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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
|---|---|
| date | Thu, 02 May 2013 11:14:40 +0200 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Galilei, Galileo</author> <title>Les méchaniques</title> <date>1634</date> <place>Paris</place> <translator>Mersenne, Marin</translator> <lang>fr</lang> <cvs_file>galil_mecha_047_fr_1634.xml</cvs_file> <cvs_version></cvs_version> <locator>047.xml</locator> </info> <text> <front> <section> <pb xlink:href="047/01/001.jpg"></pb> <p type="head"> <s id="s.000001"><emph type="center"></emph>LES <lb></lb>MECHANIQVES <lb></lb>DE GALILÉE <lb></lb>MATHEMATICIEN <lb></lb>& Ingenieur du Duc de Florence.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000002"><emph type="center"></emph><emph type="italics"></emph>AVEC PLVSIEVRS ADDITIONS <lb></lb>rares, & nouuelles, vtiles aux Archite<lb></lb>ctes, Ingenieurs, Fonteniers, Phi<lb></lb>loſophes, & Artiſans.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000003"><emph type="center"></emph>Traduites de l'Italien par L.P.M.M.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000004"><emph type="center"></emph>A PARIS, <lb></lb>Chez HENRY GVENON, ruë S. Iacques, <lb></lb>prés les Iacobins, à l'image S. Bernard.<emph.end type="center"></emph.end><lb></lb></s> </p> <p type="head"> <s id="s.000005"><emph type="center"></emph>M. DC. XXXIV. <lb></lb><emph type="italics"></emph>AVEC PRIVILEGE ET APPROBATION.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <pb xlink:href="047/01/002.jpg"></pb> <pb xlink:href="047/01/003.jpg"></pb> </section> <section> <p type="head"> <s id="s.000006"><emph type="center"></emph>A MONSIEVR <lb></lb>MONSIEVR <lb></lb>DE REFFVGE, <lb></lb>CONSEILLER DV <lb></lb>Roy au Parlement.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000007">MONSIËVR, </s> </p> <p type="main"> <s id="s.000008"><emph type="italics"></emph>Puis qu'il y a huict ans que ie vous <lb></lb>preſentay les liures de Mechaniques en <lb></lb>latin, & que ie fais voir le iour à ce <lb></lb>nouueau traitté de Galilée, qui donne <lb></lb>de nouuelles lumieres à cette ſcience, il eſt <lb></lb>raiſonnable que ie vous l'offre auſſi <lb></lb>bien que l'autre, affin que vous ſoyez le <lb></lb>premier à receuoir le contentement que <lb></lb>l'on à couſtume de reſſentir en liſant <lb></lb>tout ce qui vient de la part de cét excel<lb></lb>lent homme, qui a l'vn des plus ſubtils <emph.end type="italics"></emph.end> <pb xlink:href="047/01/004.jpg"></pb><emph type="italics"></emph>eſprits de ce ſiecle. </s> <s id="s.000009">Si la traduction <lb></lb>ſemble quelque fois obſcure, à raiſon des <lb></lb>fautes du manuſcrit Italien ie ne doute <lb></lb><expan abbr="nullemẽt">nullement</expan> que la clairté & la viuacité de <lb></lb>voſtre eſprit n'en diſſipe ayſement tous <lb></lb>les nüages, Quant aux additions que <lb></lb>i'y ay miſes, elles vous ſeront auſſi agrea<lb></lb>bles que le reſte, parce qu'elles contien<lb></lb>nent de nouuelles ſpeculations, qui peu<lb></lb>uent ſeruir pour penetrer les ſecrets de <lb></lb>la Phyfique & particulierement <lb></lb>tout ce qui concerne les mouuemens <expan abbr="tãt">tant</expan> <lb></lb>naturels que violents. </s> <s id="s.000010">Mais i'estime <lb></lb>que l'ordre, & le reglement admirable <lb></lb>que la nature obſerue dans les forces <lb></lb>mouuantes, vous donnera encore plus <lb></lb>de plaiſir, parce que vous y verrez re<lb></lb>luire vne équité, & vne iustice perpe<lb></lb>tuelle qui ſe garde, & que l'on remar<lb></lb>que ſi iuſtement entre la force, la reſi<lb></lb>ſtence, le <expan abbr="tẽps">temps</expan>, la viſteſſe &, leſpace, que <lb></lb>l'vn <expan abbr="recõpenſe">recompenſe</expan> touſiours l'autre, car ſi le <lb></lb><expan abbr="mouuemẽt">mouuement</expan> est viste, il faut beaucoup de <emph.end type="italics"></emph.end> <pb xlink:href="047/01/005.jpg"></pb><emph type="italics"></emph>force & s'il eſt <expan abbr="lẽs">lens</expan>, vne petite force ſuffit. </s> <s id="s.000011"><lb></lb>En effet il eſt impoſſible de gaigner la for<lb></lb>ce, & le téps tout <expan abbr="ensẽble">ensemble</expan>, <expan abbr="cõme">comme</expan> il eſt im<lb></lb>poſſible qu'vn homme iouyſſe des plai<lb></lb>ſirs folaſtres du monde & de ceux du <lb></lb>Ciel en meſme temps: de ſorte que les <lb></lb>Mechaniques peuuent enſeigner à bien <lb></lb>viure, ſoit en imitant les corps peſans <lb></lb>qui cherchent touſiours leur centre dans <lb></lb>celuy de la terre comme leſprit de l'hom. </s> <s id="s.000012"><lb></lb>me doit chercher le ſien dans l'eſſence <lb></lb>diuine qui eſt la ſource de tous les eſprits <lb></lb>ou en ſe tenant dans le perpetuel èquili<lb></lb>bre moral, & raiſonnable qui conſiſte à <lb></lb>rendre premierement à Dieu, & puis <lb></lb>au prochain tout ce que luy appartient. </s> <s id="s.000013"><lb></lb>L'autheur de ce traité a obmis beaucoup <lb></lb>de choſes, par <expan abbr="exẽple">exemple</expan> il n'a point parlé du <lb></lb>coin qui eſt <expan abbr="l'inſtrumẽt">l'inſtrument</expan> le plus fort de tous <lb/>car ſa force en partie depend de l'incli<lb></lb>nation du plan, comme Guid Vbalde <lb></lb>demonſtre dans le traité, qu'il en a fait, <lb></lb>de ſorte que le coin entre dautant plus <emph.end type="italics"></emph.end> <pb xlink:href="047/01/006.jpg"></pb><emph type="italics"></emph>ayſement qu'il eſt plus eſtroit, & que <lb></lb>ſes coſtez panchent dauantage ſur l'ho<lb></lb>rizon, c'eſt à dire qu'ils font de moin<lb></lb>dres angles. </s> <s id="s.000014">Or ce meſme principe eſt <lb></lb>cauſe de ce que les cousteaux coupent ſi <lb></lb>ayſement, & de pluſieurs autres effects <lb></lb>que l'on peut remarquer en mille choſes, <lb></lb>dont on cognoiſtra les raiſons ſi on liſt <lb></lb>auec attention les traitez,<emph.end type="italics"></emph.end> della Vite, <lb></lb>del Cuneo, della Taglia, della <lb></lb>Leua, della Bilancia, & dell' Aſſe <lb></lb>nella Rota, <emph type="italics"></emph>que Guido Vbalde a com<lb></lb>poſez: d'où ſe tire la nature des Ver<lb></lb>rins, des Crics, des Preſſes, & de tout <lb></lb>ce qui ſert à augmenter, à conſeruer, ou <lb></lb>à diminuer la force, ou le temps. </s> <s id="s.000015"><lb></lb>La force du coin depend auſſi de la per<lb></lb>cuſſion, qui eſt ſi admirable qu'il n'y a <lb></lb>point de fardeau ſi lourd, que l'on ne <lb></lb>puiſſe faire remüer & cheminer auec <lb></lb>des coups de marteau, pour petits qu'ils <lb></lb>puiſſent eſtre, ce que l'on tient que <lb></lb>Galilée a experimenté en frappant ſi <emph.end type="italics"></emph.end> <pb xlink:href="047/01/007.jpg"></pb><emph type="italics"></emph>ſouuent contre vn grand coffre auec vn <lb></lb>marteau d'épinette, qu'il la fait chan<lb></lb>ger de place & la fait auancer d'vn <lb></lb>pied: ce que pluſieurs ne croyront nulle<lb></lb>ment encore qu'ils ne prennent pas la <lb></lb>peine d'en faire l'experience laquelle eſt <lb></lb>tres digne de conſideration, car elle peut <lb></lb>ſeruir d'vn principe pour entrer plus <lb></lb>auant dans les ſecrets de la nature. </s> <s id="s.000016">Ie <lb></lb>laiſſe pluſieurs autres choſes, qui ſem<lb></lb>blent admirables, & que vous pouuez, <lb></lb>experimenter quand il vous plaira; <lb></lb>ie vous en diray ſeulement vne des plus <lb></lb>rares, laquelle vous verrez en <expan abbr="iettãt">iettant</expan> vne <lb></lb>bale, ou vne boule en haut le plus droit <lb></lb>que vous pourrez, lors que vous estes <lb></lb>dans vostre carroſſe, ou a cheual, & <lb></lb>lors qu'ils courent de telle viſteſſe que <lb></lb>vous voudrez, car la boule vous ſui<lb></lb>ura, tellement que vous la pourrez rece<lb></lb>uoir dans la main encore que le carroſſe, <lb></lb>ou le cheual ayent fait cent pas tandis <lb></lb>que la boule aura eſté dans l'air. </s> <s id="s.000017">Et ſi <emph.end type="italics"></emph.end> <pb xlink:href="047/01/008.jpg"></pb><emph type="italics"></emph>vous la laiſſez <expan abbr="tõber">tomber</expan>, elle vous ſuiura <lb></lb>d'autant plus loing que le cheual ira <lb></lb>plus viste. </s> <s id="s.000018">Galilèe a encore laiſſé dau<lb></lb>tres choſes dans ſon traicté comme il eſt <lb></lb>ayſé de voir dans les trois liures de <lb></lb>Mechaniques que ie vous ay preſentez <lb></lb>& qui peuuent ſuppléer à ce que l'on <lb></lb>pourroit icy deſirer; de ſorte qu'il n'eſt <lb></lb>pas neceſſaire que ie m'eſtende plus au <lb></lb>long ſur ce ſubiect, qui dépend entiere<lb></lb>ment du centre de peſanteur, que l'on <lb></lb>trouue dans toutes ſortes de corps par <lb></lb>les moyens, que Commandin & Luc <lb></lb>Valere ont donné, dont vous auez tou<lb></lb>tes les propoſitions.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000019"><emph type="italics"></emph>Ie croy que ſi la Iuſtice pouuoit par<lb></lb>ler qu'elle <expan abbr="cõfeſſeroit">confeſſeroit</expan> ingenuëment qu'il <lb></lb>n'y a nulle ſcience naturelle: qui luy <lb></lb>ſoit ſi ſemblable que celles des Mecha<lb></lb>niques, c'eſt pourquoy ie vous l'offre aſſin <lb></lb>de teſmoigner l'estat que ie fais de vos <lb></lb>vertus, qui me contraignent d'auoir <lb></lb>la meſme affection pour vous, que pour <emph.end type="italics"></emph.end> <pb xlink:href="047/01/009.jpg"></pb><emph type="italics"></emph>celuy qui eſt aymé de Dieu & des <lb></lb>hommes, de prier la diuine Maieſtè de <lb></lb>vous donner vne tres bonne ſanté, <lb></lb>qui ſoit auſſi longue que ie le deſire: & <lb></lb>de me dire auec toute ſorte de reſpect.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000020">Voſtre tres-humble <lb></lb>ſeruiteur F. M. </s> <s id="s.000021">Mer<lb></lb>ſenne Minime. </s> </p> <pb xlink:href="047/01/010.jpg"></pb> </section> <section> <p type="head"> <s id="s.000022"><emph type="center"></emph>PREFACE AV LECTEVR.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000023">IE ſeray content ſi ie ſuis cauſe <lb></lb>que le ſieur Galilée nous don<lb></lb>ne toutes ſes ſpeculations des <lb></lb>mouuemens, & de tout ce qui ap<lb></lb>partient aux Mechaniques, car ce <lb></lb>qui viendra de ſa part ſera excel<lb></lb>lent: c'eſt pourquoy ie prie ceux <lb></lb>qui ont de la correſpondance à <lb></lb>Florénce, de l'exhorter par lettres <lb></lb>à donner au public toutes ſes re<lb></lb>marques, comme i'eſpere qu'il <lb></lb>fera puis qu'il a maintenant le <lb></lb>temps, & la commodité tres libre <lb></lb>dans ſa maiſon des champs, & <lb></lb>qu'il a encor aſſez de force, quoy <lb></lb>qu'il ſoit plus que ſeptuagenaire <lb></lb>pour acheuer toutes ſes œuures, <lb></lb>comme il aſſeure dans vne lettre <lb></lb>de ſa main que l'on m'a commu<lb></lb>niquée. </s> <s id="s.000024">Or en attendant ces trai<lb></lb>tez excellent, l'on peut voir les <pb xlink:href="047/01/011.jpg"></pb>3 liures des Mechaniques, que le <lb></lb>feis imprimer l'année 1626; à quoy <lb></lb>i'aioute maintenant la conſidera<lb></lb>tion des deux cercles qu'Ariſtote <lb></lb>a propoſez dans la 24 queſtion de <lb></lb>ſes Mechaniques, parce que plu<lb></lb>ſieurs la <expan abbr="trouuẽt">trouuent</expan> admirable dau<lb></lb>tant qu'ils ne l'entendent pas. </s> <s id="s.000025"><lb></lb>Et pour ce ſujet ſoit le grand cer<lb></lb>cle ACB, & le moindre FGH, il <lb></lb><figure id="id.047.01.011.1.jpg" xlink:href="047/01/011/1.jpg"></figure><lb></lb>eſt certain <lb></lb>que quand <lb></lb>le quart du <lb></lb>grand cercle <lb></lb>BD s'eſt meu <lb></lb>iuſques au <lb></lb>poinct O, de <lb></lb>ſorte que le point D ſe rencontre <lb></lb>au point O, que le point E du <lb></lb>quart du moindre cercle FE ſe <expan abbr="rẽ-cõtre">ren<lb></lb>contre</expan> au point N, & <expan abbr="cõſequẽment">conſequemment</expan> <lb></lb>que le petit cercle fait autant de <lb></lb>chemin que le grand en meſme <pb xlink:href="047/01/012.jpg"></pb>temps, puiſque le plan FN ſur le<lb></lb>quel il ſe meut eſt égal au plan <lb></lb>DO, ſur lequel roule le grand. </s> </p> <p type="main"> <s id="s.000026">D'où quelques vns conclunt <lb></lb>qu'il n'y a point de ſi petit cercle <lb></lb>que l'on ne le puiſſe dire égal au <lb></lb>plus grand qui ſe puiſſe imaginer, <lb></lb>puis qu'il <expan abbr="reſpõd">reſpond</expan> à vn eſpace égal <lb></lb>Car pluſieurs croyent que les par<lb></lb>ties du petit ne trainent point, <lb></lb>qu'elles ne froiſſent nullement le <lb></lb>plan, & que chaque point, & cha<lb></lb>que partie de ſa circonference <lb></lb>touche <expan abbr="ſeulemẽt">ſeulement</expan> à chaque point, <lb></lb>& à chaque partie du plan. </s> <s id="s.000027">Il faut <lb></lb>dire la meſme choſe du grand <lb></lb>cercle à l'égard du petit, lors que <lb></lb>le grand ſe meut par le mouue<lb></lb>ment du petit, car le grand dimi<lb></lb>nuë ſon chemin ſuiuant les traces <lb></lb>du petit, de ſorte que ſi le petit <lb></lb>ne fait qu'vn pied de Roy dans vn <lb></lb>tour, le grand quoy qu'égal au <pb xlink:href="047/01/013.jpg"></pb>Ciel des eſtoiles, ne fait auſſi <lb></lb>qu'vn pied de Roy dans vn tour. </s> <s id="s.000028"><lb></lb>Ce que quelques vns expliquent <lb></lb>par le moyen de la rarefaction, & <lb></lb>de la condenſation, en <expan abbr="comparãt">comparant</expan> <lb></lb>le mouuement du grand cercle à <lb></lb>celle-cy, & le mouuement du <lb></lb>moindre à celle la, <expan abbr="quãd">quand</expan> le moin<lb></lb>dre eſt meu par le plus <expan abbr="grãd">grand</expan>, & au <lb></lb>contraire, lors que le moindre <lb></lb>meut le plus grand. </s> <s id="s.000029">Or il faut <lb></lb>aduoüer que la negligence des <lb></lb>hommes eſt étrange, qui ſe trom<lb></lb>pent ſi ſouuent pour ne vouloir <lb></lb>pas faire la moindre experience <lb></lb>du monde & qui ſe trauaillent eǹ <lb></lb>vain à la recherche des raiſons <lb></lb>d'vne choſe qui n'eſt point, com<lb></lb>me il arriue en celle cy, car le <lb></lb>petit cercle ne meut iamais le <expan abbr="grãd">grand</expan> <lb></lb>que pluſieurs parties du grand <lb></lb>ne touchent vne meſme partie <lb></lb>du plan, dont chaque partie eſt <pb xlink:href="047/01/014.jpg"></pb>touchée par cent parties dif<lb></lb>ferentes du grand cercle quand <lb></lb>il eſt cent fois plus grand que l'au<lb></lb>tre. </s> <s id="s.000030">Et lors que le petit eſt meu <lb></lb>parle grand, vne meſme partie <lb></lb>du petit, touche cent parties du <lb></lb>grand, comme l'experience fera <lb></lb>voir à tous ceux qui la feront en <lb></lb>aſſez grand volume. </s> </p> <p type="main"> <s id="s.000031">Les meſmes erreurs arriuent en <lb></lb>pluſieurs autres chofes, ce qui a <lb></lb>donné ſuiect à quelques vns d'eſ<lb></lb>crire <emph type="italics"></emph>derebus falſò creditis,<emph.end type="italics"></emph.end> dont ie <lb></lb>donneray encore icy vn exem<lb></lb>ple. </s> <s id="s.000032">L'on croyt que ſi on iette vne <lb></lb>pierre en haut le plus droit que <lb></lb>l'on peut: lors que l'on eſt dans <lb></lb>vn nauire qui ſingle à pleins voi<lb></lb>les, ou dans vn carroſſe qui va en <lb></lb>poſte, que la pierre tombera de<lb></lb>riere le lieu d'ou l'on la iette, quoy <lb></lb>que l'experience enſeigne qu'elle <lb></lb>retombe dans la main qui la iette <pb xlink:href="047/01/015.jpg"></pb>encore que le nauire, ou le carro<lb></lb>ſſe faſſe cent pas, tandis que la <lb></lb>pierre eſt dans l'air. </s> </p> <p type="main"> <s id="s.000033">Mais ie reſerue la raiſon de cecy <lb></lb>pour vn autre lieu, affin que ie ne <lb></lb>ſois pas containct de faire vne <lb></lb>preface, qui égale le liure qui ſuit <lb></lb>c'eſt pourquoy i'aioûte <expan abbr="ſeulemẽt">ſeulement</expan> <lb></lb>qu'auant que l'on entreprenne <lb></lb>les ouurages où les Machines <lb></lb>doiuent entrer, & que l'on ſe ſer<lb></lb>ue des ingenieurs & artiſans, qu'il <lb></lb>eſt à propos de leur faire expoſer <lb></lb>leurs deſſeins, & leurs modelles en <lb></lb>public, & <expan abbr="particulieremẽt">particulierement</expan> à la veûe <lb></lb>des excellents Geometres qui ſça<lb></lb>uent les vrayes raiſons de toutes <lb></lb>ſortes de Machines, & qui <expan abbr="peuuẽt">peuuent</expan> <lb></lb>preuoir les inconueniens, & les <lb></lb>obſtacles de l'air, de l'eau, & des <lb></lb>autres circonſtances, à faute de<lb></lb>quoy il arriue trop ſouuent que <lb></lb>pluſieurs font des deſpenſes ex- <pb xlink:href="047/01/016.jpg"></pb>ceſſiues dans leurs maiſons où ils <lb></lb>veulent faire de grandes <expan abbr="éleuatiõs">éleuations</expan> <lb></lb>d'eau, en ſe ſeruant de certains in<lb></lb>genieurs, qui ſe <expan abbr="diſẽt">diſent</expan> tres-experts, <lb></lb>& qui neantmoins ſont contrains <lb></lb>de s'enfuir honteuſement, lors <lb></lb>qu'ils n'ont peu venir à bout de <lb></lb>leurs deſſeins. </s> </p> <p type="main"> <s id="s.000034">Or pour éuiter ces deſpences <lb></lb>inutiles, il faudroit afficher par <lb></lb>les ruës, ou aduertir <expan abbr="publiquemẽt">publiquement</expan> <lb></lb>de l'ouurage que l'on veut entre<lb></lb>prendre, affin que tous les inge<lb></lb>nieurs apportaſſent leur modelle <lb></lb>en ſecret à iour nommé & qu'il <lb></lb>fuſt examiné par les plus habiles <lb></lb>Mathematiciens, par les inge<lb></lb>nieurs, & par les charpentiers de <lb></lb>moulins, qui <expan abbr="choiſiroiẽt">choiſiroient</expan> le meil<lb></lb>leur deſſein. </s> <s id="s.000035">Car il faut ioindre la <lb></lb>pratique à la theorie non ſeule<lb></lb>ment dans l'execution, mais auſſi <lb></lb>dans l'élection, des modelles, affin <pb xlink:href="047/01/017.jpg"></pb>qu'il n'y ayt rien à redire ny à re<lb></lb>faire dans les ouurages de grand <lb></lb>couſt, comme ſont les pompes <lb></lb>du pont neuf, & du nouueau que <lb></lb>l'on a fait au bas du Louure, & <lb></lb>que nul ne ſe ruine à faire accom<lb></lb>moder les lieux de plaiſir, ou l'on <lb></lb>veut auoir des fonteines des grot<lb></lb>tes, des arcs en Ciel, &c. </s> <s id="s.000036">Mais la <lb></lb>conſideration des pompes merite <lb></lb>vn diſcours plus particulier, & <lb></lb>cette preface eſt deſia trop lon<lb></lb>gue, c'eſt pourquoy i'ajoute ſeu<lb></lb>lement la table des Chapitres du <lb></lb>liure. </s> </p> <pb xlink:href="047/01/018.jpg"></pb> </section> <section> <p type="head"> <s id="s.000037"><emph type="center"></emph>TABLE DV LIVRE<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000038"><emph type="center"></emph>des Mechaniques.<emph.end type="center"></emph.end></s> </p> <p type="table"> <s id="s.000039">TABELLE WAR HIER <pb xlink:href="047/01/019.jpg"></pb></s> </p> </section> <section> <p type="head"> <s id="s.000040"><emph type="center"></emph><emph type="italics"></emph>Fautes de l'Impreſſion corrigées.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000041">Page 13, l. 13. <emph type="italics"></emph>inegaux.<emph.end type="italics"></emph.end></s> <s id="s.000042"> p. 16. l. 2. oſtez <emph type="italics"></emph>de <emph.end type="italics"></emph.end><lb></lb>ligne 7. & 8. DS <emph type="italics"></emph>à<emph.end type="italics"></emph.end> C. <emph type="italics"></emph></s> <s id="s.000043">de<emph.end type="italics"></emph.end> page 21. ligne 14. <lb></lb>au lieu de P. liſez D. </s> <s id="s.000044"> p. 24. l.1. au lieu de <emph type="italics"></emph>eſt <lb></lb>égal<emph.end type="italics"></emph.end> liſez. <emph type="italics"></emph>ſont chacune egales,<emph.end type="italics"></emph.end></s> <s id="s.000045"> l. 4. au lieu de ou <lb></lb>liſez <emph type="italics"></emph>&<emph.end type="italics"></emph.end> A<emph type="italics"></emph>tout au contraire.<emph.end type="italics"></emph.end> </s> <s id="s.000046">p.25. l. 18 pour <emph type="italics"></emph>ſap<lb></lb>prochant<emph.end type="italics"></emph.end> liſez <emph type="italics"></emph>approchent.<emph.end type="italics"></emph.end> </s> <s id="s.000047"> p.26. corrigez les <lb></lb>lettres de la 2 ligne & pour A de l'antepenul. <lb></lb>liſez E. </s> <s id="s.000048">p. 28. l 1. <emph type="italics"></emph>roüe<emph.end type="italics"></emph.end> </s> <s id="s.000049"> p. 30. l. 7. l'Organe. </s> <s id="s.000050">l <lb></lb>25. apres B liſez F </s> <s id="s.000051">p. 33. ligne 6 <emph type="italics"></emph>l'extremité<emph.end type="italics"></emph.end><lb></lb>A.</s> <s id="s.000052">l. 8. poids </s> <s id="s.000053">l.13. au lieu de F. liſez C. </s> <s id="s.000054">l. 25. <lb></lb>apres fardeau liſ E.</s> <s id="s.000055">l. 26 pour C. <emph type="italics"></emph>liſez<emph.end type="italics"></emph.end> G. </s> <s id="s.000056"><lb></lb>p. 34. l. 1 AG. </s> <s id="s.000057">l. 3. <emph type="italics"></emph>poids.<emph.end type="italics"></emph.end> </s> <s id="s.000058">l. 10. pour E. liſez. C. <lb></lb></s> <s id="s.000059">>p. 37. l. 16. apres <emph type="italics"></emph>immobile<emph.end type="italics"></emph.end> liſez A. </s> <s id="s.000060">p. 41 l. 8. <lb></lb>pour des liſ. du </s> <s id="s.000061">l.24. pour E liſez <emph type="italics"></emph>&.<emph.end type="italics"></emph.end> </s> <s id="s.000062">p. 45.l. 8 <lb></lb>pour B liſ. D.</s> <s id="s.000063">p. 51. l. antep. pour <emph type="italics"></emph>parce,<emph.end type="italics"></emph.end> liſ.<emph type="italics"></emph>par.<emph.end type="italics"></emph.end><lb></lb></s> <s id="s.000064">p. 52.l. penul. BM. </s> <s id="s.000065">p. 53 adioútez la lettre P <lb></lb>au bas de la figure. </s> <s id="s.000066">p. 57. l. 10. C A.</s> <s id="s.000067">p. 78<lb></lb>l. derniere effacez par.</s> </p> <p type="main"> <s id="s.000068">S'il y a quel qu'autre faute, le lecteur iudi<lb></lb>cieux la ſuppleera.</s> </p> <pb xlink:href="047/01/020.jpg"></pb> </section> <section> <p type="head"> <s id="s.000069"><emph type="center"></emph><emph type="italics"></emph>PRIVILEGE DV ROY.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000070">PAr lettres du Roy donnees à Paris <lb></lb>le mois d'Aouſt de l'année 1629. <lb></lb>ſignees Perrochel, & ſeelees du grand <lb></lb>ſceau de cire iaune, il eſt permis au <lb></lb>P. M. </s> <s id="s.000071">Merſenne Religieux Minime <lb></lb>de faire imprimer par tel Libraire que <lb></lb>bon luy ſemblera <emph type="italics"></emph>Pluſieurs Traittez de <lb></lb>Philoſophie, de Theologie, & de Mathema<lb></lb>tique.<emph.end type="italics"></emph.end></s> <s id="s.000072"> Et deffences ſont faites à toutes <lb></lb>perſonnes de quelque qualité qu'ils <lb></lb>ſoient de les faire imprimer, vendre & <lb></lb>diftribuer pendant le temps de ſix ans à <lb></lb>compter du iour que leſdits liures ſe<lb></lb>ront acheuez d'imprimer, comme il <lb></lb>eſt plus amplement porté dans les let<lb></lb>tres dudit Priuilege. </s> </p> <p type="main"> <s id="s.000073">Et ledit P. M. </s> <s id="s.000074">Merſenne à conſenty & con<lb></lb>ſent que Henry Guenon ioüiſſe dudit Pri<lb></lb>uilege, comme il eſt plus amplement decla<lb></lb>ré par l'accord fait entr eux. </s> </p> <p type="main"> <s id="s.000075"><emph type="center"></emph>Et leſdits liures ont eſté acheués d'imprimer le <lb></lb>30. Iuin 1634.<emph.end type="center"></emph.end></s> </p> </section> <section> <pb pagenum="1" xlink:href="047/01/021.jpg"></pb> <p type="head"> <s id="s.000076"><emph type="center"></emph>LES <lb></lb>MECHANIQVES <lb></lb>DE GALILEE FLOREN<lb></lb>TIN, INGENIEVR ET <lb></lb>Mathematicien du Duc <lb></lb>de Florence.<emph.end type="center"></emph.end></s> </p> </section> </front> <body> <chap> <p type="head"> <s id="s.000077"><emph type="center"></emph>CHAPITRE PREMIER.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000078"><emph type="center"></emph><emph type="italics"></emph>Dans lequel on void la Preface qui monſtre <lb></lb>l'vtilité des Machines.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000079">AVANT que d'entrepren<lb></lb>dre la ſpeculation des in<lb></lb>ſtrumens de la Mechani<lb></lb>que, il faut remarquer en <lb></lb>general les commoditez, & les profits <lb></lb>que l'on en peut tirer, afin que les arti<lb></lb>ſans ne croyent pas qu'ils puiſſent ſeruir <lb></lb>aux operations, dont ils ne ſont pas ca-<pb pagenum="2" xlink:href="047/01/022.jpg"></pb>pables, & que l'on puiſſe leuer de <expan abbr="grãds">grands</expan> <lb></lb>fardeaux auec peu de force: car la na<lb></lb>ture ne peut eſtre trompée, ni ceder à <lb></lb>ſes droits: & nulle reſiſtence ne peut <lb></lb>eſtre ſurmontée que par vne plus gran<lb></lb>de force, comme ie feray voir apres: & <lb></lb>conſequemment les Machines ne peu<lb></lb>uent ſeruir à leuer de plus grands far<lb></lb>deaux que ceux qu'vne force égale <lb></lb>peut leuer ſans l'ayde d'aucun inſtru<lb></lb>ment: c'eſt pourquoy il faut expliquer <lb></lb>les vrayes vtilitez des Machines, afin <lb></lb>que l'on ne trauaille pas en vain, & que <lb></lb>l'eſtude que l'on fera, reüſſiſſe heureu<lb></lb>ſement. </s> </p> <p type="main"> <s id="s.000080">Il faut donc icy conſiderer 4. choſes, <lb></lb>à ſçauoir le fardeau que l'on veut tranſ<lb></lb>porter d'vn lieu à vn autre: la force qui <lb></lb>le doit mouuoir; la diſtance par laquel<lb></lb>le ſe fait le mouuement; & le temps <lb></lb>dudit mouuement, parce qu'il ſert pour <lb></lb>en determiner la viſteſſe, puis qu'elle <lb></lb>eſt d'autant plus grande que le corps <lb></lb>mobile, ou le fardeau paſſe par vne plus <lb></lb>grande diſtance en meſme temps: de <lb></lb>ſorte que ſi l'on ſuppoſe telle reſiſtence, <lb></lb>telle force, & telle <expan abbr="diſtãce">diſtance</expan> determinée <lb></lb>que l'on voudra, il n'y a nul doute que <pb pagenum="3" xlink:href="047/01/023.jpg"></pb>la force requiſe conduira le fardeau à <lb></lb>la diſtance donnée, quoy que ladite <lb></lb>force ſoit treſ-petite, pourueu que l'on <lb></lb>diuiſe le fardeau en tant de parties que <lb></lb>la force en puiſſe mouuoir vne, car elle <lb></lb>les <expan abbr="trãſportera">tranſportera</expan> toutes les vnes apres les <lb></lb>autres; d'où il ſ'enſuit que la moindre <lb></lb>force du monde peut tranſporter tel <lb></lb>poids que l'on voudra. </s> </p> <p type="main"> <s id="s.000081">Mais l'on ne peut dire à la fin du <expan abbr="trãſ-port">tranſ<lb></lb>port</expan>, que l'on ayt remué vn grand far<lb></lb>deau auec peu de force, puis qu'elle a <lb></lb>touſiours eſté égale à chaque partie du <lb></lb>fardeau: de maniere que l'on ne gaigne <lb></lb>rien auec les inſtrumens, dautant que ſi <lb></lb>l'on applique vne petite force à vn <expan abbr="grãd">grand</expan> <lb></lb>fardeau, il faut beaucoup de temps, & <lb></lb>que ſi l'on veut le tranſporter en peu de <lb></lb>temps, il faut vne grande force. </s> <s id="s.000082">D'où <lb></lb>l'on peut conclurre qu'il eſt impoſſible <lb></lb>qu'vne petite force tranſporte vn <expan abbr="grãd">grand</expan> <lb></lb>poids dans moins de temps qu'vne plus <lb></lb>grande force. </s> </p> <p type="main"> <s id="s.000083">Neantmoins les Machines ſont vti<lb></lb>les pour mouuoir de grands fardeaux <lb></lb>tout d'vn coup ſans les diuiſer, parce <lb></lb>que l'on a ſouuent beaucoup de temps, <lb></lb>& peu de force, c'eſt pourquoy la lon- <pb pagenum="4" xlink:href="047/01/024.jpg"></pb>gueur du temps recompenſe le peu de <lb></lb>force: Mais celuy-là ſe tromperoit qui <lb></lb>voudroit abreger le temps en n'vſant <lb></lb>que d'vne petite force, & monſtreroit <lb></lb>qu'il n'entend pas la nature des Machi<lb></lb>nes, ny la raiſon de leurs effets. </s> </p> <p type="main"> <s id="s.000084">La ſeconde vtilité des inſtrumens <lb></lb>conſiſte en ce qu'on les applique à des <lb></lb>lieux <expan abbr="dõt">dont</expan> on ne pourroit tirer, ou tranſ<lb></lb>porter les fardeaux, & beaucoup de <lb></lb>choſes ſans leur ay de, comme l'on <expan abbr="ex-perimẽte">ex<lb></lb>perimente</expan> aux puits, <expan abbr="dõt">dont</expan> on tire de l'eau <lb></lb>auec vne chorde attachée aux poulies, <lb></lb>ou aux arbres des roües, par le moyen <lb></lb>deſquelles on en tire vne <expan abbr="quãtité">quantité</expan>, dans <lb></lb>vn certain <expan abbr="tẽps">temps</expan>, auec vne force limitée, <lb></lb>ſans qu'il ſoit poſſible <expan abbr="d'ẽ">d'en</expan> tirer vne plus <lb></lb>grande quantité auec vne force égale, <lb></lb>& en meſme temps. </s> <s id="s.000085">Auſſi les pompes <lb></lb>qui vuident le font des Nauires, n'ont <lb></lb>elles pas eſté inuentées pour puiſer, & <lb></lb>tirer vne plus grande quantité d'eau <lb></lb>dans le meſme temps, & par la meſme <lb></lb>force dont on vſe en puiſant auec vn <lb></lb>ſeau, mais parce qu'il eſt inutile à cet <lb></lb>effet, dautant qu'il ne peut puiſer l'eau <lb></lb>ſans ſ'enfoncer dedans, car il faudroit <lb></lb>le coucher au fond pour puiſer obli- <pb pagenum="5" xlink:href="047/01/025.jpg"></pb>quement le peu d'eau qui reſte: ce qui <lb></lb>ne peut arriuer, quand on le deſcend <lb></lb>auec vne chorde, qui le porte <expan abbr="perpen-diculairemẽt">perpen<lb></lb>diculairement</expan>: mais la pompe tire l'eau <lb></lb>iuſques à la derniere goute. </s> </p> <p type="main"> <s id="s.000086">La 3. vtilité des Machines eſt tres<lb></lb>grande, parce que l'on euite les grands <lb></lb>frais & le couſt en <expan abbr="vsãt">vsant</expan> d'vne force ina<lb></lb>nimée, ou ſans raiſon, qui fait les meſ<lb></lb>mes choſes que la force des hommes <lb></lb>animée, & conduite par le iugement, <lb></lb>comme il arriue lors que l'on fait meu<lb></lb>dre les moulins auec l'eau des eſtangs, <lb></lb>ou des fleuues, ou auec vn cheual, qui <lb></lb>ſupplée la force de 5. ou 6. hommes. </s> <s id="s.000087">Et <lb></lb>parce que le cheual a vne grande for<lb></lb>ce, & qu'il manque de diſcours, l'on <lb></lb>ſupplée le raiſonnement neceſſaire, par <lb></lb>le moyen des roües & des autres Ma<lb></lb>chines qui ſont ébranlées par la force <lb></lb>du cheual, & qui rempliſſent, & tranſ<lb></lb>portent le vaiſſeau d'vn lieu à l'autre & <lb></lb>qui le vuident ſuiuant le deſſein de l'In<lb></lb>genieur. </s> <s id="s.000088">Or il faut conclurre de tout <lb></lb>ce diſcours que l'on ne peut <expan abbr="riẽ">rien</expan> gaigner <lb></lb>en force que l'on ne le perde en temps, <lb></lb>& que la plus grande vtilité des Machi<lb></lb>nes <expan abbr="cõſiſte">conſiſte</expan> à épargner la dépence, com- <pb pagenum="6" xlink:href="047/01/026.jpg"></pb>me i'ay monſtré, & conſequemment <lb></lb>que ceux qui trauaillent à ſuppléer la <lb></lb>force, & le temps tout enſemble, ne <lb></lb>meritent nullement d'auoir du temps, <lb></lb>puis qu'ils l'employent ſi mal, comme <lb></lb>l'on verra à la ſuitte de ce traité. <lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000089"><emph type="center"></emph>CHAP. II.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000090"><emph type="center"></emph><emph type="italics"></emph>Des definitions, neceſſaires pour la ſcience <lb></lb>des Mechaniques.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000091">NOus commençons ce traité par les <lb></lb><expan abbr="definitiõs">definitions</expan>, & par les <expan abbr="ſuppoſitiõs">ſuppoſitions</expan> qui <lb></lb>ſont propres à cet art, afin d'en tirer les <lb></lb>cauſes, & les raiſons de tout ce qui ar<lb></lb>riue aux Machines, dont il faut expli<lb></lb>quer les effects, car chaque ſcience a ſes <lb></lb>definitions & ſes principes, qui ſont <expan abbr="cõ-me">com<lb></lb>me</expan> des ſemences treſ-fecondes, deſ<lb></lb>quelles naiſſent toutes les concluſions, <lb></lb>& le fruict que l'on en pretend retirer, <lb></lb>Or puis que les Machines ſeruent ordi<lb></lb>nairement pour tranſporter les choſes <lb></lb>peſantes, nous commençons par la de<lb></lb>finition de la <emph type="italics"></emph>peſanteur,<emph.end type="italics"></emph.end> que l'on peut <lb></lb>auſſi nommer <emph type="italics"></emph>grauité.<emph.end type="italics"></emph.end></s> </p> <pb pagenum="7" xlink:href="047/01/027.jpg"></pb> <p type="head"> <s id="s.000092"><emph type="center"></emph><emph type="italics"></emph>Premiere definition.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000093">La <emph type="italics"></emph>peſanteur<emph.end type="italics"></emph.end> d'vn corps eſt l'inclina<lb></lb>tion naturelle qu'il a pour ſe mouuoir, <lb></lb>& ſe porter en bas vers le centre de la <lb></lb>terre. </s> <s id="s.000094">Cette peſanteur ſe rencontre <lb></lb>dans les corps peſans à raiſon de la <expan abbr="quã-tité">quan<lb></lb>tité</expan> des parties materielles, dont ils <expan abbr="sõt">sont</expan> <lb></lb>compoſez; de ſorte qu'ils ſont dautant <lb></lb>plus peſans qu'ils ont vne plus grande <lb></lb>quantité deſdites parties ſouz vn meſ<lb></lb>me volume. </s> </p> <p type="head"> <s id="s.000095"><emph type="center"></emph><emph type="italics"></emph>Deuxieſme definition.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000096">Le <emph type="italics"></emph>moment<emph.end type="italics"></emph.end> eſt l'inclination du meſ<lb></lb>me corps, lors qu'elle n'eſt pas ſeule<lb></lb>ment conſiderée dans ledit corps, mais <lb></lb>conioinctement auec la ſituation qu'il <lb></lb>a ſur le bras d'vn leuier, ou d'vne balan<lb></lb>ce; & cette ſituation fait qu'il contre<lb></lb>peſe ſouuent à vn plus grands poids, à <lb></lb>raiſon de ſa plus <expan abbr="grãde">grande</expan> diſtance d'auec <lb></lb>le centre de la balance. </s> <s id="s.000097">Car cet éloi<lb></lb>gnement eſtant ioint à la propre peſan<lb></lb>teur du corps peſant, luy <expan abbr="dõne">donne</expan> vne plus <lb></lb>forte inclination à deſcendre: de ſorte <pb pagenum="8" xlink:href="047/01/028.jpg"></pb>que cette inclination eſt compoſée de <lb></lb>la peſanteur abſoluë du corps, & de l'é<lb></lb>loignement du centre de la balance, ou <lb></lb>de l'appuy du leuier. </s> <s id="s.000098">Nous appellerons <lb></lb>donc touſiours cette inclination com<lb></lb>poſée, <emph type="italics"></emph>moment,<emph.end type="italics"></emph.end> qui répond au <foreign lang="grc">ῥοωὴ</foreign> des <lb></lb>Grecs. </s> </p> <p type="head"> <s id="s.000099"><emph type="center"></emph><emph type="italics"></emph>Troiſieſme definition.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000100">Le centre de peſanteur de chaque <lb></lb>corps eſt le point autour duquel toutes <lb></lb>les parties dudit corps ſont également <lb></lb>balancées, ou équiponderantes: de ſor<lb></lb>te que ſi l'on ſ'imagine que le corps ſoit <lb></lb>ſouſtenu, ou ſuſpendu par ledit point, <lb></lb>les parties qui ſont à main droite, con<lb></lb>trepeſeront à celles de la gauche, celles <lb></lb>de derriere à celles de deuant, & celles <lb></lb>d'enhaut à celles d'en bas, & ſe tien<lb></lb>dront tellement en équilibre, que le <lb></lb>corps ne s'inclinera d'vn coſté ni d'au<lb></lb>tre, quelque ſituation qu'on luy puiſſe <lb></lb>donner, & qu'il demeurera touſiours <lb></lb>en cet eſtat. </s> <s id="s.000101">Or le centre de peſanteur <lb></lb>eſt le point du corps qui s'vniroit au <expan abbr="cẽ-tre">cen<lb></lb>tre</expan> des choſes peſantes, c'eſt à dire au <lb></lb>centre de la terre, s'il y pouuoit deſcen<lb></lb>dre. <pb pagenum="9" xlink:href="047/01/029.jpg"></pb></s> </p> </chap> <chap> <p type="head"> <s id="s.000102"><emph type="center"></emph>CHAP. III.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000103"><emph type="center"></emph><emph type="italics"></emph>Des ſuppoſitions de cet art.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000104"><emph type="center"></emph>I. SVPPOSITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000105">TOut corps peſant ſe meut telle<lb></lb>ment en bas que le centre de ſa <lb></lb>peſanteur ne ſort iamais hors de la ligne <lb></lb>droite, qui eſt décrite, ou imaginée de<lb></lb>puis ledit centre de peſanteur iuſques <lb></lb>à celuy de la terre. </s> <s id="s.000106">Ce qui eſt ſuppoſé <lb></lb>auec raiſon, car puis que le centre de <lb></lb>peſanteur de chaque corps ſe doit aller <lb></lb>vnir au centre commun des choſes pe<lb></lb>ſantes, il eſt neceſſaire qu'il y aille par <lb></lb>le chemin le plus court, c'eſt à dire par <lb></lb>la ligne droite, s'il n'a point d'empeſ<lb></lb>chement. </s> </p> <p type="head"> <s id="s.000107"><emph type="center"></emph>II. SVPPOSITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000108">Chaque corps peſe principalement <lb></lb>ſur le centre de ſa peſanteur, dans le<lb></lb>quel il ramaſſe, & vnit toute ſon impe<lb></lb>tuoſité, & ſa peſanteur. </s> </p> <pb pagenum="10" xlink:href="047/01/030.jpg"></pb> <p type="head"> <s id="s.000109"><emph type="center"></emph>III. SVPPOSITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000110">Le centre de la peſanteur de deux <lb></lb>corps également peſans eſt au milieu <lb></lb>de la ligne droite qui conioint les cen<lb></lb>tres de peſanteur deſdits corps; c'eſt à <lb></lb>dire que deux corps également peſans, <lb></lb>& également éloignez de l'appuy de la <lb></lb>balance ont le point de leur équilibre <lb></lb>au milieu de la commune conjonction <lb></lb>de leurs éloignemens égaux: par exem<lb></lb>ple, la diſtance CA, eſtant égale à la <lb></lb>diſtance CB, & les deux poids égaux <lb></lb>G & H, eſtant ſuſpendus aux points A <lb></lb>& B, il n'y a nulle raiſon pour laquelle <lb></lb>ils doiuent pluſtoſt s'incliner d'vn coſté <lb></lb>que de l'autre. </s> </p> <p type="main"> <s id="s.000111">Mais il faut remarquer que la diſtan<lb></lb>ce des poids, ou des corps peſans d'auec <lb></lb><figure id="id.047.01.030.1.jpg" xlink:href="047/01/030/1.jpg"></figure><lb></lb>l'appuy <lb></lb>ſe doit <lb></lb>meſurer <lb></lb>par les li<lb></lb>gnes <expan abbr="perpẽdiculaires">perpendiculaires</expan>, qui tombent des <lb></lb>points de la <expan abbr="ſuſpenſiõ">ſuſpenſion</expan>, ou des centres de <lb></lb>la peſanteur de chaque corps iuſques <lb></lb>au centre de la terre. </s> <s id="s.000112">De là vient que <pb pagenum="11" xlink:href="047/01/031.jpg"></pb>la diſtance BC, eſtant tranſportée en <lb></lb>CD, le poids D ne contrepeſera plus au <lb></lb>poids A, parce que la ligne tirée du <lb></lb>point de ſuſpenſion, ou du centre de <lb></lb>peſanteur du poids D iuſques au <expan abbr="cẽtre">centre</expan> <lb></lb>de la terre, ſera plus proche de l'appuy <lb></lb>C, que l'autre ligne tirée du point de la <lb></lb><expan abbr="ſuſpẽſion">ſuſpenſion</expan> de B, ou du <expan abbr="cẽtre">centre</expan> de peſanteur <lb></lb>du poids H. </s> <s id="s.000113">Il eſt donc neceſſaire que <lb></lb>les poids égaux ſoient tellement ſuſ<lb></lb>pendus de diſtances égales, que les li<lb></lb>gnes <expan abbr="perpẽdiculaires">perpendiculaires</expan> tirées par les cen<lb></lb>tres de leurs peſanteurs au centre de la <lb></lb>terre, ſe trouuent <expan abbr="égallemẽt">égallement</expan> éloignées <lb></lb>de l'appuy C, lors qu'elles paſſeront <lb></lb>vis à vis d'iceluy. </s> </p> <p type="head"> <s id="s.000114"><emph type="center"></emph>PREMIERE ADDITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000115">La figure qui ſuit explique mieux le <lb></lb>diſcours precedent, car il eſt euident <lb></lb>que le poids E qui pend au leuier AB <lb></lb>éleué en E ne peſe que <expan abbr="cõme">comme</expan> s'il eſtoit <lb></lb>au point K; & quand il eſt en G, il ne <lb></lb>peſe que comme s'il eſtoit au point I. </s> <s id="s.000116"><lb></lb>Or <expan abbr="l'õ">l'on</expan> peut s'inſtruire de pluſieurs cho<lb></lb>ſes par cette figure; dont nous <expan abbr="parlerõs">parlerons</expan> <lb></lb>apres, ie diray ſeulement icy que NO, <pb pagenum="12" xlink:href="047/01/032.jpg"></pb>repreſente auſſi vn leuier parallele à <lb></lb><figure id="id.047.01.032.1.jpg" xlink:href="047/01/032/1.jpg"></figure><lb></lb>BA, ou ſi l'on <lb></lb>veut, vne balan<lb></lb>ce, dont le <expan abbr="cẽtre">centre</expan> <lb></lb>ou l'appuy eſt en <lb></lb>D, & que ce le<lb></lb>uier peut ſeruir <lb></lb>pour abbaiſſer <lb></lb>les corps legers, <lb></lb>comme il arriue<lb></lb>roit ſi l'air eſtoit retenu dans l'eau: par <lb></lb>exemple, ſi LM eſtoient des veſſies <lb></lb>remplies d'air, car de n'ageantes qu'el<lb></lb>les ſeroient ſur l'eau, la force appliquée <lb></lb>à N hauſſant N vers A feroit abbaiſſer <lb></lb>ledit air; de ſorte que la Mechanique <lb></lb>peut auſſi bien s'appliquer, & ſeruir <lb></lb>pour abbaiſer les corps legers, comme <lb></lb>pour hauſſer les peſans. <lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000117"><emph type="center"></emph>CHAP. IV.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000118"><emph type="center"></emph><emph type="italics"></emph>Dans lequel l'vn des principes generaux des <lb></lb>Mechaniques eſt expliqué.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000119">APres auoir expliqué les ſuppoſi<lb></lb>tions, il faut eſtablir vn principe <pb pagenum="13" xlink:href="047/01/033.jpg"></pb>general, qui ſert pour demonſtrer ce <lb></lb>qui arriue à toutes ſortes de Machines, <lb></lb>à ſçauoir que les poids inegaux ſuſpen<lb></lb>dus à des diſtances inégales peſent éga<lb></lb>lement, & ſont en équilibre, quand leſ<lb></lb>dites diſtances ont meſme proportion <lb></lb>entr'elles que les poids. </s> <s id="s.000120">Ce qu'il faut <lb></lb>demonſtrer par la troiſieſme ſuppoſi<lb></lb>tion, dans laquelle il eſt dit, que les <lb></lb>poids égaux peſent <expan abbr="égalemẽt">également</expan> lors qu'ils <lb></lb>ſont également éloignez de l'appuy: car <lb></lb>c'eſt vne meſme choſe que d'attacher <lb></lb>des poids égaux à des <expan abbr="diſtāces">diſtances</expan> inégales. </s> </p> <p type="main"> <s id="s.000121">Ce qui ſe demonſtre par cette figure, <lb></lb><figure id="id.047.01.033.1.jpg" xlink:href="047/01/033/1.jpg"></figure><lb></lb><expan abbr="dãs">dans</expan> laquel<lb></lb>le DECF <lb></lb>repreſente <lb></lb>vn cylindre <lb></lb>homogene, <lb></lb>ou de meſ<lb></lb>me nature <lb></lb>en toutes ſes parties, lequel eſt attaché <lb></lb>par ſes deux bouts C & D aux points <lb></lb>AB, de ſorte que la ligne AB eſt égale <lb></lb>à la hauteur du cylindre CF. </s> </p> <p type="main"> <s id="s.000122">Il eſt certain que ſi on l'attache par le <lb></lb>milieu au point G, qu'il ſera en équili<lb></lb>bre, parce que ſi l'on tiroit vne ligne <pb pagenum="14" xlink:href="047/01/034.jpg"></pb>droite du point G au centre de la terre, <lb></lb>elle paſſeroit par le centre de la peſan<lb></lb>teur du ſolide EF, & par conſequent <lb></lb>toutes les parties qui ſont à l'entour de <lb></lb>ce centre ſeroient en équilibre, par la 3. <lb></lb>definition, car c'eſt meſme choſe que ſi <lb></lb>l'on attachoit les deux moitiez du cy<lb></lb>lindre aux deux points A & B. </s> </p> <p type="main"> <s id="s.000123">Suppoſons maintenant que le cylin<lb></lb>dre ſoit couppé en deux parties inéga<lb></lb>les par les points, ou par la ligne SI, il <lb></lb>eſt certain qu'elles ne ſeront pas équi<lb></lb>libres, & conſequemment qu'elles ne <lb></lb>demeureront pas en la ſituation prece<lb></lb>dente, n'ayant point d'autre ſouſtien <lb></lb>qu'aux points A & B. </s> <s id="s.000124">Mais ſi l'on atta<lb></lb>che vne chorde au point H, pour ſou<lb></lb>ſtenir le poids par le point I, G ſera en<lb></lb>core le centre de l'équilibre, parce que <lb></lb>l'on n'a pas changé la peſanteur, ny la <lb></lb>ſituation des parties du cylindre. </s> </p> <p type="main"> <s id="s.000125">D'où il s'enſuit que n'y ayant point de <lb></lb>changement aux parties du poids, ny <lb></lb>dans leur ſituation à l'égard de la ligne <lb></lb>AB, le meſme point G demeurera le <lb></lb>centre de l'équilibre, comme il l'a eſté <lb></lb>dés le commencement. </s> <s id="s.000126">Car puis que <lb></lb>la partie ES retiendra touſiours la meſ- <pb pagenum="15" xlink:href="047/01/035.jpg"></pb>me diſpoſition que la ligne AH, à la<lb></lb>quelle elle ſera parallele, ſi l'on y ad<lb></lb>iouſte le lien NL pour ſouſtenir SD <lb></lb>par ſon centre de peſanteur, & ſi l'on <lb></lb>adiouſte ſemblablement le lien MK <lb></lb>pour ſouſtenir la partie du cylindre CS <lb></lb>diſiointe d'auec SD, il n'y a nul doute <lb></lb>que ces deux parties demeureront en<lb></lb>core en équilibre au point G. </s> <s id="s.000127">Par où <lb></lb>l'on void que ces 2. parties eſtant ainſi <lb></lb>ſuſpenduës, & attachées ont vn mo<lb></lb>ment égal, lequel eſt l'origine, & la <lb></lb>ſource de l'équilibre du point G, en fai<lb></lb>ſant que la diſtance GN ſoit d'autant <lb></lb>plus grande que la diſtance GM, que <lb></lb>la partie du cylindre ES eſt plus gran<lb></lb>de que la partie SD. </s> <s id="s.000128">Ce qu'il eſt ayſé <lb></lb>de demonſtrer: dautant que la ligne <lb></lb>MH eſtant la moitié de la ligne HA, <lb></lb>& la ligne NH eſtant la moitié de la li<lb></lb>gne HB, toute la ligne MN ſera la <lb></lb>moitié de toute la ligne AB, dont GB <lb></lb>eſt encore la moitié, de ſorte que MN <lb></lb>& BG ſont égales entr'elles: deſquel<lb></lb>les ſi l'on oſte la commune partie GH, <lb></lb>MH ſera égale à GN. </s> </p> <p type="main"> <s id="s.000129">Or nous auons deſia fait voir que <lb></lb>MG eſt égale à HN. D'où il s'enſuit <pb pagenum="16" xlink:href="047/01/036.jpg"></pb>qu'il y a meſme raiſon de MN à HN, <lb></lb>que de KI à LI, & de la double de EI <lb></lb>à la double de DI, & <expan abbr="finalemẽt">finalement</expan> du ſo<lb></lb>lide CS au ſolide SD, dont CI, & DI <lb></lb>ſont les hauteurs. </s> </p> <p type="main"> <s id="s.000130">Il faut donc conclurre qu'il y a meſ<lb></lb>me raiſon de MG à GN, que de CI à <lb></lb>DS, & par conſequent que ces deux <lb></lb>corps CI & DS ne peſent pas ſeule<lb></lb>ment également, quand leurs <expan abbr="diſtãces">diſtances</expan> <lb></lb>d'auec l'appuy, ou le point d'où ils ſont <lb></lb>ſuſpendus, ſont en raiſon reciproque de <lb></lb>leurs peſanteurs, mais auſſi que c'eſt vne <lb></lb>meſme choſe que ſi l'on attachoit des <lb></lb>poids égaux à des diſtances égales: de <lb></lb>ſorte que la peſanteur de CS s'eſtend <lb></lb>& ſe communique en quelque maniere <lb></lb>virtuellement par delà le ſouſtien G, <lb></lb>duquel la peſanteur ID s'éloigne, & ſe <lb></lb>retire, comme l'on peut comprendre <lb></lb>par ce diſcours. </s> <s id="s.000131">Ce qui arriuera ſem<lb></lb>blablement ſi ces corps cylindriques <lb></lb>ſont reduits, & changez aux ſpheres X <lb></lb>& Z, ou en telles figures que l'on vou<lb></lb>dra, car l'on aura touſiours le meſme <lb></lb>équilibre, la figure n'eſtant qu'vne qua<lb></lb>lité, laquelle n'a pas la <expan abbr="puiſsãce">puiſsance</expan> de la pe<lb></lb>ſanteur, qui deriue de la ſeule <expan abbr="quãtité">quantité</expan>. </s> </p> <pb pagenum="17" xlink:href="047/01/037.jpg"></pb> <p type="main"> <s id="s.000132"><emph type="italics"></emph>Il faut donc conclurre que les poids inégaux <lb></lb>peſent également, & produiſent l'équilibre, <lb></lb>lors qu'ils ſont ſuſpendus de diſtances iné<lb></lb>gales qui ſont en raiſon reciproque deſdits <lb></lb>poids.<emph.end type="italics"></emph.end><lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000133"><emph type="center"></emph>CHAP. V.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000134"><emph type="center"></emph><emph type="italics"></emph>Où l'on void quelques aduertiſſemens ſur <lb></lb>le diſcours precedent.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000135">APres auoir <expan abbr="demõſtré">demonſtré</expan> que les mou<lb></lb>uements des poids inégaux ſont <lb></lb>égaux, quand ils ſont attachez à des <lb></lb>points, dont les diſtances d'auec l'ap<lb></lb>puy ont meſme proportion que les <lb></lb><figure id="id.047.01.037.1.jpg" xlink:href="047/01/037/1.jpg"></figure><lb></lb>poids, <lb></lb>il faut <lb></lb>enco<lb></lb>re re<lb></lb>marquer vne autre proprieté qui con<lb></lb>firme la verité precedente, car ſi l'on <lb></lb>conſidere la balance BD diuiſée en <lb></lb>parties inégales par le point C, & que les <lb></lb>poids <expan abbr="ſuſpẽdus">ſuſpendus</expan> aux points B & D ſoient <lb></lb>en raiſon reciproque des diſtances BC, <lb></lb>& CD, c'eſt à dire que le poids atta- <pb pagenum="18" xlink:href="047/01/038.jpg"></pb>ché à B ſoit d'autant plus grand que le <lb></lb>poids attaché à D, que la diſtance CD <lb></lb>eſt plus grande que la diſtance CB, il <lb></lb>eſt certain que l'vn contrepeſera l'au<lb></lb>tre, & qu'ils ſeront en equilibre: & que <lb></lb>ſi l'on adiouſte quelque choſe à l'vn, par <lb></lb>exemple, au poids D, qu'il deſcendra <lb></lb>en bas en I, & conſequemment qu'il <lb></lb>éleuera les poids B en G. </s> <s id="s.000136">Mais ſi l'on <lb></lb>conſidere le mouuement du poids D, <lb></lb>& du poids B, <expan abbr="l'õ">l'on</expan> trouuera que le mou<lb></lb>uement de D deſcendant en I ſur paſſe <lb></lb>autant le mouuement de B en G, com<lb></lb>me la diftance DC ſurpaſſe la diſtance <lb></lb>CB, ou CG, car les deux angles GCB, <lb></lb>& DC I ſont égaux, & <expan abbr="conſequemmẽt">conſequemment</expan> <lb></lb>les deux parties de cercle décrites par <lb></lb>D & par B ſont ſemblables, & ont meſ<lb></lb>me proportion entr'elles que leurs ſe<lb></lb>midiametres BC, & CD, par leſquels <lb></lb>elles ont eſté décrites. </s> </p> <p type="main"> <s id="s.000137">D'où il ſ'enſuit que la viſteſſe du poids <lb></lb>D, qui <expan abbr="deſcẽd">deſcend</expan> en I ſurpaſſe autant cel<lb></lb>le du poids B qui monte en G, que la <lb></lb>peſanteur de B eſt plus grande que cel<lb></lb>le de D; & que l'on ne peut éleuer B <lb></lb>que D ne ſe meuue plus viſte: parce <lb></lb>que la viſteſſe de D <expan abbr="recompẽſe">recompenſe</expan> la gran- <pb pagenum="19" xlink:href="047/01/039.jpg"></pb>de reſiſtence de B, qui monte <expan abbr="lentemẽt">lentement</expan> <lb></lb>en G, tandis que D deſcend bien viſte <lb></lb>en I, de ſorte que G a autant de tardi<lb></lb>ueté que de peſanteur, comme D a au<lb></lb>tant de viſteſſe que de legereté. </s> </p> <p type="main"> <s id="s.000138">Or il eſt ayſé de conclurre par tout ce <lb></lb>diſcours la grande force qu'apporte la <lb></lb>viſteſſe du mouuement, pour accroiſtre <lb></lb><figure id="id.047.01.039.1.jpg" xlink:href="047/01/039/1.jpg"></figure><lb></lb>la puiſ<lb></lb>ſance du <lb></lb>mobile, <lb></lb>laquelle <lb></lb>eſt d'autant plus grande que le mouue<lb></lb>ment eſt plus viſte. </s> <s id="s.000139">Mais auant que de <lb></lb>paſſer outre, il faut remarquer que les <lb></lb>diſtances qui ſont entre les bras de la <lb></lb>balance, & l'appuy doiuent eſtre me<lb></lb>ſurées par la diſtance horizontale: par <lb></lb>exemple, les poids A & B ſont égale<lb></lb>ment éloignez de l'appuy C: c'eſt pour<lb></lb>quoy ils ſont en équilibre, qu'ils per<lb></lb>dent, lors que le poids B eſt éleué en D, <lb></lb>dautant que la ligne tirée <expan abbr="perpendicu-lairemẽt">perpendicu<lb></lb>lairement</expan> de D ſur l'horizon BCA vers <lb></lb>le centre de la terre, s'approche plus <lb></lb>pres de l'appuy C, que ne fait le point <lb></lb>B: & partant D ne peſe pas tant que B, <lb></lb>à raiſon de ſa ſituation, & par conſe- <pb pagenum="20" xlink:href="047/01/040.jpg"></pb>quent D n'eſt plus équilibre à raiſon <lb></lb>que la diſtance horizontale de D à C <lb></lb>eſt moindre que celle de B à C. <lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000140"><emph type="center"></emph>CHAP. VI.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000141"><emph type="center"></emph><emph type="italics"></emph>De la Romaine, de la Balance, & du Leuier,<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000142">LE meſme principe qui a eſté expli<lb></lb>qué dans le 4. & le 5. chap. </s> <s id="s.000143">ſert en<lb></lb>core pour entendre la nature de ces 3. <lb></lb>inſtrumens, dont le premier (que les <lb></lb>Latins appellent <emph type="italics"></emph>Statera,<emph.end type="italics"></emph.end> les Grecs <lb></lb><foreign lang="grc">φάλαγξ</foreign> <emph type="italics"></emph>Phalanx<emph.end type="italics"></emph.end>; & que nous appellons <lb></lb>vulgairement la <emph type="italics"></emph>Romaine,<emph.end type="italics"></emph.end> le <emph type="italics"></emph>Crochet,<emph.end type="italics"></emph.end> le <lb></lb><emph type="italics"></emph>Pezon,<emph.end type="italics"></emph.end> ou le <emph type="italics"></emph>Poids<emph.end type="italics"></emph.end>) eſt vtile pour peſer <lb></lb>toutes ſortes de fardeaux par le moyen <lb></lb>d'vn contrepoids mobile, que l'on <expan abbr="nõ-me">nom<lb></lb>me</expan> le <emph type="italics"></emph>Pezon,<emph.end type="italics"></emph.end> & que les Grecs appellent <lb></lb><foreign lang="grc">αντισήχωμα, σφαίρωμα, ἀρτήμα</foreign>, & les Latins <lb></lb><emph type="italics"></emph>æquipondium.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000144">Soit donc la Romaine BD, dont le <lb></lb>ſouſtien ſoit au point C, que les Grecs <lb></lb>appellent <foreign lang="grc">σωάρτιον, & ὑπομόχλιον</foreign>, & les La<lb></lb>tins <emph type="italics"></emph>agina, ſpartum,<emph.end type="italics"></emph.end> & <emph type="italics"></emph>anſa.<emph.end type="italics"></emph.end></s> <s id="s.000145"> Que B ſoit <lb></lb>le fardeau que l'on veut peſer, & D le <lb></lb>contrepoids. </s> <s id="s.000146">Ie dis que s'il y a meſme <pb pagenum="21" xlink:href="047/01/041.jpg"></pb>raiſon de la diſtance DC à CB, que du <lb></lb>poids B au contrepoids D, qu'ils ſeront <lb></lb>en équilibre, parce que les diſtances des <lb></lb>bras, ou des branches de la Romaine <lb></lb>ſont en raiſon reciproque des poids qui <lb></lb>ſe contrebalancent. </s> </p> <p type="main"> <s id="s.000147">Or cet inſtrument n'eſt pas different <lb></lb>du leuier, qui ſert à remuer des fardeaux <lb></lb>treſ-lourds, & treſ-peſans auec peu de <lb></lb>force, comme l'on void dans cette meſ<lb></lb>me figure, dans laquelle B repreſente <lb></lb>le fardeau, qu'il faut leuer en G; & C <lb></lb>repreſente l'appuy ſur lequel le leuier <lb></lb>BP preſſe, & ſe meut & la main, ou <lb></lb>quelque autre force preſſe le leuier au <lb></lb>point D, & l abaiſſe iuſques à I pour fai<lb></lb>re monter B en G. </s> </p> <p type="main"> <s id="s.000148">Cecy eſtant poſé, la force miſe <lb></lb>en D leuera le poids B toutes & <lb></lb>quantesfois qu'il y aura meſme raiſon <lb></lb>de la <expan abbr="diſtãce">diſtance</expan> DC à la diſtance BC, que <lb></lb>du poids B à la force D, de ſorte que <lb></lb>l'on peut touſiours diminuer la force à <lb></lb>meſure que l'on allonge la partie du le<lb></lb>uier CD: par exemple, parce qu'il y a <lb></lb>5. fois plus loin de C à D que de C à B, <lb></lb>ſi B peſe 5. liures, la force d'vne liure le <lb></lb>tiendra en équilibre au point D, parce <pb pagenum="22" xlink:href="047/01/042.jpg"></pb>que CD eſt quintuple de CB. </s> </p> <p type="main"> <s id="s.000149">Mais l'auantage de ces 3. inſtru<lb></lb>mens ne conſiſte pas à ſurmonter, ou à <lb></lb>tromper la nature, en faiſant qu'vne <lb></lb>petite force ſurmonte vne grande reſi<lb></lb>ſtence, car on fera le meſme effet en <lb></lb>meſme temps, & auec meſme force <expan abbr="sãs">sans</expan> <lb></lb>la <expan abbr="diſtãce">diſtance</expan> CD, laquelle eſt cauſe que la <lb></lb>force D a cinq fois plus de chemin à fai<lb></lb>re de D en I, que le poids n'en fait de <lb></lb>B en G, & conſequemment elle em<lb></lb><figure id="id.047.01.042.1.jpg" xlink:href="047/01/042/1.jpg"></figure><lb></lb>ploye <lb></lb>5. fois <lb></lb>pl<emph type="sup"></emph>9<emph.end type="sup"></emph.end> de <lb></lb>temps <lb></lb>que ſi elle eſtoit en L, pour ſe tranſpor<lb></lb>ter en M. </s> <s id="s.000150">Or la force D eſtant en L le<lb></lb>uera la cinquieſme partie du poids B de <lb></lb>B en G, en meſme temps que D leue B, <lb></lb>de ſorte qu'elle leuera tout le poids B <lb></lb>en G en repetant 5. fois le chemin LM; <lb></lb>ce qui eſt la meſme choſe que de faire <lb></lb>vne fois le chemin DI: & conſequem<lb></lb>ment le tranſport de B en G ne requiert <lb></lb>pas moins de force, ou moins de <expan abbr="tẽps">temps</expan>, <lb></lb>ou vn chemin plus court, ſoit que l'on <lb></lb>mette la force en D, ou en L. </s> </p> <p type="main"> <s id="s.000151">D'où il faut conclurre que le leuier <pb pagenum="23" xlink:href="047/01/043.jpg"></pb>ſert ſeulement pour mouuoir les far<lb></lb>deaux tout d'vn coup, & à vne ſeule <lb></lb>fois, qu'il faudroit autrement mouuoir <lb></lb>par parties, & à pluſieurs fois. </s> </p> <p type="head"> <s id="s.000152"><emph type="center"></emph>II. ADDITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000153">L'on pourroit icy traiter des deux <lb></lb>autres ſortes de leuiers, <expan abbr="dõt">dont</expan> parle Guid<lb></lb>Vbalde dans ſes Mechaniques, mais il <lb></lb>ſuffit de comprendre la raiſon de celuy <lb></lb>que propoſe cét Autheur, car nous par<lb></lb>lerons des autres ailleurs. </s> <s id="s.000154">I'adjouſte <lb></lb>ſeulement cette figure, par laquelle <lb></lb>l'on comprendra mieux ſon intention. <lb></lb><figure id="id.047.01.043.1.jpg" xlink:href="047/01/043/1.jpg"></figure><lb></lb>Soit <expan abbr="dõc">donc</expan> le <lb></lb>leuier AF, <lb></lb>par lequel <lb></lb>la force ap<lb></lb>pliquée en F <lb></lb>leue le far<lb></lb>deau A iuſ<lb></lb>ques à G, <lb></lb>encore que <lb></lb>elle ſoit 4. <lb></lb>fois moindre qu'A, mais l'arc de ſon <lb></lb>chemin FI eſt quatre fois plus grand <lb></lb>que l'arc AG, car FM, ML, LK, <pb pagenum="24" xlink:href="047/01/044.jpg"></pb>& K I'eſt égal à AG, comme l'on void <lb></lb>par la conſtruction, de ſorte que F ne <lb></lb>gaigne rien en force qu'il ne le perde en <lb></lb>chemin, ou ne gaigne rien en chemin <lb></lb>qu'il ne le perde en force. </s> <s id="s.000155">Or la plus <lb></lb>grande difficulté des Mechaniques <expan abbr="cõ-ſiſte">con<lb></lb>ſiſte</expan>, ce me ſemble, à ſçauoir pourquoy <lb></lb>la plus grande diſtance de la force, ou <lb></lb>du poids F d'auec l'appuy B augmente <lb></lb>ladite force, & pourquoy le poids A ou <lb></lb>C eſtant tranſporté en F a quatre fois <lb></lb>plus de force que deuant. </s> <s id="s.000156">Ariſtote croit <lb></lb>que la raiſon en doit eſtre priſe de ce <lb></lb>que le centre B empeſche plus les poids <lb></lb>prochains que les éloignez, dautant <lb></lb>qu'il les contraint dauantage, & leur <lb></lb>communique <expan abbr="tãt">tant</expan> qu'il peut ſon immo<lb></lb>bilité, de ſorte que le poids eſtant en C <lb></lb>ne peut ſe mouuoir que de C en H, au <lb></lb>lieu qu'eſtant en F il fait 4. fois autant <lb></lb>de chemin en meſme temps, & eſtant <lb></lb>en D il en fait deux fois autant par le <lb></lb>quart de cercle commençant en D. </s> <s id="s.000157">Ce <lb></lb>que l'on peut <expan abbr="ayſémẽt">ayſément</expan> appliquer à l'ap<lb></lb>proche, ou à la diſtance des creatures <lb></lb>d'auec la perfection Diuine, laquelle <lb></lb>rend les creatures raiſonnables dautant <lb></lb>plus fixes & immobiles dans ſa grace, & <pb pagenum="25" xlink:href="047/01/045.jpg"></pb>dans la ferme reſolution du bien, qu'el<lb></lb>les s'en approchent plus prés. </s> </p> <p type="main"> <s id="s.000158">Mais pour retourner à la raiſon pre<lb></lb>cedente, ie dy que le poids qui eſt en F <lb></lb>veut tomber en droite ligne par FNP <lb></lb>vers le centre de la terre, & qu'eſtant <lb></lb>contraint par l'appuy, ou le centre B de <lb></lb>tomber par le cercle FI, qu'il a plus de <lb></lb>liberté, & qu'il s'approche 4. fois da<lb></lb>uantage de la perpendiculaire FP, que <lb></lb>lors qu'il deſcend par l'arc CH, com<lb></lb>me ie demonſtre par l'angle de contin<lb></lb>gence PFN, qui eſt ſouzquadruple de <lb></lb>l'angle de contingence HCO, & <expan abbr="con-ſequẽment">con<lb></lb>ſequemment</expan> la ligne de contrainte HO <lb></lb>eſt quadruple de la ligne PN: par où <lb></lb>l'on void clairement que B, & F s'ap<lb></lb>prochant également du centre de la <lb></lb>terre en meſme <expan abbr="tẽps">temps</expan> par les arcs CH, <lb></lb>& FP, puiſque les lignes FN & BH <lb></lb>ſont égales, que F eſt moins contraint <lb></lb>que C. </s> </p> <p type="main"> <s id="s.000159">L'on peut dire la meſme choſe de la <lb></lb>force de la main miſe en F, dont <expan abbr="l'intẽ-tion">l'inten<lb></lb>tion</expan> eſt de ſe mouuoir par la ligne droi<lb></lb>te FP. </s> <s id="s.000160">Ie laiſſe maintenant pluſieurs <lb></lb>autres conſiderations qui ſe peuuent <lb></lb>expliquer par cette figure: par exem- <pb pagenum="26" xlink:href="047/01/046.jpg"></pb>ple, que le poids F, ou B <expan abbr="eſtãt">eſtant</expan> en ſa plei<lb></lb>ne liberté, deſcend de F en P ou de B <lb></lb>en I en deux fois autant de temps qu'il <lb></lb>deſcend de F en N, comme i'ay mon<lb></lb>ſtré ailleurs. <lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000161"><emph type="center"></emph>CHAP. VII.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000162"><emph type="center"></emph><emph type="italics"></emph>Du Tour, de la Rouë, de la Gruë, du Guin<lb></lb>dax, & des autres inſtrumens <lb></lb>ſemblables.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000163">LEs Latins appellent le Tour <emph type="italics"></emph>axis in <lb></lb>peritrochio,<emph.end type="italics"></emph.end> parce qu'il n'eſt autre <lb></lb>choſe qu'vn axe, ou vn eſſieu, <expan abbr="dõt">dont</expan> les ex<lb></lb>tremitez ſont appuyées ſur deux pieces <lb></lb>de bois, ſur leſquelles il ſe tourne. </s> <s id="s.000164">Or la <lb></lb>nature de cet inſtrument depend im<lb></lb>mediatement du leuier, car il n'eſt au<lb></lb>tre choſe qu'vn leuier perpetuel, & <expan abbr="cõ-tinué">con<lb></lb>tinué</expan>. </s> <s id="s.000165">Car ſoit le leuier BAC, dont le <lb></lb>ſouſtien eſt en A; & que le poids G ſoit <lb></lb>attaché au point B, & que la force ſoit <lb></lb>au point C, ſi l'on tranſporte le leuier <lb></lb>en AD, le poids G ſe hauſſera vers D. </s> <s id="s.000166"><lb></lb>Mais ſi l'on veut le faire monter plus <lb></lb>haut, il faut arreſter le poids en D, afin <pb pagenum="27" xlink:href="047/01/047.jpg"></pb>de le releuer encore vne autrefois de B <lb></lb>à D en remettant le leuier dans la meſ<lb></lb>me ſituation qu'il auoit deuant, & de <lb></lb>leuer peu à peu le poids G, iuſques à ce <lb></lb>qu'il ſoit arriué au point B, ou à tel au<lb></lb>tre point que l'on voudra. </s> </p> <p type="main"> <s id="s.000167">Mais la repetition trop frequente de <lb></lb><figure id="id.047.01.047.1.jpg" xlink:href="047/01/047/1.jpg"></figure><lb></lb>cette action <expan abbr="eſtãt">eſtant</expan> <lb></lb>trop incommode, <lb></lb>ou trop ennuyeu<lb></lb>ſe, l'on a inuenté <lb></lb>le Tour, & la <lb></lb>Rouë, qui ioi<lb></lb>gnent enſemble <lb></lb>vne infinité de le<lb></lb>uiers, afin de continuer <expan abbr="l'operatiõ">l'operation</expan> ſans <lb></lb>aucune interruption. </s> <s id="s.000168">C'eſt pour ce ſu<lb></lb>iet que la rouë ſe meut à l'entour du <lb></lb>centre A, dont le rayon eſt AC, & le <lb></lb>ſemidiametre de ſon eſſieu eſt AB; le<lb></lb>quel doit eſtre d'vne matiere bien ſo<lb></lb>lide, & bien forte, parce qu'il ſupporte <lb></lb>toute la peſanteur du fardeau. </s> </p> <p type="main"> <s id="s.000169">L'eſſieu A trauerſe la rouë par le mi<lb></lb>lieu, & doit eſtre ſouſtenu de deux <lb></lb>pieds tres-forts, & eſtre enuironné de <lb></lb>la chorde DBG, à laquelle on attache <lb></lb>le fardeau G. </s> <s id="s.000170">Il faut auſſi mettre vne <pb pagenum="28" xlink:href="047/01/048.jpg"></pb>autre chorde àlentour de la <expan abbr="grãde">grande</expan> rouë, <lb></lb>afin d'y attacher l'autre fardeau I. </s> <s id="s.000171">Or <lb></lb>cecy eſtant poſé, il eſt euident que ſi <lb></lb>CA eſt à BA comme le fardeau G au <lb></lb>fardeau I, que le poids I ſouſtiendra & <lb></lb><expan abbr="contrebalãcera">contrebalancera</expan> G, & que ſi l'on adiou<lb></lb>ſte quelque force, ou poids à I, qu'il <lb></lb>l'emportera. </s> </p> <p type="main"> <s id="s.000172">Et parce que les chordes qui <expan abbr="ſouſtiẽ-nent">ſouſtien<lb></lb>nent</expan> le poids touchent touſiours la <expan abbr="cir-conferẽce">cir<lb></lb>conference</expan> de la rouë auec laquelle l'eſ<lb></lb>ſieu tourne, & conſequemment qu'el<lb></lb>les ſont touſiours en meſme ſituation à <lb></lb>l'égard des diſtances BA, & CA, le <lb></lb>mouuement ſe continuë perpetuelle<lb></lb>ment, & le poids I deſcendant fait <expan abbr="mõ-ter">mon<lb></lb>ter</expan> le poids G. </s> <s id="s.000173">Mais il faut remarquer <lb></lb>qu'il eſt neceſſaire de mettre la chorde <lb></lb>à l'entour de la rouë, afin que le poids <lb></lb>demeure ſuſpendu du point de la cir<lb></lb>conference que la chorde touche: Car <lb></lb>ſi la chorde eſtoit pendante du point F, <lb></lb>elle couperoit la rouë par FN, & par <lb></lb><expan abbr="conſequẽt">conſequent</expan> elle ne pourroit ſe mouuoir, <lb></lb>parce que le moment, ou la force du <lb></lb>poids N ſeroit diminuée, puis qu'elle <lb></lb>n'eſt pas plus grande que ſi la chorde <lb></lb>eſtoit attachée au point N, dautant que <pb pagenum="29" xlink:href="047/01/049.jpg"></pb>ſa diſtance d'auec le centre A eſt deter<lb></lb>minée par la ligne AN, (comme l'on <lb></lb>demonſtre par la perpendiculaire FN) <lb></lb>& non par le ſemidiametre FA. </s> <s id="s.000174">Il faut <lb></lb>donc que la force inanimée, qui n'a <lb></lb>point d'autre vertu que d'aller en bas, <lb></lb>ſoit pendue à vne chorde qui touche la <lb></lb>rouë & qui ne la coupe pas. </s> </p> <p type="main"> <s id="s.000175">Mais ſi la force eſt animée, elle peut <lb></lb>faire tourner la rouë pour leuer le poids <lb></lb>en quelque endroit de la rouë qu'elle ſe <lb></lb>rencontre: par exemple en F, mais elle <lb></lb>tirera par la ligne trauerſante FL qui <lb></lb>fera vn angle droit auec la ligne AF, & <lb></lb>non par la perpendiculaire FN. L'on <lb></lb>peut neantmoins faire ſeruir la force <lb></lb>inanimée à tous les points de la circon<lb></lb>ference par le moyen de la poulie L, car <lb></lb>le poids, ou la force K tirera par la ligne <lb></lb>droite LK, & leuera le poids G en B, <lb></lb>& <expan abbr="conſequemmẽt">conſequemment</expan> elle agit par la ligne <lb></lb>FL, & par ce moyen elle ſe conſerue <lb></lb>touſiours en meſme diſtance d'auec le <lb></lb>centre de la rouë, & de l'eſſieu A: de <lb></lb>ſorte que le leuier BC ſe rend perpe<lb></lb>tuel par l'entremiſe de la rouë. </s> </p> <p type="main"> <s id="s.000176">Il faut donc conclurre de tout ce diſ<lb></lb>cours que dans cét inſtrument la force <pb pagenum="30" xlink:href="047/01/050.jpg"></pb>C ou F doit touſiours auoir meſme <expan abbr="pro-portiõ">pro<lb></lb>portion</expan> auec le poids, que le ſemidiame <lb></lb>tre de l'axe BA a auec le ſemidiametre <lb></lb>de la rouë AC. </s> </p> <p type="main"> <s id="s.000177">Quant à la Gruë elle eſt de meſme <lb></lb>nature que le Tour, mais le Cabeſtan, <lb></lb>le Guindax, ou l'orgene eſt vn peu dif<lb></lb>rent, car ſon axe ſe meut perpendicu<lb></lb>laire à l'orizon, & ſa rouë ſe meut hori<lb></lb>zontalement, au lieu que l'axe du Tour <lb></lb><figure id="id.047.01.050.1.jpg" xlink:href="047/01/050/1.jpg"></figure><lb></lb>ſe meut horizontale<lb></lb>ment, & ſa rouë <expan abbr="per-pendiculairemẽt">per<lb></lb>pendiculairement</expan>. </s> <s id="s.000178">Ce <lb></lb>qui eſt tres-ayſé à <expan abbr="cõ-prendre">com<lb></lb>prendre</expan> par le moyen <lb></lb>de cette figure, dont <lb></lb>il faut s'imaginer que <lb></lb>l'axe DE ſoit <expan abbr="perpẽ-diculaire">perpen<lb></lb>diculaire</expan> à l'horizon, & que la rouë F <lb></lb>CG ſoit parallele au meſme horizon. </s> <s id="s.000179"><lb></lb>Or la chorde DH tirera, ou trainera le <lb></lb>fardeau H iuſques à l'axe B, ou iuſques <lb></lb>où l'on voudra, par la force d'vn hom<lb></lb>me, ou d'vn cheual qui conduira le le<lb></lb>uier B à l'entour de la circonference F <lb></lb>GC, & fera autant de tours comme il <lb></lb>eſt neceſſaire pour attirer le fardeau par <lb></lb>le moyen de la chorde DH, qui ſ'en- <pb pagenum="31" xlink:href="047/01/051.jpg"></pb>tortille à l'entour de l'eſſieu DEA: <lb></lb>d'où il eſt ayſé de conclurre la fabrique <lb></lb>du Guindax, ou du Cabeſtan. </s> </p> <p type="main"> <s id="s.000180">Cecy eſtant poſé, il eſt euident que <lb></lb>le point, ou le centre du ſouſtien eſt en <lb></lb>B, & que l'éloignement de la force F ſe <lb></lb>prend du point B, & celuy du poids de <lb></lb>B à D, de ſorte que FBD forme vn le<lb></lb>uier, en vertu duquel la force F acquiert <lb></lb>vne force ègale à la reſiſtance du poids, <lb></lb>lors que la diſtance FB a meſme pro<lb></lb>portion à BD, que le fardeau H à la <lb></lb>force F. </s> </p> <p type="main"> <s id="s.000181">Mais la nature n'eſt point trompée ny <lb></lb>ſurmontée, & l'on ne gaigne rien, par<lb></lb>ce que ſi le fardeau a dix fois plus de re<lb></lb>ſiſtence que la force F, la diſtance FB <lb></lb>doit neceſſairement eſtre decuple de <lb></lb>BD, & la circonference FCG decuple <lb></lb>de la <expan abbr="circõference">circonference</expan> EAD; de ſorte que <lb></lb>le poids ne fera que la dixieſme partie <lb></lb>du chemin de la circonference GCF; <lb></lb>par <expan abbr="cõſequent">conſequent</expan> ſi l'on diuiſoit le fardeau <lb></lb>en 10. parties, chacune répondroit à la <lb></lb>dixieſme partie du mouuement & de la <lb></lb>force F, c'eſt pourquoy ſi l'on portoit <lb></lb>en dix voyages chaque dixieſme partie <lb></lb>autour de l'axe, l'on ne chemineroit <pb pagenum="32" xlink:href="047/01/052.jpg"></pb>pas <expan abbr="dauãtage">dauantage</expan> que ſi l'on faiſoit vne fois <lb></lb>le tour GCF, & l'on <expan abbr="cõduiroit">conduiroit</expan> le meſ<lb></lb>me fardeau en meſme temps à la meſ<lb></lb>me diſtance. </s> </p> <p type="main"> <s id="s.000182">Il faut donc conclurre que la com<lb></lb>modité de cette Machine conſiſte ſeu<lb></lb>lement à attirer le fardeau tout à la fois <lb></lb>ſans le diuiſer; & qu'elle ne ſert pas <lb></lb>pour l'attirer plus ayſément, ou plus <lb></lb>viſte, ou plus loin que la meſme force <lb></lb>le <expan abbr="cõduiroit">conduiroit</expan> en le diuiſant en 10.parties. <lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000183"><emph type="center"></emph>CHAP. VIII.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000184"><emph type="center"></emph><emph type="italics"></emph>De la force, & de l'vſage des Poulies.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000185">APres auoir conſideré les <expan abbr="inſtrumẽs">inſtrumens</expan> <lb></lb>qui ſe reduiſent aux contrepoids, <lb></lb>& à l'équilibre, comme à leur principe, <lb></lb><figure id="id.047.01.052.1.jpg" xlink:href="047/01/052/1.jpg"></figure><lb></lb>& à leur <lb></lb><expan abbr="fondemẽt">fondement</expan> <lb></lb>il faut par<lb></lb>ler d'vne <lb></lb>autre ſor<lb></lb>te de le<lb></lb>uier pour entendre la nature des pou<lb></lb>lies, & de beaucoup d'autres effets Me- <pb pagenum="33" xlink:href="047/01/053.jpg"></pb>chaniques. </s> <s id="s.000186">Or le leuier, dont nous <lb></lb>auons parlé, ſuppoſe que le poids ſoit <lb></lb>à l'vne de ſes extremitez, & la force à <lb></lb>l'autre; de ſorte que ſon ſouſtien doit <lb></lb>eſtre entre ſes deux extremitez. </s> <s id="s.000187">Mais <lb></lb>ſi l'on met le ſouſtien à l'extremité du <lb></lb>leuier, & la force à l'autre extremité C, <lb></lb>& que le point D ſoit attaché à quelque <lb></lb>point du milieu: par exemple, au point <lb></lb>B, il eſt certain que ſi le poids eſt égale<lb></lb>ment éloigné des deux extremes, com<lb></lb>me quand il eſt au point F, que la force <lb></lb>qui le ſouſtient en F ſera également di<lb></lb>uiſée: & par conſequent la moitié du <lb></lb>poids eſt ſouſtenuë par C, & l'autre <lb></lb>moitié par A. </s> </p> <p type="main"> <s id="s.000188">S'il arriue que le fardeau ſoit attaché <lb></lb>ailleurs, par exemple en B, la force C <lb></lb>ſouſtiendra le fardeau en B, quand il <lb></lb>aura meſme proportion auec la dite for<lb></lb>ce, que la diſtance AC à la <expan abbr="diſtãce">diſtance</expan> BA. </s> <s id="s.000189"><lb></lb>Mais pour comprendre cecy, il faut <lb></lb>s'imaginer que la ligne BA ſoit prolon<lb></lb>gee en G, & que les diſtances BA, AG <lb></lb>ſoient égales, & que le fardeau ſoit at<lb></lb>taché au point C, & qu'il ſoit égal au <lb></lb>poids D, il eſt certain qu'à cauſe de l'é<lb></lb>galité des poids E, D, & des diſtances <pb pagenum="34" xlink:href="047/01/054.jpg"></pb>AC, & BA, le mouuement du poids <lb></lb>D ſuffira pour le ſouſtenir, donc la for<lb></lb>ce du moment égal à celuy du point E, <lb></lb>lequel le pourra ſouſtenir, ſuffira enco<lb></lb>re pour ſouſtenir le poids D. </s> <s id="s.000190">Mais ſi l'on <lb></lb>veut ſouſtenir E au point C, la force <lb></lb>doit eſtre à E, comme GA à CA, donc <lb></lb>la meſme force pourra ſouſtenir le <lb></lb>point D égal à E. </s> <s id="s.000191">Or la proportion qui <lb></lb>eſt de GA à EA, eſt auſſi de BA à CA, <lb></lb>GA eſtant égal à BA: Et parce que les <lb></lb>poids ED ſont égaux, chacun d'eux <lb></lb>aura la meſme <expan abbr="proportiõ">proportion</expan> à la force miſe <lb></lb>en C. D'où l'on conclud que la force C <lb></lb>eſt égale au <expan abbr="momẽt">moment</expan> D, lors qu'il a meſ<lb></lb>me proportion que la diſtance AB à <lb></lb>CA. </s> </p> <p type="main"> <s id="s.000192">Or il eſt tres-ayſé de conclurre de <lb></lb>tout ce diſcours que l'on perd autant <lb></lb>de viſteſſe comme l'on acquiert de for<lb></lb>ce tant auec le leuier ordinaire qu'auec <lb></lb>celuy-cy: car quand la force C hauſſe <lb></lb>le leuier AC, pour le <expan abbr="trãſporter">tranſporter</expan> en AI, <lb></lb>le poids ſe meut par l'interualle BH, <lb></lb>lequel eſt dautant moindre que l'eſpa<lb></lb>ce IC, qu'a fait la force, qu'AB eſt <lb></lb>moindre qu'AC. </s> </p> <p type="main"> <s id="s.000193">Ces principes ayant eſté declarez, il <pb pagenum="35" xlink:href="047/01/055.jpg"></pb>faut expliquer la raiſon des poulies, <expan abbr="dõt">dont</expan> <lb></lb>nous declarerons la conſtruction & l'v<lb></lb>ſage. </s> <s id="s.000194">Et pour ce ſuiet ſuppoſons que <lb></lb>l'on ayt la poulie ABC faite de metal, <lb></lb>ou d'vn bois fort dur, & qu'elle puiſſe <lb></lb>tourner ſur ſon eſſieu, qui paſſe par le <lb></lb>centre D: & puis il faut mettre à l'en<lb></lb><figure id="id.047.01.055.1.jpg" xlink:href="047/01/055/1.jpg"></figure><lb></lb>tour la chorde FCBAE, <lb></lb>à laquelle le poids E ſoit at<lb></lb>taché. </s> <s id="s.000195">Quant à la force, el<lb></lb>le eſt à l'autre bout de la <lb></lb>chorde au point F, où elle <lb></lb>ſouſtient le fardeau E. </s> <s id="s.000196">Car <lb></lb>ſi <expan abbr="l'õ">l'on</expan> ſ'imagine deux lignes <lb></lb>égales tirées du centre D, <lb></lb>à ſçauoir DC, & DA, l'on <lb></lb>aura l'équilibre de deux <lb></lb><expan abbr="momẽts">moments</expan>, ou de deux poids <lb></lb>égaux, également éloignez <lb></lb>de l'appuy D, qui eſt le <lb></lb>point du ſouſtien, lequel eſt <lb></lb>également éloigné de tous <lb></lb>les coſtez de la <expan abbr="circõference">circonference</expan> du cercle, <lb></lb>ou de la poulie ABC. </s> <s id="s.000197">Or ces deux li<lb></lb>gnes, qui ſont les bras du leuier, ou de <lb></lb>la balance, determinent les diſtances <lb></lb>des deux ſuſpenſions d'auec le centre <lb></lb>D: C'eſt pourquoy le poids qui eſt ſuſ- <pb pagenum="36" xlink:href="047/01/056.jpg"></pb>pendu du point A ne peut eſtre ſouſte<lb></lb>nu au point C que par vne égale force, <lb></lb>ou par vn poids égal, ſuiuant la nature <lb></lb>des poids égaux qui pendent de diſtan<lb></lb>ces égales. </s> <s id="s.000198">Car encore que la force F <lb></lb>tourne à l'entour de la poulie ABC, <lb></lb>cela ne change nullement l'habitude, <lb></lb>& le rapport que le poids, & la force <lb></lb>ont à la diſtance AD, & DC: dautant <lb></lb>que la poulie garde vn perpetuel équi<lb></lb>libre en ſe tournant. </s> <s id="s.000199">D'où il faut con<lb></lb>clurre qu'Ariſtote ſe trompe lors qu'il <lb></lb>dit que l'on leue plus ayſément les far<lb></lb>deaux auec les plus grandes poulies, car <lb></lb>encore que la diſtance, ou le demidia<lb></lb>metre de la poulie DC ſ'augmente, ce<lb></lb>la ne ſert de rien à raiſon que la diſtan<lb></lb>ce DA ſ'augmente également. </s> <s id="s.000200">De ſor<lb></lb>te que l'on ne reçoit nulle commodité <lb></lb>de cét inſtrument en ce qui concerne <lb></lb>la <expan abbr="diminutiõ">diminution</expan> de la peine. </s> <s id="s.000201">Mais ſa com<lb></lb>modité <expan abbr="cõſiſte">conſiſte</expan> à tirer de l'eau des puits, <lb></lb>parce que l'on tire de haut en bas, & <expan abbr="cõ-ſequemment">con<lb></lb>ſequemment</expan> le poids des bras, & du <lb></lb>corps ſeruent à cela, au lieu qu'en <expan abbr="tirãt">tirant</expan> <lb></lb>à force de bras de bas en haut ſans l'ay<lb></lb>de des poulies, le poids des bras, & du <lb></lb>corps nuiſent, c'eſt pourquoy la poulie <pb pagenum="37" xlink:href="047/01/057.jpg"></pb>apporte de la commodité à l'applica<lb></lb>tion de la force. </s> </p> <p type="main"> <s id="s.000202">Mais ſi l'on vſe d'vne autre ſorte de <lb></lb>poulie, dont on void icy la figure, l'on <lb></lb>pourra leuer vn fardeau auec moins de <lb></lb><figure id="id.047.01.057.1.jpg" xlink:href="047/01/057/1.jpg"></figure><lb></lb>force, car ſi la poulie BDC, <lb></lb>qui ſe doit mouuoir au tour <lb></lb>du centre E, eſt miſe dans <lb></lb>ſa quaiſſe, ou dans ſon ar<lb></lb>meure D, que G ſoit le far<lb></lb>deau, & que la chorde AB <lb></lb>CF paſſant à l'entour de la<lb></lb>dite poulie ſoit arreſté par <lb></lb>le bout à quelque cheuille, <lb></lb>au point ferme, & immobi<lb></lb>le; & <expan abbr="finalemẽt">finalement</expan> ſi l'on applique la force <lb></lb>au point C, ou F, qui ſe meuue en haut <lb></lb>vers H, & conſequemment qui faſſe <lb></lb>monter la quaiſſe D, & quant & quant <lb></lb>le fardeau G, ie dy que la force miſe en <lb></lb>C, ou en F, n'eſt que la moitié du far<lb></lb>deau qu'elle ſouſtient, & par <expan abbr="conſequẽt">conſequent</expan> <lb></lb>que le <expan abbr="momẽt">moment</expan> en C eſt ſouz double du <lb></lb>moment en G; parce que G eſt ſouſte<lb></lb>nu, & porté par les deux parties de la <lb></lb>chorde AB, & CD, de ſorte qu'il eſt <lb></lb>diuiſé en deux parties égales, parce que <lb></lb>le diametre BC eſt ſemblable au fleau <pb pagenum="38" xlink:href="047/01/058.jpg"></pb>d'vne balance, & le fardeau eſt ſuſpen<lb></lb>du du point E: & puis le ſouſtien eſt <lb></lb>au point B, & la force eſt au point C, <lb></lb>c'eſt pourquoy il y a meſme raiſon de <lb></lb>la force au fardeau, que de BE à BC, <lb></lb>donc elle eſt la moitié du fardeau. </s> </p> <p type="main"> <s id="s.000203">Car encore que la poulie ſe tourne, <lb></lb>tandis que la force ſe meut vers H, <lb></lb>neantmoins la ſuſdite proportion ne <lb></lb>change point, comme l'on void aux <lb></lb>points B, E, C, & le leuier BC eſt rendu <lb></lb>perpetuel. </s> <s id="s.000204">Mais en recompenſe le che<lb></lb>min que fait la force eſt double du che<lb></lb>min que fait le fardeau, car quand il eſt <lb></lb>arriué au point F, c'eſt à dire <expan abbr="quãd">quand</expan> il eſt <lb></lb>monté auſſi haut qu'A, la force à mon<lb></lb>té deux fois autant, c'eſt à dire de C en <lb></lb>H. </s> <s id="s.000205">Mais il arriue icy vne incommodi<lb></lb>té à la force, à raiſon de ſa peſanteur <lb></lb>qui la fait incliner en bas, c'eſt pour<lb></lb>quoy <expan abbr="l'õ">l'on</expan> y a remedié par l'<expan abbr="additiõ">addition</expan> d'vne <lb></lb>autre poulie que <expan abbr="l'õ">l'on</expan> met en haut, <expan abbr="cõme">comme</expan> <lb></lb>l'on peut comprendre par cette figure, <lb></lb>quoy que renuerſée, dans laquelle il <lb></lb>faut conſiderer la chorde IBAEF, <lb></lb>qui paſſe à l'entour des poulies BA, & <lb></lb>FE, & eſt attachée à l'armure du point <lb></lb>D de la quaiſſe CD, qui eſt attachée <pb pagenum="39" xlink:href="047/01/059.jpg"></pb>en haut à la poûtre, ou à la pierre H, de <lb></lb><figure id="id.047.01.059.1.jpg" xlink:href="047/01/059/1.jpg"></figure><lb></lb>ſorte que la force tirant la <lb></lb>chorde du point B au point <lb></lb>I, ou du point I au point F, <lb></lb>fait monter le poids at<lb></lb>taché au mouffle, ou à la <lb></lb>quaiſſe FE. </s> <s id="s.000206">Or cette force <lb></lb>ne doit pas eſtre moindre <lb></lb>qu'au point A, dautant <lb></lb>que les momens du poids, <lb></lb>& de la force ſont égale<lb></lb>ment diſtans du centre G, <lb></lb>car BG eſt égal à GA, c'eſt <lb></lb>pourquoy la poulie BA <lb></lb>n'augmente pas la force. </s> <s id="s.000207"><lb></lb>Où il faut remarquer que <lb></lb>les Italiens appellent cét inſtrument <emph type="italics"></emph>la <lb></lb>Taglia,<emph.end type="italics"></emph.end> & les Grecs, & les Latins <emph type="italics"></emph>Tro<lb></lb>chlea<emph.end type="italics"></emph.end>: mais nous le nommons en Fran<lb></lb>ce <emph type="italics"></emph>Mouffles<emph.end type="italics"></emph.end>; ce qui comprend l'armeu<lb></lb>re, ou la quaiſſe, qui ſert de boëte aux <lb></lb>poulies, & les poulies, & tout ce qui <lb></lb>ſert pour la perfection de cette machi<lb></lb>ne: on l'appelle auſſi <emph type="italics"></emph>écharpes armée de <lb></lb>poulies.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000208">Or apres auoir monſtré par les deux <lb></lb>figures precedentes que l'on peut dou<lb></lb>bler la force par le moyen des poulies, <pb pagenum="40" xlink:href="047/01/060.jpg"></pb>il faut maintenant faire voir que l'on <lb></lb>peut l'augmenter tant que l'on voudra, <lb></lb>comme ie demonſtre aux <expan abbr="nõbre">nombre</expan> pairs, <lb></lb>& impair des poulies: c'eſt pourquoy <lb></lb>ie mets le Lemme qui ſuit, afin de de<lb></lb>monſtrer la maniere de multiplier la <lb></lb>force en raiſon quadruple. </s> </p> <p type="head"> <s id="s.000209"><emph type="center"></emph><emph type="italics"></emph>LEMME.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000210">Soient donc les deux lignes AB, & <lb></lb><figure id="id.047.01.060.1.jpg" xlink:href="047/01/060/1.jpg"></figure><lb></lb>CD, qui repre<lb></lb>ſentent deux le<lb></lb>uiers, qui ont <lb></lb>leurs appuis A & <lb></lb>C à leurs extre<lb></lb>mitez, & que le <lb></lb>fardeau G ſoit <lb></lb>ſuſpendu au milieu E, & F & qu'il ſoit <lb></lb>ſouſtenu par les deux forces B & D ap<lb></lb>pliquées aux autres extremitez des le<lb></lb>uiers, leſquelles ie ſuppoſe auoir vn <lb></lb>moment égal, ie dy que le moment de <lb></lb>chacune eſt égal au moment de la qua<lb></lb>trieſme partie du poids G, car les deux <lb></lb>forces B & D ſouſtiennent également, <lb></lb>& <expan abbr="conſequemmẽt">conſequemment</expan> la force D n'eſt con<lb></lb>trariée que par la moitié du poids G qui <pb pagenum="41" xlink:href="047/01/061.jpg"></pb>eſt attaché à F. </s> <s id="s.000211">Mais quand la force D <lb></lb>ſouſtient la moitié du fardeau par le <lb></lb>moyen du leuier CD, elle a meſme <lb></lb>proportion à G que CD à CF, c'eſt à <lb></lb>dire ſouz double, donc le <expan abbr="momẽt">moment</expan> D eſt <lb></lb>double du moment de la moitié du <lb></lb>poids G qu'il ſouſtient, donc il eſt le <lb></lb>quart du moment des poids entier. </s> </p> <p type="main"> <s id="s.000212">L'on demonſtre la meſme choſe du <lb></lb>moment B, de ſorte qu'il eſt raiſonna<lb></lb>ble que le poids eſtant également ſou<lb></lb>ſtenu par les 4 poulies qui ſe voyent <lb></lb>dans cette autre figure, chacune porte <lb></lb>la quatrieſme partie du fardeau: ce que <lb></lb>ie monſtre en cette maniere. </s> </p> <p type="main"> <s id="s.000213">Que le poids X ſoit attaché au point <lb></lb>K par le moyen du mouffle KX, ie dy <lb></lb>que la force égale à la quatrieſme par<lb></lb>tie du fardeau X, le ſouſtiendra, car ſi <lb></lb>l'on s'imagine que les deux diametres <lb></lb>BA & DE ſoient deux leuiers ſembla<lb></lb>bles à ceux que nous auons expliquez <lb></lb>dans la figure precedente, & que le far<lb></lb>deau ſoit ſuſpendu aux points CEF, <expan abbr="l'õ">l'on</expan> <lb></lb>trouuera que les appuis, ou les ſupports <lb></lb>deſdits leuiers répondent aux points D <lb></lb>& A, conſequemment que la force ap<lb></lb>pliquée en B ou en E ſouſtiendra le <pb pagenum="42" xlink:href="047/01/062.jpg"></pb>poids X, dont il ſera ſousquadruple. </s> <figure id="id.047.01.062.1.jpg" xlink:href="047/01/062/1.jpg"></figure> </p> <p type="main"> <s id="s.000214">>Et ſi <expan abbr="l'õ">l'on</expan> adiouſte vne pou<lb></lb>lie en haut, & que la chor<lb></lb>de paſſe par OMB, la <lb></lb>force L, ſouſtiendra le <lb></lb>meſme poids. </s> <s id="s.000215">Mais il <lb></lb>faut accommoder les 4. <lb></lb>chordes, <expan abbr="cõme">comme</expan> elles ſont <lb></lb>dans ces mouffles, en ſor<lb></lb>te qu'elles ne ſe meſlent <lb></lb>point les vnes auec les au<lb></lb>tres. </s> <s id="s.000216">Or il faut icy remar<lb></lb>quer ce que nous auons <lb></lb>deſia dit pluſieurs fois, à <lb></lb>ſçauoir que <expan abbr="l'õ">l'on</expan> ne gaigne <lb></lb>rien auec ces inſtrumens, <lb></lb>car ſi l'on épargne la for<lb></lb>ce, l'on augmente le <expan abbr="tẽps">temps</expan>: <lb></lb>de là vient qu'il faut tirer <lb></lb>quatre pieds de chorde <lb></lb>depuis O iuſques à L pour faire monter <lb></lb>le poids X d'vn pied de X en C: & l'on <lb></lb>trouuerra perpetuellement que l'on <lb></lb>perd autant de temps, ou que l'on eſt <lb></lb>contraint d'allonger autant le chemin, <lb></lb>que l'on gaigne de force. </s> </p> <p type="main"> <s id="s.000217">Si l'on veut que la force s'augmente <lb></lb>au ſextuple, il faut adiouſter vne autre <pb pagenum="43" xlink:href="047/01/063.jpg"></pb>poulie en bas, comme ie monſtre par la <lb></lb><figure id="id.047.01.063.1.jpg" xlink:href="047/01/063/1.jpg"></figure><lb></lb>figure precedente, <expan abbr="dãs">dans</expan> <lb></lb>laquelle on void les <lb></lb>trois leuiers AB, CD, <lb></lb>& FE. </s> <s id="s.000218">Que le poids K <lb></lb>ſoit attaché a G, H, & <lb></lb>I, & que les trois for<lb></lb>ces B, D, F, ſoient éga<lb></lb>les, & qu'elles ſouſtien<lb></lb>nent <expan abbr="égalemẽt">également</expan> le poids K, afin que cha<lb></lb>cune en ſouſtienne le tiers, & parce que <lb></lb>la force B ſouſtenant le poids <expan abbr="pẽdu">pendu</expan> à G <lb></lb>eſt la moitié du poids, & que nous <expan abbr="auõs">auons</expan> <lb></lb>ſuppoſé qu'il ſouſtient le tiers dudit <lb></lb>poids, il s'enſuit que la force B eſt éga<lb></lb>le à la moitié du tiers de K, c'eſt à dire <lb></lb>à la ſixieſme partie de K. </s> <s id="s.000219">Car il ſaut tou<lb></lb>ſiours s'imaginer que les appuys A, C, E <lb></lb>ſouſtiennent autant du poids que les <lb></lb>forces B, D, F. </s> <s id="s.000220">Par où il eſt ayſè de <lb></lb>comprendre que le mouffle inferieur <lb></lb>ayant trois poulies, & le ſuperieur deux, <lb></lb>ou 3. autres, que l'on peut multiplier la <lb></lb>force ſelon le nombre ſenaire: ce que <lb></lb>l'on peut ayſément s'imaginer en con<lb></lb>ſiderant vn mouffle compoſé de ſix <lb></lb>poulies. </s> </p> <p type="main"> <s id="s.000221">Or pour expliquer la maniere de <pb pagenum="44" xlink:href="047/01/064.jpg"></pb>multiplier la force ſelon vn <expan abbr="nõbre">nombre</expan> im<lb></lb>pair: il faut encore conſiderer le leuier <lb></lb>de la page 40. AB, dont l'appuy eſt en <lb></lb>A, & le poids G eſt attaché à E, & ſou<lb></lb>ſtenu par deux forces égales, dont l'vne <lb></lb>eſt en D, & l'autre en B, & <expan abbr="l'õ">l'on</expan> trouuer<lb></lb>ra que chaque force a vn moment égal <lb></lb>au tiers du poids, G, parce que la force <lb></lb>miſe en E ſouſtient vn poids qui luy eſt <lb></lb>égal, dautant qu'elle eſt dans la ligne <lb></lb>de la ſuſpenſion dudit poids. </s> <s id="s.000222">Mais la <lb></lb>force <expan abbr="eſtãt">eſtant</expan> en B ſouſtient deux fois au<lb></lb>tant que ſon poids, parce que ſa diſtan<lb></lb>ce d'auec l'appuy A eſt double de EA. </s> <s id="s.000223"><lb></lb>Et parce que l'on ſuppoſe que les 2. for<lb></lb>ces B, & E ſont egales, il s'enſuit que la <lb></lb>partie de G ſouſtenuë par B eſt double <lb></lb>de la partie que ſouſtient E: donc ſi l'on <lb></lb>fait deux parties du poids G, & que l'v<lb></lb>ne ſoit double de l'autre, la plus grande <lb></lb>ſera de 2/3, & la moindre de 1/3 de G, donc <lb></lb>le moment de la force E ſera égal au <lb></lb>tiers de G: & parce que nous auons <lb></lb>ſuppoſé B égal à E, la force B eſt égale <lb></lb>à la force E, & conſequemment chacu<lb></lb>ne eſt égale au tiers du poids G. </s> </p> <p type="main"> <s id="s.000224">Cecy ayant eſté demonſtré, il faut <lb></lb>l'appliquer aux mouffles qui ſuiuent, <pb pagenum="45" xlink:href="047/01/065.jpg"></pb>dont la poulie ABC ſe tourne au tour <lb></lb><figure id="id.047.01.065.1.jpg" xlink:href="047/01/065/1.jpg"></figure><lb></lb>du centre G, auquel le far<lb></lb>deau H eſt attaché. </s> <s id="s.000225">L'au<lb></lb>tre poulie ſuperieure eſt <lb></lb>FE; outre leſquelles il <lb></lb>faut encore conſiderer la <lb></lb>chorde IBCAEFD, qui <lb></lb>eſt attachée au point B, & <lb></lb>puis la force qui eſt en I, <lb></lb>laquelle ne ſupportera <lb></lb>que le tiers du fardeau H. </s> <s id="s.000226"><lb></lb>Par où il eſt <expan abbr="euidẽt">euident</expan> qu' AB <lb></lb>eſt vn leuier, & que la for<lb></lb>ce I s'applique à ſes extre<lb></lb>mitez B, & A. </s> <s id="s.000227">G eſt le <lb></lb>point du ſouſtien, auquel <lb></lb>H eſt ſuſpendu. </s> <s id="s.000228">Vne autre force eſt en<lb></lb>core appliquèe en D, de ſorte que le <lb></lb>poids eſt arreſté par 3. chordes qui con<lb></lb>tribuent également à ſouſtenir le poids <lb></lb>H: car la force D eſt appliquée au mi<lb></lb>lieu du leuier, & B à ſon extremité, c'eſt <lb></lb>pourquoy chaque force ne ſupporte <lb></lb>que le tiers du poids H. D'où il s'enſuit <lb></lb>que la force I ayant ſon moment égal <lb></lb>audit tiers, peut ſouſtenir, & leuer le <lb></lb>poids entier. </s> <s id="s.000229">Mais I fera trois fois au<lb></lb>tant de chemin que le poids H, parce <pb pagenum="46" xlink:href="047/01/066.jpg"></pb>qu'il ſuit la longueur de trois chordes <lb></lb>IB, AE, & FD, dont l'vne meſure le <lb></lb>chemin du fardeau. <lb></lb></s> </p> </chap> <chap> <p type="head"> <s id="s.000230"><emph type="center"></emph>CHAP. IX.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000231"><emph type="center"></emph><emph type="italics"></emph>De la Viz.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000232">ENtre tous les inſtrumens Mecha<lb></lb>niques que l'on a inuentez pour la <lb></lb>vie humaine, la viz que les Grecs, & <lb></lb>les Latins appellent <emph type="italics"></emph>Cochlea,<emph.end type="italics"></emph.end> tient le pre<lb></lb>mier <expan abbr="rãg">rang</expan> tant pour ſa ſubtilité que pour <lb></lb>ſon vtilité, dautant qu'elle ſert pour <lb></lb>arreſter, pour faire mouuoir, & pour <lb></lb>preſſer auec vne treſ-grande force, & <lb></lb>qu'elle tient fort peu de place, quoy <lb></lb>qu'elle aye des effets treſ-ſignales que <lb></lb>les autres inſtrumens ne peuuent auoir <lb></lb>s'ils ne ſont reduits en de treſ-grandes <lb></lb>Machines. </s> <s id="s.000233">C'eſt pourquoy il faut ex<lb></lb>pliquer la nature, & l'origine de la viz, <lb></lb>& pour ce ſuiet ie <expan abbr="demõſtre">demonſtre</expan> icy vn theo<lb></lb>reſme, qui ſemblera, peuſt-eſtre, fort <lb></lb>éloigné de ce diſcours, quoy qu'il en <lb></lb>ſoit la baſe, & le fondement. </s> </p> <p type="main"> <s id="s.000234">Ie dy donc que tous les corps peſans <pb pagenum="47" xlink:href="047/01/067.jpg"></pb>ont vne inclination vers le centre de la <lb></lb>terre, non ſeulement quand ils y peu<lb></lb>uent deſcendre perpendiculairement, <lb></lb>mais auſſi quand ils y peuuent arriuer <lb></lb>par vne ligne oblique, ou par vn plan <lb></lb>incliné: ce que l'on peut confirmer par <lb></lb>l'eau qui ne tombe ſeulement pas à <lb></lb>plomb de quelque lieu éminent, mais <lb></lb>elle coule auſſi ſur la terre par vne li<lb></lb>gne qui a fort peu d'inclination, com<lb></lb>me l'on remarque aux cours des fleu<lb></lb>ues, dont les eaux deſcendent libre<lb></lb>ment, pourueu que leur lit ayt tant ſoit <lb></lb>peu de pante. </s> </p> <p type="main"> <s id="s.000235">Or ce qui arriue aux corps fluides, ſe <lb></lb>remarque, ſemblablement aux corps <lb></lb>qui ſont durs, pourueu que les figures, <lb></lb>& les autres empeſchemens acciden<lb></lb>tels, & exterieurs ne les diuertiſſent <lb></lb>point: Car ſi l'on prend vne bale par<lb></lb>faitement ronde, & polie, ſoit de mar<lb></lb>bre, de verre, ou d'autre matiere, qui <lb></lb>reçoiue vn excellent poly, & que l'on <lb></lb>la mette ſur vn <expan abbr="plã">plan</expan> incline, qui ſoit auſ<lb></lb>ſi parfaitement vni, & poly que la gla<lb></lb>ce d'vn miroir, elle deſcendra ſur ledit <lb></lb>plan, ſe mouuera <expan abbr="perpetuellemẽt">perpetuellement</expan> tan<lb></lb>dis qu'elle trouuera la moindre inclina- <pb pagenum="48" xlink:href="047/01/068.jpg"></pb>tion que l'on ſe puiſſe imaginer: de ſor<lb></lb>te qu'elle ne ſarreſtera point iuſques à <lb></lb>ce qu'elle rencontre vne ſurface qui <lb></lb>ſoit à niueau, ou équidiſtante de l'ho<lb></lb>rizon, comme eſt celle d'vn lac, ou d'vn <lb></lb>eſtang glacé, ſur laquelle la bale ſe <lb></lb>tiendroit ferme, & immobile, mais auec <lb></lb>telle condition que la moindre force <lb></lb>l'ébranleroit, & que le plan ſinclinant <lb></lb>de la largeur d'vn cheueu, elle <expan abbr="commẽ-ceroit">commen<lb></lb>ceroit</expan> incontinent à ſe mouuoir & à <lb></lb>deſcendre vers la partie inclinée, & <lb></lb>qu'au contraire elle ne pourroit eſtre <lb></lb>meuë ſans <expan abbr="violẽce">violence</expan> vers la partie du plan <lb></lb>qui monte. </s> <s id="s.000236">Or il eſt neceſſaire que la <lb></lb>boule ſarreſte ſur vne ſurface parfaite<lb></lb>ment équilibre, & qu'elle demeure <expan abbr="cõ-me">com<lb></lb>me</expan> indifferente entre le mouuement & <lb></lb>le repos: de ſorte que la moindre force <lb></lb>du <expan abbr="mõde">monde</expan> ſuffiſe pour la mouuoir, com<lb></lb>me la moindre force que l'on peut ſi<lb></lb>maginer dans l'air, ſuſfit pour la rete<lb></lb>nir. </s> </p> <p type="main"> <s id="s.000237">D'où l'on peut tirer cette concluſion, <lb></lb>que tout corps peſant, tous les empeſ<lb></lb>chemens exterieurs eſtant oſtez, peut <lb></lb>eſtre meu ſur vn plan horizontal par la <lb></lb>moindre force que ce ſoit, & qu'il faut <pb pagenum="49" xlink:href="047/01/069.jpg"></pb>d'autant plus de force pour le mouuoir <lb></lb>ſur vn plan incliné, qu'il a plus d'incli<lb></lb>nation au mouuement contraire. </s> </p> <p type="main"> <s id="s.000238">Ce qui ſera plus intelligible par <lb></lb><figure id="id.047.01.069.1.jpg" xlink:href="047/01/069/1.jpg"></figure><lb></lb>cette figure, dans <lb></lb>laquelle AB ſoit le <lb></lb>plan parallele à l'o<lb></lb>rizon, ſur lequel la <lb></lb>boule eſt indif<lb></lb>ferente au mouue<lb></lb>ment, & au repos, de ſorte que le vent <lb></lb>ou la moindre force la peut faire mou<lb></lb>uoir; mais il faut vne plus grande force <lb></lb>pour la faire mouuoir du point A au <lb></lb>point C ſur le plan incliné AC, & en<lb></lb>core vne plus grande pour la mouuoir <lb></lb>ſur les plans AD, & AE: & finalement <lb></lb>l'on ne peut la leuer ſur le plan perpen<lb></lb>diculaire AF, que par vne force égale à <lb></lb>tout le poids G. </s> </p> <p type="main"> <s id="s.000239">Or l'on ſçaura <expan abbr="cõbien">combien</expan> il faut moins de <lb></lb>force pour leuer le fardeau ſur les plans <lb></lb>AE, AD, &c, ſi <expan abbr="l'õ">l'on</expan> tire les lignes perpen<lb></lb>diculaires à l'orizon CH, DI & KE, cat <lb></lb>il y aura meſme proportion des forces <lb></lb>neceſſaires pour éleuer le fardeau ſur <lb></lb>chaſque plan audit fardeau, que des <lb></lb>lignes perpendiculaires aux lignes de <pb pagenum="50" xlink:href="047/01/070.jpg"></pb>leurs plans. </s> <s id="s.000240">Ce que Pappus <expan abbr="Alexãdrin">Alexandrin</expan> <lb></lb>s'eſt efforcé de monſtrer dans le 8. liure <lb></lb>de ſes Collections Mathematiques, <lb></lb>mais il s'eſt trompé, à mon aduis, en ce <lb></lb>qu'il a ſupposé vne force donnée pour <lb></lb>mouuoir le poids ſur le plan <expan abbr="horizõtal">horizontal</expan>, <lb></lb>ce qui eſt faux, parce qu'il ne faut nulle <lb></lb>force ſenſible, ſi l'on oſte les empeſche<lb></lb>mens exterieurs. </s> <s id="s.000241">C'eſt pourquoy il eſt <lb></lb>plus à propos de chercher la force qui <lb></lb>meut le fardeau ſur le plan vertical ou <lb></lb>perpendiculaire AF, laquelle eſt tou<lb></lb>ſiours égale à la peſanteur du fardeau, <lb></lb>que de chercher la force qui le meut <lb></lb>ſur le plan horizontal. </s> </p> <p type="main"> <s id="s.000242">Soit donc le cercle AIC, dont le dia<lb></lb><figure id="id.047.01.070.1.jpg" xlink:href="047/01/070/1.jpg"></figure><lb></lb>mettre <lb></lb>eſt ABC, <lb></lb>& le cen<lb></lb>tre B; & <lb></lb>qu'il y ait <lb></lb>deux for<lb></lb>ces éga<lb></lb>les aux <lb></lb>points A <lb></lb>& C, qui <lb></lb><expan abbr="repreſẽtẽt">repreſentent</expan> <lb></lb>vne <expan abbr="balãce">balance</expan> mobile autour du centre B, <pb pagenum="51" xlink:href="047/01/071.jpg"></pb>il eſt certain que le poids C ſera ſouſte<lb></lb>nu par la force A. </s> <s id="s.000243">Mais ſi l'on s'imagine <lb></lb>que le bras de la balance BC tombe en <lb></lb>BF, de ſorte qu'il demeure touſiours <lb></lb>continué auec le bras AB, & qu'ils <expan abbr="ayẽt">ayent</expan> <lb></lb>tous deux leur point fixe, ou leur appuy <lb></lb>en B, le moment F, ne ſera pas égal au <lb></lb>moment A, parce que la diſtance <lb></lb>du poinct, ou du poids F d'auec la ligne <lb></lb>de direction BI n'eſt pas egale à la di<lb></lb>ſtance de la force, ou du poids A d'auec <lb></lb>la meſme ligne de direction, comme <lb></lb>l'on demonſtre par la perpendiculaire <lb></lb>KF, qui determine la <expan abbr="diſtãce">diſtance</expan> du poinct <lb></lb>F auec B, ou I, de ſorte que le <expan abbr="momẽt">moment</expan>, <lb></lb>ou le poids, de C porté en F eſt dimi<lb></lb>nué de la diſtance de KC, & qu'il n'a <lb></lb>plus que le <expan abbr="momẽt">moment</expan> BK: c'eſt pourquoy <lb></lb>il faut conclure que le moment d'A <lb></lb>ſurpaſſe celuy de F de KC. </s> <s id="s.000244">Il faut dire <lb></lb>la meſme choſe du poids C tranſporté <lb></lb>au point L, ou en tel autre point du cer<lb></lb>cle que l'on voudra, car la force en A <lb></lb>ſera d'autant plus grande que la force <lb></lb>L, que BA, eſt plus grand que BM. </s> </p> <p type="main"> <s id="s.000245">Parce où l'on void que le poids C <lb></lb>diminuë ſon moment, & ſon inclina<lb></lb>tion d'aller en bas ſelon les differentes <pb pagenum="52" xlink:href="047/01/072.jpg"></pb><expan abbr="inclinatiõs">inclinations</expan> des <expan abbr="plãs">plans</expan> FB, LB &c. </s> <s id="s.000246">de ſorte <lb></lb>que l'on peut s'imaginer la deſcente de <lb></lb>C par tous les points du quart de cercle <lb></lb>CI, lequel contient vn plan qui s'incli<lb></lb>ne perpetuellement de plus en plus, <lb></lb>& que la peſanteur du poids en C eſt <lb></lb>totale & entiere, & conſequemment <lb></lb>qu'il ſe porte de toute ſon inclination à <lb></lb>deſcendre, parce qu'il n'eſt nullement <lb></lb>empeſché par la <expan abbr="circonferẽce">circonference</expan>, lors qu'il <lb></lb>ſe rencontré ſur la tangente DCE. </s> </p> <p type="main"> <s id="s.000247">Mais quand il eſt en F, il eſt en partie <lb></lb>ſouſtenu par le plan circulaire, & ſa <lb></lb>pente, ou l'inclination qu'il a vers le <lb></lb>centre de la terre eſt autant diminuée <lb></lb>que BC ſurpaſſe BK: de maniere qu'il <lb></lb>ſe tient éleué ſur ce plan de meſme que <lb></lb>s'il eſtoit appuyé ſur la tangente GFH, <lb></lb><expan abbr="d'autãt">d'autant</expan> que le point d'inclination F de <lb></lb>la circonference CI ne differe point de <lb></lb>l'inclination de la tangente GFH, que <lb></lb>par l'angle inſenſible du contact. </s> </p> <p type="main"> <s id="s.000248">Il faut dire la meſme choſe du point <lb></lb>L, lequel eſt incliné comme s'il eſtoit <lb></lb>ſur le plan de la tangeule NLO, car il <lb></lb>diminuë ſa pente, & ſon <expan abbr="inclinatiõ">inclination</expan> qu'il <lb></lb>a en C en meſme proportion que Bk eſt <lb></lb>à BC, puis qu'il eſt conſtant par la ſimi- <pb pagenum="53" xlink:href="047/01/073.jpg"></pb>litude des triangles KBF & KFH, qu'il <lb></lb>y a meſme raiſon de FK à FH que de <lb></lb>KB à BF. D'où nous conclüons que la <lb></lb>proportion du moment total & abſolu <lb></lb>du mobile dans la perpendiculaire de <lb></lb>l'orizon auec le moment qu'il a ſur le <lb></lb>plan incliné HF eſt la meſme que la <lb></lb>proportion de FH à FK. </s> </p> <p type="main"> <s id="s.000249">Ce qui ſe void plus diſtinctement <lb></lb><figure id="fig31"></figure><lb></lb>dans le triangle A <lb></lb>BC car le moment <lb></lb>du mobile ſur le <lb></lb>plan AC eſt <expan abbr="d'au-tãt">d'au<lb></lb>tant</expan> moindre que le <lb></lb>moment qu'il a <expan abbr="dãs">dans</expan> <lb></lb>la perpendiculaire CB, que CB eſt <lb></lb>moindre que CA. </s> <s id="s.000250">Et parce qu'il ſuffit <lb></lb>pour mouuoir le fardeau, que la force <lb></lb>ſurpaſſe <expan abbr="inſenſiblemẽt">inſenſiblement</expan> celle qui le ſou<lb></lb>ſtient en quel que lieu que ce ſoit, nous <lb></lb><expan abbr="faisõs">faisons</expan> icy cette propoſition vniuerſelle. </s> </p> <p type="main"> <s id="s.000251"><emph type="italics"></emph>Que ſur le plan eleué la force a la meſ<lb></lb>me proportion au poids que la perpen<lb></lb>diculaire tirée de l'extremité du plan ſur <lb></lb>l'orizon à la longueur dudit plan, c'eſt à dire <lb></lb>que la tangente à la ſecante,<emph.end type="italics"></emph.end> car FK eſt la <lb></lb>tangente du cercle deſcrit ſur le dia<lb></lb>mettre KH, & FH eſt la ſecante. </s> </p> <pb pagenum="54" xlink:href="047/01/074.jpg"></pb> <p type="main"> <s id="s.000252">Cecy eſtant poſé, ie reuiens à mon <lb></lb><figure id="id.047.01.074.1.jpg" xlink:href="047/01/074/1.jpg"></figure><lb></lb>premier deſſein, qui con<lb></lb>ſiſte à trouuer, & à expli<lb></lb>quer la nature de la viz; c'eſt <lb></lb>pour ce ſubiet qu'il faut <lb></lb>conſiderer le triangle AB <lb></lb>C, dans lequel AB repreſente la ligne <lb></lb>horizontale, BC la perpendiculaire à <lb></lb>l'orizon, & AC le plan eleué, & encliné <lb></lb>ſur l'orizon, ſur lequel le mobile E eſt <lb></lb>tiré & emporté par vne force d'autant <lb></lb>moindre que le poids E, que la ligne <lb></lb>BC eſt moindre que CA. </s> <s id="s.000253">Or quand on <lb></lb>veut eſleuer E plus haut ſur le plan fer<lb></lb>me AC, c'eſt meſme choſe que ſi le tri<lb></lb>angle BCA eſtoit pouſſé iuſques au <lb></lb><figure id="id.047.01.074.2.jpg" xlink:href="047/01/074/2.jpg"></figure><lb></lb>point H, parce que s'il ſe <lb></lb>trouuoit dans la meſme <lb></lb>aſſiette que le <expan abbr="triãgle">triangle</expan> HFG, <lb></lb>le mobile auroit monté la <lb></lb>hauteur AI, & ſeroit en E. </s> </p> <p type="main"> <s id="s.000254">D'où il s'enſuit que la na<lb></lb>ture de la viz n'eſt autre <lb></lb>choſe que le triangle ACB, <lb></lb>le quel eſtant pouſſé en <expan abbr="auãt">auant</expan> <lb></lb>ſouſtient la peſanteur & <lb></lb>l'éleue: & que c'eſt par ſon <lb></lb>moyen qu'elle a eſté inuen- <pb pagenum="55" xlink:href="047/01/075.jpg"></pb>tée. </s> <s id="s.000255">Mais l'on s'eſt auisé d'enuironner <lb></lb>le cylindre BD du meſme triangle, <lb></lb>affin de le reduire dans vne machine <lb></lb>beaucoup moindre, & plus commode. </s> </p> <p type="main"> <s id="s.000256">Et pour ce ſubiet l'on adonné la meſ<lb></lb>me hauteur du triangle au cylindre, <lb></lb>BE, & l'inclination de l'hypotenuſe <lb></lb>CA à l'helice AE, & à toutes les autres <lb></lb>qui <expan abbr="ſuiuẽt">ſuiuent</expan> de bas en haut, & qui <expan abbr="fõt">font</expan> l'he<lb></lb>lice continuë AEFGHID, laquelle on <lb></lb>appelle <expan abbr="ordinairemẽt">ordinairement</expan> le traict de la viz. </s> </p> <p type="main"> <s id="s.000257">C'eſt donc en cette maniere que l'in<lb></lb>ſtrument appellé par les Grecs & par <lb></lb>les Latins <emph type="italics"></emph>cochlea<emph.end type="italics"></emph.end> & que nous <expan abbr="appelliõs">appellions</expan> <emph type="italics"></emph>la <lb></lb>viz,<emph.end type="italics"></emph.end> à eſté <expan abbr="inuẽtée">inuentée</expan>, affin qu'en la <expan abbr="tornãt">tornant</expan> <lb></lb>on eſléue les fardeaux <expan abbr="cõme">comme</expan> l'on feroit <lb></lb>ſur le triangle precedent, car l'on trou<lb></lb>uera touſiours dans la viz, comme ſur <lb></lb>tel autre plan que ce ſoit, que la force <lb></lb>eſt au poids poſé ſur vn plan incliné <lb></lb>comme la hauteur dudit plan à ſa lon<lb></lb>gueur: & conſequemment que la force <lb></lb>de la viz ABCD ſera multipliée ſelon <lb></lb>que toute l'helice ſera plus grande que <lb></lb>toute la hauteur du cylindre. </s> <s id="s.000258">Par où il <lb></lb>eſt ayſé d'entendre, & de conclure que <lb></lb>la viz eſt d'autant plus forte que ſes <lb></lb>helices ſont plus couchées, & plus in- <pb pagenum="56" xlink:href="047/01/076.jpg"></pb>clinées ſur l'orizon, par ce que la lon<lb></lb>gueur des triangles ſuiuant leſquels el<lb></lb>les ſont formées eſt en plus grande pro<lb></lb>portion à leur hauteur. </s> <s id="s.000259">Neantmoins il <lb></lb>n'eſt pas neceſſaire de meſurer la lon<lb></lb>gueur de toute l'helice, ny la hauteur <lb></lb>totale du cylindre pour congnoiſtre la <lb></lb>force d'vne viz propoſée, car il ſuffit de <lb></lb>ſçauoir combien de fois l'vn des tours <lb></lb>de l'helice <expan abbr="contiẽt">contient</expan> ſa hauteur, par exem<lb></lb>ple, combien de fois AF eſt contenu en <lb></lb>AE, & en EF parce qu'il y à meſme <lb></lb>proportion de toute la hauteur CB à <lb></lb>toute l'helice, que de FA à A EF, que <lb></lb>les Italiens appellent <emph type="italics"></emph>verme de la vite.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000260">Or apres auoir expliqué la nature de <lb></lb>la viz, l'on peut <expan abbr="ayſemẽt">ayſement</expan> ſçauoir toutes <lb></lb>ſes proprietez, par exemple que l'on fait <lb></lb>monter le poids par le moyen de ſa ma<lb></lb>trice auec les helices concaues dans <lb></lb>leſquelles entre le noyau de la viz auec <lb></lb>ſes helices <expan abbr="cõuexes">conuexes</expan> <expan abbr="cõme">comme</expan> il eſt ayſé de <lb></lb>remarquer aux viz des preſſoirs, & de <lb></lb>toutes ſortes de preſſes à écroux, dont <lb></lb>le noyau eſtant tourné fait monter la<lb></lb>dite matrice, & quant & quant le poids <lb></lb>qui y eſt attaché. </s> </p> <pb pagenum="57" xlink:href="047/01/077.jpg"></pb> <p type="main"> <s id="s.000261">Mais il faut touſiours ſe ſouuenir que <lb></lb><expan abbr="l'õ">l'on</expan> perd <expan abbr="autãt">autant</expan> de viſteſſe, & de <expan abbr="tẽps">temps</expan>, que <lb></lb>l'on gaigne de force, car AB eſt le plan <lb></lb><expan abbr="horizõtal">horizontal</expan>, & AC le plan incliné, <expan abbr="dõt">dont</expan> la <lb></lb>hauteur eſt meſurée, & determinée par <lb></lb>la perpendiculaire CB; Or ſi l'on poſe <lb></lb>vn mobile ſur le plan AC, & que la <lb></lb>chorde EDF le tienne attaché, la force <lb></lb>qui eſt en F ayant meſme raiſon auec le <lb></lb>poids E que BC aà CB, ſouſtiendra le <lb></lb>poids en E, & en luy aioutant la moin<lb></lb>dre force du monde, il tombera en B, & <lb></lb>emportera le poids E en le faiſant mon<lb></lb>ter vers D. </s> <s id="s.000262">Mais F ne fera pas moins <lb></lb>de chemin en deſcendant perpendicu<lb></lb>lairement, que le poids E en montant <lb></lb>obliquement, c'eſt pourquoy il eſt ne<lb></lb>ceſſaire que F deſcende plus bas qu'il <lb></lb>ne fait monter le poids E, dont l'exau<lb></lb>cement ſe meſure par la ligne per<lb></lb>pendiculaire BC: de maniere que la <lb></lb>ligne de la deſcente de F ſera égalé à <lb></lb>CA, quand il aura fait monter le poids <lb></lb>de B à C. </s> <s id="s.000263">Car le poids ne reſiſte point <lb></lb>au mouuement parallele à l'orizon, <lb></lb>parce que ce mouuement ne l'éloigne <lb></lb>point du centre de la terre. </s> <s id="s.000264">C'eſt pour<lb></lb>quoy il importe grandement de con- <pb pagenum="58" xlink:href="047/01/078.jpg"></pb>ſiderer les lignes par leſquelles ſe font <lb></lb><figure id="id.047.01.078.1.jpg" xlink:href="047/01/078/1.jpg"></figure><lb></lb>les mouuemens, & <lb></lb>particulierement <lb></lb>lors qu'ils ſe font <lb></lb>par des forces ina<lb></lb>nimées, dont les <lb></lb>momens, & les reſi<lb></lb>ſtances ſont en leur ſouuerain degré <lb></lb>dans la ligne <expan abbr="perpẽdiculaire">perpendiculaire</expan> à l'orizon; <lb></lb>mais elles ſe <expan abbr="diminüẽt">diminüent</expan> à proportion que <lb></lb>la ligne ſe <expan abbr="pãche">panche</expan> ſur le plan horizontal. </s> </p> <p type="head"> <s id="s.000265"><emph type="center"></emph>III. ADDITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000266">Il y a pluſieurs choſes à remarquer <lb></lb>ſur ce ſubjet qui Peuuent ſeruir pour <lb></lb>eſtablir quelque partie de la Phyſique, <lb></lb>dont i'en mets icy quelques vnes, affin <lb></lb>d'exciter les bons eſprits qui ayment la <lb></lb>verité, à paſſer oûtre. </s> <s id="s.000267">Premierement <lb></lb><figure id="id.047.01.078.2.jpg" xlink:href="047/01/078/2.jpg"></figure><lb></lb>c'eſt vne choſe tres<lb></lb>remarquable que la <lb></lb>boule FDCE ſe <lb></lb>puiſſe mouuoir auec <lb></lb>la moindre force <lb></lb>imaginable ſur le <lb></lb>plan horizontal AB, <lb></lb>dont la raiſon eſt qu'elle ne touche le <pb pagenum="59" xlink:href="047/01/079.jpg"></pb>plan qu'au point C, & que ſes deux <lb></lb>moitiez CFE, & CFD ſont en vn par<lb></lb>fait équilibre, comme lon void au <lb></lb>leuier ED, dont le bras EG eſt égal au <lb></lb>bras GD, de ſorte que ſi l'on applique <lb></lb>la moindre force du <expan abbr="mõde">monde</expan> à D la boule <lb></lb>roullera vers A. </s> <s id="s.000268">En ſecond lieu l'on <lb></lb>peut <expan abbr="cõparer">comparer</expan> le mouuement des deux <lb></lb>boules CDF, & CHG, qui eſt huict fois <lb></lb>moindre & mois peſante que l'autre, <lb></lb>car ſon diametre CG eſt ſouz double <lb></lb>de CF, & ie ſuppoſe qu'elles ſoient de <lb></lb>meſme matiere: l'on peut donc recher<lb></lb>cher laquelle des deux ſe meut plus ay<lb></lb>ſement ſur le plan AB; car il y en a qui <lb></lb>croyent que la petite ſera 8. fois plus <lb></lb>ayſée à mouuoir ſur ce plan, quoy que <lb></lb><expan abbr="parfaictemẽt">parfaictement</expan> dur & poli, à raiſon qu'el<lb></lb>le peſe 8. fois moins, & que toutes les <lb></lb>parties de chaque corps peſent ſur le <lb></lb>centre de leurs peſanteurs, & conſe<lb></lb>quemment que toute la peſanteur de <lb></lb>ces deux globes s'vnit au point C, & <lb></lb>reſiſte tant qu'elle peut au <expan abbr="mouuemẽt">mouuement</expan>. </s> <s id="s.000269"><lb></lb>Mais puiſque toutes ſortes de globes <lb></lb>tant grands que petits ont la raiſon du <lb></lb>leuier ou de la balance comme i'ay ex<lb></lb>pliqué cy-deuant, la moindre force ap- <pb pagenum="60" xlink:href="047/01/080.jpg"></pb>pliquèe aux points D, E, ou HI eſt ca<lb></lb>pable de les oſter de leur equilibre. </s> </p> <p type="main"> <s id="s.000270">En troiſieſme lieu ſi l'on ſuppoſe que <lb></lb>le plan horizontal ſoit rude, ſcabreux, & <lb></lb>mal poli, il <expan abbr="sẽble">semble</expan> que le moindre globe <lb></lb>roulera plus ayſement parce qu'il fait <lb></lb>vn plus grand angle de contingence, & <lb></lb>s'éloigne d'auantage de la ligne droite <lb></lb>AB. </s> </p> <p type="head"> <s id="s.000271"><emph type="center"></emph>IV ADDITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000272">Sur ce que Galilee dit que Pappus ſ'eſt <lb></lb>trompé, lors qu'il a voulu determiner la <lb></lb>force neceſſaire pour mouuoir vn poids <lb></lb>donné ſur vn plan propoſé, ou ſur vn <lb></lb>plan incliné, dont l'angle d'inclination <lb></lb>eſt <expan abbr="cõnu">connu</expan> l'on peut remarquer pluſieurs <lb></lb>choſes, mais particulierement qu'il la <lb></lb>ſuppoſe beaucoup trop <expan abbr="grãde">grande</expan>, car il dit <lb></lb>qu'il faut la force de 40. hommes pour <lb></lb>mouuoir le poids de 200. talents, dans <lb></lb>la 9. propoſition de ſon 8. liure, au lieu <lb></lb>que la moindre force eſt capable de le <lb></lb>mouuoir ſur ledit plan: c'eſt pourquoy <lb></lb>il a conclud qu'il failloit 260. hommes <lb></lb>pour le mouuoir ſur vn plan incliné de <lb></lb>120 degrez. </s> <s id="s.000273">Mais l'on comprendra cecy <lb></lb>plus ayſement par cette figure, dans la- <pb pagenum="61" xlink:href="047/01/081.jpg"></pb>quelle RM repreſente le plan horizon<lb></lb><figure id="id.047.01.081.1.jpg" xlink:href="047/01/081/1.jpg"></figure><lb></lb>tal, ſur lequel ie <lb></lb>ſuppoſe que le plan <lb></lb>PM eſt eleué de 30. <lb></lb>degrez, & conſe<lb></lb>quemment qu'il <lb></lb>fait 60. degrez auec <lb></lb>le plan perpendi<lb></lb>culaire BC. </s> <s id="s.000274">Or il eſt certain que la <lb></lb>force qui retient le poids, ou le globe <lb></lb>BSA ſur le plan incliné eſt audit poids, <lb></lb>comme la perpendiculaire PR eſt à <lb></lb>l'hypotenuſe PM: & parce que cette <lb></lb>hypothenuſe eſt double de la <expan abbr="perpẽdi-culaire">perpendi<lb></lb>culaire</expan>, vne force vn peu plus <expan abbr="grãde">grande</expan> que <lb></lb>ſouz double le leuera, de ſorte que ſi le <lb></lb>globe peſe 2. liures le poids P, ou O <expan abbr="peſãt">peſant</expan> <lb></lb>vne liure, & vn grain le pourra tirer. </s> </p> <p type="main"> <s id="s.000275">Il faut encore remarquer que la force <lb></lb>qui doit empeſcher que le poids ne <lb></lb>coule & ne peſe point ſur le plan PM <lb></lb>doit eſtre au poids, comme la baſe RM <lb></lb>à l'hypotenuſe PM. </s> <s id="s.000276">Or quand on veut <lb></lb>tirer le poids ſur le plan incliné, il faut <lb></lb>mettre vne poulie au haut du plan, <lb></lb>comme l'on void en D. </s> </p> <p type="main"> <s id="s.000277">Où l'on doit conſiderer la force qui<lb></lb>ſouſtient le poids dans la ligne perpen- <pb pagenum="62" xlink:href="047/01/082.jpg"></pb>diculaire PR, pour trouuer celle qui le <lb></lb>ſouſtient ſur le plan incliné, & parce <lb></lb>que le globe BSA peſe 2 liures dans <lb></lb>ladite ligne, il n'en peſera qu'vne ſur ce <lb></lb>plan incliné de 30 degrez. </s> <s id="s.000278">Neantmoins <lb></lb>quelquesvns croyent que l'on peut <lb></lb>trouuer la force qui tire le poids ſur le <lb></lb>plan incliné par la connoiſſance de la <lb></lb>force qui le meut ſur le plan <expan abbr="horizõtal">horizontal</expan>; <lb></lb>ſur quoy l'on peut veoir Cabee au 20. <lb></lb>Chapitre du 4. liure de l'aymant. </s> </p> <p type="head"> <s id="s.000279"><emph type="center"></emph>V. ADDITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000280">Cette ſpeculation des plans differens <lb></lb>eſt grandement vtile pour trouuer la <lb></lb>force requiſe pour mouuoir toutes ſor<lb></lb>tes de fardeaux ſur les montagnes, & <lb></lb>dans les valees, & pour pluſieurs autres <lb></lb>choſes: par exemple, ſi l'on vouloit <lb></lb>tirer vn fardeau ſur le plan FB, il fau<lb></lb>droit vne force, qui euſt meſme pro<lb></lb>portion au poids, que la perpendiculai<lb></lb>re BE à l'hypotenuſe BF. </s> <s id="s.000281">Mais ſi l'on <lb></lb>vouloit l'empeſcher de couler ou de <lb></lb>peſer ſur le plan BF, il faudroit vne <lb></lb>force qui euſt meſme proportion au <lb></lb>poids que FE à FB, ſuiuant ce qui a <pb pagenum="63" xlink:href="047/01/083.jpg"></pb>eſté dit dans l'addition precedente, & <lb></lb>conſequemment il faudroit que cette <lb></lb>force fuſt ſouztriple du poids, puiſque <lb></lb>EF eſt ſouztriple de BF. </s> </p> <p type="main"> <s id="s.000282">Quant à la proportion des mouue<lb></lb><figure id="id.047.01.083.1.jpg" xlink:href="047/01/083/1.jpg"></figure><lb></lb>mens qui ſe <lb></lb>font ſur les <lb></lb>plans, nous en <lb></lb><expan abbr="parlerõs">parlerons</expan> apres: <lb></lb>Ie remarque<lb></lb>ray ſeulement <lb></lb>icy que la for<lb></lb>ce eſt tou<lb></lb>ſiours à la pe<lb></lb>ſanteur qu'il faut ſouſtenir ſur les plans <lb></lb>propoſez, <expan abbr="cõme">comme</expan> le coſté qui touche la <lb></lb>force eſt au coſté ſur lequel le poids eſt <lb></lb>appuyé, ſoit que le coſté de la force ſoit <lb></lb>per pendiculaire, ou incliné ſur l'hori<lb></lb>zon: par exemple, la force eſtant poſée <lb></lb>ſur le coſté DF eſt au poids D mis <lb></lb>ſur HD, comme FD eſt à DH. </s> </p> <p type="main"> <s id="s.000283">Et ſi l'on ſuppoſe que BE ſoit vne <lb></lb>muraille impenetrable, quiſoit polie, & <lb></lb>qui ne cede nullement aux coups, la <lb></lb>bale qui la frapera au point D ſelon <lb></lb>l'inclination de l'angle CDI, qui eſt de <lb></lb>30. degrez, ſe reflechira en H par la li- <pb pagenum="64" xlink:href="047/01/084.jpg"></pb>gne DH, dautant que l'angle de refle<lb></lb>xion LDK eſt egal à celuy de l'inci<lb></lb>dence. </s> <s id="s.000284">Mais il eſt difficile de ſçauoir où <lb></lb>ſe reflechira la bale. </s> <s id="s.000285">L'on peut encore <lb></lb>conſiderer de combien vn poids deſ<lb></lb>cend plus viſte ſur vn plan incliné que <lb></lb>ſur l'autre: par exemple, de combien <lb></lb>il <expan abbr="deſcẽd">deſcend</expan> plus viſte ſur BF, que ſur CF, <lb></lb>ou DF, & s'il y a meſme raiſon de la vi<lb></lb>ſteſſe qui s'exerce ſur BF, à celle de <lb></lb>DF, que de la ligne BF à DF: mais il <lb></lb>faut reſeruer toutes ces conſiderations <lb></lb>pour la fin de ce traité. </s> <s id="s.000286">Concluons ce<lb></lb>pendant qu'il faut d'autant moins de <lb></lb>force pour leuer le poids donné, que le <lb></lb>chemin de la force eſt plus long que <lb></lb>celuy du poids, affin que l'vn <expan abbr="recõpenſe">recompenſe</expan> <lb></lb>l'autre, & que la nature ne perde rien <lb></lb>d'vn coſté qu'elle ne le gaigne de l'au<lb></lb>tre. </s> <s id="s.000287"><expan abbr="Finalemẽt">Finalement</expan> ſivn coup de <expan abbr="canõ">canon</expan> eſt tiré <lb></lb>du point H contre la muraille BE, il <lb></lb>aura ſa force entiere dans la perpendi<lb></lb>culaire HE; & le boulet appuyera en<lb></lb>tierement contre E. </s> <s id="s.000288">Mais s'il frappe <lb></lb>obliquement en D par la ligne HD, <lb></lb>il ſera d'autant moins fort que DH eſt <lb></lb>plus long que HE. <pb pagenum="65" xlink:href="047/01/085.jpg"></pb></s> </p> </chap> <chap> <p type="head"> <s id="s.000289"><emph type="center"></emph>CHAP. X.<emph.end type="center"></emph.end></s> </p> <p type="head"> <s id="s.000290"><emph type="center"></emph><emph type="italics"></emph>De la Viz d'Archimede pour <lb></lb>eſleuer les eaux.<emph.end type="italics"></emph.end><emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000291">IL faut icy adioûter la conſideration <lb></lb>de cette viz, parce que ſon effet eſt <lb></lb><figure id="id.047.01.085.1.jpg" xlink:href="047/01/085/1.jpg"></figure><lb></lb>d'autant plus <lb></lb>admirable <lb></lb>que la cauſe <lb></lb>ſemble plus <lb></lb>éloignée de <lb></lb>la raiſon, car <lb></lb>elle fait mon<lb></lb>ter l'eau par<lb></lb>ce qu'elle la <lb></lb>fait deſcen<lb></lb>dre. </s> <s id="s.000292">Son vſa<lb></lb>ge paroiſt <expan abbr="dãs">dans</expan> <lb></lb>la figure qui <lb></lb>ſuit, dans la<lb></lb>quelle ZY <lb></lb>XVTSR & <lb></lb>Q ſignifient <lb></lb>vn canal qui <lb></lb>entoure le <lb></lb>cylindre NP. </s> <s id="s.000293"><lb></lb>Or le bout du canal N doit eſtre dans <pb pagenum="66" xlink:href="047/01/086.jpg"></pb>l'eau, & le canal doit eſtre incliné; & <lb></lb>puis il faut tourner le cylindre autour <lb></lb>des points QP, & NO, iuſques à ce que <lb></lb>l'eau ſorte par Q, apres auoir monté <lb></lb>tout au long du canal, ou de l'helice <lb></lb>NO YX &c. </s> <s id="s.000294">bans la quelle l'eau mon<lb></lb>te par ce qu'elle deſcend, comme ie fais <lb></lb>voir en cette maniere. </s> </p> <p type="main"> <s id="s.000295">Soit le <expan abbr="triãgle">triangle</expan> A KB, d'où la viz NP <lb></lb>prend ſon origine, lors que l'helice à <lb></lb>meſme inclination que KA, dont la <lb></lb>ſaillie, ou l'eleuation eſt determinée par <lb></lb>l'angle BAK; & ſi cet angle eſt du <lb></lb>tiers, ou du quart d'vn angle droit, l'e<lb></lb>leuation de l'helice NZ, ou ZY ſera <lb></lb><expan abbr="ſemblablemẽt">ſemblablement</expan> le tiers, ou le quart d'vn <lb></lb>angle droit. </s> <s id="s.000296">Cecy eſtant poſé, il eſt <lb></lb><expan abbr="euidãt">euidant</expan> que la ſaillie du canal AK ſera <lb></lb>abbaiſſée quand le point K viendra au <lb></lb>point B, & qu'elle n'aura plus de pente <lb></lb>ou d'inclination, & conſequemment ſi <lb></lb>on l'abaiſſe vn peu plus bas que B, l'eau <lb></lb>coulera, & s'engorgera naturellement <lb></lb>dans le canal AK, ou XV, & tombera <lb></lb>du point A au point K, qui ſe trouuera <lb></lb>plus bas que B ſouz l'orizon. </s> <s id="s.000297">Or il faut <lb></lb>entourer le cylindre CA du triangle <lb></lb>AKB, affin de conſtruire la viz AC <pb pagenum="67" xlink:href="047/01/087.jpg"></pb><expan abbr="perpẽdiculaire">perpendiculaire</expan> ſur l'horizon EA: & puis <lb></lb>il la faut mettre dans l'eau, & la tour<lb></lb>ner, affin que l'eau monte par le canal <lb></lb>AE, qui n'eſt pas plus incliné que KA, <lb></lb>c'eſt à dire que le tiers d'vn angle droi<lb></lb>te donc ſi l'on abbaiſſe le cylindre PN <lb></lb>du tiers d'vn angle droit, les helices <lb></lb>EF, FG &c. </s> <s id="s.000298">ſeront inclinées, comme <lb></lb>l'on void au cylindre panchant PN, & <lb></lb>à ſes helices ZYXV &c. </s> <s id="s.000299">par conſe<lb></lb>quent l'eau deſcendra de N à Z, & tou<lb></lb>tes les autres helices receuront vne <lb></lb>meſme diſpoſition pour faire couler <lb></lb>l'eau iuſques au bout de la viz, de ſorte <lb></lb>que l'eau deſcendra touſiours en mon<lb></lb>tant de N à P. D'ou il faut conclure que <lb></lb>la viz doit auoir vne inclination vn peu <lb></lb>plus grande que le triangle ſur lequel <lb></lb>on la baſtie. </s> </p> <p type="head"> <s id="s.000300"><emph type="center"></emph>VI ADDITION.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000301">Il y a pluſieurs choſes à remarquer <lb></lb>pour la pente, & la deſcente, & pour <lb></lb>l'exaltation des eaux, & pour tout ce <lb></lb>qui appartient aux Siphons, & aux <lb></lb>Pompes qui attirent l'eau, ou les autres <lb></lb>liqueurs par aſpiration, mais l'vne des <pb pagenum="68" xlink:href="047/01/088.jpg"></pb>principales conſiſte à ſçauoir que l'eau <lb></lb>ne ſe meut point naturellement ſi elle <lb></lb>n'a de la pente, <expan abbr="cõme">comme</expan> l'on experimente <lb></lb>aux ruiſſeaux, aux riuieres, aux eſtangs <lb></lb>&c. </s> <s id="s.000302">ce qui fait reconnoiſtre que le <lb></lb><expan abbr="mouuemẽt">mouuement</expan> de la mer ſuppoſe de la vio<lb></lb>lence, car ſi le reflus luy eſt naturel, le <lb></lb>flus doit eſtre violent. </s> <s id="s.000303">Quant au Siphon <lb></lb>il peut ſeruir pour faire paſſer des fon<lb></lb>taines depuis le pied d'vne montagne <lb></lb>ou d'vn rocher iuſques à l'autre coſté, <lb></lb>pour changer le vin, ou les autres li<lb></lb>queurs d'vn tonneau en vn autre, pour <lb></lb>vuider les marais, & pour pluſieurs <lb></lb>autres commoditez dont nous parle<lb></lb>rons ailleurs. </s> </p> <p type="main"> <s id="s.000304">Quant à l'vſage de l'eau dans les me<lb></lb>chaniques, il eſt tres grand, comme l'on <lb></lb>experimente aux moulins à eau, & aux <lb></lb>differentes manieres dont on ſe ſert <lb></lb>pour ſçauoir la <expan abbr="differẽce">difference</expan> des peſanteurs <lb></lb>de toutes ſortes de corps plus peſans, ou <lb></lb>plus legers que l'eau, ſoit qu'on les com<lb></lb>pare enſemble, ou auec la meſme eau: <lb></lb>mais tout cecy merite vn traicté entier <lb></lb>de l'Hydraulique, comme les vtilitez <lb></lb>de l'air & du vent requierent vn diſ<lb></lb>cours entier de la Pneumatique. </s> <s id="s.000305">Mais <pb pagenum="69" xlink:href="047/01/089.jpg"></pb>par ce que Galilée n'en a rien dit <expan abbr="dãs">dans</expan> ce <lb></lb>liure, ie <expan abbr="viẽs">viens</expan> à la derniere <expan abbr="cõſideration">conſideration</expan> <lb></lb>qu'il a faite ſur la force de la percuſſion. </s> </p> </chap> <chap> <p type="head"> <s id="s.000306"><emph type="center"></emph>CHAP. XI.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000307">Il eſt neceſſaire pour pluſieurs raiſons <lb></lb>de rechercher la cauſe de la force de la <lb></lb>percuſſion, parce qu'elle contient plus <lb></lb>de merueilles que tous les autres inſtru<lb></lb>mens Mechaniques, car on experimen<lb></lb>te qu'en <expan abbr="frappãt">frappant</expan> ſur vn clou, ſur vn pieu, <lb></lb>ou pilotis, &c. </s> <s id="s.000308">ils <expan abbr="entrẽt">entrent</expan> dans des corps <lb></lb>fort durs, & qu'ils n'entrent nullement <lb></lb>ſi l'on ne frappe deſſus, encore que l'on <lb></lb>charge & que l'on preſſe les marteaux <lb></lb>auec des fardeaux mille fois plus <expan abbr="peſãs">peſans</expan> <lb></lb>qu'eux, car à peine feroit-on entrer vn <lb></lb>coin auſſi auant en le chargeant d'vne <lb></lb>maiſon entiere, comme on le fait entrer <lb></lb>à coup de marteau. </s> <s id="s.000309">Ce qui eſt d'autant <lb></lb>plus digne d'eſtre conſideré que nul <lb></lb>n'en a donné la raiſon iuſques à preſent: <lb></lb>ce qui fait voir la difficulté de cette <lb></lb>ſpeculation: car les penſées d'Ariſtote <lb></lb>& des autres qui ont voulu prendre <lb></lb>la raiſon de cet effet de la longueur de <lb></lb>la maniuelle ou du manche des mar<lb></lb>teaux ſont trop foibles, & mal fondées, <pb pagenum="70" xlink:href="047/01/090.jpg"></pb>attendu que les poids qui tombent, & <lb></lb>qui font de ſi grands effets, nont point <lb></lb>de manches. </s> <s id="s.000310">Il faut dire la meſme <lb></lb>choſe des poids que l'on pouſſe ou que <lb></lb>l'on iette de trauers. </s> <s id="s.000311">C'eſt pourquoy <lb></lb>il faut auoir recours à vn autre principe <lb></lb>pour trouuer la verité de cét effet, le<lb></lb>quel ie taſcheray à expliquer & à le <lb></lb>rendre ſenſible. </s> <s id="s.000312">Ie di <expan abbr="dõc">donc</expan> que cet effect <lb></lb>vient de la meſme ſource que les autres <lb></lb>effets Mechaniques, à ſçauoir que la <lb></lb>force, la reſiſtance, & l'eſpace par leſ<lb></lb>quels ſe <expan abbr="fõt">font</expan> les <expan abbr="mouuemẽs">mouuemens</expan> ont vne telle <lb></lb>correſpondance & proportion entr'eux <lb></lb>que la force <expan abbr="reſpõd">reſpond</expan> ſeulement à vne re<lb></lb>ſiſtance qui luy eſt égale. </s> <s id="s.000313">& qu'elle la <lb></lb>meut ſeulement par vn eſpace égal, ou <lb></lb>d'vne égale viſteſſe, dont elle ſe meut <lb></lb>elle meſme. </s> <s id="s.000314">Semblablement quand la <lb></lb>force eſt moindre de moitié que la re<lb></lb>ſiſtence, elle la peut mouuoir, ſi elle <lb></lb>meſme ſe meut d'vne double impetuo<lb></lb>ſité, & ſi elle fait deux fois autant de <lb></lb>chemin. </s> <s id="s.000315">Ce qui ſe remarque en toutes <lb></lb>ſortes d'inſtrumens, par le moyen deſ<lb></lb>quels l'on peut mouuoir & ſurmonter <lb></lb>toute ſorte de reſiſtence pour grande <lb></lb>quelle puiſſe eſtre auec vne force ſi pe- <pb pagenum="71" xlink:href="047/01/091.jpg"></pb>tite que l'on voudra, pourueu que l'eſ<lb></lb>pace que fait la force ayt meſme pro<lb></lb>portion auec l'eſpace de la reſiſtance, <lb></lb>que la grande reſiſtance à la petite for<lb></lb>ce; ce qui ſuit entierement la conſtitu<lb></lb>tion & les regles de la nature. </s> </p> <p type="main"> <s id="s.000316">Ce n'eſt <expan abbr="dõc">donc</expan> pas merueille ſi en argu<lb></lb>mentant au contraire, la force qui meut <lb></lb>vne petite reſiſtance par vn grand in<lb></lb>terualle, en pouſſe vne cent fois plus <lb></lb>grande par vn interualle cent fois <lb></lb>moindre, puis qu'il ne peut arriuer au<lb></lb>trement. </s> <s id="s.000317">Cecy eſtant poſè, il faut con<lb></lb>ſiderer qu'elle doit eſtre la reſiſtence <lb></lb>pour eſtre meüe par le marteau, qui la <lb></lb>doit frapper & pouſſer; & pour ce ſub<lb></lb>ject il faut remarquer combien la force <lb></lb>qui a eſté imprimée au marteau le por<lb></lb>ter a loing, ſi l'on ſuppoſe qu'il ne frap<lb></lb>pe point, <expan abbr="cõme">comme</expan> il arriueroit ſi le marteau <lb></lb>ſortoit de la main auec la meſme impe<lb></lb>tuoſité <expan abbr="dõt">dont</expan> il doit frapper vne enclume, <lb></lb>vn coin, ou quelqu'autre choſe, & qu'il <lb></lb>ne <expan abbr="rencõtraſt">rencontraſt</expan> nul <expan abbr="empeſchemẽt">empeſchement</expan> en ſon <lb></lb>chemin. </s> <s id="s.000318">Et puis il faut <expan abbr="cõſiderer">conſiderer</expan> quelle <lb></lb>reſiſtance fait le corps qui eſt frappé, & <lb></lb><expan abbr="cõbien">combien</expan> il eſt pouſſé par vne telle <expan abbr="percuſ-ſiõ">percuſ<lb></lb>ſiom</expan>, & <expan abbr="ayãt">ayant</expan> remarqué de <expan abbr="cõbiẽ">combien</expan> il ſe meut <pb pagenum="72" xlink:href="047/01/092.jpg"></pb>à chaque coup, & que le coin entre <lb></lb>d'autant moins auant que le marteau <lb></lb>pouſſé de la meſme impetuoſité iroit <lb></lb>moins loing <expan abbr="l'õ">l'on</expan> trouuera que ledit coin <lb></lb>entrera d'autant moins auant dans vne <lb></lb>bûche, ou dans vn autre corps à cha<lb></lb>que coup, que la reſiſtance ſera plus <lb></lb>grande que la force du marteau: de ſor<lb></lb>te qu'il ne faut plus admirer les effects <lb></lb>de la percuſſion, puis qu'ils ne <expan abbr="ſortẽt">ſortent</expan> pas <lb></lb>hors des bornes de la nature. </s> </p> <p type="main"> <s id="s.000319">A quoy i'aioûte vn exemple pour vne <lb></lb>plus grande intelligence, en ſuppoſant <lb></lb>que le marteau qui a 4. degrez de reſi<lb></lb>ſtance ſoit pouſſé d'vne telle force que <lb></lb>ne treuuant nulle <expan abbr="reſiſtãce">reſiſtance</expan> qui l'arreſte, <lb></lb>il aille iuſques à dix pas, & qu'à ce <lb></lb>terme on luy oppoſe vne poutre qui <lb></lb>ayt 4000. degrez de <expan abbr="reſiſtãce">reſiſtance</expan> & qui ſoit <lb></lb>mille fois plus grande que la force du <lb></lb>marteau, de ſorte qu'elle ſurpaſſe ſans <lb></lb>proportion ladite force, ſi elle eſt frap<lb></lb>pée, elle ira ſeulement en auant la <lb></lb>millieſme partie de dix pas, par leſquels <lb></lb>l'on auroit pouſſé le marteau. </s> </p> <p type="main"> <s id="s.000320">D'où l'on peut conclurre que la force <lb></lb>de la percuſſion ſuit les loix des autres <lb></lb>inſtrumens mechaniques, & qu'il eſt <pb pagenum="73" xlink:href="047/01/093.jpg"></pb>auſſi ayſé de la determiner que les au<lb></lb>tres forces. </s> </p> <p type="head"> <s id="s.000321"><emph type="center"></emph>ADDITION VII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000322">Galilée promettoit pluſieurs probleſ<lb></lb>mes à la fin de ſes mechaniques, mais <lb></lb>puiſque nous ne les <expan abbr="auõs">auons</expan> point veus, il <lb></lb>faut ſeulement icy aioûter quelques <lb></lb>conſiderations <expan abbr="touchãt">touchant</expan> les <expan abbr="mouuemẽs">mouuemens</expan>; <lb></lb>en attendant que nous en donnions <lb></lb>pluſieurs <expan abbr="obſeruatiõs">obſeruations</expan> tres-exactes. </s> <s id="s.000323">Soit <lb></lb>donc le plan BG incliné de 30. degrez <lb></lb>ſur le plan horizontal BF: il eſt premie<lb></lb>rement certain que le poids peſe d'au<lb></lb>tant moins ſur BG que dans la ligne <lb></lb>perpendiculaire GX, que BG eſt plus <lb></lb>grand que GX, c'eſt à dire deux fois <lb></lb><figure id="id.047.01.093.1.jpg" xlink:href="047/01/093/1.jpg"></figure><lb></lb>moins, <expan abbr="dautãt">dautant</expan> que GX, <lb></lb>eſt ſouz double de BG, <lb></lb>par la conſtruction. </s> </p> <p type="main"> <s id="s.000324">Secondement il eſt cer<lb></lb>tain que la boule miſe au <lb></lb>point G & roulante ſur <lb></lb>GB deſcend plus lente<lb></lb>ment que par la ligne G <lb></lb>X. </s> <s id="s.000325">Mais il eſt difficile de <lb></lb>ſçauoir combien elle deſcend plus viſte <pb pagenum="74" xlink:href="047/01/094.jpg"></pb>par GX. </s> <s id="s.000326">Galilée croit dans vn autre <lb></lb>diſcours qu'en meſme <expan abbr="tẽps">temps</expan> que la boule <lb></lb>deſcend de G en H elle deſcendroit <lb></lb>de G en E, & qu'au meſme temps qu'el<lb></lb>le deſcend de G en B, elle deſcen<lb></lb>droît de Gen D. </s> <s id="s.000327">Car le point de la li<lb></lb>gne perpendiculaire, auquel ſe rencon<lb></lb>treroit le poids tombant, ſe determine <lb></lb>par les perpendiculaires deſcrites ſur le <lb></lb>plan incliné, comme l'on void icy aux <lb></lb>perpendiculaires HE & BD tirées des <lb></lb>deux points H, B, auſquels on ſuppoſe <lb></lb>que la boule eſt arriuée en roûlant: ce <lb></lb>qu'il faut auſſi, ce ſemble, conclurre des <lb></lb>autres corps qui gliſſent ſeulement. </s> <s id="s.000328"><lb></lb>En troiſieſme lieu, l'on peut conſiderer <lb></lb>ſi les poids qui ſe meuuent ſur le plan <lb></lb>incliné gardent la meſme proportion <lb></lb>en leur viſteſſe que ceux qui ſe <expan abbr="meuuẽt">meuuent</expan> <lb></lb>perpendiculairement vers le centre de <lb></lb>la terre, c'eſt à dire s'ils <expan abbr="haſtẽt">haſtent</expan> leur cour<lb></lb>ſe en raiſon doublée des <expan abbr="tẽps">temps</expan> par exem<lb></lb>ples ſi G ayant <expan abbr="deſcẽdu">deſcendu</expan> iuſque, au quart <lb></lb>de ſon plan dans le premier temps, <lb></lb>deſcend les trois autres quarts dans le <lb></lb>ſecond temps. </s> <s id="s.000329">En quatrieſme lieu, la <lb></lb>ſpeculation de Galilée eſt excellente, ſi <lb></lb>elle eſt veritable, à ſçauoir qu'vne bou- <pb pagenum="75" xlink:href="047/01/095.jpg"></pb>le deſcend en meſme temps ſur tous les <lb></lb>plans qui ſont dans le meſme demi cer<lb></lb>cle, ce que l'on comprendra par cette <lb></lb>figure dans laquelle AB eſt le diametre, <lb></lb>qui repreſente la cheute perpendicu<lb></lb><figure id="id.047.01.095.1.jpg" xlink:href="047/01/095/1.jpg"></figure><lb></lb>laire. </s> <s id="s.000330">EB, DB, <lb></lb>& CB, ou FB, <lb></lb>GB, & HB <expan abbr="mõ-ſtrẽt">mon<lb></lb>ſtrent</expan> les cheutes <lb></lb>obliques, qui ſe <lb></lb>font toutes en <lb></lb>meſme temps <lb></lb>depuis le haut <lb></lb>iuſques au bas <lb></lb>de chaque plan, de ſorte que la boule <lb></lb>va auſſi toſt de G à B que d'E à B. </s> <s id="s.000331">Par <lb></lb>ou l'on void que le mouuement de la <lb></lb>boule eſt d'autant plus lent que le plan <lb></lb>obligue s'approche <expan abbr="dauãtage">dauantage</expan> de l'hori<lb></lb>zontal IK, ſur lequel il n'a plus de mou<lb></lb>uement par ce qu'il ne peur plus s'ap<lb></lb>procher du centre de la terre. </s> <s id="s.000332">Cette <lb></lb>figure contient encore d'autres lignes, à <lb></lb>ſçauoir AF, FG, GH, AG, & AH, ſur <lb></lb>ſur leſquelles on peut encore conſide<lb></lb>rer les mouuemens d'vne boule, affin <lb></lb>de les comparer auec ceux qui ſe font <lb></lb>ſur les plans FG, GH, &c. </s> </p> <pb pagenum="76" xlink:href="047/01/096.jpg"></pb> <p type="main"> <s id="s.000333">En cinquieſme lieu, il faudroit conſi<lb></lb>derer quelle eſt la viteſſe des mouue<lb></lb>mens qui ſe font ſur les plans BE, CE: <lb></lb><figure id="id.047.01.096.1.jpg" xlink:href="047/01/096/1.jpg"></figure><lb></lb>& D<lb></lb>E, qui <lb></lb>ſont <lb></lb>dans <lb></lb>le <lb></lb>quart <lb></lb>du <lb></lb>cer<lb></lb>cle B<lb></lb>CE, & quelle proportion elle a auec la <lb></lb>viteſſe du mouuement d'A en E, dont la <lb></lb>partie AH ſe faiſant dans vn <expan abbr="tẽps">temps</expan> don<lb></lb>né, tout le reſte depuis H iuſques à E ſe <lb></lb>fait dans vn autre temps egal. </s> <s id="s.000334">Où il faut <lb></lb>encore remarquer que ſi l'on pend le <lb/>poids E à la chorde AE, & qu'on tire le <lb></lb>poids iuſques à B, que B <expan abbr="deſcẽdra">deſcendra</expan> quaſi <lb></lb>en meſme temps de B à E par le quart <lb></lb>du cercle BCE qu'il deſcendra de C, <lb></lb>ou de D au meſme E. </s> <s id="s.000335">Or les lignes Bk, <lb></lb>KL, & LM font veoir combien les <lb></lb>poids <expan abbr="deſcendẽt">deſcendent</expan> ſur les plans CE & DE, <lb></lb>& conſequemment de combien il ſont <lb></lb>retardez, & empeſchez par chaque plan <lb></lb>incliné: par <expan abbr="exẽple">exemple</expan>, le poids B roulant <pb pagenum="77" xlink:href="047/01/097.jpg"></pb>de B à C ſur le plan BC deſcend autant <lb></lb>que quand il roulle de C en E, car la li<lb></lb>gne BK eſt égale à KM; & le poids <lb></lb>roullant de C à D deſcend plus de deux <lb></lb>fois dauantage que celuy qui va de D à <lb></lb>E car LK eſt plus que double de LM. <lb></lb>D'où il eſt ayſé de <expan abbr="cõclure">conclure</expan> que le poids <lb></lb>B qui deſcend par le quart de cercle <lb></lb>BCE iroit <expan abbr="d'autãt">d'autant</expan> plus lentement qu'il <lb></lb>approche dauantage du point E, s'il n'a<lb></lb>querroit nulle impetuoſité. </s> </p> <p type="main"> <s id="s.000336">En ſixieſme lieu, la chorde AB con<lb></lb>duira le poids B iuſques au diamettre <lb></lb>AE dans vn temps donné, ſi elle eſt en <lb></lb>raiſon doublee dudit temps, lors qu'elle <lb></lb>doit ſe mouuoir dans vn plus grand <lb></lb>temps; ou en raiſon ſouzdoublée, ſi el<lb></lb>le ſe doit mouuoir dans vn moindre <lb></lb>temps: par exemple, ſi la chorde AB <lb></lb>porte B dans 4. moments iuſques à E, <lb></lb>la chorde ſouzquadruple AI portera'I <lb></lb>iuſques à H dans vn moment. </s> </p> <p type="main"> <s id="s.000337">En ſeptieſme lieu, le poids qui <expan abbr="deſcẽd">deſcend</expan> <lb></lb>de B en M, ou d'A en E va non <expan abbr="ſeulemẽt">ſeulement</expan> <lb></lb>plus lentement en commençant ſon <lb></lb>mouuement, mai, auſſi il paſſe par tous <lb></lb>les degrez poſſibles de tardiueté, de ſor<lb></lb>te que s'il n'augmentoit point la viſteſſe <pb pagenum="78" xlink:href="047/01/098.jpg"></pb>qu'il a vers le milieu de la premiere ſep<lb></lb>tieſme minute, il ſeroit deux ans & <lb></lb>20 iours à deſcendre l'eſpace d'vn <lb></lb>pied de Roy, comme ie demonſtreray <lb></lb>dans vn traité particulier. </s> </p> <p type="head"> <s id="s.000338"><emph type="center"></emph>ADDITION VIII.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000339">Il eſt certain que les poids qui deſ<lb></lb>cendent vers le centre augmentent <lb></lb>touſiours leur impetuoſité, & que ſi on <lb></lb>laiſſe cheoir vne boule ſur le plan CA, <lb></lb>elle aura autant d'impetuoſité lors <lb></lb>qu'elle ſera arriuée au point A, comme <lb></lb>quand elle ſera tombée en B du point <lb></lb>C parce qu'elle ſera auſſi proche du <lb></lb>centre en A qu'en B: & cette impetuo<lb></lb>ſité ſera aſſez grande pour faire remon<lb></lb><figure id="id.047.01.098.1.jpg" xlink:href="047/01/098/1.jpg"></figure><lb></lb>ter le meſme <lb></lb>poids iuſques à <lb></lb>C ſoit par la li<lb></lb>gne oblique <lb></lb>AC, ou par la <lb></lb>perpendiculai<lb></lb>re BC, pour<lb></lb>ueu qu'il n'y ayt nul empeſchement ex<lb></lb>terieur. </s> <s id="s.000340">Mais tandis que le poids tom<lb></lb>be de C en T, il tombe de C en B, & par <pb pagenum="79" xlink:href="047/01/099.jpg"></pb>conſequemment il acquier beaucoup <lb></lb>plus d'impetuoſité en meſme temps <lb></lb>par le plan horizontal que par l'in<lb></lb>cliné. </s> <s id="s.000341">Semblablement tandis que le <lb></lb>poids tombe par le plan AD de D en I, <lb></lb>il tombe de D en B, car la ligne IB eſt <lb></lb>perpendiculaire ſur la ligne AD; & ſi le <lb></lb>poids tombe iuſques en A, il ſera tombé <lb></lb>par la perpendiculaire DB prolongée <lb></lb>iuſques au poinct, auquel elle ſera cou<lb></lb>pée par la ligne tirée du point A paral<lb></lb>lele à IB, laquelle ſera perpendiculaire <lb></lb>au plan IA. </s> <s id="s.000342">Or il y a grande apparence <lb></lb>que le temps auquel le poids tombe <lb></lb>de C en B eſt au temps auquel il tombe <lb></lb>de C en A, comme la ligne CB eſt à la <lb></lb>ligne CA. </s> <s id="s.000343">Ce que l'on peut exami<lb></lb>ner en cette maniere. </s> <s id="s.000344">Suppoſons donc <lb></lb>que le temps de la cheute d'A en B ſur <lb></lb>le plan AB ſoit égal au temps de la <lb></lb>cheute qui ſe fait d'A en D: & <lb></lb><figure id="id.047.01.099.1.jpg" xlink:href="047/01/099/1.jpg"></figure><lb></lb>pour ce ſubiect qu'au tri<lb></lb>angle rectangle ABD le <lb></lb>coſté D ſoit de 4. parties, & <lb></lb>le coſté BA de deux, ſi A <lb></lb>D eſt 1000. AB ſera 500, <lb></lb>& partant l'angle BDA <lb></lb>ſera de 30 degrez, car DA <expan abbr="eſtãt">eſtant</expan>, le rayon <pb pagenum="80" xlink:href="047/01/100.jpg"></pb>AB ſera le Sinus de 30 degrez, & l'an<lb></lb>gle BDA ſera de 60. degrez, & conſe<lb></lb>quemment le coſté BD ſera 866, c'eſt <lb></lb>à dire le Sinus de 60. Au triangle ABC <lb></lb>rectangle, en C l'angle BCA eſt connu <lb></lb>de 60 degrez, donc l'angle ABC eſt de <lb></lb>30. degrez, dont le ſinus AC eſt 250, à <lb></lb>ſçauoir la moitié du rayon BA, & BC <lb></lb>ſinus de BAC 60. eſt 433. de telles parties <lb></lb>dont AD eſt 1000: donc ſi AC eſt 250. <lb></lb>AB ſera 500. & AD 1000, de ſorte qu'A <lb></lb>B eſt moyenne proportionnelle en<lb></lb>tre DA, & CA; donc AD eſt quadru<lb></lb>ple de CA, & conſequemment AB eſt <lb></lb>double de CA. </s> <s id="s.000345">De plus ſi l'on ſup<lb></lb>poſe qu'AC ſoit de 3. pieds, le poids <lb></lb>tombe de cet eſpace dans vne ſeconde, <lb></lb>& AD eſtant quadruple d'AC, le poids <lb></lb>tombera par AD en deux ſecondes, & <lb></lb>parce que nous <expan abbr="auõs">auons</expan> ſuppoſé qu'il chet <lb></lb>par la ligne AB en meſme temps que <lb></lb>par la perpendiculaire AD, il fera auſſi <lb></lb>l'eſpace AB en 2. ſecondes. </s> <s id="s.000346">De ſorte <lb></lb>qu'il y aura meſme raiſon du temps de <lb></lb>la cheute AC à celuy de la cheute de 3 <lb></lb>pieds AB que de la ligne BA à la ligne <lb></lb>CA, qui a ſix pieds. </s> </p> <p type="main"> <s id="s.000347">Il faut encore remarquer que comme <pb pagenum="81" xlink:href="047/01/101.jpg"></pb>AC eſt ſouz quadruple de DA, que <lb></lb>CE eſt auſſi ſouzquadruple de BD, & <lb></lb>AE de BA, & que de meſme que CD <lb></lb>eſt triple de CA, que BE eſt triple d'E <lb></lb>A, & que comme la racine de CA eſt à <lb></lb>la racine de DA, que le temps de la <lb></lb>cheute CA eſt à celuy de la cheute <lb></lb>DA. </s> <s id="s.000348">Et parce que le poids qui tombe <lb></lb>d'A en B eſt deux fois autant de temps <lb></lb>que celuy qui tombe d'A en C, l'on <lb></lb>peut dire qu'il va auſſi viſte par AB que <lb></lb>par AC, puis qu'il fait vn chemin dou<lb></lb>ble dans vn temps double. </s> </p> <p type="main"> <s id="s.000349">D'où ie conclus que le plan peut telle<lb></lb>ment eſtre incliné ſur l'horizon BC, <lb></lb>que la boule miſe deſſus ſera plus <lb></lb>d'vn an à rouler iuſques à B, & qu'vn <lb></lb>temps infini ne ſuffiroit pas pour ſon <lb></lb>roulement ſur le plan horizontal de C <lb></lb>en B, parce que ſa tardiueté deuient in<lb></lb>finie quand le plan incliné eſt reduit au <lb></lb>plan horizontal, ſur lequel la boule ne <lb></lb>ſe peut mouuoir que circulairement, <lb></lb>ſuppoſé que la terre ſoit parfaitement <lb></lb>ronde, ce qui n'arriue point ſi le mou<lb></lb>uement droit ne precede, & n'en eſt <lb></lb>cauſe: mais le poids n'aquierra point de <lb></lb>plus grande viſteſſe ſur le plan horizon- <pb pagenum="82" xlink:href="047/01/102.jpg"></pb>tal, ſur lequel il ira touſiours <expan abbr="vniforme-mẽt">vniforme<lb></lb>ment</expan> s'il ne trouue nulle <expan abbr="empeſchemẽt">empeſchement</expan>, <lb></lb>d'autant qu'il eſt touſiours également <lb></lb>éloigné de ſon centre. </s> </p> <p type="head"> <s id="s.000350"><emph type="center"></emph>ADDITION. IX.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000351">Galilée n'a point traité des <expan abbr="inſtrumẽs">inſtrumens</expan> <lb></lb>qui ſe ſeruent de roües dentelees, com<lb></lb><figure id="id.047.01.102.1.jpg" xlink:href="047/01/102/1.jpg"></figure><lb></lb>me <expan abbr="ſõt">ſont</expan> celles cy B & A, qui tournent par <lb></lb>le moyen de la maniuelle E, à laquelle <lb></lb>la moindre roüe A, que l'on appelle or<lb></lb>dinairement le Pignon, eſt attachée, <lb></lb>affin d'accommoder ſes dents à celles <lb></lb>de la grande roüe B, qui tourne ſur ſon <lb></lb>eſſieu C, à l'entour duquel l'on met la <lb></lb>chorde qui tient le poids D. </s> <s id="s.000352">Or on <pb pagenum="83" xlink:href="047/01/103.jpg"></pb>multiplie ces roües tant que l'on veut <lb></lb>iuſques à l'infini: mais plus il y en a <expan abbr="dãs">dans</expan> <lb></lb>vn inſtrument & plus on eſt long temps <lb></lb><figure id="id.047.01.103.1.jpg" xlink:href="047/01/103/1.jpg"></figure><lb></lb>à leuer <lb></lb>le poids <lb></lb>attaché <lb></lb>à celle <lb></lb>qui <lb></lb>tourne <lb></lb>le plus <lb></lb>lente<lb></lb>ment, <lb></lb><expan abbr="cõme">comme</expan> <lb></lb><expan abbr="l'õ">l'on</expan> <expan abbr="experimẽte">expe<lb></lb>rimente</expan> <lb></lb>aux hor<lb></lb>loges à <lb></lb>roües, <lb></lb>& à reſ<lb></lb>ſors. </s> <s id="s.000353">Ie <lb></lb>mets <lb></lb>ſeule<lb></lb>ment <lb></lb>icy la fi<lb></lb>gure de <lb></lb>l'inſtru<lb></lb>ment <lb></lb>que l'on appelle Cry, qui ſert pour <pb pagenum="84" xlink:href="047/01/104.jpg"></pb>releuer les caroſſes, & les charrettes qui <lb></lb>ſont verſées. </s> <s id="s.000354">La moindre figure IGH <lb></lb>fait voir ſa forme exterieure, & les <expan abbr="crãs">crans</expan>, <lb></lb>ou les dents H, qui ont la fourchette G <lb></lb>en haut pour leuer les fardeaux. </s> <s id="s.000355">CB <lb></lb>fait veoir la maniuelle & le Pignon B <lb></lb>qui fait tourner la grande roüe AB, la<lb></lb>quelle fait hauſſer le cry FE par le <lb></lb>moyen du pignon à trois dents D qui, <lb></lb>ſ'aiuſte dans les dents de FE. </s> <s id="s.000356">Si l'on <lb></lb>multiplie les roües de cry on le rendra ſi <lb></lb>fort qu'il pourra leuer vne <expan abbr="maiſõ">maiſon</expan> toute <lb></lb>entiere, mais ſon effet ſera plus tardif en <lb></lb><figure id="id.047.01.104.1.jpg" xlink:href="047/01/104/1.jpg"></figure><lb></lb>recompenſe. </s> <s id="s.000357">Mais l'on ne peut enten<pb pagenum="85" xlink:href="047/01/105.jpg"></pb>dre la nature & les proprietez de ces <lb></lb>inſtrumens, ſi l'on ne comprend les pro<lb></lb>prietez du cercle, dont ie parle dans <lb></lb>vn autre lieu. </s> <s id="s.000358">Il y a encore d'au<lb></lb>tres roües qui ont vne grande force, <lb></lb>comme ſont celles de la viz ſans fin, <lb></lb>dont ie donne ſeulement icy la figure, <lb></lb>dans laquelle EFG eſt la plus grande <lb></lb>roüe. </s> <s id="s.000359">AD eſt l'arbre entouré des fi<lb></lb>lets E qui entrent dans les dents de la <lb></lb>dite roüe: mais ſi l'on adioute la roüe <lb></lb>CB, elle redoublera la force, & la mani<lb></lb>velle L fera tourner l'arbre K, dont les <lb></lb>filets B entrent dans les dents de la ſe<lb></lb>conde roüe BC. </s> <s id="s.000360">Le poids I eſt attaché <lb></lb>à la chorde H, & ſe tient en chaque <lb></lb>degré de hauteur où l'on veut, ſans <lb></lb>qu'il ſoit beſoin d'arreſter l'inſtrument <lb></lb>par aucune force: mais les filets des ar<lb></lb>bres s'vſent bien toſt. </s> </p> <p type="main"> <s id="s.000361">Finalement ie veux adiouter vn <lb></lb>mouſſle à ſix poulies qui n'a pas eſté <lb></lb>mis en ſon lieu, dans le chapitre des <lb></lb>poulies, affin que ceux qui s'en vou<lb></lb>dront ſeruir, voyent comme il faut <lb></lb>conſtruire cet inſtrument, que Pappus <lb></lb>appelle Polyſpaſte dans la 24 propoſi<lb></lb>tion du 8. liure de ſes Recueils Mathe- <pb pagenum="86" xlink:href="047/01/106.jpg"></pb><figure id="id.047.01.106.1.jpg" xlink:href="047/01/106/1.jpg"></figure><lb></lb>matiques, où il nomme <lb></lb>l'armeure HF, ou AG <lb></lb><emph type="italics"></emph>manganum.<emph.end type="italics"></emph.end></s> </p> <p type="main"> <s id="s.000362">L'on voit donc en ce <lb></lb>mouffle ſix roües, à ſça<lb></lb>uoir 3 en bas F, D, B, & <lb></lb>3 en haut G, E, C, mais <lb></lb>la derniere d'enhaut <lb></lb>G ne multiplie point la <lb></lb>force, dautant qu'elle <lb></lb>ne ſert que comme la <lb></lb>ſimple poulie d'vn <lb></lb>puys. </s> <s id="s.000363">Or cet inſtru<lb></lb>ment eſt plaiſant en ce <lb></lb>que ſi 4 ou 5 hommes <lb></lb>employent toute leur <lb></lb>force à tirer la chorde <lb></lb>IK, celuy qui tire le <lb></lb>bout de la chorde L <lb></lb>d'vne ſeule main les <lb></lb>fait venir à luy malgré <lb></lb>qu'ils en a yent. </s> <s id="s.000364">Et l'on <lb></lb>peut y mettre tant de <lb></lb>poulies que l'on mene<lb></lb>ra les Egliſes, les tours, <lb></lb>& les autres edifices <lb></lb>où l'on voudra, pour<lb></lb>ueu <expan abbr="qu'õ">qu'on</expan> les puiſſe cein- <pb pagenum="87" xlink:href="047/01/107.jpg"></pb>dre de chordes aſſez fortes pour ce ſuiet, <lb></lb>& que les murailles ne ſe ſeparent point <lb></lb>les vnes des autres. </s> <s id="s.000365">Ceux qui veulent <lb></lb>ſerieuſement eſtudier aux Mechani<lb></lb>ques doiuent lire tout le 8 liure de <lb></lb>Pappus, <expan abbr="dãs">dans</expan> lequel il explique pluſieurs <lb></lb>ſortes d'inſtrumens; & les liure de Gui<lb></lb>don Vbalde, qui a le mieux de tous trai<lb></lb>té de la nature de ces inſtrumens. </s> </p> <p type="head"> <s id="s.000366"><emph type="center"></emph>ADDITION. X.<emph.end type="center"></emph.end></s> </p> <p type="main"> <s id="s.000367">Ie mets encore icy vne figure du plan <lb></lb>incliné, affin que l'on conſidere l'utilité <lb></lb>du triangle rectangle dans les mecha<lb></lb>niques. </s> <s id="s.000368">Soit donc le triangle BAC, <expan abbr="dõt">dont</expan> <lb></lb>la ſouſtendante ou l'hypotenuſe BC <lb></lb><figure id="id.047.01.107.1.jpg" xlink:href="047/01/107/1.jpg"></figure><lb></lb>eſt double du co<lb></lb>ſté BA, & la baſe <lb></lb>AC eſt parallele <lb></lb>à l'horizon il: eſt <lb></lb>conſtant que le <lb></lb>poids F doit eſtre 2. fois auſſi peſant que <lb></lb>le poids D pour eſtre équilibre, <expan abbr="dautãt">dautant</expan> <lb></lb>qu'ils doiuent garder entr'eux la meſme <lb></lb>raiſon que le coſté CB au coſté AB. </s> <s id="s.000369"><lb></lb>Mais lors que l'on veut ſçauoir la force <lb></lb>dont le poids F preſſe le plan BF, il faut <lb></lb>prendre la baſe du triangle AC & la <pb pagenum="88" xlink:href="047/01/108.jpg"></pb>comparer auec l'hypotenuſe BC, d'au<lb></lb>tant que la peſanteur entiere du <lb></lb>poids F eſt à celle par. </s> <s id="s.000370">laquelle il <lb></lb>preſſe le plan BC, comme CB eſt à <lb></lb>CA, de ſorte que ſi BC eſt 5, & CA 4. <lb></lb>la raiſon de la <expan abbr="peſãteur">peſanteur</expan> totale eſt ſeſqui<lb></lb>quarte de la peſanteur relatiue, & <expan abbr="con-ſequãment">con<lb></lb>ſequamment</expan> la force F ne pourroit rom<lb></lb>pre vne reſiſtance de 5. Par où lon voit <lb></lb>que la conſideration du rayon AC, de la <lb></lb>tangente BA, & de la <expan abbr="ſecãte">ſecante</expan> BC eſt en<lb></lb>tierement neceſſaire pour les mechani<lb></lb>ques, dont i'ay parlé fort amplement <lb></lb>dans le dix & l'onzieſme theorême du <lb></lb>ſecond liure de l'harmonie vniuerſelle. </s> </p> <p type="main"> <s id="s.000371">Or puiſque l'on demonſtre que la vi<lb></lb>ſteſſe des poids qui deſcendent ſur les <lb></lb>plans inclinez s'augmentent en raiſon <lb></lb>doublée des temps, il eſt ayſé de deter<lb></lb>miner vn lieu ſur vn plan incliné tel que <lb></lb>l'on voudra, auquel le poids ira auſſi <lb></lb>viſte qu'en vn autre lieu donné de ſa <lb></lb>deſcente perpendiculaire, comme l'on <lb></lb>peut conclure de ce qui a eſté dit dans la <lb></lb>8 Addition. <lb></lb></s> </p> <p> <s id="s.000372">FIN.</s> </p> </chap> </body> </text> </archimedes>