degrez qu'eſt la déclinaiſon de l'éguille vers Oüeſt; <lb/></s> <s xml:id="echoid-s8516" xml:space="preserve">& </s> <s xml:id="echoid-s8517" xml:space="preserve">ainſi toutes les fois qu'on aura reconnu une nouvelle déclinaiſon <lb/>de l'aiman, il ſaudra changer le lieu de ladite croix. </s> <s xml:id="echoid-s8518" xml:space="preserve">Quand la boë-<lb/>te eſt toute ronde on fait une marque au corps de ladite boëte, vis-<lb/>à-vis du Nord & </s> <s xml:id="echoid-s8519" xml:space="preserve">Sud.</s> <s xml:id="echoid-s8520" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8521" xml:space="preserve">Si pareillement un Vaiſſeau part des Sorlingues en Angleterre, <lb/>pour aller à l'lſle de Madere, nous trouverons ſur la Carte Marine <lb/>que la route ſe doit ſaire au Sud Sud-Oüeſt; </s> <s xml:id="echoid-s8522" xml:space="preserve">mais ſi dans ce tems la <lb/> <pb o="271" file="287" n="287" rhead="POUR LA NAVIGATION. Liv. VII. Chap. I."/> déclinaiſon de l'éguille aimantée eſt de 6 d. </s> <s xml:id="echoid-s8523" xml:space="preserve">du Nord à l'Eſt, il ſau-<lb/>dra reculer d'autant de degrez vers l'Occident la croix marquée ſur <lb/>le bord de la Bouſſolo, aſin de diriger la route du Vaiſſeau en appli-<lb/>quant ſur ladite croix le rumb de la Navigation trouvé ſur la Carte.</s> <s xml:id="echoid-s8524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8525" xml:space="preserve">Mais ſi l'on ſe ſert d'une Bouſſole dont on puiſſe changer la poſi-<lb/>tion de l'éguille aimantée, comme celle à double roſe, il faudra arrê-<lb/>ter la Fleur de Lys de la roſe des vents, de ſorte que ſa pointe mar-<lb/>que le vrai Nord, & </s> <s xml:id="echoid-s8526" xml:space="preserve">avoir le ſoin de la changer toutes les ſois que <lb/>l'on trouvera du changement à la déclinaiſon de 1 aiman; </s> <s xml:id="echoid-s8527" xml:space="preserve">& </s> <s xml:id="echoid-s8528" xml:space="preserve">en ce <lb/>cas il ne ſaudra point changer de place la croix qui marque ſur le <lb/>bord de la Bouſſole le rumb de direction du Vaiſſeau.</s> <s xml:id="echoid-s8529" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8530" xml:space="preserve">Il eſt très-néceſſaire, principalement dans les Voïages de long <lb/>cours, que les Pilotes faſſent ſouvent des obſervations celeſtes, a-<lb/>fin d'avoir exactement la déclinaiſon de l'éguille aimantée, non <lb/>ſeulement pour bien diriger la route du Vaiſſeau, mais principa-<lb/>lement pour ſçavoir où l'on eſt, après avoir eſſuïé quelque rude <lb/>tempête, pendant laquelle on aura été contraint de negliger la ve-<lb/>ritable route, en ſe laiſſant entraîner aux vents & </s> <s xml:id="echoid-s8531" xml:space="preserve">aux courans qui <lb/>auront obligé de dériver.</s> <s xml:id="echoid-s8532" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div572" type="section" level="1" n="282"> <head xml:id="echoid-head409" style="it" xml:space="preserve">Trouver la variation de l'Eguille aimantée.</head> <p> <s xml:id="echoid-s8533" xml:space="preserve">IL y a pluſieurs moyens pour reconnoître la déclinaiſon de l'ai-<lb/>man, comme par le lever & </s> <s xml:id="echoid-s8534" xml:space="preserve">le coucher d'un même Aſtre, ou par <lb/>l'obſervation de deux hauteurs égales de l'Aſtre ſur l'horiſon, parce <lb/>qu'en ces deux tems il ſera également éloigne de la vraie Méridiene <lb/>du Monde, ou bien par ſon paſſage au Méridien.</s> <s xml:id="echoid-s8535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8536" xml:space="preserve">Mais tous ces moïens ſont peu uſitez ſur Mer, premierement par-<lb/>ce que ne pouvant ſçavoir aſſez préciſément le tems que le Soleil ou <lb/>un autre Aſtre paſſe par le Méridien, on eſt obligé d'emploïer beau-<lb/>coup de tems pour découvrir par pluſieurs obſervations, quelle eſt <lb/>la plus grande hauteur du Soleil, c'eſt-à-dire, la hauteur Méridiene.</s> <s xml:id="echoid-s8537" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8538" xml:space="preserve">Secondement, parce que le Soleil peut conſiderablement changer <lb/>de déclinaiſon, & </s> <s xml:id="echoid-s8539" xml:space="preserve">le Navire de latitude entre 2 obſervations de ſes <lb/>hauteurs égales ſur l'horiſon, ou entre ſon lever & </s> <s xml:id="echoid-s8540" xml:space="preserve">ſon coucher.</s> <s xml:id="echoid-s8541" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8542" xml:space="preserve">On peut trouver la variation de l'éguille aimantée plus promte-<lb/>ment par une ſeule obſervation des amplitudes des Aſtres. </s> <s xml:id="echoid-s8543" xml:space="preserve">Mais il <lb/>en faut connoître la déclinaiſon, & </s> <s xml:id="echoid-s8544" xml:space="preserve">la latitude du lieu où l'on eſt. <lb/></s> <s xml:id="echoid-s8545" xml:space="preserve">Cela ſuppoſé on peut a voir une Table calculée des amplitudes des <lb/>Aſtres dont on prétend ſe ſervir.</s> <s xml:id="echoid-s8546" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8547" xml:space="preserve">L'amplitude Orientale d'un Aſtre eſt l'arc de l'horiſon compris <lb/> <pb o="272" file="288" n="288" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> entre le point où il ſe leve & </s> <s xml:id="echoid-s8548" xml:space="preserve">le vrai Eſt; </s> <s xml:id="echoid-s8549" xml:space="preserve">& </s> <s xml:id="echoid-s8550" xml:space="preserve">l'amplitude Occidentale <lb/>eſt l'arc de l'horiſon compris entre le point où il ſe couche & </s> <s xml:id="echoid-s8551" xml:space="preserve">le vrai <lb/>Oüeſt</s> </p> <p> <s xml:id="echoid-s8552" xml:space="preserve">Les Aſtres dont la déclinaiſon eſt Septentrionale, ont auſſi leur <lb/>amplitude Septentrionale, & </s> <s xml:id="echoid-s8553" xml:space="preserve">ceux qui l'ont Méridionalc ont leur <lb/>amplitude du même côté. </s> <s xml:id="echoid-s8554" xml:space="preserve">Plus les Aſtres ont de déclinaiſon, plus <lb/>ils ont d'amplitude; </s> <s xml:id="echoid-s8555" xml:space="preserve">les obliquitez de la Sphere augmentent auſſi les <lb/>amplitudes des Aſtres; </s> <s xml:id="echoid-s8556" xml:space="preserve">car dans la Sphere droite les amplitudes <lb/>des Aſtres ſont préciſément égales à leurs déclinaiſons, & </s> <s xml:id="echoid-s8557" xml:space="preserve">dans la <lb/>Sphere oblique elles ſont plus grandes.</s> <s xml:id="echoid-s8558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8559" xml:space="preserve">On aura par chaque obſervation une autre amplitude de l'Aſtre, <lb/>que l'on peut nommer l'amplitude obſervée, qui eſt la diſtance de <lb/>l'Eſt de la Bouſſole, juſqu'au point de l'horiſon où l'Aſtre ſe leve, ou <lb/>la diſtance de l'Oüeſt de la Bouſſole, juſqu'au point où il ſe couche.</s> <s xml:id="echoid-s8560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8561" xml:space="preserve">Cette amplitude s'obſerve en regardant par les ouvertures ou par <lb/>les pinules du compas de variation le lever ou le coucher de l'Aſtre; <lb/></s> <s xml:id="echoid-s8562" xml:space="preserve">& </s> <s xml:id="echoid-s8563" xml:space="preserve">comme le ſil qui traverſe & </s> <s xml:id="echoid-s8564" xml:space="preserve">paſſe par le centre de l'inſtrument, re-<lb/>preſente le raïon de l'Aſtre, les degrez de la roſe compris depuis ce <lb/>fil juſqu'à l'Eſt ou l'Oüeſt du Compas ou Bouſſole, marquent les de-<lb/>grez de l'amplitude obſervée; </s> <s xml:id="echoid-s8565" xml:space="preserve">enſuite comparant l'amplitude de la <lb/>table calculée avec l'amplitude obſervée, on connoîtra la variation <lb/>de l'éguille, ſi elle en a, de la maniere que nous allons expliquer.</s> <s xml:id="echoid-s8566" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div573" type="section" level="1" n="283"> <head xml:id="echoid-head410" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s8567" xml:space="preserve">Etanten Mer le 15<emph style="sub">me</emph> jour de Mai de l'année 1715, à 45 d. </s> <s xml:id="echoid-s8568" xml:space="preserve">de la-<lb/>titude Seprentrionale, je connois par une Table calculée que la dé-<lb/>clinaiſon du Soleil eſt de 19 d. </s> <s xml:id="echoid-s8569" xml:space="preserve">Septentrionale, & </s> <s xml:id="echoid-s8570" xml:space="preserve">ſon amplitude O-<lb/>rientale de 27 d. </s> <s xml:id="echoid-s8571" xml:space="preserve">25 m. </s> <s xml:id="echoid-s8572" xml:space="preserve">Septrionale. </s> <s xml:id="echoid-s8573" xml:space="preserve">Je l'obſerve à ſon lever avec <lb/>les pinules du Compas de variation, & </s> <s xml:id="echoid-s8574" xml:space="preserve">je trouve qu'il paroît ſe lever <lb/>entre le 62 & </s> <s xml:id="echoid-s8575" xml:space="preserve">le 63 d. </s> <s xml:id="echoid-s8576" xml:space="preserve">compté du Nord, allant ves l'Eſt de la roſe; <lb/></s> <s xml:id="echoid-s8577" xml:space="preserve">c'eſt-à-dire, entre le 27 & </s> <s xml:id="echoid-s8578" xml:space="preserve">le 28<emph style="sub">me</emph> d. </s> <s xml:id="echoid-s8579" xml:space="preserve">compté de l'Eſt, & </s> <s xml:id="echoid-s8580" xml:space="preserve">comme en <lb/>ce cas l'àmplitude obſervée eſt égale à l'amplitude calculée, je con-<lb/>clus qu'en cet endroit & </s> <s xml:id="echoid-s8581" xml:space="preserve">en ce tems là l'éguille n'a point de décli-<lb/>naiſon.</s> <s xml:id="echoid-s8582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8583" xml:space="preserve">Mais ſile Soleil a paru ſe lever entre le 52 & </s> <s xml:id="echoid-s8584" xml:space="preserve">53<emph style="sub">me</emph> degré compté <lb/>du Nord à l'Eſt, ſon amplitude obſervée ſera de 37 à 38 deg. </s> <s xml:id="echoid-s8585" xml:space="preserve">c'eſt-<lb/>à-dire, de 10 d. </s> <s xml:id="echoid-s8586" xml:space="preserve">plus grande que celle de la Table calculée, par où <lb/>l'on connoít que l'éguille aimantée décline du Nord à l'Eſt de 10 <lb/>d. </s> <s xml:id="echoid-s8587" xml:space="preserve">Si au contraire l'amplitude Orientale obſervée étoit moindre <lb/>que la calculée, leur difference marqueroit la déclinaiſon de l'éguil-<lb/>le du Nord à l'Oüeſt. </s> <s xml:id="echoid-s8588" xml:space="preserve">Car ſi l'amplitude obſervée eſt plus grande <lb/> <pb o="273" file="289" n="289" rhead="POUR LA NAVIGATION. Liv. VII. Chap. II."/> que la vraie, cela vient de ce que l'Eſt de la Bouſſole ſe reculant du <lb/>Soleil vers le Sud, la Fleur-de-Lys de la roſe s'approche de l'Eſt, <lb/>& </s> <s xml:id="echoid-s8589" xml:space="preserve">donne la variation Nord-Eſt. </s> <s xml:id="echoid-s8590" xml:space="preserve">La raiſon pour le contraire eſt é-<lb/>galement évidente.</s> <s xml:id="echoid-s8591" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8592" xml:space="preserve">Si l'amplitude Orientale calculée eſt du côté du Sud, auſſi-bien <lb/>que l'amplitude obſervée, & </s> <s xml:id="echoid-s8593" xml:space="preserve">que celle ci ſoit la plus grande, la dé-<lb/>clinaiſon de l'éguille ſera Nord-Oüeſt. </s> <s xml:id="echoid-s8594" xml:space="preserve">Si au contraire elle eſt plus <lb/>petite, la déclinaiſon ſera Nord-Eſt d'autant de degrez que ſera leur <lb/>difference.</s> <s xml:id="echoid-s8595" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8596" xml:space="preserve">Ce que nous avons dit des amplitudes Orientales Nord, ſe doit <lb/>entendre pour les amplitudes Occidentales Sud; </s> <s xml:id="echoid-s8597" xml:space="preserve">& </s> <s xml:id="echoid-s8598" xml:space="preserve">ce que nous a-<lb/>vons dit des amplitudes Orientales Sud, ſe doit entendre pour les <lb/>amplitudes Occidentales Nord.</s> <s xml:id="echoid-s8599" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8600" xml:space="preserve">Enſin ſi les amplitudes ſe trouvent de differente dénomination, <lb/>par exemple, aux amplitudes Orientales, ſi l'amplitude calculée eſt <lb/>de 6 d. </s> <s xml:id="echoid-s8601" xml:space="preserve">Nord, & </s> <s xml:id="echoid-s8602" xml:space="preserve">que l'obſervée ſoit de 5 d. </s> <s xml:id="echoid-s8603" xml:space="preserve">Sud, c'eſt une marque <lb/>que la variation, qui dans ce cas ſera NO, ſe trouve plus gran-<lb/>de que la vraie amplitude, étant égale à la ſomme des deux ampli-<lb/>tudes, vraie & </s> <s xml:id="echoid-s8604" xml:space="preserve">obſervée; </s> <s xml:id="echoid-s8605" xml:space="preserve">c'eſt pourquoi les ajoûtant enſemble on <lb/>aura 11 d. </s> <s xml:id="echoid-s8606" xml:space="preserve">de variation NO. </s> <s xml:id="echoid-s8607" xml:space="preserve">Il en ſeroit de même pour les ampli-<lb/>tudes Occidentales.</s> <s xml:id="echoid-s8608" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8609" xml:space="preserve">On peut encore trouver la variation de l'éguille aimantée à tou-<lb/>te heure par l'Azimut d'un Aſtre, ayant ſa hauteur & </s> <s xml:id="echoid-s8610" xml:space="preserve">ſa déclinai-<lb/>ſon avec la latitude du lieu, comme nous l'avons expliqué dans les <lb/>Uſages 26 & </s> <s xml:id="echoid-s8611" xml:space="preserve">27 du Livre qui a pour titre Uſage des Aſtrolabes.</s> <s xml:id="echoid-s8612" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div574" type="section" level="1" n="284"> <head xml:id="echoid-head411" xml:space="preserve"><emph style="bf">CHAPITRE II.</emph></head> <head xml:id="echoid-head412" style="it" xml:space="preserve">De la Conſtruction & Vſage des Inſtrumens qui ſervent à <lb/>obſerver la hauteur des Aſtres. <lb/>De l'Aſtrolabe de Mer.</head> <p> <s xml:id="echoid-s8613" xml:space="preserve">LE plus ordinaire des Inſtrumens pour prendre hauteur en Mer, <lb/> <anchor type="note" xlink:label="note-289-01a" xlink:href="note-289-01"/> eſt l'Aſtrolabe. </s> <s xml:id="echoid-s8614" xml:space="preserve">C'eſt un cercle de cuivre d'environ un pied de <lb/>diametre, & </s> <s xml:id="echoid-s8615" xml:space="preserve">de 6 à 7 lig. </s> <s xml:id="echoid-s8616" xml:space="preserve">d'épaiſſeur, afin qu'il ait du poids: </s> <s xml:id="echoid-s8617" xml:space="preserve">quelque-<lb/>fois on y attache encore un poids de 5 à 6 liv. </s> <s xml:id="echoid-s8618" xml:space="preserve">à l'endroit marqué B, <lb/>afin qu'étant ſuſpendu par ſon anneau A, qui doit être bien mobile, <lb/>il ſe puiſſe tourner facilement de toutes parts, & </s> <s xml:id="echoid-s8619" xml:space="preserve">garder la ſituation <lb/>perpendiculaire pendant les mouvemens du Navire.</s> <s xml:id="echoid-s8620" xml:space="preserve"/> </p> <div xml:id="echoid-div574" type="float" level="2" n="1"> <note position="right" xlink:label="note-289-01" xlink:href="note-289-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s8621" xml:space="preserve">Il eſt diviſé en 4 fois 90 d. </s> <s xml:id="echoid-s8622" xml:space="preserve">& </s> <s xml:id="echoid-s8623" xml:space="preserve">fort ſouvent en demis & </s> <s xml:id="echoid-s8624" xml:space="preserve">quarts de <lb/>degré.</s> <s xml:id="echoid-s8625" xml:space="preserve"/> </p> <pb o="274" file="290" n="290" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> <p> <s xml:id="echoid-s8626" xml:space="preserve">Il eſt abſolument néceſſaire que la ligne droite CD, qui repreſen-<lb/>te l'horiſon, ſoit parfaitement de niveau, aſin d'y pouvoir commen-<lb/>cer la diviſion du cercle. </s> <s xml:id="echoid-s8627" xml:space="preserve">Pour l'examiner il ſaut obſerver par les fen-<lb/>tes ou les petits trous des pinules FG, qui ſont attachées vers les ex-<lb/>trémitez de l'alidade qui tourne librement par le moyen d'un clou <lb/>à tête autour du centre E. </s> <s xml:id="echoid-s8628" xml:space="preserve">Il faut, dis-je, obſerver un même objet <lb/>éloigné, en mettant l'œil à l'une deſdites pinules; </s> <s xml:id="echoid-s8629" xml:space="preserve">après avoir tour-<lb/>né l'Aſtrolabe ſile même objet ſe voit toutes les 2 fois ſans changer <lb/>l'alidade, c'eſt une marque que la ligne de foi convient avec l'hori-<lb/>ſon. </s> <s xml:id="echoid-s8630" xml:space="preserve">Mais ſi pour voir une ſeconde fois le même objet il faut mou-<lb/>voir l'alidade, c'eſt-à-dire, la hauſſer ou baiſſer, le point milieu en-<lb/>tre ces 2 poſitions marquera la vraie ligne horiſontale, paſſant par <lb/>le centre de l'inſtrument; </s> <s xml:id="echoid-s8631" xml:space="preserve">ce qu'il ſera bon de veriſier par pluſieurs <lb/>obſervations réiterées avant que de commencer la diviſion qui ſe <lb/>fera de la maniere que nous avons expliqué ci-devant.</s> <s xml:id="echoid-s8632" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div576" type="section" level="1" n="285"> <head xml:id="echoid-head413" style="it" xml:space="preserve">Vſage de l'Aſtrolabe.</head> <p> <s xml:id="echoid-s8633" xml:space="preserve">P Our obſerver la hauteur des Aſtres ſur l'horiſon, & </s> <s xml:id="echoid-s8634" xml:space="preserve">leur diſtan-<lb/>ce du Zénith qui en eſt le complément.</s> <s xml:id="echoid-s8635" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8636" xml:space="preserve">Pour cet effet on ſuſpend l'Aſtrolabe par ſon anneau & </s> <s xml:id="echoid-s8637" xml:space="preserve">on tour-<lb/>ne ſon côtévers l'Aſtre, en hauſſant un des bouts de l'alidade F, juſ-<lb/>qu'à ce que le raïon de l'Aſtre paſſe par les 2 pinules FG; </s> <s xml:id="echoid-s8638" xml:space="preserve">alors l'a-<lb/>lidade marquera par ſes extremitez, autour du cercle diviſé, la hau-<lb/>teur de l'Aſtre H, depuis C juſqu'en F, compris entre le raïon hori-<lb/>ſontal EC, & </s> <s xml:id="echoid-s8639" xml:space="preserve">le raïon de l'Aſtre EF, parce que cet inſtrument dans <lb/>cette ſituation repreſente un vertical. </s> <s xml:id="echoid-s8640" xml:space="preserve">La diviſion AG ou ou AF mar-<lb/>quera la diſtance de l'Aſtre au Zénith.</s> <s xml:id="echoid-s8641" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div577" type="section" level="1" n="286"> <head xml:id="echoid-head414" style="it" xml:space="preserve">Conſtruction de l'Anneau.</head> <p> <s xml:id="echoid-s8642" xml:space="preserve">C Ette ſigure repreſente un anneau ou cercle de cuivre. </s> <s xml:id="echoid-s8643" xml:space="preserve">Il ſe ſait <lb/> <anchor type="note" xlink:label="note-290-01a" xlink:href="note-290-01"/> de 8 à 10 pouces de diametre; </s> <s xml:id="echoid-s8644" xml:space="preserve">il eſt néceſſaire qu'il ſoit d'une <lb/>bonne épaiſſeur, aſin qu'étant plus peſant il conſerve mieux ſa ſitua-<lb/>tion perpendiculaire; </s> <s xml:id="echoid-s8645" xml:space="preserve">la diviſion ſe marque dans ſa ſurface concave. <lb/></s> <s xml:id="echoid-s8646" xml:space="preserve">Il y a un petit trou en C, qui traverſe l'anneau parallelement à ſon <lb/>plan. </s> <s xml:id="echoid-s8647" xml:space="preserve">Ce trou eſt éloigné de 45 d. </s> <s xml:id="echoid-s8648" xml:space="preserve">du point de ſuſpenſion B, & </s> <s xml:id="echoid-s8649" xml:space="preserve">il eſt <lb/>le centre d'un quart de cercle DE, diviſé en 90 d. </s> <s xml:id="echoid-s8650" xml:space="preserve">Un de ſes raïons <lb/>CE eſt parallele au diametre vertical BH, point de ſuſpenſion; </s> <s xml:id="echoid-s8651" xml:space="preserve">& </s> <s xml:id="echoid-s8652" xml:space="preserve"><lb/>l'autre raïon horiſontal eſt perpendiculaire au même diametre.</s> <s xml:id="echoid-s8653" xml:space="preserve"/> </p> <div xml:id="echoid-div577" type="float" level="2" n="1"> <note position="left" xlink:label="note-290-01" xlink:href="note-290-01a" xml:space="preserve">XIX. <lb/>Planche. <lb/>Fig. 5.</note> </div> <p> <s xml:id="echoid-s8654" xml:space="preserve">Nous ne diſons rien ici de la préciſion avec laquelle on doit avoir <lb/>ce diametre. </s> <s xml:id="echoid-s8655" xml:space="preserve">L'habileté de l'Ouvrier y ſuppléera ſacilement. </s> <s xml:id="echoid-s8656" xml:space="preserve">Enſuite <lb/> <pb o="275" file="291" n="291" rhead="POUR LA NAVIGATION. Liv. VII. Ch. II."/> on tire des raïons du centre C à tous les degrez du quart de cercle <lb/>DE, pour les marquer dans la ſurface intérieure de l'inſtrument, de-<lb/>puis F juſqu'en G. </s> <s xml:id="echoid-s8657" xml:space="preserve">On peut faire cette diviſion à part ſur un plan, <lb/>puis la tranſporter bien exactement dans la concavité du cercle.</s> <s xml:id="echoid-s8658" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8659" xml:space="preserve">Ce qui fait eſtimer cet Inſtrument eſt que les degrez de la diviſion <lb/>ſont plus grands à proportion de ſa grandeur, que ceux de l'Aſtro-<lb/>labe.</s> <s xml:id="echoid-s8660" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div579" type="section" level="1" n="287"> <head xml:id="echoid-head415" style="it" xml:space="preserve">Uſage de l'Anneau.</head> <p> <s xml:id="echoid-s8661" xml:space="preserve">POur s'en ſervir il faut le ſuſpendre par la boucle B, & </s> <s xml:id="echoid-s8662" xml:space="preserve">le tourner <lb/>vers le Soleil A, en ſorte que ſon raïon paſſe par le trou C.</s> <s xml:id="echoid-s8663" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8664" xml:space="preserve">Il marquera au fond de l'anneau de F en I, les degrez de la hau-<lb/>teur du Soleil entre le raïon horiſontal CF, & </s> <s xml:id="echoid-s8665" xml:space="preserve">le raïon de l'Aſtre CI <lb/>la partie IHG, marquera ſa diſtance au Zénith, entre le raion CI <lb/>& </s> <s xml:id="echoid-s8666" xml:space="preserve">le raïon vertical CG.</s> <s xml:id="echoid-s8667" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div580" type="section" level="1" n="288"> <head xml:id="echoid-head416" style="it" xml:space="preserve">Du Lart de Cercle.</head> <p> <s xml:id="echoid-s8668" xml:space="preserve">L'IN ſtrument marqué par la figure ſixiéme eſt un quart de cercle <lb/> <anchor type="note" xlink:label="note-291-01a" xlink:href="note-291-01"/> d'environ un pied de raïon. </s> <s xml:id="echoid-s8669" xml:space="preserve">Il eſt diviſe en 90 deg. </s> <s xml:id="echoid-s8670" xml:space="preserve">& </s> <s xml:id="echoid-s8671" xml:space="preserve">ſouvent <lb/>de 5 en 5 min. </s> <s xml:id="echoid-s8672" xml:space="preserve">par des tranſverſales. </s> <s xml:id="echoid-s8673" xml:space="preserve">Il y a deux pinules ſur un de <lb/>ſes raïons AE. </s> <s xml:id="echoid-s8674" xml:space="preserve">Le ſil où eſt attaché le plomb eſt arrêté au centte A. <lb/></s> <s xml:id="echoid-s8675" xml:space="preserve">Nous ne nous étendrons pas ſur la conſtruction de.</s> <s xml:id="echoid-s8676" xml:space="preserve">cet Inſtrument, <lb/>en ayant ſuffiſamment parlé au Chapitre V, du Livre IV. </s> <s xml:id="echoid-s8677" xml:space="preserve">qui traite <lb/>de la Conſtruction du quarré géo métrique.</s> <s xml:id="echoid-s8678" xml:space="preserve"/> </p> <div xml:id="echoid-div580" type="float" level="2" n="1"> <note position="right" xlink:label="note-291-01" xlink:href="note-291-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s8679" xml:space="preserve">Pour s'en ſervir il faut le tourner vers l'Aſtre D, de maniere que <lb/>ſon raïon DAB paſſe par les deux pinules A&</s> <s xml:id="echoid-s8680" xml:space="preserve">E: </s> <s xml:id="echoid-s8681" xml:space="preserve">alors le ſil à plomb <lb/>qui doit raſer librement les degrez du quart de cercle, marquera en <lb/>C les degrez de la hauteur du Soleil depuis B juſqu'en C, & </s> <s xml:id="echoid-s8682" xml:space="preserve">ſon com-<lb/>plément depuis C juſqu'en E.</s> <s xml:id="echoid-s8683" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div582" type="section" level="1" n="289"> <head xml:id="echoid-head417" style="it" xml:space="preserve">De l'Arbaleſtrille.</head> <p> <s xml:id="echoid-s8684" xml:space="preserve">CEt Inſtrument eſt compoſé de deux pieces, dont l'une qui eſt <lb/> <anchor type="note" xlink:label="note-291-02a" xlink:href="note-291-02"/> d'environ trois pieds de long, s'appelle la Fleche, & </s> <s xml:id="echoid-s8685" xml:space="preserve">l'autre qui <lb/>eſt plus courte, le Marteau.</s> <s xml:id="echoid-s8686" xml:space="preserve"/> </p> <div xml:id="echoid-div582" type="float" level="2" n="1"> <note position="right" xlink:label="note-291-02" xlink:href="note-291-02a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s8687" xml:space="preserve">La Fléché AB eſt une piece d'ébeine bien quarrée en tout ſens, <lb/>de 6 à 7 lignes de groſſeur, & </s> <s xml:id="echoid-s8688" xml:space="preserve">bien égale en toute ſa longueur.</s> <s xml:id="echoid-s8689" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8690" xml:space="preserve">Le Marteau CD eſt une piece de bois de Poirier bien unie & </s> <s xml:id="echoid-s8691" xml:space="preserve">ap-<lb/>planie d'un côté, laquelle a un trou quarré juſtement dans ſon mi-<lb/>lieu, qui doit être plus épais, aſin que la Fléche gliſſant dans ce <lb/>trou, ſoit plus ſerme & </s> <s xml:id="echoid-s8692" xml:space="preserve">s'y tienne perpendiculaire au Marteau.</s> <s xml:id="echoid-s8693" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8694" xml:space="preserve">La Fléche doit être diviſée en ſa longueur, en degrez & </s> <s xml:id="echoid-s8695" xml:space="preserve">minutes <lb/> <pb o="276" file="292" n="292" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> ſur chacune de ſes 4 faces, leſquelles ne different entr'elles que dans <lb/>la grandeur de leurs degrez, proportionnez à la diſſerente grandeur <lb/>des Marteaux; </s> <s xml:id="echoid-s8696" xml:space="preserve">car chaque ſace doit avoir ſon Marteau particulier.</s> <s xml:id="echoid-s8697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8698" xml:space="preserve">Le commencement de la diviſion ſe fait vers A, où ſe place l'œil <lb/>de l'Obſervateur, mais à diſtance d'environ demi-pouce du bout de <lb/>la Fléche, à cauſe de la convexité du globe de l'œil, car c'eſt à ſon <lb/>centre que les principaux raïons des objets ſe vont croiſer.</s> <s xml:id="echoid-s8699" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8700" xml:space="preserve">Si donc on veut diviſer la face AB pour ſervir au plus grand Mar-<lb/>teau CD, il faut chercher dans les Tables calculées les tangentes <lb/>des degrez du cercle dont le raîon eſt égal à la moitiédud. </s> <s xml:id="echoid-s8701" xml:space="preserve">Marteau, <lb/>& </s> <s xml:id="echoid-s8702" xml:space="preserve">du point A, les tranſporter ſur la face AB, & </s> <s xml:id="echoid-s8703" xml:space="preserve">marquer ſur chaque <lb/>diviſion le nombre qui convient aux tangentes du complément de <lb/>la moitié de l'arc que l'on veut marquer, par le moyen d'une échelle <lb/>de mille parties qui ſoit égale à la moitié dudit Marteau.</s> <s xml:id="echoid-s8704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8705" xml:space="preserve">Si, par exemple, on veut marquer ſur la Fléche le point de 90 d. </s> <s xml:id="echoid-s8706" xml:space="preserve">ſa <lb/>moitié eſt 45, & </s> <s xml:id="echoid-s8707" xml:space="preserve">ſon complément anſſi 45, dont la tangente eſt éga-<lb/>le au raïon; </s> <s xml:id="echoid-s8708" xml:space="preserve">c'eſt pourquoi la moitié du Marteau ſera préciſément é-<lb/>gale à la diſtance depuis le bout de l'œil A, juſqu'au point de 90 d. <lb/></s> <s xml:id="echoid-s8709" xml:space="preserve">car le demi-Marteau eſt le raïon d'un cercle dont les tangentes ſont <lb/>contenuës dans la Fléche, comme il eſt aiſé de voir par la figure 8.</s> <s xml:id="echoid-s8710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8711" xml:space="preserve">Pareillement ſi on veut y marquer le point de 80 d. </s> <s xml:id="echoid-s8712" xml:space="preserve">dont la moi-<lb/>tié eſt 40, & </s> <s xml:id="echoid-s8713" xml:space="preserve">ſon complément 50, cherchez la tangente de 50 d. </s> <s xml:id="echoid-s8714" xml:space="preserve">& </s> <s xml:id="echoid-s8715" xml:space="preserve"><lb/>vous trouverez 119 175, duquel nombre il faut retrancher les 2 der-<lb/>nieres figures à cauſe que nous avons ſupoſé le raïon ou demi-Mar-<lb/>teau de mille parties égales, au lieu des 100000 qui ſont aſſignées <lb/>au raîon des tables. </s> <s xml:id="echoid-s8716" xml:space="preserve">Cette tangente ſera doncpreſque 1192, & </s> <s xml:id="echoid-s8717" xml:space="preserve">ayant <lb/>pris ſur l'échelle 192 part. </s> <s xml:id="echoid-s8718" xml:space="preserve">il faudra les porter au-delà du point de <lb/>90 d. </s> <s xml:id="echoid-s8719" xml:space="preserve">pour marquer 80 d. </s> <s xml:id="echoid-s8720" xml:space="preserve">ſur la Fléche. </s> <s xml:id="echoid-s8721" xml:space="preserve">De même pour y marquer <lb/>70d. </s> <s xml:id="echoid-s8722" xml:space="preserve">la moitié eſt 35, & </s> <s xml:id="echoid-s8723" xml:space="preserve">ſon complément 55, dont la tangente oſt <lb/>1428. </s> <s xml:id="echoid-s8724" xml:space="preserve">Il ſaudra porterl'étenduë de 428 parties égales, priſes ſur l'é-<lb/>chelle, depuis le point de 90 d. </s> <s xml:id="echoid-s8725" xml:space="preserve">pour marquer ſur la Fléche 70 d. <lb/></s> <s xml:id="echoid-s8726" xml:space="preserve">& </s> <s xml:id="echoid-s8727" xml:space="preserve">ainſi de tous les autres degrez & </s> <s xml:id="echoid-s8728" xml:space="preserve">minutes, tant que la Fleche en <lb/>pourra contenir.</s> <s xml:id="echoid-s8729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8730" xml:space="preserve">Mais ſi la moitié du grand Marteau eſt de 10 pouces, & </s> <s xml:id="echoid-s8731" xml:space="preserve">la Fléche <lb/>de 2 pieds 6 pouces, on ne pourra pas marquer ſur la face qui lui <lb/>convient les degrez au-deſſous de 40, parce que la tangente du <lb/>complément de 20 deg. </s> <s xml:id="echoid-s8732" xml:space="preserve">qui eſt 70 deg. </s> <s xml:id="echoid-s8733" xml:space="preserve">eſt de 2747 parties, c'eſt-<lb/>à-dire, preſque trois fois le raïon.</s> <s xml:id="echoid-s8734" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8735" xml:space="preserve">La moitié du <unsure/>econd Marteau étant ſuppoſée de 6 à 7 pouces on <lb/>pourra marquer les degrez ſur la face qui lui convient depuis 90 d. <lb/></s> <s xml:id="echoid-s8736" xml:space="preserve">juſqu'à 30.</s> <s xml:id="echoid-s8737" xml:space="preserve"/> </p> <pb o="277" file="293" n="293" rhead="POUR LA NAVIGATION. Liv. VII. Ch. II."/> <p> <s xml:id="echoid-s8738" xml:space="preserve">Si la moitié du 3<emph style="sub">me</emph> Marteau eſt de 4 à 5 pouces, on pourra mar-<lb/>quer ſur la facé qui lui convient les degrez depuis 90 juſqu'à 20. <lb/></s> <s xml:id="echoid-s8739" xml:space="preserve">Enſin ſi le 4<emph style="sub">me</emph>, & </s> <s xml:id="echoid-s8740" xml:space="preserve">plus petit Marteau eſt de 2 pouces & </s> <s xml:id="echoid-s8741" xml:space="preserve">{1/2}, on pourra <lb/>marquer ſur la face qui lui convient les deg. </s> <s xml:id="echoid-s8742" xml:space="preserve">depuis 90 juſqu a 10.</s> <s xml:id="echoid-s8743" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8744" xml:space="preserve">Pour les grandes hauteurs on ſe ſert des grands Marteaux, parce <lb/>que les diviſions en ſont plus juſtes; </s> <s xml:id="echoid-s8745" xml:space="preserve">& </s> <s xml:id="echoid-s8746" xml:space="preserve">pour les moindres hauteurs <lb/>il faut ſe ſervir des petits Marteaux.</s> <s xml:id="echoid-s8747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8748" xml:space="preserve">Pour trouver la face qui convient à un Marteau, il n'y a qu'à <lb/>preſenter ſa moitié ſur la Fléche; </s> <s xml:id="echoid-s8749" xml:space="preserve">ſi elle ſe trouve égale à la diſtan-<lb/>ce depuis l'extremité appellée le bout de l'œil, juſqu'à 90 degrez, <lb/>on aura la face convenable au Marteau.</s> <s xml:id="echoid-s8750" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8751" xml:space="preserve">On peut auſſi marquer méchaniquement les degrez ſur la Fléche <lb/>en la maniere ſuivante.</s> <s xml:id="echoid-s8752" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8753" xml:space="preserve">Il faut faire un grand Quart de cercle dont le raïon ſoit auſſi grand <lb/> <anchor type="note" xlink:label="note-293-01a" xlink:href="note-293-01"/> que la Fléche AB. </s> <s xml:id="echoid-s8754" xml:space="preserve">Ce Quart de cercle doit être diviſe en degrez & </s> <s xml:id="echoid-s8755" xml:space="preserve"><lb/>minutes de 10 en 10; </s> <s xml:id="echoid-s8756" xml:space="preserve">& </s> <s xml:id="echoid-s8757" xml:space="preserve">après avoir paſſé la Flêche dans ſon Mar-<lb/>teau CD, en ſorte que le plat dudit Marteau ſoit tourné vers l'ex-<lb/>tremité A de la Fléche, on l'appliquera ſur le quart de cercle, de ſor-<lb/>te que le bout A réponde exactement ſur le centre du quart de cer-<lb/>cle, & </s> <s xml:id="echoid-s8758" xml:space="preserve">que le bout D du Marteau ſoit toûjours ſur le rayon AF. </s> <s xml:id="echoid-s8759" xml:space="preserve">On <lb/>approchera doucement le Marteau CD du bout A, juſqu'à ce que <lb/>ſon autre extremité C touche le raïon AM, qui paſſe par le degré <lb/>que l'on veutmarquer ſur la fléche, lequel degré on marquera à l'en-<lb/>droit où raſera le Marteau au point E, & </s> <s xml:id="echoid-s8760" xml:space="preserve">l'on continuëra de rappro-<lb/>cher le Marteau du centre A le long du raïon ADF, juſqu'à ce qu'il <lb/>touche ſucceſſivement les rayons de tous les degrez, pour les mar-<lb/>quer ſur une colonne le long de la fléche AB, en augmentant à meſu-<lb/>re qu'ils approchent du bout A. </s> <s xml:id="echoid-s8761" xml:space="preserve">On marquera auſſi les deg. </s> <s xml:id="echoid-s8762" xml:space="preserve">de com-<lb/>plément ſur la même face, ſur une autre colonne, leſquels vont en <lb/>diminuant de B vers A. </s> <s xml:id="echoid-s8763" xml:space="preserve">On pourra mettre un fil au centre A, pour <lb/>ſervir de raïon comme AM, en le tendant ſucceſſivement ſur tous <lb/>les degrez, à meſure qu'on lui fera toucher le bout C du Marteau.</s> <s xml:id="echoid-s8764" xml:space="preserve"/> </p> <div xml:id="echoid-div583" type="float" level="2" n="2"> <note position="right" xlink:label="note-293-01" xlink:href="note-293-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s8765" xml:space="preserve">On fera la même choſe ſur les autres faces pour y marquer les <lb/>diviſions, ſuivant les differens Marteaux. </s> <s xml:id="echoid-s8766" xml:space="preserve">La petite figure P fait <lb/>voir un Marteau vû de face avec ſon trou.</s> <s xml:id="echoid-s8767" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div585" type="section" level="1" n="290"> <head xml:id="echoid-head418" style="it" xml:space="preserve">Vſage de l'Arbaleſtrille.</head> <p> <s xml:id="echoid-s8768" xml:space="preserve">POur obſerver la hauteur d'un Aſtre par devant avec l'Arbaleſ-<lb/>trille, il faut après avoir paſſé le Marteau dans la Fléche du côté <lb/>de ſa face, ſon côté plat vers le bout de l'œil A, appuïer ce même <lb/> <pb o="278" file="294" n="294" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> bout à côté de l'œil & </s> <s xml:id="echoid-s8769" xml:space="preserve">regarder l'horiſon ſenſible par le bout d'en-<lb/>bas D du Marteau DC, ſuivant le raion viſuel horiſontal ABF, en <lb/>faiſant gliſſer le Marteau le long de la Fléche en l'approchant ou <lb/>le reculant de l'œil, juſqu'à ce que l'on voye l'Aſtre par le bout C <lb/>du Marteau, & </s> <s xml:id="echoid-s8770" xml:space="preserve">alors il marquera ſur la Fléche les degrez de la <lb/>hauteur de l'Aſtre, ſur la colonne qui va en augmentant vers 90, <lb/>ou vers le bout de l'œil A, il marquera auſſi vis-à-vis la diſtance <lb/>de l'Aſtre au Zénith ou le complément de ſa hauteur ſur l'autre <lb/>colonne qui va en diminuant vers le même bout de l'œil A.</s> <s xml:id="echoid-s8771" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8772" xml:space="preserve">L'on prend hauteur par devant aux Etoiles & </s> <s xml:id="echoid-s8773" xml:space="preserve">au Soleil, lorſque <lb/>ſes raions n'ont guéres de force à cauſe de quelque nuage, en met-<lb/>tant un morceau de verre bruni au devant de l'œil pour le conſer-<lb/>ver des raions du Soleil.</s> <s xml:id="echoid-s8774" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8775" xml:space="preserve">Pour obſerver la hauteur du Soleil par derriere avec l'Arbaleſtril-<lb/>le il faut premierement ajuſter le plat du Marteau dans le bout de <lb/>la Fléche A, de ſorte que le tout ſoit à l'uni. </s> <s xml:id="echoid-s8776" xml:space="preserve">Enſuite on paſſera dans <lb/>la Fléche le plus petit des 4 Marteaux: </s> <s xml:id="echoid-s8777" xml:space="preserve">ſon côté plat auſſi vers le <lb/>bout A. </s> <s xml:id="echoid-s8778" xml:space="preserve">On ajoûtera au bout d'en-bas D du Marteau une eſpece de <lb/>pinule de cuivre, dont la fente ſoit parallele au plan de l'horiſon.</s> <s xml:id="echoid-s8779" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8780" xml:space="preserve">L'Arbaleſtrille étant ainſi préparée il faut tourner le dos au Soleil <lb/>& </s> <s xml:id="echoid-s8781" xml:space="preserve">regarder l'horiſon ſenſible par la pinule D, & </s> <s xml:id="echoid-s8782" xml:space="preserve">par deſſous la <lb/>traverſe qui eſt au milieu du petit Marteau; </s> <s xml:id="echoid-s8783" xml:space="preserve">en regardant ainſi l'ho-<lb/>riſon on approchera ou reculera ce petit Marteau juſqu'à ce que <lb/>l'ombre du bout C du grand Marteau ſe termine ſur la traverſe du <lb/>petit Marteau, à l'endroit qui répond au milieu de la groſſeur de la <lb/>Fléche; </s> <s xml:id="echoid-s8784" xml:space="preserve">alors le petit Marteau marquera ſur la Fléche les degrez de <lb/>la hauteur du Soleil & </s> <s xml:id="echoid-s8785" xml:space="preserve">de ſon complément.</s> <s xml:id="echoid-s8786" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8787" xml:space="preserve">On ſe ſert le plus ſouvent de cette ſeconde maniere, qui eſt d'ob-<lb/>ſerver la hauteur de l'Aſtre par derriere, parce qu'en ce casl'œil n'a <lb/>qu'un ſeul raion viſuel à obſerver, au lieu qu'il faut en obſerver 2 <lb/>quand on prend la hauteur par devant.</s> <s xml:id="echoid-s8788" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8789" xml:space="preserve">Quand on prend la hauteur par devant on la trouve trop grande, <lb/>& </s> <s xml:id="echoid-s8790" xml:space="preserve">quand on la prend par derriere on la trouve trop petite. </s> <s xml:id="echoid-s8791" xml:space="preserve">Cette er-<lb/>reur eſt égale de part & </s> <s xml:id="echoid-s8792" xml:space="preserve">d'autre, & </s> <s xml:id="echoid-s8793" xml:space="preserve">elle eſt d'autant plus grande que <lb/>l'on eſt plus élevé au-deſſus de la ſurface de la Mer; </s> <s xml:id="echoid-s8794" xml:space="preserve">tellement que <lb/>l'éleyation d'un pied fait erreur d'une minute, celle de 4 pieds cau-<lb/>ſe 2 minutes d'erreur; </s> <s xml:id="echoid-s8795" xml:space="preserve">l'élevation de 10 pieds, 3 min. </s> <s xml:id="echoid-s8796" xml:space="preserve">celle de 17 <lb/>pieds, 4 min. </s> <s xml:id="echoid-s8797" xml:space="preserve">celle de 15 pieds cauſe 5 min. </s> <s xml:id="echoid-s8798" xml:space="preserve">d'erreur; </s> <s xml:id="echoid-s8799" xml:space="preserve">& </s> <s xml:id="echoid-s8800" xml:space="preserve">enfin celle <lb/>de 40 pieds fait erreur de 6 min.</s> <s xml:id="echoid-s8801" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8802" xml:space="preserve">Si donc on a obſervé la hauteur d'un Aſtre avec l'Arbaleſtrille <lb/> <pb o="279" file="295" n="295" rhead="POUR LA NAVIGATION. Liv. VII. Ch. II."/> par devant & </s> <s xml:id="echoid-s8803" xml:space="preserve">qu'on l'ait trouvé, par exemple, de 20 d. </s> <s xml:id="echoid-s8804" xml:space="preserve">ſi l'œil de <lb/>l'Obſervateur en ce cas eſt élevé de 25 pieds par deſſus la ſurface de <lb/>la Mer, il faudra conclure que la hauteur de l'Aſtre n'eſt que de 19 <lb/>d. </s> <s xml:id="echoid-s8805" xml:space="preserve">55 min. </s> <s xml:id="echoid-s8806" xml:space="preserve">parce qu'il faut ſouſtraire 5 min. </s> <s xml:id="echoid-s8807" xml:space="preserve">pour l'élevation de 25 <lb/>pieds. </s> <s xml:id="echoid-s8808" xml:space="preserve">Il faudroitau contraire les ajoûter ſi la hauteur avoit été pri-<lb/>ſe par derriere.</s> <s xml:id="echoid-s8809" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div586" type="section" level="1" n="291"> <head xml:id="echoid-head419" style="it" xml:space="preserve">Du Luartier Anglois.</head> <p> <s xml:id="echoid-s8810" xml:space="preserve">CEt Inſtrument ſe fait ordinairement de bois de poirier. </s> <s xml:id="echoid-s8811" xml:space="preserve">Il con-<lb/> <anchor type="note" xlink:label="note-295-01a" xlink:href="note-295-01"/> tient un quart de cercle partagé en 2 arcs BC, DE, qui ont dif-<lb/>ferens raïons, dont le moindre eſt la moitié du plus grand.</s> <s xml:id="echoid-s8812" xml:space="preserve"/> </p> <div xml:id="echoid-div586" type="float" level="2" n="1"> <note position="right" xlink:label="note-295-01" xlink:href="note-295-01a" xml:space="preserve">Fig. 9.</note> </div> <p> <s xml:id="echoid-s8813" xml:space="preserve">L'arc BC eſt de 30 d. </s> <s xml:id="echoid-s8814" xml:space="preserve">chaque degré ſe ſubdiviſe autant qu'on le <lb/>peut de 5 en 5 m. </s> <s xml:id="echoid-s8815" xml:space="preserve">par le moyen des cercles concentriques & </s> <s xml:id="echoid-s8816" xml:space="preserve">des li-<lb/>gnes tranſverſales. </s> <s xml:id="echoid-s8817" xml:space="preserve">L'autre arc de cercle DE, contient 60 d. </s> <s xml:id="echoid-s8818" xml:space="preserve">& </s> <s xml:id="echoid-s8819" xml:space="preserve">ſe <lb/>diviſe ſeulement en degrez; </s> <s xml:id="echoid-s8820" xml:space="preserve">la diviſion de ces arcs doit commencer <lb/>du raïon AB, dont la longueur eſt environ de 2 pieds.</s> <s xml:id="echoid-s8821" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8822" xml:space="preserve">On ajuſte un petit Marteau ou Pinule fenduë immobile au cen-<lb/>tre commun de ces 2 arcs; </s> <s xml:id="echoid-s8823" xml:space="preserve">une autre qui ſe puiſſe mouvoir & </s> <s xml:id="echoid-s8824" xml:space="preserve">arrêter <lb/>avec une vis ſur chacun des degrez & </s> <s xml:id="echoid-s8825" xml:space="preserve">minutes de l'arc BC comme <lb/>en F, laquelle doit être percée pour y placer l'œil, & </s> <s xml:id="echoid-s8826" xml:space="preserve">enfin une 3<emph style="sub">me</emph> <lb/>Pinule qui puiſſe couler & </s> <s xml:id="echoid-s8827" xml:space="preserve">s'arrêter au long des diviſions de l'arc D <lb/>E, comme en G. </s> <s xml:id="echoid-s8828" xml:space="preserve">Il faut que ces arcs ſoient d'égale épaiſſeur, afin que <lb/>les Pinules ſoient toûjours bien perpendiculiaires ſur le bord de <lb/>l'Inſtrument.</s> <s xml:id="echoid-s8829" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div588" type="section" level="1" n="292"> <head xml:id="echoid-head420" style="it" xml:space="preserve">Vſage du Luartier Anglois.</head> <p> <s xml:id="echoid-s8830" xml:space="preserve">ON peutſe ſervir de cet Inſtrument pour obſerver la hauteur des <lb/>Aſtres en 2 manieres, comme par l'Arbaleſtrille, c'eſt-àdire, <lb/>en regardant l'Aſtre, ou lui tournant le dos. </s> <s xml:id="echoid-s8831" xml:space="preserve">Cette maniere eſt plus <lb/>commode. </s> <s xml:id="echoid-s8832" xml:space="preserve">Il faut pour cela ajuſter la pinule A ſur le centre, & </s> <s xml:id="echoid-s8833" xml:space="preserve">la pi-<lb/>nule G, ſur tel degré qu'on voudra de l'arc DE; </s> <s xml:id="echoid-s8834" xml:space="preserve">pourvû toutefois que <lb/>la partie GD avec les 30 d. </s> <s xml:id="echoid-s8835" xml:space="preserve">de l'arc BC ſoient du moins auſſi grands <lb/>que la hauteur de l'Aſtre; </s> <s xml:id="echoid-s8836" xml:space="preserve">après cela on lui tournera les dos, & </s> <s xml:id="echoid-s8837" xml:space="preserve">l'on <lb/>hauſſera ou baiſſera la pinule F en la faiſant gliſſer ſur l'arc BC, juſ-<lb/>qu'à ce que regardant l'horiſon ſenſible par les 2 pinules F & </s> <s xml:id="echoid-s8838" xml:space="preserve">A, le <lb/>raïon du Soleil H paſſe par l'ouverture de la Pinule G & </s> <s xml:id="echoid-s8839" xml:space="preserve">vienne a-<lb/>boutir à la fente de la Pinule qui eſt au centre A.</s> <s xml:id="echoid-s8840" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8841" xml:space="preserve">La ſomme des 2 arcs ſera la hauteur du Soleil ſur l'horiſon, en y <lb/>faiſant la même correction que nous avons dit en parlant de l'Aba-<lb/>leſtrille, & </s> <s xml:id="echoid-s8842" xml:space="preserve">le complément de cette hauteur ſera la diſtance du Zé-<lb/>nith.</s> <s xml:id="echoid-s8843" xml:space="preserve"/> </p> <pb o="280" file="296" n="296" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> <p> <s xml:id="echoid-s8844" xml:space="preserve">L'on pourra auſſi prendre hauteur par devant avec cet Inſtru-<lb/>ment, comme avec l'Arbaleſtrille, mais plus difficilement.</s> <s xml:id="echoid-s8845" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div589" type="section" level="1" n="293"> <head xml:id="echoid-head421" style="it" xml:space="preserve">Du demi-Cercle pour prendre bauteur en Mer.</head> <p> <s xml:id="echoid-s8846" xml:space="preserve">CE demi-Cercle eſt d'environ un pied de diametre: </s> <s xml:id="echoid-s8847" xml:space="preserve">il n'eſt diviſé <lb/> <anchor type="note" xlink:label="note-296-01a" xlink:href="note-296-01"/> qu'en 90 d. </s> <s xml:id="echoid-s8848" xml:space="preserve">& </s> <s xml:id="echoid-s8849" xml:space="preserve">chaque degré ſe diviſe ordinairement en 4 par-<lb/>ties qui valent 15 m. </s> <s xml:id="echoid-s8850" xml:space="preserve">chacune. </s> <s xml:id="echoid-s8851" xml:space="preserve">Il y a 2 pinules A & </s> <s xml:id="echoid-s8852" xml:space="preserve">B attachées aux <lb/>extremitez deſon diametre, & </s> <s xml:id="echoid-s8853" xml:space="preserve">une autre comme C, ajuſtée de telle <lb/>maniere qu'elle coule autour de la circonference du demi-Cercle, <lb/>aſin de recevoir le raïon de l'Aſtre.</s> <s xml:id="echoid-s8854" xml:space="preserve"/> </p> <div xml:id="echoid-div589" type="float" level="2" n="1"> <note position="left" xlink:label="note-296-01" xlink:href="note-296-01a" xml:space="preserve">Fig. 10.</note> </div> </div> <div xml:id="echoid-div591" type="section" level="1" n="294"> <head xml:id="echoid-head422" style="it" xml:space="preserve">Vſage du demi-Cercle.</head> <p> <s xml:id="echoid-s8855" xml:space="preserve">SI l'on prend la hauteur par devant, il faut mettre l'œil à l'ouver-<lb/>ture de la pinule A, regarder l'horiſon par les pinules A & </s> <s xml:id="echoid-s8856" xml:space="preserve">B, & </s> <s xml:id="echoid-s8857" xml:space="preserve"><lb/>hauſſer ou baiſſer la pinule C, en la gliſſant ſur les degrez de la cir-<lb/>conference, juſqu'à ce que le raion de l'Aſtre paſſant par la fente ou <lb/>petit trou de cette pinule, rencontre l'autre pinule en a. </s> <s xml:id="echoid-s8858" xml:space="preserve">Pour lors <lb/>les degrez compris en l'arc BC, marqueront la hauteur de l'Aſtre. <lb/></s> <s xml:id="echoid-s8859" xml:space="preserve">Si c'eſt le Soleil que l'on veut obſerver, il eſt plus commode de lui <lb/>tourner le dos à cauſe de ſa grande lumiere, mettant l'œil à la pinule <lb/>B, & </s> <s xml:id="echoid-s8860" xml:space="preserve">regardant l'horiſon par les pinules B & </s> <s xml:id="echoid-s8861" xml:space="preserve">A, & </s> <s xml:id="echoid-s8862" xml:space="preserve">hauſſant ou baiſ-<lb/>ſant la pinule C, en ſorte que le raïon du Soleil paſſant par cette pi-<lb/>nule vienne ſe rendre à l'ouverture de la pinule A, l'arc BC mar-<lb/>quera la hauteur du Soleil ſur l'horiſon.</s> <s xml:id="echoid-s8863" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8864" xml:space="preserve">Il eſt à remarquer que comme l'angle BAC a ſon ſommet à la cir-<lb/>conference, il n'a pour ſa meſure que la moitié de l'arc BC, ſur le-<lb/>quel il eſt appuié, & </s> <s xml:id="echoid-s8865" xml:space="preserve">c'eſt pour cette raiſon que l'on a diviſé tout le <lb/>demi-Cercle en 90 deg. </s> <s xml:id="echoid-s8866" xml:space="preserve">au lieu des 180 qu'il devroit contenir.</s> <s xml:id="echoid-s8867" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div592" type="section" level="1" n="295"> <head xml:id="echoid-head423" style="it" xml:space="preserve">Par la hauteur des Aſtres trouver la latitude du lieu où l'on eſt.</head> <p> <s xml:id="echoid-s8868" xml:space="preserve">AYant obſervé avec quelqu'un des Inſtruments dont nous ve-<lb/>nons de parler, la hauteur ſur l'horiſon, d'un Aſtre dont on <lb/>connoît la déclinaiſon quand il paſſe au Méridien, on connoîtra la <lb/>latitude du lieu où l'on eſt, laquelle eſt toûjours égale à la hauteur <lb/>du Pole, par les uſages 10<emph style="sub">me</emph> & </s> <s xml:id="echoid-s8869" xml:space="preserve">52<emph style="sub">me</emph> du 3<emph style="sub">me</emph> Livre de nôtre Traité <lb/>de l'uſage des Globes.</s> <s xml:id="echoid-s8870" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8871" xml:space="preserve">On pourra auſſi trouver à toute heure la latitude du lieu où ſe <lb/>fait l'obſervation par les uſages 13, 14 & </s> <s xml:id="echoid-s8872" xml:space="preserve">15, de nôtre Traité des <lb/>Aſtrolabes, pag. </s> <s xml:id="echoid-s8873" xml:space="preserve">163 & </s> <s xml:id="echoid-s8874" xml:space="preserve">ſuiv. </s> <s xml:id="echoid-s8875" xml:space="preserve">quoiqu'il y ait un peu plus de façon.</s> <s xml:id="echoid-s8876" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8877" xml:space="preserve">Nous allons donner un exemple par les hauteurs du Soleil à Midi. <lb/></s> <s xml:id="echoid-s8878" xml:space="preserve"> <pb o="281" file="297" n="297" rhead="POUR LA NAVIGATION. Liv. VII. Ch. III."/> Ayant pris hauteur juſtement à Midi, cherchez dans la Table à ce <lb/>même jour, la déclinaiſon du ſoleil. </s> <s xml:id="echoid-s8879" xml:space="preserve">Si elle eſt Septentrionale, qui eſt <lb/>depuis le 20 Mars juſqu'au 22 Septembre, ou depuis ♈ juſqu'à ♎; <lb/></s> <s xml:id="echoid-s8880" xml:space="preserve">ôtez cette declinaiſon de la hauteur du Soleil, le reſte ſera la hauteur <lb/>de l'Equateur, laquelle étant ſouſtraite de 90, le reſte ſera la hau-<lb/>teur du Pole.</s> <s xml:id="echoid-s8881" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div593" type="section" level="1" n="296"> <head xml:id="echoid-head424" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s8882" xml:space="preserve">Le Soleil étant au premier degré de 69, ſa hauteur à Midi eſt à <lb/>Paris de 64 d. </s> <s xml:id="echoid-s8883" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8884" xml:space="preserve">la déclinaiſon boreale eſt de 24 d. </s> <s xml:id="echoid-s8885" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8886" xml:space="preserve">Etant <lb/>ôtée de 64 d. </s> <s xml:id="echoid-s8887" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8888" xml:space="preserve">reſte 41 d. </s> <s xml:id="echoid-s8889" xml:space="preserve">pour la hauteur de l'Equateur, ſon <lb/>complement juſqu'à 90 eſt 49, qui ſera la hauteur du Pole à Pa-<lb/>ris; </s> <s xml:id="echoid-s8890" xml:space="preserve">mais ſi c'étoit depuis le 22 Septembre juſqu'au 20 Mars, la dé-<lb/>clinaiſon du Soleil ſeroit Méridionale. </s> <s xml:id="echoid-s8891" xml:space="preserve">Il faudroit pour lors y ajoû-<lb/>ter la hauteur Meridiene. </s> <s xml:id="echoid-s8892" xml:space="preserve">Le total ſera la hauteur de l'Equateur. <lb/></s> <s xml:id="echoid-s8893" xml:space="preserve">Exemple. </s> <s xml:id="echoid-s8894" xml:space="preserve">Le 22 Dec. </s> <s xml:id="echoid-s8895" xml:space="preserve">le Soleil eſt élevé à Midià Paris de 17 d. </s> <s xml:id="echoid-s8896" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8897" xml:space="preserve"><lb/>ſa déclinaiſon eſt 23 d. </s> <s xml:id="echoid-s8898" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8899" xml:space="preserve">laquelle ajoûtée à 17 d. </s> <s xml:id="echoid-s8900" xml:space="preserve">30 m. </s> <s xml:id="echoid-s8901" xml:space="preserve">le total eſt <lb/>41, dont le complément 49, ſera la latitude du lieu. </s> <s xml:id="echoid-s8902" xml:space="preserve">Sile Soleil n'a-<lb/>voit point de déclinaiſon comme au commencement de ♈ & </s> <s xml:id="echoid-s8903" xml:space="preserve">♎, ſa <lb/>hauteur ſeroit celle de l'Equateur, laquelle étant ſouſtraite de 90, <lb/>le reſte ſeroit la hauteur du Pole. </s> <s xml:id="echoid-s8904" xml:space="preserve">Si en ce même tems-là le Soleil <lb/>eſt élevé de 90 d. </s> <s xml:id="echoid-s8905" xml:space="preserve">à Midi, c'eſt une marque qu'on ſeroit ſousla ligne <lb/>Equinoctiale. </s> <s xml:id="echoid-s8906" xml:space="preserve">En prenant exactement la hauteur du ſoleil à toutes <lb/>les heures du jour, on pourra faire des tables des hauteurs du So-<lb/>leil ſur l'horiſon, mais elles ſe font bien plus juſte par la calcul.</s> <s xml:id="echoid-s8907" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div594" type="section" level="1" n="297"> <head xml:id="echoid-head425" xml:space="preserve">CHAPITRE III.</head> <head xml:id="echoid-head426" style="it" xml:space="preserve">Contenant la Conſtruction du Luartier de réduction <lb/>& ſes uſages.</head> <p> <s xml:id="echoid-s8908" xml:space="preserve">LE Quartier de reduction eſt un Inſtrument dont ſe ſervent les <lb/> <anchor type="note" xlink:label="note-297-01a" xlink:href="note-297-01"/> Pilotes à reduire les routes de Navigation. </s> <s xml:id="echoid-s8909" xml:space="preserve">Il eſt compoſé de <lb/>pluſieurs quarts de cercle qui ont même centre A, & </s> <s xml:id="echoid-s8910" xml:space="preserve">de pluſieurs <lb/>lignes droites paralleles; </s> <s xml:id="echoid-s8911" xml:space="preserve">ces quarts de cercle & </s> <s xml:id="echoid-s8912" xml:space="preserve">les lignes droites <lb/>ſont à diſtances égales. </s> <s xml:id="echoid-s8913" xml:space="preserve">On peu prendre l'un de ces quarts de cercle <lb/>comme BC, pour le quart de chaque grand cercle de la Sphere, & </s> <s xml:id="echoid-s8914" xml:space="preserve"><lb/>principalement pour quart de l'horiſon, & </s> <s xml:id="echoid-s8915" xml:space="preserve">du Méridien.</s> <s xml:id="echoid-s8916" xml:space="preserve"/> </p> <div xml:id="echoid-div594" type="float" level="2" n="1"> <note position="right" xlink:label="note-297-01" xlink:href="note-297-01a" xml:space="preserve">XX, <lb/>Planche.</note> </div> <p> <s xml:id="echoid-s8917" xml:space="preserve">En le prenant pour quart de l'horiſon, l'un de ſes côtez, tel <lb/>qu'on voudra, comme AB, repreſentera la ligne Meridiene, c'eſt-<lb/>à-dire, Nord & </s> <s xml:id="echoid-s8918" xml:space="preserve">Sud.</s> <s xml:id="echoid-s8919" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8920" xml:space="preserve">L'autre côté AC, qui fait angle droit avec la Méridiene, repre-<lb/>ſente la ligne Eſt & </s> <s xml:id="echoid-s8921" xml:space="preserve">Oüeſt. </s> <s xml:id="echoid-s8922" xml:space="preserve">Toutes les autres lignes paralleles au <lb/> <pb o="282" file="298" n="298" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> côté AB ſont des Méridiens, & </s> <s xml:id="echoid-s8923" xml:space="preserve">toutes celles qui ſont paralleles <lb/>an côté AC ſont des lignes Eſt & </s> <s xml:id="echoid-s8924" xml:space="preserve">Oüeſt.</s> <s xml:id="echoid-s8925" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8926" xml:space="preserve">Ce quart de cercle eſt diviſé premierement en 8 parties égales, par <lb/>7 raïons tirez du centre A, pour repreſenter les {8/4} de vent de chaque <lb/>quart de la Bouſſole ou de l'horiſon; </s> <s xml:id="echoid-s8927" xml:space="preserve">chacun de ces quarts de vent <lb/>vaut 11 d. </s> <s xml:id="echoid-s8928" xml:space="preserve">15 m. </s> <s xml:id="echoid-s8929" xml:space="preserve">comme nous avons dit ci-devant en parlant de la <lb/>Bouſſole.</s> <s xml:id="echoid-s8930" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8931" xml:space="preserve">La circonference BC eſt auſſi diviſée en 90 d. </s> <s xml:id="echoid-s8932" xml:space="preserve">& </s> <s xml:id="echoid-s8933" xml:space="preserve">chaque degré eſt <lb/>ſubdiviſé de 12 en 12 m. </s> <s xml:id="echoid-s8934" xml:space="preserve">par le moyen des lignes tranſverſales, ti-<lb/>rées de degré en degré, & </s> <s xml:id="echoid-s8935" xml:space="preserve">de 6 cercles concentriques, y compris les <lb/>2 extrêmes. </s> <s xml:id="echoid-s8936" xml:space="preserve">On attache de plus au centre un fil, comme AL, lequel <lb/>étant arrêté ſur tel degré que l'on veut du quart de cercle, ſert à di-<lb/>viſer l'horiſon de telle maniere qu'on trouve à propos. </s> <s xml:id="echoid-s8937" xml:space="preserve">La figure 20 <lb/>fait aſſez connoitre le reſte de la conſtruction de cet Inſtrument.</s> <s xml:id="echoid-s8938" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div596" type="section" level="1" n="298"> <head xml:id="echoid-head427" style="it" xml:space="preserve">Vſage du Luartier de réduction.</head> <p> <s xml:id="echoid-s8939" xml:space="preserve">ON forme ſur le Quartier de réduction des triangles ſemblables <lb/>à ceux de la Navigation, & </s> <s xml:id="echoid-s8940" xml:space="preserve">les côtez de ces triangles ſont me-<lb/>ſurez par les intervales égaux qui ſont entre les quarts de cercle & </s> <s xml:id="echoid-s8941" xml:space="preserve"><lb/>entre les lignes N & </s> <s xml:id="echoid-s8942" xml:space="preserve">S E & </s> <s xml:id="echoid-s8943" xml:space="preserve">O.</s> <s xml:id="echoid-s8944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8945" xml:space="preserve">On a diſtingué ces cercles & </s> <s xml:id="echoid-s8946" xml:space="preserve">ces lignes en les marquant de 5 en <lb/>5 par des traits plus gros que les autres; </s> <s xml:id="echoid-s8947" xml:space="preserve">de ſorte que ſi l'on prend <lb/>chaque intervale pour une lieuë, il y aura 5 lieuës depuis une groſſe <lb/>ligne juſqu'à l'autre; </s> <s xml:id="echoid-s8948" xml:space="preserve">de même ſi on prend chaque intervale pour 4 <lb/>lieuës, il y aura 20 lieuës qui ſont un degré de Marine depuis un <lb/>gros trait juſqu'à l'autre.</s> <s xml:id="echoid-s8949" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8950" xml:space="preserve">Suppoſons, par exemple, avoir couru 150 lieuës NE quart N, qui <lb/>eſt le 3<emph style="sub">me</emph> quart de vent, faiſant depuis le Nord un angle de 33 d. </s> <s xml:id="echoid-s8951" xml:space="preserve">45 <lb/>m. </s> <s xml:id="echoid-s8952" xml:space="preserve">Nous avons donc 2 choſes connuës; </s> <s xml:id="echoid-s8953" xml:space="preserve">ſçavoir, le rumb de vent & </s> <s xml:id="echoid-s8954" xml:space="preserve"><lb/>les lieuës de diſtance, par le moyen deſquelles on peut former ſur le <lb/>quartier de réduction un triangle ſemblable à celui de Navigation <lb/>pour trouver le reſte qui nous eſt inconnu; </s> <s xml:id="echoid-s8955" xml:space="preserve">ce qui ſe fait en cette <lb/>ſorte.</s> <s xml:id="echoid-s8956" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8957" xml:space="preserve">On prendra le centre A pour le point du départ, & </s> <s xml:id="echoid-s8958" xml:space="preserve">l'on comptera <lb/>par les arcs le long du rumb de vent ſuppoſé AD, les 150 lieuës de <lb/>diſtance depuis A juſqu'à D, & </s> <s xml:id="echoid-s8959" xml:space="preserve">ce point D ſera le lieu de l'arrivée <lb/>lequel on marquera par une petite pointe, & </s> <s xml:id="echoid-s8960" xml:space="preserve">on conduira DE pa-<lb/>rallele au côté AC, pour former le triangle rectangle AED, ſembla-<lb/>ble à celui de la Navigation; </s> <s xml:id="echoid-s8961" xml:space="preserve">le côté AE de ce triangle donnera 125 <lb/>lieuës de difference en latitude vers le Nord, qui valent 6 d. </s> <s xml:id="echoid-s8962" xml:space="preserve">15 m. <lb/></s> <s xml:id="echoid-s8963" xml:space="preserve"> <pb o="283" file="299" n="299" rhead="POUR LA NAVIGATION. Liv. VII. Ch. IV."/> à 20 lieuës par degré, & </s> <s xml:id="echoid-s8964" xml:space="preserve">une lieuë pour 3 m. </s> <s xml:id="echoid-s8965" xml:space="preserve">& </s> <s xml:id="echoid-s8966" xml:space="preserve">enfin le côté ED <lb/>donnera 83 lieuës mineures vers l'Eſt, leſquelles reduites, comme <lb/>nous diront ci-après, donneront la difference en longitude, & </s> <s xml:id="echoid-s8967" xml:space="preserve"><lb/>par ce moyen tout le triangle ſera connu.</s> <s xml:id="echoid-s8968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8969" xml:space="preserve">On appelle lieuës mineures celles qui répondent aux paralleles <lb/>entre l'Equateur & </s> <s xml:id="echoid-s8970" xml:space="preserve">les Poles, car ceux qui approchent le plus des <lb/>Poles ſont les plus petits, & </s> <s xml:id="echoid-s8971" xml:space="preserve">par conſequent les degrez de longitu-<lb/>de auſſi plus petits; </s> <s xml:id="echoid-s8972" xml:space="preserve">c'eſt pourquoi il y a moins de chemin à faire <lb/>pour changer de longitude, que pour changer de latitude, où ſe <lb/>comptent les lieuës majeures.</s> <s xml:id="echoid-s8973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8974" xml:space="preserve">Comme le centre A du Quartier de réduction repreſente toû-<lb/>jours le lieu d'où l'on eſt parti, lorſqu'on a trouvé par quelque ma-<lb/>niere que ce ſoit le point D où l'on eſt arrivé, tout le triangle AED <lb/>ſe trouve facilement déterminé.</s> <s xml:id="echoid-s8975" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8976" xml:space="preserve">Si le Quatier de réduction eſt pris pour un quart du Méridien, <lb/>l'un des cotez, comme AB, ſe pourra prendre pour le raïon commun <lb/>du Méridien & </s> <s xml:id="echoid-s8977" xml:space="preserve">de l'Equateur, & </s> <s xml:id="echoid-s8978" xml:space="preserve">l'autre côté AC ſera la moitié de <lb/>l'axe du Monde. </s> <s xml:id="echoid-s8979" xml:space="preserve">Les degrez de la circonference CC repreſenteront <lb/>les degrez de latitude, & </s> <s xml:id="echoid-s8980" xml:space="preserve">les lignes paralleles au côté AB, perpendi-<lb/>culaires ſur AC, priſes depuis chaque point de latitude juſqu'à l'a-<lb/>xe AC, ſeront les raïons des paralleles de ces latitudes, & </s> <s xml:id="echoid-s8981" xml:space="preserve">en même <lb/>tems les Sinus des complémens des mêmes latitudes.</s> <s xml:id="echoid-s8982" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8983" xml:space="preserve">Si, par exemple, on veut ſçavoir combien 83 lieuës mineures vers <lb/>l'Eſt valent de degrez de longitude ſur le parallele de 48 d. </s> <s xml:id="echoid-s8984" xml:space="preserve">de lati-<lb/>tude, il faut premierement tendre le fil ſur les 48 d. </s> <s xml:id="echoid-s8985" xml:space="preserve">de latitude, & </s> <s xml:id="echoid-s8986" xml:space="preserve"><lb/>compter les 83 lieuës propoſées ſur le côté AB, en commençant du <lb/>centre A; </s> <s xml:id="echoid-s8987" xml:space="preserve">elles ſe termineront au point H; </s> <s xml:id="echoid-s8988" xml:space="preserve">prenant chaque petit in-<lb/>tervale pour 4 lieuës, ou les intervales des gros traits pour 20 lieuës. <lb/></s> <s xml:id="echoid-s8989" xml:space="preserve">Il faut enſuite conduire du point H la parallele HG juſqu'au fil, a-<lb/>lors la partie du fil depuis A juſqu'en G, raïon du Méridien, mon-<lb/>trera 125 lieuës majeures, valeur de 6 d. </s> <s xml:id="echoid-s8990" xml:space="preserve">15 m. </s> <s xml:id="echoid-s8991" xml:space="preserve">à raiſon de 20 lieuës <lb/>par degré, & </s> <s xml:id="echoid-s8992" xml:space="preserve">3 min. </s> <s xml:id="echoid-s8993" xml:space="preserve">pour une lieuë ce qui fait connoître que les 83 <lb/>lieuës mineures AH, qui font la difference en longitude de la route <lb/>ſuppoſée, & </s> <s xml:id="echoid-s8994" xml:space="preserve">qui ſont égales au raïon du parallele GI, valent 6 d. </s> <s xml:id="echoid-s8995" xml:space="preserve"><lb/>15 m. </s> <s xml:id="echoid-s8996" xml:space="preserve">de ce parallele.</s> <s xml:id="echoid-s8997" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s8998" xml:space="preserve">Suppoſons, pour ſecond exemple, que l'on veüille réduire cent <lb/>lieuës mineures en degrez de longitude ſur le parallele de 60 deg. <lb/></s> <s xml:id="echoid-s8999" xml:space="preserve">A yant premierement tendu le fil ſur 60 deg. </s> <s xml:id="echoid-s9000" xml:space="preserve">on comptera les cent <lb/>lieuës de longitude du côté AB, & </s> <s xml:id="echoid-s9001" xml:space="preserve">le parallele qui les terminera é-<lb/>tant conduit au fil, retranchera le long du fil, à prendre depuis le <lb/> <pb o="284" file="300" n="300" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> centre, 200 lieuës majeures qui valent 10 deg. </s> <s xml:id="echoid-s9002" xml:space="preserve">c'eſt à-dire, que cent <lb/>lieuës ſur le parallele de 60 d. </s> <s xml:id="echoid-s9003" xml:space="preserve">valent 10 d. </s> <s xml:id="echoid-s9004" xml:space="preserve">de longitude, parce que <lb/>chaque degré d'un grand cercle eſt double d'un degré du parallele <lb/>de 60 degrez.</s> <s xml:id="echoid-s9005" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9006" xml:space="preserve">A côté du quartier de réduction on met une Echelle réduite <lb/>que l'on nomme des latitudes croiſſantes, dont la conſtruction & </s> <s xml:id="echoid-s9007" xml:space="preserve"><lb/>diviſion eſt la même que celle du Méridien des Cartes réduites, <lb/>dont nous parlerons ci-après.</s> <s xml:id="echoid-s9008" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9009" xml:space="preserve">L'uſage de cette Echelle eſt pour trouver le moyen parallele entre <lb/>celui du départ & </s> <s xml:id="echoid-s9010" xml:space="preserve">celui d'arrivée.</s> <s xml:id="echoid-s9011" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9012" xml:space="preserve">Quand on a couru une route oblique, c'eſt-à-dire, qui n'eſt exac-<lb/>tement ni Nord ou Sud, ni Eſt ou Oüeſt, ces routes outre les lieuës <lb/>majeures Nord & </s> <s xml:id="echoid-s9013" xml:space="preserve">Sud, donnent des lieuës vers l'Eſt ou vers l'Oüeſt <lb/>qu'il faut réduire en degrez de longitude. </s> <s xml:id="echoid-s9014" xml:space="preserve">Mais ces lieuës que l'on <lb/>appelle mineures, n'ont été faites ni ſur le parallele du départ, ni ſur <lb/>celui de l'arrivée, ayant été faites ſur tous les paralleles qui ſont en-<lb/>tre deux & </s> <s xml:id="echoid-s9015" xml:space="preserve">qui ſont tous inégaux; </s> <s xml:id="echoid-s9016" xml:space="preserve">c'eſt pourquoi ou eſt obligé d'en <lb/>chercher un qui ſoit moyen proportionel entr'eux, & </s> <s xml:id="echoid-s9017" xml:space="preserve">on l'appelle <lb/>pour cela moyen parallel, lequel ſert à reduire en degrez & </s> <s xml:id="echoid-s9018" xml:space="preserve">minu-<lb/>tes de l'Equateur, les lieuës qu'on a faites en parcourant divers pa-<lb/>ralleles, dont les degrez deviennent plus petits à meſure qu'ils s'é-<lb/>loignent de l'Equateur allant vers les Poles.</s> <s xml:id="echoid-s9019" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9020" xml:space="preserve">Il y a pluſieurs méthodes pour trouver ce moyen parallele. </s> <s xml:id="echoid-s9021" xml:space="preserve">Mais <lb/>je ne parlerai ici que de celle qui ſe fait par l'Echelle réduite des la-<lb/>titudes croiſſantes & </s> <s xml:id="echoid-s9022" xml:space="preserve">ſans calcul.</s> <s xml:id="echoid-s9023" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9024" xml:space="preserve">Soit propoſé, par exemple, de trouver le moïen parallele entre 40 <lb/>& </s> <s xml:id="echoid-s9025" xml:space="preserve">60 d. </s> <s xml:id="echoid-s9026" xml:space="preserve">de latitude. </s> <s xml:id="echoid-s9027" xml:space="preserve">Prenez avec un compas ſur cette Echelle le mi-<lb/>lieu d'entre 40 & </s> <s xml:id="echoid-s9028" xml:space="preserve">60 d. </s> <s xml:id="echoid-s9029" xml:space="preserve">Ce point milieu ſe terminera vis-à-vis de <lb/>51 d. </s> <s xml:id="echoid-s9030" xml:space="preserve">qui ſera par conſequent le moyen parallele de cette route.</s> <s xml:id="echoid-s9031" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9032" xml:space="preserve">Remarquez, que comme cette Echelle eſt en 2 lignes, il faudra <lb/>prendre l'eſpace depuis 40 d. </s> <s xml:id="echoid-s9033" xml:space="preserve">de latitude juſqu'à 45, qui eſt d'un <lb/>côté, & </s> <s xml:id="echoid-s9034" xml:space="preserve">le porter ſur une ligne droite; </s> <s xml:id="echoid-s9035" xml:space="preserve">prendre enſuite l'eſpace depuis <lb/>45 juſqu'à 60, qui eſt de l'autre côté pour ne faire qu'une ligne de <lb/>ces 2 eſpaces joints enſemble; </s> <s xml:id="echoid-s9036" xml:space="preserve">diviſer cette ligne en 2 également, & </s> <s xml:id="echoid-s9037" xml:space="preserve"><lb/>portant cette moitié ſur l'Echelle mettre une pointe du compas ſur <lb/>le nombre 60, l'autre pointe ira ſe terminer au nombre 51, qui ſera <lb/>le moyen parallele que l'on cherche. </s> <s xml:id="echoid-s9038" xml:space="preserve">Après quoi il ſera facile de ré-<lb/>duire les lieuës parcouruës vers l'Eſt en degrez de longitude par le <lb/>Quartier de réduction, conſideré comme quart de Méridien de la <lb/>maniere que nous venons de l'expliquer par deux exemples.</s> <s xml:id="echoid-s9039" xml:space="preserve"/> </p> <pb o="285" file="301" n="301" rhead="POUR LA NAVIGATION. Liv. VII. Ch. IV."/> </div> <div xml:id="echoid-div597" type="section" level="1" n="299"> <head xml:id="echoid-head428" style="it" xml:space="preserve">Des Cartes reduites.</head> <p> <s xml:id="echoid-s9040" xml:space="preserve">L A Planche vingt-uniéme repreſente une Carte réduite. </s> <s xml:id="echoid-s9041" xml:space="preserve">Mais <lb/>avant que d'en donner la conſtruction & </s> <s xml:id="echoid-s9042" xml:space="preserve">les uſages, il faut fça-<lb/>voir que tant qu'un Vaiſſeau eſt pouſſé par un même vent, il doit <lb/>toûjours faire le même angle avec tous les Méridiens qu'il rencon-<lb/>tre ſur la ſurface du Globe terreſtre.</s> <s xml:id="echoid-s9043" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9044" xml:space="preserve">Si le Vaiſfeau court Nord & </s> <s xml:id="echoid-s9045" xml:space="preserve">Sud, il fait un angle infiniment ai-<lb/>guavec le Méridien qu'il décrit, c'eſt-à-dire, qu'il lui eſt parallele, <lb/>ou plûtôt qu'il le ſuit & </s> <s xml:id="echoid-s9046" xml:space="preserve">ne s'en écarte point.</s> <s xml:id="echoid-s9047" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9048" xml:space="preserve">S'il court Eſt & </s> <s xml:id="echoid-s9049" xml:space="preserve">Oüeſt, il coupe à angles droits tous les Méridiens, <lb/>car il décrit ou l'Equateur ou un des cercles qui lui ſont paralle-<lb/>les. </s> <s xml:id="echoid-s9050" xml:space="preserve">Mais ſi ſa courſe eſt moyene entre ces 2, alors il ne décrira plus <lb/>un cercle, parce qu'un cercle tracé de cette maniere couperoit tous <lb/>les Méridiens à angles inégaux, ce que le Vaiſſeau ne doit pas faire. <lb/></s> <s xml:id="echoid-s9051" xml:space="preserve">Il décrit donc une autre courbe, dont la condition eſſentille eſt de <lb/>couper tous les Méridiens ſous le même angle. </s> <s xml:id="echoid-s9052" xml:space="preserve">On la nomme Loxo-<lb/>dromique, ou fimplement Loxodromie; </s> <s xml:id="echoid-s9053" xml:space="preserve">c'eſt une eſpece de ſpirale <lb/>qui fait une infinité de tours ſans pouvoir arriver à un certain point, <lb/>qui eſt le Pole où elle tend, & </s> <s xml:id="echoid-s9054" xml:space="preserve">dont elle s'approche à chaque pas.</s> <s xml:id="echoid-s9055" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9056" xml:space="preserve">La route d'un Vaiſſeau, à l'exception des 2 premicres que nous <lb/>av ons marquées, eſt donctoûjours une courbe Loxodromique. </s> <s xml:id="echoid-s9057" xml:space="preserve">Elle <lb/>eſt l'hypotenuſe d'un triangle rectangle ſpherique, dont les 2 côtez <lb/>ſont le chemin du Vaiſſeau en longitude & </s> <s xml:id="echoid-s9058" xml:space="preserve">en latitude.</s> <s xml:id="echoid-s9059" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9060" xml:space="preserve">On a d'ordinaire la latitude par obſervation; </s> <s xml:id="echoid-s9061" xml:space="preserve">on a par la Bouſſole <lb/>l'angle de la Loxodromie, avec l'un ou l'autre des deux côtez, & </s> <s xml:id="echoid-s9062" xml:space="preserve">ce <lb/>qu'on cherche par le calcul de la Trigonométrie, c'eſt la valeur de <lb/>la longitude parcouruë & </s> <s xml:id="echoid-s9063" xml:space="preserve">de la Loxodromie ou route du Vaiſſeau.</s> <s xml:id="echoid-s9064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9065" xml:space="preserve">Mais comme cette ligne courbe eſt embaraſſante pour les calculs, <lb/>on a voulu avoir la route en ligne droite, & </s> <s xml:id="echoid-s9066" xml:space="preserve">il a fallu conſerver à <lb/>cette ligne droite l'eſſence de la Loxodromie, qui eſt de couper toû-<lb/>jours le Méridens ſous le même angle. </s> <s xml:id="echoid-s9067" xml:space="preserve">Or cela eſt abſolument im-<lb/>poſſible tant que les Méridiens ne ſont point paralleles entr'eux, <lb/>comme eneffet ils ne le ſont pas. </s> <s xml:id="echoid-s9068" xml:space="preserve">Il a donc fallu ſuppoſer les Méri-<lb/>diens paralleles, dont s'eſt enſuivi que les degrez de longitude iné-<lb/>galement éloignez de l'Equateur ont été ſuppoſez de même gran-<lb/>deur, quoique réellementils diminuent toûjours depuis l'Equateur, <lb/>ſelon une certaine proportion connuë; </s> <s xml:id="echoid-s9069" xml:space="preserve">mais pour reparer cette er-<lb/>reur, les degrez de latitude, qui par la nature de la Sphere ſont égaux <lb/>par tout, ſont augmentez dans les Cartes hydrograp hiques, en mê-<lb/> <pb o="286" file="302" n="302" rhead="CONSTRUCT. ET USAGES DES INSTUMENS"/> me proportion que ceux de longitude auroient dû décroître. </s> <s xml:id="echoid-s9070" xml:space="preserve">Ainſi <lb/>l'inégalité qui devroit être dans les deg. </s> <s xml:id="echoid-s9071" xml:space="preserve">de longitude de differens <lb/>paralleles, ſe rejete ſur les degrez de latitude de la maniere que nous <lb/>dirons ci-après.</s> <s xml:id="echoid-s9072" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9073" xml:space="preserve">Les Cartes conſtruites de cette maniere s'appellent réduites, ou <lb/>au point réduit, dont on ſe ſert ordinairement comme des meilleu-<lb/>res; </s> <s xml:id="echoid-s9074" xml:space="preserve">l'experience de pluſieurs ſiecles ayant fait connoître que pour <lb/>l'uſage des Pilotes il faut des Cartes très-ſimples où les Méridiens, <lb/>les paralleles à l'Equateur & </s> <s xml:id="echoid-s9075" xml:space="preserve">les Rumbs de vent ſoient repreſentez <lb/>par des lignes droites pour la facilité du pointage de leurs routes.</s> <s xml:id="echoid-s9076" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div598" type="section" level="1" n="300"> <head xml:id="echoid-head429" xml:space="preserve">CHAPITRE IV.</head> <head xml:id="echoid-head430" style="it" xml:space="preserve">Contenant la Conſtruction des Cartes réduites & leurs Vſages.</head> <p> <s xml:id="echoid-s9077" xml:space="preserve">P Our augmenter autant à proportion les degrez de latitude, que <lb/> <anchor type="note" xlink:label="note-302-01a" xlink:href="note-302-01"/> ceux de longitude ſe trouvent agrandis en les faiſant égaux à <lb/>ceux de l'Equateur, on employe les Secantes qui augmentent autant <lb/>les unes ſur lesautres, que les Sinus de complément de latitude, qui <lb/>devroient repreſenter les deg. </s> <s xml:id="echoid-s9078" xml:space="preserve">de longitude, ont été augmentez en <lb/>les faiſant égaux au raïon de l'Equateur par le paralleliſme des Mé-<lb/>ridiens; </s> <s xml:id="echoid-s9079" xml:space="preserve">car le ſinus de complément d'un arc eſt au Sinus total, com-<lb/>me le Sinus total eſt à la Secante de ce même arc.</s> <s xml:id="echoid-s9080" xml:space="preserve"/> </p> <div xml:id="echoid-div598" type="float" level="2" n="1"> <note position="left" xlink:label="note-302-01" xlink:href="note-302-01a" xml:space="preserve">XXI. <lb/>Planche.</note> </div> <p> <s xml:id="echoid-s9081" xml:space="preserve">Ainſi prenant pour un degré de l'Equateur & </s> <s xml:id="echoid-s9082" xml:space="preserve">pour le premier de-<lb/>gré de latitude le raïon entier ou une partie aliquote quelconque de <lb/>ceraïon, on prend pour le ſccond degré de latitude la Secante d'un <lb/>degré ou la partie aliquote ſemblable de cette Secante; </s> <s xml:id="echoid-s9083" xml:space="preserve">pour le 3<emph style="sub">me</emph> <lb/>degré de latitude on prend la Secante de deux degrez ou la partie a-<lb/>liquote ſemblable, & </s> <s xml:id="echoid-s9084" xml:space="preserve">ainſi de ſuite.</s> <s xml:id="echoid-s9085" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9086" xml:space="preserve">Lorſqu'on veut avoir une Carte à plus grand point, on prend pour <lb/>30 m. </s> <s xml:id="echoid-s9087" xml:space="preserve">de latitude & </s> <s xml:id="echoid-s9088" xml:space="preserve">pour 30 m. </s> <s xml:id="echoid-s9089" xml:space="preserve">de l'Equateur, un raïon de cercle <lb/>ou une partie aliquote quelconque de ce raïon, pour un degre de la-<lb/>titude. </s> <s xml:id="echoid-s9090" xml:space="preserve">On ajoûte de ſuitela Secante de 30 m. </s> <s xml:id="echoid-s9091" xml:space="preserve">pour un degré & </s> <s xml:id="echoid-s9092" xml:space="preserve">de-<lb/>mi de latitude, on ajoûte de ſuite la Secante d'un degré, pour 2 deg. <lb/></s> <s xml:id="echoid-s9093" xml:space="preserve">de latitude; </s> <s xml:id="echoid-s9094" xml:space="preserve">on ajoûte la Secante d'un degré, 30 m. </s> <s xml:id="echoid-s9095" xml:space="preserve">ou les parties <lb/>aliquotes ſemblables de ces Secantes, & </s> <s xml:id="echoid-s9096" xml:space="preserve">ainſi de ſuite.</s> <s xml:id="echoid-s9097" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9098" xml:space="preserve">On ſeſert pour cela dans la pratique, d'une Echelle de parties éga-<lb/>les, ſur laquelle on prend le nombre des parties qui répondent à peu <lb/>près aux Secantes qui ſe trouvent dans les Tables, en retranchant <lb/>les dernieres figures.</s> <s xml:id="echoid-s9099" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9100" xml:space="preserve">Dans ces Cartes l'Echelle eſt changeante à meſure qu'on change <lb/> <pb o="287" file="303" n="303" rhead="POUR LA NAVIGATION Liv. VII. Ch. IV."/> de latitude, ainſi, par exemple, ſi on a navigé entre le 40 & </s> <s xml:id="echoid-s9101" xml:space="preserve">le 50 <lb/>parallele, les degrez des Méridiens qui ſont entre ces deux paralleles <lb/>ſerviront d'Echelle pour meſurer la route; </s> <s xml:id="echoid-s9102" xml:space="preserve">d'où il eſt évident que <lb/>l'on trouve moins de lieuës ſur les paralleles à meſure qu'ils s'appro-<lb/>chent des Poles, puiſqu'on les meſure par une grandeur qui croît <lb/>auſſi toujours en s'avançant vers les Poles.</s> <s xml:id="echoid-s9103" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9104" xml:space="preserve">Si, par exemple, vous voulez tracer une Carte réduite du 40<emph style="sub">me</emph> d. <lb/></s> <s xml:id="echoid-s9105" xml:space="preserve">de latitude Septentrionale juſqu'au 50, & </s> <s xml:id="echoid-s9106" xml:space="preserve">depuis le 6<emph style="sub">me</emph> d. </s> <s xml:id="echoid-s9107" xml:space="preserve">delon-<lb/>gitude juſqu'au 18; </s> <s xml:id="echoid-s9108" xml:space="preserve">tracez premierement la ligne AB, qui repreſen-<lb/>tera le 40<emph style="sub">e</emph> parallele à l'Equateur; </s> <s xml:id="echoid-s9109" xml:space="preserve">diviſez-la en 12 part. </s> <s xml:id="echoid-s9110" xml:space="preserve">égales pour <lb/>les 12 d. </s> <s xml:id="echoid-s9111" xml:space="preserve">de longitude que contient cette Carte; </s> <s xml:id="echoid-s9112" xml:space="preserve">ayez un compas de <lb/>proportion ou une Echelle diviſée, dont cent parties ſoient égales à <lb/>chacun de ces degrez, élevez perpendiculairement ſur les extremi-<lb/>tez de la ligne AB deux autres lignes qui repreſenteront deux Mé-<lb/>ridiens paralleles, leſquels vous diviſerez en ajoûtant bout à bout <lb/>les Secantes convenables. </s> <s xml:id="echoid-s9113" xml:space="preserve">Ainſi pour la diſtance du 40 au 41 deg. </s> <s xml:id="echoid-s9114" xml:space="preserve"><lb/>de latitude, prenez ſur vôtre Echelle 131 parties & </s> <s xml:id="echoid-s9115" xml:space="preserve">demie, qui eſt la <lb/>Secante de 40 d. </s> <s xml:id="echoid-s9116" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9117" xml:space="preserve">pour la diſtance du 41 au 42, prenez 133 <lb/>& </s> <s xml:id="echoid-s9118" xml:space="preserve">demi, qui eſt la Secante de 41 d. </s> <s xml:id="echoid-s9119" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9120" xml:space="preserve">pour la diſtance du 42 au <lb/>43, prenez 136, Secante de 42 d. </s> <s xml:id="echoid-s9121" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9122" xml:space="preserve">& </s> <s xml:id="echoid-s9123" xml:space="preserve">ainſi de ſuite juſqu'au <lb/>dernier degré de vôtre Carte qui ſera de 154 parties, Secante de 49 <lb/>d. </s> <s xml:id="echoid-s9124" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9125" xml:space="preserve">& </s> <s xml:id="echoid-s9126" xml:space="preserve">marquera la diſtance du 49 d. </s> <s xml:id="echoid-s9127" xml:space="preserve">de latitude au 50, & </s> <s xml:id="echoid-s9128" xml:space="preserve"><lb/>par ce moyen les degrez de latitude ſeront augmentez dans la mê-<lb/>me proportion que ceux de longitude auroient dû décroître.</s> <s xml:id="echoid-s9129" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9130" xml:space="preserve">Poury placer les rumbs de vent, choiſiſſez un endroit commode <lb/>vers le milieu dela Carte, comme le point R; </s> <s xml:id="echoid-s9131" xml:space="preserve">duquel comme centre <lb/>vous décrirezun cercle aſſez grand pour être divifé en 32 parties é-<lb/>gales, pour les 32 airs de vent de la Bouſlole. </s> <s xml:id="echoid-s9132" xml:space="preserve">Et ayant tracé versle <lb/>haut de la Carte le rumb de vent qui marquera le Nord, parallele <lb/>aux 2 Méridiens diviſez, vous y ferez une Fleur-de-Lys, qui fera <lb/>connoître tous les autres rumbs de vent, dont les principaux ſe doi-<lb/>vent diſtinguer par des lignes plus groſſes.</s> <s xml:id="echoid-s9133" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9134" xml:space="preserve">Enſuite vous placerez, ſuivant leurs longitudes & </s> <s xml:id="echoid-s9135" xml:space="preserve">latitudes, les <lb/>villes, Ports, Iſles, Côtes, Bancs, Ecueils, &</s> <s xml:id="echoid-s9136" xml:space="preserve">c. </s> <s xml:id="echoid-s9137" xml:space="preserve">& </s> <s xml:id="echoid-s9138" xml:space="preserve">formerez vôtre <lb/>Carte. </s> <s xml:id="echoid-s9139" xml:space="preserve">Vous pourrez auſfi faire pluſieurs Roſes de rumbs de vent, <lb/>ſuivant la grandeur de la Carte; </s> <s xml:id="echoid-s9140" xml:space="preserve">mais il faut que les lignes Nord & </s> <s xml:id="echoid-s9141" xml:space="preserve"><lb/>Sud ſoient toûjours paralleles entr'elles.</s> <s xml:id="echoid-s9142" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div600" type="section" level="1" n="301"> <head xml:id="echoid-head431" style="it" xml:space="preserve">Uſage des Cartes réduites.</head> <p> <s xml:id="echoid-s9143" xml:space="preserve">LE principal uſage des Cartes Marines eſt pour y pointer ou com-<lb/>paſſer les routes, à quoi les Cartes réduites ſont les plus propres.</s> <s xml:id="echoid-s9144" xml:space="preserve"/> </p> <pb o="288" file="304" n="304" rhead="CONSTRUCT. ET USAGES DES INSTRUMENS"/> <p> <s xml:id="echoid-s9145" xml:space="preserve">Pointer ou compaſſer une route, c'eſt marquer ſur la Carte le point <lb/>d'où l'on eſt parti, celui où l'on eſt arrivé, avecleur diſtance, & </s> <s xml:id="echoid-s9146" xml:space="preserve">le <lb/>rumb qu'on a ſuivi, comme auſſi leur longitude & </s> <s xml:id="echoid-s9147" xml:space="preserve">latitude. </s> <s xml:id="echoid-s9148" xml:space="preserve">Ce <lb/>que nons allons expliquer par quelques Exemples.</s> <s xml:id="echoid-s9149" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div601" type="section" level="1" n="302"> <head xml:id="echoid-head432" xml:space="preserve">I. EXEMPLE.</head> <p> <s xml:id="echoid-s9150" xml:space="preserve">Un Vaiſſeau part de l'lſle Oüeſſant à 48 d. </s> <s xml:id="echoid-s9151" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9152" xml:space="preserve">de latitude <lb/>Sept. </s> <s xml:id="echoid-s9153" xml:space="preserve">& </s> <s xml:id="echoid-s9154" xml:space="preserve">13 d. </s> <s xml:id="echoid-s9155" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9156" xml:space="preserve">de longitude pour aller au Cap de Finiſterre en <lb/>Galice, à 43 d. </s> <s xml:id="echoid-s9157" xml:space="preserve">de latitude & </s> <s xml:id="echoid-s9158" xml:space="preserve">8 d. </s> <s xml:id="echoid-s9159" xml:space="preserve">de longitude. </s> <s xml:id="echoid-s9160" xml:space="preserve">On demande quelle <lb/>route il faut tenir & </s> <s xml:id="echoid-s9161" xml:space="preserve">quelle eſt la diſtance de ces 2 lieux. </s> <s xml:id="echoid-s9162" xml:space="preserve">Imaginez-<lb/>vous une lig. </s> <s xml:id="echoid-s9163" xml:space="preserve">tiree de l'lſle Oüeſſant au Cap de Finiſterre, examinez <lb/>avec un Compas à quel rumb de vent marqué ſur la Carte cette li-<lb/>gne eſt parallele, ce ſera celui qu'il faut ſuivre; </s> <s xml:id="echoid-s9164" xml:space="preserve">vous trouverez que <lb/>c'eſt le Sud-Oüeſt quart au Sud qui convient à cette route.</s> <s xml:id="echoid-s9165" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9166" xml:space="preserve">A l'égard de la diſtance prenez avec un Compas l'étenduë de 5 d. <lb/></s> <s xml:id="echoid-s9167" xml:space="preserve">fur le Méridien pour en faire une Echelle de cent lieuës vis-à-vis la-<lb/>dite route; </s> <s xml:id="echoid-s9168" xml:space="preserve">c'eſt-à-dire depuis 43 d. </s> <s xml:id="echoid-s9169" xml:space="preserve">juſqu'à 48. </s> <s xml:id="echoid-s9170" xml:space="preserve">Portez une pointe <lb/>du Compas ainſi ouvert ſur l'lſle Oüeſſant, & </s> <s xml:id="echoid-s9171" xml:space="preserve">l'autre pointe ſur la <lb/>ligne occulte qui tend au Cap de Finiſterre, en y faiſant une petite <lb/>marque. </s> <s xml:id="echoid-s9172" xml:space="preserve">Cette ouverture fera cent lieuës de chemin. </s> <s xml:id="echoid-s9173" xml:space="preserve">Prenez enſuite <lb/>avec le même Compas la diſtance de puis cette marque juſqu'au <lb/>Cap de Finiſterre. </s> <s xml:id="echoid-s9174" xml:space="preserve">Portez cette ouverture ſur le Méridien, mettant <lb/>une pointe ſur le 43<emph style="sub">me</emph> degré, l'autre pointe tombera environ à un <lb/>quart moins du 45<emph style="sub">me</emph>, ce qui vaut 35 lieuës, & </s> <s xml:id="echoid-s9175" xml:space="preserve">par conſequent cet-<lb/>te diſtance entiere eſt de 135 lieuës.</s> <s xml:id="echoid-s9176" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div602" type="section" level="1" n="303"> <head xml:id="echoid-head433" xml:space="preserve">II. EXEMPLE.</head> <p> <s xml:id="echoid-s9177" xml:space="preserve">Un Vaiſſeau parti de l'Iſle Oüeſſant a ſuivi le Sud-Oüeſt quart <lb/>au Sud, pour aller au Cap de Finiſterre. </s> <s xml:id="echoid-s9178" xml:space="preserve">Le Maître Pilote ayant exa-<lb/>miné la force du vent, la quantité de voiles de déploïées, & </s> <s xml:id="echoid-s9179" xml:space="preserve">connoiſ-<lb/>ſant par experience la vîteſle de ſon Navire, eſtime avoir fait 50 <lb/>lieuës de chemin pendant 20 heures de tems qu'il eſt en route, & </s> <s xml:id="echoid-s9180" xml:space="preserve"><lb/>pour marquer ſur la Carte le point où eſt lc Vaiſſeau, il doit prendre <lb/>avec un Compas l'étenduë de 2 d. </s> <s xml:id="echoid-s9181" xml:space="preserve">& </s> <s xml:id="echoid-s9182" xml:space="preserve">demi, équivalens à 50 lieuës <lb/>ſur le Méridien, depuis le 46<emph style="sub">me</emph> deg. </s> <s xml:id="echoid-s9183" xml:space="preserve">juſqu'au 48 deg. </s> <s xml:id="echoid-s9184" xml:space="preserve">30 min & </s> <s xml:id="echoid-s9185" xml:space="preserve"><lb/>porter une pointe du Compas ainſi ouvert ſur le lieu d'où il eſt <lb/>parti, & </s> <s xml:id="echoid-s9186" xml:space="preserve">l'autre pointe étant conduite ſur la ligne de route mar-<lb/>quera le point T ou eſt arrivé le Vaiſſeau. </s> <s xml:id="echoid-s9187" xml:space="preserve">Que ſi vous ſouhaitez <lb/>de ſçavoir la lougitude & </s> <s xml:id="echoid-s9188" xml:space="preserve">latitude de ce lieu d'arrivée, mettez <lb/>une pointe de Compas ſur le point T, & </s> <s xml:id="echoid-s9189" xml:space="preserve">l'autre ſur le plus proche <lb/>parallele. </s> <s xml:id="echoid-s9190" xml:space="preserve">Conduiſez perpendiculairement le Compas ainſi ouvert <lb/>le long du parallele juſqu'au Méridien; </s> <s xml:id="echoid-s9191" xml:space="preserve">le degré où aboutira le <lb/> <pb o="289" file="305" n="305" rhead="POUR LA NAVIGATION. Liv. VII. Chap. IV."/> Compas marquera la latitude du point T. </s> <s xml:id="echoid-s9192" xml:space="preserve">Pour ſa longitude met-<lb/>tez une pointe du Compas en T, & </s> <s xml:id="echoid-s9193" xml:space="preserve">l'autre ſur le Méridien le plus <lb/>proche, faites couler le Compas vers le parallele diviſé, il vous mar-<lb/>quera le degré de longitude.</s> <s xml:id="echoid-s9194" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9195" xml:space="preserve">Comme les Paralleles & </s> <s xml:id="echoid-s9196" xml:space="preserve">les Méridiens ne traverſent point la Car-<lb/>te, pour ne la pas embaraſſer avec les rumbs de vent, on ſe ſert d'une <lb/>regle qui traverſe la Carte de part & </s> <s xml:id="echoid-s9197" xml:space="preserve">d'autre & </s> <s xml:id="echoid-s9198" xml:space="preserve">qui fait le méme effet.</s> <s xml:id="echoid-s9199" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div603" type="section" level="1" n="304"> <head xml:id="echoid-head434" xml:space="preserve">III. EXEMPLE.</head> <p> <s xml:id="echoid-s9200" xml:space="preserve">Un Pilote ſçachant le rumb de vent qu'il a ſuivi depuis ſon dé-<lb/>part, & </s> <s xml:id="echoid-s9201" xml:space="preserve">ayant pris hauteur, il connoît la latitude du lieu où eſt ſon <lb/>Vaiſſeau. </s> <s xml:id="echoid-s9202" xml:space="preserve">On demande qu'il marque ſur la Carte le lieu où il eſt, <lb/>& </s> <s xml:id="echoid-s9203" xml:space="preserve">combien de chemin il a fait. </s> <s xml:id="echoid-s9204" xml:space="preserve">Je ſuppoſe qu'étant parti de l'lſle <lb/>Oüeſſant il eſt arrivé en un lieu dont la latitude eſt de 46 d. </s> <s xml:id="echoid-s9205" xml:space="preserve">Cela <lb/>étant il ouvrira le Compas depuis 46 d. </s> <s xml:id="echoid-s9206" xml:space="preserve">du Méridien juſqu'à 48 d. <lb/></s> <s xml:id="echoid-s9207" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9208" xml:space="preserve">qur eſt la latitude du départ, où ayant place une regle juſqu'a <lb/>l'Iſle Oüeſſant, il fera couler le long de cette regle une pointe de <lb/>Compas, juſqu'à ce que l'autre pointe rencontre la ligne de route. </s> <s xml:id="echoid-s9209" xml:space="preserve"><lb/>Le point d'interſection S ſera celui où étoit le Vaiſſeau au tems de <lb/>l'obſervation. </s> <s xml:id="echoid-s9210" xml:space="preserve">A l'égard du chemin parcouru, ouvrez le Compas <lb/>depuis ce point juſqu'au lieu du départ, & </s> <s xml:id="echoid-s9211" xml:space="preserve">portez cette ouverture <lb/>ſur le Méridien; </s> <s xml:id="echoid-s9212" xml:space="preserve">elle ira depuis 46 degrez juſqu'à 49 qui font 60 <lb/>lieuës de chemin, à raiſon de 20 lieuës par degré.</s> <s xml:id="echoid-s9213" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div604" type="section" level="1" n="305"> <head xml:id="echoid-head435" xml:space="preserve">IV. EXEMPLE.</head> <p> <s xml:id="echoid-s9214" xml:space="preserve">Connoiſſant la latitude & </s> <s xml:id="echoid-s9215" xml:space="preserve">la longitude d'un lieu trouver, ce lieu <lb/>dans la Carte réduite. </s> <s xml:id="echoid-s9216" xml:space="preserve">A yant mis la pointe d'un Compas à Carte <lb/>Marine ſur le degré de latitude connuë, & </s> <s xml:id="echoid-s9217" xml:space="preserve">l'autre ſur le plus proche <lb/>parallele; </s> <s xml:id="echoid-s9218" xml:space="preserve">il faut de l'autre main mettre la pointe d'un ſecond Com-<lb/>pas ſur le degré de longitude connuë, & </s> <s xml:id="echoid-s9219" xml:space="preserve">l'autre pointe ſur le plus <lb/>proche Méridien, & </s> <s xml:id="echoid-s9220" xml:space="preserve">faire couler ces deux Compas juſqu'à ce que <lb/>deux de leurs pointes ſe rencontrent. </s> <s xml:id="echoid-s9221" xml:space="preserve">Le point de jonction ſera le <lb/>lieu cherché. </s> <s xml:id="echoid-s9222" xml:space="preserve">Cette operation eſt fort en uſage aux Gens de Mer, <lb/>après avoir trouvé leur point par le calcul ou par le Quartier de ré-<lb/>duction; </s> <s xml:id="echoid-s9223" xml:space="preserve">car ayant par ce moyen trouvé ſur la Carte le lieu où eſt <lb/>arrivé le Vaiſſeau, il leur eſt facile de connoître le rumb de vent <lb/>qu'ils doivent ſuivre pour continuer leur route.</s> <s xml:id="echoid-s9224" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div605" type="section" level="1" n="306"> <head xml:id="echoid-head436" style="it" xml:space="preserve">Des Marées ou Flux & Reflux de la Mer.</head> <p> <s xml:id="echoid-s9225" xml:space="preserve">LEs Navigateurs ne doivent pas ignorer ce que c'eſt quele Flux <lb/>& </s> <s xml:id="echoid-s9226" xml:space="preserve">Reflux de la Mer, ni l'heure qu'elle eſt baſſe ou haute dans <lb/>les differentes Côtes qu'ils navigent.</s> <s xml:id="echoid-s9227" xml:space="preserve"/> </p> <pb o="290" file="306" n="306" rhead="CONSTRUCT. ET USAGES DES INSTRUM. &c."/> <p> <s xml:id="echoid-s9228" xml:space="preserve">Le Flux ou Flot de la Mer eſt lorſqu'elle monte, & </s> <s xml:id="echoid-s9229" xml:space="preserve">le Reflux ou le <lb/>Zouſant eſt lorſqu'elle deſcend. </s> <s xml:id="echoid-s9230" xml:space="preserve">Il y a Flux & </s> <s xml:id="echoid-s9231" xml:space="preserve">Reflux deux fois par <lb/>24 h. </s> <s xml:id="echoid-s9232" xml:space="preserve">48 m. </s> <s xml:id="echoid-s9233" xml:space="preserve">c'eſt-à-dire, que la Mer venant da la Zone torride allant <lb/>vers chacun des Poles, elle monte le long des Côtes pendant 6 h. </s> <s xml:id="echoid-s9234" xml:space="preserve">12 <lb/>m. </s> <s xml:id="echoid-s9235" xml:space="preserve">& </s> <s xml:id="echoid-s9236" xml:space="preserve">puis ſe retire pendant 6 h. </s> <s xml:id="echoid-s9237" xml:space="preserve">12 m. </s> <s xml:id="echoid-s9238" xml:space="preserve">& </s> <s xml:id="echoid-s9239" xml:space="preserve">ainſi eſt à la plus grande <lb/>hauteur de 12 en 12 h. </s> <s xml:id="echoid-s9240" xml:space="preserve">24 m. </s> <s xml:id="echoid-s9241" xml:space="preserve">ce qu'on appelle pleine Mer, & </s> <s xml:id="echoid-s9242" xml:space="preserve">elle <lb/>eſt baſſe auſſi de 12 en 12 h. </s> <s xml:id="echoid-s9243" xml:space="preserve">24 m. </s> <s xml:id="echoid-s9244" xml:space="preserve">ce qu'on appclle baſſe Mer.</s> <s xml:id="echoid-s9245" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9246" xml:space="preserve">L'on appelle Vives-eaux ou Reverdies les Marées au tems des <lb/>nouvelles & </s> <s xml:id="echoid-s9247" xml:space="preserve">pleines Lunes; </s> <s xml:id="echoid-s9248" xml:space="preserve">parce que la Mer monte davantage pour <lb/>être pleine Mer, & </s> <s xml:id="echoid-s9249" xml:space="preserve">elle baiſſe davantage pour être baſſe Mer, qu'elle <lb/>ne fait dans les Quadratures, qu'on dit alors les Mortes-eaux.</s> <s xml:id="echoid-s9250" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9251" xml:space="preserve">Les Marées montent & </s> <s xml:id="echoid-s9252" xml:space="preserve">baiſlent davantage au tems des Equinoxes <lb/>qu'en toutes autres ſaiſons de l'année, c'eſt pourquoi les Reverdies <lb/>de ces tems-là ſe nomment les grandes Malines. </s> <s xml:id="echoid-s9253" xml:space="preserve">On eſtime que la <lb/>Mer monte & </s> <s xml:id="echoid-s9254" xml:space="preserve">baiſſe environ un 6<emph style="sub">me</emph> plus aux Reverdies des Equi-<lb/>noxes qu'à celles des Solſtices, & </s> <s xml:id="echoid-s9255" xml:space="preserve">dans les autres tems à proportion. <lb/></s> <s xml:id="echoid-s9256" xml:space="preserve">Lorſqu'on eſt dans des Côtes, on doit ſoigneuſement remarquer <lb/>combien les Marées y montent depuis la baſſe Mer juſqu'à la haute <lb/>& </s> <s xml:id="echoid-s9257" xml:space="preserve">par ſupputation, faire la même choſe pour les grandes Malines. </s> <s xml:id="echoid-s9258" xml:space="preserve"><lb/>On verra dans les Tables ce que les Marées montent dans chaques <lb/>Côtes aux grandes Malines. </s> <s xml:id="echoid-s9259" xml:space="preserve">Il eſt bon de ſçavoir que les vents aug-<lb/>mentent beaucoup les Marées quand ils portent vers les Côtes.</s> <s xml:id="echoid-s9260" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9261" xml:space="preserve">L'on ſçait auſſi que ſuivant toutes les apparences les mouvemens <lb/>de la Mer ſont reglez par les mouvemens de la Lune, car la Mer re-<lb/>tarde de 48 min. </s> <s xml:id="echoid-s9262" xml:space="preserve">qui font trois quarts d'heure & </s> <s xml:id="echoid-s9263" xml:space="preserve">trois minutes par <lb/>jours, comme fait la Lune & </s> <s xml:id="echoid-s9264" xml:space="preserve">par conſequent la Mer auſſi-bien que <lb/>la Lune retarde de quatre heures en cinq jours, & </s> <s xml:id="echoid-s9265" xml:space="preserve">ainſi à propor-<lb/>tion; </s> <s xml:id="echoid-s9266" xml:space="preserve">& </s> <s xml:id="echoid-s9267" xml:space="preserve">toutes les fois qu'il eſt pleine Mer dans un Port ou dans <lb/>une Côte, c'eſt toûjours au moment que la Lune ſe trouve à un mê-<lb/>me cercle horaire. </s> <s xml:id="echoid-s9268" xml:space="preserve">Nous avons donné quelque raiſon du Flux & </s> <s xml:id="echoid-s9269" xml:space="preserve"><lb/>Reflux de la Mer dans le Traité de l'Uſage des Globes.</s> <s xml:id="echoid-s9270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9271" xml:space="preserve">Il y a pluſieurs Tables trés bones qui marquent l'heure de la plei-<lb/>ne Mer au jour de la nouvelle Lune & </s> <s xml:id="echoid-s9272" xml:space="preserve">pleine Lune dans preſque <lb/>tous les Ports, Havres & </s> <s xml:id="echoid-s9273" xml:space="preserve">Côtes.</s> <s xml:id="echoid-s9274" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9275" xml:space="preserve">Voilà en abregé la conſtruction & </s> <s xml:id="echoid-s9276" xml:space="preserve">les uſages des principaux Inf-<lb/>trumens qui ſervent à la Navigation. </s> <s xml:id="echoid-s9277" xml:space="preserve">Il y a ſur cette Matiere quan-<lb/>tité d'autres choſes à dire; </s> <s xml:id="echoid-s9278" xml:space="preserve">mais comme elles ſont hors de nôtre deſ-<lb/>ſein, nous n'en dirons pas davantage. </s> <s xml:id="echoid-s9279" xml:space="preserve">Les curieux de cette ſcience <lb/>trouveront pluſieurs bons Livres qui en traitent à fond.</s> <s xml:id="echoid-s9280" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div606" type="section" level="1" n="307"> <head xml:id="echoid-head437" style="it" xml:space="preserve">Fin du ſeptiéme Livre.</head> <pb file="307" n="307"/> <figure> <image file="307-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/307-01"/> </figure> </div> <div xml:id="echoid-div607" type="section" level="1" n="308"> <head xml:id="echoid-head438" xml:space="preserve">DE LA <lb/>CONSTRUCTION <lb/>ET DES USAGES <lb/>DES CADRANS <lb/>AU SOLEIL.</head> <head xml:id="echoid-head439" style="it" xml:space="preserve">LIVRE HUITIÉME.</head> <head xml:id="echoid-head440" style="it" xml:space="preserve">Remarques & définitions appartenantes aux Cadrans.</head> <p> <s xml:id="echoid-s9281" xml:space="preserve">LE S Cadrans au Soleil prennent leurs noms des princi-<lb/>paux cercles de la Sphere auſquels ils ſont paralle-<lb/>les. </s> <s xml:id="echoid-s9282" xml:space="preserve">On appelle par exemple, Cadran horiſontal celui <lb/>qui eſt parallele à l'horiſon; </s> <s xml:id="echoid-s9283" xml:space="preserve">Cadran équinoxial, celui <lb/>qui eſt parallele à l'Equateur du Monde; </s> <s xml:id="echoid-s9284" xml:space="preserve">Cadrans verti-<lb/>caux, ceux qui ſont paralleles a quelqu'un des cercles verticaux, <lb/>& </s> <s xml:id="echoid-s9285" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s9286" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9287" xml:space="preserve">Aux ſurfaces des Cadrans pour y montrer l'heure, on met deux <lb/>ſortes de ſtyles; </s> <s xml:id="echoid-s9288" xml:space="preserve">l'un appellé droit, qui conſiſte en une verge pointuë, <lb/>laquelle par ſon extremité & </s> <s xml:id="echoid-s9289" xml:space="preserve">d'un ſeul point d'ombre marque l'heu-<lb/>re preſente; </s> <s xml:id="echoid-s9290" xml:space="preserve">l'autre eſt nommé Style oblique ou incliné, ou bren Axe <lb/>qui montre l'heure ou partie d'heure tout de ſon long.</s> <s xml:id="echoid-s9291" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9292" xml:space="preserve">Le bout du Style droit de tous les Cadrans repreſente le centre <lb/>du Monde & </s> <s xml:id="echoid-s9293" xml:space="preserve">de l'Equateur. </s> <s xml:id="echoid-s9294" xml:space="preserve">Le plan du Cadran eſt éloignédu cen-<lb/>tre de la Terre, autant que le Style droit a de longueur.</s> <s xml:id="echoid-s9295" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9296" xml:space="preserve">La diſtance du Soleil au centre de la Terre eſt ſi grande, que l'on <lb/>peut eſtimer tous les points de la ſuperficie de la Terre que nous ha-<lb/>bitons, comme s'ils étoient joints au centre même, ſans que l'on <lb/>puiſſe s'appercevoir que cette difference, qui eſt la diſtance de tout <lb/>le dcmi-diametre de la Terre, c'eſt-à-dire, plus de 1400 lieuës com-<lb/>munes de France, apporte aucun changement ſenſible au mouve-<lb/> <pb o="292" file="308" n="308" rhead="CONSTRUCTION ET USAGES"/> ment journalier du Soleil autour du centre de la Terre, ou autour <lb/>d'une ligne droite qui paſſe par ce centre, & </s> <s xml:id="echoid-s9297" xml:space="preserve">que l'on nomme l'Axe <lb/>du Monde.</s> <s xml:id="echoid-s9298" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9299" xml:space="preserve">C'eſt pourquoi l'extremité du Style de tous le Cadrans peut être <lb/>priſe pour le centre de la terre, & </s> <s xml:id="echoid-s9300" xml:space="preserve">la ligneparallele à l'Axe du Mon-<lb/>de qui paſſe par l'extremité de ce Style, peut être conſiderée comme <lb/>l'Axe du Monde.</s> <s xml:id="echoid-s9301" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9302" xml:space="preserve">Les lignes horaires que l'on trace ſur les Plans des Cadrans ſont <lb/>le rencontres des cercles horaires de la Sphere du Monde avec le <lb/>Plan des Cadrans.</s> <s xml:id="echoid-s9303" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9304" xml:space="preserve">Le centre du Cadran eſt la rencontre de ſa ſurface avec l'Axe du <lb/>Cadran qui paſſe par la pointe du Style, & </s> <s xml:id="echoid-s9305" xml:space="preserve">qui eſt parallele à l'Axe <lb/>du monde. </s> <s xml:id="echoid-s9306" xml:space="preserve">Toutes les lignes horaires ſe rencontrent au centre du <lb/>Cadran.</s> <s xml:id="echoid-s9307" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9308" xml:space="preserve">Tous les Plans des Cadrans peuvent avoir un centre, hormis ceux <lb/>qui ſont Orientaux, Occidentaux ou Polaires, dont les lignes horai-<lb/>res ſont paralleles entr'elles & </s> <s xml:id="echoid-s9309" xml:space="preserve">à l'Axe du Monde.</s> <s xml:id="echoid-s9310" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9311" xml:space="preserve">La verticale du Plan du Cadran eſt la perpendiculaire qui va de-<lb/>puis la pointe du Style juſqu'à ſon pied; </s> <s xml:id="echoid-s9312" xml:space="preserve">mais la verticale du lieu eſt <lb/>la ligne droite perpendiculaire à l'horiſon qui paſſe par l'extremité <lb/>du Style.</s> <s xml:id="echoid-s9313" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9314" xml:space="preserve">Il y a auſſi deux Méridienes, dont l'une eſt la Méridiene propre <lb/>du plan ou la ſouſtylaire, parce que ſon cercle paſſe par la verticale du <lb/>plan, & </s> <s xml:id="echoid-s9315" xml:space="preserve">par conſequent par le pied du Style; </s> <s xml:id="echoid-s9316" xml:space="preserve">l'autre, qui eſt la Méri-<lb/>diene du lieu, a ſon cercle Méridien qui paſſe par la verticale du lieu.</s> <s xml:id="echoid-s9317" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9318" xml:space="preserve">Lorſque le Cadran ne décline point à l'Orient ou à l'Occident, la <lb/>Souſtylaire ou la Méridiene du Plan eſt jointe à la Méridiene du <lb/>lieu ou ligne de 12 h. </s> <s xml:id="echoid-s9319" xml:space="preserve">quoique la ſurface du Cadran ſoit verticale <lb/>ou horiſontale, ou même inclinée en deſſus ou en deſſous.</s> <s xml:id="echoid-s9320" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9321" xml:space="preserve">La ligne horiſontale du Cadran eſt la rencontre de la ſurface du <lb/>Cadran avec un Plan horiſontal ou de niveau, qui paſſe par la poin-<lb/>te du Style.</s> <s xml:id="echoid-s9322" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9323" xml:space="preserve">La ligne équinoxiale eſt la rencontre de la ſurſace du Cadran a-<lb/>vec le Plan du cercle équinoxial. </s> <s xml:id="echoid-s9324" xml:space="preserve">Cette ligne eſt toûjours d'équerre <lb/>avec la ſouſtylaire; </s> <s xml:id="echoid-s9325" xml:space="preserve">c'eſt pourquoi lorſque la ſouſty laire eſt poſée & </s> <s xml:id="echoid-s9326" xml:space="preserve"><lb/>qne l'on a un point de la ligne équinoxiale, on a auſſi la poſition de <lb/>toute cette ligne. </s> <s xml:id="echoid-s9327" xml:space="preserve">Au contraire la ligne êquinoxiale étant donnée, <lb/>on aura la ſouſtylaire qui ſera la ligne perpendiculaire ou à angles <lb/>droits à cette équinoxiale; </s> <s xml:id="echoid-s9328" xml:space="preserve">la ſouſtylaire doit paſſer par le pied du <lb/>Style & </s> <s xml:id="echoid-s9329" xml:space="preserve">par le centre du Cadran.</s> <s xml:id="echoid-s9330" xml:space="preserve"/> </p> <pb o="293" file="309" n="309" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> <p> <s xml:id="echoid-s9331" xml:space="preserve">La ligne de 6 h. </s> <s xml:id="echoid-s9332" xml:space="preserve">paſſe toûjours par la rencontre de la ligne hori-<lb/>ſontale & </s> <s xml:id="echoid-s9333" xml:space="preserve">de l'équinoxiale aux Cadrans déclinans. </s> <s xml:id="echoid-s9334" xml:space="preserve">Ainſi le point de <lb/>rencontre de ces deux lignes eſt un des points de la ligne de 6 h.</s> <s xml:id="echoid-s9335" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9336" xml:space="preserve">Le point où ſe rencontrent la ſouſtylaire & </s> <s xml:id="echoid-s9337" xml:space="preserve">la Meridiene eſt le <lb/>centre du Cadran.</s> <s xml:id="echoid-s9338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9339" xml:space="preserve">Quand on veut ſaire un Cadran, il faut commencer par trouver <lb/>quelle eſt la poſition du Plan, par exemple, du Mur où on veut le fai-<lb/>re, à l'égard du Soleil & </s> <s xml:id="echoid-s9340" xml:space="preserve">des principaux cercles du Ciel. </s> <s xml:id="echoid-s9341" xml:space="preserve">Pour cet ef-<lb/>fet on peut prendre par obſervation quelques points d'ombre ſur le <lb/>Plan du Cardran, qui ſervent à en déterminer la poſition, & </s> <s xml:id="echoid-s9342" xml:space="preserve">à trou-<lb/>ver enſuite par les regles de la Gnomonique ou Horlogiographie <lb/>toutes les lignes que l'on veut repreſenter. </s> <s xml:id="echoid-s9343" xml:space="preserve">C'eſt de ces points que <lb/>dépend toute la juſteſſe du Cadran.</s> <s xml:id="echoid-s9344" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9345" xml:space="preserve">Ces points d'ombre ſe prennent dans un même jour à 3 ou 4 h. <lb/></s> <s xml:id="echoid-s9346" xml:space="preserve">l'un de l'autre, ils doivent être écartez le plus qu'il eſt poſſible, afin <lb/>que les autres points & </s> <s xml:id="echoid-s9347" xml:space="preserve">lignes néceſſaires en ſoient plus démêlez.</s> <s xml:id="echoid-s9348" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div608" type="section" level="1" n="309"> <head xml:id="echoid-head441" xml:space="preserve">CHAPITRE PREMIER.</head> <head xml:id="echoid-head442" style="it" xml:space="preserve">Des Cadr ans tant reguliers qu'irreguliers, qui ſe tracent ſur <lb/>des Plans & ſur des Corps de differentes figures.</head> <p> <s xml:id="echoid-s9349" xml:space="preserve">CEt Inſtrument repreſente un corps évuidé, ayant 14 Plans, ſur <lb/> <anchor type="note" xlink:label="note-309-01a" xlink:href="note-309-01"/> chacun deſquels on peut tracer un Cadran. </s> <s xml:id="echoid-s9350" xml:space="preserve">On le fait de bois, <lb/>de pierre, de cuivre ou de toute autre matiere ſolide.</s> <s xml:id="echoid-s9351" xml:space="preserve"/> </p> <div xml:id="echoid-div608" type="float" level="2" n="1"> <note position="right" xlink:label="note-309-01" xlink:href="note-309-01a" xml:space="preserve">XXII. <lb/>Planche. <lb/>Fig. I.</note> </div> <p> <s xml:id="echoid-s9352" xml:space="preserve">Le Plan ſupérieur marqué A, eſt parallele à l'horiſon, c'eſt pour-<lb/>quoi on y trace un Cadran horiſontal, auſſi-bien que ſur le Plan in-<lb/>férieur marqué E, mais celui ci eſt fort peu éclairé. </s> <s xml:id="echoid-s9353" xml:space="preserve">Le Plan B eſt <lb/>parallele à l'Axe du Monde & </s> <s xml:id="echoid-s9354" xml:space="preserve">fait un angle de 49 deg. </s> <s xml:id="echoid-s9355" xml:space="preserve">avec l'ori-<lb/>ſon de Paris, parce que nous ſuppoſons tous ces Cadrans faits pour <lb/>ladite hauteur de Pole. </s> <s xml:id="echoid-s9356" xml:space="preserve">On y trace un Polaire ſupérieur, & </s> <s xml:id="echoid-s9357" xml:space="preserve">au Plan <lb/>F qui eſt. </s> <s xml:id="echoid-s9358" xml:space="preserve">ſon oppoſé, on y trace un Polaire inſérieur. </s> <s xml:id="echoid-s9359" xml:space="preserve">Le Plan C <lb/>eſt parallele au premier vertical, & </s> <s xml:id="echoid-s9360" xml:space="preserve">comme il regarde le Midi, on y <lb/>trace un Cadran vertical Méridional, & </s> <s xml:id="echoid-s9361" xml:space="preserve">ſon oppoſé, qui eſt vers G, <lb/>étant tourné directement au Septentrion, on y trace un vertical Sep-<lb/>tentrional qui n'a pû ſe repreſenter en cette figure.</s> <s xml:id="echoid-s9362" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9363" xml:space="preserve">Le Plan H eſt parallele à l'Equateur du Monde; </s> <s xml:id="echoid-s9364" xml:space="preserve">c'eſt pourquoi <lb/>il fait un angle de 41 d. </s> <s xml:id="echoid-s9365" xml:space="preserve">avec l'horiſon, qui eſt le complement de la <lb/>hauteur du Pole à Paris. </s> <s xml:id="echoid-s9366" xml:space="preserve">On y trace un Cadran équinoxial ſupérieur, <lb/>& </s> <s xml:id="echoid-s9367" xml:space="preserve">à ſon oppoſé D un équinoxial inferieur. </s> <s xml:id="echoid-s9368" xml:space="preserve">Le Plan marqué K eſt <lb/>parallele au Plan du Méridien; </s> <s xml:id="echoid-s9369" xml:space="preserve">& </s> <s xml:id="echoid-s9370" xml:space="preserve">comme il eſt touroé directement <lb/> <pb o="294" file="310" n="310" rhead="CONSTRUCTION ET USAGES"/> à l'Occident, on y trace un Méridional Occidental, & </s> <s xml:id="echoid-s9371" xml:space="preserve">au Plan qui <lb/>lui eſt oppoſé, on y trace un Méridional Oriental. </s> <s xml:id="echoid-s9372" xml:space="preserve">Le Plan marqué I <lb/>fait un angle de 45 deg avec le vertical Méridional; </s> <s xml:id="echoid-s9373" xml:space="preserve">c'eſt pourquoi <lb/>on y trace un vertical déclinant de 45 deg. </s> <s xml:id="echoid-s9374" xml:space="preserve">du Midi à l'Occident <lb/>ſon oppoſé eſt un déclinant du Septenntrion à l'Orient de 45 d. </s> <s xml:id="echoid-s9375" xml:space="preserve">En-<lb/>fin le Plan marqué L eſt un déclinant du Septentrion à l'Occident, <lb/>auſſi de 45 deg. </s> <s xml:id="echoid-s9376" xml:space="preserve">& </s> <s xml:id="echoid-s9377" xml:space="preserve">ſon oppoſé eſt un déclinant du Midi à l'Orient <lb/>de la même déclinaiſon.</s> <s xml:id="echoid-s9378" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9379" xml:space="preserve">Les 9 premiers Cadrans ſe nomment reguliers, & </s> <s xml:id="echoid-s9380" xml:space="preserve">les 4 derniers <lb/>qui ſont des déclinans ſe nomment irreguliers.</s> <s xml:id="echoid-s9381" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9382" xml:space="preserve">Tous les Axes de ces Cadrans ſont paralleles entr'eux & </s> <s xml:id="echoid-s9383" xml:space="preserve">à l'Axe <lb/>du Monde.</s> <s xml:id="echoid-s9384" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9385" xml:space="preserve">Nous donnerons ci-après la conſtruction de tous ces Cadrans, <lb/>auſſi-bien que de ceux dont nous allons parler dans l'Inſtrument <lb/>qui ſuit.</s> <s xml:id="echoid-s9386" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div610" type="section" level="1" n="310"> <head xml:id="echoid-head443" style="it" xml:space="preserve">Conſtruction des Cadrans qui ſe tracent ſur un Dodecaëdre.</head> <p> <s xml:id="echoid-s9387" xml:space="preserve">CEtte figure eſt un des cinq Corps reguliers dont nous avons <lb/> <anchor type="note" xlink:label="note-310-01a" xlink:href="note-310-01"/> donné le dévelopement & </s> <s xml:id="echoid-s9388" xml:space="preserve">la coupe en carton, avec la maniere <lb/>de les former en réuniſſant leurs côtez, dans le premier Livre de ce <lb/>Traité. </s> <s xml:id="echoid-s9389" xml:space="preserve">Il eſt nommé Dodecaëdre, & </s> <s xml:id="echoid-s9390" xml:space="preserve">termine par 12 Pentagones <lb/>reguliers, ſur leſquels ou peut tracer autant de Cadrans, excepté <lb/>celui qui lui ſert de baſe.</s> <s xml:id="echoid-s9391" xml:space="preserve"/> </p> <div xml:id="echoid-div610" type="float" level="2" n="1"> <note position="left" xlink:label="note-310-01" xlink:href="note-310-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s9392" xml:space="preserve">Le Plan A étant placé horiſontalement, on y trace un Cadran <lb/>horiſontal, dont la ligne de 12 h. </s> <s xml:id="echoid-s9393" xml:space="preserve">coupe en 2 également un desan-<lb/>gles du Pentagone. </s> <s xml:id="echoid-s9394" xml:space="preserve">Sur le plan B, qui eſt tourné vers la partie Méri-<lb/>dionale du monde, on y trace un Cadran vertical Méridional ſans <lb/>déclinaiſon, incliné au Zénith ou vers le Ciel de 63 d. </s> <s xml:id="echoid-s9395" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9396" xml:space="preserve">ſon <lb/>centre eſt en haut, & </s> <s xml:id="echoid-s9397" xml:space="preserve">ſa ſouſtylaire eſt la ligne de 12 h. </s> <s xml:id="echoid-s9398" xml:space="preserve">ſon oppoſé <lb/>eſt un vertical Septentrional ſans declinaiſon, incliné au Nadir ou <lb/>vers la Terre de 63 d. </s> <s xml:id="echoid-s9399" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9400" xml:space="preserve">ſon centre eſt en bas. </s> <s xml:id="echoid-s9401" xml:space="preserve">Le Cadran mar-<lb/>qué C eſt un déclinant du Midi vers l'Oricnt de 36 d. </s> <s xml:id="echoid-s9402" xml:space="preserve">& </s> <s xml:id="echoid-s9403" xml:space="preserve">incliné vers <lb/>la Terre de 63 d. </s> <s xml:id="echoid-s9404" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9405" xml:space="preserve">ſon centre eſt en haut. </s> <s xml:id="echoid-s9406" xml:space="preserve">Son oppoſé eft un dé-<lb/>clinant du Septentrion vers l'Occident de 36 d. </s> <s xml:id="echoid-s9407" xml:space="preserve">incliné au Zénith <lb/>de 63 d. </s> <s xml:id="echoid-s9408" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9409" xml:space="preserve">le centre en bas. </s> <s xml:id="echoid-s9410" xml:space="preserve">Le Cadran marque D,eſt un décli-<lb/>nant du Septentrion vers Orient, de 72d. </s> <s xml:id="echoid-s9411" xml:space="preserve">incliné au Nadir de 63 d. <lb/></s> <s xml:id="echoid-s9412" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9413" xml:space="preserve">le centre en haut, ſon oppoſé eſt'un déclinant du Midi vers <lb/>l'Occident de 72 d. </s> <s xml:id="echoid-s9414" xml:space="preserve">incliné au Zénith de 63 d. </s> <s xml:id="echoid-s9415" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9416" xml:space="preserve">le centre en bas.</s> <s xml:id="echoid-s9417" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9418" xml:space="preserve">Le Cadran marqué E eſt un déclinant du Septentrion vers l'Orient <lb/>de 36 d. </s> <s xml:id="echoid-s9419" xml:space="preserve">incliné au Zénith de 63 d. </s> <s xml:id="echoid-s9420" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9421" xml:space="preserve">le centre en bas, ſon op-<lb/> <pb o="295" file="311" n="311" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> poſé eſt un déclinant du Midi vers l'Occident de 36 d. </s> <s xml:id="echoid-s9422" xml:space="preserve">incliné au <lb/>Nadir de 63 d. </s> <s xml:id="echoid-s9423" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9424" xml:space="preserve">le centre en haut. </s> <s xml:id="echoid-s9425" xml:space="preserve">Enfin le Cadran marqué F <lb/>eſt un déclinant du Midi à l'Orient de 72 d. </s> <s xml:id="echoid-s9426" xml:space="preserve">incliné au Zénith de <lb/>63 d. </s> <s xml:id="echoid-s9427" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9428" xml:space="preserve">le centre en bas, ſon oppoſé eſt un déclinant du Sep-<lb/>tentrion à l'Occident de 72 d. </s> <s xml:id="echoid-s9429" xml:space="preserve">incliné au Nadir de 63 d. </s> <s xml:id="echoid-s9430" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9431" xml:space="preserve">ſon <lb/>centre eſt en haut.</s> <s xml:id="echoid-s9432" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9433" xml:space="preserve">Tous ces Cadransſont garnis de leurs Axes qui ſont paralleles <lb/>entr'eux & </s> <s xml:id="echoid-s9434" xml:space="preserve">à l'Axe du Monde.</s> <s xml:id="echoid-s9435" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9436" xml:space="preserve">On place ces Corps ſur un pied dans un lieu bien expoſéau So-<lb/>leil. </s> <s xml:id="echoid-s9437" xml:space="preserve">On les oriente par le moyen d'une Bouſſole ou d'une ligne Mé-<lb/>ridienne tracée comme nous dirons ci-après, & </s> <s xml:id="echoid-s9438" xml:space="preserve">tous les Cadrans é-<lb/>clairez du Soleil en même tems marquent la même heure.</s> <s xml:id="echoid-s9439" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9440" xml:space="preserve">Si l'on veut placer dans un Jardin le Dodecaëdre ſur un pied d'eſ-<lb/>tal bien affermi, il faut qu'il ſoit fait de matiere ſolide, comme de <lb/>pierre ou de bon bois peint à l'huile, afin de pouvoir reſiſter aux in-<lb/>jures du tems; </s> <s xml:id="echoid-s9441" xml:space="preserve">c'eſt pourquoi nous allons ici donner la maniere <lb/>de tailler ce corps.</s> <s xml:id="echoid-s9442" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9443" xml:space="preserve">Ayez unbloc de pierre taillé en cube parfait, diviſez en 2 égale-<lb/> <anchor type="note" xlink:label="note-311-01a" xlink:href="note-311-01"/> ment chacun des 4 côtez de ſes ſurfaces par 2 diametres AC, BD. <lb/></s> <s xml:id="echoid-s9444" xml:space="preserve">Des points A & </s> <s xml:id="echoid-s9445" xml:space="preserve">C faites l'angle EAF de 116 d. </s> <s xml:id="echoid-s9446" xml:space="preserve">34 m. </s> <s xml:id="echoid-s9447" xml:space="preserve">c'eſt-à-dire, 58 <lb/>d. </s> <s xml:id="echoid-s9448" xml:space="preserve">17 m. </s> <s xml:id="echoid-s9449" xml:space="preserve">de part & </s> <s xml:id="echoid-s9450" xml:space="preserve">d'autre du diametre AC, parce que toutes les <lb/>ſurfaces du Dodecaëdre font l'une avec l'autre des angles de 116d. </s> <s xml:id="echoid-s9451" xml:space="preserve"><lb/>34 m. </s> <s xml:id="echoid-s9452" xml:space="preserve">c'eſt pourquoi deux de ſes faces étant poſées horiſontalement, <lb/>toutes les autres inclinent de 63 d. </s> <s xml:id="echoid-s9453" xml:space="preserve">26 m. </s> <s xml:id="echoid-s9454" xml:space="preserve">complément à 180 d. </s> <s xml:id="echoid-s9455" xml:space="preserve"><lb/>l'eſpace entre F & </s> <s xml:id="echoid-s9456" xml:space="preserve">G ou EH eſt la longueur de chaque côté des Pen-<lb/>tagones. </s> <s xml:id="echoid-s9457" xml:space="preserve">Portez la moitié BF de part & </s> <s xml:id="echoid-s9458" xml:space="preserve">d'autre du point d'interſec-<lb/>tion I en X, & </s> <s xml:id="echoid-s9459" xml:space="preserve">faites la même choſe ſur toutes les autres faces du <lb/>cube, les diametres perpendiculairement l'un ſur l'autre, enſuite <lb/>retranchez toute la pierre le long de ſes diametres juſqu'aux ex-<lb/>tremitez des côtez, comme depuis & </s> <s xml:id="echoid-s9460" xml:space="preserve">tout le long du diametre <lb/>KM, tirant vers B & </s> <s xml:id="echoid-s9461" xml:space="preserve">taillant en ligne droite les deux angles ſoli-<lb/>des juſqu'au point Qen la premiere ſurface, de même tout le long <lb/>du diametre LN, tirant vers K, allant droit au point S, & </s> <s xml:id="echoid-s9462" xml:space="preserve">encore <lb/>tout le long du diametre BD, tirant vers A juſqu'au point T. </s> <s xml:id="echoid-s9463" xml:space="preserve">Les <lb/>autres faces ſe tailleront de même. </s> <s xml:id="echoid-s9464" xml:space="preserve">Pour faciliter la main & </s> <s xml:id="echoid-s9465" xml:space="preserve">l'ima-<lb/>gination de l'ouvrier il eſt à propos d'avoir un de ces corps faits de <lb/>carton devant ſoi, afin de mieux repreſenter les angles & </s> <s xml:id="echoid-s9466" xml:space="preserve">les côtez <lb/>qu'il faut retrancher.</s> <s xml:id="echoid-s9467" xml:space="preserve"/> </p> <div xml:id="echoid-div611" type="float" level="2" n="2"> <note position="right" xlink:label="note-311-01" xlink:href="note-311-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s9468" xml:space="preserve">L'on peutencore tailler ces corps étants premierement de figure <lb/>cylindrique, mais la méthode que nous donnons eſt ſuffiſante.</s> <s xml:id="echoid-s9469" xml:space="preserve"/> </p> <pb o="296" file="312" n="312" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s9470" xml:space="preserve">L'on fait auſſi de ces ſortes de Cadrans en cuivre & </s> <s xml:id="echoid-s9471" xml:space="preserve">plus petits, & </s> <s xml:id="echoid-s9472" xml:space="preserve"><lb/>qui ſont fort curieux.</s> <s xml:id="echoid-s9473" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div613" type="section" level="1" n="311"> <head xml:id="echoid-head444" style="it" xml:space="preserve">Conſtruction du Cadran boriſontal.</head> <p> <s xml:id="echoid-s9474" xml:space="preserve">L A figure 4 eſt un Cadran horiſontal. </s> <s xml:id="echoid-s9475" xml:space="preserve">Pour tracer ce Cadran, ti-<lb/> <anchor type="note" xlink:label="note-312-01a" xlink:href="note-312-01"/> rez premierement les deux lignes droites AB, CD ſe coupantes <lb/>à angles droits au point E qui ſera le centre du Cadran. </s> <s xml:id="echoid-s9476" xml:space="preserve">La ligne AB <lb/>ſera la Méridiene ou ligne de 12 h. </s> <s xml:id="echoid-s9477" xml:space="preserve">& </s> <s xml:id="echoid-s9478" xml:space="preserve">CD celle de 6 h. </s> <s xml:id="echoid-s9479" xml:space="preserve">Faites l'an-<lb/>gle BEF égal à celui de l'élevation du Pole, comme à Paris de 49 d. <lb/></s> <s xml:id="echoid-s9480" xml:space="preserve">On ſçait par obſervation que Paris n'eſt qu'à 48 d. </s> <s xml:id="echoid-s9481" xml:space="preserve">51 m. </s> <s xml:id="echoid-s9482" xml:space="preserve">mais nous <lb/>négligeons les 9 m. </s> <s xml:id="echoid-s9483" xml:space="preserve">comme étant très-peu de choſe dans les Ca-<lb/>drans. </s> <s xml:id="echoid-s9484" xml:space="preserve">La ligne EF repreſente l'Axe du Monde, dans lequel ayant <lb/>choiſi le point G, comme s'il étoit le centre de la Terre, vous tirerez <lb/>à angles droits GH, qui repreſente le raïon de l'Equateur rencon-<lb/>trant la Méridiene en H. </s> <s xml:id="echoid-s9485" xml:space="preserve">Faites enſuite A B, priſe avec un Compas <lb/>égale à HG, tirez la droite LHK perpendiculaire à la Méridiene, <lb/>& </s> <s xml:id="echoid-s9486" xml:space="preserve">repreſentant la commune ſection de l'Equateur avec le Plan du <lb/>Cadran: </s> <s xml:id="echoid-s9487" xml:space="preserve">du point B, comme centre, décrivezle quart de cercle MA, <lb/>diviſez-le en 6 arcs égaux qui ſeront de 15 d. </s> <s xml:id="echoid-s9488" xml:space="preserve">chacun, & </s> <s xml:id="echoid-s9489" xml:space="preserve">tirez les <lb/>lignes ponctuées B5 B4 B3 B2 B1, qui diviſeront la ligne LK d'heu-<lb/>re en heure, y marquant les points par où vous ferez paſſer les lignes <lb/>horaires qui ſeront tirées du point E, centre du Cadran, auquel on <lb/>peut donner telle figure que l'on veut, ſoit de quarré long, comme <lb/>celui de la fig. </s> <s xml:id="echoid-s9490" xml:space="preserve">4 & </s> <s xml:id="echoid-s9491" xml:space="preserve">de la fig. </s> <s xml:id="echoid-s9492" xml:space="preserve">1, ſoit de Pentagone regulier, comme <lb/>celui de la fig. </s> <s xml:id="echoid-s9493" xml:space="preserve">2, & </s> <s xml:id="echoid-s9494" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s9495" xml:space="preserve"/> </p> <div xml:id="echoid-div613" type="float" level="2" n="1"> <note position="left" xlink:label="note-312-01" xlink:href="note-312-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s9496" xml:space="preserve">Au lieu du quart de cercle MH on peut, pour plus grande facili-<lb/>té, tracer ſeulement un arc de 60 d. </s> <s xml:id="echoid-s9497" xml:space="preserve">dont la corde eſt égale au raïon, <lb/>& </s> <s xml:id="echoid-s9498" xml:space="preserve">l'ayant diviſé en 4 arcs égaux de 15 d. </s> <s xml:id="echoid-s9499" xml:space="preserve">chacun, on en ajoûtera <lb/>un pour la cinquiéme heure.</s> <s xml:id="echoid-s9500" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9501" xml:space="preserve">Pour y tracer les demi-heures diviſez en 2 également chacun des <lb/>arcs de la circonference MH, pour avoir des arcs de 7 d. </s> <s xml:id="echoid-s9502" xml:space="preserve">30 m. </s> <s xml:id="echoid-s9503" xml:space="preserve">que <lb/>l'on peut encore ſubdiviſer en 2 pour avoir des quarts d'heure que <lb/>l'on tirera du point B par des lignes occultes, juſqu'au rencontre de <lb/>l'équinoxiale KL: </s> <s xml:id="echoid-s9504" xml:space="preserve">par ces points de rencontre & </s> <s xml:id="echoid-s9505" xml:space="preserve">par le centre E du <lb/>Cadran vous tracerez toutes les lignes horaires.</s> <s xml:id="echoid-s9506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9507" xml:space="preserve">Les diviſions marquées dans la partie LH ſe tranſportent avec <lb/>un Compas dans l'autre partie HK, parce que les heures également <lb/>éloignées de 12h. </s> <s xml:id="echoid-s9508" xml:space="preserve">tant devant qu'après midi, font avec la Méridie-<lb/>ne des angles égaux; </s> <s xml:id="echoid-s9509" xml:space="preserve">les lignes de 7 & </s> <s xml:id="echoid-s9510" xml:space="preserve">8 h. </s> <s xml:id="echoid-s9511" xml:space="preserve">du matin prolongées au <lb/>delà du centre du Cadran donnent les lignes de 7 & </s> <s xml:id="echoid-s9512" xml:space="preserve">8 h. </s> <s xml:id="echoid-s9513" xml:space="preserve">du ſoir, <lb/> <pb o="297" file="313" n="313" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> & </s> <s xml:id="echoid-s9514" xml:space="preserve">les lignes de 4 & </s> <s xml:id="echoid-s9515" xml:space="preserve">5 heures après midi prolongées de même, <lb/>donnent 4 & </s> <s xml:id="echoid-s9516" xml:space="preserve">5 h. </s> <s xml:id="echoid-s9517" xml:space="preserve">du matin.</s> <s xml:id="echoid-s9518" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9519" xml:space="preserve">Ce Cadran étant affermi ſur un Plan bien de niveau, c'eſt-à-dire, <lb/>parallele à l'horiſon, expoſé au Soleil & </s> <s xml:id="echoid-s9520" xml:space="preserve">bien orienté, en ſorte que la <lb/>ligne A 12 convienne avec la Méridiene du Monde, & </s> <s xml:id="echoid-s9521" xml:space="preserve">que le Style <lb/>ou Axe EHF étant relevé perpendiculairement ſur la ligne de 12 h. <lb/></s> <s xml:id="echoid-s9522" xml:space="preserve">l'axe EF ſoit parallele à l'axe du Monde, l'ombre de cet axe marquera <lb/>les heures exactement depuis le lever du Soleil juſqu'à ſon coucher.</s> <s xml:id="echoid-s9523" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div615" type="section" level="1" n="312"> <head xml:id="echoid-head445" style="it" xml:space="preserve">Conſtruction du Cadran vertical ſans déclinaiſon.</head> <p> <s xml:id="echoid-s9524" xml:space="preserve">CE Cadran eſt parallele au premier vertical qui coupe le Méri-<lb/>dien à angles droits & </s> <s xml:id="echoid-s9525" xml:space="preserve">paſſe par les points d'Orient & </s> <s xml:id="echoid-s9526" xml:space="preserve">d'Oc-<lb/>cident des Equinoxes ſur l'horiſon.</s> <s xml:id="echoid-s9527" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9528" xml:space="preserve">Pour le tracer, tirez premierement les lignes EB, & </s> <s xml:id="echoid-s9529" xml:space="preserve">CD à an-<lb/> <anchor type="note" xlink:label="note-313-01a" xlink:href="note-313-01"/> gles droits, dont la premiere ſera la ligne 12 h. </s> <s xml:id="echoid-s9530" xml:space="preserve">& </s> <s xml:id="echoid-s9531" xml:space="preserve">l'autre celle <lb/>de 6 h. </s> <s xml:id="echoid-s9532" xml:space="preserve">Faites au point E, centre du Cadran, l'angle BEF égal au <lb/>complement de l'élevation du Pole, comme à Paris de 41 d. </s> <s xml:id="echoid-s9533" xml:space="preserve">élevez <lb/>perpendiculairement ſur la Méridiene la ligne IG, qui ſera le Style <lb/>droit, dont le point I eſt le pied, & </s> <s xml:id="echoid-s9534" xml:space="preserve">G l'extremité; </s> <s xml:id="echoid-s9535" xml:space="preserve">qui comme nous <lb/>avons dit, peut paſſer pour centre de la Terre. </s> <s xml:id="echoid-s9536" xml:space="preserve">Cette ligne prolon-<lb/>gée de part & </s> <s xml:id="echoid-s9537" xml:space="preserve">d'autre eſt la ligne horiſontale.</s> <s xml:id="echoid-s9538" xml:space="preserve"/> </p> <div xml:id="echoid-div615" type="float" level="2" n="1"> <note position="right" xlink:label="note-313-01" xlink:href="note-313-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s9539" xml:space="preserve">La ligne EGF repreſente l'axe du Monde, ſur lequel tirez à an-<lb/>gles droits la ligne GH juſqu'au rencontre de la Méridiene. </s> <s xml:id="echoid-s9540" xml:space="preserve">Cetts <lb/>ligne GH repreſente le rayon de l'Equateur, & </s> <s xml:id="echoid-s9541" xml:space="preserve">la ligne LHK tirée <lb/>par le point H, & </s> <s xml:id="echoid-s9542" xml:space="preserve">quicoupe la Méridiene à angles droits repreſente <lb/>la commune ſection de l'Equateur avec le Plan du Cadran. </s> <s xml:id="echoid-s9543" xml:space="preserve">Faites <lb/>HB égale à HG; </s> <s xml:id="echoid-s9544" xml:space="preserve">du point B comme centre, décrivez la circonferen-<lb/>ce du quart de cercle MH, que vous diviſerez en ſix arcs égaux de <lb/>15 d. </s> <s xml:id="echoid-s9545" xml:space="preserve">chacun, par des lignes ponctuées qui diviſeront la lîgne LK en <lb/>parties inégales qui ſeront les tangentes de ces arcs; </s> <s xml:id="echoid-s9546" xml:space="preserve">enfin par ces <lb/>points de diviſion, & </s> <s xml:id="echoid-s9547" xml:space="preserve">par le centre E vous tirerez les lignes horai-<lb/>res depuis 6 h. </s> <s xml:id="echoid-s9548" xml:space="preserve">du matin juſqu'à 6 h. </s> <s xml:id="echoid-s9549" xml:space="preserve">du ſoir, qui formeront le Ca-<lb/>dran, comme il ſe voit en ladite figure 5. </s> <s xml:id="echoid-s9550" xml:space="preserve">Sil'on veut y marquer les <lb/>demi-heures & </s> <s xml:id="echoid-s9551" xml:space="preserve">les quarts, on fera comme nous avons dit au Ca-<lb/>dran horiſontal.</s> <s xml:id="echoid-s9552" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9553" xml:space="preserve">Ce Cadran ſe place ſur un Mur ou ſur un Plan bien perpendicu-<lb/>laire à l'horiſon & </s> <s xml:id="echoid-s9554" xml:space="preserve">tourné directement au Midi, c'eſt pourquoi on <lb/>le nomme vertical Méridional.</s> <s xml:id="echoid-s9555" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9556" xml:space="preserve">Sa Méridiene ou ligne de 12 h. </s> <s xml:id="echoid-s9557" xml:space="preserve">doit être parfaitement à plomb, & </s> <s xml:id="echoid-s9558" xml:space="preserve"><lb/>ſaligne horiſontale de niveau. </s> <s xml:id="echoid-s9559" xml:space="preserve">Il a le centre en haut, & </s> <s xml:id="echoid-s9560" xml:space="preserve">l'extremité <lb/> <pb o="298" file="314" n="314" rhead="CONSTRUCTION ET USAGES"/> de ſon axe tend au Pole inférieur. </s> <s xml:id="echoid-s9561" xml:space="preserve">Son oppoſé ſe nomme vertical <lb/>Septentrional; </s> <s xml:id="echoid-s9562" xml:space="preserve">il a le centre en bas, & </s> <s xml:id="echoid-s9563" xml:space="preserve">l'extremité de ſon axe tend <lb/>au Pole ſupérieur du Monde. </s> <s xml:id="echoid-s9564" xml:space="preserve">Sa conſtruction eſt la même que cel-<lb/>le du vertical Méridional; </s> <s xml:id="echoid-s9565" xml:space="preserve">car les lignes horaires & </s> <s xml:id="echoid-s9566" xml:space="preserve">l'axe font les <lb/>mêmes angles avec la Meridiene. </s> <s xml:id="echoid-s9567" xml:space="preserve">Le Cadran vertical Septentrio-<lb/>nal ne marque les heures que pendant les grands jours d'Eté; </s> <s xml:id="echoid-s9568" xml:space="preserve">ſça-<lb/>voir, le matin depuis le lever du Soleil juſqu'à ce qu'il paſſe par le <lb/>premier vertical, & </s> <s xml:id="echoid-s9569" xml:space="preserve">le ſoir depuis le tems qu'il repaſſe le premier <lb/>vertical juſqu'à ſon coucher. </s> <s xml:id="echoid-s9570" xml:space="preserve">Quand le Soleil décrit le Tropique <lb/>d'Eté, il ſe leve ſur l'horiſon de Paris à 4 h. </s> <s xml:id="echoid-s9571" xml:space="preserve">& </s> <s xml:id="echoid-s9572" xml:space="preserve">joint le premier ver-<lb/>tical entre 7 & </s> <s xml:id="echoid-s9573" xml:space="preserve">8 h. </s> <s xml:id="echoid-s9574" xml:space="preserve">du matin; </s> <s xml:id="echoid-s9575" xml:space="preserve">l'après midi il repaſſe par le premier <lb/>vertical entre 4 & </s> <s xml:id="echoid-s9576" xml:space="preserve">5 h. </s> <s xml:id="echoid-s9577" xml:space="preserve">du ſoir & </s> <s xml:id="echoid-s9578" xml:space="preserve">ſe couche à 8, c'eſt pourquoi on <lb/>marque ſur ce Cadran les heures depuis 4 h. </s> <s xml:id="echoid-s9579" xml:space="preserve">du matin juſqu'à 8, <lb/>& </s> <s xml:id="echoid-s9580" xml:space="preserve">depuis 4 h. </s> <s xml:id="echoid-s9581" xml:space="preserve">du ſoir juſqu'à 8.</s> <s xml:id="echoid-s9582" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9583" xml:space="preserve">En ce tems-là le vertical Méridional n'eſt éclairé que depuis en-<lb/>viron 8 h. </s> <s xml:id="echoid-s9584" xml:space="preserve">du matin juſqu'à 4 h. </s> <s xml:id="echoid-s9585" xml:space="preserve">du ſoir.</s> <s xml:id="echoid-s9586" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9587" xml:space="preserve">Mais quand le Soleil par ſon mouvement annuel a rejoint l'E-<lb/>quateur, il ne marque plus les heures ſur le vertical Septentrional, <lb/>& </s> <s xml:id="echoid-s9588" xml:space="preserve">il les marque ſur ſon oppoſé dépuis ſon lever juſqu'à ſon coucher.</s> <s xml:id="echoid-s9589" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div617" type="section" level="1" n="313"> <head xml:id="echoid-head446" style="it" xml:space="preserve">Conſtruction du Cadran Polaire.</head> <p> <s xml:id="echoid-s9590" xml:space="preserve">L A figure 6 repreſente un Polaire ſupérieur. </s> <s xml:id="echoid-s9591" xml:space="preserve">C'eſt un Cadran <lb/>incliné vers le Cicl, mais qui ne decline point, car il eſt parallele <lb/>à l'axe du Monde & </s> <s xml:id="echoid-s9592" xml:space="preserve">au cercle de 6 h. </s> <s xml:id="echoid-s9593" xml:space="preserve">qui coupe le Méridien à an-<lb/>gles droits. </s> <s xml:id="echoid-s9594" xml:space="preserve">C'eſt pour quoi il ne peut jamais marquer 6 h. </s> <s xml:id="echoid-s9595" xml:space="preserve">du ma-<lb/>tin ou du ſoir, parce que pour lors l'ombre du Style étant parallele <lb/>au plan du Cadran, il n'y peut pas faire ombre.</s> <s xml:id="echoid-s9596" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9597" xml:space="preserve">Ce Cadran n'a point de centre & </s> <s xml:id="echoid-s9598" xml:space="preserve">les heures ſont parralleles entr'-<lb/>elles & </s> <s xml:id="echoid-s9599" xml:space="preserve">à l'axe du Monde. </s> <s xml:id="echoid-s9600" xml:space="preserve">Son plan étant parallele à un horiſon de <lb/>la Sphere droite, paſſe parles deux Poles du Monde, d'où il tire ſon <lb/>nom de Polaire.</s> <s xml:id="echoid-s9601" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9602" xml:space="preserve">Pour le tracer tirez premierement la ligne AB, repreſentant l'é-<lb/> <anchor type="note" xlink:label="note-314-01a" xlink:href="note-314-01"/> quinoxiale, & </s> <s xml:id="echoid-s9603" xml:space="preserve">ID à l'équerre, pour la Méridienne ou ligne de 12 h. <lb/></s> <s xml:id="echoid-s9604" xml:space="preserve">prenez la longueur du ſtyle à diſcretion, ſuivant la grandeur du plan <lb/>comme ici CD; </s> <s xml:id="echoid-s9605" xml:space="preserve">de ſon extremité D faites un quart de cercle que <lb/>vous diviſerez en 6 arcs égaux ou ſeulement un arc de 60 deg. </s> <s xml:id="echoid-s9606" xml:space="preserve">que <lb/>vous diviſerezen 4 de 15 d. </s> <s xml:id="echoid-s9607" xml:space="preserve">chacun pour les 4 premieres heures a-<lb/>près midi, & </s> <s xml:id="echoid-s9608" xml:space="preserve">ajoûtezenſuite un pareil arc de 15 d. </s> <s xml:id="echoid-s9609" xml:space="preserve">pour la 5<emph style="sub">me</emph> h. </s> <s xml:id="echoid-s9610" xml:space="preserve">du <lb/>point D, tirez des lignes ponctuées depuis les diviſions de la circon-<lb/>ference dudit arc, juſqu'au rencontre de la ligne AB; </s> <s xml:id="echoid-s9611" xml:space="preserve">& </s> <s xml:id="echoid-s9612" xml:space="preserve">par ces <lb/>points de rencontre tracez les lignes horaires paralleles à la Méri-<lb/> <pb o="299" file="315" n="315" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> diene & </s> <s xml:id="echoid-s9613" xml:space="preserve">perpendiculaires à l'équinoxiale. </s> <s xml:id="echoid-s9614" xml:space="preserve">Les eſpaces des heures é-<lb/>galement éloignées de midi devant & </s> <s xml:id="echoid-s9615" xml:space="preserve">après ſont égaux, c'eſt-à-di-<lb/>re, qu'on tranſporte les diſtances de la ligne CA du côté de la ligne <lb/>CB. </s> <s xml:id="echoid-s9616" xml:space="preserve">Le Style doit être égal à CF; </s> <s xml:id="echoid-s9617" xml:space="preserve">diſtance du midi à 3 h. </s> <s xml:id="echoid-s9618" xml:space="preserve">& </s> <s xml:id="echoid-s9619" xml:space="preserve">ſe peut <lb/>faire en forme de parallelograme rectangle, comme celui qui eſt <lb/>marqué au-deſſus de la lettre K, dans ladite fig. </s> <s xml:id="echoid-s9620" xml:space="preserve">6. </s> <s xml:id="echoid-s9621" xml:space="preserve">Il ſe place le <lb/>long de la ligne de 12 h. </s> <s xml:id="echoid-s9622" xml:space="preserve">qui pour cette raiſon eſt nommée ſouſtilaire.</s> <s xml:id="echoid-s9623" xml:space="preserve"/> </p> <div xml:id="echoid-div617" type="float" level="2" n="1"> <note position="left" xlink:label="note-314-01" xlink:href="note-314-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s9624" xml:space="preserve">Si on ne mer qu'une ſimple verge pour ſtyle, comme celle qui ſe <lb/>voit au point C de la Méridiene, il ne marquera les heures que par <lb/>le bout de l'ombre, au lieu que le parallelograme les marque par <lb/>une ligne.</s> <s xml:id="echoid-s9625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9626" xml:space="preserve">Le Polaire ſupérieur peut marquer les heures depuis 7 d. </s> <s xml:id="echoid-s9627" xml:space="preserve">du ma-<lb/>tin juſqu à 4 h. </s> <s xml:id="echoid-s9628" xml:space="preserve">du ſoir.</s> <s xml:id="echoid-s9629" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9630" xml:space="preserve">Le Polaire inférieur ne peut ſervir que dans les grands jours d'E-<lb/>té; </s> <s xml:id="echoid-s9631" xml:space="preserve">il marque les heures depuis le lever du Soleil juſqu'à 5 h. </s> <s xml:id="echoid-s9632" xml:space="preserve">du ma-<lb/>tin, & </s> <s xml:id="echoid-s9633" xml:space="preserve">depuis 7 h. </s> <s xml:id="echoid-s9634" xml:space="preserve">du ſoir juſqu'au coucher du Soleel; </s> <s xml:id="echoid-s9635" xml:space="preserve">pour l'éleva-<lb/>tion du Pole de Paris, on y remarque 4 & </s> <s xml:id="echoid-s9636" xml:space="preserve">5. </s> <s xml:id="echoid-s9637" xml:space="preserve">h. </s> <s xml:id="echoid-s9638" xml:space="preserve">du matin, comme auſſi <lb/>7 & </s> <s xml:id="echoid-s9639" xml:space="preserve">8 h. </s> <s xml:id="echoid-s9640" xml:space="preserve">du ſoir. </s> <s xml:id="echoid-s9641" xml:space="preserve">Sa conſtruction eſt la même que celle du Polaire <lb/>ſupérieur, car la diſtance depuis la ſouſtylaire juſqu'à 4 & </s> <s xml:id="echoid-s9642" xml:space="preserve">5 h. </s> <s xml:id="echoid-s9643" xml:space="preserve">d'a-<lb/>près midi ſur le Polaire ſupérieur, eſt la même que celle de la ſouſty-<lb/>laire du Polaire inférieur juſqu'à 4 & </s> <s xml:id="echoid-s9644" xml:space="preserve">5 h. </s> <s xml:id="echoid-s9645" xml:space="preserve">du matin, de même que <lb/>juſqu'à 7 & </s> <s xml:id="echoid-s9646" xml:space="preserve">8 h. </s> <s xml:id="echoid-s9647" xml:space="preserve">du ſoir. </s> <s xml:id="echoid-s9648" xml:space="preserve">C'eſt pourquoi nous avons jugé inutile <lb/>d'en tracer la figure.</s> <s xml:id="echoid-s9649" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9650" xml:space="preserve">La diſtance des heures dépend de la grandeur du Style, ainſi elles <lb/>ſeront plus ou moins éloignées les unes des autres à proportion que <lb/>l'extrémité D ſera plus ou moins éloignée de l'Equinoxiale.</s> <s xml:id="echoid-s9651" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9652" xml:space="preserve">Pour placer ce Cadran à Paris, il faut que ſon Plan faſſe avec <lb/>l'horiſon un angle de 49 d. </s> <s xml:id="echoid-s9653" xml:space="preserve">ſupérieur tourné vers le Ciel, & </s> <s xml:id="echoid-s9654" xml:space="preserve">di-<lb/>rectement au Midi, afin que ſon axe ſoit parallele à l'axe du Monde; <lb/></s> <s xml:id="echoid-s9655" xml:space="preserve">ſon oppoſé qui eſt l'inférieur eſt incliné vers la Terre, les heures du <lb/>matin ſont vers l'Occident, & </s> <s xml:id="echoid-s9656" xml:space="preserve">celles du ſoir vers l'Orient.</s> <s xml:id="echoid-s9657" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9658" xml:space="preserve">Pour y tracer la ligne horiſontale, du point F, extremité du Syle, <lb/>comme centre, décrivez l'arc GH, égal à l'élevation du Pole, c'eſt-à-<lb/>dire, de 49 d. </s> <s xml:id="echoid-s9659" xml:space="preserve">pour Paris, tirez la droite FH qui coupera la Méri-<lb/>diene au point I, par lequel vous tirerez à angles droits l'horiſontale <lb/>LK, laquelle ſervira à connoître ſi le Cadran eſt bien placé; </s> <s xml:id="echoid-s9660" xml:space="preserve">& </s> <s xml:id="echoid-s9661" xml:space="preserve">s'il a <lb/>ſon inclinaiſon convenable; </s> <s xml:id="echoid-s9662" xml:space="preserve">car pour cela il faut qu'un Plan poſé le <lb/>long de la ligne horiſontale & </s> <s xml:id="echoid-s9663" xml:space="preserve">appuïé ſur la pointe du Style qui eſt <lb/>en l'air, ſoit de niveau ou parallele à l'horiſon.</s> <s xml:id="echoid-s9664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9665" xml:space="preserve">Dans les Païs où la Sphere eſt droite, le Cadran Polaire ſe place <lb/> <pb o="300" file="316" n="316" rhead="CONSTRUCTION ET USAGES"/> parallement à lhoriſon, & </s> <s xml:id="echoid-s9666" xml:space="preserve">dans la Sphere parallele il ſe place verti-<lb/>calement, c'eſt à-diré, ſur les Murs à plomb qui ne déclinent point.</s> <s xml:id="echoid-s9667" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div619" type="section" level="1" n="314"> <head xml:id="echoid-head447" style="it" xml:space="preserve">Conſtruction du Cadr an Equinoxial.</head> <p> <s xml:id="echoid-s9668" xml:space="preserve">L E Cadran Equinoxial ſupérieur ne marque les heures que pen-<lb/>dant 6 mois de l'année; </s> <s xml:id="echoid-s9669" xml:space="preserve">ſçavoir, depuis l'Equinoxe de Printems <lb/>juſqu'à celui d'Automne. </s> <s xml:id="echoid-s9670" xml:space="preserve">Son oppoſé qui eſt un équinoxial infé-<lb/>rieur marque les heures pendant les 6 autres mois; </s> <s xml:id="echoid-s9671" xml:space="preserve">c'eſt-à-dire, de-<lb/>puis l'Equinoxe d'Automne juſqu'à celui de Printems.</s> <s xml:id="echoid-s9672" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9673" xml:space="preserve">Le Plan de ces Cadrans eſt parallele à l'Equateur du Monde, & </s> <s xml:id="echoid-s9674" xml:space="preserve"><lb/>coupé à angles droits en ſon centre par l'axe du Monde.</s> <s xml:id="echoid-s9675" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9676" xml:space="preserve">Pour le conſtruire tirez à angles droits deux lignes droites AH, <lb/> <anchor type="note" xlink:label="note-316-01a" xlink:href="note-316-01"/> ED, dont la premiere ſera la ligne de 12 h. </s> <s xml:id="echoid-s9677" xml:space="preserve">& </s> <s xml:id="echoid-s9678" xml:space="preserve">l'autre celle de 6 h. </s> <s xml:id="echoid-s9679" xml:space="preserve">du <lb/>point d'interſection A, décrivez une circonference de cercle, dont <lb/>chaque quart ſera diviſé en 6 parties égales pour avoir 6 h de ſui-<lb/>te, comme depuis 6 juſqu'à 12, qui ſerviront à tirer du centre tou-<lb/>tes le lignes horaires, puiſqu'elles font toutes des angles égaux de <lb/>15 d. </s> <s xml:id="echoid-s9680" xml:space="preserve">chacun avec la Méridiene: </s> <s xml:id="echoid-s9681" xml:space="preserve">chaque eſpace diviſé en 2 donne <lb/>les demi-heures, & </s> <s xml:id="echoid-s9682" xml:space="preserve">les arcs de demi-heures ſubdiviſez en deux don-<lb/>nent les quarts.</s> <s xml:id="echoid-s9683" xml:space="preserve"/> </p> <div xml:id="echoid-div619" type="float" level="2" n="1"> <note position="right" xlink:label="note-316-01" xlink:href="note-316-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s9684" xml:space="preserve">La conſtruction de l'Equinoxial ſupérieur & </s> <s xml:id="echoid-s9685" xml:space="preserve">de l'inferieur eſt la <lb/>même. </s> <s xml:id="echoid-s9686" xml:space="preserve">Dans les Pàïs où la Sphere eſt parallele, c'eſt-à dire, qui ont <lb/>le Pole au Zénith, il n'en faut qu'un qui ſert d'horiſontal. </s> <s xml:id="echoid-s9687" xml:space="preserve">Dans les <lb/>Païs où la Sphere eſt droite, c'eſt-à-dire, où les deux Poles ſont ſur <lb/>l'horiſon, ces Cadrans ſont verticaux ſans décliner, & </s> <s xml:id="echoid-s9688" xml:space="preserve">ſe placent con-<lb/>tre les murailles, l'un tourné vers le Pole arctique, & </s> <s xml:id="echoid-s9689" xml:space="preserve">l'autre vers <lb/>l'antarctique. </s> <s xml:id="echoid-s9690" xml:space="preserve">Chacun eſt éclairé ſix mois de l'année Mais dans la <lb/>Sphere oblique, comme celle que nous habitons, ces Cadrans ſont <lb/>inclinez à l'horiſon, & </s> <s xml:id="echoid-s9691" xml:space="preserve">font un angle égal à celui du complément <lb/>de latitude, c'eſt-à-dire, à Paris de 41 deg.</s> <s xml:id="echoid-s9692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9693" xml:space="preserve">L'axe du Cadran équinoxial eſt une verge qui paſſant par le cen-<lb/>tre eſt perpendiculaire au Plan du Cadran, & </s> <s xml:id="echoid-s9694" xml:space="preserve">parallele à l'axe du <lb/>Monde, on le fait grand à volonté lorſqu'il ne ſert qu'à marquer <lb/>les heures, mais on lui donne une longueur déterminée lorſque <lb/>l'on veut lui faire marquer les Signes du Zodiaque ou la longueur <lb/>des jours, dont nous parlerons ci-après.</s> <s xml:id="echoid-s9695" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div621" type="section" level="1" n="315"> <head xml:id="echoid-head448" style="it" xml:space="preserve">Conſtruction des Cadrans Orientaux & Occidentaux.</head> <p> <s xml:id="echoid-s9696" xml:space="preserve">C Es ſortes de Cadrans ſont paralleles au plan du Méridien; </s> <s xml:id="echoid-s9697" xml:space="preserve">l'un <lb/>eſt tourné directement à l'Orient, & </s> <s xml:id="echoid-s9698" xml:space="preserve">l'autre à l'Occident.</s> <s xml:id="echoid-s9699" xml:space="preserve"/> </p> <note position="left" xml:space="preserve">XXIII. <lb/>Planche. <lb/>Fig. I.</note> <pb o="301" file="317" n="317" rhead="DES CADRANS AU SOLEIL. Liv. VIII.Ch.. I."/> <p> <s xml:id="echoid-s9700" xml:space="preserve">Cette figure repreſente un Cadran Méridional Occidetal. </s> <s xml:id="echoid-s9701" xml:space="preserve">Les li-<lb/>gnes horaires ſont paralleles entr'elles & </s> <s xml:id="echoid-s9702" xml:space="preserve">à l'axe du Monde, comme <lb/>au Cadran Polaire, & </s> <s xml:id="echoid-s9703" xml:space="preserve">leur conſtruction eſt à peu près la même.</s> <s xml:id="echoid-s9704" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9705" xml:space="preserve">Pour tracer ce Cadran tirez premierement la ligne droite AB, re-<lb/>preſentant l'horiſontal; </s> <s xml:id="echoid-s9706" xml:space="preserve">du point A pris à diſcretion dans cette ligne, <lb/>tracez l'arc BC égal au complément de la latitude, qui eſt l'éleva-<lb/>tion de l'Equateur ſur l'horiſon, c'eſt-à-dire, à Paris de 41 deg. </s> <s xml:id="echoid-s9707" xml:space="preserve">du <lb/>point C où ſe termine cet arc, tirez la ligne CD prolongée autant <lb/>qu'il eſt beſoin, laquelle reprenſente la commune ſection de l'équi-<lb/>noxiale avec le Plan du Cadran; </s> <s xml:id="echoid-s9708" xml:space="preserve">du point D tirez ED perpendicu-<lb/>laire à l'équinoxiale, cette ligne ED ſera la ſouſtylaire, c'eſt-à-di-<lb/>re, la place du Style & </s> <s xml:id="echoid-s9709" xml:space="preserve">en même tems la ligne de 6 h. </s> <s xml:id="echoid-s9710" xml:space="preserve">Pour avoir <lb/>les autres heures prenez ſur la ſouſtylaire un point E à volonté, du <lb/>quel comme centre vous décrirez un arc de 60 d. </s> <s xml:id="echoid-s9711" xml:space="preserve">que vous diviſe-<lb/>rez en 4 arcs égaux de 15 d. </s> <s xml:id="echoid-s9712" xml:space="preserve">chacun, à commencer de la ſouſtylaire. <lb/></s> <s xml:id="echoid-s9713" xml:space="preserve">Portez enſuite ſur cette circonference prolongée de part & </s> <s xml:id="echoid-s9714" xml:space="preserve">d'autre <lb/>autant d'arcs de 15 d. </s> <s xml:id="echoid-s9715" xml:space="preserve">qu'il convient, pour diviſer en heures la ligne <lb/>équinoxiale, par des lignes ponctuées qui partent toutes du point E. </s> <s xml:id="echoid-s9716" xml:space="preserve"><lb/>Enfin par les diviſions de cette ligne tirez les lignes horaires conve-<lb/>nables, paralleles à la ligne de 6 h. </s> <s xml:id="echoid-s9717" xml:space="preserve">& </s> <s xml:id="echoid-s9718" xml:space="preserve">perpendiculaires à l'équino-<lb/>xiale. </s> <s xml:id="echoid-s9719" xml:space="preserve">Ce Cadran marque les heures d'après midijuſqu'au coucher <lb/>du Soleil; </s> <s xml:id="echoid-s9720" xml:space="preserve">& </s> <s xml:id="echoid-s9721" xml:space="preserve">comme à Paris il ſe couche à 8 h. </s> <s xml:id="echoid-s9722" xml:space="preserve">en Eté, on les mar-<lb/>que depuis I juſqu'à 8, comme on les voit en la fig. </s> <s xml:id="echoid-s9723" xml:space="preserve">1 planche 23.</s> <s xml:id="echoid-s9724" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9725" xml:space="preserve">La conſtruction de l'Oriental eſt la même, & </s> <s xml:id="echoid-s9726" xml:space="preserve">on y marque les heu-<lb/>res du matin depuis le lever du Soleil en Eté c'eſt-à-dire, depuis 4 <lb/>h. </s> <s xml:id="echoid-s9727" xml:space="preserve">du matin juſqu'à II. </s> <s xml:id="echoid-s9728" xml:space="preserve">Midi ne ſe peut point marquer ſur le Plan <lb/>de ces Cadrans, parce que le Soleil étant dans le Méridien, ſes raions <lb/>ſont paralleles au Plan deces Cadrans.</s> <s xml:id="echoid-s9729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9730" xml:space="preserve">Après avoir tracé un Cadran Occidental ſur un papier, ſi on le <lb/>rend tranſparent avec un peu d'huile, on verra de l'autre côté le Ca-<lb/>dran Oriental tout tracé il n'y aura que les heures à changer, en <lb/>mettant II heures à la place d'une heure; </s> <s xml:id="echoid-s9731" xml:space="preserve">10 heures à la place de 2, <lb/>& </s> <s xml:id="echoid-s9732" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s9733" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9734" xml:space="preserve">Le Style de ces Cadrans eſt une verge de fer ou de cuivre, égale à <lb/>FD, qui eſt auſſi la diſtance depuis 6 h. </s> <s xml:id="echoid-s9735" xml:space="preserve">juſqu'à 3. </s> <s xml:id="echoid-s9736" xml:space="preserve">Elle ſe place per-<lb/>pendiculairement au point D, & </s> <s xml:id="echoid-s9737" xml:space="preserve">marque les heures par un point <lb/>d'ombre. </s> <s xml:id="echoid-s9738" xml:space="preserve">On peut auſſi, ſi l'on veut, mettre un Style dont la figure <lb/>ſoit un parallelograme, comme nous avons dit & </s> <s xml:id="echoid-s9739" xml:space="preserve">repreſenté en <lb/>parlant du Cadran Polaire.</s> <s xml:id="echoid-s9740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9741" xml:space="preserve">Ces Cadrans ſe placent ſur des murs à plomb, ou ſur des Plans <lb/> <pb o="302" file="318" n="318" rhead="CONSTRUCTION ET USAGES"/> perpendiculaires à l'horiſon, paralleles au Méridien, & </s> <s xml:id="echoid-s9742" xml:space="preserve">tournez di-<lb/>rectement l'un à l'Orient, l'autre à l'Occident; </s> <s xml:id="echoid-s9743" xml:space="preserve">de telle ſorte que <lb/>la ligne horiſontale ſoit parfaitement de niveau.</s> <s xml:id="echoid-s9744" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div622" type="section" level="1" n="316"> <head xml:id="echoid-head449" style="it" xml:space="preserve">Conſtruction des Cadrans verticaux déclinans.</head> <p> <s xml:id="echoid-s9745" xml:space="preserve">ON appelle Cadran vertical celui qui ſe fait ſur un Plan verti-<lb/>cal, c'eſt-à-dire, perpendiculaire à l'horiſon, comme un mur <lb/>bien à plomb.</s> <s xml:id="echoid-s9746" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9747" xml:space="preserve">Entreles 9 Cadrans reguliers dont nous venons de parler, il y en <lb/>a 4 verticaux qui ne déclinent point, parce qu'ils ſont tournez di-<lb/>rectement vers l'une des 4 parties cardinales du Monde; </s> <s xml:id="echoid-s9748" xml:space="preserve">l'un au Mi-<lb/>di, ſon oppoſé au Septentrion; </s> <s xml:id="echoid-s9749" xml:space="preserve">l'autre à l'Orient, & </s> <s xml:id="echoid-s9750" xml:space="preserve">ſon oppoſé à <lb/>l'Occident.</s> <s xml:id="echoid-s9751" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9752" xml:space="preserve">Ilnous reſte à parler ici des Cadrans irreguliers, dont les uns <lb/>ſont verticaux déclinans, les autres inclinez ſans déclinaiſon, & </s> <s xml:id="echoid-s9753" xml:space="preserve"><lb/>les autres enfin déclinans & </s> <s xml:id="echoid-s9754" xml:space="preserve">inclinez.</s> <s xml:id="echoid-s9755" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9756" xml:space="preserve">Les verticaux déclinans ſont de 4 ſortes, car les uns déclinent du <lb/>Midi vers l'Orient; </s> <s xml:id="echoid-s9757" xml:space="preserve">leurs oppoſez déclinent du Septentrion vers l'Oc-<lb/>cident; </s> <s xml:id="echoid-s9758" xml:space="preserve">les autres déclinent du Midi vers l'Occident, & </s> <s xml:id="echoid-s9759" xml:space="preserve">leurs op-<lb/>poſez du Septention vers l'Orient.</s> <s xml:id="echoid-s9760" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9761" xml:space="preserve">Entre les Cadrans irreguliers, les verticaux déclinans ſont les plus <lb/>en uſage, parce qu'ils ſe font ſur des murs, qui pour l'ordinaire ſont <lb/>bâtis à plomb ou ſur des corps dont les Plans ſont perpendiculaires; <lb/></s> <s xml:id="echoid-s9762" xml:space="preserve">mais avant que d'entreprendre à faire ces ſortes de Cadrans, il faut <lb/>commencer par connoître exactement la déclinaiſon du mur ou des <lb/>Plans, & </s> <s xml:id="echoid-s9763" xml:space="preserve">de quel côté, ce que l'on pourra faire par quelques-unes <lb/>des méthodes que nous dirons ci-après.</s> <s xml:id="echoid-s9764" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9765" xml:space="preserve">Suppoſé que l'on connoiſſe qu'un Plan, tel que celui marqué I, de <lb/>la figure 1. </s> <s xml:id="echoid-s9766" xml:space="preserve">de la planche 22, ou un mur vertical décline du Midi à <lb/>l'Occident de 45 d. </s> <s xml:id="echoid-s9767" xml:space="preserve">à Paris ou aux environs, où le Pole eſt élevéde <lb/>49 deg. </s> <s xml:id="echoid-s9768" xml:space="preserve">ſur l'horiſon. </s> <s xml:id="echoid-s9769" xml:space="preserve">Il s'agit de faire le modele d'un Cadran pour <lb/>appliquer contre ce Plan ou contre ce mur.</s> <s xml:id="echoid-s9770" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9771" xml:space="preserve">Tirez premierement les lignes AB, CD ſe coupantes à angles droits <lb/>au point E; </s> <s xml:id="echoid-s9772" xml:space="preserve">la premiere ſera la ligne de 12 h. </s> <s xml:id="echoid-s9773" xml:space="preserve">& </s> <s xml:id="echoid-s9774" xml:space="preserve">la ſeconde ſera l'ho-<lb/>riſontale. </s> <s xml:id="echoid-s9775" xml:space="preserve">Du point E, comme centre tracez l'arc FN de 45 deg. </s> <s xml:id="echoid-s9776" xml:space="preserve">à <lb/> <anchor type="note" xlink:label="note-318-01a" xlink:href="note-318-01"/> cauſe de pareille déclinaiſon que nous avons ſuppoſée, & </s> <s xml:id="echoid-s9777" xml:space="preserve">comme el-<lb/>le eſt du Midi à l'Occident, il faut que cet arc ſoit tracé du côté <lb/>droit de la ligne du Midi, car il faudroit le faire à gauche ſi la décli-<lb/>naiſon étoit du côté d'Orient. </s> <s xml:id="echoid-s9778" xml:space="preserve">Du point F élevez la perpendiculaire <lb/>FH, juſqu'au rencontre de l'horiſontale, pour y avoir un point de <lb/> <pb o="303" file="319" n="319" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> la ſouſty laire; </s> <s xml:id="echoid-s9779" xml:space="preserve">c'eſt-à-dire, le pied du Style. </s> <s xml:id="echoid-s9780" xml:space="preserve">Prenez avec un Com-<lb/>pas la diſtance EF, & </s> <s xml:id="echoid-s9781" xml:space="preserve">la portez ſur l'horiſontale de E en O. </s> <s xml:id="echoid-s9782" xml:space="preserve">Du point <lb/>O, comme centre, tracez l'arc EG égal â la hauteurdu Pole, com-<lb/>me ici de 49 d. </s> <s xml:id="echoid-s9783" xml:space="preserve">& </s> <s xml:id="echoid-s9784" xml:space="preserve">tirez la ligne ponctuée O A juſqu'au rencontre <lb/>de la ligne de 12 h. </s> <s xml:id="echoid-s9785" xml:space="preserve">pour y ayoir le centre du Cadran A, par lequel <lb/>vous tirerez la ſouſtylaire AH, longue à diſcretion, laquelle eſt <lb/>une des principales lignes ſervant à la conſtruction de ces Cadrans <lb/>& </s> <s xml:id="echoid-s9786" xml:space="preserve">d'où dépend preſque toute leur juſteſſe.</s> <s xml:id="echoid-s9787" xml:space="preserve"/> </p> <div xml:id="echoid-div622" type="float" level="2" n="1"> <note position="left" xlink:label="note-318-01" xlink:href="note-318-01a" xml:space="preserve">XXIII. <lb/>Planche. <lb/>Fig. 2.</note> </div> <p> <s xml:id="echoid-s9788" xml:space="preserve">Du point Hélevez perpendiculairement ſur la ſouſty laire, la droi-<lb/>te HI, pour ſtyle, égale à HF; </s> <s xml:id="echoid-s9789" xml:space="preserve">enſuite vous formerez le ſtyle triangu-<lb/>laire AHI, en tirant la ligne AI, qui eſt l'axe du Cadran. </s> <s xml:id="echoid-s9790" xml:space="preserve">Du point <lb/>I, tirez IK perpendiculaire à l'axe juſqu'à la rencontre de la ſouſ-<lb/>tylaire, ſur laquelle vous marquerez KL égale à KI. </s> <s xml:id="echoid-s9791" xml:space="preserve">Du point K ti-<lb/>rez la ligne équinoxiale MN, coupant la ſouſty laire à angles droits, <lb/>& </s> <s xml:id="echoid-s9792" xml:space="preserve">l'horiſontale au point de 6 h. </s> <s xml:id="echoid-s9793" xml:space="preserve">Ainſi ayant déja 12 h. </s> <s xml:id="echoid-s9794" xml:space="preserve">& </s> <s xml:id="echoid-s9795" xml:space="preserve">6 h. </s> <s xml:id="echoid-s9796" xml:space="preserve">ti-<lb/>rez les deux lignez ponctuées NL, L 6, leſquelles feront un angle <lb/>droit au point L, ſi les operations antérieures ont été faites exacte-<lb/>ment. </s> <s xml:id="echoid-s9797" xml:space="preserve">Dudit point L, comme centre, décrivez un quart de cercle <lb/>entre leſdites lignes ponctuées; </s> <s xml:id="echoid-s9798" xml:space="preserve">diviſez ſa circonference en 6 arcs <lb/>égaux de 15 d. </s> <s xml:id="echoid-s9799" xml:space="preserve">chacun, & </s> <s xml:id="echoid-s9800" xml:space="preserve">tirez autant de lignes occultes juſqu'au <lb/>rencontre de l'équinoxiale; </s> <s xml:id="echoid-s9801" xml:space="preserve">pour avoir les heures de devant midi & </s> <s xml:id="echoid-s9802" xml:space="preserve"><lb/>celles d'après 6 h. </s> <s xml:id="echoid-s9803" xml:space="preserve">prolongez la circonference du quart de cercle de <lb/>côté & </s> <s xml:id="echoid-s9804" xml:space="preserve">d'autre, & </s> <s xml:id="echoid-s9805" xml:space="preserve">y tranſportez autant d'arcs de 15 d. </s> <s xml:id="echoid-s9806" xml:space="preserve">qu'il en faut <lb/>pour tirer des lignes occultes du point L juſqu'au rencontre de la-<lb/>dite équinoxiale; </s> <s xml:id="echoid-s9807" xml:space="preserve">enfin par ces points de rencontre, tirez du centre A <lb/>les lignes horaires, comme on les voit en la fig. </s> <s xml:id="echoid-s9808" xml:space="preserve">2. </s> <s xml:id="echoid-s9809" xml:space="preserve">On ne doittout <lb/>au plus marquer que 12 h. </s> <s xml:id="echoid-s9810" xml:space="preserve">ſur ces ſortes de Cadrans, car tout Plan <lb/>vertical ne peut pas être éclairé du Soleil plus long-tems.</s> <s xml:id="echoid-s9811" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9812" xml:space="preserve">On peut encore avoir les points des lignes horaires ſur l'horiſon-<lb/>tale DC, en appliquant au point F le centre d'un Cadran horiſon-<lb/>tal, de telle ſorte que ſa ligne Méridiene convienne avec la ligne FE, <lb/>& </s> <s xml:id="echoid-s9813" xml:space="preserve">ſa ligne de 6h. </s> <s xml:id="echoid-s9814" xml:space="preserve">avec la ligne F 6. </s> <s xml:id="echoid-s9815" xml:space="preserve">Les points des autres heures ſe <lb/>marqueront par leur rencontre ſur ladite ligne CD.</s> <s xml:id="echoid-s9816" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9817" xml:space="preserve">Six intervales d'heures de ſuite étant donnez ſur la ſurface d'un <lb/>Cadran, tel qu'il ſoit, on peut trouver les autres heures par la mé-<lb/>thode ſuivante.</s> <s xml:id="echoid-s9818" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9819" xml:space="preserve">Je ſuppoſe en cet exemple les heures tracées depuis 6 juſqu'à 12. <lb/></s> <s xml:id="echoid-s9820" xml:space="preserve">Si vous voulez avoir 9, 10 & </s> <s xml:id="echoid-s9821" xml:space="preserve">11 h. </s> <s xml:id="echoid-s9822" xml:space="preserve">du matin, quel'on peut marquer <lb/>ſur ce Cadran, du point V pris à diſcretion ſur la ligne de 12 h. </s> <s xml:id="echoid-s9823" xml:space="preserve">tra-<lb/>cez une parallele à la ligne de 6 h. </s> <s xml:id="echoid-s9824" xml:space="preserve">comme VS, qui couperales lignes <lb/> <pb o="304" file="320" n="320" rhead="CONSTRUCTION ET USAGES"/> 1, 2 & </s> <s xml:id="echoid-s9825" xml:space="preserve">3 h. </s> <s xml:id="echoid-s9826" xml:space="preserve">après midi. </s> <s xml:id="echoid-s9827" xml:space="preserve">L'intervale depuis V juſqu'à une heure, pris <lb/>ſur cette parallele, & </s> <s xml:id="echoid-s9828" xml:space="preserve">porté de l'autre côté donnera ſur ladite paral-<lb/>lele un point de 11 h. </s> <s xml:id="echoid-s9829" xml:space="preserve">de même l'intervale V 2 y donnera un point de <lb/>10 h. </s> <s xml:id="echoid-s9830" xml:space="preserve">& </s> <s xml:id="echoid-s9831" xml:space="preserve">l'intervale V 3 donnera un point de 9 h. </s> <s xml:id="echoid-s9832" xml:space="preserve">Du centre du Ca-<lb/>dran A vous tirerez les lignes horaires paſſantes par les points mar-<lb/>quez ſur ladite parallele.</s> <s xml:id="echoid-s9833" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9834" xml:space="preserve">On peut de la même façon avoir des points de 7 & </s> <s xml:id="echoid-s9835" xml:space="preserve">8 h. </s> <s xml:id="echoid-s9836" xml:space="preserve">du ſoir, en <lb/>tirant une parallele à la ligne de 12 h. </s> <s xml:id="echoid-s9837" xml:space="preserve">qui coupe en un point celle de <lb/>6, & </s> <s xml:id="echoid-s9838" xml:space="preserve">qui rencontre celles de 4 & </s> <s xml:id="echoid-s9839" xml:space="preserve">de 5 prolongées: </s> <s xml:id="echoid-s9840" xml:space="preserve">car l'intervale de <lb/>6 à 5 ſur cette parallele, porté de l'autre côté, y donnera un point de <lb/>7 h. </s> <s xml:id="echoid-s9841" xml:space="preserve">& </s> <s xml:id="echoid-s9842" xml:space="preserve">l'intervale de 6 a 4 y donnera un point de 8 h. </s> <s xml:id="echoid-s9843" xml:space="preserve">par leſquels <lb/>points & </s> <s xml:id="echoid-s9844" xml:space="preserve">par le centre A, on tirera ces lignes horaires, & </s> <s xml:id="echoid-s9845" xml:space="preserve">le Cadran <lb/>ſera achevé. </s> <s xml:id="echoid-s9846" xml:space="preserve">Cette maniere de trouver les heures un peu éloignées <lb/>de la ſouſtylaire eſt fort commode, en ce qu'elle évite les grandes <lb/>fections qu'il faut faire ſur la ligne équinoxiale.</s> <s xml:id="echoid-s9847" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9848" xml:space="preserve">La conſtruction du Cadran vertical, déclinant du Midi à l'Orient, <lb/>eſt ſemblable à celle que nous venons de décrire, excepté que ce qui <lb/>a été fait à droite ſe doit faire à gauche, & </s> <s xml:id="echoid-s9849" xml:space="preserve">que les heures du matin <lb/>ſe placent au lieu de celles d'après midi, qui font leur complément <lb/>à 12. </s> <s xml:id="echoid-s9850" xml:space="preserve">Tellement que ſi on avoit tracé un déclinant vers Occident <lb/>ſur un papier tranſparent, on verroit de l'autre côté un déclinant <lb/>vers Orient tout tracé, il n'y auroit qu'à mettre ſur le revers du pa-<lb/>pier 3 h. </s> <s xml:id="echoid-s9851" xml:space="preserve">après midi à la place de 9 du matin 2 h. </s> <s xml:id="echoid-s9852" xml:space="preserve">à la place de 10; <lb/></s> <s xml:id="echoid-s9853" xml:space="preserve">une h. </s> <s xml:id="echoid-s9854" xml:space="preserve">à la place de 11, & </s> <s xml:id="echoid-s9855" xml:space="preserve">ainſi de ſuite; </s> <s xml:id="echoid-s9856" xml:space="preserve">par ce moyen la ſouſtylaire <lb/>qui ſe trouve dans la fig. </s> <s xml:id="echoid-s9857" xml:space="preserve">2, entre 3 & </s> <s xml:id="echoid-s9858" xml:space="preserve">4 h. </s> <s xml:id="echoid-s9859" xml:space="preserve">après midi, ſeroit dans <lb/>l'autre entre 8 & </s> <s xml:id="echoid-s9860" xml:space="preserve">9 h. </s> <s xml:id="echoid-s9861" xml:space="preserve">du matin. </s> <s xml:id="echoid-s9862" xml:space="preserve">Si la déclinaiſon étoit moindre que <lb/>de 45 d. </s> <s xml:id="echoid-s9863" xml:space="preserve">la ſouſtylaire ſeroit plus proche de midi; </s> <s xml:id="echoid-s9864" xml:space="preserve">ſi au contraire la <lb/>déclinaiſon étoit plus grande, la ſouſtylaire en ſeroit plns éloignée, <lb/>& </s> <s xml:id="echoid-s9865" xml:space="preserve">s'approcheroit de la ligne de 6 h. </s> <s xml:id="echoid-s9866" xml:space="preserve">Mais quand cela arrive, les <lb/>heures ſont ſi ſerrées aux environs de la ſouſtylaire, qu'on eſt obligé <lb/>de faire le Modele du Cadran ſur un plan bien grand, afin d'allon-<lb/>ger beaucoup les lignes horaires & </s> <s xml:id="echoid-s9867" xml:space="preserve">de retrancher la partie du Ca-<lb/>dran qui eſt vers le centre.</s> <s xml:id="echoid-s9868" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9869" xml:space="preserve">Les déclinans du Septentrion à l'Orient ou à l'Occident, ſe dé-<lb/>crivent de la même façon; </s> <s xml:id="echoid-s9870" xml:space="preserve">mais ils ont le centre en bas au-deſſous <lb/>de la ligne horiſontale, & </s> <s xml:id="echoid-s9871" xml:space="preserve">ne ſont proprement que les mêmes Ca-<lb/>dransrenverſez, comme on voit en la figure 3<emph style="sub">me</emph> qui repreſente un <lb/>déclinant du Septentrion à l'Occident de 45 d. </s> <s xml:id="echoid-s9872" xml:space="preserve">comme pour le Plan <lb/>marqué L, fig. </s> <s xml:id="echoid-s9873" xml:space="preserve">1. </s> <s xml:id="echoid-s9874" xml:space="preserve">de la planche 22. </s> <s xml:id="echoid-s9875" xml:space="preserve">Sa ſouſtylaire doit être entre 8 <lb/>& </s> <s xml:id="echoid-s9876" xml:space="preserve">9 h. </s> <s xml:id="echoid-s9877" xml:space="preserve">du ſoir, de ſorte qu'un ſeul déclinant peut ſervir pour en <lb/> <pb o="305" file="321" n="321" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> tracer quatre, s'ils ont la déclinaiſon égale, quoique de differens <lb/>côtez, deux auront le centre en haut & </s> <s xml:id="echoid-s9878" xml:space="preserve">deux l'auront en bas.</s> <s xml:id="echoid-s9879" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div624" type="section" level="1" n="317"> <head xml:id="echoid-head450" style="it" xml:space="preserve">Par deux points d'ombre obſervez ſur un Plan y tracer <lb/>la ſouſtyl.</head> <p> <s xml:id="echoid-s9880" xml:space="preserve">SErvez-vous de la figure 2, où ſuppoſant avoir placé obli-<lb/>quement une verge de fer pointuë par un bout afin que l'on <lb/>puiſſe avoir ſon pied H ſur le Plan, c'eſt-à-dire, un point qui <lb/>réponde perpendiculairement à l'extremité du Style I qui eſt en <lb/>l'air, qui ſe nomme point d'incidence, & </s> <s xml:id="echoid-s9881" xml:space="preserve">qui ſe prend par le moyen <lb/>d'une Equerre.</s> <s xml:id="echoid-s9882" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9883" xml:space="preserve">Comme cette figure repreſente un vertical déclinant du Midi à <lb/> <anchor type="note" xlink:label="note-321-01a" xlink:href="note-321-01"/> l'Occident, c'eſt pourquoi ſa ſouſtylaire ſe doit trouver entre les <lb/>heures d'après midi, à gauche de la Méridiene. </s> <s xml:id="echoid-s9884" xml:space="preserve">Suppoſé que le pre-<lb/>mier point d'ombre obſervé ſoit P, du pied du Style H, comme cen-<lb/>tre, & </s> <s xml:id="echoid-s9885" xml:space="preserve">pour raïon la diſtance HP, décrivez un arc de cercle PR. <lb/></s> <s xml:id="echoid-s9886" xml:space="preserve">Quelques heures après du même jour, lorſque l'ombre de l'extremi-<lb/>té du ſtyle rencontrera une ſeconde fois ledit arc, marquez-y le ſe-<lb/>cond point Q. </s> <s xml:id="echoid-s9887" xml:space="preserve">Diviſez en deux également l'arc P Q au point R, & </s> <s xml:id="echoid-s9888" xml:space="preserve"><lb/>tirez par le pied du ſtyle la droite RH, qui ſera la ſouſtylaire; </s> <s xml:id="echoid-s9889" xml:space="preserve">laquel-<lb/>le étant tracée exactement, & </s> <s xml:id="echoid-s9890" xml:space="preserve">connoiſſant d'ailleurs la hauteur du <lb/>Pole ſur l'horiſon du Pais où l'on veut faire ce Cadran, il ſera facile <lb/>de l'achever; </s> <s xml:id="echoid-s9891" xml:space="preserve">car premierement la Méridiene ou ligne de 12 h. </s> <s xml:id="echoid-s9892" xml:space="preserve">eſt <lb/>toûjours perpendiculaire à l'horiſon, aux Plans verticaux, & </s> <s xml:id="echoid-s9893" xml:space="preserve">lc point <lb/>de rencontre de cette Méridiene & </s> <s xml:id="echoid-s9894" xml:space="preserve">de la Souſtylaire prolongée eſt le <lb/>centre du Cadran, comme le point A. </s> <s xml:id="echoid-s9895" xml:space="preserve">La ligne horiſontale eſt une <lb/>ligne de niveau, paſſant par le pied du Style comme DHC. </s> <s xml:id="echoid-s9896" xml:space="preserve">Enſuite <lb/>pour avoir la ligne équinoxiale, formez ſur la ſouſty laire le Style <lb/>triangulaire AHI, dont l'hypotenuſe AI eſt l'axe, & </s> <s xml:id="echoid-s9897" xml:space="preserve">HI le Style <lb/>droit. </s> <s xml:id="echoid-s9898" xml:space="preserve">Du point I tirez IK, perpendiculaire à l'axe, rencontrant la <lb/>ſouſtylaire au point K, par lequel vous tirerez à angles droits ſur la-<lb/>dite ſouſty laire la droite MKN, qui ſera l'équinoxiale, & </s> <s xml:id="echoid-s9899" xml:space="preserve">le point <lb/>où elle coupe l'horiſontale ſera toûjours le point de 6 h. </s> <s xml:id="echoid-s9900" xml:space="preserve">la diſtance <lb/>KI portée ſur la ſouſtylaire, donnera le point L, qui ſera le centre <lb/>diviſeur de l'équinoxiale; </s> <s xml:id="echoid-s9901" xml:space="preserve">le reſte du Cadran s'achevera comme nous <lb/>avons expliqué ci-devant; </s> <s xml:id="echoid-s9902" xml:space="preserve">& </s> <s xml:id="echoid-s9903" xml:space="preserve">même le modele s'en pourra faire dans <lb/>le cabinet, aprèsavoir tranſporté ſur un papier la poſition & </s> <s xml:id="echoid-s9904" xml:space="preserve">la ren-<lb/>contre des principales lignes, & </s> <s xml:id="echoid-s9905" xml:space="preserve">bien exactement l'angle que fait la <lb/>ſouſtylaire avec l'horiſontale, ou avec la Méridiene, car l'un eſt le <lb/>complément de l'autre.</s> <s xml:id="echoid-s9906" xml:space="preserve"/> </p> <div xml:id="echoid-div624" type="float" level="2" n="1"> <note position="right" xlink:label="note-321-01" xlink:href="note-321-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s9907" xml:space="preserve">Pour verifier la poſition de la ligne équinoxiale, faites au centre <lb/> <pb o="306" file="322" n="322" rhead="CONSTRUCTION ET USAGES"/> du Cadran, ſur la Méridiene AB l'angle BAO égal au complément <lb/>de l'élevation du Pole; </s> <s xml:id="echoid-s9908" xml:space="preserve">c'eſt-à-dire, à Paris de 41 d. </s> <s xml:id="echoid-s9909" xml:space="preserve">tirez la ligne A <lb/>O juſqu'au rencontre de l'horiſontale; </s> <s xml:id="echoid-s9910" xml:space="preserve">faites l'angle droit AON, <lb/>afin d'avoir ſur la Méridiene ou ligne de 12 h. </s> <s xml:id="echoid-s9911" xml:space="preserve">le point N par le-<lb/>quel doit paſſer la ligne équinoxiale; </s> <s xml:id="echoid-s9912" xml:space="preserve">ayant ainſi pluſieurs méthodes <lb/>pour trouver les principaux points, l'une ſervira à verifier l'autre. <lb/></s> <s xml:id="echoid-s9913" xml:space="preserve">Lorſque le Plan décline du Midi à l'Orient, on trouvera par le <lb/>moyen des points d'ombre & </s> <s xml:id="echoid-s9914" xml:space="preserve">du pied du ſtyle que la ſouſtylaire eſt <lb/>à droite de la Méridiene. </s> <s xml:id="echoid-s9915" xml:space="preserve">Il eſt bon de marquer le premier de ces <lb/>points d'ombre le matin auſſi-tôt que le Plan commence d'être é-<lb/>clairé du Soleil, & </s> <s xml:id="echoid-s9916" xml:space="preserve">prendre garde quand l'ombre de l'extremité du <lb/>ſtyle rencontrera un 2<emph style="sub">e</emph> fois l'arc tracé par le 1<emph style="sub">r</emph> point d'ombre.</s> <s xml:id="echoid-s9917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9918" xml:space="preserve">On peut recommencer quelques jours de ſuite les mêmcs opera-<lb/>tions, afin de voir ſi la poſition de la ſouſtylaire ſe trouvera toû-<lb/>jours la même, ce qui arrivera ſi l'on opere exactement.</s> <s xml:id="echoid-s9919" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9920" xml:space="preserve">Lorſque le Plan décline du Septentrion à l'Orient ou à l'Occi-<lb/>dent, les points d'ombre ſont plus hauts que le pied du Style, ce <lb/>qui fait connoître que le centre doit être en bas.</s> <s xml:id="echoid-s9921" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9922" xml:space="preserve">Le tems le plus propre pour marquer ces points d'ombre eſt aux <lb/>environs des Solſtices, c'eſt-à-dire, 15 jours devant ou après, car <lb/>lorſque le Soleil approche des Equinoxes, ſa déclinaiſon eſt trop <lb/>ſenſible, & </s> <s xml:id="echoid-s9923" xml:space="preserve">l'operation moins exacte.</s> <s xml:id="echoid-s9924" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9925" xml:space="preserve">On pourroit cependant avoir la poſition de la ligne équinoxiale <lb/>lorſque le Soleil eſt dans les points équinoxiaux, & </s> <s xml:id="echoid-s9926" xml:space="preserve">conſtruire un <lb/>Cadran vertical déclinant par la méthode ſuivante.</s> <s xml:id="echoid-s9927" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div626" type="section" level="1" n="318"> <head xml:id="echoid-head451" style="it" xml:space="preserve">Par quelques points d'ombre obſervez ſur un Plan vertical y <lb/>tracer l'Equinoxial.</head> <p> <s xml:id="echoid-s9928" xml:space="preserve">LA plus ſimple & </s> <s xml:id="echoid-s9929" xml:space="preserve">la plus facile méthode de tracer ſur un mur la <lb/>ligne équinoxiale eſt au tems des équinoxes, (quoiqu'on la puiſ-<lb/>ſe avoir en tout tems, mais par des méthodes plus compoſées.) </s> <s xml:id="echoid-s9930" xml:space="preserve">Car <lb/>lorque le Soleil par ſon mouvement journalier décrit l'Equateur, <lb/>tous les points d'ombre de l'extremité d'un ſtyle ſe trouvent dans <lb/>une même ligne droite, qui eſt la commune ſection de l'Equateur, <lb/>du Ciel & </s> <s xml:id="echoid-s9931" xml:space="preserve">du Plan.</s> <s xml:id="echoid-s9932" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9933" xml:space="preserve">Ayant donc marqué ce jour-là pluſieurs points d'ombre ſur le <lb/>mur, aſſez éloignez l'un de l'autre, tirez par tous ces points une li-<lb/>gne droite qui ſera l'équinoxiale, comme dans ladite fig. </s> <s xml:id="echoid-s9934" xml:space="preserve">2, la ligne <lb/>M N: </s> <s xml:id="echoid-s9935" xml:space="preserve">tirez ſur cette ligne une perpendiculaire paſſant par le pied du <lb/>ſtyle, ce ſera la ſouſtylaire AHL; </s> <s xml:id="echoid-s9936" xml:space="preserve">tirez encore parle pied du ſtyle <lb/> <pb o="307" file="323" n="323" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> H, une ligne de niveau qui ſera l'horiſontale, comme DHC; </s> <s xml:id="echoid-s9937" xml:space="preserve">tirez <lb/>HI égale à la hauteur du ſtyle droit & </s> <s xml:id="echoid-s9938" xml:space="preserve">parallele à l'équinoxiale, & </s> <s xml:id="echoid-s9939" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-323-01a" xlink:href="note-323-01"/> après avoir marqué la ligne ponctuée IK, tirezà l'Equerre l'axe I A <lb/>le point A ſera le centre du Cadran, & </s> <s xml:id="echoid-s9940" xml:space="preserve">la ligne à plomb AB ſera la <lb/>Méridiene ou ligne de 12 h. </s> <s xml:id="echoid-s9941" xml:space="preserve">vous avez auſſi un point de 6h. </s> <s xml:id="echoid-s9942" xml:space="preserve">par l'in-<lb/>terſection de l'équinoxiale & </s> <s xml:id="echoid-s9943" xml:space="preserve">de l'horiſontale, & </s> <s xml:id="echoid-s9944" xml:space="preserve">par conſequent de <lb/>quoi achever le Cadran; </s> <s xml:id="echoid-s9945" xml:space="preserve">l'angle HFE ſera la déclinaiſon du Plan.</s> <s xml:id="echoid-s9946" xml:space="preserve"/> </p> <div xml:id="echoid-div626" type="float" level="2" n="1"> <note position="right" xlink:label="note-323-01" xlink:href="note-323-01a" xml:space="preserve">Fig. 2.</note> </div> </div> <div xml:id="echoid-div628" type="section" level="1" n="319"> <head xml:id="echoid-head452" style="it" xml:space="preserve">Par un point d'ombre obſervé à Midi ſur un Plan vertical y <lb/>faire nn Cadran.</head> <p> <s xml:id="echoid-s9947" xml:space="preserve">UN ſtyle étant planté dans un mur, comme HI, même figure, <lb/>dont H ſoit le pied & </s> <s xml:id="echoid-s9948" xml:space="preserve">I la pointe; </s> <s xml:id="echoid-s9949" xml:space="preserve">ſi vous connoiſſez par quelque <lb/>moyen ſur qu'il eſt midi en quelque tems de l'année que ce ſoit, ce <lb/>qu'on pourra connoître par une ligne Méridiene tracée ſur un Plan <lb/>horiſontal, comme nous dirons ci-après; </s> <s xml:id="echoid-s9950" xml:space="preserve">marquez-y un point d'om-<lb/>bre, comme ſeroit, par exemple, le point N; </s> <s xml:id="echoid-s9951" xml:space="preserve">par ce point tirez la per-<lb/>pendiculaire ANB, qui par conſequent ſera la Méridiene du lieu <lb/>ou ligne de 12 h. </s> <s xml:id="echoid-s9952" xml:space="preserve">tirez par le pied du ſtyle une ligne de niveau qui <lb/>ſera l'horiſontale, comme CHD, coupant à angles droits la Méri-<lb/>diene au point E; </s> <s xml:id="echoid-s9953" xml:space="preserve">faites HF égale au ſtyle droit HI, & </s> <s xml:id="echoid-s9954" xml:space="preserve">parallele à la <lb/>Méridiene; </s> <s xml:id="echoid-s9955" xml:space="preserve">prenez avec un Compas l'hypotenuſe EF & </s> <s xml:id="echoid-s9956" xml:space="preserve">la portez <lb/>ſur l'horiſontale de E en O pour y faire l'angle EOA, égal à l'éleva-<lb/>tion du Pole, comme ici, par exemple, de 49 deg. </s> <s xml:id="echoid-s9957" xml:space="preserve">qui vous don-<lb/>nera ſur la Méridiene le point A, centre du Cadran.</s> <s xml:id="echoid-s9958" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9959" xml:space="preserve">Tirez auſſi ſous l'horiſontale l'angle EON égal au complément de <lb/>ladite élevation de Pole, comme ici de 41 d. </s> <s xml:id="echoid-s9960" xml:space="preserve">le point N ſur la Méri-<lb/>diene ſera un point de la ligne équinoxiale. </s> <s xml:id="echoid-s9961" xml:space="preserve">Par le centre du Cadran <lb/>A, & </s> <s xml:id="echoid-s9962" xml:space="preserve">par le ſtyle H tirez la droite AHR, ce ſera la ſouſtylaire, & </s> <s xml:id="echoid-s9963" xml:space="preserve">fai-<lb/>ſant paſſer par le point N une perpendiculaire à cette ligne, vous <lb/>aurez l'équinoxiale. </s> <s xml:id="echoid-s9964" xml:space="preserve">A yant ainſi les principales lignes du Cadran, <lb/>il ſera facile de l'achever par les méthodes expliquées ci-devant.</s> <s xml:id="echoid-s9965" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9966" xml:space="preserve">Cette méthode pour tracer en tous les tems de l'année un Ca-<lb/>dran par un ſeul point d'ombre obſervé à midi, peut ſervir lorſqu'il <lb/>n'eſt pas poſſible d'avoir la ſouſtylaire par deux points d'ombre, ce <lb/>qui arrive ſur les plans qui déclinent conſiderablement vers l'O-<lb/>rient ou vers l'Occident.</s> <s xml:id="echoid-s9967" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9968" xml:space="preserve">Il y a pluſieurs autres moyens de conſtruire les Cadrans verticaux <lb/>ſur des murs bien à plomb, qu'il ſeroit trop long de rapporter en ce <lb/>petit T raité, dans lequel nous n'avons prétendu donner que les me-<lb/>thodes les plus ſimples & </s> <s xml:id="echoid-s9969" xml:space="preserve">les plus faciles à pratiquer, Et pour une <lb/> <pb o="308" file="324" n="324" rhead="CONSTRUCTION ET USAGES"/> plus grande juſteſſe dans leur conſtruction, nous donnerons ci-après <lb/>des regles pour trouver la valeur des angles que font toutes les li-<lb/>gnes horaires au centre des Cadrans, ce qui ſervira à verifier les <lb/>autres méthodes.</s> <s xml:id="echoid-s9970" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div629" type="section" level="1" n="320"> <head xml:id="echoid-head453" style="it" xml:space="preserve">Conſtruction des Cadrans inclinez ſans déclinaiſon.</head> <p> <s xml:id="echoid-s9971" xml:space="preserve">L'Inclinaiſon de ces Cadrans eſt l'angle que font leurs Plans avec <lb/> <anchor type="note" xlink:label="note-324-01a" xlink:href="note-324-01"/> l'horiſon; </s> <s xml:id="echoid-s9972" xml:space="preserve">les uns ſont tournez vers le Ciel & </s> <s xml:id="echoid-s9973" xml:space="preserve">les autres vers la <lb/>Terre. </s> <s xml:id="echoid-s9974" xml:space="preserve">Il y en a de 2 façons, eu égard au Pole, & </s> <s xml:id="echoid-s9975" xml:space="preserve">de 2 autres façons <lb/>eu égard à l'Equateur; </s> <s xml:id="echoid-s9976" xml:space="preserve">chacun a ſon ſupérieur & </s> <s xml:id="echoid-s9977" xml:space="preserve">ſon inférieur.</s> <s xml:id="echoid-s9978" xml:space="preserve"/> </p> <div xml:id="echoid-div629" type="float" level="2" n="1"> <note position="left" xlink:label="note-324-01" xlink:href="note-324-01a" xml:space="preserve">Fig. 4. <lb/>& 5.</note> </div> <p> <s xml:id="echoid-s9979" xml:space="preserve">Si le Plan regarde le Midi & </s> <s xml:id="echoid-s9980" xml:space="preserve">a l'inclinaiſon vers le Nord, elle <lb/>peut être plus petite ou plus grande que l'élevation du Pole, car ſi <lb/>l'inclinaiſon étoit égale, ce ſeroit un polaire ſuperieur ou inferieur <lb/>dont nous avons ci-devant donné la conſtruction.</s> <s xml:id="echoid-s9981" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9982" xml:space="preserve">Si l'inclinaiſon eſt moindre que l'élevation du Pole, comme à Pa-<lb/>ris où cette élevation eſt à peu près de 49d. </s> <s xml:id="echoid-s9983" xml:space="preserve">ſi vous voulez faire un <lb/>Cadran ſur un Plan qui regarde le Midi, & </s> <s xml:id="echoid-s9984" xml:space="preserve">dont l'inclinaiſon ſoit <lb/>vers le Nord de 30d. </s> <s xml:id="echoid-s9985" xml:space="preserve">ôtez 30 de 49, reſte 19 d. </s> <s xml:id="echoid-s9986" xml:space="preserve">qui ſera la hauteur <lb/>de l'axe ſur ce Plan, & </s> <s xml:id="echoid-s9987" xml:space="preserve">faites-y un Cadran horiſontal regulier pour <lb/>19 d. </s> <s xml:id="echoid-s9988" xml:space="preserve">d'élevation de Pole par la methode que nous avons donnée en <lb/>la figure 4<emph style="sub">me</emph> de la planche 22; </s> <s xml:id="echoid-s9989" xml:space="preserve">parce que ce Plan ainſi incliné eſt <lb/>parallele à l'horiſon de ceux qui ont le Pole élevé de pareille hau-<lb/>teur, qui par conſequent ſont leurs Cadrans horiſontaux. </s> <s xml:id="echoid-s9990" xml:space="preserve">Le centre <lb/>de cette ſorte de Cadrans eſt en bas au-deſſous de l'équinoxiale, les <lb/>heures du matin ſont à main gauche, & </s> <s xml:id="echoid-s9991" xml:space="preserve">celles du ſoir à droite de <lb/>ceux qui regardent ce Cadran.</s> <s xml:id="echoid-s9992" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9993" xml:space="preserve">Son oppoſé inferieur vers le Nord ne differe point du ſuperieur <lb/>vers le Sud, ſinon que le centre eſt au-deſſns de la ligne équinoxiale, <lb/>& </s> <s xml:id="echoid-s9994" xml:space="preserve">que les heures du matin ſont a droite, & </s> <s xml:id="echoid-s9995" xml:space="preserve">celles du ſoir à gauche.</s> <s xml:id="echoid-s9996" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s9997" xml:space="preserve">Si l'inclinaiſon eſt plus grande que l'élevation du Pole, comme à <lb/>Paris, ſi elle eſt de 63 d. </s> <s xml:id="echoid-s9998" xml:space="preserve">ôtez-en la hauteur du Pole 49, reſtera 14 d. <lb/></s> <s xml:id="echoid-s9999" xml:space="preserve">& </s> <s xml:id="echoid-s10000" xml:space="preserve">faites un horiſontal pour cctte élevation. </s> <s xml:id="echoid-s10001" xml:space="preserve">Le centre du ſuperieur <lb/>vers le Sud eſt en haut au-deſſus de l'équinoxiale, les heures du ma-<lb/>tin ſont à gauche, & </s> <s xml:id="echoid-s10002" xml:space="preserve">celles du ſoir à droite. </s> <s xml:id="echoid-s10003" xml:space="preserve">Son oppoſé inf. </s> <s xml:id="echoid-s10004" xml:space="preserve">vers le <lb/>Nord a le centre en bas, les heures du matin à droite & </s> <s xml:id="echoid-s10005" xml:space="preserve">celles du ſoir <lb/>à gauche, comme on voit par les figure 4 & </s> <s xml:id="echoid-s10006" xml:space="preserve">5 de la 23<emph style="sub">me</emph> planche.</s> <s xml:id="echoid-s10007" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10008" xml:space="preserve">Sile Plan regarde le Septentrion & </s> <s xml:id="echoid-s10009" xml:space="preserve">a ſon inclinaiſon vers le Sud, <lb/>elle peut être plus petite ou plus grande que celle de l'Equateur; </s> <s xml:id="echoid-s10010" xml:space="preserve">car <lb/>ſi elle étoit égale, on y feroit un Cadran équinoxial ſuperieur ou in-<lb/>ferieur, qui eſt un cercle diviſé en 24 part. </s> <s xml:id="echoid-s10011" xml:space="preserve">égales, comme nous avons <lb/>dit ce-deyant en parlant des Cadrans reguliers.</s> <s xml:id="echoid-s10012" xml:space="preserve"/> </p> <pb o="309" file="325" n="325" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> <p> <s xml:id="echoid-s10013" xml:space="preserve">Si l'inclinaiſon eſt moindre que l'élevation de l'Equateur, com-<lb/>me ſi à Paris le Plan étoit incliné de 30 d. </s> <s xml:id="echoid-s10014" xml:space="preserve">vers le Midi, ajoûtez les <lb/>30 d. </s> <s xml:id="echoid-s10015" xml:space="preserve">d'inclinaiſon à la hauteur du Pole 49, & </s> <s xml:id="echoid-s10016" xml:space="preserve">faites un horiſontal <lb/>pour 79 d. </s> <s xml:id="echoid-s10017" xml:space="preserve">d'élevation; </s> <s xml:id="echoid-s10018" xml:space="preserve">le centre du ſuperieur vers le Septentrion <lb/>ſera en haut, les heures du matin à droite, & </s> <s xml:id="echoid-s10019" xml:space="preserve">celles du ſoir à gauche; <lb/></s> <s xml:id="echoid-s10020" xml:space="preserve">ſon oppoſé inferieur vers le Midi, a le centre en bas; </s> <s xml:id="echoid-s10021" xml:space="preserve">les heures du <lb/>matin à gauche & </s> <s xml:id="echoid-s10022" xml:space="preserve">celles du ſoir à droite.</s> <s xml:id="echoid-s10023" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10024" xml:space="preserve">Enfin ſi l'inclinaiſon eſt plus grande que l'élevation de l'Equa-<lb/>teur, comme ſeroit à Paris de 60 d. </s> <s xml:id="echoid-s10025" xml:space="preserve">ajoûtez le complément de l'in-<lb/>clinaiſon qui eſt 30, à l'élevation de l'Equateur qui eſt 41, la ſom-<lb/>me eſt 71 d. </s> <s xml:id="echoid-s10026" xml:space="preserve">& </s> <s xml:id="echoid-s10027" xml:space="preserve">faites un horiſontal pour cette élevation de Pole. <lb/></s> <s xml:id="echoid-s10028" xml:space="preserve">Le ſuperieur vers le Septentrion a le centre en bas, les heures du <lb/>matin à droite; </s> <s xml:id="echoid-s10029" xml:space="preserve">ſon oppoſé qui eſt inferieur vers le midi a le centre <lb/>en haut, & </s> <s xml:id="echoid-s10030" xml:space="preserve">les heures du matin à gauche.</s> <s xml:id="echoid-s10031" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10032" xml:space="preserve">La Méridiene ou ligne de 12 h. </s> <s xml:id="echoid-s10033" xml:space="preserve">eſt la ſouſtylaire de tous les Ca-<lb/>drans inclinez ſans déclinaiſon; </s> <s xml:id="echoid-s10034" xml:space="preserve">elle paſſe par leur centre & </s> <s xml:id="echoid-s10035" xml:space="preserve">fait an-<lb/>gles droits avecla ligne de 6 h. </s> <s xml:id="echoid-s10036" xml:space="preserve">On peut la tracer ſur les Plans in-<lb/>clinez parle moyen d'un fil ſuſpendu avec ſon plomb, à l'aide de la <lb/>lumiere ou du raïon viſuel; </s> <s xml:id="echoid-s10037" xml:space="preserve">car l'ombre ou le raïon paſſant par le <lb/>centre, marquera ſa trace tout le long du Plan.</s> <s xml:id="echoid-s10038" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10039" xml:space="preserve">Pour repreſenter toutes ces differentes ſortes de Cadrans, il au-<lb/>roit fallu 8 figures; </s> <s xml:id="echoid-s10040" xml:space="preserve">4 pour les ſuperieurs, & </s> <s xml:id="echoid-s10041" xml:space="preserve">4 pour les inſerieurs; <lb/></s> <s xml:id="echoid-s10042" xml:space="preserve">mais comme ils ne ſont pas difficiles à concevoir & </s> <s xml:id="echoid-s10043" xml:space="preserve">à tracer, nous <lb/>n'en avons marqué que deux, par rapport au Dodecaëdre ſur le-<lb/>quel on les place.</s> <s xml:id="echoid-s10044" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div631" type="section" level="1" n="321"> <head xml:id="echoid-head454" style="it" xml:space="preserve">Conſtruction des Cadrans déclinans & inclinez.</head> <p> <s xml:id="echoid-s10045" xml:space="preserve">LA déclinaiſon d'un Cadran eſt l'angle que fait ſon Plan avec le <lb/>premier vertical, & </s> <s xml:id="echoid-s10046" xml:space="preserve">l'inclinaiſon eſt l'angle qu'il fait avec l'ho-<lb/>riſon. </s> <s xml:id="echoid-s10047" xml:space="preserve">Nous enſeignerons ci-après la maniere de trouver l'une & </s> <s xml:id="echoid-s10048" xml:space="preserve"><lb/>l'autre.</s> <s xml:id="echoid-s10049" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10050" xml:space="preserve">Je ſuppoſe ici, pour exemple, qu'on veüille faire un Cadran dé-<lb/>clinant de 36 d. </s> <s xml:id="echoid-s10051" xml:space="preserve">du Midi à l'Orient, incliné vers la Terre de 63d. <lb/></s> <s xml:id="echoid-s10052" xml:space="preserve">26 min. </s> <s xml:id="echoid-s10053" xml:space="preserve">comme eſt celui marqué C dans la figure 2<emph style="sub">me</emph> qui repre-<lb/>ſente un Dodecaëdre en la planche 22<emph style="sub">me</emph>.</s> <s xml:id="echoid-s10054" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10055" xml:space="preserve">Avanttoutes choſes, il faut remarquer que la ligne horiſontale <lb/>qui paſſe par le pied du ſtyle des Cadrans verticaux n'y paſſe point <lb/>aux inclinez, mais qu'elle eſt au-deſſus du pied du ſtyle aux inclinez <lb/>ſuperieurs qui regardent le Ciel, & </s> <s xml:id="echoid-s10056" xml:space="preserve">au deſſous, aux inferieurs quire-<lb/>gardent la Terre, comme eſt celui que nous avons deſſein de conſ-<lb/> <pb o="310" file="326" n="326" rhead="CONSTRUCTION ET USAGES"/> truire; </s> <s xml:id="echoid-s10057" xml:space="preserve">ſecondement, que la Méridiene ou ligne de 12. </s> <s xml:id="echoid-s10058" xml:space="preserve">h. </s> <s xml:id="echoid-s10059" xml:space="preserve">aux in-<lb/>clinez ne coupe point à angles droits l'horiſontale comme elle fait <lb/>aux verticaux; </s> <s xml:id="echoid-s10060" xml:space="preserve">ce qui fait que pour la tracer il faut deux points, <lb/>dont l'un ſe trouve ſur la ligne horiſontale par le moyen de l'angle <lb/>de déclinaiſon, & </s> <s xml:id="echoid-s10061" xml:space="preserve">l'autre ſe trouve par l'angle d'inclinaiſon ſur une <lb/>ligne verticale qui coupe l'horiſontale à angles droits.</s> <s xml:id="echoid-s10062" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10063" xml:space="preserve">Ce point de la verticale ſe nomme Zénith aux ſuperieurs, parce <lb/>que ſi le Soleil étoit au Zénith du lieu, l'ombre de l'extremité du ſty-<lb/>le parviendroit à ce point, lequel par conſequent ſeroit au-deſſous <lb/>du ſtyle de ces Cadrans. </s> <s xml:id="echoid-s10064" xml:space="preserve">On le nomme Nadir aux inferieurs, parce <lb/>que ſi le Soleil étoit au Nadir, & </s> <s xml:id="echoid-s10065" xml:space="preserve">que la Terre fût tranſparente, l'om-<lb/>bre de l'extremité du ſtyle toucheroit ce point, lequel par conſe-<lb/>quent doit être au-deſſus du ſtyle, comme il eſt au Cadran propoſé.</s> <s xml:id="echoid-s10066" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10067" xml:space="preserve">En 3<emph style="sub">me</emph> lieu, il faut remarquer que le centre de ce Cadran inferieur <lb/>qui décline du Midi à l'Orient, doit être en haut, & </s> <s xml:id="echoid-s10068" xml:space="preserve">ſa ſouſtylaire à <lb/>gauche de la verticale, & </s> <s xml:id="echoid-s10069" xml:space="preserve">de la Méridiene, entre les heures du ma-<lb/>tin, & </s> <s xml:id="echoid-s10070" xml:space="preserve">partant la Méridiene à droite de la verticale.</s> <s xml:id="echoid-s10071" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10072" xml:space="preserve">Le centre du Cadran inferieur qui décline du Midi à l'Occident <lb/>doit auſſi être en haut, mais la ſouſtylaire eſt à droite de la verticale, <lb/>& </s> <s xml:id="echoid-s10073" xml:space="preserve">de la Méridiene entre les heures d'après midi. </s> <s xml:id="echoid-s10074" xml:space="preserve">Les ſuperieurs op-<lb/>poſez ont le centre en bas, & </s> <s xml:id="echoid-s10075" xml:space="preserve">ne ſont que les mêmes Cadrans ren-<lb/>verſez. </s> <s xml:id="echoid-s10076" xml:space="preserve">C'eſt pourquoi il ſuffit d'en tracer un des quatre.</s> <s xml:id="echoid-s10077" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10078" xml:space="preserve">Pour tracer le modele du Cadran propoſé, tirez premierement les <lb/> <anchor type="note" xlink:label="note-326-01a" xlink:href="note-326-01"/> deux lignes AB, CD ſe coupant à angles droits au point E. </s> <s xml:id="echoid-s10079" xml:space="preserve">CD eſt <lb/>parallele à l'horiſontale, ſur laquelle ayant marqué à diſcretion EF <lb/>pour la longueur du ſtyle droit, dont E ſera le pied & </s> <s xml:id="echoid-s10080" xml:space="preserve">F l'extremité, <lb/>du point F, comme centre, décrivez l'angle d'inclinaiſon GFH de <lb/>63 d. </s> <s xml:id="echoid-s10081" xml:space="preserve">26 m. </s> <s xml:id="echoid-s10082" xml:space="preserve">au-deſſus de la ligne CD, & </s> <s xml:id="echoid-s10083" xml:space="preserve">au-deſſous, l'arc de com-<lb/>plément GI de 26 de. </s> <s xml:id="echoid-s10084" xml:space="preserve">34 m. </s> <s xml:id="echoid-s10085" xml:space="preserve">Tirez enſuite la droite FHA juſqu'au <lb/>rencontre de la ligne AB au point A qui ſera le Nadir & </s> <s xml:id="echoid-s10086" xml:space="preserve">un point <lb/>de la Méridiene. </s> <s xml:id="echoid-s10087" xml:space="preserve">Tirez auſſi la ligne FI, coupant la ligne AB au <lb/>point L, par lequel vous ferez l'horiſontale MLN parallele à CD; <lb/></s> <s xml:id="echoid-s10088" xml:space="preserve">prenez avec un Compas la diſtance LF, & </s> <s xml:id="echoid-s10089" xml:space="preserve">la portez de Len O, qui <lb/>ſera le centre diviſeur de l'horiſontale. </s> <s xml:id="echoid-s10090" xml:space="preserve">Du point O, comme centre, <lb/>faites à droite de la ligne AB l'arc L P de 36 d. </s> <s xml:id="echoid-s10091" xml:space="preserve">qui eſt la déclinai-<lb/>ſon du Plan, pour avoir ſur l'horiſontale un ſecond point de 12 h. </s> <s xml:id="echoid-s10092" xml:space="preserve"><lb/>par lequel & </s> <s xml:id="echoid-s10093" xml:space="preserve">par le Nadir A vous tirerez la Méridicne A 12. </s> <s xml:id="echoid-s10094" xml:space="preserve">Faites <lb/>à gauche de la ligne AB un angle du complément de la déclinaiſon, <lb/>lequel eſt ici de 54 d. </s> <s xml:id="echoid-s10095" xml:space="preserve">& </s> <s xml:id="echoid-s10096" xml:space="preserve">vous donnera ſur l'horiſontale le point de <lb/>6h. </s> <s xml:id="echoid-s10097" xml:space="preserve">& </s> <s xml:id="echoid-s10098" xml:space="preserve">un point de la ligne équinoxiale. </s> <s xml:id="echoid-s10099" xml:space="preserve">Pour achever ce Cadran, <lb/> <pb o="311" file="327" n="327" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> il ne faut plus qu'un point de la ſouſtylaire en ayant déja un qui <lb/>eſt le pied du ſtyle E.</s> <s xml:id="echoid-s10100" xml:space="preserve"/> </p> <div xml:id="echoid-div631" type="float" level="2" n="1"> <note position="left" xlink:label="note-326-01" xlink:href="note-326-01a" xml:space="preserve">XXIII. <lb/>planche. <lb/>Fig. 6.</note> </div> <p> <s xml:id="echoid-s10101" xml:space="preserve">Pour cet effet il n'y a qu'à chercher le centre du Cadran en la <lb/>maniere quiſuit. </s> <s xml:id="echoid-s10102" xml:space="preserve">Du point de 6h. </s> <s xml:id="echoid-s10103" xml:space="preserve">M, tirez la ligne MR, coupant <lb/>à angles droits la Méridiene. </s> <s xml:id="echoid-s10104" xml:space="preserve">Portez la diſtance O 12, de 12 en R, <lb/>ou bien la diſtance AF de A en R. </s> <s xml:id="echoid-s10105" xml:space="preserve">Tirez la ligne occulte 12 R, ſur <lb/>laquelle du point R, comme centre, décrivez l'arc NK de 49 deg. <lb/></s> <s xml:id="echoid-s10106" xml:space="preserve">pour pareille élevation de Pole, tirez la ligne RK qui coupera la <lb/>Méridiene au point K qui ſera le centre du Cadran. </s> <s xml:id="echoid-s10107" xml:space="preserve">Tirez la ſouſty-<lb/>laire KE, & </s> <s xml:id="echoid-s10108" xml:space="preserve">du point M une perpendiculaire ſur ladite ligne pour <lb/>avoir l'équinoxiale MQ. </s> <s xml:id="echoid-s10109" xml:space="preserve">On peut encore avoir ſur la Méridiene un <lb/>point de l'équinoxiale, en faiſant l'angle NRQ de 41 deg. </s> <s xml:id="echoid-s10110" xml:space="preserve">c'eſt-<lb/>à-dire, du complement de l'élevation du Pole.</s> <s xml:id="echoid-s10111" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10112" xml:space="preserve">Ayant trouvé la poſition des principales lignes, il ſera facile d'y <lb/>marquer les diviſions des heures en deux manieres; </s> <s xml:id="echoid-s10113" xml:space="preserve">ſçavoir, ſur la li-<lb/>gne horiſontale, & </s> <s xml:id="echoid-s10114" xml:space="preserve">ſur l'équinoxiale. </s> <s xml:id="echoid-s10115" xml:space="preserve">Pour les marquer ſur l'hori-<lb/>ſontale, appliquezau point O le centre d'un Cadran horiſontal, en <lb/>ſorte que la ligne de midi convienne avec la ligne O 12, & </s> <s xml:id="echoid-s10116" xml:space="preserve">celle de <lb/>6 h. </s> <s xml:id="echoid-s10117" xml:space="preserve">avec la ligne O 6, & </s> <s xml:id="echoid-s10118" xml:space="preserve">marquez les points des autres heures ſur <lb/>la ligne horiſontale MN.</s> <s xml:id="echoid-s10119" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10120" xml:space="preserve">Pour marquer les mêmes heures ſur la ligne équinoxile il faut <lb/>former le ſtyle triangulaire, en élevant ſur la ſouſtylaire la perpen-<lb/>diculaire ES égale à EF, & </s> <s xml:id="echoid-s10121" xml:space="preserve">tirant l'axe SK. </s> <s xml:id="echoid-s10122" xml:space="preserve">Prenez enſuite la diſ-<lb/>tance TS & </s> <s xml:id="echoid-s10123" xml:space="preserve">la portez ſur la ſouſtylaire de T en V, qui ſera le cen-<lb/>tre diviſeur de la ligne équinoxiale, laquelle étant diviſée de la mê-<lb/>me maniere que nous avons dit en parlant des déclinans, vous ti-<lb/>rerez les lignes horaires du centre K, & </s> <s xml:id="echoid-s10124" xml:space="preserve">le Cadran ſera achevé.</s> <s xml:id="echoid-s10125" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10126" xml:space="preserve">On pourra enſuite le mettre au net en n'y mettant que les prin-<lb/>cipales lignes & </s> <s xml:id="echoid-s10127" xml:space="preserve">celles des heures avec le ſtyle, comme on voit en <lb/>la figure 7 Pentagonale.</s> <s xml:id="echoid-s10128" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10129" xml:space="preserve">Par le moyen de ce Cadran on peut faire les trois autres qui ont <lb/>même déclinaiſon; </s> <s xml:id="echoid-s10130" xml:space="preserve">& </s> <s xml:id="echoid-s10131" xml:space="preserve">inclinaiſon; </s> <s xml:id="echoid-s10132" xml:space="preserve">les deux inferieurs qui déclinent <lb/>du Midi à l'Orient & </s> <s xml:id="echoid-s10133" xml:space="preserve">à l'Occident, ont le centre en haut; </s> <s xml:id="echoid-s10134" xml:space="preserve">les deux <lb/>ſuperieurs qui déclinent du Septentrion à l'Orient & </s> <s xml:id="echoid-s10135" xml:space="preserve">à l'Occident <lb/>ont le centre en bas, & </s> <s xml:id="echoid-s10136" xml:space="preserve">ne ſont que les mêmes Cadrans renverſez, <lb/>comme nous avons déja dit.</s> <s xml:id="echoid-s10137" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10138" xml:space="preserve">Le Cadran de la figure 8 repreſente celui márqué F de la figure 2 <lb/> <anchor type="note" xlink:label="note-327-01a" xlink:href="note-327-01"/> planche 22. </s> <s xml:id="echoid-s10139" xml:space="preserve">C'eſt un ſuperieur incliné vers le Ciel de 63 d. </s> <s xml:id="echoid-s10140" xml:space="preserve">26 m. <lb/></s> <s xml:id="echoid-s10141" xml:space="preserve">déclinant du Midi à l'Orient de 72 d. </s> <s xml:id="echoid-s10142" xml:space="preserve">On pourra le tracer ſuivant <lb/>la méthode que nous venons d'expliquer; </s> <s xml:id="echoid-s10143" xml:space="preserve">ſon centre ſe trouve en <lb/> <pb o="312" file="328" n="328" rhead="CONSTRUCTION ET USAGES"/> bas, mais parce que ſa déclinaiſon eſt grande, ſes heures ſont fort <lb/>ſerrées aux environs de la ſouſty laire; </s> <s xml:id="echoid-s10144" xml:space="preserve">c'eſt pourquoi on le doit tra-<lb/>cer ſur un grand Plan, afin d'en retrancher la partie qui eſt vers le <lb/>centre, & </s> <s xml:id="echoid-s10145" xml:space="preserve">terminer ſon ſtile & </s> <s xml:id="echoid-s10146" xml:space="preserve">ſes lignes horaires par deux paralleles.</s> <s xml:id="echoid-s10147" xml:space="preserve"/> </p> <div xml:id="echoid-div632" type="float" level="2" n="2"> <note position="right" xlink:label="note-327-01" xlink:href="note-327-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s10148" xml:space="preserve">Il y a un autre moyen de tracer méchaniquement ſur un Polye-<lb/>dre ou Corps à pluſieurs faces toutes ſortes de Cadrans reguliers ou <lb/>irreguliers, déclinans & </s> <s xml:id="echoid-s10149" xml:space="preserve">inclinez, même ſans connoître leur dé-<lb/>clinaiſon ni inclinaiſon, par lequel on réuſſit auſſi-bien que par tou-<lb/>tes les differentes méthodes que fournit la Gnomonique. </s> <s xml:id="echoid-s10150" xml:space="preserve">Pour cet <lb/>effet, commencez par tracer exactement ſur une des faces qui eſt pa-<lb/>rallele à l'horiſon, un Cadran horiſontal avec ſon ſtyle élevé perpen-<lb/>diculairement ſur la ligne de 12 h. </s> <s xml:id="echoid-s10151" xml:space="preserve">conformément à l'élevation du <lb/>Pole du lieu. </s> <s xml:id="echoid-s10152" xml:space="preserve">Il faut enſuite connoître le lieu & </s> <s xml:id="echoid-s10153" xml:space="preserve">la ſituation des ſouſ-<lb/>tylaires ſur chacune des faces qui peut être éclairée du Soleil, pour <lb/>y placer fixement & </s> <s xml:id="echoid-s10154" xml:space="preserve">perpendiculairement un ſtyle ou axe de cuivre <lb/>ou de quelque autre matiere ſolide, proportionné à la grandeur deſ-<lb/>dites faces; </s> <s xml:id="echoid-s10155" xml:space="preserve">en ſorte que les axes de tous ces ſtyles ſoient bien paral-<lb/>leles à celui de l'horiſontal, vous ſervant pour cet effet d'une lime <lb/>pour ôter ce qui excedera; </s> <s xml:id="echoid-s10156" xml:space="preserve">ce que vous connoîtrez en les bornaïant <lb/>tous l'un après l'autre avec l'axe d'un grand ſtyle ſemblable à celui <lb/>de l'horiſontal placé de niveau, ou bien le tenant à la main de ma-<lb/>niere que ſa baſe ſoit parallele à l'horiſon; </s> <s xml:id="echoid-s10157" xml:space="preserve">ce que l'on pourra faire <lb/>par le moyen d'un perpendicule & </s> <s xml:id="echoid-s10158" xml:space="preserve">de ſon plomb attaché au haut <lb/>dudit ſtyle, & </s> <s xml:id="echoid-s10159" xml:space="preserve">faire en ſorte que tous ces axes tendent au Pole du <lb/>Monde.</s> <s xml:id="echoid-s10160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10161" xml:space="preserve">Le tout étant ainſi préparé, expoſez ce Corps aux raîons du So-<lb/>leil; </s> <s xml:id="echoid-s10162" xml:space="preserve">tournez-le de maniere que l'axe du Cadran horiſontal marque <lb/>par ſon ombre toutes les heures l'une après l'autre; </s> <s xml:id="echoid-s10163" xml:space="preserve">& </s> <s xml:id="echoid-s10164" xml:space="preserve">à meſure qu'il <lb/>marquera chaque heure, tracez ſur les faces la même ligne d'heure <lb/>ſuivant l'ombre de leurs axes; </s> <s xml:id="echoid-s10165" xml:space="preserve">continuez ces lignes horaires juſqu'-<lb/>au centre des Cadrans qui en ont un, ſoit en haut, ſoit en bas; </s> <s xml:id="echoid-s10166" xml:space="preserve">& </s> <s xml:id="echoid-s10167" xml:space="preserve">à <lb/>ceux qui n'ont point de centre, terminez les lignes horaires par deux <lb/>paralleles, comme on les voit ſur les Cadrans du Dodecaëdre. </s> <s xml:id="echoid-s10168" xml:space="preserve">Mar-<lb/>quez-y les heures convenables du ſoir & </s> <s xml:id="echoid-s10169" xml:space="preserve">du matin, ſelon que ces <lb/>Cadrans ſeront expoſez à l'Orient ou à l'Occident, au Midi ou <lb/>au Septentrion.</s> <s xml:id="echoid-s10170" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10171" xml:space="preserve">On peut faire la même choſe de nuit à la lumiere d'un flambeau <lb/>que l'on fera tourner autour du Polyedre.</s> <s xml:id="echoid-s10172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10173" xml:space="preserve">On place quelquefois dans les Jardins de grands corps de pierre <lb/>taillez à pluſieurs faces, ſur leſquels on trace autant de Cadrans par <lb/>la méthode que nous venons d'indiquer.</s> <s xml:id="echoid-s10174" xml:space="preserve"/> </p> <pb o="313" file="329" n="329" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> <p> <s xml:id="echoid-s10175" xml:space="preserve">Il y a quelques-uns de ces Cadrans où les vives arrêtes des pier-<lb/>res ſervent d'axes, & </s> <s xml:id="echoid-s10176" xml:space="preserve">doivent être taillées de maniere qu'elles ten-<lb/>dent toutes au Pole & </s> <s xml:id="echoid-s10177" xml:space="preserve">ſoient paralleles à l'axe du Monde.</s> <s xml:id="echoid-s10178" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div634" type="section" level="1" n="322"> <head xml:id="echoid-head455" style="it" xml:space="preserve">Conſtruction des Cadrans par le calcul des Angles.</head> <p> <s xml:id="echoid-s10179" xml:space="preserve">CEtte méthode eſt d'un grand ſecours pour verifier toutes les <lb/>operations de la Gnomonique où l'on a beſoin de beaucoup <lb/>d'exactitude, principalement quand on eſt obligé de faire un petit <lb/>modele pour tracer un grand Cadran, car une erreur preſque inſen-<lb/>ſible dans le modele devient très-conſiderable dans les longues li-<lb/>gnes qu'il faut tracer ſur un Plan de grande étenduë.</s> <s xml:id="echoid-s10180" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10181" xml:space="preserve">En la conſtruction des Cadrans reguliers, comme par exemple, de <lb/> <anchor type="note" xlink:label="note-329-01a" xlink:href="note-329-01"/> l'horiſontal, fig. </s> <s xml:id="echoid-s10182" xml:space="preserve">4, planche 22, les diviſions de la ligne équinoxialé <lb/>LK ſont les tangentes des angles du quart de cercle MH, & </s> <s xml:id="echoid-s10183" xml:space="preserve">les li-<lb/>gnes ponctuées en ſont les ſecantes, c'eſt pourquoi on les peut mar-<lb/>quer avec une Echelle de parties égales ou un Compas de propor-<lb/>tion, en ſuppoſant, par exemple, le raïon HB de cent parties, la diſ-<lb/>tance HI, tangente de 15 deg. </s> <s xml:id="echoid-s10184" xml:space="preserve">ſera de 27 des mêmes parties; </s> <s xml:id="echoid-s10185" xml:space="preserve">H2, <lb/>tangente de 30 d. </s> <s xml:id="echoid-s10186" xml:space="preserve">ſera de 58; </s> <s xml:id="echoid-s10187" xml:space="preserve">H3, tangente de 45d. </s> <s xml:id="echoid-s10188" xml:space="preserve">égale au raïon <lb/>ſera de 100. </s> <s xml:id="echoid-s10189" xml:space="preserve">H4, tangente de 60 d. </s> <s xml:id="echoid-s10190" xml:space="preserve">ſera de 173; </s> <s xml:id="echoid-s10191" xml:space="preserve">& </s> <s xml:id="echoid-s10192" xml:space="preserve">H5, tangente <lb/>de 75 d. </s> <s xml:id="echoid-s10193" xml:space="preserve">eſt de 373. </s> <s xml:id="echoid-s10194" xml:space="preserve">Les diviſions de l'autre moitié de cette ligno <lb/>pour les heures avant midi ſont ſemblables.</s> <s xml:id="echoid-s10195" xml:space="preserve"/> </p> <div xml:id="echoid-div634" type="float" level="2" n="1"> <note position="right" xlink:label="note-329-01" xlink:href="note-329-01a" xml:space="preserve">XXII, <lb/>planche. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s10196" xml:space="preserve">On peut de même trouver ſur cette ligne les points des demi-<lb/>heures & </s> <s xml:id="echoid-s10197" xml:space="preserve">des quarts, en prenant les tangentes des arcs convenables, <lb/>qu'il ſera facile de trouver dans les Tables imprimées; </s> <s xml:id="echoid-s10198" xml:space="preserve">à quoi l'on <lb/>peut ajoûter quelques abregez tirez de la valeur des ſecantes; </s> <s xml:id="echoid-s10199" xml:space="preserve">com-<lb/>me par exemple, laligne B4, ſecante de 60 d. </s> <s xml:id="echoid-s10200" xml:space="preserve">étant double du raïon, <lb/>ſi vous poïtez le double de BH, de B en 4, vous aurez le point de 4 <lb/>h. </s> <s xml:id="echoid-s10201" xml:space="preserve">ſur la ligne Equinoxiale. </s> <s xml:id="echoid-s10202" xml:space="preserve">Cette même ſecante portée de 4 en L, <lb/>donnera le point de 5; </s> <s xml:id="echoid-s10203" xml:space="preserve">& </s> <s xml:id="echoid-s10204" xml:space="preserve">ſi vous en faites autant de l'autre côté, <lb/>vous aurez le point d'onze heures.</s> <s xml:id="echoid-s10205" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10206" xml:space="preserve">A l'égard des demi-heures on peut les trouver par le moyen des <lb/>ſecantes des heures qui ſont en nombre impair; </s> <s xml:id="echoid-s10207" xml:space="preserve">par exemple, la ſe-<lb/>cante B3, portée ſur la ligne Equinoxiale au point 3, donnera d'un <lb/>côté 4 h. </s> <s xml:id="echoid-s10208" xml:space="preserve">& </s> <s xml:id="echoid-s10209" xml:space="preserve">demie, & </s> <s xml:id="echoid-s10210" xml:space="preserve">de l'autre 10 h. </s> <s xml:id="echoid-s10211" xml:space="preserve">& </s> <s xml:id="echoid-s10212" xml:space="preserve">demie. </s> <s xml:id="echoid-s10213" xml:space="preserve">La ſecante B 6, <lb/>donue 7 h. </s> <s xml:id="echoid-s10214" xml:space="preserve">& </s> <s xml:id="echoid-s10215" xml:space="preserve">demie & </s> <s xml:id="echoid-s10216" xml:space="preserve">une & </s> <s xml:id="echoid-s10217" xml:space="preserve">demie. </s> <s xml:id="echoid-s10218" xml:space="preserve">B11, donne 8 & </s> <s xml:id="echoid-s10219" xml:space="preserve">demie & </s> <s xml:id="echoid-s10220" xml:space="preserve">2 <lb/>& </s> <s xml:id="echoid-s10221" xml:space="preserve">demie B1, donne 3 & </s> <s xml:id="echoid-s10222" xml:space="preserve">demie & </s> <s xml:id="echoid-s10223" xml:space="preserve">9 & </s> <s xml:id="echoid-s10224" xml:space="preserve">demie. </s> <s xml:id="echoid-s10225" xml:space="preserve">B7, donne 6 & </s> <s xml:id="echoid-s10226" xml:space="preserve">de-<lb/>mie & </s> <s xml:id="echoid-s10227" xml:space="preserve">12 & </s> <s xml:id="echoid-s10228" xml:space="preserve">demie. </s> <s xml:id="echoid-s10229" xml:space="preserve">Enfin B5, donne 11 & </s> <s xml:id="echoid-s10230" xml:space="preserve">demi & </s> <s xml:id="echoid-s10231" xml:space="preserve">5 & </s> <s xml:id="echoid-s10232" xml:space="preserve">demie.</s> <s xml:id="echoid-s10233" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10234" xml:space="preserve">La diviſion de cette ligne ſert à faire exactement les Cadrans ho-<lb/>riſontaux, verticaux, & </s> <s xml:id="echoid-s10235" xml:space="preserve">principalement les Cadrans reguliers ſans <lb/> <pb o="314" file="330" n="330" rhead="CONSTR UCTION ET USAGES"/> centre, comme ſont les Polaires, les Orientaux & </s> <s xml:id="echoid-s10236" xml:space="preserve">Occidentaux; </s> <s xml:id="echoid-s10237" xml:space="preserve">car <lb/>pour les Equinoxiaux on ne peut rien ajoûter à la facilité de les <lb/>conſtruire, puiſque ſes angles horaires ſont tous égaux à leur centre.</s> <s xml:id="echoid-s10238" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10239" xml:space="preserve">A l'êgard des horiſontaux on peut trouver par le calcul de la Tri-<lb/>gonométrie les angles que font au ccntre du Cadran les lignes ho-<lb/>raires avec la Méridienne par cette Analogie. </s> <s xml:id="echoid-s10240" xml:space="preserve">Comme le Sinus total <lb/>eſt au Sinus de l'élevation du Pole, ainſi la tangente de la diſtance <lb/>horaire eſt à la tangente de l'arc horaire.</s> <s xml:id="echoid-s10241" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10242" xml:space="preserve">Parle mot de diſtance horaire on doit entendre l'angle de la mê-<lb/>me heure avec la Méridiene au centre d'un Cadran Equinoxial, tels <lb/>que ſont 15 d. </s> <s xml:id="echoid-s10243" xml:space="preserve">pour une & </s> <s xml:id="echoid-s10244" xml:space="preserve">11 h. </s> <s xml:id="echoid-s10245" xml:space="preserve">30d. </s> <s xml:id="echoid-s10246" xml:space="preserve">pour 2 & </s> <s xml:id="echoid-s10247" xml:space="preserve">10, & </s> <s xml:id="echoid-s10248" xml:space="preserve">ainſi des au-<lb/>tres, augmentant 15 d. </s> <s xml:id="echoid-s10249" xml:space="preserve">pour chaque heure, & </s> <s xml:id="echoid-s10250" xml:space="preserve">7 d. </s> <s xml:id="echoid-s10251" xml:space="preserve">30 m. </s> <s xml:id="echoid-s10252" xml:space="preserve">pour cha-<lb/>que demie.</s> <s xml:id="echoid-s10253" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10254" xml:space="preserve">Si donc on propoſe de trouver l'arc horaire d'une heure au centre <lb/>d'un Cadran horiſontal pour 49 d. </s> <s xml:id="echoid-s10255" xml:space="preserve">de latitude ou élevation de Pole, <lb/>il faut faire une regle de 3, dont le premier terme ſoit le Sinustotal <lb/>100000; </s> <s xml:id="echoid-s10256" xml:space="preserve">le ſecond ſoit le Sinus de 49 d. </s> <s xml:id="echoid-s10257" xml:space="preserve">qui eſt 75471; </s> <s xml:id="echoid-s10258" xml:space="preserve">le 3<emph style="sub">me</emph> ter-<lb/>me, la tangente de 15 d. </s> <s xml:id="echoid-s10259" xml:space="preserve">qui eſt 26795. </s> <s xml:id="echoid-s10260" xml:space="preserve">Laregle étant faite, on trou-<lb/>vera pour 4<emph style="sub">me</emph> terme 20222, lequel étant cherché dans les Tables <lb/>des Sinus, ſous la colonne des tangentes, répond à 11 d. </s> <s xml:id="echoid-s10261" xml:space="preserve">26 m. </s> <s xml:id="echoid-s10262" xml:space="preserve">c'eſt <lb/>pourquoi l'angle propoſé avec la Méridiene eſt dc 11 d. </s> <s xml:id="echoid-s10263" xml:space="preserve">26 m.</s> <s xml:id="echoid-s10264" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10265" xml:space="preserve">On trouvera par ce moyen les angles que font avec la Méridiene <lb/>toutes les autres heures & </s> <s xml:id="echoid-s10266" xml:space="preserve">demi-heures au centre du Cadran hori-<lb/>ſontal, par autant de regles de 3, dont les premiers termes ſeront <lb/>toûjours les mêmes; </s> <s xml:id="echoid-s10267" xml:space="preserve">ſçavoir, le Sinus total & </s> <s xml:id="echoid-s10268" xml:space="preserve">le Sinus de l'élevation <lb/>du Pole; </s> <s xml:id="echoid-s10269" xml:space="preserve">c'eſt pourquoi il n'y aura que le 3<emph style="sub">me</emph> terme à chercher dans <lb/>les Tables, ſçavoir la tangente de la diſtance horaire.</s> <s xml:id="echoid-s10270" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10271" xml:space="preserve">On pourra, ſi l'on veut, prendre leurs logarithmes, afin d'éviter la <lb/>peine de multiplier & </s> <s xml:id="echoid-s10272" xml:space="preserve">diviſer.</s> <s xml:id="echoid-s10273" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10274" xml:space="preserve">Cette mêmer regle peut ſervir auſſi pour les verticaux en prenant <lb/>pour ſecond terme le Sinus de complément de l'élevation de Pole, <lb/>c'eſt;</s> <s xml:id="echoid-s10275" xml:space="preserve">-à-dire, le Sinus de 41 d. </s> <s xml:id="echoid-s10276" xml:space="preserve">aux euvirons de Paris, puiſque tout <lb/>Cadran vertical peut être conſideré comme un horiſontal pour un <lb/>Païs où le Pole ſeroit élevé d'autant de degrez ſur l'horiſon.</s> <s xml:id="echoid-s10277" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10278" xml:space="preserve">C'eſt encore la même regle pour les Cadrans inclinez ſans décli-<lb/>naiſon, en prenant pour ſecond terme de la regle de 3, le Sinus de <lb/>l'angle que fait l'axeavec la Méridiene au centre du Cadran, comme <lb/>par exemple, au Cadran marqué B, ſur le Dodecaëdre de la planche <lb/>22. </s> <s xml:id="echoid-s10279" xml:space="preserve">Nousavons dit ci-devant qu'étant incliné à l'horiſon de 63 d. <lb/></s> <s xml:id="echoid-s10280" xml:space="preserve">26 min. </s> <s xml:id="echoid-s10281" xml:space="preserve">il en faut ſouſtraire l'élevation du Pole du lieu que nous <lb/> <pb o="315" file="331" n="331" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> avons ſuppoſé de 49 d. </s> <s xml:id="echoid-s10282" xml:space="preserve">& </s> <s xml:id="echoid-s10283" xml:space="preserve">par conſequent il doit être fait comme un <lb/>horiſontal pour un Païs où le Pole ſeroit élevé de 14 deg. </s> <s xml:id="echoid-s10284" xml:space="preserve">26 m. </s> <s xml:id="echoid-s10285" xml:space="preserve">Si <lb/>donc vous voulez calculer ſes angles horaires, prenez pour ſecond <lb/>terme de la regle de 3, le Sinus de 14 deg. </s> <s xml:id="echoid-s10286" xml:space="preserve">26 min</s> </p> </div> <div xml:id="echoid-div636" type="section" level="1" n="323"> <head xml:id="echoid-head456" style="it" xml:space="preserve">Table des Arcs horaires avec la Méridiene, au centre d'un <lb/>Cadran horiſontal.</head> <note position="right" xml:space="preserve"> <lb/>Latitude # I & XI heur. # II & xh. # III & IX # IV & VIII # V & VII <lb/>41 deg. # 9 d. 58 min. # 20 45 # 33 16 # 48 39 # 67 47 <lb/>49 # II 26 # 23 33 # 37 3 # 52 35 # 70 27 <lb/></note> <p> <s xml:id="echoid-s10287" xml:space="preserve">A l'égard de la lig. </s> <s xml:id="echoid-s10288" xml:space="preserve">de 6 h. </s> <s xml:id="echoid-s10289" xml:space="preserve">elle fait toûjours angle droit avec la Mé-<lb/>ridiene au centre des horiſontaux & </s> <s xml:id="echoid-s10290" xml:space="preserve">des verticaux ſans déclinaiſon.</s> <s xml:id="echoid-s10291" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div637" type="section" level="1" n="324"> <head xml:id="echoid-head457" style="it" xml:space="preserve">Tracer par le calcul de la Trigonométrie les principales lignes <lb/>d'un Cadran, vertical déclinant.</head> <p> <s xml:id="echoid-s10292" xml:space="preserve">CE calcul ſe fait parle moyen des cinq Regles que nous allons <lb/>expliquer.</s> <s xml:id="echoid-s10293" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div638" type="section" level="1" n="325"> <head xml:id="echoid-head458" xml:space="preserve">PREMIERE PROPOSITION.</head> <p> <s xml:id="echoid-s10294" xml:space="preserve">Connoiſſant la déclinaiſon du Plan trouver l'angle de la ſouſty-<lb/>laire avec la Mérediene.</s> <s xml:id="echoid-s10295" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div639" type="section" level="1" n="326"> <head xml:id="echoid-head459" xml:space="preserve">I. REGLE.</head> <p> <s xml:id="echoid-s10296" xml:space="preserve">Comme le Sinus total eſt au Sinus de la déclinaiſon du Plan, ainſi <lb/>la tangente du complément de la latitude eſt à la tangente de l'an-<lb/>gle de la ſouſtylaire avec la Méridiene au centre des verticaux dé-<lb/>clinans.</s> <s xml:id="echoid-s10297" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10298" xml:space="preserve">L'angle de ladite ſouſtylaire avec l'horiſontale au lieu du ſtyle <lb/>droit eſt le complément de celui qui ſe fait au centre du Cadran qui <lb/>eſt la rencontre de la Méridiene & </s> <s xml:id="echoid-s10299" xml:space="preserve">de la ſouſtylaire.</s> <s xml:id="echoid-s10300" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10301" xml:space="preserve">L'angle de l'Equinoxiale avec l'horiſontale en la ſection de 6. </s> <s xml:id="echoid-s10302" xml:space="preserve">h. <lb/></s> <s xml:id="echoid-s10303" xml:space="preserve">eſt égal à celui de la ſouſtylaire avec la Méridiene. </s> <s xml:id="echoid-s10304" xml:space="preserve">L'angle de l'E. </s> <s xml:id="echoid-s10305" xml:space="preserve"><lb/>quinoxiale avec la Méridiene eſt ſon complément.</s> <s xml:id="echoid-s10306" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div640" type="section" level="1" n="327"> <head xml:id="echoid-head460" xml:space="preserve">II. REGLE.</head> <p> <s xml:id="echoid-s10307" xml:space="preserve">Pour trouver l'angle de l'Axe avec la ſouſtylaire, que l'on peut <lb/>auſſi nommer l'élevation particuliere du Pole ſur le Plan du verti-<lb/>cal.</s> <s xml:id="echoid-s10308" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10309" xml:space="preserve">Comme le Sinus total eſt au Sinus du complement de la hauteur <lb/>du Pole ſur l'horiſon, ainſi le Sinus du complément de la déclinai-<lb/>ſon du Plan eſt au Sinus de l'angle requis. </s> <s xml:id="echoid-s10310" xml:space="preserve">L'angle de l'axe avecle <lb/>ſtyle droit eſt le complément dudit angle.</s> <s xml:id="echoid-s10311" xml:space="preserve"/> </p> <pb o="316" file="332" n="332" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s10312" xml:space="preserve">L'angle du raïon de l'Equateur ou de l'Equinoxiale avec le ſtyle <lb/>droit, eſt égal à l'angle de l'axe avec la ſouſtylaîre. </s> <s xml:id="echoid-s10313" xml:space="preserve">L'angle du raïon <lb/>équinoxial avec la ſouſty laire en eſt le complément.</s> <s xml:id="echoid-s10314" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div641" type="section" level="1" n="328"> <head xml:id="echoid-head461" xml:space="preserve">III. REGLE.</head> <p> <s xml:id="echoid-s10315" xml:space="preserve">Pour trouver l'arc de l'Equateur & </s> <s xml:id="echoid-s10316" xml:space="preserve">les degrez de l'Equinoxiale <lb/>entre la ſouſtylaire & </s> <s xml:id="echoid-s10317" xml:space="preserve">la Méridiene des verticaux déclinans; </s> <s xml:id="echoid-s10318" xml:space="preserve">ce qui <lb/>ſe nomme auſſi la difference entre le Méridien du lieu & </s> <s xml:id="echoid-s10319" xml:space="preserve">le Méridien <lb/>particulier du Plan, car la ſouſtylaire eſt la Méridiene du Plan.</s> <s xml:id="echoid-s10320" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10321" xml:space="preserve">Comme le Sinus total eſt au Sinus de la hauteur du Pole ſur l'ho-<lb/>riſon, ainſi la tangente du complément de la déclinaiſon du Plan eſt <lb/>à la tangente d'un arc, duquel le complement ſera le requis.</s> <s xml:id="echoid-s10322" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div642" type="section" level="1" n="329"> <head xml:id="echoid-head462" xml:space="preserve">IV. REGLE.</head> <p> <s xml:id="echoid-s10323" xml:space="preserve">Pour trouver l'angle de la ligne de 6 heures avecl'horiſontale, <lb/>& </s> <s xml:id="echoid-s10324" xml:space="preserve">enſuite avec la Méridiene au centre.</s> <s xml:id="echoid-s10325" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10326" xml:space="preserve">Comme le Sinus total eſt au Sinus de la déclinaiſon du Plan, ainſi <lb/>la tangente de la hauteur du Pole ſur l'horiſon eſt à la tangente de <lb/>l'angle que fait la ligne de 6 h. </s> <s xml:id="echoid-s10327" xml:space="preserve">avec l'horiſontale.</s> <s xml:id="echoid-s10328" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10329" xml:space="preserve">Le complement de cet angle eſt celui de la ligne de 6 h. </s> <s xml:id="echoid-s10330" xml:space="preserve">avec la <lb/>Méridiene au centre des verticaux declinans.</s> <s xml:id="echoid-s10331" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div643" type="section" level="1" n="330"> <head xml:id="echoid-head463" xml:space="preserve">V. REGLE.</head> <p> <s xml:id="echoid-s10332" xml:space="preserve">Trouver les angles de toutes les heures avec la ſouſtylaire, & </s> <s xml:id="echoid-s10333" xml:space="preserve">en-<lb/>ſuite avec la Meridiene au centre des verticaux declinans.</s> <s xml:id="echoid-s10334" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10335" xml:space="preserve">Cette propoſition eſt fondée ſur ce principe de Gnomenique que <lb/>tout Plan peut être parallele à un horiſon ſur lequel le Pole ſéroit é-<lb/>levé de même façon. </s> <s xml:id="echoid-s10336" xml:space="preserve">Ainſi les Cadrans qui s'y font ſe peuvent faire <lb/>comme les horiſontaux, de même élevation, pourvû toutefois qu'on <lb/>y obſerve les diſtances horaires convenables de part & </s> <s xml:id="echoid-s10337" xml:space="preserve">d'autre de-<lb/>puis la ſouſtylaire.</s> <s xml:id="echoid-s10338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10339" xml:space="preserve">Mais auparavant il faut connoître l'angle de la ſouſtylaire avec la <lb/>Méridiene par la premiere propoſition, 2°. </s> <s xml:id="echoid-s10340" xml:space="preserve">l'élevation particuliere <lb/>du Pole ſur le Plan propoſé par la ſeconde; </s> <s xml:id="echoid-s10341" xml:space="preserve">3°. </s> <s xml:id="echoid-s10342" xml:space="preserve">l'arc de l'Equateur <lb/>ou les degrez de l'Equinoxiale entre la ſouſtylaire & </s> <s xml:id="echoid-s10343" xml:space="preserve">la Méridiene <lb/>par la troiſiéme, avec la difference ou les degrez des deux premieres <lb/>diſtances depuis le ſtyle, dont l'une eſt entre la ſouſty laire & </s> <s xml:id="echoid-s10344" xml:space="preserve">la <lb/>Méridiene, & </s> <s xml:id="echoid-s10345" xml:space="preserve">l'autre entre la ſouſtylaire & </s> <s xml:id="echoid-s10346" xml:space="preserve">la ligne de 6 h.</s> <s xml:id="echoid-s10347" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div644" type="section" level="1" n="331"> <head xml:id="echoid-head464" xml:space="preserve">REGLE GENERALE.</head> <p> <s xml:id="echoid-s10348" xml:space="preserve">Comme le Sinustotal eſt au Sinus de l'élevation particuliere du <lb/>Pole ſur le Plan déclinant, ainſi la tangente de la diſtance horaire, <lb/>convenable depuis la ſouſtylaire, (ſoit la premiere, ſoit les ſuivantes <lb/>avec elle,) eſt à la tangente de l'angle de l'heure propoſée avec la <lb/>ſouſtylaire, au centre des yerticaux déclinans.</s> <s xml:id="echoid-s10349" xml:space="preserve"/> </p> <pb o="317" file="333" n="333" rhead="DES CADRANS AU SOLEIL. LIv. VIII. Ch. I."/> <p> <s xml:id="echoid-s10350" xml:space="preserve">Si la ſouſtylaire ſe rencontre juſtement ſur une demie heure ou ſur <lb/>quelque heure complete, les deux premieres diſtances horaires ſeront <lb/>égales chacune de 7 deg. </s> <s xml:id="echoid-s10351" xml:space="preserve">30 m. </s> <s xml:id="echoid-s10352" xml:space="preserve">ou de 15 deg. </s> <s xml:id="echoid-s10353" xml:space="preserve">& </s> <s xml:id="echoid-s10354" xml:space="preserve">en ce cas les angles <lb/>trouvez pour un côté, ſeront les mêmes reſpectivement pour l'au-<lb/>tre, comme ſi c'étoit un Cadran regulier, & </s> <s xml:id="echoid-s10355" xml:space="preserve">comme ſi la ſouſtylaire <lb/>étoit la Méridiene.</s> <s xml:id="echoid-s10356" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div645" type="section" level="1" n="332"> <head xml:id="echoid-head465" style="it" xml:space="preserve">Application des Regles precedentes pour un vertical déclinant <lb/>de 45 degrez du Midi à l'Occident, & 49 degrez de latitu-<lb/>de, tel qu'eſt celui de la Figure 2 de la Planche 23.</head> <p> <s xml:id="echoid-s10357" xml:space="preserve">PAr la premiere Regle on trouvera que l'angle de la ſouſty laire a-<lb/>vec la Méridiene au centre du Cadran eſt de 31 deg. </s> <s xml:id="echoid-s10358" xml:space="preserve">35 min.</s> <s xml:id="echoid-s10359" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10360" xml:space="preserve">Par la ſeconde Regle on trouvera que l'angle de l'axe avec la ſouſ-<lb/>tylaire eſt de 27 d. </s> <s xml:id="echoid-s10361" xml:space="preserve">38 m.</s> <s xml:id="echoid-s10362" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10363" xml:space="preserve">Par la troiſiéme, que l'arc de l'Equateur entre la ſouſtylaire & </s> <s xml:id="echoid-s10364" xml:space="preserve">la <lb/>Méridiene eſt de 52 d. </s> <s xml:id="echoid-s10365" xml:space="preserve">58 m. </s> <s xml:id="echoid-s10366" xml:space="preserve">& </s> <s xml:id="echoid-s10367" xml:space="preserve">par conſequent que la ſouſtylaire <lb/>eſt entre 3 & </s> <s xml:id="echoid-s10368" xml:space="preserve">4 heures.</s> <s xml:id="echoid-s10369" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10370" xml:space="preserve">Par la quatriéme, que l'angle de la ligne de 6 h. </s> <s xml:id="echoid-s10371" xml:space="preserve">avec la Méridie-<lb/>ne eſt de 50 d. </s> <s xml:id="echoid-s10372" xml:space="preserve">52 m.</s> <s xml:id="echoid-s10373" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10374" xml:space="preserve">Ayant trouve que l'arc de l'Equateur entre la ſouſtylaire & </s> <s xml:id="echoid-s10375" xml:space="preserve">la Mé-<lb/>ridiene eſt de 52 d. </s> <s xml:id="echoid-s10376" xml:space="preserve">58 m. </s> <s xml:id="echoid-s10377" xml:space="preserve">ôtez-en 45 d. </s> <s xml:id="echoid-s10378" xml:space="preserve">qui eſt larc de l'Equateur, <lb/>qui convient à 3 h. </s> <s xml:id="echoid-s10379" xml:space="preserve">reſte 7 d. </s> <s xml:id="echoid-s10380" xml:space="preserve">58 m. </s> <s xml:id="echoid-s10381" xml:space="preserve">pour la diſtance horaire entre <lb/>ladite ſouſtylaire & </s> <s xml:id="echoid-s10382" xml:space="preserve">la ligne de 3 h. </s> <s xml:id="echoid-s10383" xml:space="preserve">& </s> <s xml:id="echoid-s10384" xml:space="preserve">par conſequent 7 d. </s> <s xml:id="echoid-s10385" xml:space="preserve">2 m. </s> <s xml:id="echoid-s10386" xml:space="preserve">en-<lb/>tre la ſouſtylaire & </s> <s xml:id="echoid-s10387" xml:space="preserve">celle de 4 h.</s> <s xml:id="echoid-s10388" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10389" xml:space="preserve">C'eſt pourquoi pour trouver les angles que ſont avec la ſouſtylai-<lb/>re les lignes des heures au centre du Cadran, il faut commencer <lb/>par une de ces diſtances, en diſant, par exemple, comme le Sinus to-<lb/>tal 100000 eſt au Sinus de l'élevation particuliere du Pole, ſur le <lb/>Plan déclinant qui eſt en cet exemple de 27 d. </s> <s xml:id="echoid-s10390" xml:space="preserve">38 m. </s> <s xml:id="echoid-s10391" xml:space="preserve">dont le Sinus <lb/>eſt 46381, ainſi la tangente de 7 d. </s> <s xml:id="echoid-s10392" xml:space="preserve">2 m. </s> <s xml:id="echoid-s10393" xml:space="preserve">qui eſt 12337, eſt à un 4<emph style="sub">me</emph> <lb/>nombre, qui ſe trouvera 5722, tangentede 3 d. </s> <s xml:id="echoid-s10394" xml:space="preserve">16 m. </s> <s xml:id="echoid-s10395" xml:space="preserve">& </s> <s xml:id="echoid-s10396" xml:space="preserve">par conſe-<lb/>quent l'angle de la ſouſty laire avec la ligne de 4 h. </s> <s xml:id="echoid-s10397" xml:space="preserve">eſt de 3 d. </s> <s xml:id="echoid-s10398" xml:space="preserve">16 m.</s> <s xml:id="echoid-s10399" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10400" xml:space="preserve">Pour avoir l'angle de 5 h. </s> <s xml:id="echoid-s10401" xml:space="preserve">il faut ajoûter 15 d. </s> <s xml:id="echoid-s10402" xml:space="preserve">à la diſtance horaire <lb/>de 4 h. </s> <s xml:id="echoid-s10403" xml:space="preserve">& </s> <s xml:id="echoid-s10404" xml:space="preserve">chercher la tangente de 22 d. </s> <s xml:id="echoid-s10405" xml:space="preserve">2 m. </s> <s xml:id="echoid-s10406" xml:space="preserve">& </s> <s xml:id="echoid-s10407" xml:space="preserve">ainſi de ſuite.</s> <s xml:id="echoid-s10408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10409" xml:space="preserve">Ce qui étant fait, l'angle de la ſouſtylaire avec la ligne de 5 heures</s> </p> <note position="right" xml:space="preserve"> <lb/>ſera de # # 10 d. # 38 m. <lb/> # Avec la ligne de 6 h. de . . # 19 # 17 <lb/> # Avec la la ligne de 7 h. de . . # 30 # 44 <lb/> # Avec la ligne de 8 h. du ſoir, de . # 47 # 35 <lb/></note> <p> <s xml:id="echoid-s10410" xml:space="preserve">Mais ſi on veut avoir les angles de ces mêmes heures avec la Mé-<lb/> <pb o="318" file="334" n="334" rhead="CONSTRUCTION ET USAGES"/> ridiene, il faut y ajoûter 31 d. </s> <s xml:id="echoid-s10411" xml:space="preserve">35 m. </s> <s xml:id="echoid-s10412" xml:space="preserve">& </s> <s xml:id="echoid-s10413" xml:space="preserve">par conſequent l'angle de la</s> </p> <note position="right" xml:space="preserve"> <lb/> ## ligne de 4 h. avec la Méridiene, ſera de # 34 d. # 51 m. <lb/> # De celle de 5 h # 42 # 13 <lb/> # De celle de 6 h # 50 # 52 <lb/> # De celle de 7 h # 62 # 19 <lb/> # De celle de 8 h # 79 # 10 <lb/></note> <p> <s xml:id="echoid-s10414" xml:space="preserve">Ayant fait un pareil calcul pour les heures qui ſont de l'autre cô-<lb/>te de la ſouſty laire on trouvera que l'angle de ladite ſouſty laire a-</s> </p> <note position="right" xml:space="preserve"> <lb/> ## vec la ligne de 3 h. eſt de # 3 d. # 45 m. <lb/> # Avec la ligne de 2 h. . . . # 11 # 7 <lb/> # Avec la ligne d'une heure. . . # 19 # 54 <lb/> # Avec la ligne de 12 h. . . . # 31 # 35 <lb/> # Avec la ligne de 11 h. . . . # 48 # 54 <lb/> # Avec la ligne de 10 h. . . . # 75 # 7 <lb/> # Avec celle de 9 heures. . . . # 106 # 48 <lb/></note> <p> <s xml:id="echoid-s10415" xml:space="preserve">De ces derniers angles ſi on ſouſtrait 31 d. </s> <s xml:id="echoid-s10416" xml:space="preserve">35 m. </s> <s xml:id="echoid-s10417" xml:space="preserve">trouvez entre la <lb/>ſouſtylaire & </s> <s xml:id="echoid-s10418" xml:space="preserve">la Méridiene, on connoîtra que l'angle de la ligne de</s> </p> <note position="right" xml:space="preserve"> <lb/> ## 9 h. avec la Méridiene eſt de # 75 d. # 13 m. <lb/> # Celui de la ligne de 10 h. . . # 43 # 32 <lb/> # Celui de la ligne de 11 h. . . # 17 # 19 <lb/> # Et ainſi des autres. <lb/></note> <p> <s xml:id="echoid-s10419" xml:space="preserve">Lorſque la déclinaiſon du Plan eſt fort grande, on ne peut com-<lb/>modément y marquer le centre, parce que les lignes horaires y ſont <lb/>trop ſerrées, mais en ce cas on les tracera entre deux lignes horiſon-<lb/>tales, & </s> <s xml:id="echoid-s10420" xml:space="preserve">les angles des lignes horaires au deſſus deſdites horiſonta-<lb/>les ſeront les complémens de ceux qu'elles feroient avec la Méri-<lb/>diene au centre du Cadran vertical.</s> <s xml:id="echoid-s10421" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div646" type="section" level="1" n="333"> <head xml:id="echoid-head466" style="it" xml:space="preserve">Méthode pour connoitre la déclinaiſon d'un Mur vertical par <lb/>le calcul de la Trigonométrie, & par quelques points <lb/>d'ombre obſervez.</head> <p> <s xml:id="echoid-s10422" xml:space="preserve">COmme la juſteſſe des Cadrans verticaux dépend principale-<lb/>ment de la connoiſſance qu'il faut avoir de la ſituation des <lb/>Murs ſur leſquels on veut les conſtruire à l'égard du Ciel, c'eſt-à-<lb/>dire, de leur déclinaiſon, il eſt à propos de chercher à la connoî-<lb/>tre avec toute l'exactitude poſſible; </s> <s xml:id="echoid-s10423" xml:space="preserve">ce que nons allons faire avant <lb/>que de finir ce Chapitre.</s> <s xml:id="echoid-s10424" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div647" type="section" level="1" n="334"> <head xml:id="echoid-head467" xml:space="preserve"><emph style="sc">Preparations</emph>.</head> <p> <s xml:id="echoid-s10425" xml:space="preserve">Il faut premierement planter obliquement dans le Mur une ver-<lb/>ge de fer, dont l'extremité qui eſt en l'air ſoit pointuë & </s> <s xml:id="echoid-s10426" xml:space="preserve">aſſez éloi-<lb/> <pb o="319" file="335" n="335" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> gnée dudit Mur, comme eſt la verge AI, dont la pointe ou extre-<lb/> <anchor type="note" xlink:label="note-335-01a" xlink:href="note-335-01"/> mité pointuë eſt I.</s> <s xml:id="echoid-s10427" xml:space="preserve"/> </p> <div xml:id="echoid-div647" type="float" level="2" n="1"> <note position="right" xlink:label="note-335-01" xlink:href="note-335-01a" xml:space="preserve">XXIII. <lb/>Planche. <lb/>Fig.2.</note> </div> <p> <s xml:id="echoid-s10428" xml:space="preserve">Secondement, il faut marquer le pied du ſtyle H, qui eſt un <lb/>point de la ſurface du Cadran où elle eſt rencontrêe par la perpen-<lb/>diculaire, menée de l'extremité du ſtyle I H, & </s> <s xml:id="echoid-s10429" xml:space="preserve">tracer la verticale <lb/>HF qui paſſe par ce point, & </s> <s xml:id="echoid-s10430" xml:space="preserve">qui repreſente le vertical perpendi-<lb/>culaire au Plan du Cadran, il faut auſſi tracer la ligne horiſontale <lb/>DC qui coupe à angles droits cette verticale au pied du ſtyle H.</s> <s xml:id="echoid-s10431" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10432" xml:space="preserve">Vous meſurerez enſuite exactement la longueur du ſtyle droit HI <lb/>ou HF ſon égale; </s> <s xml:id="echoid-s10433" xml:space="preserve">c'eſt-à-dire, la diſtance du pied du ſtyle a ſa pointe <lb/>qui eſt en l'air, avecune ɔchelle qui ait de fort petites parties, com-<lb/>me des lignes de pied de Roi.</s> <s xml:id="echoid-s10434" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10435" xml:space="preserve">Ayant marqué ſur le Mur pluſieurs points d'ombre en un beau <lb/>jour, comme les points 2, 3, 4, on meſure avec la même échelle <lb/>la diſtance de chaque point d'ombre à la ligne horiſontale, comme <lb/>ici, par exemple, la diſtance du point d'ombre 2, au point Z ſur <lb/>l'horiſontale; </s> <s xml:id="echoid-s10436" xml:space="preserve">& </s> <s xml:id="echoid-s10437" xml:space="preserve">de même la diſtance du même point à la vertica-<lb/>le qui paſſe par le pied du ſtyle, comme ici du point 2 au point X; <lb/></s> <s xml:id="echoid-s10438" xml:space="preserve">on ecrit les nombres qui expriment ces diſtances avec ordre ſur un <lb/>Memoire, pour en faire les Analogies ſuivantes.</s> <s xml:id="echoid-s10439" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10440" xml:space="preserve">Pour marquer ces points d'ombre avec préciſion & </s> <s xml:id="echoid-s10441" xml:space="preserve">juſteſſe, on <lb/>ſe ſervira de la méthode ſuivante, que nous tenons de M. </s> <s xml:id="echoid-s10442" xml:space="preserve">de la <lb/>Hire. </s> <s xml:id="echoid-s10443" xml:space="preserve">On attache vers la pointe du ſtyle une petite platine de fer <lb/>blanc, ou de quelque autre étofe très-mince, qui eſt percée d'un <lb/>petit trou rond, en ſorte que le centre de ce petit trou touche exac-<lb/>tement la pointe du ſtyle; </s> <s xml:id="echoid-s10444" xml:space="preserve">& </s> <s xml:id="echoid-s10445" xml:space="preserve">que la platine ſoit expoſée directe-<lb/>ment au Soleil; </s> <s xml:id="echoid-s10446" xml:space="preserve">on verra ſur la ſurface du Cadran une petite ovale <lb/>de lumiere qui paroîtra dans l'ombre de la Platine. </s> <s xml:id="echoid-s10447" xml:space="preserve">Cette obſer-<lb/>vation ſe fait en traçant promtement avec un craïon un trait leger <lb/>autour de cette ovale de lumiere, qui change continuellement de <lb/>place; </s> <s xml:id="echoid-s10448" xml:space="preserve">le centre de cette ovale ſe peut prendre pour la veritable om-<lb/>bre de la pointe du ſtyle.</s> <s xml:id="echoid-s10449" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10450" xml:space="preserve">Ayant ainſi marqué pluſieurs points d'ombre, il faut trouver par <lb/>le calcul l'amplitude & </s> <s xml:id="echoid-s10451" xml:space="preserve">la hauteur du Soleil qui conviennent à cha-<lb/>cun, & </s> <s xml:id="echoid-s10452" xml:space="preserve">les cotter ſur le Memoire.</s> <s xml:id="echoid-s10453" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10454" xml:space="preserve">On appelle ici amplitude l'angle que la hauteur du ſtyle fait avec <lb/>la ligne tirée de chaque point d'ombre à la ligne horiſontale; </s> <s xml:id="echoid-s10455" xml:space="preserve">cha-<lb/>cune de ces lignes repreſente ſur le Mur le vertical du Soleil au <lb/>tems de l'obſervation; </s> <s xml:id="echoid-s10456" xml:space="preserve">cet angle eſt marqué dans ladite figure HFZ, <lb/>& </s> <s xml:id="echoid-s10457" xml:space="preserve">c'eſt l'amplitude qui convient au point 2.</s> <s xml:id="echoid-s10458" xml:space="preserve"/> </p> <pb o="320" file="336" n="336" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s10459" xml:space="preserve">Pour avoir cet angle, on dira, comme la hauteur du ſtyle eſt à <lb/>la diſtance du point d'ombre à la ligne verticale; </s> <s xml:id="echoid-s10460" xml:space="preserve">ainſi le raïon <lb/>eſt à la tangente.</s> <s xml:id="echoid-s10461" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10462" xml:space="preserve">On fera cette Analogie pour chaque point d'ombre, & </s> <s xml:id="echoid-s10463" xml:space="preserve">on aura <lb/>les amplitudes dont on fera une colonne.</s> <s xml:id="echoid-s10464" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10465" xml:space="preserve">Enſuite pour trouver la hauteur du Soleil ſur l'horiſon, il faut <lb/>prendre le complément de l'amplitude & </s> <s xml:id="echoid-s10466" xml:space="preserve">la diſtance de chaque <lb/>point d'ombre à la ligne horiſontale, & </s> <s xml:id="echoid-s10467" xml:space="preserve">dire: </s> <s xml:id="echoid-s10468" xml:space="preserve">Comme la hauteur <lb/>du ſtyle eſt au Sinus du complément de l'amplitude; </s> <s xml:id="echoid-s10469" xml:space="preserve">ainſi la diſtan-<lb/>ce du point d'ombre à la ligne horiſontale eſt à la tangente de la <lb/>hauteur du Soleil ſur l'horiſon.</s> <s xml:id="echoid-s10470" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10471" xml:space="preserve">Ayant trouvé l'élevation du Soleil pour chaque point d'ombre, <lb/>on en fera une colonne.</s> <s xml:id="echoid-s10472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10473" xml:space="preserve">Si le point d'ombre obſervé ſe rencontre ſur la verticale qui paſ-<lb/>ſe par le pied du ſtyle, il n'y aura point d'amplitude, & </s> <s xml:id="echoid-s10474" xml:space="preserve">l'on aura <lb/>par une ſeule Regle la hauteur du Soleil, en diſant. </s> <s xml:id="echoid-s10475" xml:space="preserve">Comme la hau-<lb/>teur du ſtyle eſt à la diſtance du point d'ombre au pied du ſtyle; </s> <s xml:id="echoid-s10476" xml:space="preserve">ainſi <lb/>le raïon eſt à la tangente de la hauteur du Soleil.</s> <s xml:id="echoid-s10477" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10478" xml:space="preserve">A près quoi il faut trouver la diſtance de chaque vertical ou azi-<lb/>muth obſervé au Méridien; </s> <s xml:id="echoid-s10479" xml:space="preserve">& </s> <s xml:id="echoid-s10480" xml:space="preserve">pour y parvenir il ſaut avoir la dé-<lb/>clinaiſon du Soleil pour le tems auquel on a pris les points d'om-<lb/>bre: </s> <s xml:id="echoid-s10481" xml:space="preserve">ſi c'eſt pendant les Solſtices, la même déclinaiſon ſervira pour <lb/>tous les points d'ombre obſervez dans un même jour; </s> <s xml:id="echoid-s10482" xml:space="preserve">mais dans <lb/>le tems des Equinoxes, il faut avoir la déclinaiſon du Soleil pour <lb/>l'heure qu'on a obſervé chaque point d'ombre, en prenant les par-<lb/>ties proportionelles, comme il eſt expliqué dans le Livre de la Con-<lb/>noiſſance des Tems.</s> <s xml:id="echoid-s10483" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10484" xml:space="preserve">Ayant la déclinaiſon du Soleil, on en prendra le complément, <lb/>comme auſſi le complément de la hauteur du Pole, & </s> <s xml:id="echoid-s10485" xml:space="preserve">le complé-<lb/>ment de la hauteur du Soleil.</s> <s xml:id="echoid-s10486" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10487" xml:space="preserve">On ajoûte enſemble ces trois complémens; </s> <s xml:id="echoid-s10488" xml:space="preserve">du produit on en <lb/>prend la moitié; </s> <s xml:id="echoid-s10489" xml:space="preserve">de cette moitié on en ôte le complément de la hau-<lb/>teur du Soleil, pour avoir la premiere difference; </s> <s xml:id="echoid-s10490" xml:space="preserve">on ôte encore de <lb/>cette même moitié le complément de l'élevation du Pole, pour a-<lb/>voir une ſeconde difference, & </s> <s xml:id="echoid-s10491" xml:space="preserve">l'on en forme les deux Analogies <lb/>ſuivantes.</s> <s xml:id="echoid-s10492" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10493" xml:space="preserve">Comme le Sinus de complément de l'élevation du Pole eſt au <lb/>Sinus de la premiere difference; </s> <s xml:id="echoid-s10494" xml:space="preserve">ainſi le Sinus de la deuxiéme dif-<lb/>ference eſt à un quatriéme Sinus.</s> <s xml:id="echoid-s10495" xml:space="preserve"/> </p> <pb o="321" file="337" n="337" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> <p> <s xml:id="echoid-s10496" xml:space="preserve">Comme le Sinus de complément de la hauteur du Soleil eſt au Si-<lb/>nus total, ainſi le quatriéme Sinus trouvé ci-devant eſt à un autre <lb/>Sinus, qu'il faut multiplier par le Sinus total, & </s> <s xml:id="echoid-s10497" xml:space="preserve">du produit en pren-<lb/>dre la racine quarrée, laquelle ſera le Sinus de la motié de la diſtan-<lb/>ce du point d'ombre obſervé, ou de ſon vertical à la Méridiene ou <lb/>ligne de 12 heures.</s> <s xml:id="echoid-s10498" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10499" xml:space="preserve">Ayant donc cherché ce Sinus dans les Tables, & </s> <s xml:id="echoid-s10500" xml:space="preserve">ayant trouvé <lb/>les degrez & </s> <s xml:id="echoid-s10501" xml:space="preserve">minutés auſquels ils répond, il faut doubler ces degrez <lb/>& </s> <s xml:id="echoid-s10502" xml:space="preserve">minutes pour avoir la diſtance au Méridien.</s> <s xml:id="echoid-s10503" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10504" xml:space="preserve">Enfin pour avoir la déclinaiſon du Mur qui eſt ici marquée par <lb/>l'angle HFE, il y a cinq cas que nous allons expliquer par la ſuſ-<lb/>dite figure, qui repreſente un vertical déclinant du Midi à l'Oc-<lb/>cident.</s> <s xml:id="echoid-s10505" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10506" xml:space="preserve">En premier lieu, ſi le point d'ombre eſt entrele vertical qui paſſe <lb/>par le pied du ſtyle & </s> <s xml:id="echoid-s10507" xml:space="preserve">la ligne de 12 h. </s> <s xml:id="echoid-s10508" xml:space="preserve">comme eſt ici le point 2 que <lb/>je ſuppoſe avoir été obſervé quelque tems après midi, il faut ajoû-<lb/>ter l'amplitude à la diſtance du vertical au Méridien.</s> <s xml:id="echoid-s10509" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10510" xml:space="preserve">2°. </s> <s xml:id="echoid-s10511" xml:space="preserve">Si le point d'ombre eſt au-delà du vertical qui paſſe par le <lb/>pied du Stile, comme eſt ici le point 3, il faut ſouſtraire l'amplitu-<lb/>de de la diſtance au Méridien pour avoir la déclinaiſon.</s> <s xml:id="echoid-s10512" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10513" xml:space="preserve">3°. </s> <s xml:id="echoid-s10514" xml:space="preserve">Si le point d'ombre obſervé ſe trouve préciſement ſur le ver-<lb/>tical qui paſſe parle pied du ſtyle, il n'y a point d'amplitude, & </s> <s xml:id="echoid-s10515" xml:space="preserve">ſa <lb/>diſtance au Méridien ſera la déclinaiſon du Mur.</s> <s xml:id="echoid-s10516" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10517" xml:space="preserve">4°. </s> <s xml:id="echoid-s10518" xml:space="preserve">Si le point d'ombre eſt au-delà du Méridien, comme eſt ici <lb/>le point 4, que je ſuppoſe avoir été obſervé avant midi, l'amplitu-<lb/>de ſera plus grande que la déclinaiſon, & </s> <s xml:id="echoid-s10519" xml:space="preserve">pour l'avoir, il faudroit <lb/>ſouſtraire la diſtance au Méridien de l'amplitude.</s> <s xml:id="echoid-s10520" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10521" xml:space="preserve">En cinquiéme & </s> <s xml:id="echoid-s10522" xml:space="preserve">dernier lieu, ſi le point d'ombre étoit obſervé <lb/>préciſément à l'heure de Midi, la déclinaiſon du Mur ſeroit égale à <lb/>l'amplitude; </s> <s xml:id="echoid-s10523" xml:space="preserve">& </s> <s xml:id="echoid-s10524" xml:space="preserve">comme je ſuppoſe que l'on connoît la déclinaiſon <lb/>du Soleil & </s> <s xml:id="echoid-s10525" xml:space="preserve">la hauteur du Pole du lieu, il ſera facile de connoître ſi <lb/>la hauteur du Soleil obſervée eſt la plus grande du jour, ou la hau-<lb/>teur Méridiene.</s> <s xml:id="echoid-s10526" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10527" xml:space="preserve">Ce que nous venons de dire peut s'appliquer ſans peine à toute <lb/>ſorte de déclinaiſon, ſoit vers l'Orient, ſoit vers l'Occident, en <lb/>obſervant que la ligne de mi-nuit tient lieu de celle de midi pour <lb/>les Murs qui déclinent du Septentrion à l'Orient où à l'Occident</s> </p> <p> <s xml:id="echoid-s10528" xml:space="preserve">Un exemple éclaircira ce que nous venons de dire: </s> <s xml:id="echoid-s10529" xml:space="preserve">Suppoſons <lb/>pour cet effet, que dans un lieu où le Pole Septentrional eſt élevé de <lb/>48 deg. </s> <s xml:id="echoid-s10530" xml:space="preserve">50 m. </s> <s xml:id="echoid-s10531" xml:space="preserve">nous ayons obſervé un point d'ombre ſur un Mur <lb/> <pb o="422" file="338" n="338" rhead="CONSTRUCTION ET USAGES"/> bien vertical aux environs du Solſtice d'Eté, ſoit la hauteur du ſty-<lb/>le de 300 parties égales, & </s> <s xml:id="echoid-s10532" xml:space="preserve">la diſtance du point d'ombre au verti-<lb/>cal qui paſſe par le pied du ſtyle, de 100 des mêmes parties.</s> <s xml:id="echoid-s10533" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div649" type="section" level="1" n="335"> <head xml:id="echoid-head468" style="it" xml:space="preserve">Operation par les Logarithmes.</head> <note position="right" xml:space="preserve"> <lb/> ## Logarithme de 100. # 20000000 <lb/> ## Logarithme Sinus total. # 100000000 <lb/> # Somme # 120000000 <lb/> ## Logarithme de 300. # 24771212 <lb/> # Reſte # 95228788 <lb/></note> <p> <s xml:id="echoid-s10534" xml:space="preserve">Ce nombre reſtant eſt logarithme tangente de 18 d. </s> <s xml:id="echoid-s10535" xml:space="preserve">26 m. </s> <s xml:id="echoid-s10536" xml:space="preserve">pour <lb/>l'amplitude du point obſervé, & </s> <s xml:id="echoid-s10537" xml:space="preserve">ſon complément 71 d. </s> <s xml:id="echoid-s10538" xml:space="preserve">34 m.</s> <s xml:id="echoid-s10539" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10540" xml:space="preserve">Enſuite pour trouver la hauteur du Soleil ſur l'horiſon, je ſup-<lb/>poſe la diſtance du point d'ombre obſervé à la ligne horiſontale de <lb/>600 des mêmes parties.</s> <s xml:id="echoid-s10541" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/> ## Logarithme Sinus de 71 d. 34 m. # 99771253 <lb/> ## Logarithme de 600. # 27781512 <lb/> # Somme # 127552765 <lb/> ## Logarithme de 300. # 24771212 <lb/> # Reſte # 102781553 <lb/></note> <p> <s xml:id="echoid-s10542" xml:space="preserve">Ce nombre reſtant eſt logarithme tangente de 62 d. </s> <s xml:id="echoid-s10543" xml:space="preserve">13 m. </s> <s xml:id="echoid-s10544" xml:space="preserve">pour <lb/>la hauteur du Soleil.</s> <s xml:id="echoid-s10545" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Suppoſant donc la hauteur du Pole # 48 d. # 50 m. <lb/>La déclinaiſon Septentrionale du Soleil # 23 # 15 <lb/>La hauteur du Soleil obſervée # 62 # 13 <lb/></note> </div> <div xml:id="echoid-div650" type="section" level="1" n="336"> <head xml:id="echoid-head469" style="it" xml:space="preserve">Operation pour trouver la diſtance au Méridien.</head> <note position="right" xml:space="preserve"> <lb/> ### Complément de l'élevation du Pole # 41 d. # 10 m. <lb/> ### Complément de la déclinaiſon du Soleil # 66 # 45 <lb/> ### Complément de la hauteur du Soleil # 27 # 47 <lb/> # # Somme # 135 # 42 <lb/> ### Moitié de ladite ſomme # 67 # 51 <lb/> ### Otant le complément de l'élevation du Pole # 41 # 10 <lb/> # ## Premiere difference # 26 # 41 <lb/></note> <pb o="323" file="339" n="339" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. I."/> <note position="right" xml:space="preserve"> <lb/> ## Otant encore de # 67 d. # 51 m. <lb/> ## Le complément de la hauteur du Soleil # 27 # 47 <lb/> # Seconde difference # 40 # 4 <lb/></note> </div> <div xml:id="echoid-div651" type="section" level="1" n="337"> <head xml:id="echoid-head470" xml:space="preserve">PREMIERE ANALOGIE.</head> <note position="right" xml:space="preserve"> <lb/> ### Log. Sin. de la premiere difference # 26 d. 41 m. # 96523035 <lb/> ### Log. Sin. de la ſeconde difference # 40 # 4 # 98086690 <lb/> # # # ### Somme # 194609725 <lb/> ### Oter le logarithme Sinus de # 41 d. # 10 m. # 98183919 <lb/> # #### Quatrieme Sinus reſtant # 96425806 <lb/></note> </div> <div xml:id="echoid-div652" type="section" level="1" n="338"> <head xml:id="echoid-head471" xml:space="preserve">SECONDE ANALOGIE.</head> <note position="right" xml:space="preserve"> <lb/> ##### Logarithme Sinus total # 100000000 <lb/> ##### Quatriéme Sinus # 96425806 <lb/> # # ### Somme # 196425806 <lb/> ### Oter le logarithme Sinus de # 27 d. # 47 m. # 96685064 <lb/> # #### Sinus reſtant # 99740742 <lb/> ##### A multiplier par le Sinus total # 100000000 <lb/> # # # # # 199740742 <lb/> ##### Moitié dudit nombre pour racine quarrée # 99870371 <lb/></note> <p> <s xml:id="echoid-s10546" xml:space="preserve">Ce dernier nombre répond au Sinus logarithme de 76 d. </s> <s xml:id="echoid-s10547" xml:space="preserve">4 m. <lb/></s> <s xml:id="echoid-s10548" xml:space="preserve">lequel étant doublé fait 152 deg. </s> <s xml:id="echoid-s10549" xml:space="preserve">8 m. </s> <s xml:id="echoid-s10550" xml:space="preserve">mais parce que cet angle eſt <lb/>obtus il faut le ſouſtraire de 180, le reſte 27 d. </s> <s xml:id="echoid-s10551" xml:space="preserve">52 m. </s> <s xml:id="echoid-s10552" xml:space="preserve">eſt la diſtan-<lb/>ce du vertical obſervé au Méridien; </s> <s xml:id="echoid-s10553" xml:space="preserve">& </s> <s xml:id="echoid-s10554" xml:space="preserve">comme le point d'ombre 2, <lb/>ſur lequel je ſuppoſe avoir ſait ce calcul, eſt entre le vertical qui <lb/>paſſe par le pied du ſtyle & </s> <s xml:id="echoid-s10555" xml:space="preserve">la ligne de 12 h. </s> <s xml:id="echoid-s10556" xml:space="preserve">il faut ajoûter la ſuſ-<lb/>dite diſtance à l'amplitude calculée 18 deg. </s> <s xml:id="echoid-s10557" xml:space="preserve">26 min. </s> <s xml:id="echoid-s10558" xml:space="preserve">pour avoir la <lb/>déclinaiſon 46 d. </s> <s xml:id="echoid-s10559" xml:space="preserve">18 m.</s> <s xml:id="echoid-s10560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10561" xml:space="preserve">Par un ſeul point d'ombre obſervé bien exactement, on peut <lb/>trouver la déclinaiſon d'un Mur; </s> <s xml:id="echoid-s10562" xml:space="preserve">mais il eſt mieux d'en obſerver <lb/>pluſieurs ſoit en un même jour, ſoit en différens tems, afin qu'ayant <lb/>calculé autant de fois la déclinaiſon, qui y a de points d'ombre ob-<lb/>ſervez, on puiſſe prendre la partie proportionelle des differences, qui <lb/>ne doivent pas néanmoins être conſiderables quand on fait les ope-<lb/>rations exactes; </s> <s xml:id="echoid-s10563" xml:space="preserve">& </s> <s xml:id="echoid-s10564" xml:space="preserve">ſi par exemple on avoit marqué ſix points d'om-<lb/>bre, on prendroit la ſixiéme partie des differences que produiroient <lb/>les calculs, pour en conclure la veritable déclinaiſon du Mur.</s> <s xml:id="echoid-s10565" xml:space="preserve"/> </p> <pb o="324" file="340" n="340" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div653" type="section" level="1" n="339"> <head xml:id="echoid-head472" xml:space="preserve">CHAPITRE II.</head> <head xml:id="echoid-head473" style="it" xml:space="preserve">Contenant la Conſtruction & les Vſages d'un Inſtrument pro-<lb/>pre à connoitre la déclinaiſon & inclinaiſon des Plans.</head> <p> <s xml:id="echoid-s10566" xml:space="preserve">CEt Inſtrument ſe nomme Déclinatoire & </s> <s xml:id="echoid-s10567" xml:space="preserve">Inclinatoire. </s> <s xml:id="echoid-s10568" xml:space="preserve">Il eſt <lb/>fait d'une plaque de cuivre ou de bois ſec, bien unie, de figure <lb/> <anchor type="note" xlink:label="note-340-01a" xlink:href="note-340-01"/> rectangle, d'environ un pied de long & </s> <s xml:id="echoid-s10569" xml:space="preserve">de 7 à 8 pouces de large. </s> <s xml:id="echoid-s10570" xml:space="preserve">On <lb/>trace bien parallelement à un de ſes longs côtez, comme à AB, le <lb/>diametre d'un demi-cercle que l'on diviſe en deux quarts de 90 d. <lb/></s> <s xml:id="echoid-s10571" xml:space="preserve">chacun, leſquels on ſubdiviſe quelquefois en demi-degrez. </s> <s xml:id="echoid-s10572" xml:space="preserve">La di-<lb/>viſion doit commencer du point H, comme on le voit par la figure <lb/>de l'inſtrument On y ajoûte une alidade marquée I, qui tourne au-<lb/>tour du centre G par le moyen d'un clou à tête. </s> <s xml:id="echoid-s10573" xml:space="preserve">On attache avec des <lb/>vis à la ligne de foy de l'alidade, une Bouſſole dont le Nord eſt tour-<lb/>né vers le centre G, & </s> <s xml:id="echoid-s10574" xml:space="preserve">même quelquefois un petit Cadran horiſon-<lb/>tal dont la ligne de 12 h. </s> <s xml:id="echoid-s10575" xml:space="preserve">eſt pareillement tournée vers le centre G. </s> <s xml:id="echoid-s10576" xml:space="preserve">Je <lb/>ne m'arrêterai pas davantage ſur la conſtruction de cet Inſtrument; </s> <s xml:id="echoid-s10577" xml:space="preserve"><lb/>il ſera facile de l'entendre après ce qui a été dit ci-devant.</s> <s xml:id="echoid-s10578" xml:space="preserve"/> </p> <div xml:id="echoid-div653" type="float" level="2" n="1"> <note position="left" xlink:label="note-340-01" xlink:href="note-340-01a" xml:space="preserve">XXIV. <lb/>Planche. <lb/>Fig. 1.</note> </div> </div> <div xml:id="echoid-div655" type="section" level="1" n="340"> <head xml:id="echoid-head474" style="it" xml:space="preserve">Vſage du Déclinatoire.</head> <p> <s xml:id="echoid-s10579" xml:space="preserve">UN Plan eſt dit déclinant lorſqu'il n'eſt pas tourné directément <lb/>vers une des 4 parties cardinales du Monde, qui ſont le Sep-<lb/>tentrion, le Midi, l'Orient & </s> <s xml:id="echoid-s10580" xml:space="preserve">l'Occident: </s> <s xml:id="echoid-s10581" xml:space="preserve">& </s> <s xml:id="echoid-s10582" xml:space="preserve">la déclinaiſon ſe meſu-<lb/>re par l'arc de l'horiſon compris entre le premier vertical & </s> <s xml:id="echoid-s10583" xml:space="preserve">le verti-<lb/>cal parallele au Plan, s'il eſt vertical, c'eſt-à-dire, perpendiculaire à <lb/>l'horiſon: </s> <s xml:id="echoid-s10584" xml:space="preserve">car ſi le Plan eſt incliné il ne peut être parallele à aucun <lb/>vertical, ſi ne n'eſt par ſa baſe; </s> <s xml:id="echoid-s10585" xml:space="preserve">& </s> <s xml:id="echoid-s10586" xml:space="preserve">pour lors l'arc de l'horiſon com-<lb/>pris entre le premier vertical & </s> <s xml:id="echoid-s10587" xml:space="preserve">celui qui eſt parallele à la baſe du <lb/>Plan incliné, eſt la meſure de ſa déclinaiſon ou bien l'arc de l'hori-<lb/>ſon, compris entre le Méridien du lieu & </s> <s xml:id="echoid-s10588" xml:space="preserve">le vertical perpendiculai-<lb/>re au Plan.</s> <s xml:id="echoid-s10589" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10590" xml:space="preserve">Il n'y a que les Plans verticaux ou inclinez qui puiſlent être dé-<lb/>clinans; </s> <s xml:id="echoid-s10591" xml:space="preserve">car pour l'horiſontal il ne peut décliner, parce que ſa face <lb/>ſupérieure regardant directement le Zénith, ſon Plan eſt tourné in-<lb/>differemment vers les quatre parties cardinales du Monde.</s> <s xml:id="echoid-s10592" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10593" xml:space="preserve">Pour connoître la déclinaiſon d'un Plan, ſoit vertical, ſoit incli-<lb/>né, tracez-y une ligne de niveau, c'eſt-à dire, parallele à l'horiſon; <lb/></s> <s xml:id="echoid-s10594" xml:space="preserve">appliquez le long de cette ligne le côté AB de l'inſtrument, & </s> <s xml:id="echoid-s10595" xml:space="preserve">tour-<lb/>nez l'alidade avec la Bouſſole, juſqu'à ce que l'éguille aimantée s'ar-<lb/> <pb o="325" file="341" n="341" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch.. II."/> rête juſtement ſur ſa ligne de déclinaiſon qui doit être marquée au <lb/>fond de la Bouſſole; </s> <s xml:id="echoid-s10596" xml:space="preserve">cela étant, le nombre des degrez coupez par la <lb/>ligne de foi de l'alidade marquera la déclinaiſon du Plan vers la <lb/>partie du Monde, indiquée par l'écriture gravée ſur le déclinatoire. <lb/></s> <s xml:id="echoid-s10597" xml:space="preserve">Si, par exemple, l'Alidade ſe trouve arrêtée entre H & </s> <s xml:id="echoid-s10598" xml:space="preserve">B, ſur le 45<emph style="sub">me</emph> <lb/>d. </s> <s xml:id="echoid-s10599" xml:space="preserve">& </s> <s xml:id="echoid-s10600" xml:space="preserve">ſi le bout de l'éguille qui marque le Nord ou le Septentrion, <lb/>eſt directement ſur le point S de ſa ligne de déclinaiſon, le Plan dé-<lb/>cline de 45 d. </s> <s xml:id="echoid-s10601" xml:space="preserve">du Midi à l'Occident; </s> <s xml:id="echoid-s10602" xml:space="preserve">mais ſi dans cette même ſi-<lb/>tuation du déclinatoire, le bout oppoſé de l'éguille qui marque le <lb/>Midi étoit arrêté ſur le point S de ladite ligne de déclinaiſon, le Plan <lb/>obſervé déclineroit de 45 deg. </s> <s xml:id="echoid-s10603" xml:space="preserve">du Septentrion à l'Orient.</s> <s xml:id="echoid-s10604" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10605" xml:space="preserve">Si l'alidade ſe trouve entre A & </s> <s xml:id="echoid-s10606" xml:space="preserve">H, & </s> <s xml:id="echoid-s10607" xml:space="preserve">le Nord de l'éguille ſur le <lb/>point S, la déclinaiſon du Plan ſera du Midi à l'Orient; </s> <s xml:id="echoid-s10608" xml:space="preserve">mais ſi dans <lb/>cette ſituation de l'alidade, le Midi de l'éguille eſt arrêté ſur ledit <lb/>point S, le Plan décline du Septentrion à l'Occident.</s> <s xml:id="echoid-s10609" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10610" xml:space="preserve">Si le lieu où l'on fait l'obſervation étoit éclairé du Soleil, & </s> <s xml:id="echoid-s10611" xml:space="preserve">qu'on <lb/>fût aſſuré de l'heure preſente par quelque bon Cadran, comme par <lb/>un anneau aſtronomique, on pourroit trouver la déclinaiſon du mur <lb/>ou Plan propoſé, par le moyen du petit Cadran horiſontal attaché à <lb/>l'alidade, laquelle on feroit tourner juſqu'à ce que le ſtyle de ce Ca-<lb/>dran marquât l'heure juſte, & </s> <s xml:id="echoid-s10612" xml:space="preserve">pour lors les degrez du quart de cercle <lb/>qui ſeroit à l'interſection de la ligne de foi de l'alidade, feroient con-<lb/>noître la déclinaiſon, & </s> <s xml:id="echoid-s10613" xml:space="preserve">par ce moyen on éviteroit les erreurs que <lb/>peut cauſer la Bouſſole, tant par la variation de l'aiman, que par <lb/>l'approche du fer qui peut être caché dans les murs.</s> <s xml:id="echoid-s10614" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10615" xml:space="preserve">Lorſqu'un mur eſt éclairé du Soleil, on peut trouver la ſouſtylaire <lb/>ou Méridiene propre, par le moyen de deux points d'ombre obſervez <lb/>de la maniere que nous avons dit, & </s> <s xml:id="echoid-s10616" xml:space="preserve">enſuite ſa déclinaiſon; </s> <s xml:id="echoid-s10617" xml:space="preserve">ou bien <lb/>l'on peut t<unsure/>racer une ligne Méridiene ſur un Plan horiſontal proche <lb/>dudit mur, laquelle étant prolongée juſqu'à ſon rencontre, ſervira à <lb/>connoître ſa déclinaiſon, comme auſſi la variation de l'éguille ai-<lb/>mantée en la maniere qui ſuit.</s> <s xml:id="echoid-s10618" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10619" xml:space="preserve">Tracez un cercle ſur un Plan de niveau, comme il eſt repreſenté <lb/>par la figure M, placez un ſtyle pointu & </s> <s xml:id="echoid-s10620" xml:space="preserve">bien perpendiculaire à ſon <lb/> <anchor type="note" xlink:label="note-341-01a" xlink:href="note-341-01"/> centre, ou bien plantez un ſtyle courbé en quelqu'endroit, comme <lb/>en A, de maniere que ſon extremité pointuë réponde juſtement au <lb/>centre du cercle; </s> <s xml:id="echoid-s10621" xml:space="preserve">ce qu'il ſera facile de faire par le moyen d'une E-<lb/>querre. </s> <s xml:id="echoid-s10622" xml:space="preserve">Avant que de tracer ce cercle il eſt à propos de voir la lon-<lb/>gueur de l'ombre de vôtre ſtyle, afin de faire paſſer ſa circonference <lb/>par le premier point d'ombre quelques heures avant midi; </s> <s xml:id="echoid-s10623" xml:space="preserve">lorſque <lb/> <pb o="326" file="342" n="342" rhead="CONSTRUCTION ET USAGES"/> l'ombre de l'extremité du ſtyle touchera la circonference du cercle, <lb/>marquez-y un point comme G; </s> <s xml:id="echoid-s10624" xml:space="preserve">l'ombre ſe racourcira juſqu'à midi, <lb/>& </s> <s xml:id="echoid-s10625" xml:space="preserve">enſuite ſe ralongera quelques heures après; </s> <s xml:id="echoid-s10626" xml:space="preserve">lorſqu'elle touchera <lb/>encore une fois la circonference du même cercle, marquez-y un ſe-<lb/>cond point comme F; </s> <s xml:id="echoid-s10627" xml:space="preserve">diviſez l'arc FG en deux parties égales, & </s> <s xml:id="echoid-s10628" xml:space="preserve">par <lb/>ſon milieu C, tirez le diametre BC, qui ſera la Méridiene.</s> <s xml:id="echoid-s10629" xml:space="preserve"/> </p> <div xml:id="echoid-div655" type="float" level="2" n="1"> <note position="right" xlink:label="note-341-01" xlink:href="note-341-01a" xml:space="preserve">Fig. M.</note> </div> <p> <s xml:id="echoid-s10630" xml:space="preserve">Si cette operation ſe faiſoit au tems des Equinoxes, il ne ſeroit pas <lb/>beſoin de tracer de cercle, car tous les points d'ombre ſeroient en li-<lb/>gne droite, comme ED, qui ſeroit la commune ſection de l'Equa-<lb/>teur & </s> <s xml:id="echoid-s10631" xml:space="preserve">du Plan, & </s> <s xml:id="echoid-s10632" xml:space="preserve">toute ligne, la coupant à angles droits, comme <lb/>BC, ſeroit la Méridiene du Plan horiſontal.</s> <s xml:id="echoid-s10633" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10634" xml:space="preserve">Ayant donc une Méridiene tracée, ſi on y applique un Cadran ho-<lb/>riſontal, dont le Midi ſoit tourné vers C, qui repreſente le Nord, on <lb/>connoîtra l'heure preſente, & </s> <s xml:id="echoid-s10635" xml:space="preserve">on tournera en même tems l'alidade, <lb/>en ſorte que le petit Cadran qui y eſt attaché marque la même heu-<lb/>re, pour lors les degrez de la circonference du déclinatoire, cou-<lb/>pez par l'alidade, vous feront connoître la déclinaiſon du Mur ou <lb/>du Plan.</s> <s xml:id="echoid-s10636" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10637" xml:space="preserve">Ou bien ſi vous prolongez la ſuſdite Méridiene juſqu'au rencon-<lb/>tre du Plan déclinant, elle fera 2 angles inégaux avec la ligne hori-<lb/>ſontale que vous y aurez tracée, ſçavoir, l'un aigu & </s> <s xml:id="echoid-s10638" xml:space="preserve">l'autre obtus, <lb/>que vous meſurerez le plus juſte qu'il vous ſera poſſible; </s> <s xml:id="echoid-s10639" xml:space="preserve">la differen-<lb/>ce de l'un ou l'autre de ces 2 angles, à l'angle droit, ſera la déclinai-<lb/>ſon du Plan. </s> <s xml:id="echoid-s10640" xml:space="preserve">Si, par exemple, l'angle aigu étoit de 50 d. </s> <s xml:id="echoid-s10641" xml:space="preserve">& </s> <s xml:id="echoid-s10642" xml:space="preserve">l'obtus <lb/>par conſequent de 130, leur difference à l'angle droit, ſeroit 40 d. <lb/></s> <s xml:id="echoid-s10643" xml:space="preserve">pour ladite déclinaiſon.</s> <s xml:id="echoid-s10644" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10645" xml:space="preserve">Pour obſerver la variation de l'éguille aimantée, appliquez un des <lb/>côtez de la plaque quarrée de la Bouſſole au long de la ligne Meri-<lb/>diene tracée ſur le Plan; </s> <s xml:id="echoid-s10646" xml:space="preserve">lorſque l'éguille ſera arrêtée, remarquez de <lb/>combien de degrez ſa pointe qui marque le Nord, ſera éloignée de <lb/>la Fleur-de-Lys qui eſt à la Bouſſole, & </s> <s xml:id="echoid-s10647" xml:space="preserve">par ce moyen vous con-<lb/>noîtrez la variation ou déclinaiſon de l'aiman; </s> <s xml:id="echoid-s10648" xml:space="preserve">mais ce ne ſera pas <lb/>pour long-tems, car elle change toûjours. </s> <s xml:id="echoid-s10649" xml:space="preserve">Quand on prend la dé-<lb/>clinaiſon des Plans avec la Bouſſole, il faut avoir égard à la varia-<lb/>tion de l'éguille aimantée, en la laiſſant arrêter ſur une ligne qui <lb/>marque ſa variation, & </s> <s xml:id="echoid-s10650" xml:space="preserve">que l'on trace ordinairement au fond de la <lb/>boëte de la Bouſſole.</s> <s xml:id="echoid-s10651" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div657" type="section" level="1" n="341"> <head xml:id="echoid-head475" style="it" xml:space="preserve">Uſage de l'Inclinatoire.</head> <p> <s xml:id="echoid-s10652" xml:space="preserve">LE même inſtrument qui ſert à prendre la déclinaiſon des Plans, <lb/>ſert auſſi à prendre leur inclinaiſon, c'eſt-à-dire, l'angle que fait <lb/> <pb o="327" file="343" n="343" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. II."/> le Plan avec l'horiſon, & </s> <s xml:id="echoid-s10653" xml:space="preserve">pour cet effet il y a un petit trou au centre <lb/>G, où l'on paſſe une ſoie, au bout de laquelle il y a un plomb.</s> <s xml:id="echoid-s10654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10655" xml:space="preserve">La figure 2, fait connoître la maniere de prendre la déclinaiſon <lb/>& </s> <s xml:id="echoid-s10656" xml:space="preserve">l'inclinaiſon des Plans.</s> <s xml:id="echoid-s10657" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10658" xml:space="preserve">Le Plan A, où eſt appliqué le déclinatoire eſt un Plan vertical <lb/>Méridional ſans déclinaiſon.</s> <s xml:id="echoid-s10659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10660" xml:space="preserve">Le Plan B décline du Midi à l'Occident de 45 deg.</s> <s xml:id="echoid-s10661" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10662" xml:space="preserve">Le Plan C eſt un Occidental étant tourné directement au cou-<lb/> <anchor type="note" xlink:label="note-343-01a" xlink:href="note-343-01"/> chant.</s> <s xml:id="echoid-s10663" xml:space="preserve"/> </p> <div xml:id="echoid-div657" type="float" level="2" n="1"> <note position="right" xlink:label="note-343-01" xlink:href="note-343-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s10664" xml:space="preserve">Le Plan D eſt un déclinant du Septentron à l'Occident de 45 d.</s> <s xml:id="echoid-s10665" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10666" xml:space="preserve">Les autres déclinaiſons plus ou moins grandes ſe prennent de la <lb/>même maniere en approchant du Mur le côté AB du déclinatoire, <lb/>en ſorte que le Plan du demi-cercle ſoit parallele à l'horiſon.</s> <s xml:id="echoid-s10667" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div659" type="section" level="1" n="342"> <head xml:id="echoid-head476" style="it" xml:space="preserve">Maniere de prendre l'inolinaiſon des Plans</head> <p> <s xml:id="echoid-s10668" xml:space="preserve">P Our meſurer l'angle d'inclinaiſon, il faut approcher du Mur <lb/>quelqu'un des autres côtez du même Inſtrument, & </s> <s xml:id="echoid-s10669" xml:space="preserve">tenir le <lb/>Plan du demi-cercle perpendiculaire a l'horiſon, afin que la ſoie du <lb/>plomb ſuſpenduë au centre, raſant la circonference, y marque la <lb/>valeur dudit angle.</s> <s xml:id="echoid-s10670" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10671" xml:space="preserve">Si, par exemple, on applique le côté C D ſur le Plan E, & </s> <s xml:id="echoid-s10672" xml:space="preserve">que la <lb/>ſoie tombe le long de la ligne GH, c'eſt une marque que ce Plan eſt <lb/>parallele à l'horiſon.</s> <s xml:id="echoid-s10673" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10674" xml:space="preserve">Appliquant le côté CA de l'inſtrument ſur le Plan F, ſi le plomb <lb/>tombe comme la figure lé marque, ce Plan eſt incliné de 45 degrez <lb/>vers le Ciel.</s> <s xml:id="echoid-s10675" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10676" xml:space="preserve">Le même inſtrument appliqué au Plan G, ſile plomb tombe le <lb/>long du diametre, ce Plan eſt vertical.</s> <s xml:id="echoid-s10677" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10678" xml:space="preserve">Enfin, le côte AC étant appliqué ſu le Plan H, & </s> <s xml:id="echoid-s10679" xml:space="preserve">la ſoie du <lb/>plomb tombant comme la figure le montre, marque ſon inclinai-<lb/>ſon de 45 d. </s> <s xml:id="echoid-s10680" xml:space="preserve">vers la Terre.</s> <s xml:id="echoid-s10681" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div660" type="section" level="1" n="343"> <head xml:id="echoid-head477" xml:space="preserve">CHAPITRE III.</head> <head xml:id="echoid-head478" style="it" xml:space="preserve">Contenant la Conſtruction & les Vſages des Inſtrumens propres <lb/>à marquer ſur les Cadrans les Arcs des Signes, les Arcs <lb/>Diurnes, les beures Babyloniques, les heures Italiques, les <lb/>Almucantarats & les Méridiens des principales Villes.</head> <p> <s xml:id="echoid-s10682" xml:space="preserve">IL s'agit preſentement de marquer ſur les Cadrans certaines li-<lb/>gnes que l'ombre de l'extremité du Style parcourera, lorſque <lb/> <pb o="328" file="344" n="344" rhead="CONSTRUCTION ET USAGES"/> le Soleil entrera dans chacun des douze Signes du Zodiaque.</s> <s xml:id="echoid-s10683" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div661" type="section" level="1" n="344"> <head xml:id="echoid-head479" style="it" xml:space="preserve">Du Trigone des Signes.</head> <p> <s xml:id="echoid-s10684" xml:space="preserve">LA figure 3 repreſente le triangle ou trigone des Signes. </s> <s xml:id="echoid-s10685" xml:space="preserve">On le <lb/>fait de cuivre ou de quelque autre matiere ſolide, grand à diſ-<lb/>cretion. </s> <s xml:id="echoid-s10686" xml:space="preserve">Pour le conſtruire tirez premierement la ligne a b, qui re-<lb/> <anchor type="note" xlink:label="note-344-01a" xlink:href="note-344-01"/> preſente l'axe du Monde, & </s> <s xml:id="echoid-s10687" xml:space="preserve">a c perpendiculaire à l'axe, pour re-<lb/>preſenter le raïon de l'Equateur. </s> <s xml:id="echoid-s10688" xml:space="preserve">Du point a, comme centre, tra-<lb/>cez à diſcretion l'arc d c e. </s> <s xml:id="echoid-s10689" xml:space="preserve">Du point c comptez de part & </s> <s xml:id="echoid-s10690" xml:space="preserve">d'autre 23 <lb/>degrez & </s> <s xml:id="echoid-s10691" xml:space="preserve">demi, pour la plus grande déclinaiſon du Soleil, & </s> <s xml:id="echoid-s10692" xml:space="preserve">tirez <lb/>les lignes a d, a e pour les deux tropiques, l'un d'Eté & </s> <s xml:id="echoid-s10693" xml:space="preserve">l'autre d'Hy-<lb/>ver. </s> <s xml:id="echoid-s10694" xml:space="preserve">Tirez auſſi la ligne d e, laquelle ſera diviſée en deux également <lb/>par le raïon de l'Equateur au point o, duquel comme centre, tracez <lb/>un cercle dont la circonference doit paſſer par les points des Tropi-<lb/>ques d & </s> <s xml:id="echoid-s10695" xml:space="preserve">e; </s> <s xml:id="echoid-s10696" xml:space="preserve">diviſez cette circonference en 12 parties egales en com-<lb/>mençant du point d: </s> <s xml:id="echoid-s10697" xml:space="preserve">par chaque point de diviſion également éloi-<lb/>gné des points d & </s> <s xml:id="echoid-s10698" xml:space="preserve">e, tirez des lignes occultes paralleles au raïon <lb/>de l'Equateur, qui marqueront ſur l'arc d c des points, par leſquels <lb/>& </s> <s xml:id="echoid-s10699" xml:space="preserve">du centre a vous titerez des lignes qui repreſenteront les com-<lb/>mencemens des Signes du Zodiaque, diſtans l'un de l'autre de 30 <lb/>deg. </s> <s xml:id="echoid-s10700" xml:space="preserve">Pour les diviſer de 10 en 10 deg. </s> <s xml:id="echoid-s10701" xml:space="preserve">il faut diviſer la circonferen-<lb/>ce du cercle en 36 parties égales, & </s> <s xml:id="echoid-s10702" xml:space="preserve">en 72 pour avoit cette diviſion <lb/>de 5 en 5 deg. </s> <s xml:id="echoid-s10703" xml:space="preserve">On marque les caracteres des Signes ſur chaque li-<lb/>gne, comme on le voit par la figure 4<emph style="sub">me</emph>. </s> <s xml:id="echoid-s10704" xml:space="preserve">Quand le Trigone eſt di-<lb/>viſé de 10 en 10 deg. </s> <s xml:id="echoid-s10705" xml:space="preserve">ou de 5 en 5, à l'endroit de chaque premiere <lb/>dixaine des Signes on met la lettre du mois qui lui convient.</s> <s xml:id="echoid-s10706" xml:space="preserve"/> </p> <div xml:id="echoid-div661" type="float" level="2" n="1"> <note position="left" xlink:label="note-344-01" xlink:href="note-344-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s10707" xml:space="preserve">On peut encore faire ce Trigone des Signes plus promptement, <lb/>par le moyen de la Table des déclinaiſons du Soleil marquées ci-<lb/>après; </s> <s xml:id="echoid-s10708" xml:space="preserve">car ayant tracé les deux lignes a b, a c à angles droits, met-<lb/>tez le centre d'un rapporteur au point A, ſon angle de 90 deg. </s> <s xml:id="echoid-s10709" xml:space="preserve">vers <lb/>le point c, & </s> <s xml:id="echoid-s10710" xml:space="preserve">le tenant ainſi fixement, comptez de part & </s> <s xml:id="echoid-s10711" xml:space="preserve">d'autre <lb/>du raion a c, 23 deg. </s> <s xml:id="echoid-s10712" xml:space="preserve">30 min. </s> <s xml:id="echoid-s10713" xml:space="preserve">pour les Tropiques de 69 & </s> <s xml:id="echoid-s10714" xml:space="preserve">♑ 20 <lb/>d. </s> <s xml:id="echoid-s10715" xml:space="preserve">12 m. </s> <s xml:id="echoid-s10716" xml:space="preserve">pour les commencemens des Signes ♌, Π ♐ & </s> <s xml:id="echoid-s10717" xml:space="preserve">♒, & </s> <s xml:id="echoid-s10718" xml:space="preserve"><lb/>11 d. </s> <s xml:id="echoid-s10719" xml:space="preserve">30 m. </s> <s xml:id="echoid-s10720" xml:space="preserve">pour ♉, ♍, ♏ & </s> <s xml:id="echoid-s10721" xml:space="preserve">♓. </s> <s xml:id="echoid-s10722" xml:space="preserve">On diviſera de même chaque <lb/>eſpace des Signes de 10 en 10 deg. </s> <s xml:id="echoid-s10723" xml:space="preserve">ou de 5 en 5, par les déclinai-<lb/>ſons marquees dans la Table ci-après. </s> <s xml:id="echoid-s10724" xml:space="preserve">Les points Equinoxiaux de <lb/>♈ & </s> <s xml:id="echoid-s10725" xml:space="preserve">♎ ſe placent au bout du raïon de l'Equateur a c.</s> <s xml:id="echoid-s10726" xml:space="preserve"/> </p> <pb o="329" file="345" n="345" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> <p> <s xml:id="echoid-s10727" xml:space="preserve">Table des declinaiſons du Soleil en tous les degrez de l'Ecliptique.</s> <s xml:id="echoid-s10728" xml:space="preserve"/> </p> <note position="right" xml:space="preserve">Degr. \\ de \\ l'Ecl. # Signes. \\ ♈ ♎ \\ D. M. # Signes. \\ ♉ ♏> \\ D. M. # Signes. \\ ♊ ♐ \\ D. M. # Degr. <lb/> # 1 # 0 24 # 11 51 # 20 25 # 29 <lb/> # 2 # 0 48 # 12 12 # 20 36 # 28 <lb/> # 3 # 1 12 # 12 32 # 20 48 # 27 <lb/> # 4 # 1 36 # 12 53 # 21 0 # 26 <lb/> # 5 # 2 0 # 13 13 # 21 11 # 25 <lb/> # 6 # 2 23 # 13 33 # 21 21 # 24 <lb/> # 7 # 2 47 # 13 53 # 21 32 # 23 <lb/> # 8 # 3 11 # 14 12 # 21 42 # 22 <lb/> # 9 # 3 35 # 14 32 # 21 51 # 21 <lb/>Quantiéme des Signes. # 10 # 3 58 # 14 51 # 22 0 # 20 # Quantiéme des Signes. <lb/> # 11 # 4 22 # 15 9 # 22 8 # 19 <lb/> # 12 # 4 45 # 15 28 # 22 27 # 18 <lb/> # 13 # 5 9 # 15 47 # 22 24 # 17 <lb/> # 14 # 5 32 # 16 5 # 22 32 # 16 <lb/> # 15 # 5 55 # 16 22 # 22 39 # 15 <lb/> # 16 # 6 19 # 16 40 # 22 46 # 14 <lb/> # 17 # 6 42 # 16 57 # 22 52 # 13 <lb/> # 18 # 7 5 # 17 14 # 22 57 # 12 <lb/> # 19 # 7 28 # 17 30 # 23 2 # 11 <lb/> # 20 # 7 50 # 17 47 # 23 7 # 10 <lb/> # 21 # 8 13 # 18 3 # 23 11 # 9 <lb/> # 22 # 8 35 # 18 16 # 23 15 # 8 <lb/> # 23 # 8 58 # 18 34 # 23 18 # 7 <lb/> # 24 # 9 20 # 18 49 # 23 21 # 6 <lb/> # 25 # 9 42 # 19 3 # 23 24 # 5 <lb/> # 26 # 10 4 # 19 18 # 23 26 # 4 <lb/> # 27 # 10 26 # 19 32 # 23 27 # 3 <lb/> # 28 # 10 47 # 19 46 # 23 28 # 2 <lb/> # 29 # 11 9 # 19 59 # 23 29 # 1 <lb/> # 30 # 11 30 # 20 12 # 23 30 # 0 <lb/> # # 1 )( # ♍ 1 ♒ # ♌ 1 ♑ # ♋ 1 <lb/></note> <p> <s xml:id="echoid-s10729" xml:space="preserve">Par la Table des déclinaiſons on connoît par tout & </s> <s xml:id="echoid-s10730" xml:space="preserve">à chaque <lb/> <pb o="330" file="346" n="346" rhead="CONSTRUCTION ET USAGES"/> jour à Midi combien le Soleil décline & </s> <s xml:id="echoid-s10731" xml:space="preserve">s'éloigne des Equinoxes en <lb/>chaque degré des Signes du Zodiaque, la plus grande étant ſuppo-<lb/>ſée 23 d. </s> <s xml:id="echoid-s10732" xml:space="preserve">30 m. </s> <s xml:id="echoid-s10733" xml:space="preserve">bien qu'à preſent elle ne ſoit que d'environ 23 d. <lb/></s> <s xml:id="echoid-s10734" xml:space="preserve">29 m. </s> <s xml:id="echoid-s10735" xml:space="preserve">mais une minute de difference eſt peu conſiderable dans l'u-<lb/>ſage des Cadrans. </s> <s xml:id="echoid-s10736" xml:space="preserve">Les degrez qui vont en croiſſant de haut en bas <lb/>dans la premiere colonne vers la gauche ſont pour les Signes mar-<lb/>quez au-deſſus; </s> <s xml:id="echoid-s10737" xml:space="preserve">& </s> <s xml:id="echoid-s10738" xml:space="preserve">les degrez qui vont en décroiſſant de haut en bas <lb/>dans la derniere colonne vers la droite, ſont pour les Signes mar-<lb/>quez en deſſous.</s> <s xml:id="echoid-s10739" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div663" type="section" level="1" n="345"> <head xml:id="echoid-head480" style="it" xml:space="preserve">Du Trigone des Arcs diurnes.</head> <p> <s xml:id="echoid-s10740" xml:space="preserve">LA figure 4 repreſente le triangle ou Secteur des Arcs diurnes <lb/>& </s> <s xml:id="echoid-s10741" xml:space="preserve">nocturnes.</s> <s xml:id="echoid-s10742" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10743" xml:space="preserve">Ils ſe tracent ſur les Cadrans au Soleil par des lignes courbes, <lb/>comme les arcs des Signes, & </s> <s xml:id="echoid-s10744" xml:space="preserve">l'ombre du bout du ſtyle parcourant <lb/>ces arcs fait connoître combien d'heures le Soleil reſte ce jour-là ſur <lb/>l'horiſon, c'eſt à-dire, la longueur du jour, & </s> <s xml:id="echoid-s10745" xml:space="preserve">par conſequent <lb/>celle de la nuit qui eſt ſon complément à 24 heures.</s> <s xml:id="echoid-s10746" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10747" xml:space="preserve">Le triangle des Signes eſt le même pour toutes les élevations de <lb/>Pole, parce que les déclinaiſons du Soleil ſont les mêmes pour toute <lb/>la terre; </s> <s xml:id="echoid-s10748" xml:space="preserve">mais les arcs diurnes ſont differens pour chaque élevation <lb/>particuliere de Pole, & </s> <s xml:id="echoid-s10749" xml:space="preserve">on en met ſur les Cadrans autant qu'il y a <lb/>d'heures de difference entre le plus court & </s> <s xml:id="echoid-s10750" xml:space="preserve">le plus long jour de <lb/>l'année.</s> <s xml:id="echoid-s10751" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10752" xml:space="preserve">Pour conſtruire le triangle des arcs diurnes ſur une plaque de cui-<lb/> <anchor type="note" xlink:label="note-346-01a" xlink:href="note-346-01"/> vre ou de quelque matiere ſolide, tirez premierement la ligne droi-<lb/>te RZ, qui eſt le raïon de 12 h. </s> <s xml:id="echoid-s10753" xml:space="preserve">ou de l'Equateur; </s> <s xml:id="echoid-s10754" xml:space="preserve">du point R, com-<lb/>me centre & </s> <s xml:id="echoid-s10755" xml:space="preserve">d'une ouverture de Compas à volonté, décrivez l'arc <lb/>de cercle TSV; </s> <s xml:id="echoid-s10756" xml:space="preserve">portez de S en V un arc égal à celui de l'élevation <lb/>de l'Equateur, ou ce qui eſt le même, du complément de l'élevation <lb/>du Pole, comme, par exemple, ſile Pole eſt élevé de 49 d. </s> <s xml:id="echoid-s10757" xml:space="preserve">faites l'arc <lb/>SV de 41 d. </s> <s xml:id="echoid-s10758" xml:space="preserve">auſſi-bien que l'arc ST; </s> <s xml:id="echoid-s10759" xml:space="preserve">tirez enſuite la droitre TXV, <lb/>& </s> <s xml:id="echoid-s10760" xml:space="preserve">du point X comme centre décrivez la circonference de cercle T <lb/>ZVY, que vous diviſerez en 48 parties égales par des lignes ponc-<lb/>tuées paralleles au raïon de l'Equateur RZ. </s> <s xml:id="echoid-s10761" xml:space="preserve">Ces lignes couperont <lb/>le diametre TXV en des points, par où & </s> <s xml:id="echoid-s10762" xml:space="preserve">par le point R vous ti-<lb/>rerez les raïons des heures.</s> <s xml:id="echoid-s10763" xml:space="preserve"/> </p> <div xml:id="echoid-div663" type="float" level="2" n="1"> <note position="left" xlink:label="note-346-01" xlink:href="note-346-01a" xml:space="preserve">XXIV. <lb/>Planche. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s10764" xml:space="preserve">Comme le plus long jour à Paris eſt de 16 h. </s> <s xml:id="echoid-s10765" xml:space="preserve">& </s> <s xml:id="echoid-s10766" xml:space="preserve">le plus court de <lb/>8, il ne ſera neceſſaire de marquer que quatre raïons d'un côté de <lb/>la ligne RZ, & </s> <s xml:id="echoid-s10767" xml:space="preserve">autant de l'autre:</s> <s xml:id="echoid-s10768" xml:space="preserve"/> </p> <pb o="331" file="347" n="347" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> <p> <s xml:id="echoid-s10769" xml:space="preserve">On peut encore trouver par la Trigonométrie les angles que <lb/>font au point R tous les raïons, en faiſant cette Analogie.</s> <s xml:id="echoid-s10770" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10771" xml:space="preserve">Comme le Sinus total eſt à la tangente du complément de l'éle-<lb/>vation du Pole, ainſi le Sinus de la difference de l'arc ſemi-diurne <lb/>des Equinoxes & </s> <s xml:id="echoid-s10772" xml:space="preserve">de l'arc propoſé, eſt à la tangente de la déclinai-<lb/>ſon du Soleil requiſe.</s> <s xml:id="echoid-s10773" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10774" xml:space="preserve">Si, par exemple, on veut tracer ſur le Trigone l'arc de 11 h. </s> <s xml:id="echoid-s10775" xml:space="preserve">de jour <lb/>ou de 13, le demi-arc diurne eſt de 5 h. </s> <s xml:id="echoid-s10776" xml:space="preserve">& </s> <s xml:id="echoid-s10777" xml:space="preserve">demie ou de de 6 h. </s> <s xml:id="echoid-s10778" xml:space="preserve">& </s> <s xml:id="echoid-s10779" xml:space="preserve">de-<lb/>mie, le jour des Equinoxes eſt de 12, & </s> <s xml:id="echoid-s10780" xml:space="preserve">par conſequent le demi-arc <lb/>diurne eſt de 6 h. </s> <s xml:id="echoid-s10781" xml:space="preserve">& </s> <s xml:id="echoid-s10782" xml:space="preserve">la difference eſt de demie heure; </s> <s xml:id="echoid-s10783" xml:space="preserve">c'eſt pourquoi <lb/>il faudra mettre pour premier terme de la regle de 3 le Sinus total, <lb/>pour ſecond terme la tangente de 41 d ſi c'eſt pour Paris, & </s> <s xml:id="echoid-s10784" xml:space="preserve">pour <lb/>troiſiéme terme le Sinus de 7 d. </s> <s xml:id="echoid-s10785" xml:space="preserve">30 m. </s> <s xml:id="echoid-s10786" xml:space="preserve">La regle étant faite, on trou-<lb/>vera que la déclinaiſon du Soleil eſt de 6 deg. </s> <s xml:id="echoid-s10787" xml:space="preserve">28 m. </s> <s xml:id="echoid-s10788" xml:space="preserve">Méridionale, <lb/>lorſque le jour à Paris eſt de 11 h. </s> <s xml:id="echoid-s10789" xml:space="preserve">completes & </s> <s xml:id="echoid-s10790" xml:space="preserve">la nuit de 13, & </s> <s xml:id="echoid-s10791" xml:space="preserve">que <lb/>pareillement ſa déclinaiſon étant de 6 d. </s> <s xml:id="echoid-s10792" xml:space="preserve">28 m. </s> <s xml:id="echoid-s10793" xml:space="preserve">Septentrionale, le <lb/>jour y eſt de 13 h. </s> <s xml:id="echoid-s10794" xml:space="preserve">& </s> <s xml:id="echoid-s10795" xml:space="preserve">la nuit de 11 h.</s> <s xml:id="echoid-s10796" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10797" xml:space="preserve">En faiſant trois autres Regles de 4, on trouvera que la déclinai-<lb/>ſon de l'arc diurne de 10 h. </s> <s xml:id="echoid-s10798" xml:space="preserve">& </s> <s xml:id="echoid-s10799" xml:space="preserve">de 14 h. </s> <s xml:id="echoid-s10800" xml:space="preserve">eſt de . </s> <s xml:id="echoid-s10801" xml:space="preserve">12 d. </s> <s xml:id="echoid-s10802" xml:space="preserve">41 m.</s> <s xml:id="echoid-s10803" xml:space="preserve"/> </p> <note position="right" xml:space="preserve"> <lb/>Celui de 9 h. & de 15 h. eſt de # 18 # 25 <lb/>Et celui de 8 h. & de 16 h. de # 23 # 30 <lb/></note> </div> <div xml:id="echoid-div665" type="section" level="1" n="346"> <head xml:id="echoid-head481" style="it" xml:space="preserve">Du Trigone avec une Alidade.</head> <p> <s xml:id="echoid-s10804" xml:space="preserve">LA figure 5 eſt un triangle des Signes monté ſur une regle ou a-<lb/> <anchor type="note" xlink:label="note-347-02a" xlink:href="note-347-02"/> lidade A, pour tracer les arcs des Signes ſur les grands Cadrans. <lb/></s> <s xml:id="echoid-s10805" xml:space="preserve">On peut auſſi marquer ſur le même triangle les arcs diurnes; </s> <s xml:id="echoid-s10806" xml:space="preserve">mais il <lb/>ne faut mettre que les uns ou les autres ſur le même Cadran, pour <lb/>éviter la confuſion des lignes. </s> <s xml:id="echoid-s10807" xml:space="preserve">Il y a un petit trou au centre avec un <lb/>clou, par le moyen duquel l'inſtrument peut tourner autour du cen-<lb/>tre du Cadran. </s> <s xml:id="echoid-s10808" xml:space="preserve">On ajuſte une couliſſe à ce triangle pour qu'il puiſſe <lb/>couler le long de la ligne de foi de la Regle, & </s> <s xml:id="echoid-s10809" xml:space="preserve">une vis marquée B, <lb/>pour l'arrêter où l'on veut. </s> <s xml:id="echoid-s10810" xml:space="preserve">Les arcs des Signes avec leurs caracteres <lb/>ſont autour de la circonference & </s> <s xml:id="echoid-s10811" xml:space="preserve">une ſoie fine au centre du Sec-<lb/>teur, pour l'étendre le long des raïons juſqu'au rencontre des lignes <lb/>horaires du Cadran, de la maniere que nous dirons ci-après.</s> <s xml:id="echoid-s10812" xml:space="preserve"/> </p> <div xml:id="echoid-div665" type="float" level="2" n="1"> <note position="right" xlink:label="note-347-02" xlink:href="note-347-02a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s10813" xml:space="preserve">La figure 6, repreſente la moitié d'un Cadran horiſontal avec les <lb/> <anchor type="note" xlink:label="note-347-03a" xlink:href="note-347-03"/> lignes horaires du matin juſqu'à midi, & </s> <s xml:id="echoid-s10814" xml:space="preserve">ſa ligne équinoxiale CD; <lb/></s> <s xml:id="echoid-s10815" xml:space="preserve">ce qui doit ſuffire pour expliquer la maniere d'y tracer les arcs des <lb/>Signes par le moyen de la fig. </s> <s xml:id="echoid-s10816" xml:space="preserve">7, laquelle repreſente un triangle des <lb/>Signes tracé ſur une plaque, ſur lequel on a rapporté les heures du-<lb/>dit Cadran horiſontal en cette maniere.</s> <s xml:id="echoid-s10817" xml:space="preserve"/> </p> <div xml:id="echoid-div666" type="float" level="2" n="2"> <note position="right" xlink:label="note-347-03" xlink:href="note-347-03a" xml:space="preserve">Fig. 6.</note> </div> <pb o="332" file="348" n="348" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s10818" xml:space="preserve">Prenez avec un Compas ſur le Cadran la grandeur de l'axe VR <lb/>& </s> <s xml:id="echoid-s10819" xml:space="preserve">la portez ſur l'axe du triangle de O en C; </s> <s xml:id="echoid-s10820" xml:space="preserve">prenez enſuite au Ca-<lb/>dran la diſtance du centre V juſqu'au point C, où la ligne de 12 h. <lb/></s> <s xml:id="echoid-s10821" xml:space="preserve">coupe l'Equinoxiale, & </s> <s xml:id="echoid-s10822" xml:space="preserve">la portez au triangle de C en A, pour y tra-<lb/>cer legerement CA, 12 qui coupera toutes les 7 lignes du triangle.</s> <s xml:id="echoid-s10823" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10824" xml:space="preserve">Prenez ſur cette ligne la diſtance du point C juſqu'au rencontre <lb/>du Tropique d'Eté, & </s> <s xml:id="echoid-s10825" xml:space="preserve">portez-la au Cadran du centre V, ſur la li-<lb/>gne de 12 h. </s> <s xml:id="echoid-s10826" xml:space="preserve">pour y marquer un point du d. </s> <s xml:id="echoid-s10827" xml:space="preserve">Tropique; </s> <s xml:id="echoid-s10828" xml:space="preserve">prenez de <lb/> <anchor type="note" xlink:label="note-348-01a" xlink:href="note-348-01"/> même ſur le triangle la diſtance depuis C juſqu'au rencontre du pa-<lb/>rallele des ♊, & </s> <s xml:id="echoid-s10829" xml:space="preserve">la portez au Cadran ſur la même ligne de 12 heur. <lb/></s> <s xml:id="echoid-s10830" xml:space="preserve">pour y marquer un point dudit parallele; </s> <s xml:id="echoid-s10831" xml:space="preserve">prenez auſſi toutes les au-<lb/>tres diſtances ſur le triangle, & </s> <s xml:id="echoid-s10832" xml:space="preserve">les portez l'une après l'autre au Ca-<lb/>dran ſur la ligne de 12 h. </s> <s xml:id="echoid-s10833" xml:space="preserve">depuis le centre juſqu'au point du Tropi-<lb/>que d'Hyver, qui doit être le plus éloigné du centre ſur le Cadran <lb/>horiſontal; </s> <s xml:id="echoid-s10834" xml:space="preserve">faites la même choſe pour toutes les autres heures l'une <lb/>après l'autre. </s> <s xml:id="echoid-s10835" xml:space="preserve">Prenez, par exemple, ſur la ligne d' 11 h. </s> <s xml:id="echoid-s10836" xml:space="preserve">du Cadran <lb/>la diſtance depuis le centre juſqu'au point où cette ligne coupe l'é-<lb/>quinoxiale, portez-la au triangle de C vers A, tirez la ligne C ij, <lb/>prenez les diſtances du point C juſqu'à l'interſection de chaque pa-<lb/>rallele des Signes, & </s> <s xml:id="echoid-s10837" xml:space="preserve">les portez au Cadran depuis le centre juſqu'aux <lb/>points marquez 2 ſur ladite ligne de ij, & </s> <s xml:id="echoid-s10838" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s10839" xml:space="preserve"/> </p> <div xml:id="echoid-div667" type="float" level="2" n="3"> <note position="left" xlink:label="note-348-01" xlink:href="note-348-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s10840" xml:space="preserve">A l'égard de la ligne de 6 h. </s> <s xml:id="echoid-s10841" xml:space="preserve">laquelle ſur le Cadran eſt parallele à <lb/>l'équinoxiale, faites-la auſſi parallele au raïon de l'Equateur GA ſur <lb/>le triangle. </s> <s xml:id="echoid-s10842" xml:space="preserve">Pour y marquer la ligne de 7 h. </s> <s xml:id="echoid-s10843" xml:space="preserve">du ſoir, faites du point <lb/>C, comme centre, un arc depuis la ligne de 6 h. </s> <s xml:id="echoid-s10844" xml:space="preserve">juſqu'à celle de 5; <lb/></s> <s xml:id="echoid-s10845" xml:space="preserve">& </s> <s xml:id="echoid-s10846" xml:space="preserve">portez la même ouverture de l'autre côté de la ligne de 6 h. </s> <s xml:id="echoid-s10847" xml:space="preserve">pour <lb/>y tracer la ligne de 7 h. </s> <s xml:id="echoid-s10848" xml:space="preserve">laquelle ne rencontrera que le Tropique <lb/>d'Eté, & </s> <s xml:id="echoid-s10849" xml:space="preserve">à peine le parallele de II. </s> <s xml:id="echoid-s10850" xml:space="preserve">Enfin la ligne de 8 h. </s> <s xml:id="echoid-s10851" xml:space="preserve">du ſoir doit <lb/>faire avec celle de 6, le même angle que fait de l'autre côté celle de <lb/>4; </s> <s xml:id="echoid-s10852" xml:space="preserve">mais il eſt inutile de la marquer pour la latitude de 49 deg. </s> <s xml:id="echoid-s10853" xml:space="preserve"><lb/>puiſque cette ligne ne peut couper aucun raïon des Signes, étant <lb/>parallele au Tropique de 69. </s> <s xml:id="echoid-s10854" xml:space="preserve">Quand tous ces points ſeront mar-<lb/>quez ſur les heures du Cadran, on joindra le mieux qu'il ſera poſ-<lb/>ſible, tous ceux qui appartiennent à un même Signe, par des lignes <lb/>courbes qui repreſenteront les paralleles des Signes du Zodiaque, <lb/>dont on marquera les caracteres, comme on les voit en la Figure. </s> <s xml:id="echoid-s10855" xml:space="preserve"><lb/>On y joint quelqueſois les noms des mois & </s> <s xml:id="echoid-s10856" xml:space="preserve">de quelque Fête im-<lb/>mobile remarquable. </s> <s xml:id="echoid-s10857" xml:space="preserve">Faites la même choſe pour les Cadrans ver-<lb/>ticaux, ſinon que le Tropique d'Hyver y doit être le plus proche <lb/>du centre, & </s> <s xml:id="echoid-s10858" xml:space="preserve">celui d'Eté le plus éloigné.</s> <s xml:id="echoid-s10859" xml:space="preserve"/> </p> <pb o="333" file="349" n="349" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> <p> <s xml:id="echoid-s10860" xml:space="preserve">Pour marquer les arcs des Signes ou les arcs diurnes ſur les grands <lb/>Cadrans, on ſe ſervira de la figure 5, en la maniere qui ſuit.</s> <s xml:id="echoid-s10861" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10862" xml:space="preserve">Attachez la regle par un clou au centre du Cadran, en ſorte que <lb/>vous la puiſſiez tourner & </s> <s xml:id="echoid-s10863" xml:space="preserve">arrêter ſur ſes lignes horaires, comme <lb/>on voit par la figure 8; </s> <s xml:id="echoid-s10864" xml:space="preserve">après avoir pris la diſtance depuis le centre <lb/>du Cadran juſqu'au bout de ſon axe, & </s> <s xml:id="echoid-s10865" xml:space="preserve">arrêté fixement avec la vis <lb/> <anchor type="note" xlink:label="note-349-01a" xlink:href="note-349-01"/> R, prenez d'une main la ſoie, & </s> <s xml:id="echoid-s10866" xml:space="preserve">de l'autre hauſſez ou baiſſez l'Inſ-<lb/>trument ſur le Plan du Cadran, en ſorte que la ſoie tenduë le <lb/>long du raïon de l'Equateur du Trigone rencontre la ſection de <lb/>l'heure & </s> <s xml:id="echoid-s10867" xml:space="preserve">de la ligne équinoxiale du Cadran; </s> <s xml:id="echoid-s10868" xml:space="preserve">arrêtez l'Inſtrument <lb/>dans cette ſituation, étendez la ſoie ſur les raïons du Trigone, & </s> <s xml:id="echoid-s10869" xml:space="preserve"><lb/>marquez ſur chaque ligne horaire les points par où doivent paſſer <lb/>les paralleles de Signes tant au-deſſus qu'au-deſſous de la ligne <lb/>équinoxiale, comme il paroît que l'on a fait ſur la ligne de 12 h. <lb/></s> <s xml:id="echoid-s10870" xml:space="preserve">du Cadran repreſenté par la figure 8.</s> <s xml:id="echoid-s10871" xml:space="preserve"/> </p> <div xml:id="echoid-div668" type="float" level="2" n="4"> <note position="right" xlink:label="note-349-01" xlink:href="note-349-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s10872" xml:space="preserve">Faites le même ſur toutes les lignes horaires l'une après l'autre, <lb/>& </s> <s xml:id="echoid-s10873" xml:space="preserve">par les points du même Signe, tracez les lignes courbes qui re-<lb/>preſenteront leurs paralleles ſur la ſurface du Cadran.</s> <s xml:id="echoid-s10874" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10875" xml:space="preserve">Pour les marquer ſur la ligne de 6 h tournez l'inſtrument de ſor-<lb/>te que la ligne de foi de la regle ſoit ſur la ligne de 12 h. </s> <s xml:id="echoid-s10876" xml:space="preserve">& </s> <s xml:id="echoid-s10877" xml:space="preserve">le raïon <lb/>de l'Equateur parallele à la ligne de 6 h. </s> <s xml:id="echoid-s10878" xml:space="preserve">après quoi vous étendrez <lb/>la ſoie ſur les raïons des Signes, juſqu'à ce qu'elle coupe la ligne de <lb/>6 h. </s> <s xml:id="echoid-s10879" xml:space="preserve">pour y marquer les points des paralleles.</s> <s xml:id="echoid-s10880" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10881" xml:space="preserve">Quand vous aurez marqué les arcs des Signes d'un côté du Ca-<lb/>dran, par exemple, ſur les heures du matin, vous tranſporterez a-<lb/>vec un Compas les mêmes diſtances du centre ſur les heures de <lb/>l'autre côté de la Méridiene, les points marquez ſur la ligne de 11 <lb/>heures ſeront portez ſur celle d'une heure, ceux de la ligne de 10 <lb/>h. </s> <s xml:id="echoid-s10882" xml:space="preserve">ſeront portez ſur celle de 2, & </s> <s xml:id="echoid-s10883" xml:space="preserve">ainſi des autres également éloi-<lb/>gnez de la Méridiene, & </s> <s xml:id="echoid-s10884" xml:space="preserve">vous y mettrez les caracteres des Signes <lb/>qui leur conviennent.</s> <s xml:id="echoid-s10885" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10886" xml:space="preserve">C'eſt de la même maniere qu'ils ſe marquent ſur les Cadrans dé-<lb/>clinans, en prenant la ſouſtylaire pour la Méridiene, & </s> <s xml:id="echoid-s10887" xml:space="preserve">les diſtan-<lb/>ces depuis le centre doivent être égales aux heures également éloi-<lb/>gnées de la ſouſtylaire.</s> <s xml:id="echoid-s10888" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10889" xml:space="preserve">Si au lieu des arcs des Signes on y marque les arcs diurnes, c'eſt-<lb/>à-dire, la longueur des jours, on y pourra mettre auſſi l'heure du <lb/>lever & </s> <s xml:id="echoid-s10890" xml:space="preserve">du coucher du Soleil, en partageant la longueur du jour <lb/>en deux également; </s> <s xml:id="echoid-s10891" xml:space="preserve">car, par exemple, lorſque le jour eſt de 15 h. <lb/></s> <s xml:id="echoid-s10892" xml:space="preserve">le Soleil ſe couche à 7 h. </s> <s xml:id="echoid-s10893" xml:space="preserve">& </s> <s xml:id="echoid-s10894" xml:space="preserve">demie du ſoir, & </s> <s xml:id="echoid-s10895" xml:space="preserve">ſe leve autant avant <lb/> <pb o="334" file="350" n="350" rhead="CONSTRUCTION ET USAGES"/> midi, c'eſt-à-dire, à 4 h. </s> <s xml:id="echoid-s10896" xml:space="preserve">& </s> <s xml:id="echoid-s10897" xml:space="preserve">demie du matin, & </s> <s xml:id="echoid-s10898" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s10899" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10900" xml:space="preserve">Pour tracer les arcs des Signes ſur les Cadrans Equinoxiaux; <lb/></s> <s xml:id="echoid-s10901" xml:space="preserve">comme, par exemple, ſur le Cadran de la figure 7 de la planche 22, <lb/>prenez la longueur du ſtyle AD, & </s> <s xml:id="echoid-s10902" xml:space="preserve">la portez ſur l'axe du Trigone <lb/>de la figure 7, planche 24; </s> <s xml:id="echoid-s10903" xml:space="preserve">du point O, juſqu'en P, tirez la ligne <lb/>PN, parallele au raïon de l'Equateur; </s> <s xml:id="echoid-s10904" xml:space="preserve">elle coupera le Tropique <lb/>d'Eté & </s> <s xml:id="echoid-s10905" xml:space="preserve">deux autres paralleles. </s> <s xml:id="echoid-s10906" xml:space="preserve">Prenez avec un Compas la diſtan-<lb/>ce du point P, juſqu'à l'interſection du Tropique; </s> <s xml:id="echoid-s10907" xml:space="preserve">portez cette ou-<lb/>verture au centre A du Cadran, & </s> <s xml:id="echoid-s10908" xml:space="preserve">tracez un cercle qui repreſente-<lb/>ra le Tropique de 69. </s> <s xml:id="echoid-s10909" xml:space="preserve">Prenez de même les deux autres diſtances ſur <lb/>la parallele du Trigone, pour en tracer deux autres cercles ſur le <lb/>Cadran, dont l'un ſera le parallele de ♊ & </s> <s xml:id="echoid-s10910" xml:space="preserve">de ♌, & </s> <s xml:id="echoid-s10911" xml:space="preserve">l'autre ce-<lb/>lui de ♉ & </s> <s xml:id="echoid-s10912" xml:space="preserve">de ♍, que l'on peut tracer ſur l'Equinoxial ſupérieur. </s> <s xml:id="echoid-s10913" xml:space="preserve"><lb/>Si c'étoit un inférieur, on y marqueroit les paralleles de ♏, ♐, ♑, <lb/>♒ & </s> <s xml:id="echoid-s10914" xml:space="preserve">♓, car pour les cercles de ♈ & </s> <s xml:id="echoid-s10915" xml:space="preserve">♎, on ne peut les décrite ſur <lb/>les Cadrans Equinoxiaux, parce que le Soleil étant dans le Plan de <lb/>l'Equateur celeſte, ſes raïons raſent la ſurface de ces Cadrans, & </s> <s xml:id="echoid-s10916" xml:space="preserve"><lb/>l'ombre de leur ſtyle eſt indéfinie; </s> <s xml:id="echoid-s10917" xml:space="preserve">c'eſt pourquoi ils ne marquent <lb/>pas l'heure en ce tems-là.</s> <s xml:id="echoid-s10918" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10919" xml:space="preserve">La ligne horiſontale ſe trace de cette maniere: </s> <s xml:id="echoid-s10920" xml:space="preserve">La longueur du <lb/>ſtyle étant poſée ſur la ligne de 6 h. </s> <s xml:id="echoid-s10921" xml:space="preserve">de ſon extremité D, comme cen-<lb/>tre, tracez au-deſſus, pour le ſupérieur, l'arc EF égal à l'élevation <lb/>du Pole, comme ici, par exemple, de 49 d. </s> <s xml:id="echoid-s10922" xml:space="preserve">tirez la ligne DF, qui <lb/>coupera la Méridiene au point H, par lequel vous tracerez la ligne <lb/>horiſontale parallele à celle de 6 heures, comme on voit en la figure <lb/>7, planche 22.</s> <s xml:id="echoid-s10923" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10924" xml:space="preserve">Cette ligne ſert à faire connoître le lever & </s> <s xml:id="echoid-s10925" xml:space="preserve">le coucher du Soleil <lb/>au commencement de chaque Signe; </s> <s xml:id="echoid-s10926" xml:space="preserve">car, par exemple, comme <lb/>elle coupe en ce Cadran le Tropique de Cancer aux aux points de 4 h. <lb/></s> <s xml:id="echoid-s10927" xml:space="preserve">du matin, & </s> <s xml:id="echoid-s10928" xml:space="preserve">de 8 h. </s> <s xml:id="echoid-s10929" xml:space="preserve">du ſoir, il s'enſuit que le Soleil au jour du Solſ-<lb/>tice d'Eté ſe leve à 4 h. </s> <s xml:id="echoid-s10930" xml:space="preserve">du matin, & </s> <s xml:id="echoid-s10931" xml:space="preserve">ſe couche à 8 h. </s> <s xml:id="echoid-s10932" xml:space="preserve">du ſoir ſur <lb/>l'horiſon de Paris; </s> <s xml:id="echoid-s10933" xml:space="preserve">& </s> <s xml:id="echoid-s10934" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s10935" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div670" type="section" level="1" n="347"> <head xml:id="echoid-head482" style="it" xml:space="preserve">Pour tracer les arcs des Signes ſur les Cadrans Polaires.</head> <p> <s xml:id="echoid-s10936" xml:space="preserve">LE Cadran étant conſtruit, comme on le voit en la figure 6 de <lb/>la planche 22, les raïons des heures ponctuées depuis le point <lb/>D, centre du quart de cercle, & </s> <s xml:id="echoid-s10937" xml:space="preserve">bout du ſtyle, juſqu'au rencontre <lb/>de la ligne équinoxiale AB, portez ces diſtances l'une après l'autre <lb/>ſur le raïon de l'Equateur du Trigone de Signes, fig. </s> <s xml:id="echoid-s10938" xml:space="preserve">7 de la plan-<lb/>che 24, pour y tracer autant de perpendiculaires qu'il y a d'heures <lb/> <pb o="335" file="351" n="351" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> ponctuées, c'eſt-à-dire, une pour 12 h. </s> <s xml:id="echoid-s10939" xml:space="preserve">& </s> <s xml:id="echoid-s10940" xml:space="preserve">5 autres pour 1, 2, 3, 4 <lb/>& </s> <s xml:id="echoid-s10941" xml:space="preserve">5 h. </s> <s xml:id="echoid-s10942" xml:space="preserve">leſquelles couperont les raïons des Signes du Trigone; </s> <s xml:id="echoid-s10943" xml:space="preserve">pre-<lb/>nez enſuite ſur ces perpendiculaires la diſtance depuis le raïon de <lb/>l'Equateur du triangle juſqu'aux autres raïons des Signes, & </s> <s xml:id="echoid-s10944" xml:space="preserve">les <lb/>tranſportez ſur les lignes horaires du Cadran, depuis l'Equinoxia-<lb/>le AB de part & </s> <s xml:id="echoid-s10945" xml:space="preserve">d'autre. </s> <s xml:id="echoid-s10946" xml:space="preserve">Prenez, par exemple, ſur le triangle l'eſ-<lb/>pace 12 ♑, & </s> <s xml:id="echoid-s10947" xml:space="preserve">le portez au Cadran du point C, ſur la ligne de 12 <lb/>h. </s> <s xml:id="echoid-s10948" xml:space="preserve">pour y marquer les points des Tropiques. </s> <s xml:id="echoid-s10949" xml:space="preserve">De même l'eſpace pris <lb/>au triangle, ſur la ligne 5 ♑ ou 69, ſera portée ſur la ligne de 5 & </s> <s xml:id="echoid-s10950" xml:space="preserve"><lb/>de 7 h. </s> <s xml:id="echoid-s10951" xml:space="preserve">du Cadran de part & </s> <s xml:id="echoid-s10952" xml:space="preserve">d'autre également depuis la ligne E-<lb/>quinoxiale, & </s> <s xml:id="echoid-s10953" xml:space="preserve">ainſi des autres Signes dont vous tracerez les paral-<lb/>leles par des lignes courbes; </s> <s xml:id="echoid-s10954" xml:space="preserve">ſçavoir, les Signes Septentrionaux au <lb/>deſſous de la ligne Equinoxiale, & </s> <s xml:id="echoid-s10955" xml:space="preserve">les Méridionaux au deſſus. <lb/></s> <s xml:id="echoid-s10956" xml:space="preserve">Nous n'avons tracé que les deux Tropiques en la figure de ce Ca-<lb/>dran, pour ne pas l'embaraſſer.</s> <s xml:id="echoid-s10957" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10958" xml:space="preserve">Les Arcs diurnes ſe tracent de la même maniere que les Arcs <lb/>des Signes.</s> <s xml:id="echoid-s10959" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div671" type="section" level="1" n="348"> <head xml:id="echoid-head483" style="it" xml:space="preserve">Pour tracer les Arcs des Signes ſur les Cadrans Orientaux <lb/>& Occidentaux.</head> <p> <s xml:id="echoid-s10960" xml:space="preserve">ON fait à peu près la même choſe que pour les tracer ſur les Po-<lb/>laires.</s> <s xml:id="echoid-s10961" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10962" xml:space="preserve">Soit, par exemple, la figure premiere de la planche 23<emph style="sub">me</emph>, qui re-<lb/>preſente un Cadran Occidental. </s> <s xml:id="echoid-s10963" xml:space="preserve">Les raïons des heures étant ponc-<lb/>tuez depuis le point E, centre du quart de cercle & </s> <s xml:id="echoid-s10964" xml:space="preserve">longueur du ſty-<lb/>le, juſqu'à la ligne équinoxiale CD, ſeront portez avec un Compas <lb/>au Trigone de la figure 3, planche 24, depuis le point A, ſur le raïon <lb/>de l'Equateur, pour y tracer autant de perpendiculaires qui coupe-<lb/>ront les raïons des Signes; </s> <s xml:id="echoid-s10965" xml:space="preserve">vous prendrez ſur ces perpendiculaires <lb/>les diſtances depuis le raion de l'Equateur juſqu'aux interſections <lb/>des raïons des autres Signes, & </s> <s xml:id="echoid-s10966" xml:space="preserve">les reporterez ſur les lîgnes horaires <lb/>du Cadran, de côté & </s> <s xml:id="echoid-s10967" xml:space="preserve">d'autre de la ligne équinoxiale.</s> <s xml:id="echoid-s10968" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10969" xml:space="preserve">Prenez, par exemple, au Trigone l'eſpace 6 69 ou ♑, & </s> <s xml:id="echoid-s10970" xml:space="preserve">por-<lb/>tez-le au Cadran ſur la ligne de 6 h. </s> <s xml:id="echoid-s10971" xml:space="preserve">de part & </s> <s xml:id="echoid-s10972" xml:space="preserve">d'autre du point D; <lb/></s> <s xml:id="echoid-s10973" xml:space="preserve">faites-en de même pour les autres heures, & </s> <s xml:id="echoid-s10974" xml:space="preserve">par les points que vous <lb/>y aurez marquez tracez les lignes courbes, que repreſenteront les pa-<lb/>ralleles des Signes; </s> <s xml:id="echoid-s10975" xml:space="preserve">ſçavoir, les Septentrionaux au-deſſous de la li-<lb/>gne équinoxiale, & </s> <s xml:id="echoid-s10976" xml:space="preserve">les Meridionaux au-deſſus.</s> <s xml:id="echoid-s10977" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10978" xml:space="preserve">Les Arcs diurnes ſe tracent de la même façon.</s> <s xml:id="echoid-s10979" xml:space="preserve"/> </p> <pb o="336" file="352" n="352" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s10980" xml:space="preserve">Nous n'avons tracé que les deux Tropiques ſur ce Cadran, pour <lb/>ne pas embaraſſer la figure.</s> <s xml:id="echoid-s10981" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div672" type="section" level="1" n="349"> <head xml:id="echoid-head484" style="it" xml:space="preserve">Cnnſtruction d'un Cadran horiſontal avec les heures Italiques, <lb/>Babyloniques, les Almucantarats & les Méridiens.</head> <p> <s xml:id="echoid-s10982" xml:space="preserve">APrès avoir marqué ſur les Cadrans au Soleil les heures Aſtro-<lb/>nomiques ou Françoiſes, avec les Arcs diurnes ou ceux des <lb/>Signes, comme nous venons d'expliquer, on peut encore y repreſen-<lb/>ter pluſieurs autres cercles de la Sphere, qui ſeront des choſes cu-<lb/>rieuſes & </s> <s xml:id="echoid-s10983" xml:space="preserve">utiles, que l'extremité de l'ombre du ſtyle y marquera; <lb/></s> <s xml:id="echoid-s10984" xml:space="preserve">comme ſont les heures Italienes & </s> <s xml:id="echoid-s10985" xml:space="preserve">Babylonienes, les Azimuths; </s> <s xml:id="echoid-s10986" xml:space="preserve"><lb/>les Almucantarats & </s> <s xml:id="echoid-s10987" xml:space="preserve">les Méridiens des principales Villes de la <lb/>Terre.</s> <s xml:id="echoid-s10988" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10989" xml:space="preserve">Les heures Italiques & </s> <s xml:id="echoid-s10990" xml:space="preserve">Babyloniques ont pour premiere ligne <lb/>l'horiſon, comme les heures Aſtronomiques ont pour commence-<lb/>ment le Méridien. </s> <s xml:id="echoid-s10991" xml:space="preserve">Les Italiens commencent à compter les heures <lb/>lorſque le centre du Soleil touche l'horiſon en ſe couchant, & </s> <s xml:id="echoid-s10992" xml:space="preserve">les <lb/>Babyloniens lorſqu'il le touche en ſe levant.</s> <s xml:id="echoid-s10993" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s10994" xml:space="preserve">La figure premiere de la planche 25, repreſente un Cadran hori-<lb/>ſontal, ſur le quel on a tracé pluſieurs cercles de la Sphere, de la <lb/>maniere que nous allons l'expliquer.</s> <s xml:id="echoid-s10995" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div673" type="section" level="1" n="350"> <head xml:id="echoid-head485" style="it" xml:space="preserve">Méthode generale pour tracer ſur toutes ſortes de Cadrans les <lb/>heures Italienes & Babylonienes.</head> <p> <s xml:id="echoid-s10996" xml:space="preserve">LEs heures Aſtronomiques étant tracées avec la ligne Equino-<lb/> <anchor type="note" xlink:label="note-352-01a" xlink:href="note-352-01"/> xiale & </s> <s xml:id="echoid-s10997" xml:space="preserve">un Arc diurne ou un parallele du lever du Soleil à telle <lb/>heure qu'on voudra, comme, par exemple, à 4 h. </s> <s xml:id="echoid-s10998" xml:space="preserve">qui eſt le même <lb/>que le Tropique d'Eté, pour 49 d. </s> <s xml:id="echoid-s10999" xml:space="preserve">de latitude, vous trouverez par <lb/>la méthode que nous allons enſeigner, deux points de chacune de <lb/>ces lignes, un ſur la ligne Equinoxiale, & </s> <s xml:id="echoid-s11000" xml:space="preserve">l'autre ſur le parallele <lb/>tracé, par le moyen deſquelsil ſera facile de marquer ces lignes ho-<lb/>raires, parce qu étant les communes Sections des grands cercles de <lb/>la Sphere avec le Plan du Cadran, elles s'y doivent repreſenter en <lb/>lignes droites.</s> <s xml:id="echoid-s11001" xml:space="preserve"/> </p> <div xml:id="echoid-div673" type="float" level="2" n="1"> <note position="left" xlink:label="note-352-01" xlink:href="note-352-01a" xml:space="preserve">XXV. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s11002" xml:space="preserve">Voulant donc tracer la premiere heure Babylonique conſiderez <lb/>que le le Soleil étant dans l'Equateur, il ſe leve à 6 heures, & </s> <s xml:id="echoid-s11003" xml:space="preserve">qu'à <lb/>7 il y a une heure qu'il eſt levé; </s> <s xml:id="echoid-s11004" xml:space="preserve">d'où il s'enſuit que cette premiere <lb/>heure doit paſſer par le point où la ſeptiéme heure Aſtronomique <lb/> <pb o="337" file="353" n="353" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> coupe l'Equinoxiale. </s> <s xml:id="echoid-s11005" xml:space="preserve">La ſeconde heure paſſera par l'interſection de <lb/>8 heures du matin; </s> <s xml:id="echoid-s11006" xml:space="preserve">la troiſiéme, par celle de 9, & </s> <s xml:id="echoid-s11007" xml:space="preserve">ainſi de ſuite.</s> <s xml:id="echoid-s11008" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11009" xml:space="preserve">Mais quand le Soleil ſe leve à 4 h. </s> <s xml:id="echoid-s11010" xml:space="preserve">le point de 5 h. </s> <s xml:id="echoid-s11011" xml:space="preserve">ſur le parallele <lb/>de 69, eſt celui de la premiere heure Babylonique, le point de 6 eſt <lb/>pour la ſeconde heure; </s> <s xml:id="echoid-s11012" xml:space="preserve">celui de 7, pour la 3<emph style="sub">me</emph>, & </s> <s xml:id="echoid-s11013" xml:space="preserve">ainſi des autres. <lb/></s> <s xml:id="echoid-s11014" xml:space="preserve">Mettez donc une Regle ſur le point d'interſection de 5 heures au <lb/>Tropique du Cancer, & </s> <s xml:id="echoid-s11015" xml:space="preserve">ſur le point d'interſection de 7 h. </s> <s xml:id="echoid-s11016" xml:space="preserve">en l'E-<lb/>quinoxiale, & </s> <s xml:id="echoid-s11017" xml:space="preserve">par ces deux points tracez la premiere heure Babylo-<lb/>niene; </s> <s xml:id="echoid-s11018" xml:space="preserve">continuant de même, vous trouverez que la 8<emph style="sub">me</emph> heure paſ-<lb/>ſera par le point de 12 heures Aſtronomiques ſur ce Tropique, & </s> <s xml:id="echoid-s11019" xml:space="preserve"><lb/>par celui de 2 heures après midi ſur l'Equinoxiale; </s> <s xml:id="echoid-s11020" xml:space="preserve">& </s> <s xml:id="echoid-s11021" xml:space="preserve">que la quin-<lb/>ziéme heure paſlera par le point de 7 heures du ſoir ſur ledit Tro-<lb/>pique, & </s> <s xml:id="echoid-s11022" xml:space="preserve">par celui de 5 heures ſur l'Equinoxiale.</s> <s xml:id="echoid-s11023" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11024" xml:space="preserve">Il eſt facile de tracer toutes ces lignes horaires, lorſqu'on en a <lb/>une, parce qu'elles ſe ſuivent toutes par ordre d'heure en heure <lb/>Aſtronomique ſur le parallele & </s> <s xml:id="echoid-s11025" xml:space="preserve">ſur la ligne Equinoxiale, comme <lb/>il eſt aiſé de voir par ladite figure.</s> <s xml:id="echoid-s11026" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11027" xml:space="preserve">Enfin le Soleil ſe couche à 16 heures Babylonienes, lorſque le <lb/>jour eſt de 16 heures, il ſe couche à 12 heures pendant les Equi-<lb/>noxes, & </s> <s xml:id="echoid-s11028" xml:space="preserve">à 8 heures, lorſque la nuit eſt de 16 heures, puiſqu'il ſe <lb/>leve toûjours à 24 heures.</s> <s xml:id="echoid-s11029" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11030" xml:space="preserve">Il faut faire à peu près le même raiſonnement pour marquer les <lb/>heures Italienes. </s> <s xml:id="echoid-s11031" xml:space="preserve">Ou compte toûjours 24 heures quand le Soleil <lb/>ſe couche; </s> <s xml:id="echoid-s11032" xml:space="preserve">c'eſt pourquoi en Eté quand les nuits ſont de 8 heures, <lb/>il ſe leve à 8 heures Italiques; </s> <s xml:id="echoid-s11033" xml:space="preserve">pendant les Equinoxes il ſe leve à 12 <lb/>heures, & </s> <s xml:id="echoid-s11034" xml:space="preserve">en Hyver, quand les nuits ſont de 16 heures, il ſe leve <lb/>à 16 heures; </s> <s xml:id="echoid-s11035" xml:space="preserve">d'où s'enſuit que la 23<emph style="sub">me</emph> heure Italiene doit paſſer par <lb/>les points de 7 heures du ſoir au Tropique d'Eté, de 5 heures ſur <lb/>l'Equinoxiale, & </s> <s xml:id="echoid-s11036" xml:space="preserve">de 3 heures ſur Tropique d'Hyver. </s> <s xml:id="echoid-s11037" xml:space="preserve">Il ſuffit d'a-<lb/>voir deux de ces points pour la tracer. </s> <s xml:id="echoid-s11038" xml:space="preserve">La 22<emph style="sub">me</emph> heure paſſe par les <lb/>points de 6 heures du ſoir au Tropique d'Eté, de 4 heures ſur l'E-<lb/>quinoxiale, & </s> <s xml:id="echoid-s11039" xml:space="preserve">de 2 heures ſur le Tropique d'Hyver. </s> <s xml:id="echoid-s11040" xml:space="preserve">Continuant <lb/>de même, on trouvera que la 18<emph style="sub">me</emph> heure paſſe par les points de 12 <lb/>heures équinoxiales; </s> <s xml:id="echoid-s11041" xml:space="preserve">c'eſt à-dire, que pendant les Equinoxes il <lb/>eſt midi à 18 heures, au lieu qu'au Solſtice d'Eté il eſt midi à 16 <lb/>heures, & </s> <s xml:id="echoid-s11042" xml:space="preserve">pendant le Solſtice d'Hyver à 20 heures dans les Païs <lb/>qui ont 49 degrez de latitude, comme on voit dans les Tables ci-<lb/>après.</s> <s xml:id="echoid-s11043" xml:space="preserve"/> </p> <pb o="338" file="354" n="354" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div675" type="section" level="1" n="351"> <head xml:id="echoid-head486" style="it" xml:space="preserve">Tables pour trouver les heures Babyloniques & Italiques.</head> <note position="right" xml:space="preserve"> <lb/> ## Heures \\ Babyloniques # 1. # 2. # 3. # 4. # 5. # 6. # 7. # 8. # 9. # 10. # 11. # 12. # 13. # 14. # 15. # 16. <lb/>paſſent # 69 # # 5. # 6. # 7. # 8. # 9. # 10. # 11. # 12. # 1. # 2. # 3. # 4. # 5. # 6. # 7. # 8. <lb/>en l'arc # ♈ # par # 7. # 8. # 9. # 10. # 11. # 12. # 1. # 2. # 3. # 4. # 5. # 6. # 7. # 8. # 9. # 10. <lb/>de # ♑ # 9. # 10. # 11. # 12. # 1. # 2. # 3. # 4. # 5. # 6. # 7. # 8. # 9. # 10. # 11. # 12. <lb/> ## Heures Italiques. # 23. # 22. # 21. # 20. # 19. # 18. # 17. # 16. # 15. # 14. # 13. # 12. # 11. # 10. # 9. # 8. <lb/>paſſent # 69 # # 7. # 6. # 5. # 4. # 3. # 2. # 1. # 12. # 11. # 10. # 9. # 8. # 7. # 6. # 5. # 4. <lb/>en l'arc # ♈ par # 5. # 4. # 3. # 2. # 1. # 12. # 11. # 10. # 9. # 8. # 7. # 6. # 5. # 4. # 3. # 2. <lb/>de # ♑ # # 3. # 2. # 1. # 12. # 11. # 10. # 9. # 8. # 7. # 6. # 5. # 4. # 3. # 2. # 1. # 12. <lb/></note> <p> <s xml:id="echoid-s11044" xml:space="preserve">Par les heures Italienes on voit dans combien de tems le Soleil ſe <lb/>doit coucher, en ôtant l'heure preſente du nombre 24; </s> <s xml:id="echoid-s11045" xml:space="preserve">& </s> <s xml:id="echoid-s11046" xml:space="preserve">par les <lb/>heures Babylonienes on voit combien il y a de tems qu'il eſt levé.</s> <s xml:id="echoid-s11047" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div676" type="section" level="1" n="352"> <head xml:id="echoid-head487" style="it" xml:space="preserve">Maniere de tracer les Almucantarats & les Azimuths.</head> <p> <s xml:id="echoid-s11048" xml:space="preserve">LEs Almucantarats, ou Cercles de hauteur, ſe repreſentent ſur <lb/> <anchor type="note" xlink:label="note-354-02a" xlink:href="note-354-02"/> l'horiſontal par des cercles concentriques, & </s> <s xml:id="echoid-s11049" xml:space="preserve">les Azimuths par <lb/>des lig. </s> <s xml:id="echoid-s11050" xml:space="preserve">droites qui aboutiſſent au pied du ſtyle B, lequel repreſente <lb/>le Zétith, & </s> <s xml:id="echoid-s11051" xml:space="preserve">qui eſt le centre commun de tous les Almucantarats.</s> <s xml:id="echoid-s11052" xml:space="preserve"/> </p> <div xml:id="echoid-div676" type="float" level="2" n="1"> <note position="left" xlink:label="note-354-02" xlink:href="note-354-02a" xml:space="preserve">XXV. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s11053" xml:space="preserve">C'eſt pourquoi il n'y a qu'à diviſer en degrez la Méridiene B <lb/><emph style="sc">XII</emph>, du bout du ſtyle C, comme centre. </s> <s xml:id="echoid-s11054" xml:space="preserve">Les tangentes des arcs ſe-<lb/>ront les demi-diametres des Almucantarats qui ſe termineront aux <lb/>deux Tropiques. </s> <s xml:id="echoid-s11055" xml:space="preserve">Pour avoir ces tangentes on peut ſe ſervir d'un <lb/>quart de cercle diviſé comme celui de la figure 2. </s> <s xml:id="echoid-s11056" xml:space="preserve">Pour cet effet <lb/>portez la longueur du ſtyle CB de A en H, & </s> <s xml:id="echoid-s11057" xml:space="preserve">tirez la ligne HI, ſur <lb/>laquelle vous prendrez avec un Compas les diſtances, & </s> <s xml:id="echoid-s11058" xml:space="preserve">les porte-<lb/>rez ſur la ligne B <emph style="sc">XII</emph>, en ſorte que le 90<emph style="sub">me</emph> degré réponde au point <lb/>B. </s> <s xml:id="echoid-s11059" xml:space="preserve">Mais comme ce Cadran eſt fait pour 49 deg. </s> <s xml:id="echoid-s11060" xml:space="preserve">de latitude, & </s> <s xml:id="echoid-s11061" xml:space="preserve">que <lb/>par conſequent le Soleil ne peut s'élever ſur cet horiſon que de 64 <lb/>deg. </s> <s xml:id="echoid-s11062" xml:space="preserve">30 min. </s> <s xml:id="echoid-s11063" xml:space="preserve">il ſuffira de marquer cette plus grande hauteur du So-<lb/>leil, qui ſe terminera au Tropique d'Eté.</s> <s xml:id="echoid-s11064" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11065" xml:space="preserve">Enſuite ſi l'on diviſe un de ces cercles de hauteur de 10 en 10 de-<lb/>grez, en commençant depuis la Méridiene B <emph style="sc">XII</emph>, qui eſt le 90 <emph style="sub">me</emph> <lb/>Azimuth, & </s> <s xml:id="echoid-s11066" xml:space="preserve">que par ces points de diviſion on tire au pied du ſtyle <lb/>B autant de lignes droites, on aura la repreſentation des Azimuths <lb/> <pb o="339" file="355" n="355" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> ou cercles verticaux. </s> <s xml:id="echoid-s11067" xml:space="preserve">Nous ne les avons point marquez ſur ce Ca-<lb/>dran pour éviter la confuſion, mais il eſt facile de les concevoir.</s> <s xml:id="echoid-s11068" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11069" xml:space="preserve">Par les Almucantarats on connoît à toute heure la hauteur du <lb/>Soleil ſur l'horiſon; </s> <s xml:id="echoid-s11070" xml:space="preserve">& </s> <s xml:id="echoid-s11071" xml:space="preserve">par les Azimuths on connoît en quel Azi-<lb/>muth ou cercle vertical il ſe trouve; </s> <s xml:id="echoid-s11072" xml:space="preserve">cela ſe voit en remarquant <lb/>l'endroit où l'extremité de l'ombre du ſtyle droit donne ſur le cer-<lb/>cle de hauteur & </s> <s xml:id="echoid-s11073" xml:space="preserve">ſur la ligne de l'Azimuth.</s> <s xml:id="echoid-s11074" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div678" type="section" level="1" n="353"> <head xml:id="echoid-head488" style="it" xml:space="preserve">Méthode pour marquer les Méridiens ou cercles de longitude <lb/>terreſtre, ſur le Cadran boriſontal.</head> <p> <s xml:id="echoid-s11075" xml:space="preserve">DU point D, centre diviſeur de la ligne Equinoxiale, tracez <lb/> <anchor type="note" xlink:label="note-355-01a" xlink:href="note-355-01"/> une circonference de cercle & </s> <s xml:id="echoid-s11076" xml:space="preserve">la diviſez en 360 parties éga-<lb/>les ou degrez, ou ſeulement en 36 parties pour y marquer les de-<lb/>grez de 10 en 10. </s> <s xml:id="echoid-s11077" xml:space="preserve">De la ligne de Midi, qui repreſente le Méridien <lb/>du lieu pour lequel eſt conſtruit le Cadran, comme, par exemple, <lb/>de Paris, comptez vers Occident 20 deg. </s> <s xml:id="echoid-s11078" xml:space="preserve">pour ſa longitude ou diſ-<lb/>tance du premier Méridien qui paſſe par le point G; </s> <s xml:id="echoid-s11079" xml:space="preserve">ſur lequelayane <lb/>écrit 360 deg. </s> <s xml:id="echoid-s11080" xml:space="preserve">vous prolongerez la ligne GD juſqu'en E, ſur l'E-<lb/>quinoxial; </s> <s xml:id="echoid-s11081" xml:space="preserve">enſuite du centre A, & </s> <s xml:id="echoid-s11082" xml:space="preserve">par E tracezle premier Méridien <lb/>qui eſt l'Iſle de Fer, & </s> <s xml:id="echoid-s11083" xml:space="preserve">ainſi des autres; </s> <s xml:id="echoid-s11084" xml:space="preserve">mais il vous ſera plus facile <lb/>en marquant d'Occident vers Orient les Méridiens ou cercles de <lb/>longitude de 5 en 5 deg ou de 10 en 10, & </s> <s xml:id="echoid-s11085" xml:space="preserve">y placerez les princi-<lb/>pales Villes dont les longitudes vous ſont connuës; </s> <s xml:id="echoid-s11086" xml:space="preserve">comme, par <lb/>exemple, Rome, à 10 deg. </s> <s xml:id="echoid-s11087" xml:space="preserve">& </s> <s xml:id="echoid-s11088" xml:space="preserve">demi plus Orientale que Paris, Vien-<lb/>ne en Autriche, à 15 deg. </s> <s xml:id="echoid-s11089" xml:space="preserve">plus Orientale que ladite Ville de Paris, <lb/>& </s> <s xml:id="echoid-s11090" xml:space="preserve">ainſi des autres Villes conſiderables dont vous connoîtrez la dif-<lb/>ference des Méridiens à celui de Paris, par le moyen d'un bon Glo-<lb/>be ou par une bonne Carte de Géographie, conſtruite ſur les Obſer-<lb/>vations exactes de Meſſieurs de l'Académie Roïale des Sciences.</s> <s xml:id="echoid-s11091" xml:space="preserve"/> </p> <div xml:id="echoid-div678" type="float" level="2" n="1"> <note position="right" xlink:label="note-355-01" xlink:href="note-355-01a" xml:space="preserve">Fig. 1.</note> </div> <p> <s xml:id="echoid-s11092" xml:space="preserve">Son uſage eſt, qu'à tout moment que le Soleil luira ſur vôtre <lb/>Cadran, vous connoîtrez quelle heure il eſt en tous les lieux mar-<lb/>quez ſur les Méridiens, en ajoûtant à l'heure de Paris, pour lequel <lb/>eſt fait ce Cadran, autant d'heures qu'il y a de fois 15 deg. </s> <s xml:id="echoid-s11093" xml:space="preserve">de dif-<lb/>ference, & </s> <s xml:id="echoid-s11094" xml:space="preserve">4 min. </s> <s xml:id="echoid-s11095" xml:space="preserve">d'heure pour chaque degré.</s> <s xml:id="echoid-s11096" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11097" xml:space="preserve">Par exemple, quand ce Cadran marquera midi à Paris, il <lb/>ſera une heure à Vienne en Autriche, puiſque cette Ville eſt plus <lb/>Orientale que Paris de 15 deg. </s> <s xml:id="echoid-s11098" xml:space="preserve">& </s> <s xml:id="echoid-s11099" xml:space="preserve">par conſequent reçoit la lumie-<lb/>re du Soleil plûtôt que Paris.</s> <s xml:id="echoid-s11100" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11101" xml:space="preserve">Il ſera 42 minutes après midi à Rome, puiſqu'elle eſt 10. </s> <s xml:id="echoid-s11102" xml:space="preserve">d. </s> <s xml:id="echoid-s11103" xml:space="preserve">& </s> <s xml:id="echoid-s11104" xml:space="preserve"><lb/>demi à l'Orient de Paris, & </s> <s xml:id="echoid-s11105" xml:space="preserve">ainſi des autres. </s> <s xml:id="echoid-s11106" xml:space="preserve">Cette ligne de lon-<lb/> <pb o="340" file="356" n="356" rhead="CONSTRUCTION ET USAGES"/> gitude repreſente les Méridiens des lieux qui leur ſont attribuez, <lb/>en ſorte que quand l'ombre du ſtyle ou axe donne ſur quelques-<lb/>unes de ces villes, c'eſt une marque qu'il y eſt midi.</s> <s xml:id="echoid-s11107" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div680" type="section" level="1" n="354"> <head xml:id="echoid-head489" xml:space="preserve">CHAPITRE IV.</head> <head xml:id="echoid-head490" style="it" xml:space="preserve">Contenant la Conſtruction & les Uſages des Inſtrumens pro-<lb/>pres à tracer les Cadrans ſur les differens Plans.</head> <p> <s xml:id="echoid-s11108" xml:space="preserve">LA figure 2 de la planche 25<emph style="sub">me</emph>, eſt un quart de cercle diviſé en <lb/>ſes 90 deg. </s> <s xml:id="echoid-s11109" xml:space="preserve">ſa grandeur eſt à volonté. </s> <s xml:id="echoid-s11110" xml:space="preserve">Il ſe fait ſur une plaque <lb/>de cuivre ou d'autre matiere ſolide.</s> <s xml:id="echoid-s11111" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11112" xml:space="preserve">Il peut ſervir à trouver la longueur des tangentes, & </s> <s xml:id="echoid-s11113" xml:space="preserve">par ce moïen <lb/> <anchor type="note" xlink:label="note-356-01a" xlink:href="note-356-01"/> à diviſer en degrez une ligne droite, comme nous avons fait ſur la <lb/>Méridiene du Cadran horiſontal, fig. </s> <s xml:id="echoid-s11114" xml:space="preserve">1. </s> <s xml:id="echoid-s11115" xml:space="preserve">de cette même planche, <lb/>pour y marquer les raïons des Almucantarats ou cercles de hauteur.</s> <s xml:id="echoid-s11116" xml:space="preserve"/> </p> <div xml:id="echoid-div680" type="float" level="2" n="1"> <note position="left" xlink:label="note-356-01" xlink:href="note-356-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s11117" xml:space="preserve">On y peut pareillement trouver les diviſions des heures ſur la <lb/>ligne Equinoxiale des Cadrans reguliers, & </s> <s xml:id="echoid-s11118" xml:space="preserve">même des Cadrans dé-<lb/>clinans, dont la ſouſtylaire ſe rencontre ſur une heure complete, <lb/>en portant du centre A juſqu'en H ou en D, la longueur du raïon de <lb/>l'Equateur, & </s> <s xml:id="echoid-s11119" xml:space="preserve">tirantune ligne droite comme HI ou LM, parallele <lb/>au raïon extérieur du quart de cercle AC; </s> <s xml:id="echoid-s11120" xml:space="preserve">car par exemple, la diſ-<lb/>tance L 1 h. </s> <s xml:id="echoid-s11121" xml:space="preserve">ou 11 h. </s> <s xml:id="echoid-s11122" xml:space="preserve">qui repond à 15 d. </s> <s xml:id="echoid-s11123" xml:space="preserve">de la diviſion du quart de <lb/>cercle, ſera tangente de la premiere heure comptée depuis la Mé-<lb/>ridiene ou ſouſtylaire du Cadran; </s> <s xml:id="echoid-s11124" xml:space="preserve">c'eſt pourquoi étant portée ſur <lb/>la ligne équinoxiale, dontje ſuppoſe que AE eſt le raïon, elle y dé-<lb/>terminera le point par où doit paſſer cette ligne horaire. </s> <s xml:id="echoid-s11125" xml:space="preserve">L 2, quiré-<lb/>pond à 30 d. </s> <s xml:id="echoid-s11126" xml:space="preserve">de la circonference du quart de cercle, ſera latangen-<lb/>te de la 2<emph style="sub">me</emph> heure. </s> <s xml:id="echoid-s11127" xml:space="preserve">L 3, qui répond à 45 d. </s> <s xml:id="echoid-s11128" xml:space="preserve">ſera la tangente de la 3<emph style="sub">me</emph> <lb/>heure, & </s> <s xml:id="echoid-s11129" xml:space="preserve">ainſi des autres; </s> <s xml:id="echoid-s11130" xml:space="preserve">ou bien par ce moyen on a déja 3 h. </s> <s xml:id="echoid-s11131" xml:space="preserve">de <lb/>ſuite de chaque côté de la Méridiene ou ſouſtylaire; </s> <s xml:id="echoid-s11132" xml:space="preserve">ce qui fait <lb/>en tout ſix eſpaces d'heures de ſuite, & </s> <s xml:id="echoid-s11133" xml:space="preserve">qui peut ſuffire pour trou-<lb/>ver toutes les autres lignes horaires du Cadran, en ſuivant la mé-<lb/>thode que nous avons expliquée ci-devant en parlant des Cadrans <lb/>déclinans, & </s> <s xml:id="echoid-s11134" xml:space="preserve">qui peut s'appliquer de même à tous les Cadrans re-<lb/>guliers, comme eſt un horiſontal, ſur lequel ayant ſix intervalles <lb/>d'heure de ſuite, comme ſeroit, par exemple, depuis 9 du matin, <lb/>juſqu'à 3 h. </s> <s xml:id="echoid-s11135" xml:space="preserve">après midi; </s> <s xml:id="echoid-s11136" xml:space="preserve">on pourra par cette même méthode trou-<lb/>ver toutes les autres heures du Cadran, comme les heures de 7 & </s> <s xml:id="echoid-s11137" xml:space="preserve"><lb/>8 h. </s> <s xml:id="echoid-s11138" xml:space="preserve">du matin, 4 & </s> <s xml:id="echoid-s11139" xml:space="preserve">5 h. </s> <s xml:id="echoid-s11140" xml:space="preserve">du ſoir, que l'on a quelquefois peine à <lb/> <pb o="341" file="357" n="357" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. IV."/> marquer ſur la ligne équinoxiale du Cadran, principàlement les <lb/>points de 5 & </s> <s xml:id="echoid-s11141" xml:space="preserve">de 7 h. </s> <s xml:id="echoid-s11142" xml:space="preserve">à cauſe de la longueur de leurs tangentes.</s> <s xml:id="echoid-s11143" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11144" xml:space="preserve">Les lignes horaires trouvées par cette méthode, que nous ne re-<lb/>peterons pas ici, pourront ſervir à en trouver d'autres, & </s> <s xml:id="echoid-s11145" xml:space="preserve">celles qui <lb/>ſont trouvées étant prolongées au-delà du centre donneront leurs <lb/>oppoſées.</s> <s xml:id="echoid-s11146" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11147" xml:space="preserve">Ce même quart de cercle peut encore ſervir de Cadran portatif, <lb/>parce que les heures s'y peuvent tracer par le moyen d'un Table <lb/>des hauteurs du Soleil ſur l'horiſon du lieu pour lequel on veut le <lb/>conſtruire, comme nous l'expliquerons au Chapitre ſuivant.</s> <s xml:id="echoid-s11148" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div682" type="section" level="1" n="355"> <head xml:id="echoid-head491" style="it" xml:space="preserve">Conſtruction de l'Horiſontal mobile.</head> <p> <s xml:id="echoid-s11149" xml:space="preserve">CEt Inſtrument eſt compoſé de deux plaques de cuivre ou autre <lb/> <anchor type="note" xlink:label="note-357-01a" xlink:href="note-357-01"/> matiere ſolide, bien droites & </s> <s xml:id="echoid-s11150" xml:space="preserve">bien unies, appliquées l'une ſur <lb/>l'autre & </s> <s xml:id="echoid-s11151" xml:space="preserve">jointes enſemble par le moyen d'un clou rond mis au cen-<lb/>tre A. </s> <s xml:id="echoid-s11152" xml:space="preserve">La piece de deſſous eſt quarrée, ayant 6 à 8 pouces de cha-<lb/>que côté; </s> <s xml:id="echoid-s11153" xml:space="preserve">elle eſt diviſée en deux fois 90 deg. </s> <s xml:id="echoid-s11154" xml:space="preserve">pour ſervir à connoî-<lb/>tre la déclinaiſon des Plans. </s> <s xml:id="echoid-s11155" xml:space="preserve">La piece de deſſus eſt ronde avec un <lb/>petit index joint à la ligne de midi, qui marque ſur le degré la dé-<lb/>clinaiſon des Plans; </s> <s xml:id="echoid-s11156" xml:space="preserve">elle eſt environ de 4 lignes plus petite de cha-<lb/>que côté que la plaque quarrée qui eſt deſſous.</s> <s xml:id="echoid-s11157" xml:space="preserve"/> </p> <div xml:id="echoid-div682" type="float" level="2" n="1"> <note position="right" xlink:label="note-357-01" xlink:href="note-357-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s11158" xml:space="preserve">Il y a un Cadran horiſontal tracé du centre A, ſur la platine ſu-<lb/>périeure pour l'élevation du Pole du lieu où l'on veut s'en ſervir. <lb/></s> <s xml:id="echoid-s11159" xml:space="preserve">L'Axe B eſt ajuſté de maniere que ſa pointe aboutiſſe au centre ou <lb/>l'on fait un petit trou pour y paſſer une ſoie. </s> <s xml:id="echoid-s11160" xml:space="preserve">On y joint une Bouſ-<lb/>ſole D, avec ſon éguille aimantée, couverte d'un verrc pour la ga-<lb/>rantir des injures du temps, & </s> <s xml:id="echoid-s11161" xml:space="preserve">dans le fonds de la Bouſſole on tra-<lb/>ce une ligne qui marque la déclinaiſon de l'aiman.</s> <s xml:id="echoid-s11162" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div684" type="section" level="1" n="356"> <head xml:id="echoid-head492" style="it" xml:space="preserve">Uſage du Cadran horiſontal mobile.</head> <p> <s xml:id="echoid-s11163" xml:space="preserve">CEt Inſtrument ſert à tracer des Cadrans au Soleil ſur toute <lb/>ſorte de Plans, de telle ſituation qu'ils puiſſent être, comme <lb/>déclinans, inclinez, ou l'un & </s> <s xml:id="echoid-s11164" xml:space="preserve">l'autre tout enſemble, en la maniere <lb/>qui ſuit.</s> <s xml:id="echoid-s11165" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11166" xml:space="preserve">Tracez ſur le Plan propoſé une ligne horiſontale ou de niveau, <lb/>& </s> <s xml:id="echoid-s11167" xml:space="preserve">mettez le long de cette ligne le côté du quadre où eſt écrit, Côté <lb/>appliqué au Mur, tournez le Cadran horiſontal tant que l'éguille <lb/>aimantée s'arrête ſur ſa ligne de déclinaiſon; </s> <s xml:id="echoid-s11168" xml:space="preserve">étendez la ſoie au <lb/>long de l'Axe, juſqu'à ce quelle rencontre le Plan en un point qui <lb/>ſera le centre du Cadran. </s> <s xml:id="echoid-s11169" xml:space="preserve">Etendez enſuite la ſoie ſur toutes les li-<lb/> <pb o="342" file="358" n="358" rhead="CONSTRUCTION ET USAGES"/> gnes horaires que le Plan pourra recevoir, & </s> <s xml:id="echoid-s11170" xml:space="preserve">marquez autant de <lb/>points ſur la ligne de niveau, par leſquels vous conduirez du cen-<lb/>tre les lignes des heures, y marquant les mêmes chifres qu'à celles <lb/>du Cadran horiſontal. </s> <s xml:id="echoid-s11171" xml:space="preserve">Si le Cadran eſt vertical, ſans inclinaiſon, <lb/>la ligne de 12 heures ſera perpendiculaire ſur la ligne horiſontale du <lb/>Plan, en la faiſant tomber du centre du Cadran par le moyen d'un <lb/>fil avec ſon plomb.</s> <s xml:id="echoid-s11172" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11173" xml:space="preserve">La ſouſtylaire ſe tracera par le centre & </s> <s xml:id="echoid-s11174" xml:space="preserve">par un point de l'angle <lb/>droit d'un côté d'Equerre miſe ſur la ligne de niveau, l'autre côté <lb/>touchant l'Axe. </s> <s xml:id="echoid-s11175" xml:space="preserve">Cette diſtance du côté de l'Equerre poſée au Mur <lb/>juſqu'à l'axe, eſt la longueur du ſtyle droit, lequel étant couché au <lb/>même lieu à angles droits ſur la ſouſtylaire, vous tirerez du centre <lb/>par ſon extemité, l'axe, que vous formerez ſur le Plan par le moyen <lb/>d'une verge de fer, parallele à la ſituation de la ſoie étenduë le long <lb/>de l'axe du Cadran horiſontal, & </s> <s xml:id="echoid-s11176" xml:space="preserve">ſoutenuë par quelque appui plan-<lb/>té dans le Mur perpendiculairement à la ſouſty laire.</s> <s xml:id="echoid-s11177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11178" xml:space="preserve">Si l'on ne vouloit qu'un ſtyle droit, on choiſira ſur la ſouſtylaire <lb/>un point éloigné du centre à proportion de la grandeur du Cadran, <lb/>pour y planter une verge de fer perpendiculaire; </s> <s xml:id="echoid-s11179" xml:space="preserve">mais il faut que ſa <lb/>pointe ne paſſe pas la ſoie tenduë le long de l'Axe.</s> <s xml:id="echoid-s11180" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11181" xml:space="preserve">Enfin vous donnerez à vôtre Cadran telle figure que vous juge-<lb/>rez à propos, & </s> <s xml:id="echoid-s11182" xml:space="preserve">prolongerez les lignes horaires autant qu'il ſera be-<lb/>ſoin, ſuivant la grandeur de vôtre Plan.</s> <s xml:id="echoid-s11183" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11184" xml:space="preserve">On peut éloigner l'inſtrument du Mur pour y tracer de grands <lb/>Cadrans, mais il faut qu'il ſoit toûjours poſé bien parallelement <lb/>& </s> <s xml:id="echoid-s11185" xml:space="preserve">de niveau.</s> <s xml:id="echoid-s11186" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11187" xml:space="preserve">Pour les Cadrans, Septentrionaux, ayant trouvé la déclinaiſon du <lb/>Plan, comme, par exemple, de 45 deg. </s> <s xml:id="echoid-s11188" xml:space="preserve">du Septentrion à l'Occi-<lb/>dent, placez l'index du Cadran ſur la déclinaiſon oppoſée, c'eſt-à-<lb/>dire du Midi à lOrient; </s> <s xml:id="echoid-s11189" xml:space="preserve">renverſez' enſuite l'inſtrument ſens deſſus <lb/>deſſous; </s> <s xml:id="echoid-s11190" xml:space="preserve">étendez la ſoie le long de l'Axe pour avoir le centre en <lb/>bas au-deſſous de la ligne horiſontale, ſur laquelle ayant marqué <lb/>les points des heures, vous les prolongerez juſqu'au centre, & </s> <s xml:id="echoid-s11191" xml:space="preserve">fe-<lb/>rez le reſte comme nous venons de dire; </s> <s xml:id="echoid-s11192" xml:space="preserve">la ligne de midi ſera celle <lb/>de minuit.</s> <s xml:id="echoid-s11193" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div685" type="section" level="1" n="357"> <head xml:id="echoid-head493" style="it" xml:space="preserve">Conſtruction du Sciaterre.</head> <p> <s xml:id="echoid-s11194" xml:space="preserve">L'In ſtrument repreſenté par la figure 4, ſe nomme Sciaterre. </s> <s xml:id="echoid-s11195" xml:space="preserve">Il <lb/> <anchor type="note" xlink:label="note-358-01a" xlink:href="note-358-01"/> eſt compoſé d'un cercle Equinoxial A, fait de cuivre ou de <lb/>quelque autre matiere ſolide, monté ſur un Quart de cercle B. </s> <s xml:id="echoid-s11196" xml:space="preserve">Le <lb/> <pb o="343" file="359" n="359" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. IV."/> point de Midi de l'Equinoxial eſt attaché à un des bouts du Quart <lb/>de cercle, & </s> <s xml:id="echoid-s11197" xml:space="preserve">une petite broche d'acier ronde d'une à 2 lignes de dia-<lb/>metre, qui ſert d'axe & </s> <s xml:id="echoid-s11198" xml:space="preserve">paſſe par le centre de l'Equinoxial, tient à <lb/>l'autre extremité du Quart de cercle, de telle ſorte que l'Equino-<lb/>xial & </s> <s xml:id="echoid-s11199" xml:space="preserve">le Quart de cercle ſont fixement attachez enſemble à angles <lb/>droits. </s> <s xml:id="echoid-s11200" xml:space="preserve">Le Quart de cercle eſt diviſé en 90 d. </s> <s xml:id="echoid-s11201" xml:space="preserve">& </s> <s xml:id="echoid-s11202" xml:space="preserve">le Cercle Equino-<lb/>xial en heures & </s> <s xml:id="echoid-s11203" xml:space="preserve">demi-heures par les méthodes expliquées ci-de-<lb/>vant. </s> <s xml:id="echoid-s11204" xml:space="preserve">La piece G eſt d'une épaiſſeur convenable pour contenir par <lb/>le haut une couliſſe qui entre des deux côtez dans une rainure qui <lb/>eſt au bord extérieur du Quart de cercle, pour hauſſer ou baiſſer l'E-<lb/>quinoxial ſuivant la hauteur du Pole. </s> <s xml:id="echoid-s11205" xml:space="preserve">La petite Boule eſt attachée <lb/>au bout d'une ſoie, arrêtée au haut d'une ligne perpendiculaire, <lb/>pour placer la machine à plomb par le moyen du genoüil H, qui <lb/>tient à la piece G, ſervant à tourner l'Inſtrument en tout ſens. </s> <s xml:id="echoid-s11206" xml:space="preserve">Le <lb/>genoüil eſt rivé à une branche, dont le bout eſt d'acier, que l'on en-<lb/>fonce dans le Mur pour tenir ferme toute la Machine, quand on <lb/>veut la mettre en uſage.</s> <s xml:id="echoid-s11207" xml:space="preserve"/> </p> <div xml:id="echoid-div685" type="float" level="2" n="1"> <note position="left" xlink:label="note-358-01" xlink:href="note-358-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s11208" xml:space="preserve">Le trigone de Signes D, eſt paſſé dans l'axe, & </s> <s xml:id="echoid-s11209" xml:space="preserve">tourne autour <lb/>du Cadran par le moyen d'une virolle. </s> <s xml:id="echoid-s11210" xml:space="preserve">Il y a une ſoie attachée au <lb/>ſommet du Trigone, & </s> <s xml:id="echoid-s11211" xml:space="preserve">une autre au centre du Cadran. </s> <s xml:id="echoid-s11212" xml:space="preserve">On ne pla-<lb/>ce le Trigone que quand on veut tracer les Arcs des Signes ſur les <lb/>Cadrans.</s> <s xml:id="echoid-s11213" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div687" type="section" level="1" n="358"> <head xml:id="echoid-head494" style="it" xml:space="preserve">Uſage du Sciaterre.</head> <p> <s xml:id="echoid-s11214" xml:space="preserve">IL faut d'abord enfoncer dans le Mur la pointe d'acier attachée <lb/>au pied de l'Inſtrument, à l'endroit où l'on veut faire un Cadran, <lb/>& </s> <s xml:id="echoid-s11215" xml:space="preserve">mettre le degré de l'élevation du Pole du lieu du Quart de cercle, <lb/>vis-à-vis d'un trait à plomb marqué ſur la couliſſe.</s> <s xml:id="echoid-s11216" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11217" xml:space="preserve">Il faut auſſi avoir une Bouſſole quarrée, que vous poſerez au long <lb/>du Plan du Quart de cercle, & </s> <s xml:id="echoid-s11218" xml:space="preserve">vous tournerez la Machine juſ-<lb/>qu'à ce que l'éguille aimantée ſoit arrêtée juſtement ſur la ligne de <lb/>déclinaiſon, ou bien ſans Bouſſole, ſi le Soleil luit, & </s> <s xml:id="echoid-s11219" xml:space="preserve">que vous ſça-<lb/>chiez l'heure qu'il eſt, tournez la Machine de ſorte que l'Axe qui <lb/>traverſe l'Equinoxial, marque préciſément l'heure ſur le cercle des <lb/>heures. </s> <s xml:id="echoid-s11220" xml:space="preserve">L'Inſtrument étant ainſi diſpoſé, étendez la ſoie E, qui part <lb/>du centre, tout le long de l'axe juſqu'à la rencontre du Plan propo-<lb/>ſé, pour y marquer un point qui ſera le centre du Cadran; </s> <s xml:id="echoid-s11221" xml:space="preserve">puis ra-<lb/>ſant les heures l'une après l'autre avec la même ſoie, prolongée juſ-<lb/>qu'au Mur, marquez-y autant de points que vous pourrez, & </s> <s xml:id="echoid-s11222" xml:space="preserve">par <lb/>ces points, tracez les lignes horaires juſqu'au centre du Cadran, où <lb/> <pb o="344" file="360" n="360" rhead="CONSTRUCTION ET USAGES"/> elles ſe doivent rencontrer. </s> <s xml:id="echoid-s11223" xml:space="preserve">Donnez telle figure qu'il vous plaira à <lb/>ce Cadran, & </s> <s xml:id="echoid-s11224" xml:space="preserve">placez-y les mêmes chifres que ceux des heures de <lb/>l'Equinoxial.</s> <s xml:id="echoid-s11225" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11226" xml:space="preserve">Le ſtyle ſe poſera de la maniere qui vient d'être expliquée en par-<lb/>lant de l'horiſontal mobile.</s> <s xml:id="echoid-s11227" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11228" xml:space="preserve">Pour tracer les Arcs des Signes ou les Arcs Diurnes, faites entrer <lb/>l'axe dans la virolle qui eſt à l'extremité du Trigone, que vous fe-<lb/>rez tourner ſur toutes les heures, en l'arrêtant avec la vis l'une après <lb/>l'autre, puis étendant la ſoie F le long des lignes qui appartiennent <lb/>à chaque Signe pour marquer autant de points ſur chaque ligne ho-<lb/>raire du Mur; </s> <s xml:id="echoid-s11229" xml:space="preserve">enſuite vous tracerez des lignes courbes de points en <lb/>points, qui formeront les Arcs des Signes, & </s> <s xml:id="echoid-s11230" xml:space="preserve">y marquerez les ca-<lb/>racteres convenables.</s> <s xml:id="echoid-s11231" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11232" xml:space="preserve">On peut encore tracer les arcs des Signes de cette maniere: </s> <s xml:id="echoid-s11233" xml:space="preserve">l'A-<lb/>xe du Cadran étant bien affermi, choiſiſſez un point ſur ledit <lb/>Axe pour l'extremité du ſtyle droit, qui repreſente le centre de la <lb/>Terre; </s> <s xml:id="echoid-s11234" xml:space="preserve">faites entrer cet Axe dans la virolle de vôtre Trigone, en <lb/>ſorte que l'extremité du ſtyle droit convienne exactement avec le <lb/>ſommet du Trigone qui repreſente le centre de l'Equateur & </s> <s xml:id="echoid-s11235" xml:space="preserve">du <lb/>Monde, & </s> <s xml:id="echoid-s11236" xml:space="preserve">ayant arrêté le Trigone par le moyen de la vis qui preſ-<lb/>ſera ſur l'Axe, faites-le tourner de ſorte qu'un de ces Plans (car ils <lb/>doivent être marquez également) ſe trouve exactement ſur les li-<lb/>gnes horaires; </s> <s xml:id="echoid-s11237" xml:space="preserve">étendez la ſoie F le long des raïons des Signes du Tri-<lb/>gone, & </s> <s xml:id="echoid-s11238" xml:space="preserve">marquez autant de points ſur chaque ligne horaire l'une <lb/>après l'autre; </s> <s xml:id="echoid-s11239" xml:space="preserve">joignez ces points par des lignes courbes qui repre-<lb/>ſenteront les Arcs des Signes. </s> <s xml:id="echoid-s11240" xml:space="preserve">Enfin vous mettrez un bouton ou <lb/>un petit Soleil à ce point de l'Axe, lequel par ſon ombre marquera <lb/>ſur le Cadran les paralleles des Signes ou des Arcs Diurnes, pendant <lb/>que l'Axe entier fera ombre ſur les lignes des heures.</s> <s xml:id="echoid-s11241" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11242" xml:space="preserve">S'il s'agit de tracer un Cadran Septentrional, faites la même <lb/>choſe, excepté que l'operation ſe fera en deſſous, afin que le centre <lb/>ſoit en bas.</s> <s xml:id="echoid-s11243" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11244" xml:space="preserve">On fait les mêmes operations pour tracer les Cadransſur les Plans <lb/>inclinez & </s> <s xml:id="echoid-s11245" xml:space="preserve">déclinans.</s> <s xml:id="echoid-s11246" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div688" type="section" level="1" n="359"> <head xml:id="echoid-head495" style="it" xml:space="preserve">Conſtruction du Sciaterre du P. Pardies.</head> <p> <s xml:id="echoid-s11247" xml:space="preserve">CEt Inſtrument eſt de l'invention du P. </s> <s xml:id="echoid-s11248" xml:space="preserve">Pardies Jéſuite. </s> <s xml:id="echoid-s11249" xml:space="preserve">Il <lb/> <anchor type="note" xlink:label="note-360-01a" xlink:href="note-360-01"/> ſe fait de cuivre ou autre matiere ſolide, d'une grandeur arbi-<lb/>traire. </s> <s xml:id="echoid-s11250" xml:space="preserve">Il eſt compoſé de quatre principales pieces; </s> <s xml:id="echoid-s11251" xml:space="preserve">la premiere eſt <lb/>une plaque quarrée bien dreſſée, marquée D, qu'on nomme Plan <lb/> <pb o="345" file="361" n="361" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. IV."/> horiſontal, parce que dans l'uſage il doit être mis horiſontalement <lb/>ou à niveau.</s> <s xml:id="echoid-s11252" xml:space="preserve"/> </p> <div xml:id="echoid-div688" type="float" level="2" n="1"> <note position="left" xlink:label="note-360-01" xlink:href="note-360-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s11253" xml:space="preserve">Au milieu de ce Plan il y a un trou rond, dans lequel eſt un pivot <lb/>à l'endroit marqué E, ſur lequel doit tourner la ſeconde piece, que <lb/>l'on nomme Plan Méridional, de ſorte qu'il demeure toûjours à an-<lb/>gles droits avec le Plan horiſontal. </s> <s xml:id="echoid-s11254" xml:space="preserve">Au côté & </s> <s xml:id="echoid-s11255" xml:space="preserve">ſur l'épaiſſeur du <lb/>Plan Méridional il y a un plomb ſuſpendu en C, qui ſert à placer <lb/>l'Inſtrument à niveau. </s> <s xml:id="echoid-s11256" xml:space="preserve">Le haut de cette piece eſt taillé en Quart de <lb/>cercle concave, qui ſe diviſe de chaque côté en 90 d. </s> <s xml:id="echoid-s11257" xml:space="preserve">commençant <lb/>à la perpendiculaire qui répond au milieu du pivot. </s> <s xml:id="echoid-s11258" xml:space="preserve">Cette piece eſt <lb/>fenduë par le milieu de ſon épaiſſeur pour recevoir la 3<emph style="sub">me</emph> piece, qui <lb/>eſt un demi cercle où il y a une piece qui le déborde, pour entrer <lb/>dans la fente du Quart de cercle, & </s> <s xml:id="echoid-s11259" xml:space="preserve">qui par ce moyen l'engage dans <lb/>le Quart de cercle, aveclequel il fait le même Plan Méridional, de <lb/>maniere qu'il peut tourner, en s'inclinant ou ſe dreſſant tant que <lb/>l'on veut, ſelon les differentes élevations de Pole. </s> <s xml:id="echoid-s11260" xml:space="preserve">Le diametre de ce <lb/>demi-cercle s'appelle l'Axe, & </s> <s xml:id="echoid-s11261" xml:space="preserve">ſon centre s'appelle ſimplement le <lb/>Centre de l'Inſtrument, comme le filet qui en ſort s'appelle le Fi-<lb/>let du centre.</s> <s xml:id="echoid-s11262" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11263" xml:space="preserve">La 4<emph style="sub">me</emph> piece marquée A, eſt un cercle de même matiere, bien <lb/>dreſſé & </s> <s xml:id="echoid-s11264" xml:space="preserve">de bien égale épaiſſeur; </s> <s xml:id="echoid-s11265" xml:space="preserve">il eſt diviſé en 24 parties égales de <lb/>côté & </s> <s xml:id="echoid-s11266" xml:space="preserve">d'autre pour les 24 h. </s> <s xml:id="echoid-s11267" xml:space="preserve">du jour, dont chacune ſe peut ſubdi-<lb/>viſer en 2 ou en 4, comme étant un Cadran équinoxial. </s> <s xml:id="echoid-s11268" xml:space="preserve">Ce Cercle <lb/>eſt tellement engagé avec le demi-cercle par des entailles faites à <lb/>moitié dans l'un & </s> <s xml:id="echoid-s11269" xml:space="preserve">moitié dans l'autre, qu'il fait toûjours avec lui <lb/>des angles droits en toutes ſes differentes ſituations; </s> <s xml:id="echoid-s11270" xml:space="preserve">l'une des faces <lb/>de ce cercle ſe nomme ſupérieure, & </s> <s xml:id="echoid-s11271" xml:space="preserve">l'autre inférieure.</s> <s xml:id="echoid-s11272" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11273" xml:space="preserve">On trace de part & </s> <s xml:id="echoid-s11274" xml:space="preserve">d'autre ſur le demi-cercle le Trigone des Si-<lb/>gnes, dont le ſommet eſt le point A, extremité du diametre du cer-<lb/>cle Equinoxial, de la maniere que nous avons ci-devant expliquée. <lb/></s> <s xml:id="echoid-s11275" xml:space="preserve">En marquant ſur les raïons les caracteres des Signes, & </s> <s xml:id="echoid-s11276" xml:space="preserve">diviſant par <lb/>la même méthode chaque eſpace en trois, on y pourra graver les <lb/>premieres Lettres des mois dans les places qui leur conviennent à <lb/>peu près en ſuppoſant que l'entrée du Soleil en chaque Signe ſe <lb/>fait le 20<emph style="sub">me</emph> jour des mois. </s> <s xml:id="echoid-s11277" xml:space="preserve">On en met 6 ſur le côté Oriental, & </s> <s xml:id="echoid-s11278" xml:space="preserve">6 <lb/>ſur l'Occidental, car chaque ligne eſt toûjours pour deux Signes. </s> <s xml:id="echoid-s11279" xml:space="preserve"><lb/>Le Tropique de l'Ecreviſſe ſe marque en bas, & </s> <s xml:id="echoid-s11280" xml:space="preserve">celui du Capricor-<lb/>ne en haut, de même que ſur les Cadrans verticaux. </s> <s xml:id="echoid-s11281" xml:space="preserve">Nous ne par-<lb/>lons pas de la maniere de tracer les heures, les degrez, ni les Signes, <lb/>étant la même que nous avons expliquée ci-devant.</s> <s xml:id="echoid-s11282" xml:space="preserve"/> </p> <pb o="346" file="362" n="362" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div690" type="section" level="1" n="360"> <head xml:id="echoid-head496" xml:space="preserve">Uſage de cette Machine.</head> <p> <s xml:id="echoid-s11283" xml:space="preserve">APrès avoir mis les points de ♈ & </s> <s xml:id="echoid-s11284" xml:space="preserve">♎ du demi-cercle & </s> <s xml:id="echoid-s11285" xml:space="preserve">le Plan <lb/>du cercle Equinoxial ſur le degré de l'élevation du Pole du <lb/>Païs où l'on veut faire le Cadran, placez la Machine ſur un Plan ſta-<lb/>ble & </s> <s xml:id="echoid-s11286" xml:space="preserve">horiſontal, vis-à-vis du Mur ou autre ſurface preparée pour <lb/>y tracer un Cadran.</s> <s xml:id="echoid-s11287" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11288" xml:space="preserve">Tournez-la de ſorte que l'ombre du bord du Cercle équinoxial <lb/>rencontre ſur l'axe le jour du mois ou le degré du Signe où eſt pour <lb/>lors le Soleil; </s> <s xml:id="echoid-s11289" xml:space="preserve">cela étant, l'ombre du diametre du demi-cercle qui <lb/>ſert d'axe; </s> <s xml:id="echoid-s11290" xml:space="preserve">marquera l'heure preſente, & </s> <s xml:id="echoid-s11291" xml:space="preserve">toute la Machine ſera bien <lb/>fituée. </s> <s xml:id="echoid-s11292" xml:space="preserve">Le Plan Méridional répondra au Méridien du Ciel; </s> <s xml:id="echoid-s11293" xml:space="preserve">le Cer-<lb/>cle équinoxial ſera parallele à l'Equateur de la Sphere celeſte, & </s> <s xml:id="echoid-s11294" xml:space="preserve"><lb/>l'Axe du Cadran à l'Axe du Monde.</s> <s xml:id="echoid-s11295" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11296" xml:space="preserve">Tendez la ſoie qui part du centre le long de l'Axe juſqu'au ren-<lb/>contre du Mur, ſoit en haut vers le Pole Arctique, ſoit en bas vers <lb/>l'Antarctique. </s> <s xml:id="echoid-s11297" xml:space="preserve">Le point où le filet rencontrera le mur ſera le centre <lb/>du Cadran. </s> <s xml:id="echoid-s11298" xml:space="preserve">Ce filet ainſi tendu marquera la poſition du ſtyle ou axe, <lb/>car ſi l'on met une verge de fer au même endroit & </s> <s xml:id="echoid-s11299" xml:space="preserve">dans la même <lb/>fituation, elle marquera les heures tout le long de ſon ombre. </s> <s xml:id="echoid-s11300" xml:space="preserve">Si on <lb/>ne veut mettre qu'un ſtyle droit, il n'y aura qu'à planter une verge <lb/>dans le mur, dont le bout vienne toucher la ſoie tenduë au long de <lb/>l'axe. </s> <s xml:id="echoid-s11301" xml:space="preserve">On peut donner à cette verge la figure que l'on voudra, com-<lb/>med'un Serpent ou d'un Oiſeau, pourvû que l'extremité de ſon bec <lb/>ren contre ladite ſoie; </s> <s xml:id="echoid-s11302" xml:space="preserve">& </s> <s xml:id="echoid-s11303" xml:space="preserve">de cette maniere l'heure ne ſera marquée <lb/>que par le bout de l'ombre.</s> <s xml:id="echoid-s11304" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11305" xml:space="preserve">Pour marquer les heures, étendez le filet du centre ſur le Plan du <lb/>Cercle équinoxial, tout au long des lignes horaires, l'une après l'au-<lb/>tre, juſqu'au rencontre du Mur, & </s> <s xml:id="echoid-s11306" xml:space="preserve">marquez-y autant de points; </s> <s xml:id="echoid-s11307" xml:space="preserve">ti-<lb/>rez enſuite des lignes du centre par ces points, & </s> <s xml:id="echoid-s11308" xml:space="preserve">vous aurez les li-<lb/>gnes des heures.</s> <s xml:id="echoid-s11309" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11310" xml:space="preserve">On pourroit encore marquer les heures pendant la nuit par la lu-<lb/>miere d'un ffambeau ou d'une bougie. </s> <s xml:id="echoid-s11311" xml:space="preserve">Le filet du centre étant éten-<lb/>du au long de l'Axe & </s> <s xml:id="echoid-s11312" xml:space="preserve">attaché au mur, tournez le flambeau de ſor-<lb/>te que l'ombre de l'axe marque l'heure ſur le Cercle équinoxial; </s> <s xml:id="echoid-s11313" xml:space="preserve">a-<lb/>lors l'ombre du même Axe ou du filet tendu marquera ſur le mur la <lb/>même heure, & </s> <s xml:id="echoid-s11314" xml:space="preserve">il ne faut que paſſer le craïon tout le long de cet <lb/>ombre pour marquer la ligne horaire. </s> <s xml:id="echoid-s11315" xml:space="preserve">Changez enſuite le flambeau <lb/>de place, afin que l'ombre du filet marque une autre heure que vous <lb/>tracerez de même, & </s> <s xml:id="echoid-s11316" xml:space="preserve">ainſi de toutes les autres. </s> <s xml:id="echoid-s11317" xml:space="preserve">Cette maniere eſt <lb/> <pb o="347" file="363" n="363" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> très-bonne, particulierement lorſque le Plan n'eſt pas plat & </s> <s xml:id="echoid-s11318" xml:space="preserve">uni, <lb/>ou que le centre du Cadran eſt trop éloigné.</s> <s xml:id="echoid-s11319" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11320" xml:space="preserve">Il eſt à remarquer que l'ombre de l'Axe marque les heures ſur le <lb/>Cadran ſupérieur, depuis le 20 de Mars juſqu'au 22 de Septembre, <lb/>& </s> <s xml:id="echoid-s11321" xml:space="preserve">ſur l'inférieur pendant les autres ſix mois. </s> <s xml:id="echoid-s11322" xml:space="preserve">Il faut toûjours que <lb/>la ſurface du cercle éclairée & </s> <s xml:id="echoid-s11323" xml:space="preserve">dont on ſe doit ſervir, touche le cen-<lb/>tre du demi cercle ſans le couvrir.</s> <s xml:id="echoid-s11324" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div691" type="section" level="1" n="361"> <head xml:id="echoid-head497" xml:space="preserve">CHAPITRE V.</head> <head xml:id="echoid-head498" xml:space="preserve">De la Conſtruction & des Uſage des Cadrans portatifs. <lb/>Conſtruction du Globe.</head> <p> <s xml:id="echoid-s11325" xml:space="preserve">CEtte figure repreſente un Globe ſur lequel ſont tracez les Méri-<lb/> <anchor type="note" xlink:label="note-363-01a" xlink:href="note-363-01"/> diens ou cercles horaires. </s> <s xml:id="echoid-s11326" xml:space="preserve">On en fait de differentes grandeurs; <lb/></s> <s xml:id="echoid-s11327" xml:space="preserve">les grands ſont expoſez dans les Jardins, & </s> <s xml:id="echoid-s11328" xml:space="preserve">ſe font de pierre ou de <lb/>bois peint en huile; </s> <s xml:id="echoid-s11329" xml:space="preserve">les petits ſe font de cuivre avec une Bouſſole, & </s> <s xml:id="echoid-s11330" xml:space="preserve"><lb/>peuvent être mis au rang des Cadrans portatifs.</s> <s xml:id="echoid-s11331" xml:space="preserve"/> </p> <div xml:id="echoid-div691" type="float" level="2" n="1"> <note position="right" xlink:label="note-363-01" xlink:href="note-363-01a" xml:space="preserve">XXVI. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s11332" xml:space="preserve">Pour bien arrondir une boule, de quelque matiere que ce puiſſe <lb/>être, il faut la mettre ſur le Tour, & </s> <s xml:id="echoid-s11333" xml:space="preserve">la tourner ſur pluſieurs centres; <lb/></s> <s xml:id="echoid-s11334" xml:space="preserve">c'eſt-à-dire, que l'ayant miſe ſur un Mandrin quarré on la tourne <lb/>ſur un ſens, enſuite on change le Mandrin & </s> <s xml:id="echoid-s11335" xml:space="preserve">on l'applique à l'autre <lb/>diametre pour la tourner ſur l'autre ſens, & </s> <s xml:id="echoid-s11336" xml:space="preserve">repetant cela deux ou <lb/>trois fois, on aura une Boule parfaite; </s> <s xml:id="echoid-s11337" xml:space="preserve">que l'on pourra examiner a-<lb/>vec un Compas ſpherique.</s> <s xml:id="echoid-s11338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11339" xml:space="preserve">Les groſſes Boules de pierre qu'on ne peut mettre ſur le Tour à <lb/>cauſe de leur poids ſe font ainſi. </s> <s xml:id="echoid-s11340" xml:space="preserve">A près les avoir dégroſſies au ciſeau <lb/>ayez un demi-cercle concave de bois ou de cuivre de même diame-<lb/>tre que la Boule propoſée à tailler; </s> <s xml:id="echoid-s11341" xml:space="preserve">faites tourner le demi-cercle tout <lb/>autour de la Boule, & </s> <s xml:id="echoid-s11342" xml:space="preserve">ôtez avec une râpe tout ce qu'il y a de ſuper-<lb/>flu, juſqu'à ce que le demi-cercle joigne par tout & </s> <s xml:id="echoid-s11343" xml:space="preserve">en tout ſens; </s> <s xml:id="echoid-s11344" xml:space="preserve">& </s> <s xml:id="echoid-s11345" xml:space="preserve"><lb/>enſuite on l'adoucira avec de la ponce ou chien-de-mer, &</s> <s xml:id="echoid-s11346" xml:space="preserve">c.</s> <s xml:id="echoid-s11347" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11348" xml:space="preserve">Le Globe étant ainſi bien arrondi & </s> <s xml:id="echoid-s11349" xml:space="preserve">bien uni, il en faut prendre <lb/>le diametre avec un Compas ſpherique, c'eſt-à-dire, qui ait les poin-<lb/>tes courbes, l'ouvrant juſqu'à ce qu'il embraſſe exactement la plus <lb/>grande groſſeur du Globe, & </s> <s xml:id="echoid-s11350" xml:space="preserve">vous aurez ſon diametre repreſenté <lb/>par la ligne AB, qui eſt diviſée en deux parties égales par le point <lb/>d'interſection E, de la ligne verticale ZN, dont le point ſupérieur <lb/>Z repréſente le Zénith, & </s> <s xml:id="echoid-s11351" xml:space="preserve">le point inférieur N le Nadir. </s> <s xml:id="echoid-s11352" xml:space="preserve">Ouvrez le <lb/>Compas ſpherique, arrêtez une de ſes pointes en E, étendez l'autre <lb/>juſqu'en A, & </s> <s xml:id="echoid-s11353" xml:space="preserve">de cette ouverture tracez le cercle Méridien AZBN, <lb/> <pb o="348" file="364" n="364" rhead="CONSTRUCTION ET USAGES"/> tracez de même du point Z, comme centre, le cercle AEB, quire pre-<lb/>ſente l'horiſon: </s> <s xml:id="echoid-s11354" xml:space="preserve">du point A, comptez vers C, ſur le Méridien la hau-<lb/>teur du Pole, comme ici de 49 d. </s> <s xml:id="echoid-s11355" xml:space="preserve">du même point B, comptez au-<lb/>deſſous de l'horiſon & </s> <s xml:id="echoid-s11356" xml:space="preserve">ſur le Méridien les degrez du complément <lb/>de l'élevation du Pole, qui eſt ici 41 d. </s> <s xml:id="echoid-s11357" xml:space="preserve">afin d'y tracer l'Equateur, en <lb/>mettant une pointe du Compas ſpherique ſur un des Poles C ou D, <lb/>comme centre, & </s> <s xml:id="echoid-s11358" xml:space="preserve">l'autre ſur le 60<emph style="sub">me</emph> degré du Méridien.</s> <s xml:id="echoid-s11359" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11360" xml:space="preserve">Mettez pareillement une des pointes du Compas ſpherique ſur le <lb/>90<emph style="sub">me</emph> d. </s> <s xml:id="echoid-s11361" xml:space="preserve">du Méridien où il eſt coupé par l'Equateur, & </s> <s xml:id="echoid-s11362" xml:space="preserve">de la même <lb/>ouverture tracez le cercle de 6 h. </s> <s xml:id="echoid-s11363" xml:space="preserve">paſſant par les Poles C & </s> <s xml:id="echoid-s11364" xml:space="preserve">D; </s> <s xml:id="echoid-s11365" xml:space="preserve">par <lb/>ce moyen l'Equateur ſe trouvera partagé en 4 parties égales par le <lb/>Méridien, & </s> <s xml:id="echoid-s11366" xml:space="preserve">le cercle de 6 h. </s> <s xml:id="echoid-s11367" xml:space="preserve">diviſez enſuite chacune de ces parties <lb/>en 6, pour avoir les 24 h. </s> <s xml:id="echoid-s11368" xml:space="preserve">du jour naturel, & </s> <s xml:id="echoid-s11369" xml:space="preserve">par ces points de divi-<lb/>ſion, comme centre, tenant le Compas toûjours ouvert d'un quart <lb/>de cercle, vous tracerez les cercles horaires paſſans tous par les Poles <lb/>du Monde. </s> <s xml:id="echoid-s11370" xml:space="preserve">Sivous voulez les demi-heures ou les quarts, vous par-<lb/>tagerez chaque eſpace en 2 ou en 4. </s> <s xml:id="echoid-s11371" xml:space="preserve">Les chifres des heures ſe gra-<lb/>vent autour de l'Equateur, 12 h. </s> <s xml:id="echoid-s11372" xml:space="preserve">au point E, 6 h ſur le Méridien <lb/>deſſus & </s> <s xml:id="echoid-s11373" xml:space="preserve">deſſous, & </s> <s xml:id="echoid-s11374" xml:space="preserve">les autres de ſuite en 2 fois 12.</s> <s xml:id="echoid-s11375" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11376" xml:space="preserve">Pour y marquer les paralleles des Signes, comptez depuis l'Equa-<lb/>teur ſur le Méridien; </s> <s xml:id="echoid-s11377" xml:space="preserve">de part & </s> <s xml:id="echoid-s11378" xml:space="preserve">d'autre, la déclinaiſon de chaque <lb/>Signe; </s> <s xml:id="echoid-s11379" xml:space="preserve">ſuivant la Table marquée ci-devant, comme pour les 2 T ro-<lb/>piques, comptez depuis l'Equateur 23 d. </s> <s xml:id="echoid-s11380" xml:space="preserve">30 m. </s> <s xml:id="echoid-s11381" xml:space="preserve">& </s> <s xml:id="echoid-s11382" xml:space="preserve">des Poles C & </s> <s xml:id="echoid-s11383" xml:space="preserve">D, <lb/>comme centres, tracez autant de cercles autour du Globe. </s> <s xml:id="echoid-s11384" xml:space="preserve">Pour les <lb/>2 cercles Polaires, vous les tracerez à 23 d. </s> <s xml:id="echoid-s11385" xml:space="preserve">30 m. </s> <s xml:id="echoid-s11386" xml:space="preserve">des Poles, ou 66 <lb/>d. </s> <s xml:id="echoid-s11387" xml:space="preserve">30 m de l'Equateur.</s> <s xml:id="echoid-s11388" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11389" xml:space="preserve">Le Globe ain ſi préparé doit être placé ſur un pied proportionné à <lb/>ſa groſſeur dans un trou fait au Nadir marqué N, éloigné du Pole, <lb/>du complément de ſon élevation; </s> <s xml:id="echoid-s11390" xml:space="preserve">c'eſt-à-dire, en cet exemple de 41 <lb/>d. </s> <s xml:id="echoid-s11391" xml:space="preserve">arrêté fixement & </s> <s xml:id="echoid-s11392" xml:space="preserve">orienté conformément à la Sphere du Mon-<lb/>de, dans le lieu du Jardin où le Soleil luit plus long-tems.</s> <s xml:id="echoid-s11393" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11394" xml:space="preserve">Si c'eſt un petit Globe portatif, on place ſur ſon pied une petit <lb/>Bouſſole pour l'orienter toutes les fois qu'on voudra s'en ſervir pour <lb/>voir l'heure, que l'on y connoît ſans ſtyle, par l'ombre du Globe mê-<lb/>me car l'ombre ou la lumiere occupe toujours la moitié de ſa con-<lb/>vexité, tant que le Soleil l'éclaire, comme ſi c'étoit le Globe de la <lb/>Terre; </s> <s xml:id="echoid-s11395" xml:space="preserve">& </s> <s xml:id="echoid-s11396" xml:space="preserve">leur extremité marque l'heure, qui eſt la même en deux en-<lb/>droits oppoſez. </s> <s xml:id="echoid-s11397" xml:space="preserve">Si de plus on deſſinoit ſur le Globe les differens <lb/>Païs qui ſont ſur la ſurface de la Terre, avecles principales Villes, <lb/>ſuivant leur longitude & </s> <s xml:id="echoid-s11398" xml:space="preserve">latitude, on y verroit à chaque moment, <lb/> <pb o="349" file="365" n="365" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> par la moitié du Globe illuminé, quels ſont les endroits de la Terre <lb/>qui ſont éclairez du Soleil; </s> <s xml:id="echoid-s11399" xml:space="preserve">& </s> <s xml:id="echoid-s11400" xml:space="preserve">quels ſont ceux qui ſont dans l'obſcu-<lb/>rité. </s> <s xml:id="echoid-s11401" xml:space="preserve">L'extremité de l'ombre feroit connoître les Païs où le Soleil ſe <lb/>leve ou ſe couche, ceux qui ont les longs jours & </s> <s xml:id="echoid-s11402" xml:space="preserve">ceux qui ont les <lb/>longues nuits; </s> <s xml:id="echoid-s11403" xml:space="preserve">on y diſtingueroit vers les Poles les endroits qui ont <lb/>une nuit perpetuelle, & </s> <s xml:id="echoid-s11404" xml:space="preserve">ceux qui ont le jour ſans interruption. </s> <s xml:id="echoid-s11405" xml:space="preserve">Le <lb/>tout eſt aiſé à comprendre à ceux qui ont l'intelligence de la Sphe-<lb/>re. </s> <s xml:id="echoid-s11406" xml:space="preserve">Ce Cadran eſt le plus naturel de tous, puiſqu'il reſſemble à la <lb/>Terre, & </s> <s xml:id="echoid-s11407" xml:space="preserve">qu'il eſt éclairé comme elle.</s> <s xml:id="echoid-s11408" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11409" xml:space="preserve">On peut encore connoître l'heure ſur le Globe par le moyen d'un <lb/>demi-cercle de cuivre mince, diviſé en deux fois 90 d. </s> <s xml:id="echoid-s11410" xml:space="preserve">qu'on ajuſte <lb/>par le moïen de deux petites virolles aux deux Poles ou aux deux ex-<lb/>tremitez de l'axe. </s> <s xml:id="echoid-s11411" xml:space="preserve">Ce demi-cercle que l'on fait tourner avec la main <lb/>autour du Globe, juſqu'à ce qu'il n'y faſſe qu'une ombre perpendi-<lb/>culaire, repreſente le cercle horaire où eſt pour lors le Soleil, & </s> <s xml:id="echoid-s11412" xml:space="preserve">par <lb/>conſequent indique l'heure preſente.</s> <s xml:id="echoid-s11413" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11414" xml:space="preserve">Ce demi-cercle étant tourné directement au Soleil, & </s> <s xml:id="echoid-s11415" xml:space="preserve">ne faiſant <lb/>point d'ombre à ſes côtez, montrera ſous ſon épaiſſeur tous les lieux <lb/>de la Terre où il eſt midi.</s> <s xml:id="echoid-s11416" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11417" xml:space="preserve">Mais dans ce cas 12 h. </s> <s xml:id="echoid-s11418" xml:space="preserve">doivent étre marquées ſur le Méridien, & </s> <s xml:id="echoid-s11419" xml:space="preserve"><lb/>6 h. </s> <s xml:id="echoid-s11420" xml:space="preserve">aux deux points où l'Equateur coupe l'horiſon. </s> <s xml:id="echoid-s11421" xml:space="preserve">Ce qui fait <lb/>qu'on met ordinairement deux rangs d'heures, comme la figure le <lb/>marque.</s> <s xml:id="echoid-s11422" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11423" xml:space="preserve">Si l'on fait ſortir des Poles deux bouts d'Axe & </s> <s xml:id="echoid-s11424" xml:space="preserve">que les heures <lb/>ſoient marquées ſur les cercles Polaires, ils ſerviront auſſi à con-<lb/>noître l'heure; </s> <s xml:id="echoid-s11425" xml:space="preserve">ſçavoir, le ſupérieur pendant les longs jours, & </s> <s xml:id="echoid-s11426" xml:space="preserve">l'in-<lb/>férieur pendant les courts jours.</s> <s xml:id="echoid-s11427" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11428" xml:space="preserve">Il y a encore beaucoup d'autres uſages qui ſe peuvent pratiquer <lb/>avecle Globe, dont nous ne parlerons point ici, les ayant ſuffiſam-<lb/>ment expliquez dans le Livre qui traite de cette Matiere.</s> <s xml:id="echoid-s11429" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11430" xml:space="preserve">Je dirai ſeulement qu'on rend les petits Globes portatifs, univer-<lb/>ſels, en y ajuſtant un Quart de cercle au deſſous pour faire couler le <lb/>pied ſuivant l'élevation du Pole du lieu; </s> <s xml:id="echoid-s11431" xml:space="preserve">cela eſt facile a entendre.</s> <s xml:id="echoid-s11432" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div693" type="section" level="1" n="362"> <head xml:id="echoid-head499" xml:space="preserve">Conſtruction & uſage du demi-Cylindre concave & convexe.</head> <p> <s xml:id="echoid-s11433" xml:space="preserve">CE Cadran ſe fait de differentes groſſeurs; </s> <s xml:id="echoid-s11434" xml:space="preserve">les petits ſe font de <lb/> <anchor type="note" xlink:label="note-365-01a" xlink:href="note-365-01"/> cuivre, & </s> <s xml:id="echoid-s11435" xml:space="preserve">les grands de pierre ou de bois. </s> <s xml:id="echoid-s11436" xml:space="preserve">Il eſt fort curieux, <lb/>en ce qu'il marque les heures ſans ſtyle. </s> <s xml:id="echoid-s11437" xml:space="preserve">Sa juſteſſe conſiſte en ce <lb/>qu'il ſoit bien arrondi & </s> <s xml:id="echoid-s11438" xml:space="preserve">bien uni en-dedans comme en-dehors; <lb/></s> <s xml:id="echoid-s11439" xml:space="preserve">c'eſt à quoi il faut bien s'appliquer pour le rendre regulier.</s> <s xml:id="echoid-s11440" xml:space="preserve"/> </p> <div xml:id="echoid-div693" type="float" level="2" n="1"> <note position="right" xlink:label="note-365-01" xlink:href="note-365-01a" xml:space="preserve">Fig. 2.</note> </div> <pb o="350" file="366" n="366" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s11441" xml:space="preserve">Il eſt monté & </s> <s xml:id="echoid-s11442" xml:space="preserve">attaché ſur ſon pied, & </s> <s xml:id="echoid-s11443" xml:space="preserve">incliné comme l'Axe du <lb/>Monde ſur l'horiſon & </s> <s xml:id="echoid-s11444" xml:space="preserve">tourné droit au Midi, & </s> <s xml:id="echoid-s11445" xml:space="preserve">par conſequent <lb/>les lignes des heures & </s> <s xml:id="echoid-s11446" xml:space="preserve">les vives arrêtes qui ſervent de ſtyle, ſont <lb/>toutes paralleles à l'Axe du Monde. </s> <s xml:id="echoid-s11447" xml:space="preserve">Le Cylindre convexe entier ſe <lb/>diviſe en 24 parties égales, ou deux fois 12 h. </s> <s xml:id="echoid-s11448" xml:space="preserve">par des lignes paral-<lb/>leles. </s> <s xml:id="echoid-s11449" xml:space="preserve">Le demi-Cylindre concave faiſant un demi-cercle, ſe diviſe <lb/>en 6 parties égales, qui ſervent depuis 6 h. </s> <s xml:id="echoid-s11450" xml:space="preserve">du matin juſqu'à 6 <lb/>h. </s> <s xml:id="echoid-s11451" xml:space="preserve">du ſoir.</s> <s xml:id="echoid-s11452" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11453" xml:space="preserve">Le Soleil éclairant la moitié du Cylindre convexe, comme il <lb/>éclaire la moitié du Globe, y marque l'heure par le défaut de lu-<lb/>miere, c'eſt-à-dire, par une ligne qui termine la lumiere & </s> <s xml:id="echoid-s11454" xml:space="preserve">la ſé-<lb/>pare de l'ombre.</s> <s xml:id="echoid-s11455" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11456" xml:space="preserve">Au Cylindre concave l'heure eſt marquée par une des vives ar-<lb/>rêtes qui ſert d'Axe, de ſorte que le matin lorſque le Soleil eſt par-<lb/>venu au cercle de 6 h. </s> <s xml:id="echoid-s11457" xml:space="preserve">la vive arrête qui eſt du côté d'Orient, jet-<lb/>te ſon ombre ſur l'arrête oppoſée, & </s> <s xml:id="echoid-s11458" xml:space="preserve">y marque 6 h. </s> <s xml:id="echoid-s11459" xml:space="preserve">& </s> <s xml:id="echoid-s11460" xml:space="preserve">à meſure <lb/>que le Soleil s'éleve ſur l'horiſon, l'ombre deſcend & </s> <s xml:id="echoid-s11461" xml:space="preserve">marque <lb/>l'heure; </s> <s xml:id="echoid-s11462" xml:space="preserve">les heures du matin ſont marquées vers le haut du Cylin-<lb/>dre, & </s> <s xml:id="echoid-s11463" xml:space="preserve">celles d'après midi vers le bas. </s> <s xml:id="echoid-s11464" xml:space="preserve">Lorſque le Soleil eſt arrivé <lb/>au Méridien, il regarde en face le Cadran, & </s> <s xml:id="echoid-s11465" xml:space="preserve">pour lors il n'y a <lb/>point d'ombre; </s> <s xml:id="echoid-s11466" xml:space="preserve">lorſque le Soleil deſcend vers la partie Occiden-<lb/>tale, la vive arrête qui eſt du même côté, jette ſon ombre dans <lb/>la partie oppoſée, & </s> <s xml:id="echoid-s11467" xml:space="preserve">y marque les heures d'après midi juſqu'à 6 h. <lb/></s> <s xml:id="echoid-s11468" xml:space="preserve">du ſoir ſur la partie inférieure du Cylindre. </s> <s xml:id="echoid-s11469" xml:space="preserve">Si l'on veut les demi-<lb/>heures & </s> <s xml:id="echoid-s11470" xml:space="preserve">les quarts, il n'y a qu'à doubler les diviſions. </s> <s xml:id="echoid-s11471" xml:space="preserve">Aux petits <lb/>Cadrans on met une Bouſſole au pied pour les orienter.</s> <s xml:id="echoid-s11472" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div695" type="section" level="1" n="363"> <head xml:id="echoid-head500" xml:space="preserve">Conſtruction & uſage du Cylindre vertical.</head> <p> <s xml:id="echoid-s11473" xml:space="preserve">CEtte figure repreſente un Cadran vertical, tracé ſur la ſur-<lb/>face d'un Cylindre par le moyen de la Table des hauteurs du <lb/>Soleil ſur l'horiſon à toutes les heures du jour, pour la latitude <lb/>du lieu où l'on veut conſtruire le Cylindre, & </s> <s xml:id="echoid-s11474" xml:space="preserve">de dix en dix de-<lb/>grez de chaque Signe.</s> <s xml:id="echoid-s11475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11476" xml:space="preserve">La Table ci-jointe eſt calculée pour 49 degrez de latitude ou <lb/>d'élevation de Pole, qui peut ſervir dans la conſtruction de ces <lb/>Cadrans pour Paris, & </s> <s xml:id="echoid-s11477" xml:space="preserve">pour les lieux qui ont même élevation, <lb/>ou à peu près.</s> <s xml:id="echoid-s11478" xml:space="preserve"/> </p> <pb o="351" file="367" n="367" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> <note position="right" xml:space="preserve"> <lb/>Table des hauteurs du Soleil dans toutes les beures du jour pour <lb/>la latitude de 49. d. & de 10 en 10 degrez de chaque Signe. <lb/> ## Heur. # ## XII. # ## XI. # ## X. # ## IX. # ## VIII. # ## VII. # ## VI. # ## V. <lb/> # # I. # II. # III. # IIII. # V. # VI. # VII. <lb/>Signes # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. <lb/>30 # 69 # 64 # 30 # 61 # 56 # 55 # 19 # 46 # 35 # 37 # 1 # 27 # 10 # 17 # 30 # 8 # 21 <lb/>20 # 10 # 64 # 9 # 61 # 33 # 55 # 1 # 46 # 18 # 36 # 42 # 26 # 54 # 17 # 10 # 8 # 4 <lb/>10 # 20 # 63 # 2 # 60 # 31 # 54 # 4 # 45 # 28 # 35 # 5 # 26 # 6 # 16 # 20 # 7 # 12 <lb/>11 # ♌ # 61 # 12 # 58 # 49 # 52 # 34 # 44 # 7 # 34 # 39 # 24 # 50 # 16 # 6 # 5 # 50 <lb/>20 # 10 # 58 # 48 # 56 # 30 # 50 # 29 # 42 # 14 # 32 # 53 # 23 # 6 # 13 # 20 # 3 # 57 <lb/>10 # 20 # 55 # 52 # 53 # 42 # 47 # 57 # 39 # 55 # 30 # 41 # 20 # 57 # 11 # 11 # 1 # 40 <lb/>♉ # ♍ # 52 # 30 # 50 # 30 # 45 # 1 # 37 # 14 # 28 # 10 # 18 # 28 # 8 # 40 <lb/>20 # 10 # 48 # 51 # 46 # 48 # 41 # 44 # 34 # 13 # 25 # 19 # 15 # 43 # 5 # 54 <lb/>10 # 20 # 44 # 58 # 43 # 12 # 38 # 15 # 31 # 0 # 22 # 18 # 12 # 48 # 2 # 59 <lb/>♈ # ♎ # 41 # 0 # 39 # 20 # 34 # 37 # 27 # 38 # 19 # 9 # 9 # 47 <lb/>20 # 10 # 37 # 2 # 35 # 26 # 30 # 58 # 24 # 15 # 15 # 58 # 6 # 42 <lb/>10 # 20 # 33 # 9 # 31 # 40 # 27 # 24 # 20 # 55 # 12 # 51 # 3 # 44 <lb/>♓ # ♏ # 29 # 30 # 28 # 4 # 23 # 58 # 17 # 42 # 9 # 50 # 0 # 54 <lb/>20 # 10 # 26 # 8 # 24 # 46 # 20 # 51 # 14 # 45 # 7 # 6 <lb/>10 # 20 # 23 # 12 # 21 # 52 # 18 # 5 # 12 # 12 # 4 # 43 <lb/>♒ # ♐ # 20 # 48 # 19 # 30 # 15 # 48 # 10 # 3 # 2 # 42 <lb/>20 # 10 # 18 # 48 # 17 # 44 # 14 # 9 # 8 # 27 # 1 # 13 <lb/>10 # 20 # 17 # 52 # 16 # 38 # 13 # 3 # 7 # 27 # 0 # 19 <lb/>♑ # 30 # 17 # 30 # 15 # 15 # 12 # 42 # 7 # 8 <lb/></note> </div> <div xml:id="echoid-div696" type="section" level="1" n="364"> <head xml:id="echoid-head501" style="it" xml:space="preserve">Nous allons donner la Conſtruction de ce Cadran ſur un Plan <lb/>développé, qui eſt la ſurface convexe du Cylindre. Lamême <lb/>choſe ſe peut faire ſnr le Cylindre même en traçant les lignes <lb/>ſur le corps rond, de même que ſi c'étoit ſur un Plan.</head> <p> <s xml:id="echoid-s11479" xml:space="preserve">SUr une plaque de cuivre ou ſur une feüille de papier ou carton <lb/> <anchor type="note" xlink:label="note-367-02a" xlink:href="note-367-02"/> décrivez le Parallelograme rectangle ABCD, dont la largeur <lb/>AB ou CD eſt à peu près égale à la circonference du Cylindre; </s> <s xml:id="echoid-s11480" xml:space="preserve">pro-<lb/>longez la ligne AB, pour y marquer la longueur du ſtyle AE, qui <lb/>détermine la hauteur du Cylindre. </s> <s xml:id="echoid-s11481" xml:space="preserve">Du point E, comme centre & </s> <s xml:id="echoid-s11482" xml:space="preserve"><lb/>pour raïon EA, faites un arc égal à la hauteur du Soleil à midi, dans <lb/> <pb o="352" file="368" n="368" rhead="CONSTRUCTION ET USAGES"/> le plus long jour d'Eté. </s> <s xml:id="echoid-s11483" xml:space="preserve">Tirez la ligne occulte ED, qui donnera la <lb/>hauteur du Cylindre AD; </s> <s xml:id="echoid-s11484" xml:space="preserve">mais ſi cette longueur étoit donnée, pour <lb/>déterminer la longueur du ſtyle, du point D, comme centre, faites <lb/>ſur AD un arc égal au complément de la plus grande hauteur Mé-<lb/>ridiene du Soleil ſur l'horiſon du lieu propoſé. </s> <s xml:id="echoid-s11485" xml:space="preserve">Si cette plus grande <lb/>hauteur eſt de 64 d. </s> <s xml:id="echoid-s11486" xml:space="preserve">30 m. </s> <s xml:id="echoid-s11487" xml:space="preserve">ſon complément ſera 25 d. </s> <s xml:id="echoid-s11488" xml:space="preserve">30 m. </s> <s xml:id="echoid-s11489" xml:space="preserve">tirez <lb/>la ligne occulte DE, qui déterminera la longueur du ſtyle FA, pro-<lb/>portionnée à la hauteur du Cylindre.</s> <s xml:id="echoid-s11490" xml:space="preserve"/> </p> <div xml:id="echoid-div696" type="float" level="2" n="1"> <note position="right" xlink:label="note-367-02" xlink:href="note-367-02a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s11491" xml:space="preserve">Diviſez enſuite l'arc AF en degrez & </s> <s xml:id="echoid-s11492" xml:space="preserve">minutes, & </s> <s xml:id="echoid-s11493" xml:space="preserve">du point E ti-<lb/>rez des lignes occultes par tous les degrez de l'arc de cercle, juſqu'à <lb/>la ligne AD, pour en faire l'échelle des hauteurs, qui contient les <lb/>tangentes de tous ces arcs, & </s> <s xml:id="echoid-s11494" xml:space="preserve">ſe peut encore marquer par les nom-<lb/>bres quileur conviennent dans les Tables des Sinus imprimées, en <lb/>ſuppoſant le raïon AE de 100 parties égales ou de 1000, ſelon la <lb/>grandeur du Cylindre.</s> <s xml:id="echoid-s11495" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11496" xml:space="preserve">Les choſes étant ainſi preparées, diviſez la largeur ABCD en 6 <lb/>parties égales pour les 12 Signes; </s> <s xml:id="echoid-s11497" xml:space="preserve">par chaque point de diviſion tirez <lb/>autant de lignes paralleles, qui repreſenteront les commencemens <lb/>des Signes du Zodiaque; </s> <s xml:id="echoid-s11498" xml:space="preserve">ſubdiviſez encore chaque eſpace en 3 par-<lb/>ties égales, afin d'y pouvoir marquer les degrez de 10 en 10, & </s> <s xml:id="echoid-s11499" xml:space="preserve">par <lb/>même moyen les commencemens des mois, parce qu'en ces ſortes <lb/>de Cadrans il n'y a pas d'erreur ſenſible à fixer l'entrée du Soleil <lb/>en chaque Signe au 20 de chaque mois.</s> <s xml:id="echoid-s11500" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11501" xml:space="preserve">Pour marquer les points des heures ſur toutes ces lignes l'une après <lb/>l'autre, ſervez-vous de la Table des hauteurs du Soleil ſur l'horiſon <lb/>du lieu; </s> <s xml:id="echoid-s11502" xml:space="preserve">comme, par exemple, pour marquer 10 h. </s> <s xml:id="echoid-s11503" xml:space="preserve">du matin ou 2 h. <lb/></s> <s xml:id="echoid-s11504" xml:space="preserve">après midiſur la lig. </s> <s xml:id="echoid-s11505" xml:space="preserve">AD, qui repreſente le Tropique de l'Ecreviſſe.</s> <s xml:id="echoid-s11506" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11507" xml:space="preserve">Vous trouverez dans la Table, que le Soleil eſt élevéſur l'horiſon <lb/>de Paris de 55 d. </s> <s xml:id="echoid-s11508" xml:space="preserve">19 m. </s> <s xml:id="echoid-s11509" xml:space="preserve">c'eſt pourquoi vous prendrez avec un com-<lb/>pas ſur l'échelle des hauteurs AD, la tangente de pareil nombre de <lb/>deg. </s> <s xml:id="echoid-s11510" xml:space="preserve">& </s> <s xml:id="echoid-s11511" xml:space="preserve">min. </s> <s xml:id="echoid-s11512" xml:space="preserve">& </s> <s xml:id="echoid-s11513" xml:space="preserve">cette ouverture étant tranſportée ſur led. </s> <s xml:id="echoid-s11514" xml:space="preserve">Tropique, <lb/>vous y ferez un point par où doit paſſer la ligne horaire propoſée. <lb/></s> <s xml:id="echoid-s11515" xml:space="preserve">Pour marquer la même heure ſur un autre parallele, comme ſur ce-<lb/>lui du commencement du Lyon ou de la fin des Jumeaux, vous ver-<lb/>rez dans ladite Table que la hauteur du Soleil en ce tems-là eſt de <lb/>52 d. </s> <s xml:id="echoid-s11516" xml:space="preserve">34 m. </s> <s xml:id="echoid-s11517" xml:space="preserve">dont vous prendrez la tangente ſur l'échelle des hau-<lb/>teurs & </s> <s xml:id="echoid-s11518" xml:space="preserve">la marquerez ſur ledit parallele en comptant toûjours de-<lb/>puis le haut du Cylindre, c'eſt-à-dire, en mettant une pointe du <lb/>Compas ſur la ligne AB; </s> <s xml:id="echoid-s11519" xml:space="preserve">vous en ferez de même ſur tous les autres <lb/>paralleles, & </s> <s xml:id="echoid-s11520" xml:space="preserve">même ſur leurs diviſions de 10 en 10 degrez, & </s> <s xml:id="echoid-s11521" xml:space="preserve">par <lb/> <pb o="353" file="369" n="369" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. II."/> tous ces points vous tracerez la ligne horaire courbe de 10 h. </s> <s xml:id="echoid-s11522" xml:space="preserve">du <lb/>matin, & </s> <s xml:id="echoid-s11523" xml:space="preserve">de 2 h. </s> <s xml:id="echoid-s11524" xml:space="preserve">apres midi.</s> <s xml:id="echoid-s11525" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11526" xml:space="preserve">Vous en ferez de même pour toutes les autres lignes horaires; <lb/></s> <s xml:id="echoid-s11527" xml:space="preserve">vous joindrez le mieux qu'il vous ſera poſſible, par des lignes cour-<lb/>bes, tous les points qui appartiennent à une même heure, & </s> <s xml:id="echoid-s11528" xml:space="preserve">mar-<lb/>querez les caracteres des Signes & </s> <s xml:id="echoid-s11529" xml:space="preserve">les premieres Lettres des mois, <lb/>comme auſſi les chifres des heures, chacun en leur place, comme la <lb/>figure le montre, & </s> <s xml:id="echoid-s11530" xml:space="preserve">le Cadran ſera achevé.</s> <s xml:id="echoid-s11531" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11532" xml:space="preserve">Vous contournerez enſuite ce Parallelograme autour du Cylin-<lb/>dre, enſorte que les lignes qui repreſentent les deux Tropiques, <lb/>ſoient bien paralleles entr'elles. </s> <s xml:id="echoid-s11533" xml:space="preserve">On peut tracer de même les Signes <lb/>& </s> <s xml:id="echoid-s11534" xml:space="preserve">les heures ſur les corps mêmes des Cylindres.</s> <s xml:id="echoid-s11535" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11536" xml:space="preserve">Le ſtyle eſt attaché à un chapiteau qui ſert d'ornement, & </s> <s xml:id="echoid-s11537" xml:space="preserve">doit <lb/>être d'équerre & </s> <s xml:id="echoid-s11538" xml:space="preserve">mobile ſur la ligne A B, afin de pouvoir le placer <lb/>ſur le degré du Signe ou le jour du mois courant. </s> <s xml:id="echoid-s11539" xml:space="preserve">Ce Cadran étant <lb/>poſé perpendiculairement ou ſuſpendu par un anneau, tournez-lc <lb/>vis-à-vis le Soleil, juſqu'à ce que l'ombre du ſtyle tombe à plomb <lb/>ſur le parallele du jour; </s> <s xml:id="echoid-s11540" xml:space="preserve">ſon extremité marquera l'heure, ou partie <lb/>d'heure preſente.</s> <s xml:id="echoid-s11541" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11542" xml:space="preserve">On peut encore par cet Inſtrument connoître à toute heure la <lb/>hauteur du Soleil. </s> <s xml:id="echoid-s11543" xml:space="preserve">Pour cet effet poſez le ſtyle ſur l'échelle des hau-<lb/>teurs, tenez le Cylindre ſuspendu ou placé horiſontalement, tour-<lb/>nez-le de ſorte que le ſtyle ſoit vers le Soleil, pour lors l'extremité de <lb/>ſon ombre perpendiculaire marquera la hauteur du Soleil ſur l'ho-<lb/>riſon.</s> <s xml:id="echoid-s11544" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11545" xml:space="preserve">Ce Parallelograme peut ſervir auſſi de Cadran, ſans être contour-<lb/> <anchor type="note" xlink:label="note-369-01a" xlink:href="note-369-01"/> né ſur un Cylindre, en ajuſtant le ſtyle de maniere qu'il puiſſe cou-<lb/>ler au long de la ligne AB, & </s> <s xml:id="echoid-s11546" xml:space="preserve">s'arrêter ſur le parallele du Signe ou <lb/>du jour du mois. </s> <s xml:id="echoid-s11547" xml:space="preserve">Il n'y a qu'à faire une petite fente au haut de la <lb/>Platine, & </s> <s xml:id="echoid-s11548" xml:space="preserve">applatir le pied du ſtyle de telle ſorte qu'il puiſſe couler <lb/>dans cette fente ſans changer de longueur.</s> <s xml:id="echoid-s11549" xml:space="preserve"/> </p> <div xml:id="echoid-div697" type="float" level="2" n="2"> <note position="right" xlink:label="note-369-01" xlink:href="note-369-01a" xml:space="preserve">Fig. 3.</note> </div> <p> <s xml:id="echoid-s11550" xml:space="preserve">Pour s'en ſervir il faut que ſon Plan ſoit bien perpendiculaire & </s> <s xml:id="echoid-s11551" xml:space="preserve"><lb/>la ligne AB de niveau, ce que l'on fait aiſement par le moyen d'un <lb/>petit plomb dont la ſoie eſt attachée ſur un côté de la Platine. </s> <s xml:id="echoid-s11552" xml:space="preserve">Le <lb/>tenant ainſi d'une main, ou ſuſpendu par un anneau, on l'expoſe <lb/>directement au Soleil, de telle ſorte que l'ombre du ſtyle ſoit étenduë <lb/>ſur la ligne qui repreſente le parallele du Signe ou du mois, & </s> <s xml:id="echoid-s11553" xml:space="preserve">ſon <lb/>extremité marquera l'heure.</s> <s xml:id="echoid-s11554" xml:space="preserve"/> </p> <pb o="354" file="370" n="370" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div699" type="section" level="1" n="365"> <head xml:id="echoid-head502" xml:space="preserve">Conſtruction & uſage du Cadran tracé ſur un Quart de cercle.</head> <p> <s xml:id="echoid-s11555" xml:space="preserve">LA figure 2 de la planche 25<emph style="sub">me</emph>, repreſente un Cadran portatif, <lb/> <anchor type="note" xlink:label="note-370-01a" xlink:href="note-370-01"/> tracé ſur un Quart de cercle, dont nous plaçons ici la conſtruc-<lb/>tion, attendu qu'il ſe fait, auſſi-bien que le Cylindre, par le moyen <lb/>de la Table des hauteurs du Soleil, calculée pour la latitude du lieu.</s> <s xml:id="echoid-s11556" xml:space="preserve"/> </p> <div xml:id="echoid-div699" type="float" level="2" n="1"> <note position="left" xlink:label="note-370-01" xlink:href="note-370-01a" xml:space="preserve">XXV. <lb/>Planche. <lb/>Fig. 2.</note> </div> <p> <s xml:id="echoid-s11557" xml:space="preserve">A près avoir diviſé en degrez la circonference BC du Quart de <lb/>cercle, du centre A, tracez une autre circonference, joignant cette <lb/>diviſion pour repreſenter le Tropique d'Eté; </s> <s xml:id="echoid-s11558" xml:space="preserve">diviſez à peu près en <lb/>trois parties égales le raïon AB, & </s> <s xml:id="echoid-s11559" xml:space="preserve">de l'ouverture AD tracez un arc <lb/>de cercle pour le Tropique d'Hyver; </s> <s xml:id="echoid-s11560" xml:space="preserve">diviſez l'eſpace DB en 6 par-<lb/>ties égales, & </s> <s xml:id="echoid-s11561" xml:space="preserve">du centre A décrivez autant de portions de cercles qui <lb/>repreſenteront les paralleles des autres Signes, comme ils ſont mar-<lb/>quez ſur le côté AC de ladite figure.</s> <s xml:id="echoid-s11562" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11563" xml:space="preserve">Les heures ſe tracent par des lignes courbes en la maniere ſuivan-<lb/>te. </s> <s xml:id="echoid-s11564" xml:space="preserve">Pour trouver, par exemple, le point de midi ſur le Tropique d'E-<lb/>té, ayant trouvé dans la Table que la hauteur du Soleil ſur l'horiſon <lb/>de Paris eſt en ce tems-là de 64 d. </s> <s xml:id="echoid-s11565" xml:space="preserve">29 m. </s> <s xml:id="echoid-s11566" xml:space="preserve">ſervez-vous d'un filet que <lb/>vous aurez attaché au centre, ou d'une Regle étenduë juſqu'à ce <lb/>nombre de degrez & </s> <s xml:id="echoid-s11567" xml:space="preserve">minutes gravez ſur la circonference extérieure <lb/>& </s> <s xml:id="echoid-s11568" xml:space="preserve">marquez ſur le Tropique d'Eté le point de midi; </s> <s xml:id="echoid-s11569" xml:space="preserve">cherchez en-<lb/>ſuite dans ladite Table la hauteur du Soleil à midi, lorſqu'il eſt à la <lb/>fin des Jumeaux ou au commencement du Lyon, & </s> <s xml:id="echoid-s11570" xml:space="preserve">ayant trouvé <lb/>61. </s> <s xml:id="echoid-s11571" xml:space="preserve">d 12 min. </s> <s xml:id="echoid-s11572" xml:space="preserve">étendez la Regle depuis le centre juſqu'à la circonfe-<lb/>rence ſur pareil nombre de degrez & </s> <s xml:id="echoid-s11573" xml:space="preserve">minutes, & </s> <s xml:id="echoid-s11574" xml:space="preserve">marquez le point <lb/>de midi ſur ce parallele qui ſert pour ces deux Signes.</s> <s xml:id="echoid-s11575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11576" xml:space="preserve">Faites-en de même pour tous les autres paralleles des Signes, mê-<lb/>me pour leurs parties, de 10 en 10 d. </s> <s xml:id="echoid-s11577" xml:space="preserve">fi le Quart de cercle eſt aſſez <lb/>grand. </s> <s xml:id="echoid-s11578" xml:space="preserve">Joignez tous ces points de midi par une ligne cour be, depuis <lb/>un Tropique juſqu'à l'autre, & </s> <s xml:id="echoid-s11579" xml:space="preserve">vous aurez la ligne de 12 h. </s> <s xml:id="echoid-s11580" xml:space="preserve">Faites-<lb/>en de même pour toutes les autres heures, ajoûtez deux pinules per-<lb/>cées d'un petit trou ſur le raïon AC, & </s> <s xml:id="echoid-s11581" xml:space="preserve">le Cadran ſera achévé.</s> <s xml:id="echoid-s11582" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div701" type="section" level="1" n="366"> <head xml:id="echoid-head503" xml:space="preserve">Uſage du Quart de Cercle.</head> <p> <s xml:id="echoid-s11583" xml:space="preserve">ELevez l'Inſtrument vers le Soleil, en ſorte que ſon raïon entre <lb/>par les trous des 2 pinules G; </s> <s xml:id="echoid-s11584" xml:space="preserve">ou ſi au lieu de pinules il n'y avoit <lb/>qu'une petite pointe au centre A, faites que ſon ombre ſoit directe-<lb/>ment au long de la ligne AC. </s> <s xml:id="echoid-s11585" xml:space="preserve">Pour lors le filet du centre pendant li-<lb/>brement avec ſon plomb, & </s> <s xml:id="echoid-s11586" xml:space="preserve">raſant le Plan du Quart de cercle, y <lb/>montrera l'heure à l'endroit où il coupe le parallele du jour courant.</s> <s xml:id="echoid-s11587" xml:space="preserve"/> </p> <pb o="355" file="371" n="371" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> <p> <s xml:id="echoid-s11588" xml:space="preserve">Vous pouvez auſſi paſſer dans le filet du plomb une petite perle <lb/>ou tête d'épingle; </s> <s xml:id="echoid-s11589" xml:space="preserve">en ce cas étendez le filet du centre, & </s> <s xml:id="echoid-s11590" xml:space="preserve">arrêtez la <lb/>petite perle ſur le degré du Signe ou ſur le jour du mois; </s> <s xml:id="echoid-s11591" xml:space="preserve">le raïon du <lb/>Soleil entrant par les pinules, le filet & </s> <s xml:id="echoid-s11592" xml:space="preserve">la perle raſeront le Plan en <lb/>l'heure preſente.</s> <s xml:id="echoid-s11593" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div702" type="section" level="1" n="367"> <head xml:id="echoid-head504" xml:space="preserve">Conſtruction & uſage d'un Cadran rectiligne particulier.</head> <p> <s xml:id="echoid-s11594" xml:space="preserve">CE Cadran que nous appellons particulier, à cauſe qu'il ne ſert <lb/> <anchor type="note" xlink:label="note-371-01a" xlink:href="note-371-01"/> que pour une élevation de Pole ou latitude déterminée, ſe fait <lb/>ſur une Platine de laiton, bien droite, ou d'autre métail, grande en-<lb/>viron comme une carte à joüer, & </s> <s xml:id="echoid-s11595" xml:space="preserve">épaiſſe comme un liard.</s> <s xml:id="echoid-s11596" xml:space="preserve"/> </p> <div xml:id="echoid-div702" type="float" level="2" n="1"> <note position="right" xlink:label="note-371-01" xlink:href="note-371-01a" xml:space="preserve">XXVI. <lb/>Planche. <lb/>Fig. 4.</note> </div> <p> <s xml:id="echoid-s11597" xml:space="preserve">Pour le conſtruire, tirez premierement les deux lignes droites A <lb/>B, CD, ſe croiſant à angles dtoits au point E, duquel comme centre <lb/>& </s> <s xml:id="echoid-s11598" xml:space="preserve">du raïon EC décrivez le cercle CBD, diviſez le en 24 parties <lb/>égales, commençant du point D; </s> <s xml:id="echoid-s11599" xml:space="preserve">des diviſions également diſtantes, <lb/>tirez des lignes paralleles qui ſeront les lignes horaires; </s> <s xml:id="echoid-s11600" xml:space="preserve">DR ſera <lb/>pour midi, EB pour 6 h. </s> <s xml:id="echoid-s11601" xml:space="preserve">CM pour minuit; </s> <s xml:id="echoid-s11602" xml:space="preserve">formez le Parallelogra-<lb/>me rectangle PMQR. </s> <s xml:id="echoid-s11603" xml:space="preserve">Du point de midi D, faites ſur la ligne CD <lb/>un arc égal à l'élevation du Pole, comme ici de 49 d. </s> <s xml:id="echoid-s11604" xml:space="preserve">par l'extre-<lb/>mité de cet arc & </s> <s xml:id="echoid-s11605" xml:space="preserve">par le point D tirez la ligne occulte qui repreſen-<lb/>tera le raïon de l'Equateur, & </s> <s xml:id="echoid-s11606" xml:space="preserve">qui ſervira à former le Trigone des <lb/>Signes, dont le ſommet ſera le point D.</s> <s xml:id="echoid-s11607" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11608" xml:space="preserve">Prolongez l'heure du lever du Soleil au plus long jour d'Eté, qui <lb/>eſt ici 4 h. </s> <s xml:id="echoid-s11609" xml:space="preserve">Prolongez auſſi la ligne de 6 h. </s> <s xml:id="echoid-s11610" xml:space="preserve">juſqu'à ce qu'elle ren-<lb/>contre le raïon de l'Equateur en un point qui ſera le centre d'un <lb/>cercle dont le diametre ſera perpendiculaire audit raïon & </s> <s xml:id="echoid-s11611" xml:space="preserve">terminé <lb/>par l'interſection de la ligne de 4 h. </s> <s xml:id="echoid-s11612" xml:space="preserve">du matin. </s> <s xml:id="echoid-s11613" xml:space="preserve">De ce centre & </s> <s xml:id="echoid-s11614" xml:space="preserve">de <lb/>l'ouverture de ſon diametre décrivez un cercle, que vous diviſerez <lb/>en 12 parties égales, pour former le Trigone des Signes, comme nous <lb/>avons expliqué ci-devant au Chapitre 3 de ce Livre. </s> <s xml:id="echoid-s11615" xml:space="preserve">Les deux Tro-<lb/>piques ſeront aux extremitez de ce diametre, faiſans avec le raïon <lb/>de l'équateur chacun un angle de 23 d. </s> <s xml:id="echoid-s11616" xml:space="preserve">30 m. </s> <s xml:id="echoid-s11617" xml:space="preserve">dont le ſommet eſt le <lb/>point D. </s> <s xml:id="echoid-s11618" xml:space="preserve">Le Tropique d'Eté doit être dans la partie inférieure, & </s> <s xml:id="echoid-s11619" xml:space="preserve">le <lb/>Tropique d'Hyver dans la partie ſupérieure, comme on voit par la <lb/>figure. </s> <s xml:id="echoid-s11620" xml:space="preserve">Faites une petite fente au long de ce diametre pour faire <lb/>couler un petit Curſeur percé au milieu pour y paſſer un filet qui <lb/>porte un plomb, dans lequel on a paſſé une petite perle on tête <lb/>d'épingle, enſuite on place denx pinules aux extremitez de la li-<lb/>gne PQ.</s> <s xml:id="echoid-s11621" xml:space="preserve"/> </p> <pb o="356" file="372" n="372" rhead="CONSTRUCTION ET USAGES"/> <head xml:id="echoid-head505" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s11622" xml:space="preserve">FAites couler le Curſeur, arrêtez le trou qui porte la ſoie, ſur le <lb/>degré du Signe ou ſur le jour du mois courant; </s> <s xml:id="echoid-s11623" xml:space="preserve">faites auſſi cou-<lb/>ler la petite perle ou tête d'épingle au long de la ſoie juſqu'à ce qu'el-<lb/>le ſoit ſur le point de 12 h. </s> <s xml:id="echoid-s11624" xml:space="preserve">expoſez au Soleil la pinule P, & </s> <s xml:id="echoid-s11625" xml:space="preserve">hauſ-<lb/>ſez ou baiſſez le Cadran juſqu'à ce que le raïon du Soleil paſſe par <lb/>les deux pinules, & </s> <s xml:id="echoid-s11626" xml:space="preserve">que la ſoie du plomb raſe le Plan. </s> <s xml:id="echoid-s11627" xml:space="preserve">L'endroit des <lb/>heures où ſera la perle ſera l'heure preſente.</s> <s xml:id="echoid-s11628" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div704" type="section" level="1" n="368"> <head xml:id="echoid-head506" xml:space="preserve">Conſtruction du Cadran rectiligne univerſel.</head> <p> <s xml:id="echoid-s11629" xml:space="preserve">LA figure 5 repreſente un Cadran rectiligne qui peut ſervir pour <lb/>toutes les differentes latitudes ou élevations de Pole. </s> <s xml:id="echoid-s11630" xml:space="preserve">Il ſe fait <lb/>ſur une Platine de cuivre ou d'autre matiere ſolide bien unie, gran-<lb/>de à volonté, épaiſſe à proportion.</s> <s xml:id="echoid-s11631" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11632" xml:space="preserve">Pour le conſtruire tirez les lignes AB, CD, s'entre-coupant à <lb/> <anchor type="note" xlink:label="note-372-01a" xlink:href="note-372-01"/> angles droits au point E; </s> <s xml:id="echoid-s11633" xml:space="preserve">duquel, comme centre, décrivez le Quart <lb/>de cercle AF, & </s> <s xml:id="echoid-s11634" xml:space="preserve">le diviſez en 90 d. </s> <s xml:id="echoid-s11635" xml:space="preserve">Du point E faites un triangle <lb/>des Signes par la méthode expliquée au Chapitre 2. </s> <s xml:id="echoid-s11636" xml:space="preserve">Diviſez cha-<lb/>que Signe de 10 en 10 d. </s> <s xml:id="echoid-s11637" xml:space="preserve">& </s> <s xml:id="echoid-s11638" xml:space="preserve">placez les premieres Lettres des mois <lb/>aux endroits qui leur conviennent, en ſuppoſant, comme nous a-<lb/>vons déja dit l'entrée du Soleil en chaque Signe le 20 des mois <lb/>comme, par exemple, ſon entrée en ♈, le 20 de Mars, ſon entrée <lb/>dans le ♉, le 20 d'Avril, & </s> <s xml:id="echoid-s11639" xml:space="preserve">ainſi de ſuite; </s> <s xml:id="echoid-s11640" xml:space="preserve">ce qui ſe peut faire ſans <lb/>erreur ſenſible ſur un ſi petit Inſtrument. </s> <s xml:id="echoid-s11641" xml:space="preserve">Tirez enſuite du centre <lb/>E, par les diviſions du quart de cercle des lignes ponctuées juſqu'à <lb/>la ligne AG, pour la diviſer en des points, deſquels vous menerez <lb/>des paralleles à la ligne AB, qui ſeront les differentes latitudes ou <lb/>hauteurs de Pole, que vous marquerez ſeulement entre les deux <lb/>Tropiques, comme on les voit ſur cette figure, où elles ont été tra-<lb/>cées de 5 en 5 d. </s> <s xml:id="echoid-s11642" xml:space="preserve">Du point B portez de part & </s> <s xml:id="echoid-s11643" xml:space="preserve">d'autre ſur la ligne <lb/>BH, les diviſions des Signes pris au grand triangle ſur la latitude <lb/>de 45 d. </s> <s xml:id="echoid-s11644" xml:space="preserve">pour y faire la repreſentation d'un autre Zodiaque.</s> <s xml:id="echoid-s11645" xml:space="preserve"/> </p> <div xml:id="echoid-div704" type="float" level="2" n="1"> <note position="left" xlink:label="note-372-01" xlink:href="note-372-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s11646" xml:space="preserve">Pour tracer les lignes horaires ſur ce Cadran, tirez de 15 en 15 d. <lb/></s> <s xml:id="echoid-s11647" xml:space="preserve">au Quart de cercle AF, des lignes paralleles à ED, qui ſera la ligne <lb/>de 6 h. </s> <s xml:id="echoid-s11648" xml:space="preserve">le point A pour minuit; </s> <s xml:id="echoid-s11649" xml:space="preserve">tranſportez avec un Compas les <lb/>mêmes diſtances depuis la ligne ED allant vers B, qui ſera le point <lb/>de midi. </s> <s xml:id="echoid-s11650" xml:space="preserve">Pour les demi-heures prenez au Quart de cercle 7 d. </s> <s xml:id="echoid-s11651" xml:space="preserve">30 <lb/>m. </s> <s xml:id="echoid-s11652" xml:space="preserve">& </s> <s xml:id="echoid-s11653" xml:space="preserve">tirez d'autres paralleles entre les lignes des heures.</s> <s xml:id="echoid-s11654" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11655" xml:space="preserve">On peut encore tracer les heures par le moyen d'un Cercle, dont <lb/> <pb o="357" file="373" n="373" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch.. V."/> le diametre ſoit la ligne AB, diviſant ſa circonference en 24 parties <lb/>égales pour les heures, & </s> <s xml:id="echoid-s11656" xml:space="preserve">en 48 pour les demi-heures. </s> <s xml:id="echoid-s11657" xml:space="preserve">Puis tirant <lb/>des points de diviſions oppoſez, des lignes paralleles, on aura les <lb/>heures & </s> <s xml:id="echoid-s11658" xml:space="preserve">demi-heures, comme nous avons dit en la conſtruction <lb/>de l'autre rectiligne.</s> <s xml:id="echoid-s11659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11660" xml:space="preserve">Du point I, comme centre, on trace un autre Quart de cercle oc-<lb/>culte, qu'on diviſe en 90 d. </s> <s xml:id="echoid-s11661" xml:space="preserve">leſquels ſe marquent ſur le bord exté-<lb/>rieur de la Platine, comme il paroît en la figure, où ils ſont ſeule-<lb/>ment diviſez de 5 en 5 deg.</s> <s xml:id="echoid-s11662" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11663" xml:space="preserve">Cette diviſion ſert à prendre la hauteur du Soleil ſur l'horiſon, <lb/>comme nous dirons ci-après.</s> <s xml:id="echoid-s11664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11665" xml:space="preserve">On attache au bord ſupérieur, ſur la ligne GH, deux pinules <lb/>percées chacune d'un petit trou, pour donner paſſage aux raïons <lb/>du Soleil.</s> <s xml:id="echoid-s11666" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11667" xml:space="preserve">La piece marquée K, eſt un petit bras ou index, fait de 3 lames <lb/>de laiton attachées l'une ſur l'autre par des clous à tête rivez de ma-<lb/>niere qu'clles puiſſent avoir du mouvement à droite & </s> <s xml:id="echoid-s11668" xml:space="preserve">à gauche; <lb/></s> <s xml:id="echoid-s11669" xml:space="preserve">au bout pointu qui eſt percé d'un fort petit trou, on attache une <lb/>ſoie qui porte un plomb dans laquelle on a enfilé une très petite <lb/>perle ou tête d'épingle; </s> <s xml:id="echoid-s11670" xml:space="preserve">ce petit bras s'attache ſur la platine avec un <lb/>clou à tête, afin qu'il ait un mouvement, à l'endroit marqué K.</s> <s xml:id="echoid-s11671" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div706" type="section" level="1" n="369"> <head xml:id="echoid-head507" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s11672" xml:space="preserve">POur connoître l'heure, ajuſtez le bout de l'index ſur l'interſec-<lb/>tion que fait la ligne de la latitude du lieu avec le degré du Si-<lb/>gne ou le jour du mois; </s> <s xml:id="echoid-s11673" xml:space="preserve">étendez la ſoie & </s> <s xml:id="echoid-s11674" xml:space="preserve">faites couler la perle ſur pa-<lb/>reil degré du Signe au petit Zodiaque, qui eſt tracé ſur la ligne de <lb/>Midi Bl; </s> <s xml:id="echoid-s11675" xml:space="preserve">élevez vers le Soleil la pinule G, de ſorte que ſon raïon <lb/>paſle par les deux trous ou fentes des pinules; </s> <s xml:id="echoid-s11676" xml:space="preserve">pour lors l'endroit <lb/>où la perle raſera le Plan, ſera l'heure preſente.</s> <s xml:id="echoid-s11677" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11678" xml:space="preserve">Pour connoître l'heure du lever & </s> <s xml:id="echoid-s11679" xml:space="preserve">du coucher du Soleil en tous <lb/>les Signes du Zodiaque, & </s> <s xml:id="echoid-s11680" xml:space="preserve">pour les latitudes marquées ſur le Ca-<lb/>dran, arrêtez le bout de l'index ſur l'interſection de la latitude du <lb/>lieu & </s> <s xml:id="echoid-s11681" xml:space="preserve">du degré du Signe, laiſſant tomber librement la ſoie paralle-<lb/>le aux lignes horaires, elle montrera l'heure du lever & </s> <s xml:id="echoid-s11682" xml:space="preserve">du coucher <lb/>du Soleil. </s> <s xml:id="echoid-s11683" xml:space="preserve">Par exemple, le bout de l'index étant arrêté ſur l'interſe-<lb/>ction du Signe de 69, & </s> <s xml:id="echoid-s11684" xml:space="preserve">la latitude de 49 d. </s> <s xml:id="echoid-s11685" xml:space="preserve">le filet raſera la ligne <lb/>de 4 h. </s> <s xml:id="echoid-s11686" xml:space="preserve">du matin, & </s> <s xml:id="echoid-s11687" xml:space="preserve">de 8 h. </s> <s xml:id="echoid-s11688" xml:space="preserve">du ſoir; </s> <s xml:id="echoid-s11689" xml:space="preserve">ce qui fera connoître qu'envi-<lb/>ron le 20 de Juin le Soleil ſe leve à Paris à 4 h. </s> <s xml:id="echoid-s11690" xml:space="preserve">du matin, & </s> <s xml:id="echoid-s11691" xml:space="preserve">ſe <lb/>couche à 8 h. </s> <s xml:id="echoid-s11692" xml:space="preserve">du ſoir, & </s> <s xml:id="echoid-s11693" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s11694" xml:space="preserve"/> </p> <pb o="358" file="374" n="374" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s11695" xml:space="preserve">Pour connoître l'élevation du Soleil ſur l'horiſon, placez le bout <lb/>de l'index au point I, hauſſez ou baiſſez l'inſtrument de ſorte que <lb/>le raïon du Soleil paſſe parle trou de la pinule H, & </s> <s xml:id="echoid-s11696" xml:space="preserve">ſe rende dans <lb/>l'autre pinule, la ſoie tenduë par ſon plomb marquera l'élevation <lb/>du Soleil ſur les degrez tracez au bord extérieur de la platine.</s> <s xml:id="echoid-s11697" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11698" xml:space="preserve">Toutes ces ſortes de Cadrans qui marquent les heures par les <lb/>hauteurs du Soleil, ont cela de commode qu'ils n'ont pas beſoin de <lb/>Bouſſole, mais leur commun défaut eſt qu'aux environs de midion <lb/>ne peut ſçavoir l'heure juſte, ſi ce n'eſt par pluſieurs obſervations, <lb/>qui font cnnnoître ſi le Soleil hauſſe ou baiſſe, & </s> <s xml:id="echoid-s11699" xml:space="preserve">par conſequent <lb/>s'il eſt dans la partie Orientale ou Occidentale.</s> <s xml:id="echoid-s11700" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div707" type="section" level="1" n="370"> <head xml:id="echoid-head508" xml:space="preserve">Conſtruction du Cadran boriſontal pour pluſieurs élevations <lb/>de Pole.</head> <p> <s xml:id="echoid-s11701" xml:space="preserve">CE Cadran ſe fait ſur une platine de cuivre ou d'autre matiere <lb/> <anchor type="note" xlink:label="note-374-01a" xlink:href="note-374-01"/> ſolide bien dreſſée au marteau, ſur un taſſeau ou enclume bien <lb/>uni; </s> <s xml:id="echoid-s11702" xml:space="preserve">enſuite on adoucira à la pierré ladite plaque qu'on fera de gran-<lb/>deur à volonté. </s> <s xml:id="echoid-s11703" xml:space="preserve">Il y a une petite piece de cuivre en formé d'oiſeau, <lb/>dont la partie inférieure eſt ajuſtée dans deux petits tenons pour le <lb/>rendre mobile & </s> <s xml:id="echoid-s11704" xml:space="preserve">le coucher d'un côté ou d'autre; </s> <s xml:id="echoid-s11705" xml:space="preserve">il eſt retenu droit <lb/>par le moyen d'un reſſort qui eſt deſſous la platine, & </s> <s xml:id="echoid-s11706" xml:space="preserve">qui la traver-<lb/>ſant par un petit trou quarré, fait tenir l'oiſeau ferme ſur ſon pied. <lb/></s> <s xml:id="echoid-s11707" xml:space="preserve">Il y a un ſtyle ou axe qui entre dans l'épaiſſeur de l'oiſeau qui eſt <lb/>double; </s> <s xml:id="echoid-s11708" xml:space="preserve">le bout d'en-bas de l'axe entre dans un petit tenon qui eſt <lb/>au centre du Cadran, pour donner moyen de le hauſſer ou baiſler <lb/>ſuivant la hauteur du Pole. </s> <s xml:id="echoid-s11709" xml:space="preserve">Il y a ſur le ſtyle un arc de cercle diviſé <lb/>où les degrez ſont marquez depuis 35 ou 40 d. </s> <s xml:id="echoid-s11710" xml:space="preserve">juſqu'à 60. </s> <s xml:id="echoid-s11711" xml:space="preserve">On fait <lb/>une fente au long de la circonference diviſée par le moyen d'une pe-<lb/>tite goupille rivée, & </s> <s xml:id="echoid-s11712" xml:space="preserve">paſſant par l'œil de l'oiſeau, on arrête ſon bec <lb/>ſur le nombre des degrez, & </s> <s xml:id="echoid-s11713" xml:space="preserve">on maintient l'axe à la hauteur du Pole <lb/>requiſe. </s> <s xml:id="echoid-s11714" xml:space="preserve">On fait une ouverture circulaire à la platine pour y joindre <lb/>une Bouſſole attachée en deſſous par deux vis. </s> <s xml:id="echoid-s11715" xml:space="preserve">L'éguille & </s> <s xml:id="echoid-s11716" xml:space="preserve">le verre <lb/>qui la couvre ſe placent de même qu'aux autres Bouſſoles dont <lb/>nous avons parlé.</s> <s xml:id="echoid-s11717" xml:space="preserve"/> </p> <div xml:id="echoid-div707" type="float" level="2" n="1"> <note position="left" xlink:label="note-374-01" xlink:href="note-374-01a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s11718" xml:space="preserve">La ſurface du Cadran eſt partagée en 4 ou 5 circonferences que <lb/>l'on diviſe l'une après l'autre, pour autant de differentes latitudes, <lb/>ſuivant quelques-unes des méthodes expliquées ci-devant, dont <lb/>celle qui ſe fait par le calcul des angles au centre du Cadran eſt la <lb/>plus en uſage pour ces petites ſurfaces.</s> <s xml:id="echoid-s11719" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11720" xml:space="preserve">On peut encore tracer ces Cadans par le moyen d'une Platefor-<lb/> <pb o="359" file="375" n="375" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> me ſur laquelle on aura diviſé divers Cadrans par les regles que <lb/>nous avons données ci-devant, pour les marquer ſur la plaque par <lb/>le moyen d'une Regle à centre, ayant affermi ladite plaque de ma-<lb/>niere qu'elle ne branle point.</s> <s xml:id="echoid-s11721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11722" xml:space="preserve">La circonference extérieure qui eſt diviſée pour 55 d. </s> <s xml:id="echoid-s11723" xml:space="preserve">de latitude, <lb/>peut ſervir pour les Païs qui ſont compris entre le 58 & </s> <s xml:id="echoid-s11724" xml:space="preserve">53<emph style="sub">me</emph> deg.</s> <s xml:id="echoid-s11725" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11726" xml:space="preserve">La ſeconde qui eſt diviſée pour 50, ſert pour les Païs compris en-<lb/>tre le 53 & </s> <s xml:id="echoid-s11727" xml:space="preserve">le 47<emph style="sub">me</emph> degré.</s> <s xml:id="echoid-s11728" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11729" xml:space="preserve">La troiſiéme, qui eſt diviſée pour 45, peut ſervir pour les Païs <lb/>compris entres 47 & </s> <s xml:id="echoid-s11730" xml:space="preserve">42<emph style="sub">me</emph>.</s> <s xml:id="echoid-s11731" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11732" xml:space="preserve">La quatriéme, qui eſt diviſée pour 40 d. </s> <s xml:id="echoid-s11733" xml:space="preserve">ſert pour les Païs com-<lb/>pris entre les 42 & </s> <s xml:id="echoid-s11734" xml:space="preserve">38 deg. </s> <s xml:id="echoid-s11735" xml:space="preserve">de latitude.</s> <s xml:id="echoid-s11736" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11737" xml:space="preserve">Quand on y met un cinquiéme Cadran pour 35 deg. </s> <s xml:id="echoid-s11738" xml:space="preserve">il ſert pour <lb/>tous les Païs compris entre les 37 & </s> <s xml:id="echoid-s11739" xml:space="preserve">les 32. </s> <s xml:id="echoid-s11740" xml:space="preserve">On peut voir ſur une <lb/>bonne Mappemonde ou ſur un Globe terreſtre les Païs où ces Ca-<lb/>drans peuvent ſervir, car celui qui eſt fait pour une latitude peut ſer-<lb/>vir pourtous les Pais autour de la Terre qui ont une pareille latitu-<lb/>de Septentrionale ou Méridionale. </s> <s xml:id="echoid-s11741" xml:space="preserve">Sous la platine du Cadran on <lb/>grave une Table des principales Villes du Monde, avec leurs latitu-<lb/>des, pour y pouvoir faire le choix des circonferences de ce Cadran, <lb/>en élevant ſon axe à proportion du lieu où l'on veut s'en ſervir.</s> <s xml:id="echoid-s11742" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div709" type="section" level="1" n="371"> <head xml:id="echoid-head509" xml:space="preserve">Vſage de ce Cadran.</head> <p> <s xml:id="echoid-s11743" xml:space="preserve">POur trouver l'heure, hauſſez ou baiſſez le ſtyle en ſorte que le <lb/>bout du bec du petit oiſeau réponde au degré de l'élevation du <lb/>Pole du lieu marqué ſur le ſtyle, comme à Paris, vis-à-vis de 49 d. </s> <s xml:id="echoid-s11744" xml:space="preserve">le <lb/>ſtyle étant ainſi élevé, placez le Cadran parallele à l'horiſon, c'eſt-à-<lb/>dire de niveau, tournez-le au Soleil juſqu'à ce que la pointe Septen-<lb/>trionale de l'éguille aimantée, marquée ordinairement d'un petit <lb/>anneau, ſoit arrêtée ſur la ligne de déclinaiſon où il y a une Fleur-<lb/>de-Lys & </s> <s xml:id="echoid-s11745" xml:space="preserve">où eſt écrit Nord. </s> <s xml:id="echoid-s11746" xml:space="preserve">Pour lors l'ombre du ſtyle marquera <lb/>l'heure qu'il eſt ſur la circonference diviſée pour la latitude du lieu.</s> <s xml:id="echoid-s11747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11748" xml:space="preserve">Il faut ſe ſouvenir de ne pas approcher le Cadran d'aucun fer, car <lb/>il changeroit la direction de l'éguile aimantée.</s> <s xml:id="echoid-s11749" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div710" type="section" level="1" n="372"> <head xml:id="echoid-head510" xml:space="preserve">Conſtruction d'un Cadran à Anneau.</head> <p> <s xml:id="echoid-s11750" xml:space="preserve">SOit fait un cercle bien rond de cuivre ou d'autre matiere ſolide, <lb/> <anchor type="note" xlink:label="note-375-01a" xlink:href="note-375-01"/> d'environ deux pouces de diametre, ſur 4 à 5 lignes de largeur, <lb/>d'une épaiſſeur convenable pour ne pas ſe forcer. </s> <s xml:id="echoid-s11751" xml:space="preserve">Marquez à volon-<lb/>té ſur la circonference le point A, où il y ait un petit trou; </s> <s xml:id="echoid-s11752" xml:space="preserve">du point <lb/> <pb o="360" file="376" n="376" rhead="CONSTRUCTION ET USAGES"/> A, comme centre, décrivez un quart dc cercle diviſé en 90 d. </s> <s xml:id="echoid-s11753" xml:space="preserve">cher-<lb/>chez dans la Table des élevations du Soleil, ſa hauteur pour cha-<lb/>que heure du jour des Equinoxes ſur l'horiſon du Païs, leſquels vous <lb/>marquerez par le moyen du quart de cercle, en tirant des lignes du <lb/>centre A, juſqu'à la ſurface concave de l'anneau, & </s> <s xml:id="echoid-s11754" xml:space="preserve">ce Cadran ſera <lb/>bon pour le tems des Equinoxes, le ſuſpendant par l'anneau B, en <lb/>ſorte que la lígne AD ſoit à plomb.</s> <s xml:id="echoid-s11755" xml:space="preserve"/> </p> <div xml:id="echoid-div710" type="float" level="2" n="1"> <note position="right" xlink:label="note-375-01" xlink:href="note-375-01a" xml:space="preserve">Fig. 7.</note> </div> <p> <s xml:id="echoid-s11756" xml:space="preserve">On pourra le faire ſervir pour les autres tems de l'année, ſi on <lb/>rend le trou A mobile. </s> <s xml:id="echoid-s11757" xml:space="preserve">Pour cet effet coupez les angles AE, Al de <lb/>23 d. </s> <s xml:id="echoid-s11758" xml:space="preserve">pour les Signes du ♉, ♏ ♍ & </s> <s xml:id="echoid-s11759" xml:space="preserve">♓, AF, AK de 40 d. </s> <s xml:id="echoid-s11760" xml:space="preserve">26 m. <lb/></s> <s xml:id="echoid-s11761" xml:space="preserve">pour les Signes de ♊, ♌, ♒ & </s> <s xml:id="echoid-s11762" xml:space="preserve">♐. </s> <s xml:id="echoid-s11763" xml:space="preserve">Enfin l'arc AG, AL de 47 d. </s> <s xml:id="echoid-s11764" xml:space="preserve"><lb/>pour les Signes de 69 & </s> <s xml:id="echoid-s11765" xml:space="preserve">♑. </s> <s xml:id="echoid-s11766" xml:space="preserve">On prend le double de la déclinaiſon des <lb/>Signes, parce que les angles à la circonference ne ſont que moitié <lb/>des angles au centre; </s> <s xml:id="echoid-s11767" xml:space="preserve">vous aurez par ce moyen ſur la ſurface con-<lb/>vexe de l'anneau une eſpece de Zodiaque, y marquant les Signes <lb/>chacun en leur place, ou bien les premieres Lettres des mois, afin <lb/>de pouvoir mettre le trou A ſur le degré du Signe ou le jour du mois <lb/>courant. </s> <s xml:id="echoid-s11768" xml:space="preserve">Il faut auſſi décrire dans la ſuperficie concave de l'Anneau <lb/>7 cercles; </s> <s xml:id="echoid-s11769" xml:space="preserve">celui du milieu ſera pour l'Equateur, & </s> <s xml:id="echoid-s11770" xml:space="preserve">les autres cercles <lb/>pour les autres paralleles.</s> <s xml:id="echoid-s11771" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11772" xml:space="preserve">Des points A, E, F, G, I, K, L, comme centres, faites autant de <lb/>quarts de 90 d. </s> <s xml:id="echoid-s11773" xml:space="preserve">ſur leſquels vous marquerez pour chaque Signe les <lb/>hauteurs du Soleil à chaque heure; </s> <s xml:id="echoid-s11774" xml:space="preserve">& </s> <s xml:id="echoid-s11775" xml:space="preserve">prolongeant les raïons juſ-<lb/>qu'aux circonferences, vous y marquerez des points, & </s> <s xml:id="echoid-s11776" xml:space="preserve">joindrez par <lb/>une ligne courbe tous ceux qui appartiennent à une même heure.</s> <s xml:id="echoid-s11777" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11778" xml:space="preserve">On peut tracer à part ces diviſions & </s> <s xml:id="echoid-s11779" xml:space="preserve">les rapporter enſuite ſur cet <lb/>anneau en prenant les mêmes diſtances avec un Compas.</s> <s xml:id="echoid-s11780" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div712" type="section" level="1" n="373"> <head xml:id="echoid-head511" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s11781" xml:space="preserve">PLacez le trou mobile ſur le degré du Signe oú eſt le Soleil; </s> <s xml:id="echoid-s11782" xml:space="preserve">tenez <lb/>l'anneau ſuſpendu & </s> <s xml:id="echoid-s11783" xml:space="preserve">le tournez au Soleil, de ſorte que ſon raïon <lb/>paſſant par le trou, tombe ſur la circonference convenable du Si-<lb/>gne, il y marquera l'heure preſente.</s> <s xml:id="echoid-s11784" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div713" type="section" level="1" n="374"> <head xml:id="echoid-head512" xml:space="preserve">Décrire les heures ſur une autre ſorte d'Anneau.</head> <p> <s xml:id="echoid-s11785" xml:space="preserve">LA figure 9 repreſente cet Anneau tout fait, & </s> <s xml:id="echoid-s11786" xml:space="preserve">le parallelogra-<lb/>me ABCD, le repreſente étendu & </s> <s xml:id="echoid-s11787" xml:space="preserve">dévelopé, afin d'y marquer <lb/>les heures avant que de le contourner en cercle.</s> <s xml:id="echoid-s11788" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11789" xml:space="preserve">Il eſt fait d'une lame de laiton ou d'autre matiere ſolide, de lon-<lb/>gueur proportionnée à la grandeur qu'on veut donner à l'Anneau. <lb/></s> <s xml:id="echoid-s11790" xml:space="preserve"> <pb o="361" file="377" n="377" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> large au moins de 4 à 5 lignes & </s> <s xml:id="echoid-s11791" xml:space="preserve">d'une épaiſſeur proportionnée, & </s> <s xml:id="echoid-s11792" xml:space="preserve"><lb/> <anchor type="note" xlink:label="note-377-01a" xlink:href="note-377-01"/> dont les extremitez AC, BD, ſont coupées à angles droits. </s> <s xml:id="echoid-s11793" xml:space="preserve">Des <lb/>points C & </s> <s xml:id="echoid-s11794" xml:space="preserve">D, faites deux quarts de cercle; </s> <s xml:id="echoid-s11795" xml:space="preserve">diviſez-les en 9 parties <lb/>égales; </s> <s xml:id="echoid-s11796" xml:space="preserve">de chaque diviſion oppoſée tirez les paralleles des Signes, la <lb/>ligne CFM ſera pour ♈ & </s> <s xml:id="echoid-s11797" xml:space="preserve">♎, AEB pour les deux Tropiques; </s> <s xml:id="echoid-s11798" xml:space="preserve">les <lb/>autres ſont pour les autres Signes placez ſuivant leur ordre. </s> <s xml:id="echoid-s11799" xml:space="preserve">Divi-<lb/>ſeztoute la longueur en deux également par la ligne EF; </s> <s xml:id="echoid-s11800" xml:space="preserve">tracez à <lb/>part la ligne GH égale à AE pour en faire une Echelle, que vous <lb/>diviſerez en neuf parties égales, dont chaque partie ſera ſubdiviſée <lb/>en 10, par de petits points pour faire en tout 90 parties égales, ré-<lb/>pondantes aux 90 deg. </s> <s xml:id="echoid-s11801" xml:space="preserve">d'un quart de cercle. </s> <s xml:id="echoid-s11802" xml:space="preserve">Prenez dans la Table <lb/>les degrez de hauteur du Soleil ſur l'horiſon du Pais à chaque heu-<lb/>re du jour des Solſtices & </s> <s xml:id="echoid-s11803" xml:space="preserve">des Equinoxes; </s> <s xml:id="echoid-s11804" xml:space="preserve">comme, par exemple, <lb/>pour Paris où la hauteur Méridiene du Soleil étant au premier point <lb/>de 69, eſt de 64 d. </s> <s xml:id="echoid-s11805" xml:space="preserve">29 m. </s> <s xml:id="echoid-s11806" xml:space="preserve">prenez avec un Compas ſur l'Echelle GH <lb/>64 parties & </s> <s xml:id="echoid-s11807" xml:space="preserve">demie, portez cette ouverture ſur la bande de laiton <lb/>depuis E de part & </s> <s xml:id="echoid-s11808" xml:space="preserve">d'autre, juſqu'à I & </s> <s xml:id="echoid-s11809" xml:space="preserve">K, & </s> <s xml:id="echoid-s11810" xml:space="preserve">de même du point F, <lb/>juſqu'à L & </s> <s xml:id="echoid-s11811" xml:space="preserve">M; </s> <s xml:id="echoid-s11812" xml:space="preserve">joignez les points IL, KM par des lignes droites; <lb/></s> <s xml:id="echoid-s11813" xml:space="preserve">prenez enſuite en la Table pour une heure & </s> <s xml:id="echoid-s11814" xml:space="preserve">11 h. </s> <s xml:id="echoid-s11815" xml:space="preserve">au Solſtice d'Eté <lb/>61 d. </s> <s xml:id="echoid-s11816" xml:space="preserve">54 m. </s> <s xml:id="echoid-s11817" xml:space="preserve">c'eſt-à-dire, peu moins de 62 d. </s> <s xml:id="echoid-s11818" xml:space="preserve">ſur l'échelle, que vous <lb/>porterez ſur le Cadran de K vers E; </s> <s xml:id="echoid-s11819" xml:space="preserve">prenez auſſi 41 d. </s> <s xml:id="echoid-s11820" xml:space="preserve">ſur l'échelle <lb/>pour le point de midi des Equinoxes, que vous porterez de M en O <lb/>& </s> <s xml:id="echoid-s11821" xml:space="preserve">de L en N pour 12 h. </s> <s xml:id="echoid-s11822" xml:space="preserve">prenez de même 39 d. </s> <s xml:id="echoid-s11823" xml:space="preserve">20 m. </s> <s xml:id="echoid-s11824" xml:space="preserve">pour le point <lb/>d'une heure & </s> <s xml:id="echoid-s11825" xml:space="preserve">d'onze, que vous porterez ſur la même ligne des mê-<lb/>mes points M & </s> <s xml:id="echoid-s11826" xml:space="preserve">L; </s> <s xml:id="echoid-s11827" xml:space="preserve">des points de la même heure des Solſtices & </s> <s xml:id="echoid-s11828" xml:space="preserve">des <lb/>Equinoxes tirez des lignes droites; </s> <s xml:id="echoid-s11829" xml:space="preserve">pour le Tropique du Capricor-<lb/>ne prenez ſur l'échelle GH 17 d. </s> <s xml:id="echoid-s11830" xml:space="preserve">& </s> <s xml:id="echoid-s11831" xml:space="preserve">demie, hauteur Méridîene, que <lb/>vous porterez de I en P; </s> <s xml:id="echoid-s11832" xml:space="preserve">pour une heure, & </s> <s xml:id="echoid-s11833" xml:space="preserve">pour 11 prenez 16 d. </s> <s xml:id="echoid-s11834" xml:space="preserve">17 <lb/>m. </s> <s xml:id="echoid-s11835" xml:space="preserve">que vous porterez de I vers P, & </s> <s xml:id="echoid-s11836" xml:space="preserve">ainſi de toutes les autres heures <lb/>qui ſeront repreſentées par des lignes droites.</s> <s xml:id="echoid-s11837" xml:space="preserve"/> </p> <div xml:id="echoid-div713" type="float" level="2" n="1"> <note position="right" xlink:label="note-377-01" xlink:href="note-377-01a" xml:space="preserve">Fig. 8.</note> </div> <p> <s xml:id="echoid-s11838" xml:space="preserve">Mais ſi pour plus grande juſteſſe vous prenez en la Table les nom-<lb/>bres qui conviennent aux difſerentes hauteurs du Soleil en chaque <lb/>Signe, & </s> <s xml:id="echoid-s11839" xml:space="preserve">même de 10 en 10 deg. </s> <s xml:id="echoid-s11840" xml:space="preserve">vous aurez ſur les paralleles des <lb/>points qui étant joints enſemble, formeront des lignes courbes pour <lb/>les lignes horaires, & </s> <s xml:id="echoid-s11841" xml:space="preserve">en ce cas le Cadran en ſera plus regulier & </s> <s xml:id="echoid-s11842" xml:space="preserve"><lb/>plus juſte.</s> <s xml:id="echoid-s11843" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11844" xml:space="preserve">Vous écrirez le nombre des heures aux deux côtez, comme auſſi <lb/>les caracteres des Signes & </s> <s xml:id="echoid-s11845" xml:space="preserve">les premieres Lettres des mois, chacun <lb/>en leur place, comme la figure le montre. </s> <s xml:id="echoid-s11846" xml:space="preserve">Au milieu des lignes IL, <lb/>KM aux points R & </s> <s xml:id="echoid-s11847" xml:space="preserve">S, percez 2 petits trous en dedans, s'élargiſſans <lb/> <pb o="362" file="378" n="378" rhead="CONSTRUCTION ET USAGES"/> en dehors de l'Anneau, pour mieux recevoir le raïon du Soleil.</s> <s xml:id="echoid-s11848" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11849" xml:space="preserve">Arrondiſſez enſuite cette lame, ſoudez les deux extremitez en-<lb/>ſemble; </s> <s xml:id="echoid-s11850" xml:space="preserve">mettez au milieu de la jointure un petit bouton avec un <lb/>anneau, de ſorte que le tout ſoit bien en équilibre. </s> <s xml:id="echoid-s11851" xml:space="preserve">Il faut pour <lb/>cela le tourner en dehors.</s> <s xml:id="echoid-s11852" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div715" type="section" level="1" n="375"> <head xml:id="echoid-head513" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s11853" xml:space="preserve">TEnez l'Anneau ſuſpendu, tournez le trou propre pour le tems <lb/>vers le Soleil, de ſorte que ſon raïon tombe ſur le parallele du <lb/>jour; </s> <s xml:id="echoid-s11854" xml:space="preserve">l'heure y ſera marquée par un point de lumiere.</s> <s xml:id="echoid-s11855" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11856" xml:space="preserve">Le trou S ſert depuis le 20 Mars juſqu'au 22 Septembre, & </s> <s xml:id="echoid-s11857" xml:space="preserve">le <lb/>trou R pour les autres ſix mois.</s> <s xml:id="echoid-s11858" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11859" xml:space="preserve">On écrit ſur la ſuperficie convexe de l'Anneau proche des petits <lb/>trous; </s> <s xml:id="echoid-s11860" xml:space="preserve">par exemple ſur celui S, 20 Mars, & </s> <s xml:id="echoid-s11861" xml:space="preserve">ſur celui R, 22 Sep-<lb/>tembre, comme la figure 9 le montre. </s> <s xml:id="echoid-s11862" xml:space="preserve">Ces deux derniers Cadrans <lb/>ne ſont propres que pour une élevation de Pole.</s> <s xml:id="echoid-s11863" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div716" type="section" level="1" n="376"> <head xml:id="echoid-head514" xml:space="preserve">Conſtruction & uſage de l'Anneau Aſtronomique univer ſel.</head> <p> <s xml:id="echoid-s11864" xml:space="preserve">CEt Inſtrument, dont l'uſage eſt de marquer l'heure par un raïon <lb/> <anchor type="note" xlink:label="note-378-01a" xlink:href="note-378-01"/> du Soleil, en quelque endroit de la terre que l'on puiſſe ſe trou-<lb/>ver, ſe fait de cuivre ou d'autre métail. </s> <s xml:id="echoid-s11865" xml:space="preserve">Il eſt compoſé de deux cer-<lb/>cles plats, tournez en dedans comme en dehors. </s> <s xml:id="echoid-s11866" xml:space="preserve">L'extérieur marqué <lb/>A, repreſente le Méridien du lieu où l'on eſt; </s> <s xml:id="echoid-s11867" xml:space="preserve">il porte deux diviſions <lb/>de 90 deg. </s> <s xml:id="echoid-s11868" xml:space="preserve">diametralement oppoſées, dont l'une ſert depuis nôtre <lb/>Pole Septentrional juſqu'à l'Equateur, & </s> <s xml:id="echoid-s11869" xml:space="preserve">l'autre depuis l'Equateur <lb/>juſqu'au Pole Méridional.</s> <s xml:id="echoid-s11870" xml:space="preserve"/> </p> <div xml:id="echoid-div716" type="float" level="2" n="1"> <note position="left" xlink:label="note-378-01" xlink:href="note-378-01a" xml:space="preserve">XXVII. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s11871" xml:space="preserve">Le cercle intérieur repreſente l'Equateur. </s> <s xml:id="echoid-s11872" xml:space="preserve">Il doit tourner bien <lb/>juſte dans l'extérieur par le moyen de deux pivots ou goupilles qui <lb/>traverſent les deux cercles, par des trous juſtement oppoſez l'un a <lb/>l'autre aux points de 12 h.</s> <s xml:id="echoid-s11873" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11874" xml:space="preserve">Il ſe fait de ces Cadrans depuis 2 juſqu'à 6 pouces de diametre. </s> <s xml:id="echoid-s11875" xml:space="preserve">Les <lb/>cercles ſont larges & </s> <s xml:id="echoid-s11876" xml:space="preserve">épais à proportion de leur grandeur. </s> <s xml:id="echoid-s11877" xml:space="preserve">Au mi-<lb/>lieu de ces cercles eſt une regle ou lame mince avec un Curſeur mar-<lb/>qué C, compoſé de deux petites pieces qui coulent dans une ouver-<lb/>ture faite au milieu de cette lame, & </s> <s xml:id="echoid-s11878" xml:space="preserve">qui ſont retenuës par deux pe-<lb/>tites vis; </s> <s xml:id="echoid-s11879" xml:space="preserve">il y a un fort petit trou percé au milieu de ce Curſeur pour <lb/>recevoir le raïon du Soleil. </s> <s xml:id="echoid-s11880" xml:space="preserve">Le milieu de cette regle peut être conſi-<lb/>deré comme l'axe du Monde, & </s> <s xml:id="echoid-s11881" xml:space="preserve">les extremitez comme les deux Po-<lb/>les. </s> <s xml:id="echoid-s11882" xml:space="preserve">On y marque d'un côté les Signes du Zodiaque avec leurs ca-<lb/>racteres, & </s> <s xml:id="echoid-s11883" xml:space="preserve">de l'autre côté les quantiémes & </s> <s xml:id="echoid-s11884" xml:space="preserve">les noms des mois, ou <lb/> <pb o="363" file="379" n="379" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> ſeulement leurs premieres Lettres. </s> <s xml:id="echoid-s11885" xml:space="preserve">On les place ſuivant le rapport <lb/>qu'ils ont avec les Signes. </s> <s xml:id="echoid-s11886" xml:space="preserve">On diviſe les Signes de 10 en 10 deg ou <lb/>même de 5 en 5, ſelon leur déclinaiſon, & </s> <s xml:id="echoid-s11887" xml:space="preserve">ce par le moyen d'un Tri-<lb/>gone déja tout diviſé, & </s> <s xml:id="echoid-s11888" xml:space="preserve">dont l'extremité du raïon de l'Equateur <lb/>c'eſt-à-dire, l'angle du ſommet eſt à l'intérieur du cercle Equino-<lb/>xial, comme au point F. </s> <s xml:id="echoid-s11889" xml:space="preserve">Les deux pieces marquées D, ſont ployées <lb/>à l'équerre, pour réunir l'un dans l'autre les deux cercles; </s> <s xml:id="echoid-s11890" xml:space="preserve">elles ſont <lb/>auſſi percées en deſſous pour tenir l'axe. </s> <s xml:id="echoid-s11891" xml:space="preserve">Ces deux pieces ſont atta-<lb/>chées avec deux vis au cercle exterieur; </s> <s xml:id="echoid-s11892" xml:space="preserve">il y en a une à un côté du <lb/>cercle & </s> <s xml:id="echoid-s11893" xml:space="preserve">une à l'autre, auſſi-bien que le deux pieces marquées E, <lb/>pour ſervir d'appui au cercle Equinoxial, & </s> <s xml:id="echoid-s11894" xml:space="preserve">maintenir les deux cer-<lb/>cles ou verts à angles droits.</s> <s xml:id="echoid-s11895" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11896" xml:space="preserve">Nous ne repetons pas la maniere de diviſer le quart de cercle en <lb/>degrez, & </s> <s xml:id="echoid-s11897" xml:space="preserve">le cercle Equinoxial en heures, demies & </s> <s xml:id="echoid-s11898" xml:space="preserve">quarts, l'ayant <lb/>dit ſuffiſamment ailleurs. </s> <s xml:id="echoid-s11899" xml:space="preserve">Nous dirons ſeulement que toutes les di-<lb/>viſions du cercle Equinoxial doivent être tracées ſur l'épaiſſeur con-<lb/>cave dudit cercle ce qui ſe fait par le moyen d'une piece d'acier <lb/>ployée en équerre, ſelon la courbure du cercle.</s> <s xml:id="echoid-s11900" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11901" xml:space="preserve">Il y a une rainure au bord exterieur des deux côtez du cercle <lb/>Méridien pour faire couler le pendant G, dont le milieu du coulant <lb/>eſt ployé par en bas pour entrer dans ladite rainure.</s> <s xml:id="echoid-s11902" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11903" xml:space="preserve">Les deux côtez de cette piece, qui doit être fort écroüie au mar-<lb/>teau, afin de faire plus de reſſort, ſont applatis pour appuïer ſur l'é-<lb/>paiſſeur convexe du cercle, & </s> <s xml:id="echoid-s11904" xml:space="preserve">faire tenir le pendant ferme ſur tous <lb/>les degrez de la diviſion. </s> <s xml:id="echoid-s11905" xml:space="preserve">Le bouton où eſt paſſé l'anneau de ſuſpen-<lb/>ſion, eſt rivé au milieu de ladite piece, de maniere qu'il tourne fort <lb/>librement; </s> <s xml:id="echoid-s11906" xml:space="preserve">le tout afin que l'inſtrument puiſſe être ſuſpendu bien <lb/>perpendiculairement, car c'eſt une des principales circonſtances <lb/>pour la juſteſſe de cet Inſtrument.</s> <s xml:id="echoid-s11907" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div718" type="section" level="1" n="377"> <head xml:id="echoid-head515" xml:space="preserve">Vſage du Cadran Aſtronomique.</head> <p> <s xml:id="echoid-s11908" xml:space="preserve">PLacez la petite ligne tracée au milieu du pendant, ſur le degré de <lb/>latitude du Païs ou vous êtes, par exemple, pour Paris à 49 d. <lb/></s> <s xml:id="echoid-s11909" xml:space="preserve">mettez enſuite la ligne qui traverſe le petit trou du Curſeur de la re-<lb/>gle, ſur le degré du Signe ou ſur le jour du mois courant; </s> <s xml:id="echoid-s11910" xml:space="preserve">ouvrez l'in-<lb/>ſtrument en ſorte que les deux cercles ſoient à angles droits, & </s> <s xml:id="echoid-s11911" xml:space="preserve">le te-<lb/>nez ſuſpendu par l'anneau, de maniere que l'axe du Cadran, repre-<lb/>ſenté par le milieu de la regle où ſont les Signes, ſoit parallele à l'axe <lb/>du Monde.</s> <s xml:id="echoid-s11912" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11913" xml:space="preserve">Tournez le plat de ladite regle vis à-vis le Soleil, en ſorte que ſon <lb/> <pb o="364" file="380" n="380" rhead="CONSTRUCTION ET USAGES"/> raïon paſſant par la petite ouverture du Curſeur, tombe préciſé-<lb/>ment ſur la ligne tracée au milieu de l'épaiſſeur du cercle intérieur <lb/>qui repreſente l'Equateur. </s> <s xml:id="echoid-s11914" xml:space="preserve">Pour lors le raïon ou point lumineux <lb/>marquera l'heure preſente dans la concavité de ce cercle.</s> <s xml:id="echoid-s11915" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11916" xml:space="preserve">Ce Cadran ne peut point marquer l'heure de midi, parce que <lb/>ſon cercle exterieur ſe trouvant dans le Plan du Méridien, empé-<lb/>che le raïon du Soleil de paſſer juſqu'à l'Equateur.</s> <s xml:id="echoid-s11917" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11918" xml:space="preserve">Il ne marque pas même les heures au tems des Equinoxes, parce <lb/>que pour lors les raïons du Soleil ſont paralleles au Plan du cercle <lb/>équinoxial. </s> <s xml:id="echoid-s11919" xml:space="preserve">Ce n'eſt qu'environ une heure tous les jours, & </s> <s xml:id="echoid-s11920" xml:space="preserve">quatre <lb/>jours par an.</s> <s xml:id="echoid-s11921" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div719" type="section" level="1" n="378"> <head xml:id="echoid-head516" xml:space="preserve">Conſtruction & uſage d'un Anneau Aſtronom. à trois cercles.</head> <p> <s xml:id="echoid-s11922" xml:space="preserve">CEt Inſtrument ne differe de l'autre dont nous venons de par-<lb/> <anchor type="note" xlink:label="note-380-01a" xlink:href="note-380-01"/> ler, que par le 3<emph style="sub">me</emph> cercle qui porte la déclinaiſon du Soleil. </s> <s xml:id="echoid-s11923" xml:space="preserve">Le <lb/>cercle A repreſente le Méridien du lieu où l'on s'en ſert; </s> <s xml:id="echoid-s11924" xml:space="preserve">le cercle B, <lb/>l'Equinoxial, & </s> <s xml:id="echoid-s11925" xml:space="preserve">le cercle D, qui tourne juſte dans ledit Equinoxial <lb/>fait le même effet que la regle qui repreſente l'axe du Monde dans <lb/>le precedent Inſtrument. </s> <s xml:id="echoid-s11926" xml:space="preserve">Les deux extremitez de ſon diametre ou <lb/>les 2 points de ſa circonference, par où il eſt attaché au Méridien, <lb/>répondent aux deux Poles du Monde. </s> <s xml:id="echoid-s11927" xml:space="preserve">Aux parties oppoſées D, on <lb/>marque un double Trigone des Signes ſur la circonference de ce <lb/>cercle, dont le centre eſt le ſommet où ſe réuniſſent tous les raïons. <lb/></s> <s xml:id="echoid-s11928" xml:space="preserve">Les arcs de chaque Signe ſe ſubdiviſent de 10 en 10, ou de 5 en 5 <lb/>degrez, auſquels on peut joindre les jours des mois correſpondans. </s> <s xml:id="echoid-s11929" xml:space="preserve"><lb/>Nous ne repetons pas la maniere de tracer toutes ces diviſions, étant <lb/>les mêmes que celles de l'autre Anneau Aſtronomique.</s> <s xml:id="echoid-s11930" xml:space="preserve"/> </p> <div xml:id="echoid-div719" type="float" level="2" n="1"> <note position="left" xlink:label="note-380-01" xlink:href="note-380-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s11931" xml:space="preserve">L'Alidade E eſt attachée au centre du cercle intérieur; </s> <s xml:id="echoid-s11932" xml:space="preserve">il y a deux <lb/>pinules rivées aux extremitez de l'alidade, percées chacune d'un <lb/>fort petit trou pour recevoir le raïon du Soleil.</s> <s xml:id="echoid-s11933" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11934" xml:space="preserve">Les Cadrans compoſez de cette maniere marquent l'heure de <lb/>midi, parce que l'Alidade eſt hors du Plan du cercle Méridien <lb/>Quand on le fait grand, comme de 9 à 10 pouces de diametre, on <lb/>diviſe le cercle équinoxial de 2 en 2 minutes, ou de 5 en 5, pour <lb/>faire des obſervations exactes.</s> <s xml:id="echoid-s11935" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11936" xml:space="preserve">Il y a un pendant comme à l'autre Cadran, qui entre dans la rai-<lb/>nure du cercle Méridien pour le faire couler ſur le degré de latitu-<lb/>de du lieu. </s> <s xml:id="echoid-s11937" xml:space="preserve">On ajoûte quelquefois à cet Inſtrument un pied à peu <lb/>prés comme à une Sphere, qu'on fait couler ſur le degré de l'éleva-<lb/>tion, & </s> <s xml:id="echoid-s11938" xml:space="preserve">pour lors il ſe place ſur un Plan horiſontal. </s> <s xml:id="echoid-s11939" xml:space="preserve">On y joint <lb/> <pb o="365" file="381" n="381" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. III."/> auſſi une Bouſſole, & </s> <s xml:id="echoid-s11940" xml:space="preserve">par ce moyen on connoît exactement la dé-<lb/>clinaiſon de l'aiman.</s> <s xml:id="echoid-s11941" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div721" type="section" level="1" n="379"> <head xml:id="echoid-head517" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s11942" xml:space="preserve">PLacez la petite ligne qui eſt au milieu du Curſeur du pendant F, <lb/>ſur le degré de l'élevation du Pole du lieu où vous faites l'obſer-<lb/>vation, & </s> <s xml:id="echoid-s11943" xml:space="preserve">la ligne defoy de l'alidade ſur le jour du mois ou ſur le de-<lb/>gré du Signe que le Soleil parcourt.</s> <s xml:id="echoid-s11944" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11945" xml:space="preserve">Le cercle Equinoxial étant ouvert à angles droits avec le Méri-<lb/>dien, & </s> <s xml:id="echoid-s11946" xml:space="preserve">tenant l'Inſtrument ſuſpendu, hauſſez ou baiſſez le cercle <lb/>inférieur, enſorte que la raïon du Soleil paſſe par les trous des deux <lb/>pinules. </s> <s xml:id="echoid-s11947" xml:space="preserve">Alors la ligne qui eſt tracée au milieu de l'épaiſſeur conve-<lb/>xe dudit cercle, montrera l'heure ou partie d'heure tracée au mi-<lb/>lieu de l'épaiſſeur concave du cercle Equinoxial; </s> <s xml:id="echoid-s11948" xml:space="preserve">& </s> <s xml:id="echoid-s11949" xml:space="preserve">cela à toutes <lb/>les heures du jour.</s> <s xml:id="echoid-s11950" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11951" xml:space="preserve">La même choſe ſe ſera lorſque l'Inſtrument ſera poſé horiſonta-<lb/>lement ſur un pied; </s> <s xml:id="echoid-s11952" xml:space="preserve">alors on fera les obſervations plus commode-<lb/>ment.</s> <s xml:id="echoid-s11953" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div722" type="section" level="1" n="380"> <head xml:id="echoid-head518" style="it" xml:space="preserve">Conſtruction d'un Cadran horiſontal incliné univer ſel, & <lb/>d'un Equinoxial.</head> <p> <s xml:id="echoid-s11954" xml:space="preserve">CE Cadran eſt compoſé de deux platines de laiton ou autre ma-<lb/> <anchor type="note" xlink:label="note-381-01a" xlink:href="note-381-01"/> tiere; </s> <s xml:id="echoid-s11955" xml:space="preserve">l'inférieure marquée A eſt évuidée vers le milieu pour re-<lb/>cevoir une Bouſſole ordinaire qui eſt attachée en deſſous avec des <lb/>vis; </s> <s xml:id="echoid-s11956" xml:space="preserve">l'autre Platine B eſt mobile par le moyen d'une forte charniere à <lb/>l'endroit marqué C. </s> <s xml:id="echoid-s11957" xml:space="preserve">On trace ſur la platine ſupérieure un Cadran <lb/>horiſontal, diviſé pour une latitude plus grande qu'aucune de celles <lb/>où l'on veut le faire ſervir, & </s> <s xml:id="echoid-s11958" xml:space="preserve">on y met un ſtyle proportioné à cette <lb/>hauteur, caren l'élevant par le moyen du quart de cercle D, le Plan <lb/>horiſontal aura toûjours moins de latitude, ou bien le Pole y ſera <lb/>moins élevé qu'il n'étoit dans le lieu pour lequel il a été fait.</s> <s xml:id="echoid-s11959" xml:space="preserve"/> </p> <div xml:id="echoid-div722" type="float" level="2" n="1"> <note position="right" xlink:label="note-381-01" xlink:href="note-381-01a" xml:space="preserve">Fig. 3</note> </div> <p> <s xml:id="echoid-s11960" xml:space="preserve">On ne met ordinairement qu'une portion de cercle depuis l'E-<lb/>quateur juſqu'à 60 deg. </s> <s xml:id="echoid-s11961" xml:space="preserve">& </s> <s xml:id="echoid-s11962" xml:space="preserve">qui doivent être marquez au bas de la <lb/>portion du cercle. </s> <s xml:id="echoid-s11963" xml:space="preserve">Le Cadran horiſontal ſe trace ordinairement <lb/>pour cette élevation de Pole de 60 deg. </s> <s xml:id="echoid-s11964" xml:space="preserve">Cette portion de cercle eſt <lb/>attachée par deux petits tenons & </s> <s xml:id="echoid-s11965" xml:space="preserve">ſe couche ſur la platine in férieu-<lb/>re, auſſi-bien que le ſtyle ſur l'extérieure, & </s> <s xml:id="echoid-s11966" xml:space="preserve">ils ſont retenus droits <lb/>par le moyen d'un petit reſſort qui eſt ſous chaque plaque. </s> <s xml:id="echoid-s11967" xml:space="preserve">La fi-<lb/>gure fait aſſez connoître le reſte de la conſtruction de ce Cadran.</s> <s xml:id="echoid-s11968" xml:space="preserve"/> </p> <pb o="366" file="382" n="382" rhead="CONSTRUCTION ET USAGES"/> </div> <div xml:id="echoid-div724" type="section" level="1" n="381"> <head xml:id="echoid-head519" style="it" xml:space="preserve">Vſage de l'horiſontal incliné.</head> <p> <s xml:id="echoid-s11969" xml:space="preserve">ELevez la Platine ſupérieure au degré de latitude ou élevation <lb/>du Pole du lieu où vous êtes par le moyen de la diviſion du <lb/>quart de cercle.</s> <s xml:id="echoid-s11970" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11971" xml:space="preserve">L'éguille aimantée étant arrêtée ſur ſa ligne de déclinaiſon, & </s> <s xml:id="echoid-s11972" xml:space="preserve"><lb/>le Cadran placé horiſontalement, l'ombre de l'axe marquera l'heu-<lb/>re juſte qu'il eſt.</s> <s xml:id="echoid-s11973" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11974" xml:space="preserve">On grave ſous ces deux Platines les noms des principales Villes <lb/>avec leur latitude, pour épargner la peine de les chercher dans les <lb/>Cartes Géographiques.</s> <s xml:id="echoid-s11975" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11976" xml:space="preserve">Les Cadrans Equinoxiaux ſe rendent univerſels par tout le Mon-<lb/>de de la même maniere, mais en ce cas il faut un quart de cercle <lb/>entier. </s> <s xml:id="echoid-s11977" xml:space="preserve">La platine ſupérieure ſe fait pour l'ordinaire en forme de cer-<lb/>cle évuidé que l'on diviſe en 24 parties égales pour les heures, que <lb/>l'on ſubdiviſe en 2 pour les demi-heures, & </s> <s xml:id="echoid-s11978" xml:space="preserve">en 4 pour les quarts. <lb/></s> <s xml:id="echoid-s11979" xml:space="preserve">Toutes ces diviſions ſe tracent auſſi dans la concavité du cercle.</s> <s xml:id="echoid-s11980" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s11981" xml:space="preserve">Il y a une piece qui traverſe le cercle, & </s> <s xml:id="echoid-s11982" xml:space="preserve">qui porte le ſtyle droit <lb/>qui ſe tient ferme au milieu du cercle par le moyen d'un petit reſ-<lb/>ſort qui eſt attaché ſous le cercle, qui par ce moyen donne la liberté <lb/>au ſtyle droit de ſe lever au-deſſus de ce cercle, & </s> <s xml:id="echoid-s11983" xml:space="preserve">de s'abaiſſer en <lb/>deſſous; </s> <s xml:id="echoid-s11984" xml:space="preserve">& </s> <s xml:id="echoid-s11985" xml:space="preserve">quand le Cadran Equinoxial eſt tracé ſur une Platine, <lb/>on ſe ſert de la petite piece marquée F, qu'on met qu centre, & </s> <s xml:id="echoid-s11986" xml:space="preserve">qui <lb/>ſert de ſtyle; </s> <s xml:id="echoid-s11987" xml:space="preserve">la partie ſupérieure du Cadran marque les heures de-<lb/>puis le 22 Mars juſqu'au 22 Septembre, & </s> <s xml:id="echoid-s11988" xml:space="preserve">ſa partie inferieure les <lb/>marque pendant les ſix autres mois de l'année.</s> <s xml:id="echoid-s11989" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div725" type="section" level="1" n="382"> <head xml:id="echoid-head520" style="it" xml:space="preserve">Vſage du Cadran Equinoxial.</head> <p> <s xml:id="echoid-s11990" xml:space="preserve">IL faut mettre le bord de la platine ou du cercle ſur le degré d'é-<lb/>levation du Pole par le moyen du quart de cercle, & </s> <s xml:id="echoid-s11991" xml:space="preserve">le Cadran <lb/>étant bien orientéavec la Bouſſole, l'ombre du ſtyle marquera l'heu-<lb/>re preſente en tout tems, même pendant les Equinoxes, à cauſe <lb/>que les diviſions des heures ſont continuées juſques dans la conca-<lb/>vité du cercle, lequel eſt coupé par le haut.</s> <s xml:id="echoid-s11992" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div726" type="section" level="1" n="383"> <head xml:id="echoid-head521" style="it" xml:space="preserve">Conſtruction d'un Cadran Azimutal.</head> <p> <s xml:id="echoid-s11993" xml:space="preserve">CE Cadran ſe fait ordinairement au fond d'une Bouſſole & </s> <s xml:id="echoid-s11994" xml:space="preserve">eſt <lb/> <anchor type="note" xlink:label="note-382-01a" xlink:href="note-382-01"/> nommé Azimutal, parce qu'il ſe fait par le moyen des Azi-<lb/>muths ou Cercles verticaux du Soleil, ſur une platine de cuivre ou <lb/>d'autre matiere ſolide, parallele à l'oriſon. </s> <s xml:id="echoid-s11995" xml:space="preserve">Tirez la ligne AB pour <lb/> <pb o="367" file="383" n="383" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> la Méridiene, ſur laquelle décrivez un cercle à volonté. </s> <s xml:id="echoid-s11996" xml:space="preserve">Nous n'en <lb/>faiſons ici que la moitié pour les heures du matin; </s> <s xml:id="echoid-s11997" xml:space="preserve">celles del'après <lb/>midi ſe tracent de la même maniere. </s> <s xml:id="echoid-s11998" xml:space="preserve">Diviſez ce cercle en degrez, <lb/>commençant du point A, qui repreſente le Pole arctique; </s> <s xml:id="echoid-s11999" xml:space="preserve">diviſez en <lb/>3 le demi-diametre AC, dont les deux tiers AD ſeront partagez en <lb/>6 intervales poury tracer du centre C des circonferences qui repre-<lb/>ſenteront les paralleles des Signes du Zodiaque; </s> <s xml:id="echoid-s12000" xml:space="preserve">la circonference H, <lb/>ſera pour le Tropique d'Eté, & </s> <s xml:id="echoid-s12001" xml:space="preserve">la plus proche du centre pour le <lb/>Tropique d'Hyver; </s> <s xml:id="echoid-s12002" xml:space="preserve">chacune des autres ſera pour deux Signes éga-<lb/>lement diſtans des Tropiques, comme on voit par la figure 4.</s> <s xml:id="echoid-s12003" xml:space="preserve"/> </p> <div xml:id="echoid-div726" type="float" level="2" n="1"> <note position="left" xlink:label="note-382-01" xlink:href="note-382-01a" xml:space="preserve">Fig.4.</note> </div> <p> <s xml:id="echoid-s12004" xml:space="preserve">On pourroit encore tracer les paralleles des Signes, en faiſant ſur <lb/>la ligne HD un demi-cercle, que l'on diviſera en 6 arcs égaux, d'où <lb/>abaiſſant autant de lignes ponctuées paralleles ſur HD, elle ſe trou-<lb/>vera diviſée en parties inégales, & </s> <s xml:id="echoid-s12005" xml:space="preserve">par ces points de diviſion vous <lb/>tracerez du point C, comme centre, des circonferences qui feront <lb/>les intervales des Signes inégaux.</s> <s xml:id="echoid-s12006" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12007" xml:space="preserve">Pout marquer les lignes horaires ſervez-vous de la Table ci-<lb/>après, ſupputée pour les complémens au premïer vertical pour la la-<lb/>titude de 49 deg. </s> <s xml:id="echoid-s12008" xml:space="preserve">parce qu'au lieu de compter la diſtance des Azi-<lb/>muths depuis le premier, on les compteici depuis le Méridien. </s> <s xml:id="echoid-s12009" xml:space="preserve">Pour <lb/>marquer, par exemple, le point d'une heure après midi ou d'onze <lb/>heures du matin ſur le Ttopique de Cancer, on trouve que l'Azi-<lb/>muth du Soleil en ce tems-là eſt éloigné du Méridien de 30 d. </s> <s xml:id="echoid-s12010" xml:space="preserve">17 <lb/>m. </s> <s xml:id="echoid-s12011" xml:space="preserve">& </s> <s xml:id="echoid-s12012" xml:space="preserve">qu'au commencement des Jumeaux, ou à la fin du Lion, l'A-<lb/>zimuth où ſe trouve le Soleil à la même heure eſt de 27 d. </s> <s xml:id="echoid-s12013" xml:space="preserve">58 m. <lb/></s> <s xml:id="echoid-s12014" xml:space="preserve">& </s> <s xml:id="echoid-s12015" xml:space="preserve">ainſi des autres; </s> <s xml:id="echoid-s12016" xml:space="preserve">c'eſt pourquoi mettez une regle au centre C & </s> <s xml:id="echoid-s12017" xml:space="preserve"><lb/>ſur le 30 d. </s> <s xml:id="echoid-s12018" xml:space="preserve">17 m. </s> <s xml:id="echoid-s12019" xml:space="preserve">de la circonference extérieure diviſée, pour mar-<lb/>quer ſur le Tropique d'Eté le point d'onze heures du matin; </s> <s xml:id="echoid-s12020" xml:space="preserve">tour-<lb/>nez la regle autour du centre du Cadran & </s> <s xml:id="echoid-s12021" xml:space="preserve">l'arrêtez ſur le 27 d. </s> <s xml:id="echoid-s12022" xml:space="preserve">58 <lb/>m. </s> <s xml:id="echoid-s12023" xml:space="preserve">pour marquer ſur le parallele des Jumeaux & </s> <s xml:id="echoid-s12024" xml:space="preserve">du Lyon le point <lb/>d'onze heures; </s> <s xml:id="echoid-s12025" xml:space="preserve">mettez la regle ſur le 23<emph style="sub">me</emph> d. </s> <s xml:id="echoid-s12026" xml:space="preserve">30 m. </s> <s xml:id="echoid-s12027" xml:space="preserve">pour le paral-<lb/>lele du Taureau & </s> <s xml:id="echoid-s12028" xml:space="preserve">de la Vierge, ſur le 19<emph style="sub">me</emph> d.</s> <s xml:id="echoid-s12029" xml:space="preserve">. 33 m. </s> <s xml:id="echoid-s12030" xml:space="preserve">pour le jour <lb/>des Equinoxes, & </s> <s xml:id="echoid-s12031" xml:space="preserve">ainſi des autres, conformément à la Table.</s> <s xml:id="echoid-s12032" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12033" xml:space="preserve">Joignez tousles points d'une même heure par des lignes courbes <lb/>bien adoucies & </s> <s xml:id="echoid-s12034" xml:space="preserve">ne faiſant aucun angle qui ſeront les lignes horai-<lb/>res. </s> <s xml:id="echoid-s12035" xml:space="preserve">Pour marquer les heures d'après midi prenez avec un Com-<lb/>pas les mêmes diſtances ſur chaque parallele & </s> <s xml:id="echoid-s12036" xml:space="preserve">les tranſportez de <lb/>l'autre côté de la Méridiene, parce que les Azimuths des heures <lb/>êgalement diſtantes de midi, font des angles égaux avec la Mé-<lb/>ridiene.</s> <s xml:id="echoid-s12037" xml:space="preserve"/> </p> <pb o="368" file="384" n="384" rhead="CONSTR UCTION ET USAGES"/> <p> <s xml:id="echoid-s12038" xml:space="preserve">L'Eguille aimantée étant placée ſur ſon pivot, il faut la recou-<lb/>vrir d'un verre comme aux Bouſſoles ordinaires.</s> <s xml:id="echoid-s12039" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div728" type="section" level="1" n="384"> <head xml:id="echoid-head522" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s12040" xml:space="preserve">TOurnez le côté B au Soleil, juſqu'a ce que le ſtyle droit planté <lb/>en ce point hors de la Bouſſole & </s> <s xml:id="echoid-s12041" xml:space="preserve">parallele à la ligne de midi, <lb/>faſſe ombre tout le long de la Méridiene. </s> <s xml:id="echoid-s12042" xml:space="preserve">L'éguille aimantée étant <lb/>arrêtée Nord & </s> <s xml:id="echoid-s12043" xml:space="preserve">Sud, marquera l'heure qu'il eſt en l'interſection <lb/>du degré du Signe courant, quand l'aiman n'a point de déclinaiſon.</s> <s xml:id="echoid-s12044" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12045" xml:space="preserve">Mais à preſent que l'aiman décline de plus de 12 deg. </s> <s xml:id="echoid-s12046" xml:space="preserve">on place le <lb/>ſtyle ſur la ligne de déclinaiſon K I au point E, & </s> <s xml:id="echoid-s12047" xml:space="preserve">on ajuſte l'ombre <lb/>du ſtyle ſur ladite ligne de déclinaiſon, alors l'erreur que pourroit <lb/>faire la declinaiſon de l'aiman ſera rectifiée par ce moyen.</s> <s xml:id="echoid-s12048" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div729" type="section" level="1" n="385"> <head xml:id="echoid-head523" style="it" xml:space="preserve">Table des verticaux du Soleil depuis le Méridien à chaque <lb/>heure du jour, pour la latitude de 49 degrez.</head> <note position="right" xml:space="preserve"> <lb/> ## Heur. # ## XI. # ## X. # ## IX. # ## VIII. # ## VII. # ## VI. # ## V. # ## IIII. <lb/> # # ## I. # ## II. # ## III. # ## IIII. # ## V. # ## VI. # ## VII. # ## VIII. <lb/> ## Signes # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. # D. # M. <lb/> ## ♋ # 30 # 17 # 53 # 40 # 70 # 30 # 83 # 57 # 95 # 20 # 105 # 56 # 116 # 28 # 127 # 26 <lb/>♌ # ♊ # 27 # 58 # 50 # 33 # 67 # 34 # 81 # 6 # 92 # 45 # 103 # 35 # 114 # 56 <lb/>♍ # ♉ # 23 # 30 # 43 # 52 # 60 # 29 # 74 # 17 # 86 # 21 # 97 # 36 <lb/>♎ # ♈ # 19 # 33 # 37 # 25 # 52 # 58 # 66 # 57 # 78 # 34 <lb/>♏ # ♓ # 16 # 42 # 32 # 25 # 46 # 30 # 59 # 28 # 71 # 12 <lb/>♐ # ♒14 # 56 # 29 # 11 # 42 # 23 # 54 # 26 <lb/> ## ♑ # 14 # 19 # 28 # 2 # 40 # 48 <lb/></note> </div> <div xml:id="echoid-div730" type="section" level="1" n="386"> <head xml:id="echoid-head524" style="it" xml:space="preserve">Conſtruction & uſage du Cadran horiſontal Analemmatique.</head> <p> <s xml:id="echoid-s12049" xml:space="preserve">CE Cadran ſe nomme Analemmatique, parce qu'il ſe fait par le <lb/>moyen de l'Analemme, qui eſt la projection ou repreſentation <lb/>des principaux cercles de la Sphere ſur un Plan.</s> <s xml:id="echoid-s12050" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12051" xml:space="preserve">La figure 5 eſt l'Analemme, & </s> <s xml:id="echoid-s12052" xml:space="preserve">la figure 6 repreſente le Cadran <lb/>tout fait, qui marque les heures ſans Bouſſole.</s> <s xml:id="echoid-s12053" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12054" xml:space="preserve">Pour conſtruire l'Analemme ſur une plaque de laiton ou d'autre <lb/> <anchor type="note" xlink:label="note-384-02a" xlink:href="note-384-02"/> matiere bien droite & </s> <s xml:id="echoid-s12055" xml:space="preserve">bien polie, de grandeur & </s> <s xml:id="echoid-s12056" xml:space="preserve">épaiſſeur convena-<lb/>ble, tirez premierement les lignes A B, C D, ſe coupant à angles <lb/>droits au point E; </s> <s xml:id="echoid-s12057" xml:space="preserve">duquel, comme centre, décrivez le cercle AC; <lb/></s> <s xml:id="echoid-s12058" xml:space="preserve">BD repreſentant le Méridien, ſon diametre C D l'horiſon, & </s> <s xml:id="echoid-s12059" xml:space="preserve">A B <lb/>le premier vertical. </s> <s xml:id="echoid-s12060" xml:space="preserve">Du point D comptez juſqu'en F l'élevatiou du <lb/> <pb o="369" file="385" n="385" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> Pole, qui eſt ici de 49 d. </s> <s xml:id="echoid-s12061" xml:space="preserve">& </s> <s xml:id="echoid-s12062" xml:space="preserve">tirez la ligne FE, repreſentant l'axe du <lb/>Monde; </s> <s xml:id="echoid-s12063" xml:space="preserve">de l'autre côté comptez ſur le Méridien de Cen G l'éleva-<lb/>tion de l'Equateur, qui eſt ici de 41 d. </s> <s xml:id="echoid-s12064" xml:space="preserve">& </s> <s xml:id="echoid-s12065" xml:space="preserve">tirez la ligne GE pour l'E-<lb/>quateur, du point G comptez de part & </s> <s xml:id="echoid-s12066" xml:space="preserve">d'autre juſqu'en H & </s> <s xml:id="echoid-s12067" xml:space="preserve">en I, <lb/>23 d. </s> <s xml:id="echoid-s12068" xml:space="preserve">30 m. </s> <s xml:id="echoid-s12069" xml:space="preserve">pour la plus grande déclinaiſon du Soleil, tirez la ligne <lb/>HI, coupant l'Equateur au point Y, duquel, comme centre vous <lb/>décrirez le cercle HLIK, ou ſeulement ſa moitié, que vous diviſe-<lb/>rez en 6 parties égales; </s> <s xml:id="echoid-s12070" xml:space="preserve">par chaque point de diviſion tirez les paral-<lb/>leles à l'Equateur, juſqu'à la ligne horiſontale; </s> <s xml:id="echoid-s12071" xml:space="preserve">des ſections que font <lb/>les paralleles ſur le grand cercle, abaiſſez les perpendiculaires MN <lb/>OP ſur l'horiſontale, & </s> <s xml:id="echoid-s12072" xml:space="preserve">des ſections faites par leſdites paralleles ſur <lb/>l'axe EF, abaiſſez des perpendiculaires indefinies S c, R b, Q a; <lb/></s> <s xml:id="echoid-s12073" xml:space="preserve">ouvrez enſuite le Compas de l'eſpace EM, & </s> <s xml:id="echoid-s12074" xml:space="preserve">de cette même ouver-<lb/>ture poſez un pied ſur N, & </s> <s xml:id="echoid-s12075" xml:space="preserve">de l'autre coupez par un petit arc la li-<lb/>gne Q a; </s> <s xml:id="echoid-s12076" xml:space="preserve">poſez un pied ſur O & </s> <s xml:id="echoid-s12077" xml:space="preserve">coupez la ligne R b; </s> <s xml:id="echoid-s12078" xml:space="preserve">puis toûjours <lb/>de la même ouverture EM poſez un pied en P, & </s> <s xml:id="echoid-s12079" xml:space="preserve">de l'autre pointe <lb/>coupez la ligne S c au point C. </s> <s xml:id="echoid-s12080" xml:space="preserve">Pour conſtruire le petit Zodiaque, <lb/>prenez la diſtance ♐ C, que vous porterez de E vers A & </s> <s xml:id="echoid-s12081" xml:space="preserve">vers B, <lb/>pour les Tropiques de 69 & </s> <s xml:id="echoid-s12082" xml:space="preserve">de ♑; </s> <s xml:id="echoid-s12083" xml:space="preserve">prenez la diſtance 4 b & </s> <s xml:id="echoid-s12084" xml:space="preserve">la por-<lb/>tez de même au point E, pour le parallele des ♊ d'un côté, & </s> <s xml:id="echoid-s12085" xml:space="preserve">celui <lb/>de ♒ de l'autre; </s> <s xml:id="echoid-s12086" xml:space="preserve">prenez enfin la diſtance X a pour marquer d'un <lb/>côté le parallele de ♉, & </s> <s xml:id="echoid-s12087" xml:space="preserve">de l'autre celui des ♓, après quoi vous <lb/>formerez le petit Zodiaque, comme il ſe voit en la figure. </s> <s xml:id="echoid-s12088" xml:space="preserve">Pour <lb/>avoir les points des heures, du centre E, & </s> <s xml:id="echoid-s12089" xml:space="preserve">de l'intervale EM, dé-<lb/>crive2 le cercle MTZV, diviſez-le en 24 parties égales, auſſi-bien <lb/>que le grand cercle ABCD, & </s> <s xml:id="echoid-s12090" xml:space="preserve">de chaque diviſion oppoſée tirez <lb/>des lignes droites, ſçavoir, celles du grand cercle, paralleles à la li-<lb/>gne AB, & </s> <s xml:id="echoid-s12091" xml:space="preserve">celles du petit cercle paralleles à la ligne CD; </s> <s xml:id="echoid-s12092" xml:space="preserve">par les <lb/>ſections de ces lignes les plus proches du grand cercle, tracez dou-<lb/>cement à la main de point en point l'ovale, comme la figure le mon-<lb/>tre. </s> <s xml:id="echoid-s12093" xml:space="preserve">Les points de ſection ſeront les heures, celles du matin à gauche <lb/>& </s> <s xml:id="echoid-s12094" xml:space="preserve">celles du ſoir à droite. </s> <s xml:id="echoid-s12095" xml:space="preserve">Pour avoir les demi-heures on diviſe les <lb/>cercles en 48 part. </s> <s xml:id="echoid-s12096" xml:space="preserve">égales, & </s> <s xml:id="echoid-s12097" xml:space="preserve">en 2 fois autant pour avoir les quarts.</s> <s xml:id="echoid-s12098" xml:space="preserve"/> </p> <div xml:id="echoid-div730" type="float" level="2" n="1"> <note position="left" xlink:label="note-384-02" xlink:href="note-384-02a" xml:space="preserve">Fig. 5.</note> </div> <p> <s xml:id="echoid-s12099" xml:space="preserve">Le tout étant ainſi preparé, tranſportez avec un Compas ſur une <lb/> <anchor type="note" xlink:label="note-385-01a" xlink:href="note-385-01"/> autre plaque de laiton toutes les ſectîons des heures, formez-y l'o-<lb/>vale B, en la traçant legerement de point, en point, & </s> <s xml:id="echoid-s12100" xml:space="preserve">gravez-y les <lb/>heures comme elles ſont marquées en ladite figure 6.</s> <s xml:id="echoid-s12101" xml:space="preserve"/> </p> <div xml:id="echoid-div731" type="float" level="2" n="2"> <note position="right" xlink:label="note-385-01" xlink:href="note-385-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s12102" xml:space="preserve">Tranſportez y auſſi le Trigone des Signes, prenant avec un <lb/>Compas toutes les diſtances l'une après l'autre, de telle ſorte que les <lb/>Signes de ♈ & </s> <s xml:id="echoid-s12103" xml:space="preserve">♎ ſoient dans la ligne de 6 h. </s> <s xml:id="echoid-s12104" xml:space="preserve">placez-y les caracteres <lb/> <pb o="370" file="386" n="386" rhead="CONSTRUCTION ET USAGES"/> des Signes & </s> <s xml:id="echoid-s12105" xml:space="preserve">les premieres Lettres des mois chacun en leur ordre. <lb/></s> <s xml:id="echoid-s12106" xml:space="preserve">Ee milieu du Trigone doit être fendu pour y faire couler un Cur-<lb/>ſeur C, qui porte le ſtyle droit D, qui ſe leve & </s> <s xml:id="echoid-s12107" xml:space="preserve">ſe couche par le <lb/>moyen de deux petits tenons.</s> <s xml:id="echoid-s12108" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12109" xml:space="preserve">Sur l'autre partie de la même plaque on y trace un Cadran hori-<lb/>ſontal, ſuivant les Regles ordinaires pour la même latitude qu'a été <lb/>faite l'Analemme; </s> <s xml:id="echoid-s12110" xml:space="preserve">on y place le ſtyle ou axe E, perpendiculairement <lb/>ſur la ligne de midi, qui ſe leve, ſe baiſſe & </s> <s xml:id="echoid-s12111" xml:space="preserve">ſe tient droit par le <lb/>moyen d'un reſſort qui eſt ſous la plaque.</s> <s xml:id="echoid-s12112" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div733" type="section" level="1" n="387"> <head xml:id="echoid-head525" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s12113" xml:space="preserve">PLacez ce Cadran bien parallele à l'horiſon, mettez le Curſeur <lb/>avec ſon ſtyle droit ſur le jour du mois ou ſur le degré du Signe <lb/>que le Soleil parcourt; </s> <s xml:id="echoid-s12114" xml:space="preserve">tournez l'inſtrument juſqu'a ce que les <lb/>deux Cadrans s'accordent & </s> <s xml:id="echoid-s12115" xml:space="preserve">marquent la même heure.</s> <s xml:id="echoid-s12116" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12117" xml:space="preserve">Si, par exemple, le ſtyle droit du Cadran Analemmatique mar-<lb/>que 10 h. </s> <s xml:id="echoid-s12118" xml:space="preserve">du matin, il faut que l'Axe du Cadran horiſontal marque <lb/>pareillement 10 h. </s> <s xml:id="echoid-s12119" xml:space="preserve">En ce cas ce ſera la veritable heure. </s> <s xml:id="echoid-s12120" xml:space="preserve">La com-<lb/>modité de ce Cadran eſt qu'il marque l'heure ſans ligne Méridiene, <lb/>& </s> <s xml:id="echoid-s12121" xml:space="preserve">ſans éguille aimantée; </s> <s xml:id="echoid-s12122" xml:space="preserve">mais pour bien faire il faut qu'il ſoit un <lb/>peu grand.</s> <s xml:id="echoid-s12123" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div734" type="section" level="1" n="388"> <head xml:id="echoid-head526" style="it" xml:space="preserve">Conſtruction du Cadran Polaire, Oriental & Occidental univerſel.</head> <p> <s xml:id="echoid-s12124" xml:space="preserve">CEt Inſtrument eſt compoſé d'une piece circulaire de cuivre ou <lb/> <anchor type="note" xlink:label="note-386-01a" xlink:href="note-386-01"/> autre métal bien droite, & </s> <s xml:id="echoid-s12125" xml:space="preserve">bien égale d'épaiſſeur, un peu forte <lb/>pour conſerver ſon poids perpendiculaire, & </s> <s xml:id="echoid-s12126" xml:space="preserve">pour y faire un rai-<lb/>nure autour du bord, dans laquelle doit couler un pendant ſembla-<lb/>ble à celui que nous avons décrit pour l'Anneau Aſtronomique.</s> <s xml:id="echoid-s12127" xml:space="preserve"/> </p> <div xml:id="echoid-div734" type="float" level="2" n="1"> <note position="left" xlink:label="note-386-01" xlink:href="note-386-01a" xml:space="preserve">XXV III. <lb/>Planche. <lb/>Fig. 1.</note> </div> <p> <s xml:id="echoid-s12128" xml:space="preserve">Du centre de cette piece décrivez la circonference d'un demi-<lb/>cercle & </s> <s xml:id="echoid-s12129" xml:space="preserve">la diviſez en deux fois 90. </s> <s xml:id="echoid-s12130" xml:space="preserve">d. </s> <s xml:id="echoid-s12131" xml:space="preserve">Du point 90 & </s> <s xml:id="echoid-s12132" xml:space="preserve">par le centre <lb/>tirez une ligne droite qui ſera l'Equinoxiale; </s> <s xml:id="echoid-s12133" xml:space="preserve">vers le haut de cette <lb/>ligne choiſiſſez un point à volonté, duquel vous tirerez une per-<lb/>pendiculaire ſur l'Equinoxiale, qui ſera la ligne de 6 h. </s> <s xml:id="echoid-s12134" xml:space="preserve">Pour avoir <lb/>les autres heures portez ſur ladite Equinoxiale, de part & </s> <s xml:id="echoid-s12135" xml:space="preserve">d'autre, <lb/>du point d'interſection, les tangentes convenables, comme celle <lb/>de 15 d. </s> <s xml:id="echoid-s12136" xml:space="preserve">pour les points de 5 & </s> <s xml:id="echoid-s12137" xml:space="preserve">de 7 h. </s> <s xml:id="echoid-s12138" xml:space="preserve">la tangente de 30 d. </s> <s xml:id="echoid-s12139" xml:space="preserve">pour 4 & </s> <s xml:id="echoid-s12140" xml:space="preserve"><lb/>8, celle de 45 pour 3 & </s> <s xml:id="echoid-s12141" xml:space="preserve">9. </s> <s xml:id="echoid-s12142" xml:space="preserve">Cette tangente qui eſt égale au raïon eſt <lb/>la longueur du ſtyle, lequel ſe doit placer perpendiculiarement ſur <lb/> <pb o="371" file="387" n="387" rhead="DE CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> la ligne de 6 h. </s> <s xml:id="echoid-s12143" xml:space="preserve">au point où elle coupe la ligne équinoxiale. </s> <s xml:id="echoid-s12144" xml:space="preserve">Lesheu-<lb/>res de ce Cadran ſont paralleles entr'elles & </s> <s xml:id="echoid-s12145" xml:space="preserve">à l'Axe du Monde, <lb/>comme nous avons dit ci-devant en parlant des Orientaux & </s> <s xml:id="echoid-s12146" xml:space="preserve">Oc-<lb/>cidentaux, & </s> <s xml:id="echoid-s12147" xml:space="preserve">ſe tracent de même.</s> <s xml:id="echoid-s12148" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12149" xml:space="preserve">Sur la ligne de 9 h. </s> <s xml:id="echoid-s12150" xml:space="preserve">du matin, & </s> <s xml:id="echoid-s12151" xml:space="preserve">de 3 h. </s> <s xml:id="echoid-s12152" xml:space="preserve">après midi on ajuſte aux <lb/>point C, deux petits tenons de charniere pour y placer la piece <lb/>marquée V, laquelle ſe couche ſur la piece circulaire, & </s> <s xml:id="echoid-s12153" xml:space="preserve">ſe leve de <lb/>maniere qu'elle s'y arrête à angles droits. </s> <s xml:id="echoid-s12154" xml:space="preserve">On marque ſur cette pie-<lb/>ce les heures d'un Cadran Polaire depuis 9 heur. </s> <s xml:id="echoid-s12155" xml:space="preserve">du matin juſqu'à <lb/>midi, & </s> <s xml:id="echoid-s12156" xml:space="preserve">depuis midi juſqu'à 3 h. </s> <s xml:id="echoid-s12157" xml:space="preserve">du ſoir. </s> <s xml:id="echoid-s12158" xml:space="preserve">Nous ne parlerons point <lb/>davantage de la diviſion de ces heures, l'ayant expliquée ci-devant <lb/>en ſon lieu, auſſi-bien que la maniere de placer les Signes ſur tous <lb/>ces Cadrans Orientaux, Occidentaux & </s> <s xml:id="echoid-s12159" xml:space="preserve">Polaires.</s> <s xml:id="echoid-s12160" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12161" xml:space="preserve">En ladite figure les paralleles des Signes ſont diviſez de 10 en 10 <lb/>d. </s> <s xml:id="echoid-s12162" xml:space="preserve">& </s> <s xml:id="echoid-s12163" xml:space="preserve">on y ajoûté les premieres Lettres des noms des mois chacun <lb/>en leur place, vers le haut de la plaque circulaire, proche le point <lb/>de 90 degrez.</s> <s xml:id="echoid-s12164" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12165" xml:space="preserve">On ajuſte le ſtyle B avec une charniere, afin qu'il puiſſe ſe lever <lb/>& </s> <s xml:id="echoid-s12166" xml:space="preserve">ſe coucher ſur ladite plaque; </s> <s xml:id="echoid-s12167" xml:space="preserve">mais il faut qu'il ſe leve de maniere <lb/>que ſa pointe réponde juſte ſur le point de 6 h. </s> <s xml:id="echoid-s12168" xml:space="preserve">en la ligne équino-<lb/>xiale, & </s> <s xml:id="echoid-s12169" xml:space="preserve">que ſa hauteur ſoit égale à la diſtance de 6 à 9 h. </s> <s xml:id="echoid-s12170" xml:space="preserve">Cela ſe <lb/>peut faire facilement par le moyen d'une petite queuë faite de biais <lb/>au bas dudit ſtyle.</s> <s xml:id="echoid-s12171" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div736" type="section" level="1" n="389"> <head xml:id="echoid-head527" style="it" xml:space="preserve">Vſage dudit Cadran.</head> <p> <s xml:id="echoid-s12172" xml:space="preserve">SI c'eſt avant midi, placez la petite ligne qui eſt au milieu du <lb/>pendant ſur le degré de l'élevation du Pole du lieu où vous êtes, <lb/>au quart où eſt écrit: </s> <s xml:id="echoid-s12173" xml:space="preserve">Heures avant midi. </s> <s xml:id="echoid-s12174" xml:space="preserve">Levez le ſtyle & </s> <s xml:id="echoid-s12175" xml:space="preserve">preſentez <lb/>vôtre Cadran au Soleïl, le tenant ſuſpendu par l'anneau, en ſorte <lb/>que le bout de l'ombre du ſtyle tombe ſur le jour du mois courant; <lb/></s> <s xml:id="echoid-s12176" xml:space="preserve">vous y verrez l'heure preſente ſur l'Oriental ou ſur le Polaire.</s> <s xml:id="echoid-s12177" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12178" xml:space="preserve">Mais ſi c'eſt après midi, mettez le pendant ſur la latitude du <lb/>lieu, au quart où eſt écrit: </s> <s xml:id="echoid-s12179" xml:space="preserve">Heures après midi. </s> <s xml:id="echoid-s12180" xml:space="preserve">Tournez le Cadran <lb/>au Soleil de maniere que le bout de l'ombre du ſtyle tombe ſur le <lb/>degré du Signe ou ſur le jour du mois courant. </s> <s xml:id="echoid-s12181" xml:space="preserve">Il y marquera l'heu-<lb/>re preſente ſur l'Occidental ou ſur le Polaire.</s> <s xml:id="echoid-s12182" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12183" xml:space="preserve">Il eſt aiſé de remarquer que le Cadran Oriental étant retourné <lb/>de cette maniere devient Occidental, & </s> <s xml:id="echoid-s12184" xml:space="preserve">que les heures ſe trouvent <lb/>paralleles à l'Axe du Monde.</s> <s xml:id="echoid-s12185" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12186" xml:space="preserve">Voilà la conſtruction & </s> <s xml:id="echoid-s12187" xml:space="preserve">les uſages des Cadrans portatifs quis'o-<lb/> <pb o="372" file="388" n="388" rhead="CONSTRUCTION ET USAGES"/> rientent ſans Bouſſole ou ſans ligne Méridiene, les plus faciles à ſe <lb/>ſervir. </s> <s xml:id="echoid-s12188" xml:space="preserve">Je vais cependant donner en abregé la deſcription de quel-<lb/>ques autres que je fais, qui ne laiſſant pas d'être aſſez curieux, <lb/>mais dont la conſtruction eſt un peu plus embarraſſante.</s> <s xml:id="echoid-s12189" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12190" xml:space="preserve">Le premier de ces Cadrans eſt un horiſontal de deux ou trois <lb/>pouces en quarré, qu'on fait de cuivre ou de quelque autre mé-<lb/>tal, diviſé pour une élevation de Pole particuliere, & </s> <s xml:id="echoid-s12191" xml:space="preserve">dont l'Axe <lb/>qui marque les heures, eſt une ſoie attachée par un bout au centre <lb/>dudit Cadran, & </s> <s xml:id="echoid-s12192" xml:space="preserve">l'autre bout s'accroche au haut d'une lame de <lb/>cuivre un peu forte, qui eſt placée à l'extremité du Cadran vers la <lb/>ligne de 12 heures; </s> <s xml:id="echoid-s12193" xml:space="preserve">cette lame ſe couche & </s> <s xml:id="echoid-s12194" xml:space="preserve">ſe tient auſſi droite par <lb/>le moyen d'un reſſort qui eſt deſſous ledit Cadran; </s> <s xml:id="echoid-s12195" xml:space="preserve">la hauteur de <lb/>la coche pour retenir la ſoie, eſt égale à la tangente de la hauteur du <lb/>Pole, comme pour Paris, de 49 deg.</s> <s xml:id="echoid-s12196" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12197" xml:space="preserve">Environ au quart de la hauteur de la lame on ajuſte un cercle <lb/>d'une grandeur proportionnée à la grandeur de la plaque du Ca-<lb/>dran; </s> <s xml:id="echoid-s12198" xml:space="preserve">ce cercle ſe ploye par le moyen d'une charniere, & </s> <s xml:id="echoid-s12199" xml:space="preserve">de l'au-<lb/>tre côté il y a un appui pour l'arrêter à la hauteur de l'Equateur, <lb/>qui eſt pour Paris 41 deg. </s> <s xml:id="echoid-s12200" xml:space="preserve">en ſorte que ce cercle ſe couche ſur la <lb/>lame, & </s> <s xml:id="echoid-s12201" xml:space="preserve">la lamé ſur la plaque du Cadran horiſontal; </s> <s xml:id="echoid-s12202" xml:space="preserve">il faut ſur tout <lb/>que le centre de ce cercle réponde juſte dans la ſoie qui ſert d'axe <lb/>lorſqu'elle eſt tenduë.</s> <s xml:id="echoid-s12203" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12204" xml:space="preserve">On diviſe ce cercle dans ſa concavité en heures, demies & </s> <s xml:id="echoid-s12205" xml:space="preserve"><lb/>quarts du Cadran Equinoxial, comme un des cercles de l'Anneau <lb/>Aſtronomique; </s> <s xml:id="echoid-s12206" xml:space="preserve">on paſſe la ſoie dans une très-petite perle ou une <lb/>tête d'épingle, que l'on conduira ſur le Signe que parcourt le <lb/>Soleil, & </s> <s xml:id="echoid-s12207" xml:space="preserve">qui ſervira de Curſeur pour marquer les heures dans le <lb/>milieu de la concavité du cercle équinoxial.</s> <s xml:id="echoid-s12208" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12209" xml:space="preserve">Pour placer cette tête d'épingle ſur le Signe ou le mois conve-<lb/>nable, il faut avoir à part une petite regle de cuivre étroite, ſur <lb/>laquelle on aura tracé les Signes du Zodiaque, & </s> <s xml:id="echoid-s12210" xml:space="preserve">les quantiémes <lb/>du mois, en la maniere qu'on les trace ſur la petite regle qui eſt au <lb/>milieu des Anneaux Aſtronomiques; </s> <s xml:id="echoid-s12211" xml:space="preserve">c'eſt-à-dire, que la décli-<lb/>naiſon du Soleil ſe prend de l'extremité du cercle équinoxial, & </s> <s xml:id="echoid-s12212" xml:space="preserve"><lb/>que le raïon de l'Equateur doit partir en ligne droite du ſommet <lb/>intérieur dudit cercle, & </s> <s xml:id="echoid-s12213" xml:space="preserve">les Signes d'un côté & </s> <s xml:id="echoid-s12214" xml:space="preserve">d'autre ſuivant <lb/>leurs déclinaiſons.</s> <s xml:id="echoid-s12215" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12216" xml:space="preserve">Pour placer la petite perle au point où elle doit être pour mar-<lb/>quer les heures, on place ladite regle, depuis le centre du Cadran <lb/>horiſontal, au long de la ſoie qui ſert d'axe, & </s> <s xml:id="echoid-s12217" xml:space="preserve">on coule la petite <lb/> <pb o="373" file="389" n="389" rhead="DES CADRANS AU SOLEIL. Liv. VIII. Ch. V."/> perle ſur le degré du Signe que le Soleil parcourt, enſuite on <lb/>retire la petite regle.</s> <s xml:id="echoid-s12218" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12219" xml:space="preserve">On trace une ligne perpendiculaire derriere la lame qui tient le <lb/>cercle équinoxial, d'où on laiſſe pendre une ſoie, au bout de la-<lb/>quelle on aura attaché un petit plomb pour mettre le Cadran de ni-<lb/>veau. </s> <s xml:id="echoid-s12220" xml:space="preserve">On peut rendre ce Cadran univerſel, en ajuſtant une por-<lb/>tion de cercle derriere la lame, & </s> <s xml:id="echoid-s12221" xml:space="preserve">qui ſe couche deſſus par le moyen <lb/>d'une charniere; </s> <s xml:id="echoid-s12222" xml:space="preserve">cette portion de cercle doit être diviſée en degrez, <lb/>& </s> <s xml:id="echoid-s12223" xml:space="preserve">le haut de ladite lame, d'où pend le plomb, ſervira de centre; <lb/></s> <s xml:id="echoid-s12224" xml:space="preserve">par ce moyen on pourra élever plus ou moins le côté du centre du <lb/>Cadran, ſuivant l'élevation du Pole, en faiſant pendre la ſoie qui <lb/>porte le plomb ſur la latitude du lieu. </s> <s xml:id="echoid-s12225" xml:space="preserve">Il eſt bon de dire auſſi qu'on <lb/>peut retrancher au cercle équinoxial les heures depuis 8 h. </s> <s xml:id="echoid-s12226" xml:space="preserve">du ſoir <lb/>juſqu'à 4 h. </s> <s xml:id="echoid-s12227" xml:space="preserve">du matin, afin qu'il puiſſe ſervir au tems des Equino-<lb/>xes. </s> <s xml:id="echoid-s12228" xml:space="preserve">L'Ouvrier intelligent ſuppléra facilement à l'abregé de cette <lb/>conſtruction.</s> <s xml:id="echoid-s12229" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div737" type="section" level="1" n="390"> <head xml:id="echoid-head528" style="it" xml:space="preserve">Vſage dudit Cadran.</head> <p> <s xml:id="echoid-s12230" xml:space="preserve">A Yant placé la petite tête d'épingle ſur le Signe ou ſur le jour <lb/>du mois, comme nous avons dit, on expoſera le Cadran au So-<lb/>leil, & </s> <s xml:id="echoid-s12231" xml:space="preserve">on le tournera de côté & </s> <s xml:id="echoid-s12232" xml:space="preserve">d'autre juſqu'à ce que la ſoie qui <lb/>ſert d'axe, marque la même heure ſur le Cadran horiſontal, que la <lb/>petite perle au milieu & </s> <s xml:id="echoid-s12233" xml:space="preserve">dans la concavité du cercle équinoxial, & </s> <s xml:id="echoid-s12234" xml:space="preserve"><lb/>ce ſera la veritable heure.</s> <s xml:id="echoid-s12235" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12236" xml:space="preserve">Nous faiſons encore d'autres Cadrans portatifs, comme un Aſ-<lb/>trolabe horiſontal, ſuivant la projection des cercles de la Sphere, <lb/>ſur le Plan de l'horiſon; </s> <s xml:id="echoid-s12237" xml:space="preserve">d'autres, ſuivant l'Aſtrolabe de Royas, <lb/>qui ſervent verticalement par le moyen d'un plomb; </s> <s xml:id="echoid-s12238" xml:space="preserve">des Cadrans <lb/>horiſontaux faits par les hauteurs du Soleil, qui s'orientent auſſi <lb/>ſans éguille aimantée, dont les Signes du Zodiaque ſont tirez en <lb/>lignes droites & </s> <s xml:id="echoid-s12239" xml:space="preserve">d'un même centre, & </s> <s xml:id="echoid-s12240" xml:space="preserve">les lignes des heures en li-<lb/>gnes courbes; </s> <s xml:id="echoid-s12241" xml:space="preserve">comme auſſi d'autres Cadrans portatifs, qui ſont aſ-<lb/>ſez curieux, dont je reſerve à un autre tems de donner la conſ-<lb/>truction & </s> <s xml:id="echoid-s12242" xml:space="preserve">les figures.</s> <s xml:id="echoid-s12243" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12244" xml:space="preserve">Les Cadrans horiſontaux où les Signes ſont tracez, comme celui <lb/>de la planche 25, figure 1, peuvent auſſi s'orienter ſans Bouſſole, <lb/>en placant au Soleil ledit Cadran, de maniere que l'ombre du ſty-<lb/>le droit donne ſur le degré du Signe que le Soleil parcourt ce jour-<lb/>là; </s> <s xml:id="echoid-s12245" xml:space="preserve">mais ce qu'il y a d'incommode, c'eſt que la diſtance du Signe <lb/>de Cancer eſt ſi petite avec les Signes voiſins, qu'on ne peut diſ-<lb/> <pb o="374" file="390" n="390" rhead="CONSTRUCTION ET USAGES"/> tinguer le quantiéme de 10 en 10 jours; </s> <s xml:id="echoid-s12246" xml:space="preserve">de ſorte que quelque choſe <lb/>qu'on faſſe il eſt preſque impoſſible de faire un Cadran portatif qui <lb/>s'oriente ſans Bouſſole ou ſans ligne Méridiene, ſans tomber dans <lb/>un des deux inconveniens, ou d'avoir les heures fort ſerrées vers le <lb/>midi, ou d'être de peu de préciſion dans le tems des Solſtices; </s> <s xml:id="echoid-s12247" xml:space="preserve">à <lb/>cauſe du peu de difference qui ſe trouve dans l'élevation & </s> <s xml:id="echoid-s12248" xml:space="preserve">décli-<lb/>naiſon du Soleil en ces tems-là; </s> <s xml:id="echoid-s12249" xml:space="preserve">ce ſeroit promettre ce qu'on ne <lb/>pourroit tenir que de ſe vanter de faire autrement.</s> <s xml:id="echoid-s12250" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div738" type="section" level="1" n="391"> <head xml:id="echoid-head529" xml:space="preserve">CHAPITRE VI.</head> <head xml:id="echoid-head530" style="it" xml:space="preserve">Contenant la Conſtruction & les Vſages des Cadrans à la <lb/>Lune & aux Etoiles.</head> <head xml:id="echoid-head531" style="it" xml:space="preserve">Conſtruction d'un Cadran boriſontal pour connoître l'beure à la Lune.</head> <p> <s xml:id="echoid-s12251" xml:space="preserve">ON appelle Cadran à la Lune celui qui montre de nuit aux <lb/> <anchor type="note" xlink:label="note-390-01a" xlink:href="note-390-01"/> raïons de la Lune l'heure qu'il eſt au Soleil; </s> <s xml:id="echoid-s12252" xml:space="preserve">c'eſt-à-dire, en <lb/>quel cercle horaire eſt pour lors le Soleil.</s> <s xml:id="echoid-s12253" xml:space="preserve"/> </p> <div xml:id="echoid-div738" type="float" level="2" n="1"> <note position="left" xlink:label="note-390-01" xlink:href="note-390-01a" xml:space="preserve">Fig. 2.</note> </div> <p> <s xml:id="echoid-s12254" xml:space="preserve">Ce Cadran eſt compoſé de deux pieces de laiton ou d'autre ma-<lb/>tiere ſolide, de grandeur à volonté.</s> <s xml:id="echoid-s12255" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12256" xml:space="preserve">La platine inférieure marquée A, eſt en forme de Parallelogra-<lb/>me, & </s> <s xml:id="echoid-s12257" xml:space="preserve">la ſupérieure marquée A, eſt circulaire & </s> <s xml:id="echoid-s12258" xml:space="preserve">doit tourner au-<lb/>tour de la partie ombrée & </s> <s xml:id="echoid-s12259" xml:space="preserve">du centre marqué B. </s> <s xml:id="echoid-s12260" xml:space="preserve">Sur la platine ſu-<lb/>périeure ſont tracées les heures d'un Cadran horiſontal pour la la-<lb/>titude du lieu, ſuivant les regles ci-devant expliquées.</s> <s xml:id="echoid-s12261" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12262" xml:space="preserve">La platine inférieure porte un cercle diviſé en 30 parties inéga-<lb/>les pour les jours du mois Lunaire. </s> <s xml:id="echoid-s12263" xml:space="preserve">Pour faire cette diviſion, ſoitla <lb/>ligne Equinoxiale DE qui a ſervi à tracer le Cadran horiſontal, & </s> <s xml:id="echoid-s12264" xml:space="preserve"><lb/>ſon centre diviſeur F, duquel ayant décrit le cercle ponctué G, divi-<lb/>ſez-le en 30 parties égales, ou la moitié en 15; </s> <s xml:id="echoid-s12265" xml:space="preserve">la regle étant miſe <lb/>au centre F, tournez-la ſur toutes les diviſions dudit cercle, & </s> <s xml:id="echoid-s12266" xml:space="preserve"><lb/>marquez des points ſur la ligne équinoxiale; </s> <s xml:id="echoid-s12267" xml:space="preserve">enſuite mettez la regle <lb/>au centre B, & </s> <s xml:id="echoid-s12268" xml:space="preserve">ſur tous les points de diviſion de la ligne équino-<lb/>xiale, pour diviſer le cercle H; </s> <s xml:id="echoid-s12269" xml:space="preserve">quand vous en aurez la moitié, <lb/>tranſportez les mêmes diviſions ſur l'autre demi-cercle, & </s> <s xml:id="echoid-s12270" xml:space="preserve">par ce <lb/>moyen tout le cercle ſe trouvera diviſé en 30 parties inégales pour <lb/>les 30 jours du mois Lunaire, autour deſquels on gravera les chi-<lb/>fres, comme la figure la montre.</s> <s xml:id="echoid-s12271" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12272" xml:space="preserve">Placez l'Axe BC, à la hauteur du Pole du lieu & </s> <s xml:id="echoid-s12273" xml:space="preserve">diſpoſé de ma-<lb/> <pb o="375" file="391" n="391" rhead="DES CADRANS A LA LUNE. Liv. VIII. Ch. VI."/> niere qu'étant élevé il n'empêche pas la platine des heures de tour-<lb/>ner autour du centre B.</s> <s xml:id="echoid-s12274" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div740" type="section" level="1" n="392"> <head xml:id="echoid-head532" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s12275" xml:space="preserve">IL faut ſçavoir le quantiéme de la Lune par des Ephemerides ou <lb/>par le moyen des Epactes, afin d'appliquer le point de 12 h. </s> <s xml:id="echoid-s12276" xml:space="preserve">ſur <lb/>le jour de la Lune.</s> <s xml:id="echoid-s12277" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12278" xml:space="preserve">On doit remarquer que la Lune par ſon mouvement propre s'é-<lb/>loigne du Soleil chaque jour vers l'Orient d'environ 48 m. </s> <s xml:id="echoid-s12279" xml:space="preserve">d'heu-<lb/>re, c'eſt-à-dire, que ſi étant nouvelle ou conjointe au Soleil elle ſe <lb/>trouve un jour avec lui dans le Méridien, le lendemain elle paſſera <lb/>par ce même Méridien environ trois quarts d'heure & </s> <s xml:id="echoid-s12280" xml:space="preserve">quelques mi-<lb/>nutes après le Soleil, ce qui fait que les jours Lunaires ſont plus <lb/>grands que les jours Solaires. </s> <s xml:id="echoid-s12281" xml:space="preserve">On appelle jour Lunaire le tems de-<lb/>puis le paſſage de la Lune par le Méridien juſqu'au paſſage immé-<lb/>diatement ſuivant. </s> <s xml:id="echoid-s12282" xml:space="preserve">Ces jours ſont fort inégaux à cauſe de l'irregu-<lb/>larité du mouvement apparent de la Lune.</s> <s xml:id="echoid-s12283" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12284" xml:space="preserve">Quand la Lune eſt pleine, c'eſt-à-dire, oppoſée au Soleil, elle ſe <lb/>retrouve dans le même cercle horaire que le Soleil, de ſorte que ſi, <lb/>par exemple, en ce tems-la le Soleil étoit au Méridien de nos An-<lb/>tipodes, la Lune ſeroit dans nôtre Méridien, & </s> <s xml:id="echoid-s12285" xml:space="preserve">marqueroit par <lb/>conſequent ſur nos Cadrans la même heure que feroit le Soleil, s'il <lb/>étoit ſur nôtre horiſon. </s> <s xml:id="echoid-s12286" xml:space="preserve">Mais cette conformité ne dure pas long-<lb/>tems, puiſqu'à chaque heure elle retarderoit d'environ deux minu-<lb/>tes. </s> <s xml:id="echoid-s12287" xml:space="preserve">De même ſile Soleil au tems de ſon oppoſition ſe couche ſous <lb/>nôtre horiſon, la Lune lui étant diametralement oppoſée ſe levera, <lb/>& </s> <s xml:id="echoid-s12288" xml:space="preserve">ainſi du reſte; </s> <s xml:id="echoid-s12289" xml:space="preserve">c'eſt pour remedier à ſon retardement qu'on a divi-<lb/>ſé ce cercle en 30 parties. </s> <s xml:id="echoid-s12290" xml:space="preserve">Le point de 12 h. </s> <s xml:id="echoid-s12291" xml:space="preserve">du Cadran horiſontal <lb/>étant mis exactement vis-à-vis de l'âge de la Lune, le Cadran o-<lb/>rienté par le moyen d'une Bouſſole ou d'une ligne Méridiene, mar-<lb/>quera l'heure preſente; </s> <s xml:id="echoid-s12292" xml:space="preserve">mais pour l'avoir plus exactement, il fau-<lb/>droit ſçavoir ſi la Lune eſt dans le premier, ſecond ou troiſiéme <lb/>quart de ſon jour, afin de mettre le point de 12 h. </s> <s xml:id="echoid-s12293" xml:space="preserve">à proportion en <lb/>l'eſpace de ſon quantiéme de Lune.</s> <s xml:id="echoid-s12294" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12295" xml:space="preserve">Cette même pratique ſert auſſi pour les verticaux, mais pour les <lb/>Equinoxiaux la diviſion ſe fera en 30 parties égales, la rouë mobile <lb/>qui porte les heures en 24, & </s> <s xml:id="echoid-s12296" xml:space="preserve">le reſte de même que ci-devant.</s> <s xml:id="echoid-s12297" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12298" xml:space="preserve">La Table qui eſt au bas de la plaque, ſert auſſi pour connoître <lb/>l'heure au clair de la Lune avec un Cadran ordinare.</s> <s xml:id="echoid-s12299" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12300" xml:space="preserve">Pour la conſtruire tirez quatre lignes paralleles droites ou cour-<lb/> <pb o="376" file="392" n="392" rhead="CONSTRUCTION ET USAGES"/> bes longues à volonté, diviſez l'eſpace II en 12 parties égales pour <lb/>les 12 h. </s> <s xml:id="echoid-s12301" xml:space="preserve">& </s> <s xml:id="echoid-s12302" xml:space="preserve">les deux autres eſpaces KK en 15, pour y marquer les <lb/>30 jours lunaires, comme on voit par la figure 2.</s> <s xml:id="echoid-s12303" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div741" type="section" level="1" n="393"> <head xml:id="echoid-head533" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s12304" xml:space="preserve">VOyez avec un Cadran au Soleil l'heure que la Lune y marque-<lb/>ra, puis ſçachant l'âge de la Lune, voyez dans la Table l'heu-<lb/>re qui correſpond vis-à-vis ſon âge, à laquelle ajoûtez l'heure mar-<lb/>quée par le Cadran; </s> <s xml:id="echoid-s12305" xml:space="preserve">ſi la ſomme des deux enſemble n'excede pas 12, <lb/>ou bien ſon excès au-deſſus de 12, elle vous donnera la vraie heure.</s> <s xml:id="echoid-s12306" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div742" type="section" level="1" n="394"> <head xml:id="echoid-head534" xml:space="preserve">EXEMPLE.</head> <p> <s xml:id="echoid-s12307" xml:space="preserve">SUppoſons que le Cadran Solaire marque 6 h. </s> <s xml:id="echoid-s12308" xml:space="preserve">au clair de la Lu-<lb/>ne, & </s> <s xml:id="echoid-s12309" xml:space="preserve">que ſon âge ſoit de 5 jours ou de 20, on verra par la Ta-<lb/>ble vis-à-vis de ces chifres, 4 h. </s> <s xml:id="echoid-s12310" xml:space="preserve">leſquelles ajoûtées à 6 font 10, <lb/>qui ſera l'heure preſente. </s> <s xml:id="echoid-s12311" xml:space="preserve">Si à tel jour la Lune marquoit 8 h. </s> <s xml:id="echoid-s12312" xml:space="preserve">il ſe-<lb/>roit minuit.</s> <s xml:id="echoid-s12313" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12314" xml:space="preserve">Pareillement ſi la Lune marquoit 9 h. </s> <s xml:id="echoid-s12315" xml:space="preserve">à ſon 10<emph style="sub">me</emph> ou 25<emph style="sub">me</emph> jour, <lb/>auxquels répondent 8 h. </s> <s xml:id="echoid-s12316" xml:space="preserve">8 & </s> <s xml:id="echoid-s12317" xml:space="preserve">9 font 17; </s> <s xml:id="echoid-s12318" xml:space="preserve">ôtez 12, reſtent 5 pour <lb/>la vraie heure, & </s> <s xml:id="echoid-s12319" xml:space="preserve">ainſi des autres.</s> <s xml:id="echoid-s12320" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12321" xml:space="preserve">On connoît l'âge de la Lune par le moyen de l'épacte de l'année <lb/>courante en cette maniere. </s> <s xml:id="echoid-s12322" xml:space="preserve">A l'épacte, ajoûtez le nombre des mois <lb/>paſſez, commençant à Mars avec le nombre des jours du mois pre-<lb/>ſent; </s> <s xml:id="echoid-s12323" xml:space="preserve">la ſomme ſera l'âge de la Lune, en rejettant les 30 s'il excede; <lb/></s> <s xml:id="echoid-s12324" xml:space="preserve">comme, par exemple, l'an 1716, au 25 Mars, l'épacte étant 6, & </s> <s xml:id="echoid-s12325" xml:space="preserve"><lb/>le nombre des mois 1, la ſomme totale ſera 32, de laquelle <lb/>ôtant 30, reſtera 2 pour l'âge de la Lune, en ajoûtant cependant <lb/>1, d'autant que la Lune ſe joint au Soleil plûtôt preſque d'un jour <lb/>que ne donne l'épacte.</s> <s xml:id="echoid-s12326" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12327" xml:space="preserve">L'on trouve facilement des Tables qui marquent les épactes, <lb/>mais on pourra les connoître en ajoûtant 11 à l'épacte courante; </s> <s xml:id="echoid-s12328" xml:space="preserve">ſi <lb/>le nombre paſſe 30, ôtez 30, le reſte ſera l'épacte, & </s> <s xml:id="echoid-s12329" xml:space="preserve">s'il eſt 30, <lb/>comptez 1, & </s> <s xml:id="echoid-s12330" xml:space="preserve">non pas 30. </s> <s xml:id="echoid-s12331" xml:space="preserve">Cette maniere de trouver l'âge de la <lb/>Lune n'eſt pas ſi exacte que par le calcul des Ephemerides.</s> <s xml:id="echoid-s12332" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div743" type="section" level="1" n="395"> <head xml:id="echoid-head535" style="it" xml:space="preserve">Conſtruction d'un Cadran pour connoitre l'beure aux Etoiles.</head> <p> <s xml:id="echoid-s12333" xml:space="preserve">LA figure 3 repreſente l'arrangement des principales Etoiles qui <lb/>compoſent la conſtellation de la grande Ourſe & </s> <s xml:id="echoid-s12334" xml:space="preserve">celle de la pe-<lb/>tite Ourſe autour du Pole, & </s> <s xml:id="echoid-s12335" xml:space="preserve">de l'Etoile Polaire.</s> <s xml:id="echoid-s12336" xml:space="preserve"/> </p> <pb o="377" file="393" n="393" rhead="DES CADRANS AUX ETOILES. Liv. VIII. Ch. VI."/> <p> <s xml:id="echoid-s12337" xml:space="preserve">Le Cadran aux Etoiles, dont nous allons parler, ſe fait par la con-<lb/>noiſſance du mouvement journalier que font autour du Pole ou de <lb/>l'Etoile Polaire qui n'en eſt preſentement éloignée que de deux de-<lb/>grez ou environ, les deux Etoiles de la grande Ourſe que l'on ap-<lb/>pelle ſes gardes, ou la Claire du quarré de la petite Ourſe, com-<lb/>me elles ſont marquées en ladite figure.</s> <s xml:id="echoid-s12338" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12339" xml:space="preserve">Pour la conſtruction de ce Cadran il faut premierement ſçavoir <lb/>l'aſcenſion droite de ces Etoiles, ou à quels jours de l'année elles ſe <lb/>trouvent dans le même cercle horaire que le Soleil; </s> <s xml:id="echoid-s12340" xml:space="preserve">ce qui ſe peut <lb/>connoître par le calcul Aſtronomique ou par un Globe, ou avec un <lb/>Planiſphere celeſte conſtruit ſur les nouvelles Obſervations, en met-<lb/>tant ſous le Méridien l'Etoile dont il s'agit, & </s> <s xml:id="echoid-s12341" xml:space="preserve">en examinant quel <lb/>degré de l'Ecliptique ſe trouve en même tems ſous ce Méridien. <lb/></s> <s xml:id="echoid-s12342" xml:space="preserve">Par cette méthode on trouvera, par exemple, que la Claire du <lb/>quarré de la petite Ourſe ſe trouve avec le Soleil 4ous le Méridien <lb/>deux fois l'année; </s> <s xml:id="echoid-s12343" xml:space="preserve">ſçavoir, en l'année 1715, une fois le 8 May, au-<lb/>deſſus du Pole; </s> <s xml:id="echoid-s12344" xml:space="preserve">& </s> <s xml:id="echoid-s12345" xml:space="preserve">l'autre fois le 8 Novembre, au-deſſous du Pole, <lb/>c'eſt pourquoi en ces deux jours de l'année cette Etoile marquera <lb/>les mêmes heures que le Soleil. </s> <s xml:id="echoid-s12346" xml:space="preserve">On trouvera de même que les deux <lb/>Etoiles que l'on nomme les gardes de la grande Ourſe, ſe trouvent <lb/>deux autres jours de l'année ſous le même Méridien ou Cercle ho-<lb/>raire que le Soleil; </s> <s xml:id="echoid-s12347" xml:space="preserve">ſçavoir, le premier jour de Septembre, au-deſ-<lb/>ſous du Pole, & </s> <s xml:id="echoid-s12348" xml:space="preserve">le premier jour de Mars au-deſſus.</s> <s xml:id="echoid-s12349" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12350" xml:space="preserve">En ces deux jours de l'année ces Etoiles marqueront les mêmes <lb/>heures que le Soleil; </s> <s xml:id="echoid-s12351" xml:space="preserve">mais comme les Etoiles fixes retournent au <lb/>même Méridien chaque jour plûtôt que le Soleil d'environ 1 d. </s> <s xml:id="echoid-s12352" xml:space="preserve">ou <lb/>4 m. </s> <s xml:id="echoid-s12353" xml:space="preserve">d'heure, ce qui fait 2 h. </s> <s xml:id="echoid-s12354" xml:space="preserve">par mois, c'eſt ce qu'il faut remarquer <lb/>pour avoir l'heure du Soleil, qui eſt la meſure de nos jours.</s> <s xml:id="echoid-s12355" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12356" xml:space="preserve">Ces connoiſſances étant ainſi établies, il ſera facile de conſtrui-<lb/>re un Cadran aux Etoiles en la maniere ſuivante.</s> <s xml:id="echoid-s12357" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12358" xml:space="preserve">Cet Inſtrument eſt compoſé de deux plaques circulaires appli-<lb/>quées l'une ſur l'autre; </s> <s xml:id="echoid-s12359" xml:space="preserve">la plus grande a un manche pour tenir à <lb/>la main l'Inſtrument dans les uſages qu'on en fait.</s> <s xml:id="echoid-s12360" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12361" xml:space="preserve">La plus grande rouë qui a environ deux pouces & </s> <s xml:id="echoid-s12362" xml:space="preserve">demi de dia-<lb/> <anchor type="note" xlink:label="note-393-01a" xlink:href="note-393-01"/> metre, eſt diviſée en 12 pour les 12 mois de l'année, & </s> <s xml:id="echoid-s12363" xml:space="preserve">chaque mois <lb/>de 5 en 5 jours; </s> <s xml:id="echoid-s12364" xml:space="preserve">de telle ſorte que le milieu du manche réponde juſ-<lb/>tement au jour de l'année auquel l'Etoile, dont on veut ſe ſervir, a <lb/>même aſcenſion droite que le Soleil. </s> <s xml:id="echoid-s12365" xml:space="preserve">Si, par exemple, cet Inſtrument <lb/>eſt fait pour les deux gardes de la grande Ourſe, il faut que le pre-<lb/>mier jour de Septembre ſoit vis-à-vis le milieu du manche; </s> <s xml:id="echoid-s12366" xml:space="preserve">& </s> <s xml:id="echoid-s12367" xml:space="preserve">s'il <lb/> <pb o="378" file="394" n="394" rhead="CONSTRUCTION ET USAGES"/> eſt fait pour la Claire de la petite Ourſe, il faut que le 8<emph style="sub">me</emph> jour de <lb/>Novembre ſoit au milieu du manche; </s> <s xml:id="echoid-s12368" xml:space="preserve">c'eſt pourquoi ſi l'on veut <lb/>que le même Cadran ſerve pour l'une & </s> <s xml:id="echoid-s12369" xml:space="preserve">l'autre de ces Etoiles, il <lb/>faut rendre le manche mobile autour de ladite rouë, afin de l'arrê-<lb/>ter où l'on voudra; </s> <s xml:id="echoid-s12370" xml:space="preserve">ce qui eſt facile à faire par le moyen de deux pe-<lb/>tites vis.</s> <s xml:id="echoid-s12371" xml:space="preserve"/> </p> <div xml:id="echoid-div743" type="float" level="2" n="1"> <note position="right" xlink:label="note-393-01" xlink:href="note-393-01a" xml:space="preserve">Fig. 4.</note> </div> <p> <s xml:id="echoid-s12372" xml:space="preserve">La rouë de deſſus qui eſt la plus petite, doit être diviſée en 24 <lb/>parties égales, ou deux fois 12 h. </s> <s xml:id="echoid-s12373" xml:space="preserve">pour les 24 h. </s> <s xml:id="echoid-s12374" xml:space="preserve">du jour, & </s> <s xml:id="echoid-s12375" xml:space="preserve">chaque <lb/>heure en quarts, ſelon l'ordre qui paroît en ladite figure. </s> <s xml:id="echoid-s12376" xml:space="preserve">Ces 24 h. <lb/></s> <s xml:id="echoid-s12377" xml:space="preserve">ſe diſtinguent par autant de dents, dont celles où ſont marquées 12 <lb/>h. </s> <s xml:id="echoid-s12378" xml:space="preserve">ſont plus longues que les autres, afin de pouvoir compter les heu-<lb/>res pendant la nuit ſans lumiere.</s> <s xml:id="echoid-s12379" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12380" xml:space="preserve">A ces deux rouës on ajoûte une regle ou alidade qui tourne au-<lb/>tour du centre, & </s> <s xml:id="echoid-s12381" xml:space="preserve">qui déborde au-delà de la plus grande circon-<lb/>ference.</s> <s xml:id="echoid-s12382" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12383" xml:space="preserve">Ces trois pieces doivent être jointes enſemble par le moyen d'un <lb/>clou à tête, & </s> <s xml:id="echoid-s12384" xml:space="preserve">percé de telle ſorte qu'il y ait au centre un petit trou <lb/>d'environ 2 lignes de diametre pour voir facilement à travers, l'E-<lb/>toile Polaire. </s> <s xml:id="echoid-s12385" xml:space="preserve">Il eſt à propos que le mouvement de ces pieces ſoit un <lb/>peu ferme, afin que chacune reſte où l'on la met pendant l'Obſer-<lb/>vation.</s> <s xml:id="echoid-s12386" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div745" type="section" level="1" n="396"> <head xml:id="echoid-head536" xml:space="preserve">USAGE.</head> <p> <s xml:id="echoid-s12387" xml:space="preserve">TOurnez la rouë des heures juſqu'à ce que la plus grande dent <lb/>où eſt marqué 12 h. </s> <s xml:id="echoid-s12388" xml:space="preserve">ſoit ſur le jour du mois courant; </s> <s xml:id="echoid-s12389" xml:space="preserve">appro-<lb/>chez l'Inſtrument de vos yeux, le tenant par le manche, en ſorte <lb/>qu'il ne panche ni à droite ni à gauche, & </s> <s xml:id="echoid-s12390" xml:space="preserve">qu'il ſoit à peu près pa-<lb/>rallele au Plan de l'Equateur; </s> <s xml:id="echoid-s12391" xml:space="preserve">& </s> <s xml:id="echoid-s12392" xml:space="preserve">ayant vû par le trou du centre l'E-<lb/>toile Polaire, tournez l'alidade juſqu'à ce que ſon extremité, qui <lb/>paſſe au-delà des circonferences des cercles, raſe la Claire du quarré <lb/>de la petite Ourſe. </s> <s xml:id="echoid-s12393" xml:space="preserve">Si l'Inſtrument eſt diſpoſé pour cette Etoile, la <lb/>dent de la rouë des heures qui ſera ſous l'alidade marquera l'heure <lb/>preſente, que vous pourrez connoître ſans lumiere en comptant les <lb/>dents depuis la plus grande qui eſt pour 12 h.</s> <s xml:id="echoid-s12394" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12395" xml:space="preserve">Cette Etoile que nous appellons la Claire de la petite Ourſe, eſt <lb/>une des deux qui forment le derriere du quarré. </s> <s xml:id="echoid-s12396" xml:space="preserve">Elle precede l'autre <lb/>dans le mouvement journalier, & </s> <s xml:id="echoid-s12397" xml:space="preserve">eſt moins éloignée qu'elle de l'E-<lb/>toile Polaire. </s> <s xml:id="echoid-s12398" xml:space="preserve">On fait la même operation pour les gardes de la gran-<lb/>de Ourſe, quand l'Inſtrument eſt fait pour ces Etoiles.</s> <s xml:id="echoid-s12399" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12400" xml:space="preserve">Les deux Etoiles, que nous appellons les Gardes de la grande <lb/> <pb o="379" file="395" n="395" rhead="D'UN HORLOGE A L'EAU. Liv. VIII. Ch. VII."/> Ourſe, ſont preſque en ligne droite avec l'Etoile Polaire & </s> <s xml:id="echoid-s12401" xml:space="preserve">ſont de <lb/>ſa même grandeur. </s> <s xml:id="echoid-s12402" xml:space="preserve">Ces deux Etoiles ſervent beaucoup à la faire <lb/>connoître.</s> <s xml:id="echoid-s12403" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div746" type="section" level="1" n="397"> <head xml:id="echoid-head537" xml:space="preserve">CHAPITRE VII.</head> <head xml:id="echoid-head538" style="it" xml:space="preserve">Contenant la Conſtruction d'un Horloge à l'Eau.</head> <p> <s xml:id="echoid-s12404" xml:space="preserve">CEt Horloge eſt compoſé d'une eſpece de tambour ou boëte <lb/> <anchor type="note" xlink:label="note-395-01a" xlink:href="note-395-01"/> ronde, marquée B, faite de métail, bien ſoudée; </s> <s xml:id="echoid-s12405" xml:space="preserve">dans laquelle <lb/>il y a une certaine quantité d'eau préparée & </s> <s xml:id="echoid-s12406" xml:space="preserve">pluſieurs cellules qui <lb/>ont communication les unes avec les autres par un petit trou qui <lb/>eſt proche de la circonference, & </s> <s xml:id="echoid-s12407" xml:space="preserve">qui ne laiſſe écouler l'eau qu'-<lb/>autant qu'il eſt néceſſaire pour faire deſcendre peu à peu cette Mon-<lb/>tre par ſon propre poids; </s> <s xml:id="echoid-s12408" xml:space="preserve">elle eſt ſuſpenduë aux points A, par deux <lb/>ficelles fines & </s> <s xml:id="echoid-s12409" xml:space="preserve">égales de groſſeur, & </s> <s xml:id="echoid-s12410" xml:space="preserve">qui ſont entortillées autour <lb/>de l'aiſſieu de ſer marqué D, qui traverſe à angles droits de part & </s> <s xml:id="echoid-s12411" xml:space="preserve"><lb/>d'autre le milieu juſte du tambour, & </s> <s xml:id="echoid-s12412" xml:space="preserve">qui en deſcendant ſans faire <lb/>aucun bruit, montre les heures par les deux bouts dudit aiſſieu. </s> <s xml:id="echoid-s12413" xml:space="preserve">Les <lb/>heures ſont marquées des deux côtez de la boëte ſur un Plan verti-<lb/>cal. </s> <s xml:id="echoid-s12414" xml:space="preserve">Leurs diviſions ſe font en cette maniere: </s> <s xml:id="echoid-s12415" xml:space="preserve">On remonte le tam-<lb/>bour en tortillant la ficelle, juſqu'à ce que le tambour ſoit au haut <lb/>du Plan où l'on veut commencer la diviſion des heures; </s> <s xml:id="echoid-s12416" xml:space="preserve">puis on laiſ-<lb/>ſe deſcendre le tambour pendant 12 h. </s> <s xml:id="echoid-s12417" xml:space="preserve">on ſe regle ſur une bonne <lb/>Pendule ou ſur un Cadran au Soleil; </s> <s xml:id="echoid-s12418" xml:space="preserve">on diviſe enſuite tout l'eſpace <lb/>que l'aiſſieu a parcouru, en autant de parties égales qu'il s'eſt é-<lb/>coulé d'heures ou de demi-heures, puis on place les heures vis-à-<lb/>vis ces parties.</s> <s xml:id="echoid-s12419" xml:space="preserve"/> </p> <div xml:id="echoid-div746" type="float" level="2" n="1"> <note position="right" xlink:label="note-395-01" xlink:href="note-395-01a" xml:space="preserve">XXVIII. <lb/>Planche. <lb/>fig. 5.</note> </div> <p> <s xml:id="echoid-s12420" xml:space="preserve">Il ſe fait auſſi de ces machines qui marquent les heures par une <lb/>éguille qui tourne autour d'un Cadran de Pendule ordinaire, com-<lb/>me la même figure le montre. </s> <s xml:id="echoid-s12421" xml:space="preserve">Cela ſe fait par le moyen d'une rouë <lb/>ou poulie de 4 à 5 pouces de diametre, qui eſt attachée derriere <lb/>le Cadran par une verge de cuivre ou d'acier qui la traverſe au cen-<lb/>tre; </s> <s xml:id="echoid-s12422" xml:space="preserve">un des bouts ds ladîte verge eſt retenu dans un petit trou qui <lb/>lui ſert de ſupport, & </s> <s xml:id="echoid-s12423" xml:space="preserve">l'autre bout porte l'éguille qui marque les <lb/>heures. </s> <s xml:id="echoid-s12424" xml:space="preserve">Ladite éguille tourne par le moyen d'un cordon de ſoie tor-<lb/>ſe un peu groſſe, qui paſſe autour de la Poulie & </s> <s xml:id="echoid-s12425" xml:space="preserve">qui a un de ſes <lb/>bouts accroché à l'aiſſieu à l'endroit marqué H; </s> <s xml:id="echoid-s12426" xml:space="preserve">on attache à l'autre <lb/>bout de la ſoie un petit plomb, comme F, alors le tambour deſcen-<lb/>dant doucement, entraîne avec lui le crochet H, & </s> <s xml:id="echoid-s12427" xml:space="preserve">fait tourner en <lb/> <pb o="380" file="396" n="396" rhead="CONSTRUCTION ET USAGES"/> même tems la poulie qui fait elle-même tourner l'éguille, laquelle <lb/>par ce mo yen marque l'heure qu'il eſt. </s> <s xml:id="echoid-s12428" xml:space="preserve">La circonference de la pou-<lb/>lie doit être proportionnée à l'eſpace ou diſtance que l'aiſſieu du <lb/>tambour a occupé pendant 12 h. </s> <s xml:id="echoid-s12429" xml:space="preserve">c'eſt-à-dire, qu'on prend avec <lb/>une ficelle la longueur juſte de cette diſtance, & </s> <s xml:id="echoid-s12430" xml:space="preserve">on fait une poulie <lb/>dont la circonfererence ſoit juſte de la longueur de cette ficelle, alors <lb/>la poulie & </s> <s xml:id="echoid-s12431" xml:space="preserve">l'éguille auront fait un tour autour du Cadran en 12h. <lb/></s> <s xml:id="echoid-s12432" xml:space="preserve">Quand le tambour deſcend un peu trop vîte, & </s> <s xml:id="echoid-s12433" xml:space="preserve">que la montre a-<lb/>vance, alors on met un plomb en F un peu plus peſant, & </s> <s xml:id="echoid-s12434" xml:space="preserve">quand <lb/>il va un peu trop doucement, il en faut mettre un plus leger. </s> <s xml:id="echoid-s12435" xml:space="preserve">L'on <lb/>fait auſſi de ces Montres qui ſervent de réveil-matin; </s> <s xml:id="echoid-s12436" xml:space="preserve">cela ſe fait <lb/>par le moyen d'une détente qu'on ajuſte au deſſous de l'Horloge, <lb/>& </s> <s xml:id="echoid-s12437" xml:space="preserve">ayant placé l'aiſſieu ſur cette détente, on met l'éguille ſur l'heu-<lb/>re qu'on veut s'éveiller, puis on remonte le tambour, & </s> <s xml:id="echoid-s12438" xml:space="preserve">on repla-<lb/>ce l'éguille ſur l'heure qu'il eſt; </s> <s xml:id="echoid-s12439" xml:space="preserve">le lendemain l'axe du tambour po-<lb/>ſant ſur la détente la fera tomber, alors un cordon auquel eſt at-<lb/>taché un plomb, étant paſſé autour d'une petite poulie de cuivre, <lb/>fait mouvoir une rouë de balancier, qui par ſon mouvement fait <lb/>fraper avec vîteſſe un petit marteau ſur un timbre, juſqu'à ce que <lb/>le plomb ſoit en bas.</s> <s xml:id="echoid-s12440" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div748" type="section" level="1" n="398"> <head xml:id="echoid-head539" style="it" xml:space="preserve">Conſtruction du Tambour.</head> <p> <s xml:id="echoid-s12441" xml:space="preserve">IL ſe fait quelquefois d'argent battu, mais pour le plus facile on <lb/> <anchor type="note" xlink:label="note-396-01a" xlink:href="note-396-01"/> le fait d'étain fin; </s> <s xml:id="echoid-s12442" xml:space="preserve">le diametre de chaque fonds eſt d'environ 5 <lb/>pouces, & </s> <s xml:id="echoid-s12443" xml:space="preserve">tout le tambour a deux pouces d'épaiſſeur tout monté. <lb/></s> <s xml:id="echoid-s12444" xml:space="preserve">Il doit être bien parallele & </s> <s xml:id="echoid-s12445" xml:space="preserve">bien égal en tout ſens; </s> <s xml:id="echoid-s12446" xml:space="preserve">le dedans eſt di-<lb/>viſé en ſept caſes ou cellules, & </s> <s xml:id="echoid-s12447" xml:space="preserve">quelquefois en cinq, comme la fi-<lb/>gure le marque. </s> <s xml:id="echoid-s12448" xml:space="preserve">On ajuſte autant de Plans inclinez en languetes de <lb/>même matiere, qu'on ſoude à chaque fonds & </s> <s xml:id="echoid-s12449" xml:space="preserve">à la circonference <lb/>concave du tambour; </s> <s xml:id="echoid-s12450" xml:space="preserve">elles ſont longues d'environ deux pouces <lb/>chacune, comme BF, AL. </s> <s xml:id="echoid-s12451" xml:space="preserve">EI, DH, CG. </s> <s xml:id="echoid-s12452" xml:space="preserve">Elles ont une telle <lb/>pente en tournant, qu'elles reçoivent l'eau par un petit trou qui eſt <lb/>au haut de chaque languete vers la circonference, & </s> <s xml:id="echoid-s12453" xml:space="preserve">la fait aller <lb/>d'une cellule à l'autre; </s> <s xml:id="echoid-s12454" xml:space="preserve">à meſure que la machine roule en deſcen-<lb/>dant, elle marque les heures ſur un Plan vertical par l'extremité de <lb/>l'axe, qui, comme nous avons dit, la traverſe à angles droits en en-<lb/>trant en ſon milieu dans un trou quarré M; </s> <s xml:id="echoid-s12455" xml:space="preserve">on met ordinairement <lb/>dans les tambours de cette grandeur 6 à 7 onces d'eau diſtilée. </s> <s xml:id="echoid-s12456" xml:space="preserve">A-<lb/>vant que de mettre l'eau, il faut avoir grand ſoin de bien ſouder les <lb/>lames au fond & </s> <s xml:id="echoid-s12457" xml:space="preserve">à la circonference; </s> <s xml:id="echoid-s12458" xml:space="preserve">on les ſoude d'abord ſur un <lb/> <pb o="381" file="397" n="397" rhead="D'UN HORLOGE A L'EAU. Liv. VIII. Ch. VII."/> des fonds, comme la figure le repreſente; </s> <s xml:id="echoid-s12459" xml:space="preserve">puis on a un petit quarré <lb/>d'argent qu'on ajuſte aux deux fonds, & </s> <s xml:id="echoid-s12460" xml:space="preserve">qui traverſe le tambour, <lb/>enſuite on ſoude le tout au fond avec de la ſoudure bien coulante; <lb/></s> <s xml:id="echoid-s12461" xml:space="preserve">puis on ſoude la bande en cercle qui forme la circonference; </s> <s xml:id="echoid-s12462" xml:space="preserve">de ma-<lb/>niere que l'eau ne puiſſe ſortir par aucun endroit. </s> <s xml:id="echoid-s12463" xml:space="preserve">On la fait entrer <lb/>par deux trous poſez ſur un même diametre, & </s> <s xml:id="echoid-s12464" xml:space="preserve">éloignez également <lb/>du centre M, puis on les bouche bien, en les ſoudant de la même <lb/>matiere, afin d'empêcher l'air d'entrer, & </s> <s xml:id="echoid-s12465" xml:space="preserve">l'eau d'en ſortir dans les <lb/>mouvemens que la machine fait en tournant avec ſon aiſſieu & </s> <s xml:id="echoid-s12466" xml:space="preserve">en <lb/>deſcendant inſenſiblement par le dévelopement des deux cordes <lb/>fines qui entortillent l'axe.</s> <s xml:id="echoid-s12467" xml:space="preserve"/> </p> <div xml:id="echoid-div748" type="float" level="2" n="1"> <note position="left" xlink:label="note-396-01" xlink:href="note-396-01a" xml:space="preserve">Fig. 6.</note> </div> <p> <s xml:id="echoid-s12468" xml:space="preserve">Cette conſtruction ſe fait de cette maniere, quand les tambours <lb/>ſont faits d'argent; </s> <s xml:id="echoid-s12469" xml:space="preserve">mais lorſqu'ils ſont faits d'étain, qui ſont les <lb/>plus commodes, on fond dans un moule la circonference avec un <lb/>des fonds, enſuite l'on tourne l'une & </s> <s xml:id="echoid-s12470" xml:space="preserve">l'autre en-dedans & </s> <s xml:id="echoid-s12471" xml:space="preserve">en de-<lb/>hors, afin que le tout ſoit bien égal d'épaiſſeur, puis on acheve le <lb/>tambour de la maniere que je viens d'expliquer, en ſoudant les cel-<lb/>lules avec de la ſoudure d'étain, en ſe ſervant pour cela de petits <lb/>fers chauds.</s> <s xml:id="echoid-s12472" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12473" xml:space="preserve">On voit par la figure 6, que les languetes ou diviſions qui ſont <lb/>en-dedans du tambour ne viennent point ſe joindre l'une à l'autre, <lb/>mais finiſſent en G, H, I, L, F, afin que lorſqu'on remonte le <lb/>tambour l'eau paſſe vîte d'une diviſion dans l'autre, de ſorte <lb/>que le tambour reſte à telle hauteur qu'on le voudra, parce qu'à <lb/>chaque mouvement qu'on lui donnera en le remontant, l'eau paſ-<lb/>ſant en groſſe quantité par les vuides qui ſeront de G en M, elle <lb/>prendra auſſi-tôt ſon équilibre, ce qui n'arriveroit pas ſi les caſes <lb/>étoient abſolument fermées; </s> <s xml:id="echoid-s12474" xml:space="preserve">les petits trous qui ſont aux extremi-<lb/>tez des languetes, n'étant pas ſuffiſans pour faire écouler l'eau auſſi <lb/>promptement qu'il le faudroit, l'eau ne paſſant que goutte à goutte <lb/>par les petits trous.</s> <s xml:id="echoid-s12475" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12476" xml:space="preserve">Il eſt évident que ſi cette Pendule étoit ſuſpenduë par ſon centre <lb/>de gravité, comme il arriveroit ſi la ſurface de l'aiſſieu paſſoit exac-<lb/>tement par le centre de la machine, elle demeureroit immobile, & </s> <s xml:id="echoid-s12477" xml:space="preserve"><lb/>que ce qui la fait mouvoir eſt qu'elle eſt ſuſpenduë hors de ſon cen-<lb/>tre de peſanteur par les ficelles qui entourent ſon aiſſieu, qui ne <lb/>doit avoir, par rapport à la grandeur du tambour & </s> <s xml:id="echoid-s12478" xml:space="preserve">à l'eau qu'il <lb/>contient, qu'environ une ligne ou une ligne & </s> <s xml:id="echoid-s12479" xml:space="preserve">demie de groſſeur, & </s> <s xml:id="echoid-s12480" xml:space="preserve"><lb/>être bien égal en toute ſa longueur; </s> <s xml:id="echoid-s12481" xml:space="preserve">il n'eſt pas néceſſaire d'avertir <lb/>qu'il doit être quarré par le milieu, afin de remplir juſte le trou des <lb/>fonds du tambour.</s> <s xml:id="echoid-s12482" xml:space="preserve"/> </p> <pb o="382" file="398" n="398" rhead="CONSTRUCTION ET USAGES"/> <p> <s xml:id="echoid-s12483" xml:space="preserve">De la groſſeur de l'aiſſieu dépend la vîteſſe ou la modération du <lb/>mouvement du tambour; </s> <s xml:id="echoid-s12484" xml:space="preserve">car plus l'axe eſt gros, plus il deſcend <lb/>vîte, & </s> <s xml:id="echoid-s12485" xml:space="preserve">moins il a de diametre, plus il va lentement, en ce qu'il y a <lb/>plus ou moins d'excentricité, & </s> <s xml:id="echoid-s12486" xml:space="preserve">que par conſequent l'eau paſſe plus <lb/>ou moins vîte d'une cellule à l'autre, ce qui fait que la force de ſon <lb/>mouvement ſe trouve plus ou moins balancée par la peſanteur de <lb/>l'eau que contient la cellule oppoſée.</s> <s xml:id="echoid-s12487" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12488" xml:space="preserve">Si on vouloit avoir le plaiſir de voir la circulation de l'eau dans <lb/>une de ces machines, on pourroit faire faire un tambour, dont il y <lb/>eût un des fonds qui fut vitré; </s> <s xml:id="echoid-s12489" xml:space="preserve">toute la difficulté ne ſeroit que de <lb/>trouver un maſtique qui pût faire tenir les morceaux de glace qui <lb/>compoſeroient ce fond ſur le métal du tambour.</s> <s xml:id="echoid-s12490" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12491" xml:space="preserve">Pour monter cette Montre, quand elle eſt deſcenduë preſqu'au <lb/>bas des cordes, il faut la hauſſer avec la main en la faiſant tourner, <lb/>en ſorte que les cordes s'entortillent tout au long de l'aiſſieu éga-<lb/>lement, & </s> <s xml:id="echoid-s12492" xml:space="preserve">qu'il ſoit ſuſpendu horiſontalement.</s> <s xml:id="echoid-s12493" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12494" xml:space="preserve">J'ai dit qu'il falloit que l'eau qu'on met dans les tambours fût <lb/>diſtilée, autrement il faudroit la changer ſouvent, en ce qu'il ſe for-<lb/>meroit un limon ou craſſe autour des petits trous, qui empêcheroit <lb/>l'eau de paſſer comme il faut.</s> <s xml:id="echoid-s12495" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12496" xml:space="preserve">Pour diſtiler l'eau facilement ſans feu, on la fera paſſer dans une <lb/>bouteille de verre ou de terre bien nette, mettant dans ſon ouver-<lb/>ture un entonnoir de telle grandeur qu'on voudra, & </s> <s xml:id="echoid-s12497" xml:space="preserve">on mettra <lb/>dedans deux morceaux de papier blanc fait auſſi en entonnoir, puis <lb/>ayant mis l'eau on la fera paſſer goutte à goutte à dans la bouteille, <lb/>& </s> <s xml:id="echoid-s12498" xml:space="preserve">ayant repeté cette operation pluſieurs fois, l'eau deviendra pure <lb/>& </s> <s xml:id="echoid-s12499" xml:space="preserve">claire & </s> <s xml:id="echoid-s12500" xml:space="preserve">ſe conſervera long-tems: </s> <s xml:id="echoid-s12501" xml:space="preserve">on filtre encore l'eau au tra-<lb/>vers d'un morceau de drap, & </s> <s xml:id="echoid-s12502" xml:space="preserve">l'ayant fait repaſſer quatre à cinq <lb/>fois, on lui ôtera toute ſa crudité & </s> <s xml:id="echoid-s12503" xml:space="preserve">ſon impureté.</s> <s xml:id="echoid-s12504" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12505" xml:space="preserve">On peut mettre un peu d'eau diſtilée avec du thim ou du roma-<lb/>@in, ou de l'eſprit-de-vin parmi l'eau, pour l'empêcher de geler <lb/>l'Hyver, mais comme cela la rendroit un peu mordiquante, & </s> <s xml:id="echoid-s12506" xml:space="preserve">par <lb/>ce moyen pourroit faire agrandir les trous des cellules, j'aimerois <lb/>mieux la laiſler ſeule, & </s> <s xml:id="echoid-s12507" xml:space="preserve">mettre la machine à un endroit où elle ne <lb/>pût pas geler dans le grand froid.</s> <s xml:id="echoid-s12508" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12509" xml:space="preserve">On peut faire de ces ſortes d'Horloges, dont le tambour ſeroit <lb/>enfermé dans une boëte à pendule ordinaire, dont le mouvement <lb/>pourroit étre tellement ralenti qu'il ne deſcendroit en 24 h. </s> <s xml:id="echoid-s12510" xml:space="preserve">que <lb/>d'environ 10 pouces, & </s> <s xml:id="echoid-s12511" xml:space="preserve">qui ſonneroit les heures, & </s> <s xml:id="echoid-s12512" xml:space="preserve">marqueroit les <lb/>autres choſes que marquent les Pendules à rouës, les plus curieuſes, <lb/> <pb o="383" file="399" n="399" rhead="D'UN CADRAN AU VENT. Liv. VIII. Ch. VIII."/> dont je reſerve à un autre tems de donner la conſtruction; </s> <s xml:id="echoid-s12513" xml:space="preserve">com-<lb/>me auſſi celle des Pendules à rouës, à reſſorts & </s> <s xml:id="echoid-s12514" xml:space="preserve">à ſonneries, qui <lb/>marquent les ſecondes & </s> <s xml:id="echoid-s12515" xml:space="preserve">ſervent à l'Aſtronomie.</s> <s xml:id="echoid-s12516" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div750" type="section" level="1" n="399"> <head xml:id="echoid-head540" xml:space="preserve">CHAPITRE VIII.</head> <head xml:id="echoid-head541" style="it" xml:space="preserve">Contenant la Conſtruction d'un Cadran pour connoître le vent <lb/>qui ſouffle, ſans ſortir de ſa Chambre.</head> <p> <s xml:id="echoid-s12517" xml:space="preserve">IL faut attacher au plancher de la Chambre ou au manteau de la <lb/>cheminée, ou bien a une muraille, un grand cercle diviſé en 32 <lb/>airs ou rumbs de vents, en ſorte que le Nord & </s> <s xml:id="echoid-s12518" xml:space="preserve">Sud réponde à la <lb/>ligne Méridiene, ce qu'on pourra facilement faire par le moyen <lb/>d'une Bouſlole; </s> <s xml:id="echoid-s12519" xml:space="preserve">il faut que ce Cadran ait une éguille mobile antour <lb/>de ſon centre, comme les Cadrans des Horloges ordinaires, & </s> <s xml:id="echoid-s12520" xml:space="preserve">que <lb/>cette éguille ſoit attachée à un aiſſieu perpendiculaire à l'horiſon <lb/>qui ſe puiſſe mouvoir facilement au moindre vent, & </s> <s xml:id="echoid-s12521" xml:space="preserve">ce par le <lb/>moyen d'une giroüete qui doit être placée au-deſſus du toit de la <lb/>même Chambre; </s> <s xml:id="echoid-s12522" xml:space="preserve">car le vent faiſant tourner la giroüete fera auſſi <lb/>tourner ſon aiſſieu & </s> <s xml:id="echoid-s12523" xml:space="preserve">en même tems l'éguille qui lui eſt attachée, <lb/>laquelle de cette maniere montrera ſur le Cadran le vent qui ſoufle.</s> <s xml:id="echoid-s12524" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12525" xml:space="preserve">Par le mouvement de la giroüete AB, qui doit être de fer, & </s> <s xml:id="echoid-s12526" xml:space="preserve">fixe-<lb/>ment attachée avec l'aiſſieu CD, cet aiſſieu auſſi tourne avec elle. <lb/></s> <s xml:id="echoid-s12527" xml:space="preserve">Cette branche de fer eſt poſée verticalement à l'horiſon, & </s> <s xml:id="echoid-s12528" xml:space="preserve">ſoûte-<lb/>nuë en haut par le Plan horiſontal EF, qui eſt une piece de fer at-<lb/>tachée à quelque endroit pour maintenir l'aiſſieu. </s> <s xml:id="echoid-s12529" xml:space="preserve">Au bas dudit <lb/>aiſſieu eſt poſé un quarré d'acier GH, ſur lequel eſt frapé un coup <lb/>de pointeau pour faire entrer la pointe de l'axe qui doit être d'a-<lb/>cier trempé, ſur lequel il s'appuie en D; </s> <s xml:id="echoid-s12530" xml:space="preserve">de ſorte que ne s'appuïant <lb/>preſque que ſur un point, il puiſſe ſe mouvoir avec beaucoup de <lb/>facilité & </s> <s xml:id="echoid-s12531" xml:space="preserve">au moindre vent. </s> <s xml:id="echoid-s12532" xml:space="preserve">Le pignon IK doit avoir huit dents <lb/>cannelées & </s> <s xml:id="echoid-s12533" xml:space="preserve">égales pour les huit principaux vents, & </s> <s xml:id="echoid-s12534" xml:space="preserve">dans leſquel-<lb/>les on fait engrainer les dents du roüet LM, qui en a 16 ou 32, <lb/>ſuivant les vents marquez au Cadran, & </s> <s xml:id="echoid-s12535" xml:space="preserve">qui par ce moyen eſt mis <lb/>en mouvement par la giroüete, & </s> <s xml:id="echoid-s12536" xml:space="preserve">fait auſſi tourner ſon aiſſieu P Q, <lb/>qui étant poſé parallele à l'horiſon, traverſe le mur T à angles <lb/>droits auſſi-bien que le Cadran qu'on attache à la muraille. </s> <s xml:id="echoid-s12537" xml:space="preserve">L'é-<lb/>guille R, qui marque les vents, eſt attachée au bout de cet aiſſieu <lb/>& </s> <s xml:id="echoid-s12538" xml:space="preserve">ſait le même mouvement que lui. </s> <s xml:id="echoid-s12539" xml:space="preserve">Les noms des vents doivent <lb/> <pb o="384" file="400" n="400" rhead="DESCRIPTION"/> être diſtinguez au Cadran par des Lettres capitales, comme aux <lb/>Bouſſoles dont nous avons parlé ci-devant.</s> <s xml:id="echoid-s12540" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12541" xml:space="preserve">L'on voit par la diſpoſition de toute la machine que le vent fai-<lb/>ſant tourner la giroüete AB, elle entraîne avec elle le grand aiſſieu <lb/>CD, qui fait auſſi tourner en même tems le pignon IK, auquel <lb/>engrainent les dents du roüet LM, lequel le faiſant tourner auſſi-<lb/>bien que ſon axe, entraîne par conſequent l'éguille qui lui eſt at-<lb/>tachée à ſon extremité; </s> <s xml:id="echoid-s12542" xml:space="preserve">& </s> <s xml:id="echoid-s12543" xml:space="preserve">par ce moyen on a le plaiſir de ſçavoir le <lb/>vent qui regne, ſans ſortir de ſa Chambre.</s> <s xml:id="echoid-s12544" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12545" xml:space="preserve">Quand le lieu où l'on veut placer le Cadran eſt un peu éloigné <lb/>du haut de la Maiſon où doit être toûjours placée la giroüete, on <lb/>peut allonger le grand axe tant qu'on voudra avec des vis, & </s> <s xml:id="echoid-s12546" xml:space="preserve">mê-<lb/>me faire des renvois par des pignons & </s> <s xml:id="echoid-s12547" xml:space="preserve">des rouës; </s> <s xml:id="echoid-s12548" xml:space="preserve">tout cela eſt fa-<lb/>cile à entendre.</s> <s xml:id="echoid-s12549" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div751" type="section" level="1" n="400"> <head xml:id="echoid-head542" style="it" xml:space="preserve">Fin du huitiéme Livre.</head> <figure> <image file="400-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/400-01"/> </figure> </div> <div xml:id="echoid-div752" type="section" level="1" n="401"> <head xml:id="echoid-head543" style="it" xml:space="preserve">Deſcription des principaux Outils dont on ſe ſert <lb/>pour la conſtruction des Inſtrumens de <lb/>Mathematique.</head> <p> <s xml:id="echoid-s12550" xml:space="preserve">LE principal Outil & </s> <s xml:id="echoid-s12551" xml:space="preserve">le plus néceſſaire eſt un gros Etau. </s> <s xml:id="echoid-s12552" xml:space="preserve">Il ſert <lb/>à tenir l'ouvrage pour le limer, & </s> <s xml:id="echoid-s12553" xml:space="preserve">autre uſage, Il faut que l'E-<lb/>tau ſoit bien limé, que les mords ſe joignent bien, qu'ils ſoient tail-<lb/>lez en lime & </s> <s xml:id="echoid-s12554" xml:space="preserve">d'une bonne trempe, & </s> <s xml:id="echoid-s12555" xml:space="preserve">que la vis s'ajuſte comme il <lb/>faut dans ſa boëte. </s> <s xml:id="echoid-s12556" xml:space="preserve">On l'attache fortement à un Etabli qui doit être <lb/>ſcelé fixement. </s> <s xml:id="echoid-s12557" xml:space="preserve">en quelque endroit que ce ſoit.</s> <s xml:id="echoid-s12558" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12559" xml:space="preserve">On ſe ſert auſſi de petits Etaux à main, de differente groſſeur, <lb/>ſuivant l'ouvrage qu'on veut limer.</s> <s xml:id="echoid-s12560" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12561" xml:space="preserve">L'Enclume ou Taſſeau ſert pour écroüir & </s> <s xml:id="echoid-s12562" xml:space="preserve">dreſſer l'ouvrage au <lb/>Marteau. </s> <s xml:id="echoid-s12563" xml:space="preserve">Elle doit être d'acier trempé & </s> <s xml:id="echoid-s12564" xml:space="preserve">bien unie, & </s> <s xml:id="echoid-s12565" xml:space="preserve">eſt placée <lb/>ſur un gros billot de bois pour la maintenir à la place où elle eſt <lb/>poſée.</s> <s xml:id="echoid-s12566" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12567" xml:space="preserve">Il y a des Taſſeaux d'Etabli qui ſervent à dreſſer & </s> <s xml:id="echoid-s12568" xml:space="preserve">à river les <lb/> <pb o="385" file="401" n="401" rhead="DES PRINCIPAUX OUTILS."/> petits ouvrages; </s> <s xml:id="echoid-s12569" xml:space="preserve">à quelques-uns il y a d'un côté un bout qui eſt <lb/>rond & </s> <s xml:id="echoid-s12570" xml:space="preserve">qui va en pointe, il ſert à arrondir les Virolles; </s> <s xml:id="echoid-s12571" xml:space="preserve">& </s> <s xml:id="echoid-s12572" xml:space="preserve">de l'autre <lb/>côté le bout eſt quarré & </s> <s xml:id="echoid-s12573" xml:space="preserve">va auſſi en diminuant. </s> <s xml:id="echoid-s12574" xml:space="preserve">On nomme cette <lb/>ſorte de Taſſaux, Bigornes.</s> <s xml:id="echoid-s12575" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12576" xml:space="preserve">Les Scies à main ſont faites de maniere qu'il y a une branche qui <lb/>bande les feüillets de differentes épaiſſeurs, & </s> <s xml:id="echoid-s12577" xml:space="preserve">qu'on arrête par le <lb/>moyen d'une vis & </s> <s xml:id="echoid-s12578" xml:space="preserve">d'un écrou.</s> <s xml:id="echoid-s12579" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12580" xml:space="preserve">Il eſt néceſſaire d'avoir de bonnes Limes. </s> <s xml:id="echoid-s12581" xml:space="preserve">Celles d'Allemagne <lb/>ſont les meilleures pour les rudes: </s> <s xml:id="echoid-s12582" xml:space="preserve">pour les bâtardes & </s> <s xml:id="echoid-s12583" xml:space="preserve">les douces, <lb/>celles d'<emph style="sc">A</emph>ngleterre ſont fort bonnes. </s> <s xml:id="echoid-s12584" xml:space="preserve">On doit auſſi avoir de peti-<lb/>tes Limes rudes & </s> <s xml:id="echoid-s12585" xml:space="preserve">douces, à refendre, en triangle, de quarrées, de <lb/>rondes, demi-rondes, &</s> <s xml:id="echoid-s12586" xml:space="preserve">c. </s> <s xml:id="echoid-s12587" xml:space="preserve">des rapes pour dégroſſir le bois; </s> <s xml:id="echoid-s12588" xml:space="preserve">des <lb/>Marteaux un peu gros à panne droite & </s> <s xml:id="echoid-s12589" xml:space="preserve">à panne de travers, pour <lb/>étirer, dreſſer & </s> <s xml:id="echoid-s12590" xml:space="preserve">planir l'ouvrage; </s> <s xml:id="echoid-s12591" xml:space="preserve">des petits Marteaux d'Etabli pour <lb/>river les clous; </s> <s xml:id="echoid-s12592" xml:space="preserve">des Marteaux à tête ronde pour emboutir les pieces <lb/>en rond, &</s> <s xml:id="echoid-s12593" xml:space="preserve">c.</s> <s xml:id="echoid-s12594" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12595" xml:space="preserve">Des Filieres doubles & </s> <s xml:id="echoid-s12596" xml:space="preserve">ſimples qui ſervent à faire des vis, dont <lb/>les Pas & </s> <s xml:id="echoid-s12597" xml:space="preserve">Taraux ſoient de differente groſſeur & </s> <s xml:id="echoid-s12598" xml:space="preserve">fineſſe.</s> <s xml:id="echoid-s12599" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12600" xml:space="preserve">Tenailles & </s> <s xml:id="echoid-s12601" xml:space="preserve">Pinces de pluſieurs façons. </s> <s xml:id="echoid-s12602" xml:space="preserve">Ciſoires de differentes <lb/>grandeurs pour couper le métal. </s> <s xml:id="echoid-s12603" xml:space="preserve">Bruniſſoir pour polir l'ouvrage. <lb/></s> <s xml:id="echoid-s12604" xml:space="preserve">Des Forets d'acier de diverſes groſſeurs pour percer les trous, dont <lb/>un bout eſt limé en langue de chat, & </s> <s xml:id="echoid-s12605" xml:space="preserve">l'autre en pointe: </s> <s xml:id="echoid-s12606" xml:space="preserve">on s'en ſert <lb/>de differente maniere. </s> <s xml:id="echoid-s12607" xml:space="preserve">Il y en a qu'on met dans un Tour à percer, <lb/>qui eſt compoſé d'une moyene barre de fer quarrée, de deux petites <lb/>Poupées qui portent une Boëte à bobine, dans laquelle on place le <lb/>Foret dans un trou quarré qui traverſe le corps de la Boëte, & </s> <s xml:id="echoid-s12608" xml:space="preserve">qu'on <lb/>fait tourner par le moyen d'un Archet fait d'un bout de Fleuret <lb/>qui eſt percé par le haut, dans le trou duquel on paſſe une corde à <lb/>boyau. </s> <s xml:id="echoid-s12609" xml:space="preserve">On met cet Outil dans l'Etau quand on veut s'en ſervir. </s> <s xml:id="echoid-s12610" xml:space="preserve"><lb/>On perce auſſi en mettant l'ouvrage dans l'Etau, & </s> <s xml:id="echoid-s12611" xml:space="preserve">le Foret dans <lb/>une bobine, ſoit de bois ou de cuivre. </s> <s xml:id="echoid-s12612" xml:space="preserve">On applique le bout du Foret <lb/>dans un petit creux qu'on fait à une plaque de cuivre ou de fer, & </s> <s xml:id="echoid-s12613" xml:space="preserve"><lb/>qu'on appuie contre l'eſtomach; </s> <s xml:id="echoid-s12614" xml:space="preserve">alors plaçant la pointe du Foret à <lb/>l'endroit qu'on veut percer, on fait tourner le Foret par le moyen <lb/>d'un Archet.</s> <s xml:id="echoid-s12615" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12616" xml:space="preserve">Le Tour eſt auſſi d'un grand uſage; </s> <s xml:id="echoid-s12617" xml:space="preserve">le plus ſimple eſt fait de deux <lb/>Poupées de cuivre ou d'acier qui coulent au long d'une barre de fer <lb/>quarrée, & </s> <s xml:id="echoid-s12618" xml:space="preserve">d'un ſupport qui coule pareillement au long de ladite <lb/>barre & </s> <s xml:id="echoid-s12619" xml:space="preserve">qui ſert d'appui aux Outils. </s> <s xml:id="echoid-s12620" xml:space="preserve">Au haut des Poupées ſont deux <lb/>vis d'acier trempé qui les traverſent, & </s> <s xml:id="echoid-s12621" xml:space="preserve">qu'on arrête par le moyen <lb/> <pb o="386" file="402" n="402" rhead="DESCRIPTION"/> d'un écrou. </s> <s xml:id="echoid-s12622" xml:space="preserve">Pour ſe ſervir de ce Tour on le place dans l'Etau & </s> <s xml:id="echoid-s12623" xml:space="preserve">on <lb/>met l'ouvrage qu'on veut tourner entre les deux pointes des vis; <lb/></s> <s xml:id="echoid-s12624" xml:space="preserve">quand on veut tourner à la main on ſe ſert d'un Archet fait d'un <lb/>Fleuret mince, dans le bout duquel on paſſe une corde à boyau ou <lb/>de foüet.</s> <s xml:id="echoid-s12625" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12626" xml:space="preserve">Les grands Tours pour tourner au pied, ſont compoſez de deux <lb/>poupées & </s> <s xml:id="echoid-s12627" xml:space="preserve">de deux jumelles ou couliſſes de bois, de la longueur & </s> <s xml:id="echoid-s12628" xml:space="preserve"><lb/>groſſeur proportionnée au Tour; </s> <s xml:id="echoid-s12629" xml:space="preserve">elles ſont ſoutenuës par deux pie-<lb/>ces de bois qu'on nomme les pieds du Tour. </s> <s xml:id="echoid-s12630" xml:space="preserve">Les couliſſes ſont po-<lb/>ſées de niveau & </s> <s xml:id="echoid-s12631" xml:space="preserve">diſtantes l'une de l'autre de deux à trois pouces <lb/>ſuivant la groſſeur des poupées qui doivent ſe mettre entre deux. <lb/></s> <s xml:id="echoid-s12632" xml:space="preserve">Ces couliſſes ſont aſſemblées par les bouts ſur les pieds qui ont en-<lb/>viron quatre pieds de hauteur, & </s> <s xml:id="echoid-s12633" xml:space="preserve">ſont aſſemblées en bas dans deux <lb/>autres pieces de bois poſées de travers pour rendre la machine plus <lb/>ſtable & </s> <s xml:id="echoid-s12634" xml:space="preserve">plus ſolide.</s> <s xml:id="echoid-s12635" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12636" xml:space="preserve">Les Poupées ſont deux pieces de bois d'égale groſſeur & </s> <s xml:id="echoid-s12637" xml:space="preserve">lon-<lb/>gueur; </s> <s xml:id="echoid-s12638" xml:space="preserve">une partie de ces Poupées doit être entaillée pour ſe met-<lb/>tre entre les deux couliſſes; </s> <s xml:id="echoid-s12639" xml:space="preserve">le reſte qui eſt la tête de la Poupée, & </s> <s xml:id="echoid-s12640" xml:space="preserve"><lb/>qui eſt coupé quarrément, poſe ſolidement deſſus la couliſſe, & </s> <s xml:id="echoid-s12641" xml:space="preserve"><lb/>afin qu'elles ſoient plus fermes, il y a des clefs de bois que l'on fait <lb/>entrer à coups de maillet dans des mortoiſes, qui ſont au bas des <lb/>Poupées au-deſſous de là couliſſe.</s> <s xml:id="echoid-s12642" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12643" xml:space="preserve">Au haut de chaque Poupée il y a une pointe d'acier trempé ſoli-<lb/>dement enclavée dans le bois; </s> <s xml:id="echoid-s12644" xml:space="preserve">les deux pointes doivent être ſi juſte-<lb/>ment placées, qu'elles ſe touchent dans un même point quand on <lb/>les approche l'une de l'autre.</s> <s xml:id="echoid-s12645" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12646" xml:space="preserve">Il y a auſſi une barre de bois qui va tout du long & </s> <s xml:id="echoid-s12647" xml:space="preserve">qui eſt ſoûte-<lb/>nuë par les bras des poupées qui s'approchent & </s> <s xml:id="echoid-s12648" xml:space="preserve">s'éloignent comme <lb/>on veut. </s> <s xml:id="echoid-s12649" xml:space="preserve">Cette barre ſert d'appui pour les outils lorſqu'on travaille.</s> <s xml:id="echoid-s12650" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12651" xml:space="preserve">Contre le plancher & </s> <s xml:id="echoid-s12652" xml:space="preserve">au-deſſus du Tour eſt une perche diſpoſée <lb/>en arc, au bout de laquelle il y a une corde qui deſcend juſques à <lb/>terre & </s> <s xml:id="echoid-s12653" xml:space="preserve">qui s'attache au bout d'une piece de bois qu'on nomme le <lb/>Marche-pied. </s> <s xml:id="echoid-s12654" xml:space="preserve">Quand on veut travailler l'on tourne la corde autour <lb/>de la piece qu'on veut tourner, ou d'un Mandrin qui lui eſt ajuſté; </s> <s xml:id="echoid-s12655" xml:space="preserve">& </s> <s xml:id="echoid-s12656" xml:space="preserve"><lb/>en apuïant le pied ſur la Marche, l'on fait tourner l'ouvrage par <lb/>le moyen de la perche ou de l'arc qui fait reſſort, puis avec des Ou-<lb/>tils propres aux ouvrages qu'on appuie ſue le ſupport, & </s> <s xml:id="echoid-s12657" xml:space="preserve">qu'on poſe <lb/>contre les pieces qu'on veut tourner, on les dégroſſit d'abord avec <lb/>de gros outils, & </s> <s xml:id="echoid-s12658" xml:space="preserve">enſuite on les finit avec d'autres plus délicats.</s> <s xml:id="echoid-s12659" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12660" xml:space="preserve">Comme toutes ſortes d'ouvrages ne ſe peuvent pas tourner en-<lb/> <pb o="387" file="403" n="403" rhead="DES PRINCIPAUX OUTILS"/> tre deux pointes, & </s> <s xml:id="echoid-s12661" xml:space="preserve">qu'il les faut ſouvent tourner en l'air, on ôte <lb/>une des poupées, & </s> <s xml:id="echoid-s12662" xml:space="preserve">on y met à ſa place une piece de bois garnie <lb/>de fer, qu'on nomme Lunete, qui s'ajuſte dans les couliſſes de mê-<lb/>me que les poupées ordinaires, & </s> <s xml:id="echoid-s12663" xml:space="preserve">qui au lieu de pointe ont un trou <lb/>bien rond, dans lequel on fait entrer le colet d'un arbre de fer, dont <lb/>l'autre bout eſt ſoûtenu par la pointe de l'autre Poupée.</s> <s xml:id="echoid-s12664" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12665" xml:space="preserve">Cet arbre a 15 ou 18 pouces de longueur & </s> <s xml:id="echoid-s12666" xml:space="preserve">eſt compoſé de cette <lb/>maniere: </s> <s xml:id="echoid-s12667" xml:space="preserve">Au bout, qui eſt appuïé contre la Lunete, eſt une vis <lb/>d'un fort gros pas, ſur lequel on monte à vis differentes boëtes de <lb/>cuivre, dans leſquelles on fait tenir fermes des morceaux de bois, <lb/>qui fervent à placer les differentes pieces qu'on veut tourner. </s> <s xml:id="echoid-s12668" xml:space="preserve">A <lb/>l'autre bout de l'arbre on fait pluſieurs pas de vis de differentes <lb/>groſſeurs & </s> <s xml:id="echoid-s12669" xml:space="preserve">fineſſes, afin de pouvoir faire des vis ſur le Tour aux <lb/>ouvrages.</s> <s xml:id="echoid-s12670" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12671" xml:space="preserve">Environ au milieu de cet arbre eſt un Mandrin ou Poulie de bois <lb/>autour de laquelle eſt la corde. </s> <s xml:id="echoid-s12672" xml:space="preserve">Pour que cet outil ſoit bien juſte & </s> <s xml:id="echoid-s12673" xml:space="preserve"><lb/>bien dreſſé, il eſt néceſſaire qu'il ſoit fait ſur le tour.</s> <s xml:id="echoid-s12674" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12675" xml:space="preserve">On peut rapporter ſur cet arbre pluſieurs autres piecés pour for-<lb/>mer le tour des figures irregulieres, comme l'ovale, des roſes, <lb/>des cœurs, des godrons, des colonnes torſes, &</s> <s xml:id="echoid-s12676" xml:space="preserve">c. </s> <s xml:id="echoid-s12677" xml:space="preserve">Toutes ces pieces <lb/>ſont limées de la figure qu'on veut qu'elles faſſent, & </s> <s xml:id="echoid-s12678" xml:space="preserve">ont un trou <lb/>quarré au milieu, qu'on ajuſte à un quarré qui eſt vers le bout de <lb/>l'arbre.</s> <s xml:id="echoid-s12679" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12680" xml:space="preserve">Quand les pieces ſont diſpoſées dans l'arbre, l'on met ſon bout <lb/>qui eſt en pointe dans un petit trou qui eſt à la Poupée, & </s> <s xml:id="echoid-s12681" xml:space="preserve">l'autre <lb/>bout eſt paſſé dans la Lunete, qui eſt faite de maniere qu'il y a deux <lb/>pieces qui font reſſort, qui appuie & </s> <s xml:id="echoid-s12682" xml:space="preserve">repouſſe la figure, & </s> <s xml:id="echoid-s12683" xml:space="preserve">par <lb/>ce moyen fait avancer ou reculer l'arbre plus ou moins ſelon la fi-<lb/>gure, & </s> <s xml:id="echoid-s12684" xml:space="preserve">c'eſt ce qui fait que l'outil de celui qui travaille donne la <lb/>forme à l'ouvrage, qui s'en approche ou s'en éloigne ſelon que l'ar-<lb/>bre approche ou recule de ſa rencontre; </s> <s xml:id="echoid-s12685" xml:space="preserve">car il faut toûjours tenir <lb/>l'outil ferme ſur l'appui. </s> <s xml:id="echoid-s12686" xml:space="preserve">Comme on ne ſe ſert pas ordinairement de <lb/>ces ſortes de figures pour les Inſtrumens de Mathematique, je ne <lb/>m'étendrai pas d'avantage ſur cette maniere de tourner.</s> <s xml:id="echoid-s12687" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12688" xml:space="preserve">Le principal uſage de cet arbre eſt de ſervir à tourner des cercles <lb/>en l'air, à faire des rainures dans les Bouſſoles, & </s> <s xml:id="echoid-s12689" xml:space="preserve">autres choſes ſem-<lb/>blables. </s> <s xml:id="echoid-s12690" xml:space="preserve">Cela fe fait en plaçant les pieces qu'on veut tourner ſur le <lb/>bois qui tient aux boëtes dont nous avons parlé ci-devant, & </s> <s xml:id="echoid-s12691" xml:space="preserve">qu'on <lb/>ajuſte ſur le Tour pour récevoir leſdites pieces.</s> <s xml:id="echoid-s12692" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12693" xml:space="preserve">Les appuis ou ſupports ſont auſſi diſpoſez ſuivant l'ouvrage <lb/> <pb o="388" file="404" n="404" rhead="DESCRIPTION"/> qu'on veut faire, les uns ſur le devant, & </s> <s xml:id="echoid-s12694" xml:space="preserve">les autres ſur le côté.</s> <s xml:id="echoid-s12695" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12696" xml:space="preserve">A l'égard des vis elles ſe forment en dedans comme en dehors de <lb/>l'ouvrage, en faiſait entrer le pas qu'on ſouhaite dans une piece de <lb/>bois tarodée du même pas, & </s> <s xml:id="echoid-s12697" xml:space="preserve">qu'on place à la poupée qui porte le <lb/>bout de l'arbre; </s> <s xml:id="echoid-s12698" xml:space="preserve">on ajuſte à cette poupée autant de pieces tarodées <lb/>qu'il y a de pas au bout dudit arbre. </s> <s xml:id="echoid-s12699" xml:space="preserve">L'autre bout de l'arbre où eſt <lb/>un colet d'une même groſleur, entre juſte dans le trou de la Lune-<lb/>te; </s> <s xml:id="echoid-s12700" xml:space="preserve">alors appuyant avec le pied ſur la marche, cela fait avancer ou <lb/>reculer l'ouvrage, de maniere que vous formez la vis ou l'écrou a-<lb/>vec des fers à pluſieurs dents que l'on fait expres, ſuivant les pas <lb/>marquez ſur vôtre arbre.</s> <s xml:id="echoid-s12701" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12702" xml:space="preserve">Pour les Outils à Tourner on ſe ſert pour le bois, de Gouges, <lb/>de Ciſeaux, de Becs-d'âne, &</s> <s xml:id="echoid-s12703" xml:space="preserve">c. </s> <s xml:id="echoid-s12704" xml:space="preserve">pour le cuivre ou autres métaux <lb/>on ſe ſert de plus petits Outils faits de bon acier trempé, comme <lb/>gros Burins pour dégroſſir l'ouvrage, des plates-bandes, d'autres <lb/>pour faire des groges rondes & </s> <s xml:id="echoid-s12705" xml:space="preserve">des Gorges quarrées, des Fers <lb/>crochus, des Outils dentelez par le bout, d'autres dentelez par le <lb/>Côté pour former les vis, &</s> <s xml:id="echoid-s12706" xml:space="preserve">c.</s> <s xml:id="echoid-s12707" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12708" xml:space="preserve">Voilà en partie les principaux Outils avec ceux dont j'ai parlé <lb/>dans le corps de l'ouvrage dont on ſe ſert plus communement. </s> <s xml:id="echoid-s12709" xml:space="preserve">On <lb/>pourra facillement ſuppléer aux autres, ſuivant le beſoin qu'on en <lb/>aura.</s> <s xml:id="echoid-s12710" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12711" xml:space="preserve">Comme la plûpart de ces Outils doivent être faits par ceux qui <lb/>s'en ſervent, je vais donner la maniere de bien choiſir le métal pro-<lb/>pre à leur conſtruction.</s> <s xml:id="echoid-s12712" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12713" xml:space="preserve">Le meilleur acier pour faire les Outils vient d'Allemagne. </s> <s xml:id="echoid-s12714" xml:space="preserve">Pour <lb/>être bon il doit être ſans pailles, veines noires, ni fourrures de fer; <lb/></s> <s xml:id="echoid-s12715" xml:space="preserve">ce qu'on pourra connoître en le caſſant, & </s> <s xml:id="echoid-s12716" xml:space="preserve">voyant ſi le grain eſt <lb/>bien fin & </s> <s xml:id="echoid-s12717" xml:space="preserve">bien égal.</s> <s xml:id="echoid-s12718" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12719" xml:space="preserve">Il faut prendre garde en forgeant les Outils ou autre choſe, de ne <lb/>pas brûler ni ſurchaufer l'acier, & </s> <s xml:id="echoid-s12720" xml:space="preserve">le forger avec le plus de promti-<lb/>tude qu'il ſera poſſible, car plus il eſt au ſeu, plus il ſe gâte.</s> <s xml:id="echoid-s12721" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12722" xml:space="preserve">Pour tremper les Outils, après qu'ils ont été forgez & </s> <s xml:id="echoid-s12723" xml:space="preserve">limez, on <lb/>les fait rougir dans le feu un peu plus que la couleur de ceriſe, après <lb/>quoi on les trempe dans de l'eau de fontaine ou de puits; </s> <s xml:id="echoid-s12724" xml:space="preserve">la plus <lb/>froide eſt la meilleure. </s> <s xml:id="echoid-s12725" xml:space="preserve">On ne retire l'Outil qu'aprés qu'il eſt froid, <lb/>& </s> <s xml:id="echoid-s12726" xml:space="preserve">on lui donne un peu de recuit, c'eſt-à-dire, qu'on le met auſſi-<lb/>tôt ſur une piece de fer chaud, juſques à ce que la blancheur qu'il a <lb/>contractée par la trempe, vienne à ſe perdre en devenant de cou. <lb/></s> <s xml:id="echoid-s12727" xml:space="preserve">leur jaunâtre, & </s> <s xml:id="echoid-s12728" xml:space="preserve">alors on rejette promtement l'Outil dans l'eau, <lb/> <pb o="389" file="405" n="405" rhead="DES PRINCIPAUX OUTILS."/> ſans attendre qu'il devienne bleu, parce qu'il perdroit ſa force.</s> <s xml:id="echoid-s12729" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12730" xml:space="preserve">Pour tremper les Limes en paquet & </s> <s xml:id="echoid-s12731" xml:space="preserve">autres pieces que l'on fait <lb/>de fer, on prend de la ſuie de cheminée, la plus dure & </s> <s xml:id="echoid-s12732" xml:space="preserve">la plus groſ-<lb/>ſe, qu'on met en poudre bien fine, & </s> <s xml:id="echoid-s12733" xml:space="preserve">qu'on fait tremper dans de l'u-<lb/>rine & </s> <s xml:id="echoid-s12734" xml:space="preserve">du vinaigre, y ajoûtant un peu de ſel fondu pour la rendre <lb/>comme une pâte liquide.</s> <s xml:id="echoid-s12735" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12736" xml:space="preserve">A près que l'on a détrempé la ſuie on en couvre les Outils, en <lb/>faiſant un paquet du tout, qu'on couvre enſuite de terre; </s> <s xml:id="echoid-s12737" xml:space="preserve">on met le <lb/>tout chaufer dans un feu ardent de charbon de bois, & </s> <s xml:id="echoid-s12738" xml:space="preserve">quand il <lb/>eſt un peu plus rouge que la couleur de ceriſe, on le jette dans <lb/>quelque vaiſſeau plein d'eau très-froide, & </s> <s xml:id="echoid-s12739" xml:space="preserve">l'ouvrage ſera ſuffiſam-<lb/>ment dur.</s> <s xml:id="echoid-s12740" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12741" xml:space="preserve">Nous avons parlé ci-devant de la maniere de ſouder le cuivre <lb/>ou l'argent l'un avec l'autre; </s> <s xml:id="echoid-s12742" xml:space="preserve">il eſt bon de ſçavoir que le fer ſe braſe <lb/>auſſi l'un avec l'autre; </s> <s xml:id="echoid-s12743" xml:space="preserve">en mettant du laiton mince ſur la piece qu'on <lb/>veut braſer, & </s> <s xml:id="echoid-s12744" xml:space="preserve">du borax en poudre, & </s> <s xml:id="echoid-s12745" xml:space="preserve">la couvrant de charbon de <lb/>tous côtez, que l'on chaufe juſques à ce que l'on voye fondre & </s> <s xml:id="echoid-s12746" xml:space="preserve"><lb/>couler le lation.</s> <s xml:id="echoid-s12747" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12748" xml:space="preserve">J'ai donné la maniere de faire la ſoudure d'argent, comme auſſi <lb/>celle de cuivre. </s> <s xml:id="echoid-s12749" xml:space="preserve">On en fait une avec de l'étain qu'on met en groſſe <lb/>limaille avec une râpe dans laquelle on y mêle une ſixiéme partie <lb/>de Sel armoniac, avec de l'huile d'olive. </s> <s xml:id="echoid-s12750" xml:space="preserve">Cette ſoudure eſt fort <lb/>coulante, & </s> <s xml:id="echoid-s12751" xml:space="preserve">eſt bonne pour les ouvrages qu'on ne veut pas trop <lb/>chaufer.</s> <s xml:id="echoid-s12752" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12753" xml:space="preserve">Il eſt bon d'avertir qu'on ne doit pas battre ni forger le laiton <lb/>jaune étant chaud, car il ſe caſſe. </s> <s xml:id="echoid-s12754" xml:space="preserve">A l'égard du cuivre rouge il ſe <lb/>bat à chaud & </s> <s xml:id="echoid-s12755" xml:space="preserve">à froid, mais on ne s'en ſert guéres dans la fabrique <lb/>des Inſtrumens de Mathématique, le cuivre jaune étant plus beau <lb/>& </s> <s xml:id="echoid-s12756" xml:space="preserve">plus propre pour ces ouvrages-là.</s> <s xml:id="echoid-s12757" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12758" xml:space="preserve">Le laiton ſe fait avec le cuivre rouge & </s> <s xml:id="echoid-s12759" xml:space="preserve">la calamine, que eſt une <lb/>pierre qui donne la teinture jaune au métal; </s> <s xml:id="echoid-s12760" xml:space="preserve">elle ſe trouve en Fran-<lb/>ce & </s> <s xml:id="echoid-s12761" xml:space="preserve">au Païs de Liége.</s> <s xml:id="echoid-s12762" xml:space="preserve"/> </p> <p> <s xml:id="echoid-s12763" xml:space="preserve">L'or & </s> <s xml:id="echoid-s12764" xml:space="preserve">l'argent ſe battent & </s> <s xml:id="echoid-s12765" xml:space="preserve">ſe forgent à chaud & </s> <s xml:id="echoid-s12766" xml:space="preserve">à froid. </s> <s xml:id="echoid-s12767" xml:space="preserve">Ils ſe <lb/>fondent auſſi à peu près comme le cuivre, mais pour dégraiſſer & </s> <s xml:id="echoid-s12768" xml:space="preserve"><lb/>ſéparer l'ordure de la limaille, & </s> <s xml:id="echoid-s12769" xml:space="preserve">on la met dans le creuſet avec en-<lb/>viron une dixiéme partie de ſalpêtre. </s> <s xml:id="echoid-s12770" xml:space="preserve">Les Inſtrumens de Mathé-<lb/>matique ſe travaillent avec l'or & </s> <s xml:id="echoid-s12771" xml:space="preserve">l'argent de la même maniere <lb/>qu'avec le laiton.</s> <s xml:id="echoid-s12772" xml:space="preserve"/> </p> </div> <div xml:id="echoid-div753" type="section" level="1" n="402"> <head xml:id="echoid-head544" xml:space="preserve">FIN.</head> <pb file="406" n="406"/> <figure> <image file="406-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/406-01"/> </figure> </div> <div xml:id="echoid-div754" type="section" level="1" n="403"> <head xml:id="echoid-head545" xml:space="preserve"><emph style="bf">TABLE</emph></head> <head xml:id="echoid-head546" xml:space="preserve"><emph style="bf">DES LIVRES, CHAPITRES ET SECTIONS</emph></head> <head xml:id="echoid-head547" xml:space="preserve">Contenus en ce Traité.</head> <note position="right" xml:space="preserve"> <lb/>DE finitions néceſſaires pour l'intelligence de ce Traité, # Page 1 <lb/> ## Des Inſtrumens les plus ordinaires. <lb/> ## <emph style="bf">LIVER PREMIER</emph>. <lb/>Chapitre I. DE la conſtruction & des uſages du Compas, de la Re- \\ gle, du Tire-ligne & du Porte-craïon, # 9 <lb/>Chap. II. De la conſtruction & uſage de l'equerre, # 24 <lb/>Chap. III. De la conſtruction & des uſages du Rapporteur, # 26 <lb/> ## Du Compas de Proportion. <lb/> ## <emph style="bf">LIVRE SECOND</emph>. <lb/>Chap. I. DE la conſtruction du Compas de Proportion, # 29 <lb/>Sect. I. De la Ligne des parties égales, # 30 <lb/>Section II. De la Ligne des Plans, # 31 <lb/>Section III. De la Ligne des Polygones, # 34 <lb/>Section IV. De la Ligne des Cordes, # 37 <lb/>Section V. Le la Ligne des Solides, # 38 <lb/>Section VI. De la Ligne des Métaux, # 40 <lb/>Section VII. Des preuves des diviſions des ſix Lignes, # 42 <lb/>Chap. II. Des uſages du Compas de Proportion, # 46 <lb/>Section I. Des uſages de la Ligne des parties égales, # ibid. <lb/>Section II. Des uſages de la Ligne des Plans, # 49 <lb/>Section III. Des uſages de la Ligne des Polygones, # 53 <lb/>Section IV. Des uſages de la Ligne des Cordes, # 54 <lb/>Section V. Des uſages de la Ligne des Solides, # 57 <lb/>Section VI. Contenant le conſtruction & l'uſage de pluſieurs autres \\ ſortes de fauges, # 64 <lb/>Section VII. Des uſages de la Ligne des Métaux, # 73 <lb/> ## De pluſieurs autres Inſtrumens curieux qui ſervent au Cabinet. <lb/> ## <emph style="bf">LIVRE TROISIE'ME</emph>. <lb/>Chap. I. DE la conſtruction & des uſages de pluſieurs differens \\ Compas, # 77 <lb/> <pb file="407" n="407" rhead="TABLE DES CHAPITRES"/> Chap. II. De la conſtruction & des uſages de pluſieurs differens Inſtru. \\ mens de Mathematique, # 86 <lb/> ## Des Inſtrumens qui ſervent à la Campagne. <lb/> ## <emph style="bf">LIVRE QUATRIE'ME</emph>. <lb/>Chap. I. COntenant la conſtruction & les uſages des Piquets, des \\ Cordeaux, de la Toiſe & de la Chaine, # 120 <lb/>Chap. II. Contenant la deſcription & l'uſage de l'equerre d'Arpen- \\ teur, # 133 <lb/>Chap. III. Contenant la conſtruction & uſages de differens recipian- \\ gles, # 136 <lb/>Chap. IV. Contenant la conſtruction & l'uſage de la Planchete, # 139 <lb/>Chap. V. Contenant la conſtruction & les uſages du Luart de Cercle \\ & du Luarré Géométrique, # 143 <lb/>Chap. VI. Contenant la conſtruction & les uſages du demi-cercle, # 157 <lb/>Chap. VII. Contenant la conſtruction & les uſages de la Bouſſole, # 165 <lb/>Chap. VIII. Uſages des ſuſdits Inſtrumens de Mathématique appli- \\ quez a la Fortification des Places, # 171 <lb/> ## De pluſieurs differentes Niveaux, comme auſſi des Inſtrumens \\ ſervans à l'Artillerie. <lb/> ## <emph style="bf">LIVRE CINQUIE'ME.</emph> <lb/>Chap. I. DE la conſtruction de pluſieurs Niveaux, # 185 <lb/>Chap. II. Des uſages des ſuſdits Inſtrumens pour niveler, # 192 <lb/>Chap. III. De la conſtruction & uſages de la fauge pour le partage \\ des eaux, # 299 <lb/>Chap. IV. Contenant la conſtruction & les uſages des Inſtrumens \\ ſervans à l'Artillerie, # 203 <lb/> ## Des Inſtrumens qui ſervent à l'Aſtronomie. <lb/> ## <emph style="bf">LIVRE SIXIE'ME</emph>. <lb/>Chap. I. DE la conſtruction & des uſages du Luart de Cercle \\ Aſtronomique, # 211 <lb/>Chap. II. De la conſtruction & uſage du Micrometre, # 226 <lb/>Chap. III. Maniere d'obſerver les Aſtres, # 235 <lb/>Chap. IV. De la conſtruction & uſage d'une Macbine qni montre les \\ eclipſes tant du Soleil que de la Lune, # 254 <lb/>Chap. V. Deſcription d'un Horloge à Pendule à Secondes & à Con- \\ tre-poids pour les Obſervations Aſtronomiques, # 262 <lb/> <pb file="408" n="408" rhead="TABLE DES CHAPITRES"/> ## Des Inſtrumens qui ſervent à la Navigation. <lb/> ## <emph style="bf">LIVRE SEPTIE'ME.</emph> <lb/>Chap. I. DE la conſtruction & des uſages de la Bouſſole Ma- \\ rine, # 267 <lb/>Chap. II. De la conſtruction & des uſages des Inſtrumens qui ſervent \\ à obſerver la hauteur des Aſtres en Mer, # 273 <lb/>Chap. III. Contenant la conſtruction du quartier de reduction & \\ ſes uſages, # 281 <lb/>Chap. IV. Contenant la conſtruction des Cartes réduites & leurs \\ uſages, # 286 <lb/> ## Des Cadrans au Soleil, à la Lune & aux Etoiles. <lb/> ## <emph style="bf">LIVRE HUITIE'ME.</emph> <lb/>Remarques & déſinitions appartenantes aux Cadrans, # 291 <lb/>Chap. I. DEs Cadrans tant reguliers qu'irreguliers, qui ſe tra- \\ cent ſur des Plans & ſur des Corps de differentes \\ figures, # 293 <lb/>Chap. II. Contenant la conſtruction & les uſages d'un Inſtrument pro- \\ pre à connoître la dêclinaiſon & inclinaiſon des Plans, # 324 <lb/>Chap. III. Contenant la conſtruction & les uſages des Inſtrumens \\ propres à marquer ſur les Cadrans les arcs des Signes, les arcs \\ Diurnes, les beures Babyloniques, les beures Italiques, les Al- \\ mucantarats & les Méridiens des principales Villes, # 327 <lb/>Chap. IV. Contenant la conſtruction & les uſages des Siaterres ou \\ Inſtrumens propres à tracer les Cadrans ſur les differens \\ Plans, # 340 <lb/>Chap. V. Coutenant la conſtruction & les uſages des Cadrans por- \\ tatiſs, # 347 <lb/>Chap. VI. Contenant la conſtruction & les uſages des Cadrans a la \\ Lune & aux etoiles, # 374 <lb/>Chap. VII. Contenant la conſtruction d'un Horloge a l'eau, # 379 <lb/>Chap. VIII. Contenant la conſtruction d'un Cadran pour connoître \\ le vent qui ſouffle, ſans ſortir de ſa Chambre, # 383 <lb/>Deſcription des principaux Outils dont on ſe ſert pour la conſtruction \\ des Inſtrumens de Mathematique, # 384 <lb/></note> <pb file="409" n="409"/> </div> <div xml:id="echoid-div755" type="section" level="1" n="404"> <head xml:id="echoid-head548" style="it" xml:space="preserve">Planche Premiere. Page 6.</head> <figure> <caption xml:id="echoid-caption9" xml:space="preserve">1</caption> </figure> <figure> <caption xml:id="echoid-caption10" xml:space="preserve">2</caption> </figure> <figure> <caption xml:id="echoid-caption11" xml:space="preserve">3</caption> </figure> <figure> <caption xml:id="echoid-caption12" xml:space="preserve">4</caption> </figure> <figure> <caption xml:id="echoid-caption13" xml:space="preserve">5</caption> </figure> <figure> <caption xml:id="echoid-caption14" xml:space="preserve">5</caption> </figure> <figure> <caption xml:id="echoid-caption15" xml:space="preserve">6</caption> </figure> <figure> <caption xml:id="echoid-caption16" xml:space="preserve">7</caption> </figure> <figure> <caption xml:id="echoid-caption17" xml:space="preserve">8</caption> </figure> <figure> <caption xml:id="echoid-caption18" xml:space="preserve">9</caption> <variables xml:id="echoid-variables7" xml:space="preserve">A B C D</variables> </figure> <figure> <caption xml:id="echoid-caption19" xml:space="preserve">10</caption> </figure> <figure> <caption xml:id="echoid-caption20" xml:space="preserve">11</caption> <variables xml:id="echoid-variables8" xml:space="preserve">F D E M P N O F</variables> </figure> <figure> <caption xml:id="echoid-caption21" xml:space="preserve">12</caption> </figure> <figure> <caption xml:id="echoid-caption22" xml:space="preserve">13</caption> </figure> <figure> <caption xml:id="echoid-caption23" xml:space="preserve">14</caption> </figure> <figure> <caption xml:id="echoid-caption24" xml:space="preserve">14</caption> </figure> <figure> <caption xml:id="echoid-caption25" xml:space="preserve">15</caption> <variables xml:id="echoid-variables9" xml:space="preserve">G E D H A B I C F</variables> </figure> <figure> <caption xml:id="echoid-caption26" xml:space="preserve">16</caption> </figure> <figure> <caption xml:id="echoid-caption27" xml:space="preserve">17</caption> </figure> <figure> <caption xml:id="echoid-caption28" xml:space="preserve">18</caption> </figure> <figure> <caption xml:id="echoid-caption29" xml:space="preserve">19</caption> </figure> <figure> <caption xml:id="echoid-caption30" xml:space="preserve">20</caption> </figure> <figure> <caption xml:id="echoid-caption31" xml:space="preserve">21</caption> </figure> <figure> <caption xml:id="echoid-caption32" xml:space="preserve">22</caption> </figure> <figure> <caption xml:id="echoid-caption33" xml:space="preserve">23</caption> </figure> <figure> <caption xml:id="echoid-caption34" xml:space="preserve">24</caption> </figure> <figure> <caption xml:id="echoid-caption35" xml:space="preserve">25</caption> </figure> <figure> <caption xml:id="echoid-caption36" xml:space="preserve">26</caption> </figure> <figure> <caption xml:id="echoid-caption37" xml:space="preserve">27</caption> </figure> <figure> <caption xml:id="echoid-caption38" xml:space="preserve">28</caption> </figure> <figure> <caption xml:id="echoid-caption39" xml:space="preserve">29</caption> </figure> <figure> <caption xml:id="echoid-caption40" xml:space="preserve">30</caption> </figure> <figure> <caption xml:id="echoid-caption41" xml:space="preserve">31</caption> </figure> <figure> <caption xml:id="echoid-caption42" xml:space="preserve">32</caption> <variables xml:id="echoid-variables10" xml:space="preserve">A B</variables> </figure> <pb file="410" n="410"/> </div> <div xml:id="echoid-div756" type="section" level="1" n="405"> <head xml:id="echoid-head549" style="it" xml:space="preserve">Planche Deuxieme. Page 8.</head> <figure> <caption xml:id="echoid-caption43" xml:space="preserve">1</caption> </figure> <figure> <caption xml:id="echoid-caption44" xml:space="preserve">2</caption> </figure> <figure> <caption xml:id="echoid-caption45" xml:space="preserve">3</caption> </figure> <figure> <caption xml:id="echoid-caption46" xml:space="preserve">4</caption> </figure> <figure> <caption xml:id="echoid-caption47" xml:space="preserve">5</caption> </figure> <figure> <caption xml:id="echoid-caption48" xml:space="preserve">6</caption> </figure> <figure> <caption xml:id="echoid-caption49" xml:space="preserve">7</caption> </figure> <figure> <caption xml:id="echoid-caption50" xml:space="preserve">8</caption> </figure> <figure> <caption xml:id="echoid-caption51" xml:space="preserve">9</caption> </figure> <figure> <caption xml:id="echoid-caption52" xml:space="preserve">10</caption> <variables xml:id="echoid-variables11" xml:space="preserve">C B D A</variables> </figure> <figure> <caption xml:id="echoid-caption53" xml:space="preserve">10</caption> <variables xml:id="echoid-variables12" xml:space="preserve">c b d a</variables> </figure> <figure> <caption xml:id="echoid-caption54" xml:space="preserve">11</caption> <variables xml:id="echoid-variables13" xml:space="preserve">B A C</variables> </figure> <figure> <caption xml:id="echoid-caption55" xml:space="preserve">11</caption> <variables xml:id="echoid-variables14" xml:space="preserve">B C A D</variables> </figure> <figure> <caption xml:id="echoid-caption56" xml:space="preserve">12</caption> </figure> <figure> <caption xml:id="echoid-caption57" xml:space="preserve">13</caption> </figure> <figure> <caption xml:id="echoid-caption58" xml:space="preserve">14</caption> </figure> <figure> <caption xml:id="echoid-caption59" xml:space="preserve">15</caption> </figure> <figure> <caption xml:id="echoid-caption60" xml:space="preserve">16</caption> </figure> <figure> <caption xml:id="echoid-caption61" xml:space="preserve">17</caption> </figure> <figure> <caption xml:id="echoid-caption62" xml:space="preserve">18</caption> </figure> <figure> <caption xml:id="echoid-caption63" xml:space="preserve">19</caption> </figure> <figure> <caption xml:id="echoid-caption64" xml:space="preserve">19</caption> </figure> <figure> <caption xml:id="echoid-caption65" xml:space="preserve">20</caption> </figure> <figure> <caption xml:id="echoid-caption66" xml:space="preserve">20</caption> </figure> <figure> <caption xml:id="echoid-caption67" xml:space="preserve">21</caption> </figure> <figure> <caption xml:id="echoid-caption68" xml:space="preserve">21</caption> </figure> <figure> <caption xml:id="echoid-caption69" xml:space="preserve">21</caption> </figure> <figure> <caption xml:id="echoid-caption70" xml:space="preserve">22</caption> </figure> <figure> <caption xml:id="echoid-caption71" xml:space="preserve">22</caption> </figure> <figure> <caption xml:id="echoid-caption72" xml:space="preserve">22</caption> </figure> <figure> <caption xml:id="echoid-caption73" xml:space="preserve">23</caption> </figure> <figure> <caption xml:id="echoid-caption74" xml:space="preserve">23</caption> </figure> <pb file="411" n="411"/> </div> <div xml:id="echoid-div757" type="section" level="1" n="406"> <head xml:id="echoid-head550" style="it" xml:space="preserve">Planche Troisieme. Page 14.</head> <figure> <caption xml:id="echoid-caption75" xml:space="preserve">A</caption> </figure> <figure> <caption xml:id="echoid-caption76" xml:space="preserve">A</caption> </figure> <figure> <caption xml:id="echoid-caption77" xml:space="preserve">A</caption> </figure> <figure> <caption xml:id="echoid-caption78" xml:space="preserve">B</caption> <description xml:id="echoid-description8" style="it" xml:space="preserve">Demy</description> <description xml:id="echoid-description9" style="it" xml:space="preserve">Pied</description> <description xml:id="echoid-description10" style="it" xml:space="preserve">du</description> <description xml:id="echoid-description11" style="it" xml:space="preserve">Roy</description> <variables xml:id="echoid-variables15" xml:space="preserve">1 2 3 4 5 6</variables> </figure> <figure> <caption xml:id="echoid-caption79" xml:space="preserve">C</caption> </figure> <figure> <caption xml:id="echoid-caption80" xml:space="preserve">D</caption> <description xml:id="echoid-description12" style="it" xml:space="preserve">Demy</description> <description xml:id="echoid-description13" style="it" xml:space="preserve">Pied</description> <description xml:id="echoid-description14" style="it" xml:space="preserve">du</description> <description xml:id="echoid-description15" style="it" xml:space="preserve">Polm</description> <description xml:id="echoid-description16" style="it" xml:space="preserve">Rhin</description> <description xml:id="echoid-description17" style="it" xml:space="preserve">Echelle</description> <variables xml:id="echoid-variables16" xml:space="preserve">10 20 30 40 50 60</variables> </figure> <figure> <caption xml:id="echoid-caption81" xml:space="preserve">E</caption> <description xml:id="echoid-description18" style="it" xml:space="preserve">N. Bion A Paris.</description> <variables xml:id="echoid-variables17" xml:space="preserve">B E C G D F A O 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10</variables> </figure> <figure> <caption xml:id="echoid-caption82" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables18" xml:space="preserve">D H F A B C G E</variables> </figure> <figure> <caption xml:id="echoid-caption83" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables19" xml:space="preserve">G H E D F A C B</variables> </figure> <figure> <caption xml:id="echoid-caption84" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables20" xml:space="preserve">F E H D G C B</variables> </figure> <figure> <caption xml:id="echoid-caption85" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables21" xml:space="preserve">F D C B</variables> </figure> <figure> <caption xml:id="echoid-caption86" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables22" xml:space="preserve">D P C A B</variables> </figure> <figure> <caption xml:id="echoid-caption87" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables23" xml:space="preserve">C A D G E B</variables> </figure> <figure> <caption xml:id="echoid-caption88" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables24" xml:space="preserve">C A 2 1 B D</variables> </figure> <figure> <caption xml:id="echoid-caption89" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables25" xml:space="preserve">A D G C F E B</variables> </figure> <figure> <caption xml:id="echoid-caption90" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables26" xml:space="preserve">F C A B</variables> </figure> <figure> <caption xml:id="echoid-caption91" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables27" xml:space="preserve">E F G</variables> </figure> <figure> <caption xml:id="echoid-caption92" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables28" xml:space="preserve">C D A B</variables> </figure> <figure> <caption xml:id="echoid-caption93" style="it" xml:space="preserve">Fig. 11.</caption> <variables xml:id="echoid-variables29" xml:space="preserve">C D A B</variables> </figure> <figure> <caption xml:id="echoid-caption94" style="it" xml:space="preserve">Fig. 12.</caption> <variables xml:id="echoid-variables30" xml:space="preserve">C D A B</variables> </figure> <pb file="412" n="412"/> </div> <div xml:id="echoid-div758" type="section" level="1" n="407"> <head xml:id="echoid-head551" style="it" xml:space="preserve">Planche Luatrieme. Page 18</head> <figure> <caption xml:id="echoid-caption95" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables31" xml:space="preserve">C A B D</variables> </figure> <figure> <caption xml:id="echoid-caption96" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables32" xml:space="preserve">C A B a b</variables> </figure> <figure> <caption xml:id="echoid-caption97" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables33" xml:space="preserve">10 9 8 7 6 5 4 3 2 1<lb/> 10. 20. 30. 40. 50. 60. 70. 80.<lb/> D E F G H C Y Z A B</variables> </figure> <figure> <caption xml:id="echoid-caption98" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables34" xml:space="preserve">10 9 8 7 6 5 4 3 2 1<lb/> 100 90 80 70 60 50 40 30 20 10<lb/> 10 20 30 40 50 60 70 80 90 100<lb/> 5 5 5 5 5<lb/> 200. 300. 400. 500. 600. 700. 800. 900. 1000.<lb/> B F C A E D</variables> </figure> <figure> <caption xml:id="echoid-caption99" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables35" xml:space="preserve">C 4 3 2 1 A D B</variables> </figure> <figure> <caption xml:id="echoid-caption100" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables36" xml:space="preserve">F E K G A D I H B C</variables> </figure> <figure> <caption xml:id="echoid-caption101" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables37" xml:space="preserve">A D E B</variables> </figure> <figure> <caption xml:id="echoid-caption102" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables38" xml:space="preserve">A B</variables> </figure> <figure> <caption xml:id="echoid-caption103" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables39" xml:space="preserve">A D E F C B</variables> </figure> <figure> <caption xml:id="echoid-caption104" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables40" xml:space="preserve">C A B</variables> </figure> <figure> <caption xml:id="echoid-caption105" style="it" xml:space="preserve">Fig. 11.</caption> <variables xml:id="echoid-variables41" xml:space="preserve">C A B</variables> </figure> <figure> <caption xml:id="echoid-caption106" style="it" xml:space="preserve">Fig. 12.</caption> <variables xml:id="echoid-variables42" xml:space="preserve">C A B</variables> </figure> <figure> <caption xml:id="echoid-caption107" style="it" xml:space="preserve">Fig. 13.</caption> <variables xml:id="echoid-variables43" xml:space="preserve">F D E</variables> </figure> <figure> <caption xml:id="echoid-caption108" style="it" xml:space="preserve">Fig. 14.</caption> <variables xml:id="echoid-variables44" xml:space="preserve">C A B</variables> </figure> <figure> <caption xml:id="echoid-caption109" style="it" xml:space="preserve">Fig. 15.</caption> <variables xml:id="echoid-variables45" xml:space="preserve">G H I</variables> </figure> <figure> <caption xml:id="echoid-caption110" style="it" xml:space="preserve">Fig. 16.</caption> <variables xml:id="echoid-variables46" xml:space="preserve">F D E</variables> </figure> <figure> <caption xml:id="echoid-caption111" style="it" xml:space="preserve">Fig. 17.</caption> <variables xml:id="echoid-variables47" xml:space="preserve">D E C F F A B</variables> </figure> <figure> <caption xml:id="echoid-caption112" style="it" xml:space="preserve">Fig. 18.</caption> <variables xml:id="echoid-variables48" xml:space="preserve">D E A B</variables> </figure> <figure> <caption xml:id="echoid-caption113" style="it" xml:space="preserve">Fig. 19.</caption> <variables xml:id="echoid-variables49" xml:space="preserve">C A E B D</variables> </figure> <pb file="413" n="413"/> </div> <div xml:id="echoid-div759" type="section" level="1" n="408"> <head xml:id="echoid-head552" style="it" xml:space="preserve">Planche Cinquieme. Page 28.</head> <figure> <caption xml:id="echoid-caption114" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables50" xml:space="preserve">C A 1 2 3 4 5 B D</variables> </figure> <figure> <caption xml:id="echoid-caption115" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables51" xml:space="preserve">D F B A C H G E</variables> </figure> <figure> <caption xml:id="echoid-caption116" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables52" xml:space="preserve">D E G F A B C</variables> </figure> <figure> <caption xml:id="echoid-caption117" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables53" xml:space="preserve">D A C B</variables> </figure> <figure> <caption xml:id="echoid-caption118" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables54" xml:space="preserve">E K G A C D B F I H</variables> </figure> <figure> <caption xml:id="echoid-caption119" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables55" xml:space="preserve">D A E G F B C</variables> </figure> <figure> <caption xml:id="echoid-caption120" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables56" xml:space="preserve">O P T H C H P I L A F G E B P H D H P</variables> </figure> <figure> <caption xml:id="echoid-caption121" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables57" xml:space="preserve">D E C A B</variables> </figure> <figure> <caption xml:id="echoid-caption122" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables58" xml:space="preserve">d e c a b</variables> </figure> <figure> <caption xml:id="echoid-caption123" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables59" xml:space="preserve">D d E e F c C a b A B</variables> </figure> <figure> <caption xml:id="echoid-caption124" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables60" xml:space="preserve">D E C A B</variables> </figure> <figure> <caption xml:id="echoid-caption125" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables61" xml:space="preserve">d e c a b<lb/> 20 40 60 80 100<lb/> 10 30 50 70 90<lb/> K L<lb/> 20 40 60 80 100<lb/> 10 30 50 70 90<lb/> G H</variables> </figure> <figure> <caption xml:id="echoid-caption126" style="it" xml:space="preserve">Fig. 11.</caption> <variables xml:id="echoid-variables62" xml:space="preserve">D E C A B</variables> </figure> <figure> <caption xml:id="echoid-caption127" style="it" xml:space="preserve">Fig. 11.</caption> <variables xml:id="echoid-variables63" xml:space="preserve">I N L G K M H</variables> </figure> <figure> <caption xml:id="echoid-caption128" style="it" xml:space="preserve">Fig. 11.</caption> <variables xml:id="echoid-variables64" xml:space="preserve">d e c a b</variables> </figure> <figure> <caption xml:id="echoid-caption129" style="it" xml:space="preserve">Fig. 12.</caption> <variables xml:id="echoid-variables65" xml:space="preserve">D C A B<lb/> d c a b</variables> </figure> <figure> <caption xml:id="echoid-caption130" style="it" xml:space="preserve">Fig. 13.</caption> <variables xml:id="echoid-variables66" xml:space="preserve">C A D B</variables> </figure> <figure> <caption xml:id="echoid-caption131" style="it" xml:space="preserve">Fig. 14.</caption> <variables xml:id="echoid-variables67" xml:space="preserve">50<lb/> D C A B</variables> </figure> <figure> <caption xml:id="echoid-caption132" style="it" xml:space="preserve">Fig. 15.</caption> <variables xml:id="echoid-variables68" xml:space="preserve">C 7 2 B</variables> </figure> <figure> <caption xml:id="echoid-caption133" style="it" xml:space="preserve">Fig. 16.</caption> <variables xml:id="echoid-variables69" xml:space="preserve">54 54<lb/> F C D</variables> </figure> <pb file="414" n="414"/> </div> <div xml:id="echoid-div760" type="section" level="1" n="409"> <head xml:id="echoid-head553" style="it" xml:space="preserve">Planche Seizieme. Page 210.</head> <figure> <caption xml:id="echoid-caption134" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables70" xml:space="preserve">45 58 32 22 67<lb/> 10 20 30 40 50 60 70 80 90</variables> </figure> <figure> <caption xml:id="echoid-caption135" xml:space="preserve">A</caption> <description xml:id="echoid-description19" style="it" xml:space="preserve">Pouces Du Pied du Roy</description> <description xml:id="echoid-description20" style="it" xml:space="preserve">Poids des Boulets</description> <variables xml:id="echoid-variables71" xml:space="preserve">1 2 3 4<lb/> 48 40 36 30 24 20 16 10 8 6 4 2 1 {1/2} {1/4}</variables> </figure> <figure> <caption xml:id="echoid-caption136" xml:space="preserve">B</caption> <description xml:id="echoid-description21" style="it" xml:space="preserve">lignes. Pouces.</description> <description xml:id="echoid-description22" style="it" xml:space="preserve">Calibre des pieces</description> <description xml:id="echoid-description23" style="it" xml:space="preserve">Poids des Boulets de Fer</description> <variables xml:id="echoid-variables72" xml:space="preserve">48 40 36 30 24 20 16 12 8 6 4 3 2 1 {1/2} {1/4} 10 20 30 40 50 60 70 80 90</variables> </figure> <figure> <caption xml:id="echoid-caption137" xml:space="preserve">C</caption> </figure> <figure> <caption xml:id="echoid-caption138" xml:space="preserve">D</caption> <variables xml:id="echoid-variables73" xml:space="preserve">45 35 25 15 40 30 20 10</variables> </figure> <figure> <caption xml:id="echoid-caption139" xml:space="preserve">E</caption> <variables xml:id="echoid-variables74" xml:space="preserve">6 4 2 1 {1/2} {1/4}<lb/> 55 50 45 40 35 30 25 20 15 10 8<lb/> 45 45</variables> </figure> <figure> </figure> <figure> <caption xml:id="echoid-caption140" xml:space="preserve">F</caption> <variables xml:id="echoid-variables75" xml:space="preserve">40 30 20 10 5 45 35 25 15</variables> </figure> <figure> <caption xml:id="echoid-caption141" xml:space="preserve">G</caption> </figure> <figure> <caption xml:id="echoid-caption142" xml:space="preserve">H</caption> <variables xml:id="echoid-variables76" xml:space="preserve">f b g c e H a c</variables> </figure> <pb file="415" n="415"/> </div> <div xml:id="echoid-div761" type="section" level="1" n="410"> <head xml:id="echoid-head554" style="it" xml:space="preserve">Planche Septieme. Page 76.</head> <figure> <caption xml:id="echoid-caption143" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables77" xml:space="preserve">A 1 2 3 4 5 6 7 B</variables> </figure> <figure> <caption xml:id="echoid-caption144" style="it" xml:space="preserve">Fig. 2.</caption> <description xml:id="echoid-description24" style="it" xml:space="preserve">Parties</description> <description xml:id="echoid-description25" style="it" xml:space="preserve">Egalles</description> <variables xml:id="echoid-variables78" xml:space="preserve">20 40 60 80 100 120 140 160 180 200<lb/> 20 40 60 80 100 120 140 160 180 200</variables> </figure> <figure> <caption xml:id="echoid-caption145" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables79" xml:space="preserve">A B C D<lb/> 40 20 10</variables> </figure> <figure> <caption xml:id="echoid-caption146" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables80" xml:space="preserve">B A C</variables> </figure> <figure> <caption xml:id="echoid-caption147" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables81" xml:space="preserve">B A C</variables> </figure> <figure> <caption xml:id="echoid-caption148" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description26" style="it" xml:space="preserve">Surface 20. Toiſes</description> <description xml:id="echoid-description27" style="it" xml:space="preserve">Surface 30 Toiſes</description> <variables xml:id="echoid-variables82" xml:space="preserve">a b A B</variables> </figure> <figure> <caption xml:id="echoid-caption149" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables83" xml:space="preserve">C A B</variables> </figure> <figure> <caption xml:id="echoid-caption150" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables84" xml:space="preserve">D E F</variables> </figure> <figure> <caption xml:id="echoid-caption151" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables85" xml:space="preserve">36 72 72<lb/> D F</variables> </figure> <figure> <caption xml:id="echoid-caption152" style="it" xml:space="preserve">Fig. 9.</caption> <description xml:id="echoid-description28" style="it" xml:space="preserve">Cordes</description> <description xml:id="echoid-description29" style="it" xml:space="preserve">Cordes</description> <variables xml:id="echoid-variables86" xml:space="preserve">10 20 30 40 50 60 70 80 90 100 120 150 180<lb/> 10 20 30 40 50 60 70 80 90 100 120 150 180</variables> </figure> <figure> <caption xml:id="echoid-caption153" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables87" xml:space="preserve">40<lb/> B D C A</variables> </figure> <figure> <caption xml:id="echoid-caption154" style="it" xml:space="preserve">Fig. 11</caption> <variables xml:id="echoid-variables88" xml:space="preserve">D F G</variables> </figure> <figure> <caption xml:id="echoid-caption155" style="it" xml:space="preserve">Fig. 12.</caption> </figure> <figure> <caption xml:id="echoid-caption156" style="it" xml:space="preserve">Fig. 13.</caption> <variables xml:id="echoid-variables89" xml:space="preserve">C A D B</variables> </figure> <figure> <caption xml:id="echoid-caption157" style="it" xml:space="preserve">Fig. 15.</caption> <description xml:id="echoid-description30" style="it" xml:space="preserve">3.p.u.l.{1/3}</description> <description xml:id="echoid-description31" style="it" xml:space="preserve">Pour' les Diametres</description> <variables xml:id="echoid-variables90" xml:space="preserve">C A B 1 2 3 4 5 6 7 8 9 10 D</variables> </figure> <figure> <caption xml:id="echoid-caption158" style="it" xml:space="preserve">Fig. 14.</caption> <description xml:id="echoid-description32" style="it" xml:space="preserve">Partie Egalles.</description> <variables xml:id="echoid-variables91" xml:space="preserve">1 2 3</variables> </figure> <figure> <caption xml:id="echoid-caption159" style="it" xml:space="preserve">Fig. 16.</caption> <description xml:id="echoid-description33" style="it" xml:space="preserve">3.p.3.p.6.l.</description> <variables xml:id="echoid-variables92" xml:space="preserve">5 10 15 20 25 30 35 40</variables> </figure> <figure> <caption xml:id="echoid-caption160" style="it" xml:space="preserve">Fig. 17.</caption> <description xml:id="echoid-description34" style="it" xml:space="preserve">Diametres</description> <description xml:id="echoid-description35" style="it" xml:space="preserve">Iongeur's</description> <description xml:id="echoid-description36" style="it" xml:space="preserve">3.p.11.l {1/3}</description> <description xml:id="echoid-description37" style="it" xml:space="preserve">Contenu</description> <description xml:id="echoid-description38" style="it" xml:space="preserve">Pintes</description> <description xml:id="echoid-description39" style="it" xml:space="preserve">Jauge de NT: Sauveur.</description> <variables xml:id="echoid-variables93" xml:space="preserve">1.2.3.4. 1 2 3 4</variables> </figure> <figure> <caption xml:id="echoid-caption161" style="it" xml:space="preserve">Fig. 18.</caption> <description xml:id="echoid-description40" style="it" xml:space="preserve">Fer</description> <description xml:id="echoid-description41" style="it" xml:space="preserve">Plom</description> <variables xml:id="echoid-variables94" xml:space="preserve">C D<lb/> A B</variables> </figure> <figure> <caption xml:id="echoid-caption162" style="it" xml:space="preserve">Fig. 19.</caption> <variables xml:id="echoid-variables95" xml:space="preserve">E F G H K L</variables> </figure> <figure> <caption xml:id="echoid-caption163" style="it" xml:space="preserve">Fig. 20.</caption> <variables xml:id="echoid-variables96" xml:space="preserve">10. £<lb/> 10. £<lb/> 15. £<lb/> M N O P Q R</variables> </figure> <pb file="416" n="416"/> </div> <div xml:id="echoid-div762" type="section" level="1" n="411"> <head xml:id="echoid-head555" style="it" xml:space="preserve">Planche Huitieme. Page 86.</head> <figure> <caption xml:id="echoid-caption164" xml:space="preserve">A</caption> <variables xml:id="echoid-variables97" xml:space="preserve">1</variables> </figure> <figure> <caption xml:id="echoid-caption165" xml:space="preserve">B</caption> <variables xml:id="echoid-variables98" xml:space="preserve">2</variables> </figure> <figure> <caption xml:id="echoid-caption166" xml:space="preserve">C</caption> <variables xml:id="echoid-variables99" xml:space="preserve">3</variables> </figure> <figure> <caption xml:id="echoid-caption167" xml:space="preserve">D</caption> <variables xml:id="echoid-variables100" xml:space="preserve">1 2</variables> </figure> <figure> <caption xml:id="echoid-caption168" xml:space="preserve">E</caption> <variables xml:id="echoid-variables101" xml:space="preserve">1</variables> </figure> <figure> <caption xml:id="echoid-caption169" xml:space="preserve">F</caption> </figure> <figure> <caption xml:id="echoid-caption170" xml:space="preserve">G</caption> <variables xml:id="echoid-variables102" xml:space="preserve">3 4 5</variables> </figure> <figure> <caption xml:id="echoid-caption171" xml:space="preserve">H</caption> <description xml:id="echoid-description42" style="it" xml:space="preserve">Poligones</description> <variables xml:id="echoid-variables103" xml:space="preserve">3 2 1 4 5 6 7 8</variables> </figure> <figure> <caption xml:id="echoid-caption172" xml:space="preserve">I</caption> <description xml:id="echoid-description43" style="it" xml:space="preserve">Egalles</description> <variables xml:id="echoid-variables104" xml:space="preserve">2 3 4 5 6 7 8</variables> </figure> <figure> <caption xml:id="echoid-caption173" xml:space="preserve">K</caption> </figure> <figure> <caption xml:id="echoid-caption174" xml:space="preserve">L</caption> <variables xml:id="echoid-variables105" xml:space="preserve">1</variables> </figure> <figure> <caption xml:id="echoid-caption175" xml:space="preserve">M</caption> </figure> <figure> <caption xml:id="echoid-caption176" xml:space="preserve">N</caption> </figure> <figure> <caption xml:id="echoid-caption177" xml:space="preserve">O</caption> </figure> <pb file="417" n="417"/> </div> <div xml:id="echoid-div763" type="section" level="1" n="412"> <head xml:id="echoid-head556" style="it" xml:space="preserve">Planche Neuvieme. Page 96.</head> <figure> <caption xml:id="echoid-caption178" xml:space="preserve">I</caption> </figure> <figure> <caption xml:id="echoid-caption179" xml:space="preserve">M</caption> <description xml:id="echoid-description44" style="it" xml:space="preserve">{1/2} Grains</description> <variables xml:id="echoid-variables106" xml:space="preserve">5 4 3 2 1</variables> </figure> <figure> <caption xml:id="echoid-caption180" xml:space="preserve">H</caption> </figure> <figure> <caption xml:id="echoid-caption181" xml:space="preserve">G</caption> </figure> <figure> <caption xml:id="echoid-caption182" xml:space="preserve">F</caption> </figure> <figure> <variables xml:id="echoid-variables107" xml:space="preserve">1</variables> </figure> <figure> <caption xml:id="echoid-caption183" xml:space="preserve">E</caption> </figure> <figure> <caption xml:id="echoid-caption184" xml:space="preserve">D</caption> <variables xml:id="echoid-variables108" xml:space="preserve">1</variables> </figure> <figure> <caption xml:id="echoid-caption185" xml:space="preserve">C</caption> </figure> <figure> <caption xml:id="echoid-caption186" xml:space="preserve">B</caption> </figure> <figure> <caption xml:id="echoid-caption187" xml:space="preserve">A</caption> <description xml:id="echoid-description45" style="it" xml:space="preserve">Poligoner</description> <description xml:id="echoid-description46" style="it" xml:space="preserve">Cordes</description> <variables xml:id="echoid-variables109" xml:space="preserve">12 11 10 9 8 7 6 5 4 3<lb/> 10 20 30 40 50 60 70 80 90</variables> </figure> <figure> <caption xml:id="echoid-caption188" xml:space="preserve">L</caption> </figure> <figure> <caption xml:id="echoid-caption189" xml:space="preserve">N</caption> </figure> <figure> <caption xml:id="echoid-caption190" xml:space="preserve">O</caption> <variables xml:id="echoid-variables110" xml:space="preserve">1 2 3 4 5 6 7 8 9 10 11 12</variables> </figure> <figure> <caption xml:id="echoid-caption191" xml:space="preserve">K</caption> <variables xml:id="echoid-variables111" xml:space="preserve">1 1 2 2 2 5 3 5 3 4 4</variables> </figure> <figure> <caption xml:id="echoid-caption192" xml:space="preserve">P</caption> <description xml:id="echoid-description47" style="it" xml:space="preserve">Londres</description> <description xml:id="echoid-description48" style="it" xml:space="preserve">Rhein</description> <description xml:id="echoid-description49" style="it" xml:space="preserve">Paris</description> <variables xml:id="echoid-variables112" xml:space="preserve">1 2 4 5 6 7 8 9 10 11 12<lb/> 1 2 4 5 6 7 8 9 10 11 12<lb/> 1 2 4 5 6 7 8 9 10 11 12</variables> </figure> <figure> <caption xml:id="echoid-caption193" xml:space="preserve">R</caption> </figure> <figure> <caption xml:id="echoid-caption194" xml:space="preserve">Q</caption> </figure> <figure> <caption xml:id="echoid-caption195" xml:space="preserve">V</caption> <variables xml:id="echoid-variables113" xml:space="preserve">100 101</variables> </figure> <figure> <caption xml:id="echoid-caption196" xml:space="preserve">T</caption> <variables xml:id="echoid-variables114" xml:space="preserve">1 2 3 4 5</variables> </figure> <figure> <caption xml:id="echoid-caption197" xml:space="preserve">S</caption> <variables xml:id="echoid-variables115" xml:space="preserve">10 20 30 40 50 60 70 80 90 100<lb/> 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000</variables> </figure> <pb file="418" n="418"/> </div> <div xml:id="echoid-div764" type="section" level="1" n="413"> <head xml:id="echoid-head557" style="it" xml:space="preserve">Planche Dixieme. Page 118.</head> <figure> <caption xml:id="echoid-caption198" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables116" xml:space="preserve">A 5 2 1 6 3 4 35 59 60 72 81 90 102 108 120</variables> </figure> <figure> <caption xml:id="echoid-caption199" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables117" xml:space="preserve">7 1 7 2 2 9 9</variables> </figure> <figure> <caption xml:id="echoid-caption200" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables118" xml:space="preserve">1 6 4 3 2 5</variables> </figure> <figure> <caption xml:id="echoid-caption201" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables119" xml:space="preserve">3 4</variables> </figure> <figure> <caption xml:id="echoid-caption202" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description50" style="it" xml:space="preserve">Nord</description> <description xml:id="echoid-description51" style="it" xml:space="preserve">Sud</description> <variables xml:id="echoid-variables120" xml:space="preserve">8<lb/> 6 B 6 a b 1 5 1<lb/> 6 4 6 C 1 1 5 5 2 3<lb/> F 1 2 1 4<lb/> 5 6 1 D 2 3 4<lb/> E 5 1 2 4 3<lb/> 30 20 20 15 10 5 5 10 15 25 30<lb/> BB 4 2 5 6<lb/> 3 3 3 3<lb/> 2 2 8 6 1 G 4 1 12 3 3 9 2 2 7 5 1 1<lb/> H 10 11<lb/> 1 3 4 2 L 5<lb/> 2 4 5 1 6 I 2 3<lb/> 3 K 1 2<lb/> 3 2 4 M 5 9 6 7 1 10 8</variables> </figure> <pb file="419" n="419"/> </div> <div xml:id="echoid-div765" type="section" level="1" n="414"> <head xml:id="echoid-head558" style="it" xml:space="preserve">Planche Onzieme. Page 132.</head> <figure> <variables xml:id="echoid-variables121" xml:space="preserve">A A B B C D E E E E<lb/> 1 2 Pied 3 4 5 6</variables> </figure> <figure> <caption xml:id="echoid-caption203" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables122" xml:space="preserve">F A E C D B</variables> </figure> <figure> <caption xml:id="echoid-caption204" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables123" xml:space="preserve">H A C G B</variables> </figure> <figure> <caption xml:id="echoid-caption205" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables124" xml:space="preserve">F A C B</variables> </figure> <figure> <caption xml:id="echoid-caption206" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables125" xml:space="preserve">C D A B</variables> </figure> <figure> <caption xml:id="echoid-caption207" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables126" xml:space="preserve">30. 36. 30.<lb/> A B C</variables> </figure> <figure> <caption xml:id="echoid-caption208" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables127" xml:space="preserve">30. 36. 30.<lb/> F B D C</variables> </figure> <figure> <caption xml:id="echoid-caption209" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables128" xml:space="preserve">A B E C D</variables> </figure> <figure> <caption xml:id="echoid-caption210" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables129" xml:space="preserve">E L K F M I H G N</variables> </figure> <figure> <caption xml:id="echoid-caption211" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables130" xml:space="preserve">E C A D B</variables> </figure> <figure> <caption xml:id="echoid-caption212" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables131" xml:space="preserve">C D A B</variables> </figure> <figure> <caption xml:id="echoid-caption213" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables132" xml:space="preserve">H G D E A C B<lb/> 4 8 P 6. p</variables> </figure> <figure> <caption xml:id="echoid-caption214" style="it" xml:space="preserve">Fig. 11.</caption> <variables xml:id="echoid-variables133" xml:space="preserve">A B C E D</variables> </figure> <figure> <caption xml:id="echoid-caption215" style="it" xml:space="preserve">Fig. 12</caption> <variables xml:id="echoid-variables134" xml:space="preserve">B C A D</variables> </figure> <figure> <caption xml:id="echoid-caption216" style="it" xml:space="preserve">Fig. 13.</caption> <variables xml:id="echoid-variables135" xml:space="preserve">A B E D C</variables> </figure> <figure> <caption xml:id="echoid-caption217" style="it" xml:space="preserve">Fig. 14.</caption> <variables xml:id="echoid-variables136" xml:space="preserve">Q F I L E P B M A H D O G C</variables> </figure> <pb file="420" n="420"/> </div> <div xml:id="echoid-div766" type="section" level="1" n="415"> <head xml:id="echoid-head559" style="it" xml:space="preserve">Planche Douzieme. Page 138.</head> <figure> <caption xml:id="echoid-caption218" xml:space="preserve">A</caption> </figure> <figure> <caption xml:id="echoid-caption219" xml:space="preserve">B</caption> </figure> <figure> <caption xml:id="echoid-caption220" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables137" xml:space="preserve">E D A F G H C B<lb/> 7 10 14 12 8 10</variables> </figure> <figure> <caption xml:id="echoid-caption221" style="it" xml:space="preserve">Fig. 2.</caption> <description xml:id="echoid-description52" style="it" xml:space="preserve">1. Pentagone Fortifié.</description> <description xml:id="echoid-description53" style="it" xml:space="preserve">2. Bastigns.</description> <description xml:id="echoid-description54" style="it" xml:space="preserve">3. Courtines.</description> <description xml:id="echoid-description55" style="it" xml:space="preserve">4. les Hancs.</description> <description xml:id="echoid-description56" style="it" xml:space="preserve">5. les Faces.</description> <description xml:id="echoid-description57" style="it" xml:space="preserve">6. la Gorge.</description> <description xml:id="echoid-description58" style="it" xml:space="preserve">7. Demie Lune.</description> <description xml:id="echoid-description59" style="it" xml:space="preserve">8. Ouvrage a Corne.</description> <description xml:id="echoid-description60" style="it" xml:space="preserve">9. Fcsse.</description> <description xml:id="echoid-description61" style="it" xml:space="preserve">10. Chemin Couvert.</description> <description xml:id="echoid-description62" style="it" xml:space="preserve">11. Palissade.</description> <description xml:id="echoid-description63" style="it" xml:space="preserve">12. Glacis.</description> <variables xml:id="echoid-variables138" xml:space="preserve">M N H L I G E F K<lb/> A<lb/> B<lb/> C<lb/> 12 12 12 7 8 10 7 7 10 20 2 7 2 2 2 9 2 3 3 3 3 3 6 1 <lb/> 1 2 D 4 3</variables> </figure> <figure> <caption xml:id="echoid-caption222" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables139" xml:space="preserve">e a d b c</variables> </figure> <figure> <caption xml:id="echoid-caption223" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables140" xml:space="preserve">E A D B C D</variables> </figure> <figure> <caption xml:id="echoid-caption224" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables141" xml:space="preserve">a b c e g f d</variables> </figure> <figure> <caption xml:id="echoid-caption225" style="it" xml:space="preserve">Fig. 2</caption> <variables xml:id="echoid-variables142" xml:space="preserve">A B C E G F D</variables> </figure> <pb file="421" n="421"/> </div> <div xml:id="echoid-div767" type="section" level="1" n="416"> <head xml:id="echoid-head560" style="it" xml:space="preserve">Planche Treizieme. Page 156.</head> <figure> <caption xml:id="echoid-caption226" style="it" xml:space="preserve">Fig. A.</caption> <description xml:id="echoid-description64" xml:space="preserve">Vaugirard</description> <description xml:id="echoid-description65" xml:space="preserve">Montrouge</description> <description xml:id="echoid-description66" xml:space="preserve">Gentilly</description> <description xml:id="echoid-description67" xml:space="preserve">Ivry</description> <description xml:id="echoid-description68" xml:space="preserve">Salpetrier</description> <variables xml:id="echoid-variables143" xml:space="preserve">120 110 100 90 80 70 60 50 40 30 20 10 10 20 30 40 60 70 80 90 100 110 120 130 <lb/>140 150 160 170 180 170 160 150 140<lb/> B C F D E</variables> </figure> <figure> <caption xml:id="echoid-caption227" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description69" xml:space="preserve">Obſervatoire</description> <description xml:id="echoid-description70" xml:space="preserve">Salpetrier</description> <description xml:id="echoid-description71" xml:space="preserve">Vaugirard</description> <description xml:id="echoid-description72" xml:space="preserve">Echelle de 1000 Toiſes</description> <description xml:id="echoid-description73" xml:space="preserve">Montrouge</description> <description xml:id="echoid-description74" xml:space="preserve">Gentilly</description> <description xml:id="echoid-description75" xml:space="preserve">Ivry</description> <variables xml:id="echoid-variables144" xml:space="preserve">100 200 400 600 800 1000</variables> </figure> <figure> <caption xml:id="echoid-caption228" style="it" xml:space="preserve">Fig. 2.</caption> <description xml:id="echoid-description76" xml:space="preserve">Echelle de 10. Toiſes</description> <variables xml:id="echoid-variables145" xml:space="preserve">A 1 2 3 4 5 6 7 8 9 10 B<lb/> A B C</variables> </figure> <figure> <caption xml:id="echoid-caption229" style="it" xml:space="preserve">Fig G</caption> <description xml:id="echoid-description77" xml:space="preserve">Umbre Verſe</description> <description xml:id="echoid-description78" xml:space="preserve">Umbre Droite</description> <variables xml:id="echoid-variables146" xml:space="preserve">20 30 40 50 60 70 80 90 100 <lb/>20 30 40 50 60 70 80 90 100 <lb/>10 20 30 40 50 60 70 80 90 <lb/>10 20 30 40 50 60 70 80 90 100<lb/> 15 30 45 60 <lb/>10 20 30 40 50 60 70 80 90 <lb/>10 20 30 40 50 60 70 80 90 <lb/>15 30 45 60</variables> </figure> <figure> <caption xml:id="echoid-caption230" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables147" xml:space="preserve">D G F E</variables> </figure> <figure> <caption xml:id="echoid-caption231" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables148" xml:space="preserve">A D C</variables> </figure> <figure> <caption xml:id="echoid-caption232" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables149" xml:space="preserve">B A C D</variables> </figure> <figure> <caption xml:id="echoid-caption233" style="it" xml:space="preserve">Fig. H</caption> <variables xml:id="echoid-variables150" xml:space="preserve">65 60 55 50 45 40 35 30 25 20 15 10 5 5 10 15<lb/> A e D E F B<lb/> 5 10 20 30 40 50 60 70 80 90</variables> </figure> <pb file="422" n="422"/> </div> <div xml:id="echoid-div768" type="section" level="1" n="417"> <head xml:id="echoid-head561" style="it" xml:space="preserve">Planche Quatorzieme Page 170.</head> <figure> <caption xml:id="echoid-caption234" style="it" xml:space="preserve">Fig. A</caption> <variables xml:id="echoid-variables151" xml:space="preserve">10 20 30 40 50 60 70 80 90 100 110 120 130 140 160 170 180<lb/> B C F E B G D</variables> </figure> <figure> <caption xml:id="echoid-caption235" style="it" xml:space="preserve">Fig. B.</caption> <variables xml:id="echoid-variables152" xml:space="preserve">10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180<lb/> 10 20 30 40 50 60 70 80 90 100 110 120 130 160 170 180<lb/> C</variables> </figure> <figure> <caption xml:id="echoid-caption236" style="it" xml:space="preserve">Fig. H</caption> <variables xml:id="echoid-variables153" xml:space="preserve">N S R</variables> </figure> <figure> <caption xml:id="echoid-caption237" style="it" xml:space="preserve">Fig. D</caption> <variables xml:id="echoid-variables154" xml:space="preserve">1 2 3<lb/> 1 2 6 7 3</variables> </figure> <figure> <caption xml:id="echoid-caption238" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description79" style="it" xml:space="preserve">Echelle</description> <description xml:id="echoid-description80" style="it" xml:space="preserve">Toiſes</description> <description xml:id="echoid-description81" style="it" xml:space="preserve">50 Toiſes</description> <variables xml:id="echoid-variables155" xml:space="preserve">10 20 30 40 50 60<lb/> D C E A B</variables> </figure> <figure> <caption xml:id="echoid-caption239" style="it" xml:space="preserve">Fig. 2.</caption> <description xml:id="echoid-description82" style="it" xml:space="preserve">Echelle</description> <description xml:id="echoid-description83" style="it" xml:space="preserve">32 Toiſes</description> <variables xml:id="echoid-variables156" xml:space="preserve">10 20 30 40 50 60<lb/> C B D E<lb/> 123 32 26 123</variables> </figure> <figure> <caption xml:id="echoid-caption240" style="it" xml:space="preserve">Fig. 3.</caption> <description xml:id="echoid-description84" style="it" xml:space="preserve">Echelle</description> <description xml:id="echoid-description85" style="it" xml:space="preserve">12 Toiſes</description> <variables xml:id="echoid-variables157" xml:space="preserve">C<lb/> B C D A<lb/> 2 10 20</variables> </figure> <figure> <caption xml:id="echoid-caption241" style="it" xml:space="preserve">Fig. 4.</caption> <description xml:id="echoid-description86" style="it" xml:space="preserve">200 Toiſes</description> <variables xml:id="echoid-variables158" xml:space="preserve">D H E G F C I A B</variables> </figure> <figure> <caption xml:id="echoid-caption242" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description87" style="it" xml:space="preserve">Septent.</description> <description xml:id="echoid-description88" style="it" xml:space="preserve">Occident</description> <description xml:id="echoid-description89" style="it" xml:space="preserve">Midy</description> <description xml:id="echoid-description90" style="it" xml:space="preserve">Occident</description> <variables xml:id="echoid-variables159" xml:space="preserve">E<lb/> 10 10 30 50 70 90 70 50 30 10 10 30 50 70 90 70 50 30 10<lb/> C G H D E F<lb/> 30 40</variables> </figure> <figure> <caption xml:id="echoid-caption243" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables160" xml:space="preserve">E A D</variables> </figure> <figure> <caption xml:id="echoid-caption244" style="it" xml:space="preserve">Fig. 3</caption> <description xml:id="echoid-description91" style="it" xml:space="preserve">100. deg.</description> <description xml:id="echoid-description92" style="it" xml:space="preserve">70. T@@ses</description> <description xml:id="echoid-description93" style="it" xml:space="preserve">65. Toiſes</description> <description xml:id="echoid-description94" style="it" xml:space="preserve">130. deg</description> <description xml:id="echoid-description95" style="it" xml:space="preserve">50. Toiſes</description> <description xml:id="echoid-description96" style="it" xml:space="preserve">30. deg</description> <description xml:id="echoid-description97" style="it" xml:space="preserve">94. Toiſes</description> <description xml:id="echoid-description98" style="it" xml:space="preserve">300. deg</description> <description xml:id="echoid-description99" style="it" xml:space="preserve">240. deg</description> <description xml:id="echoid-description100" style="it" xml:space="preserve">70. Toiſes</description> <description xml:id="echoid-description101" style="it" xml:space="preserve">Toiſes</description> <description xml:id="echoid-description102" style="it" xml:space="preserve">Echelle</description> <variables xml:id="echoid-variables161" xml:space="preserve">C B D A E<lb/> 70 100 30 150 110 70 90 120 60<lb/> 10 20 30 40 50 60 70 80 90 100</variables> </figure> <pb file="423" n="423"/> </div> <div xml:id="echoid-div769" type="section" level="1" n="418"> <head xml:id="echoid-head562" style="it" xml:space="preserve">Planche Quinzieme. Page 202.</head> <figure> <caption xml:id="echoid-caption245" xml:space="preserve">A</caption> </figure> <figure> <caption xml:id="echoid-caption246" xml:space="preserve">B</caption> </figure> <figure> <caption xml:id="echoid-caption247" xml:space="preserve">C</caption> <variables xml:id="echoid-variables162" xml:space="preserve">3 3 3 2 4 5 6</variables> </figure> <figure> <caption xml:id="echoid-caption248" xml:space="preserve">D</caption> </figure> <figure> <caption xml:id="echoid-caption249" xml:space="preserve">E</caption> <variables xml:id="echoid-variables163" xml:space="preserve">1 2 3<lb/> 1 4</variables> </figure> <figure> <caption xml:id="echoid-caption250" xml:space="preserve">I</caption> </figure> <figure> <caption xml:id="echoid-caption251" xml:space="preserve">H</caption> </figure> <figure> <caption xml:id="echoid-caption252" xml:space="preserve">F</caption> </figure> <figure> <caption xml:id="echoid-caption253" xml:space="preserve">K</caption> <variables xml:id="echoid-variables164" xml:space="preserve">3 2 1 4 5 6</variables> </figure> <figure> <caption xml:id="echoid-caption254" xml:space="preserve">G</caption> <variables xml:id="echoid-variables165" xml:space="preserve">2 5 3 1 4</variables> </figure> <figure> <caption xml:id="echoid-caption255" xml:space="preserve">I</caption> <variables xml:id="echoid-variables166" xml:space="preserve">3 2 3 4 1 4 5 3 8 6 8 3 7</variables> </figure> <figure> <caption xml:id="echoid-caption256" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables167" xml:space="preserve">B D E C F G A</variables> </figure> <figure> <caption xml:id="echoid-caption257" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables168" xml:space="preserve">E A D C B</variables> </figure> <figure> <caption xml:id="echoid-caption258" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables169" xml:space="preserve">B C D A</variables> </figure> <figure> <caption xml:id="echoid-caption259" xml:space="preserve">M</caption> <variables xml:id="echoid-variables170" xml:space="preserve">4 2 3</variables> </figure> <figure> <caption xml:id="echoid-caption260" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables171" xml:space="preserve">L A K I G F C D E H B</variables> </figure> <pb file="424" n="424"/> </div> <div xml:id="echoid-div770" type="section" level="1" n="419"> <head xml:id="echoid-head563" style="it" xml:space="preserve">Planche Sixieme. Page 44.</head> <figure> <caption xml:id="echoid-caption261" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables172" xml:space="preserve">K M N L<lb/> 1 2 3 4 5 6 7 8 9 10 25 36 49 64</variables> </figure> <figure> <caption xml:id="echoid-caption262" style="it" xml:space="preserve">Fig. 4.</caption> <description xml:id="echoid-description103" style="it" xml:space="preserve">Poids des Boulets</description> <description xml:id="echoid-description104" style="it" xml:space="preserve">Les Cordes</description> <description xml:id="echoid-description105" style="it" xml:space="preserve">Les Solides</description> <description xml:id="echoid-description106" style="it" xml:space="preserve">les Metaux</description> <description xml:id="echoid-description107" style="it" xml:space="preserve">Figure de l'Etuy de Six pouces de long.</description> <description xml:id="echoid-description108" style="it" xml:space="preserve">Les Cordes</description> <description xml:id="echoid-description109" style="it" xml:space="preserve">Les Solides</description> <description xml:id="echoid-description110" style="it" xml:space="preserve">les Meraux</description> <variables xml:id="echoid-variables173" xml:space="preserve">A F H G H F<lb/> 8 7 6 5 4 3 2 1 1/2 1/4<lb/> 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160<lb/> 1 5 10 20 30 40 50 60 64<lb/> 9 10 15 20 25 30 35 40 45 50 55 60 64<lb/> 10 20 30 40 50 60 70 80 90 100 110 120 130 140 160 180<lb/> 1 5 10 20 30 40 50 60 64</variables> </figure> <figure> <caption xml:id="echoid-caption263" style="it" xml:space="preserve">Fig. 3.</caption> <description xml:id="echoid-description111" style="it" xml:space="preserve">Les Cordes</description> <description xml:id="echoid-description112" style="it" xml:space="preserve">Les Cordes</description> <variables xml:id="echoid-variables174" xml:space="preserve">10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180<lb/> A F F<lb/> 10 20 30 40 50 60 70 80 90 100 110 120</variables> </figure> <figure> <caption xml:id="echoid-caption264" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description113" style="it" xml:space="preserve">Calibre des Pieces</description> <description xml:id="echoid-description114" style="it" xml:space="preserve">Les Parttes Egalles</description> <description xml:id="echoid-description115" style="it" xml:space="preserve">les Poligones</description> <description xml:id="echoid-description116" style="it" xml:space="preserve">Figure de l'Etuy de quatre pouces de long.</description> <description xml:id="echoid-description117" style="it" xml:space="preserve">Les Parties Egalles</description> <description xml:id="echoid-description118" style="it" xml:space="preserve">les Plans</description> <description xml:id="echoid-description119" style="it" xml:space="preserve">les Poligones</description> <variables xml:id="echoid-variables175" xml:space="preserve">A B C D D C B<lb/> 8 7 6 5 4 3 2 1 1/2 1/4<lb/> 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200<lb/> 1 5 10 20 30 40 50 60 64<lb/> 12 11 10 9 8 7 6 5 4 3<lb/> 9 10 15 20 25 30 35 40 45 50 55 60 64<lb/> 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200<lb/> 1 5 10 20 30 40 50 60 64<lb/> 12 11 10 9 8 7 6 5 4 3</variables> </figure> <figure> <caption xml:id="echoid-caption265" style="it" xml:space="preserve">Fig. 2.</caption> <description xml:id="echoid-description120" style="it" xml:space="preserve">Figure de l'Etuy de poche de trois pouces de long.</description> <variables xml:id="echoid-variables176" xml:space="preserve">A C L O B D P N E F<lb/> 1 2 3 4 5 6 7 8 9 10<lb/> 100 90 80 70 60 50 40 30 20 10<lb/> 100 90 80 70 60 50 40 30 20 10<lb/> 1 2 3 4 5 6 7 8 9<lb/> 00 00 00 00 00 00 00 00 00<lb/> 1 2 3 4 5 6 7 8 9 10</variables> </figure> <pb file="425" n="425"/> </div> <div xml:id="echoid-div771" type="section" level="1" n="420"> <head xml:id="echoid-head564" style="it" xml:space="preserve">Planche Dix-ſeptieme. Page 224.</head> <figure> <caption xml:id="echoid-caption266" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables177" xml:space="preserve">B F X C D E V O O A</variables> </figure> <figure> <caption xml:id="echoid-caption267" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables178" xml:space="preserve">B D F E A</variables> </figure> <figure> <caption xml:id="echoid-caption268" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables179" xml:space="preserve">B A C E O D</variables> </figure> <figure> <caption xml:id="echoid-caption269" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables180" xml:space="preserve">I R V R Q M</variables> </figure> <figure> <caption xml:id="echoid-caption270" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables181" xml:space="preserve">a a </variables> </figure> <figure> <caption xml:id="echoid-caption271" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables182" xml:space="preserve">T S S Y S X</variables> </figure> <figure> <caption xml:id="echoid-caption272" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables183" xml:space="preserve">Z N Z M O</variables> </figure> <figure> <caption xml:id="echoid-caption273" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables184" xml:space="preserve">A</variables> </figure> <figure> <caption xml:id="echoid-caption274" style="it" xml:space="preserve">Fig. 9.</caption> </figure> <pb file="426" n="426"/> </div> <div xml:id="echoid-div772" type="section" level="1" n="421"> <head xml:id="echoid-head565" style="it" xml:space="preserve">Planche Dix-huitieme. Paqe 260.</head> <figure> <caption xml:id="echoid-caption275" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables185" xml:space="preserve">L L C D G H K E F A B L L O N I N M<lb/> 2 2 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2</variables> </figure> <figure> <caption xml:id="echoid-caption276" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables186" xml:space="preserve">B P D R A S C S d D R</variables> </figure> <figure> <caption xml:id="echoid-caption277" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables187" xml:space="preserve">A B N Q P C M T R O</variables> </figure> <figure> <caption xml:id="echoid-caption278" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description121" style="it" xml:space="preserve">Fevrier. 28</description> <description xml:id="echoid-description122" style="it" xml:space="preserve">Janvi@er. 31</description> <description xml:id="echoid-description123" style="it" xml:space="preserve">Decembre. 31</description> <description xml:id="echoid-description124" style="it" xml:space="preserve">Novembre 30</description> <description xml:id="echoid-description125" style="it" xml:space="preserve">Octobre 31</description> <description xml:id="echoid-description126" style="it" xml:space="preserve">Septembre 30</description> <description xml:id="echoid-description127" style="it" xml:space="preserve">Aoust 31</description> <description xml:id="echoid-description128" style="it" xml:space="preserve">Juillet 31</description> <description xml:id="echoid-description129" style="it" xml:space="preserve">Juin 30</description> <description xml:id="echoid-description130" style="it" xml:space="preserve">May 31</description> <description xml:id="echoid-description131" style="it" xml:space="preserve">Avril. 30</description> <description xml:id="echoid-description132" style="it" xml:space="preserve">Mare. 31</description> <description xml:id="echoid-description133" style="it" xml:space="preserve">Nouvel les Lunos.</description> <description xml:id="echoid-description134" style="it" xml:space="preserve">Cercle des</description> <description xml:id="echoid-description135" style="it" xml:space="preserve">Cercle des</description> <description xml:id="echoid-description136" style="it" xml:space="preserve">Pleines Lunes.</description> <description xml:id="echoid-description137" style="it" xml:space="preserve">Epoques des Années Lunaires.</description> <description xml:id="echoid-description138" style="it" xml:space="preserve">Armees</description> <description xml:id="echoid-description139" style="it" xml:space="preserve">Lun. Sol.</description> <description xml:id="echoid-description140" xml:space="preserve">Mois J. H. M.</description> <variables xml:id="echoid-variables188" xml:space="preserve">20 10 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 20 10 <lb/>V. X. XV. XXX<lb/> 44 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41<lb/> 29. 30. 31. 32. 33. 34. 35. 36. 37. 38.<lb/> 1708. 1709. 1710. 1711. 1712. 1713. 1714. 1715. 1716. 1717.<lb/> A. 20. 5. 55.<lb/> A. 9. 14. 43.<lb/> M. 29. 23. 32.<lb/> M. 19. 8. 21.<lb/> M. 7. 17. 9.<lb/> @. 25. 1. 58.<lb/> @ 14. 10. 47.<lb/> F. 3. 19. 35.<lb/> J. 4. 4. 24.<lb/> J. @ 12. 12</variables> </figure> <figure> <caption xml:id="echoid-caption279" style="it" xml:space="preserve">Fig. 4.</caption> </figure> <pb file="427" n="427"/> </div> <div xml:id="echoid-div773" type="section" level="1" n="422"> <head xml:id="echoid-head566" style="it" xml:space="preserve">Planche Dix-neufieme. Page 280.</head> <figure> <caption xml:id="echoid-caption280" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables189" xml:space="preserve">N.<lb/> N. 1/4 N. E.<lb/> N. N. E.<lb/> N.E. 1/4 N.<lb/> N. E.<lb/> N. E. 1/4 E.<lb/> E. N. E.<lb/> E. 1/4 N. E.<lb/> E.<lb/> E 1/4 S.E.<lb/> E. S. E<lb/> S. E. 1/4 E.<lb/> S. E.<lb/> S. E. 1/4 S.<lb/> S. S. E<lb/> S 1/4 S E.<lb/> S.<lb/> S 1/4 S. O.<lb/> S. S. O.<lb/> S. O. 1/4 S.<lb/> S. O.<lb/> S. O. 1/4 O.<lb/> O. S. O.<lb/> O 1/4 S. O.<lb/> O.<lb/> O 1/4 N. O.<lb/> O. N. O.<lb/> N. O. 1/4 O.<lb/> N. O.<lb/> N. O. 1/4 N.<lb/> N N. O.<lb/> N 1/4 N. O.</variables> </figure> <figure> <caption xml:id="echoid-caption281" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables190" xml:space="preserve">A A B A A</variables> </figure> <figure> <caption xml:id="echoid-caption282" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables191" xml:space="preserve">C B C B A</variables> </figure> <figure> <caption xml:id="echoid-caption283" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables192" xml:space="preserve">H A F C E D G B</variables> </figure> <figure> <caption xml:id="echoid-caption284" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables193" xml:space="preserve">A B C F D I G H E<lb/> 15 30 45 60 75 90</variables> </figure> <figure> <caption xml:id="echoid-caption285" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables194" xml:space="preserve">D A E C B<lb/> 80 70 60 50 40 30 20 10</variables> </figure> <figure> <caption xml:id="echoid-caption286" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables195" xml:space="preserve">90 75 60 45 30 15<lb/> G M C B N E F D H A</variables> </figure> <figure> <caption xml:id="echoid-caption287" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables196" xml:space="preserve">P<lb/> B E C H G F A<lb/> 90 75 60 45 30 60 90</variables> </figure> <figure> <caption xml:id="echoid-caption288" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables197" xml:space="preserve">E H G B D A F C</variables> </figure> <figure> <caption xml:id="echoid-caption289" style="it" xml:space="preserve">Fig. 10.</caption> <variables xml:id="echoid-variables198" xml:space="preserve">C A B<lb/> 10 20 30 40 50 60 70 80 90 80 70 60 50 40 30 20 10<lb/> 90 80 70 60 50 45 40 30 20 10</variables> </figure> <pb file="428" n="428"/> </div> <div xml:id="echoid-div774" type="section" level="1" n="423"> <head xml:id="echoid-head567" style="it" xml:space="preserve">Planche Vingtieme. Page 284.</head> <figure> <caption xml:id="echoid-caption290" xml:space="preserve">QUARTIER DE REDUCTION.</caption> <variables xml:id="echoid-variables199" xml:space="preserve">45 40 35 30 25 20 15 10 5<lb/> 70 65 60 55 50 45<lb/> 50 45 40 35 30 25 20 15 10 5<lb/> Q B a E O H d h A<lb/> V<emph style="sub">+</emph> R M c b q L N l G e f Y T X S Z g F I P C<lb/> 5 10 15 20 25 30 35 40<lb/> 50 45 40 35 30 25 20 15 10 5<lb/> 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5<lb/> 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90<lb/> 5 10 15 20 25 30 35 40</variables> </figure> <pb file="429" n="429"/> </div> <div xml:id="echoid-div775" type="section" level="1" n="424"> <head xml:id="echoid-head568" style="it" xml:space="preserve">Planche Vingt-unieme. Page 288.</head> <figure> <caption xml:id="echoid-caption291" style="it" xml:space="preserve"><emph style="sc">Golfede</emph> <emph style="sc">Gascogne</emph> <emph style="sc">Espagne</emph></caption> <description xml:id="echoid-description141" style="it" xml:space="preserve"><emph style="sc">Irlande</emph></description> <description xml:id="echoid-description142" style="it" xml:space="preserve">I. Blasques</description> <description xml:id="echoid-description143" style="it" xml:space="preserve">Bantrie</description> <description xml:id="echoid-description144" style="it" xml:space="preserve">Roſſe</description> <description xml:id="echoid-description145" style="it" xml:space="preserve">Youghill</description> <description xml:id="echoid-description146" style="it" xml:space="preserve">Port de Corke</description> <description xml:id="echoid-description147" style="it" xml:space="preserve">P<emph style="sub">te</emph> de Schylling</description> <description xml:id="echoid-description148" style="it" xml:space="preserve">Kinſale</description> <description xml:id="echoid-description149" style="it" xml:space="preserve">C. Dorſes</description> <description xml:id="echoid-description150" xml:space="preserve">C de Clare</description> <description xml:id="echoid-description151" style="it" xml:space="preserve">H. de. Milfort</description> <description xml:id="echoid-description152" style="it" xml:space="preserve">Neathe</description> <description xml:id="echoid-description153" style="it" xml:space="preserve">Gloceſter</description> <description xml:id="echoid-description154" style="it" xml:space="preserve"><emph style="sc">Canal de</emph> <emph style="sc">Bristol</emph></description> <description xml:id="echoid-description155" style="it" xml:space="preserve">Briſtol</description> <description xml:id="echoid-description156" style="it" xml:space="preserve">I. Lundey</description> <description xml:id="echoid-description157" style="it" xml:space="preserve">P<emph style="sub">te</emph> de Stoupart</description> <description xml:id="echoid-description158" style="it" xml:space="preserve">C Cornwal</description> <description xml:id="echoid-description159" xml:space="preserve">I. Sorlingues</description> <description xml:id="echoid-description160" style="it" xml:space="preserve">Falmout</description> <description xml:id="echoid-description161" style="it" xml:space="preserve">C Lezart</description> <description xml:id="echoid-description162" style="it" xml:space="preserve">P<emph style="sub">te</emph> de Goutſtart</description> <description xml:id="echoid-description163" style="it" xml:space="preserve">Darmouth</description> <description xml:id="echoid-description164" style="it" xml:space="preserve">Ham</description> <description xml:id="echoid-description165" style="it" xml:space="preserve"><emph style="sc">Angleterre</emph></description> <description xml:id="echoid-description166" style="it" xml:space="preserve">Excester</description> <description xml:id="echoid-description167" style="it" xml:space="preserve">Weymouth</description> <description xml:id="echoid-description168" style="it" xml:space="preserve">Watham</description> <description xml:id="echoid-description169" style="it" xml:space="preserve">Hampton</description> <description xml:id="echoid-description170" style="it" xml:space="preserve">Porstmouth</description> <description xml:id="echoid-description171" style="it" xml:space="preserve">Arundel</description> <description xml:id="echoid-description172" style="it" xml:space="preserve">Iorbay</description> <description xml:id="echoid-description173" style="it" xml:space="preserve">I. Portland</description> <description xml:id="echoid-description174" style="it" xml:space="preserve">I de Wight</description> <description xml:id="echoid-description175" style="it" xml:space="preserve"><emph style="sc">LA</emph> <emph style="sc">Manche</emph></description> <description xml:id="echoid-description176" style="it" xml:space="preserve">I. Guernesey</description> <description xml:id="echoid-description177" style="it" xml:space="preserve">Aurigny</description> <description xml:id="echoid-description178" style="it" xml:space="preserve">C. de la Hague</description> <description xml:id="echoid-description179" style="it" xml:space="preserve">C. de Barfleur</description> <description xml:id="echoid-description180" style="it" xml:space="preserve">I. Jersey</description> <description xml:id="echoid-description181" style="it" xml:space="preserve">Cherbourg</description> <description xml:id="echoid-description182" style="it" xml:space="preserve">Vay</description> <description xml:id="echoid-description183" style="it" xml:space="preserve">Bayeux</description> <description xml:id="echoid-description184" style="it" xml:space="preserve">Eſtrchan</description> <description xml:id="echoid-description185" style="it" xml:space="preserve">P<emph style="sub">te</emph> de Cloquerbreton</description> <description xml:id="echoid-description186" style="it" xml:space="preserve">Brest</description> <description xml:id="echoid-description187" style="it" xml:space="preserve">Dolas</description> <description xml:id="echoid-description188" style="it" xml:space="preserve">Roslohan</description> <description xml:id="echoid-description189" style="it" xml:space="preserve">Quimpercorantin</description> <description xml:id="echoid-description190" style="it" xml:space="preserve">Quimperle</description> <description xml:id="echoid-description191" style="it" xml:space="preserve">Port Louis</description> <description xml:id="echoid-description192" style="it" xml:space="preserve">Irebulden</description> <description xml:id="echoid-description193" style="it" xml:space="preserve">St Brieux</description> <description xml:id="echoid-description194" style="it" xml:space="preserve">St Malo</description> <description xml:id="echoid-description195" style="it" xml:space="preserve">M. St. Michel</description> <description xml:id="echoid-description196" style="it" xml:space="preserve">FRANCE</description> <description xml:id="echoid-description197" style="it" xml:space="preserve">la Roche</description> <description xml:id="echoid-description198" style="it" xml:space="preserve">Bernard</description> <description xml:id="echoid-description199" style="it" xml:space="preserve">Nantes</description> <description xml:id="echoid-description200" style="it" xml:space="preserve">I. de Boving</description> <description xml:id="echoid-description201" style="it" xml:space="preserve">St. Gilles</description> <description xml:id="echoid-description202" style="it" xml:space="preserve">le Jart</description> <description xml:id="echoid-description203" style="it" xml:space="preserve">la Rochelle</description> <description xml:id="echoid-description204" style="it" xml:space="preserve">Rochefort</description> <description xml:id="echoid-description205" style="it" xml:space="preserve">Brouage</description> <description xml:id="echoid-description206" style="it" xml:space="preserve">I. Arvert</description> <description xml:id="echoid-description207" style="it" xml:space="preserve">Blaye</description> <description xml:id="echoid-description208" style="it" xml:space="preserve">Soulac</description> <description xml:id="echoid-description209" style="it" xml:space="preserve">Libourne</description> <description xml:id="echoid-description210" style="it" xml:space="preserve">Bourdeaus</description> <description xml:id="echoid-description211" xml:space="preserve">Id' Ouessant</description> <description xml:id="echoid-description212" style="it" xml:space="preserve">Pte St. Mathieu</description> <description xml:id="echoid-description213" style="it" xml:space="preserve">Les Saints</description> <description xml:id="echoid-description214" style="it" xml:space="preserve">Pte de Penmarck</description> <description xml:id="echoid-description215" style="it" xml:space="preserve">Iſles de Glenau</description> <description xml:id="echoid-description216" style="it" xml:space="preserve">I. de Croix</description> <description xml:id="echoid-description217" style="it" xml:space="preserve">Pte de Quiberon</description> <description xml:id="echoid-description218" style="it" xml:space="preserve">Bell Isle</description> <description xml:id="echoid-description219" style="it" xml:space="preserve">I. Houat</description> <description xml:id="echoid-description220" style="it" xml:space="preserve">I. Hedic</description> <description xml:id="echoid-description221" style="it" xml:space="preserve">le Croisie</description> <description xml:id="echoid-description222" style="it" xml:space="preserve">I. de Noirmoustier</description> <description xml:id="echoid-description223" style="it" xml:space="preserve">I. Dieu</description> <description xml:id="echoid-description224" style="it" xml:space="preserve">Roches bonne</description> <description xml:id="echoid-description225" style="it" xml:space="preserve">I. de Re</description> <description xml:id="echoid-description226" style="it" xml:space="preserve">I. d'Oleron</description> <description xml:id="echoid-description227" style="it" xml:space="preserve">Iour de Cordouan</description> <description xml:id="echoid-description228" style="it" xml:space="preserve">Bassin d'Arcasson</description> <description xml:id="echoid-description229" style="it" xml:space="preserve">Lict</description> <description xml:id="echoid-description230" style="it" xml:space="preserve">Le Passage</description> <description xml:id="echoid-description231" style="it" xml:space="preserve">C Machicaco</description> <description xml:id="echoid-description232" style="it" xml:space="preserve">C Pinas</description> <description xml:id="echoid-description233" style="it" xml:space="preserve">C d' Ortegal</description> <description xml:id="echoid-description234" style="it" xml:space="preserve">C Prior</description> <description xml:id="echoid-description235" style="it" xml:space="preserve">C ge Terol</description> <description xml:id="echoid-description236" style="it" xml:space="preserve">La Corogne</description> <description xml:id="echoid-description237" style="it" xml:space="preserve">C Veillanc</description> <description xml:id="echoid-description238" style="it" xml:space="preserve">C. Lriane</description> <description xml:id="echoid-description239" xml:space="preserve">C de Finiſterre</description> <description xml:id="echoid-description240" style="it" xml:space="preserve">C de Fasellis</description> <description xml:id="echoid-description241" style="it" xml:space="preserve">C de Montego</description> <description xml:id="echoid-description242" style="it" xml:space="preserve">Bayonne</description> <description xml:id="echoid-description243" style="it" xml:space="preserve">St Jean de Luz</description> <description xml:id="echoid-description244" style="it" xml:space="preserve">Fontarabie</description> <description xml:id="echoid-description245" style="it" xml:space="preserve">St Sebastien</description> <description xml:id="echoid-description246" style="it" xml:space="preserve">Gataria</description> <description xml:id="echoid-description247" style="it" xml:space="preserve">Hondaro</description> <description xml:id="echoid-description248" style="it" xml:space="preserve">Vernieillo</description> <description xml:id="echoid-description249" style="it" xml:space="preserve">Bilbao</description> <description xml:id="echoid-description250" style="it" xml:space="preserve">Caſtro</description> <description xml:id="echoid-description251" style="it" xml:space="preserve">St Andero</description> <description xml:id="echoid-description252" style="it" xml:space="preserve">Llanes</description> <description xml:id="echoid-description253" style="it" xml:space="preserve">Villa Vilioſa</description> <description xml:id="echoid-description254" style="it" xml:space="preserve">Gyon</description> <description xml:id="echoid-description255" style="it" xml:space="preserve">Aviles</description> <description xml:id="echoid-description256" style="it" xml:space="preserve">Ribadec</description> <description xml:id="echoid-description257" style="it" xml:space="preserve">Vivero</description> <description xml:id="echoid-description258" style="it" xml:space="preserve">St Carins</description> <description xml:id="echoid-description259" style="it" xml:space="preserve">Sidere</description> <description xml:id="echoid-description260" style="it" xml:space="preserve">Pontesdeime</description> <description xml:id="echoid-description261" style="it" xml:space="preserve">Laxa</description> <description xml:id="echoid-description262" style="it" xml:space="preserve">Corcubion</description> <description xml:id="echoid-description263" style="it" xml:space="preserve">Mouros</description> <description xml:id="echoid-description264" style="it" xml:space="preserve">Noya</description> <description xml:id="echoid-description265" style="it" xml:space="preserve">Villa N<emph style="sub">a</emph></description> <description xml:id="echoid-description266" style="it" xml:space="preserve">Porte NS</description> <description xml:id="echoid-description267" style="it" xml:space="preserve">Pontevedre</description> <description xml:id="echoid-description268" style="it" xml:space="preserve">Vigo</description> <description xml:id="echoid-description269" style="it" xml:space="preserve">Bayonne</description> <description xml:id="echoid-description270" style="it" xml:space="preserve">Camina</description> <description xml:id="echoid-description271" style="it" xml:space="preserve">Viana</description> <description xml:id="echoid-description272" style="it" xml:space="preserve">Ville del Conde</description> <description xml:id="echoid-description273" style="it" xml:space="preserve">Porto</description> <description xml:id="echoid-description274" style="it" xml:space="preserve">Villa N<emph style="sub">a</emph></description> <description xml:id="echoid-description275" style="it" xml:space="preserve">Aviero</description> <description xml:id="echoid-description276" style="it" xml:space="preserve">Lagos</description> <description xml:id="echoid-description277" style="it" xml:space="preserve">Figuero</description> <description xml:id="echoid-description278" style="it" xml:space="preserve"><emph style="sc">Portugal</emph></description> <description xml:id="echoid-description279" style="it" xml:space="preserve"><emph style="sc">Carte</emph> <emph style="sc">Reduite</emph> de partie des Costes de France d'Espagne, d'Angleterre, et d' Irlande.</description> <variables xml:id="echoid-variables200" xml:space="preserve">6 7 8 9 10 11 12 13 14 15 16 17 18<lb/> 51 50 49 48 47 46 45 44 43 42 41 A. 40<lb/> 51 50 49 48 47 46 45 44 43 42 41 B 40<lb/> 6 7 8 9 10 11 12 13 14 15 16 17 18<lb/> S R T</variables> </figure> <pb file="430" n="430"/> </div> <div xml:id="echoid-div776" type="section" level="1" n="425"> <head xml:id="echoid-head569" style="it" xml:space="preserve">Planche Vingt-deuxieme Page 300.</head> <figure> <caption xml:id="echoid-caption292" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables201" xml:space="preserve">A H B L K I G C F D E</variables> </figure> <figure> <caption xml:id="echoid-caption293" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables202" xml:space="preserve">A B F E C D</variables> </figure> <figure> <caption xml:id="echoid-caption294" style="it" xml:space="preserve">Fig. 3.</caption> <description xml:id="echoid-description280" style="it" xml:space="preserve">Angle de 116. d. 34</description> <variables xml:id="echoid-variables203" xml:space="preserve">V L P N T K A S O E I F D X Q B R H C G M</variables> </figure> <figure> <caption xml:id="echoid-caption295" style="it" xml:space="preserve">Fig. 4.</caption> <description xml:id="echoid-description281" style="it" xml:space="preserve">Horizontal.</description> <variables xml:id="echoid-variables204" xml:space="preserve">VIII IIII VII VI V IIII III II I XII XI X IX VIII VII VI V<lb/> A C E D I G L H N F K M B<lb/> 4 3 2 1</variables> </figure> <figure> <caption xml:id="echoid-caption296" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description282" style="it" xml:space="preserve">Vertical.</description> <description xml:id="echoid-description283" style="it" xml:space="preserve">Ligne</description> <description xml:id="echoid-description284" style="it" xml:space="preserve">Horizontale</description> <variables xml:id="echoid-variables205" xml:space="preserve">6 7 8 9 10 11 12 1 2 3 4 5 6<lb/> C E D G L I H K M B F</variables> </figure> <figure> <caption xml:id="echoid-caption297" style="it" xml:space="preserve">Fig. 6</caption> <description xml:id="echoid-description285" style="it" xml:space="preserve">Polaire Superieur.</description> <variables xml:id="echoid-variables206" xml:space="preserve">VII VIII IX XXI XII I II III IIII V<lb/> H I L K B G C F A D 69 69<lb/> 7 8 9 10 11 12 12 3 4 5</variables> </figure> <figure> <caption xml:id="echoid-caption298" style="it" xml:space="preserve">Fig. 7.</caption> <description xml:id="echoid-description286" style="it" xml:space="preserve">Equinoxial Superieur</description> <description xml:id="echoid-description287" style="it" xml:space="preserve">Arc diurne</description> <variables xml:id="echoid-variables207" xml:space="preserve">7 14 15 II 16 160 15 14 5<lb/> 49. d.<lb/> 13 6 5 4 3 2 1 12 11 10 9 8 7 6 13<lb/> F H D A E B C</variables> </figure> <pb file="431" n="431"/> </div> <div xml:id="echoid-div777" type="section" level="1" n="426"> <head xml:id="echoid-head570" style="it" xml:space="preserve">Planche Vingt-troisiême. Page 326.</head> <figure> <caption xml:id="echoid-caption299" style="it" xml:space="preserve">Fig. 1.<emph style="sub">e</emph></caption> <description xml:id="echoid-description288" style="it" xml:space="preserve">Cadran Occidental pour 49. degrez.</description> <description xml:id="echoid-description289" xml:space="preserve">41. d</description> <description xml:id="echoid-description290" style="it" xml:space="preserve">Ligni Horizontale</description> <variables xml:id="echoid-variables208" xml:space="preserve">1 2 3 4 5 6 7 8<lb/> F E D C A B<lb/> ♉ ♈ ♋<lb/> VIII VII VI V IIII III II I<lb/> 69</variables> </figure> <figure> <caption xml:id="echoid-caption300" style="it" xml:space="preserve">Fig. 2<emph style="sub">e</emph>.</caption> <description xml:id="echoid-description291" style="it" xml:space="preserve">Cadran Vertical declinant du Midy à l'Occident de 45.d.</description> <description xml:id="echoid-description292" style="it" xml:space="preserve">49 deg.</description> <description xml:id="echoid-description293" style="it" xml:space="preserve">Axe</description> <description xml:id="echoid-description294" style="it" xml:space="preserve">Equinoxial</description> <description xml:id="echoid-description295" style="it" xml:space="preserve">Souſtil</description> <variables xml:id="echoid-variables209" xml:space="preserve">IX X XI XII I II III IIII VIII VII VI V<lb/> A G S O D E Z H I 6 M C V K N F L 3 2 B P X R Q</variables> </figure> <figure> <caption xml:id="echoid-caption301" style="it" xml:space="preserve">Fig. 3.<emph style="sub">e</emph></caption> <description xml:id="echoid-description296" style="it" xml:space="preserve">Axe</description> <description xml:id="echoid-description297" style="it" xml:space="preserve">Souſtilaire</description> <description xml:id="echoid-description298" style="it" xml:space="preserve">Cadran declin t du Septent<emph style="sub">n</emph> à l'Occicent de 45. deg.</description> <variables xml:id="echoid-variables210" xml:space="preserve">VIII VII VI V IIII</variables> </figure> <figure> <caption xml:id="echoid-caption302" style="it" xml:space="preserve">Fig. 4.<emph style="sub">e</emph></caption> <description xml:id="echoid-description299" style="it" xml:space="preserve">Caldran incliné à l'horizon de 63. deg.</description> <description xml:id="echoid-description300" style="it" xml:space="preserve">Supr Vers Midy</description> <description xml:id="echoid-description301" style="it" xml:space="preserve">Axe</description> <variables xml:id="echoid-variables211" xml:space="preserve">VI VI VII VIII IX X XI XII I II III IIII</variables> </figure> <figure> <caption xml:id="echoid-caption303" style="it" xml:space="preserve">Fig. 5.<emph style="sub">e</emph></caption> <description xml:id="echoid-description302" style="it" xml:space="preserve">Cadran incliné à l'horizon de 63. deg. Infrvens Sept.</description> <description xml:id="echoid-description303" style="it" xml:space="preserve">Axe</description> <variables xml:id="echoid-variables212" xml:space="preserve">VIII VII VI VI V IIIi</variables> </figure> <figure> <caption xml:id="echoid-caption304" style="it" xml:space="preserve">Fig. 6.<emph style="sub">e</emph></caption> <description xml:id="echoid-description304" style="it" xml:space="preserve">Nadir</description> <description xml:id="echoid-description305" style="it" xml:space="preserve">Equinoxial</description> <description xml:id="echoid-description306" style="it" xml:space="preserve">Horizontal</description> <description xml:id="echoid-description307" style="it" xml:space="preserve">26 d 34 63. d. 26. m.</description> <description xml:id="echoid-description308" style="it" xml:space="preserve">Souſil</description> <description xml:id="echoid-description309" style="it" xml:space="preserve">Conſtruction du Cadran declin<emph style="sub">t</emph>. de 36. degrez du Midy à l'Orient et incliné vens la terre de 63. d. 26.m.</description> <variables xml:id="echoid-variables213" xml:space="preserve">A H S K R C G E F D M L N I T P O V B Q<lb/> pace="preserve">49. e. 41. d.<lb/> pace="preserve">54 e. 36. d.<lb/> 6 6 7 8 9 10 11 12</variables> </figure> <figure> <caption xml:id="echoid-caption305" style="it" xml:space="preserve">Fig. 7.<emph style="sub">e</emph></caption> <description xml:id="echoid-description310" style="it" xml:space="preserve">Cadran declinant de 36. degrez, et incliné vers la terre de 63. deg. 26. m.</description> <description xml:id="echoid-description311" style="it" xml:space="preserve">Inſerteur</description> <description xml:id="echoid-description312" style="it" xml:space="preserve">Vertical</description> <description xml:id="echoid-description313" style="it" xml:space="preserve">Axe</description> <description xml:id="echoid-description314" style="it" xml:space="preserve">Equt</description> <description xml:id="echoid-description315" style="it" xml:space="preserve">Horizontal</description> <description xml:id="echoid-description316" style="it" xml:space="preserve">Souſtil</description> <description xml:id="echoid-description317" style="it" xml:space="preserve">noxial</description> <variables xml:id="echoid-variables214" xml:space="preserve">IIII V VI VII VIII IX X XI XII I II III</variables> </figure> <figure> <caption xml:id="echoid-caption306" style="it" xml:space="preserve">Fig. 8.<emph style="sub">e</emph></caption> <description xml:id="echoid-description318" style="it" xml:space="preserve">Cadran declinant de 72. deg. du Midy, et incliné vers le Ciel de 63. deg. 26. m.</description> <description xml:id="echoid-description319" style="it" xml:space="preserve">Superieur</description> <description xml:id="echoid-description320" style="it" xml:space="preserve">Axe</description> <variables xml:id="echoid-variables215" xml:space="preserve">IIII V VI VII VIII IX X XI XII I<lb/> 4 5 6 7 8 9 10 11 12 1</variables> </figure> <pb file="432" n="432"/> </div> <div xml:id="echoid-div778" type="section" level="1" n="427"> <head xml:id="echoid-head571" style="it" xml:space="preserve">Planche Vingt-quatriême. Page 336.</head> <figure> <caption xml:id="echoid-caption307" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description321" style="it" xml:space="preserve">Ce Coſté est appliqué au Plan pour avoir la derlinaiſon.</description> <description xml:id="echoid-description322" style="it" xml:space="preserve">Declinatoire et Inclinatoire.</description> <description xml:id="echoid-description323" style="it" xml:space="preserve">En ce quart ſe trouve la declinouſon du Midy au Couchant et du Septerttrion au I eva@u.</description> <description xml:id="echoid-description324" style="it" xml:space="preserve">En ce quart ſe trouve la declinouſon du Midy au Levant ou du Septentr@on au Couchaiu.</description> <description xml:id="echoid-description325" style="it" xml:space="preserve">Coſté pour l'inclinqiſon au Nadir et vers la terre.</description> <variables xml:id="echoid-variables216" xml:space="preserve">B G A Ot OR. L M S O I H K D C<lb/> 90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90</variables> </figure> <figure> <caption xml:id="echoid-caption308" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables217" xml:space="preserve">E D F C G B A H</variables> </figure> <figure> <caption xml:id="echoid-caption309" style="it" xml:space="preserve">Fig. M.</caption> <variables xml:id="echoid-variables218" xml:space="preserve">B E A D G C F</variables> </figure> <figure> <caption xml:id="echoid-caption310" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables219" style="it" xml:space="preserve">b a b 6 5 4 3 2 0 d o e c 1 l II ne m</variables> </figure> <figure> <caption xml:id="echoid-caption311" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables220" xml:space="preserve">R Y T X V S Z<lb/> 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0</variables> </figure> <figure> <caption xml:id="echoid-caption312" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables221" xml:space="preserve">A B A</variables> </figure> <figure> <caption xml:id="echoid-caption313" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables222" xml:space="preserve">V ♋ ♊ B R ♉ ♈ C D 7 ♓ ♒ ♉<lb/> 5 6 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 7 8 12 11 10 9</variables> </figure> <figure> <caption xml:id="echoid-caption314" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables223" xml:space="preserve">c p o i a t c e b N<lb/> 10 1 2 3 12 1. 11 8 4 7 5 5 10 2 7 5 6 5 7 4 8 3 9 ♊ ♋ ♌ ♉ ♍ ♈ ♎ ♓ ♒ ♏ ♉ ♐</variables> </figure> <figure> <caption xml:id="echoid-caption315" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables224" xml:space="preserve">5 6 7 R 1 12 11 10 9 8</variables> </figure> <pb file="433" n="433"/> </div> <div xml:id="echoid-div779" type="section" level="1" n="428"> <head xml:id="echoid-head572" style="it" xml:space="preserve">Planche Vingt-cinquiême. Page 346.</head> <figure> <caption xml:id="echoid-caption316" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description326" style="it" xml:space="preserve">Cadran Horiſontal.</description> <description xml:id="echoid-description327" style="it" xml:space="preserve">Arcs des</description> <description xml:id="echoid-description328" style="it" xml:space="preserve">Meridiens</description> <description xml:id="echoid-description329" style="it" xml:space="preserve">Signes</description> <description xml:id="echoid-description330" style="it" xml:space="preserve">Heures Babyloniques</description> <description xml:id="echoid-description331" style="it" xml:space="preserve">Almu cantaraths</description> <description xml:id="echoid-description332" style="it" xml:space="preserve">Paris</description> <description xml:id="echoid-description333" style="it" xml:space="preserve">Is. de Fer</description> <description xml:id="echoid-description334" style="it" xml:space="preserve">Heures Italiques</description> <description xml:id="echoid-description335" style="it" xml:space="preserve">Heures Astrononiques Françoiſes.</description> <variables xml:id="echoid-variables225" xml:space="preserve">IX X XI XII I II III VIII VII VI IIII V VI VII VIII IIII V<lb/> ♑ ♒ ♓ ♈ ♉ ♊ ♋ ♑ ♐ ♏ ♎ ♍ ♌ ♋<lb/> G F D E B C A<lb/> 320 330 340 350 360 10 20 30 40 50 60 70 80<lb/> 17 16 15 14 13 12 11 10<lb/> 10 230 220 210 190 180 170<lb/> 2 18 3 19 4 20 5 21 6 22 7 23<lb/> 15 20 25 30 35<lb/> 8 9 10 11 12 13 14</variables> </figure> <figure> <caption xml:id="echoid-caption317" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables226" xml:space="preserve">D I N F O M S A A M I I<lb/> A H L D B G G C I M E F<lb/> 1 2 3 4 5 11 10 9 8 7<lb/> 1 2 3 4 5 11 10 9 8 7<lb/> 4 5 6 7 8 9 10 11 12<lb/> 8 7 6 5 4 3 2 1<lb/> 90 80 70 60 50 40 30 20 10<lb/> 10 20 30 40 50 60 70 80 90</variables> </figure> <figure> <caption xml:id="echoid-caption318" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables227" xml:space="preserve">III IIII V VI VII I II III IIII V VI VII VIII IX<lb/> ♊ ♉ ♈ ♓ ♒ ♑ ♋ ♌ ♍ ♎ ♏ ♐<lb/> A D F E C B H I<lb/> 10 20 30 40 50 60</variables> </figure> <figure> <caption xml:id="echoid-caption319" style="it" xml:space="preserve">Fig. 3.</caption> <description xml:id="echoid-description336" style="it" xml:space="preserve">Coste apltqué au Mur</description> <description xml:id="echoid-description337" style="it" xml:space="preserve">declinaison du Midy à l'Occident</description> <description xml:id="echoid-description338" style="it" xml:space="preserve">declinaison du Midy à l'Orient</description> <description xml:id="echoid-description339" style="it" xml:space="preserve">nord</description> <description xml:id="echoid-description340" style="it" xml:space="preserve">Ouest</description> <description xml:id="echoid-description341" style="it" xml:space="preserve">Est</description> <description xml:id="echoid-description342" style="it" xml:space="preserve">Sud</description> <variables xml:id="echoid-variables228" xml:space="preserve">90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90<lb/> 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8<lb/> B A D</variables> </figure> <figure> <caption xml:id="echoid-caption320" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description343" style="it" xml:space="preserve">Axe</description> <description xml:id="echoid-description344" style="it" xml:space="preserve">Costé Oriental</description> <description xml:id="echoid-description345" style="it" xml:space="preserve">Plan Horisontal</description> <variables xml:id="echoid-variables229" xml:space="preserve">A B F C G D E<lb/> ♓ ♒ ♑ ♐ ♏ ♎<lb/> XI X IX VIII VII VI V IIII III III I XIII XI X IX VII VII VI<lb/> 10 20 30 40 50 60 70 80 90</variables> </figure> <pb file="434" n="434"/> </div> <div xml:id="echoid-div780" type="section" level="1" n="429"> <head xml:id="echoid-head573" style="it" xml:space="preserve">Planche Vingt-Sixiême. Page 362.</head> <figure> <caption xml:id="echoid-caption321" style="it" xml:space="preserve">Fig. 1.</caption> <variables xml:id="echoid-variables230" xml:space="preserve">90 80 70 60 50 40 30 20 10 10 20 30 40 50 60 70 80 90<lb/> D A Z C B N ♑ E ♋<lb/> 5 4 3 2 1 1 2 11 10 9 8 10 9 8 7 6 5 4 3 2</variables> </figure> <figure> <caption xml:id="echoid-caption322" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables231" xml:space="preserve">6 7 8 9 12 1 12 11</variables> </figure> <figure> <caption xml:id="echoid-caption323" style="it" xml:space="preserve">Fig. 3.</caption> <description xml:id="echoid-description346" style="it" xml:space="preserve">Diametre du Cilindre</description> <description xml:id="echoid-description347" style="it" xml:space="preserve">Longueur du ſtile hors du Clinidre</description> <variables xml:id="echoid-variables232" xml:space="preserve">E A B F D C<lb/> 10 20 30 40 50 60 64 30<lb/> 25 30<lb/> 10 20 30 40 50 60<lb/> 7 5 6 6 5 7 4 8 3 9 2 10 1 11 12<lb/> 6 5 7 4 8 3 9 2 10 1 11 12<lb/> ♋ ♊ ♉ ♈ ♓ ♒ ♌ ♍ ♎ ♏ ♐ ♑</variables> </figure> <figure> <caption xml:id="echoid-caption324" style="it" xml:space="preserve">Fig. 4.</caption> <description xml:id="echoid-description348" style="it" xml:space="preserve">Hauteur Polaire de 49. deg.</description> <description xml:id="echoid-description349" style="it" xml:space="preserve">Heures devant midi</description> <description xml:id="echoid-description350" style="it" xml:space="preserve">Aprés Midi</description> <variables xml:id="echoid-variables233" xml:space="preserve">P A O Q C E D M B R<lb/> ♋ ♌ ♍ ♎ ♏ ♐ ♊ ♉ ♈ ♓ ♒<lb/> 1 2 3 4 5 6 7 8 9 10 11 12<lb/> 12 11 10 9 8 7 6 5 4 3 2 1</variables> </figure> <figure> <caption xml:id="echoid-caption325" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description351" style="it" xml:space="preserve">Heures devant midi</description> <description xml:id="echoid-description352" style="it" xml:space="preserve">Aprés Midi</description> <description xml:id="echoid-description353" style="it" xml:space="preserve">Centre du guart do Cercle</description> <variables xml:id="echoid-variables234" xml:space="preserve">G C H I A S O N D I M A M F I K I E A B K D<lb/> ♋ ♌ ♍ ♎ ♏ ♐ ♑ ♊ ♉ ♈ ♓ ♒<lb/> 90 80 70 60 50 40 30 20 10 <lb/> 69 60 50 40 30 20 10<lb/> 40 50 60<lb/> 1 2 3 4 5 6 7 8 9 10 11 12<lb/> ♋ ♌ ♍ ♎ ♏ ♐ ♑ ♊ ♉ ♈ ♓ ♒<lb/> 11 10 9 8 7 6 5 4 3 2 1 12</variables> </figure> <figure> <caption xml:id="echoid-caption326" style="it" xml:space="preserve">Fig. 7.</caption> <description xml:id="echoid-description354" style="it" xml:space="preserve">41. Degrez</description> <variables xml:id="echoid-variables235" xml:space="preserve">♋ ♌ ♍ ♎ ♏ ♐ ♑ ♊ ♉ ♈ ♓ ♒<lb/> B G F E A I K L D E C A<lb/> 90 80 70 60 50 40 30 20 10<lb/> 11 10 9 8 7 6 5 4<lb/> 12 1 2 3 4 5 6 7 8</variables> </figure> <figure> <caption xml:id="echoid-caption327" style="it" xml:space="preserve">Fig. 6.</caption> <description xml:id="echoid-description355" style="it" xml:space="preserve">pour 50</description> <description xml:id="echoid-description356" style="it" xml:space="preserve">pour 40</description> <description xml:id="echoid-description357" style="it" xml:space="preserve">pour 40</description> <variables xml:id="echoid-variables236" xml:space="preserve">IIII V VI VII VIII XII I II III IIII V VI VII VIII<lb/> V VI VII VIII II I II III IIII V VI VII<lb/> 45 5 6 7 8 9<lb/> 1 2 3 4 5 6 7 45<lb/> 1 2pour 50.</variables> </figure> <figure> <caption xml:id="echoid-caption328" style="it" xml:space="preserve">Fig. 9.</caption> <variables xml:id="echoid-variables237" xml:space="preserve">20 M.<lb/> 22. S.</variables> </figure> <figure> <caption xml:id="echoid-caption329" style="it" xml:space="preserve">Fig. 8.</caption> <variables xml:id="echoid-variables238" xml:space="preserve">A I P G E K H B S R C L N F O M D<lb/> 10 20 30 40 50 60 70 80 90<lb/> 321 ♑ ♋ 11 10 9 8 7 6 5 4<lb/> ♐ ♒ ♌ ♊ ♏ ♓ ♍ ♉ ♎<lb/> 12 12 6 7 8 9 10 11 1 2 3 4 5 6</variables> </figure> <pb file="435" n="435"/> </div> <div xml:id="echoid-div781" type="section" level="1" n="430"> <head xml:id="echoid-head574" style="it" xml:space="preserve">Planche Vingt-septiême. Page 370.</head> <figure> <caption xml:id="echoid-caption330" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description358" style="it" xml:space="preserve">Paris 49. Madrid 41</description> <description xml:id="echoid-description359" style="it" xml:space="preserve">Amsterdam 52.</description> <variables xml:id="echoid-variables239" xml:space="preserve">G F D A B C D E<lb/> 10 20 30 40 50 60 70 80 10 20 30 40 50 60 70 80<lb/> I II III IIII V VII VIII IX XI II III IIIIV VI VII VIII IX X XI XII I</variables> </figure> <figure> <caption xml:id="echoid-caption331" style="it" xml:space="preserve">Fig. 2.</caption> <description xml:id="echoid-description360" style="it" xml:space="preserve">Rome 42. Vienne 49.</description> <description xml:id="echoid-description361" style="it" xml:space="preserve">Paris 49. la Haye 52.</description> <variables xml:id="echoid-variables240" xml:space="preserve">F D A B E C D<lb/> 10 20 30 40 50 60 70 80 90 10 20 30 40 50 60 70 80 90<lb/> I II III V VI IX X XI XII I II III IIII V VI VII VIII IX X XI X</variables> </figure> <figure> <caption xml:id="echoid-caption332" style="it" xml:space="preserve">Fig. 3.</caption> <variables xml:id="echoid-variables241" xml:space="preserve">80 7@ 60 50 40 30 20 10<lb/> D B E F C A<lb/> V VI VII XI XII I II III IIII V VI VII VIII</variables> </figure> <figure> <caption xml:id="echoid-caption333" style="it" xml:space="preserve">Fig. 4.</caption> <variables xml:id="echoid-variables242" xml:space="preserve">A H D C F G I E B K<lb/> 10 20 30 40 50 60 70 80 90 100 110 120 130<lb/> 11 10 9 8 7 6 5 4<lb/> 12 11 10 9 8 7 6 5 4<lb/> 6 7 8 9 10 11<lb/> ♋ ♌ ♊ ♍ ♉ ♎ ♈ ♏ ♓ ♐ ♒ ♑</variables> </figure> <figure> <caption xml:id="echoid-caption334" style="it" xml:space="preserve">Fig. 5.</caption> <description xml:id="echoid-description362" style="it" xml:space="preserve">Zodiac 23. d 1/2.</description> <description xml:id="echoid-description363" style="it" xml:space="preserve">49. deg.</description> <description xml:id="echoid-description364" style="it" xml:space="preserve">Egunteur 41. deg.</description> <description xml:id="echoid-description365" style="it" xml:space="preserve">Horiſontale</description> <description xml:id="echoid-description366" style="it" xml:space="preserve">Pole</description> <variables xml:id="echoid-variables243" xml:space="preserve">♌ ♋ ♊ ♉ ♈ ♓ ♒ ♑ ♐ ♏ ♎ ♍<lb/> A H L G I C B D F T Y M N O P E X Z S R Q<lb/> 7 6 5 4 8 7 6 5 4 3 2 1 12 11 10 9 8<lb/> m a b c</variables> </figure> <figure> <caption xml:id="echoid-caption335" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables244" xml:space="preserve">V VI VIII VIII IX VII I II II IIII V VI VII<lb/> E A D B C<lb/> V VI VII VIII IX X XI XII I II III IIII V VI VII<lb/> I A S O N I F M A M I<lb/> ♋ ♊ ♉ ♈ ♓ ♒ ♌ ♍ ♎ ♏ ♐</variables> </figure> <pb file="436" n="436"/> </div> <div xml:id="echoid-div782" type="section" level="1" n="431"> <head xml:id="echoid-head575" style="it" xml:space="preserve">Planche Vingt-Huitieme. Page 384.</head> <figure> <caption xml:id="echoid-caption336" style="it" xml:space="preserve">Fig. 1.</caption> <description xml:id="echoid-description367" style="it" xml:space="preserve">Heures Apres Midy</description> <description xml:id="echoid-description368" style="it" xml:space="preserve">Heures Avant Midy</description> <variables xml:id="echoid-variables245" xml:space="preserve">L C V I M A B F I I A S O N D C<lb/> 10 20 30 40 50 60 70 80 80 70 60 50 40 30 20 10<lb/> 12 11 10 9 8 7 6 5 69 4<lb/> 12 1 2 69 3 4 5 6 7 8</variables> </figure> <figure> <caption xml:id="echoid-caption337" style="it" xml:space="preserve">Fig. 2.</caption> <variables xml:id="echoid-variables246" xml:space="preserve">H A B D F E H I G I E K<lb/> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30<lb/> 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12<lb/> 1 2 3 4 5 6 7 8 9 10 11 12<lb/> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15<lb/> 16 17 18 10 20 21 22 23 24 25 26 27 28 29 30</variables> </figure> <figure> <caption xml:id="echoid-caption338" style="it" xml:space="preserve">Fig. 3.</caption> <description xml:id="echoid-description369" style="it" xml:space="preserve">Grande Ourse</description> <description xml:id="echoid-description370" style="it" xml:space="preserve">les 2. Gardes</description> <description xml:id="echoid-description371" style="it" xml:space="preserve">Pole du monde</description> <description xml:id="echoid-description372" style="it" xml:space="preserve">Etoille Polaire</description> <description xml:id="echoid-description373" style="it" xml:space="preserve">Petite Ourse</description> <description xml:id="echoid-description374" style="it" xml:space="preserve">la Claire</description> <variables xml:id="echoid-variables247" style="it" xml:space="preserve">d e o c</variables> </figure> <figure> <caption xml:id="echoid-caption339" style="it" xml:space="preserve">Fig. 7.</caption> <variables xml:id="echoid-variables248" xml:space="preserve">C A B E F I L Q K M G D H F N N E E SE S SO R O NO P</variables> </figure> <figure> <caption xml:id="echoid-caption340" style="it" xml:space="preserve">Fig. 4.</caption> <description xml:id="echoid-description375" style="it" xml:space="preserve">8. may</description> <description xml:id="echoid-description376" style="it" xml:space="preserve">La Claire de la Petite Ourſe</description> <description xml:id="echoid-description377" style="it" xml:space="preserve">8. nov.</description> <variables xml:id="echoid-variables249" xml:space="preserve">10 31 20 10 2@ 20 10 31 20 10 30 20 10 30 20 10 31 20 10 30 20 10 31 20 10 31 20 10 30 20 10 31 20 10 30 20<lb/> 30 M. 31. F 20 I. 31 D 31 N 30 O 31 S 30 A 31 I. 31. I. 30. M.31.A.<lb/> 12 11 10 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1</variables> </figure> <figure> <caption xml:id="echoid-caption341" style="it" xml:space="preserve">Fig. 5.</caption> <variables xml:id="echoid-variables250" xml:space="preserve">E A A D B D F<lb/> XI XII I II III IIII V VI VII VIII IX X<lb/> 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9<lb/> 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9</variables> </figure> <figure> <caption xml:id="echoid-caption342" style="it" xml:space="preserve">Fig. 6.</caption> <variables xml:id="echoid-variables251" xml:space="preserve">B A G F M H L C I E D</variables> </figure> <pb file="437" n="437"/> <pb file="438" n="438"/> </div></text> </echo>