| version 1.4, 2007/08/03 14:37:49 |
version 1.9, 2007/09/06 15:16:21 |
| |
| <pb xlink:href="047/01/005.jpg"/><emph type="italics"/>force & s'il e&longs;t <expan abbr="l&etilde;s">lens</expan>, vnepetite force &longs;uffit. </s> | <pb xlink:href="047/01/005.jpg"/><emph type="italics"/>force & s'il e&longs;t <expan abbr="l&etilde;s">lens</expan>, vnepetite force &longs;uffit. </s> |
| <s id="s.000011"><lb/>En effet il e&longs;timpo&longs;&longs;ible de gaigner la for­<lb/>ce, & le téps tout <expan abbr="ens&etilde;ble">ensemble</expan>, <expan abbr="cõme">comme</expan> il e&longs;t im­<lb/>po&longs;&longs;ible qu'vn homme iouy&longs;&longs;e des plai­<lb/>&longs;irs fola&longs;tres du monde & de ceux du <lb/>Ciel en me&longs;me temps: de &longs;orte que les <lb/>Mechaniques peuuent en &longs;eigner à bien <lb/>viure, &longs;oit en imitant les corps pe&longs;ans <lb/>quicherchent tou&longs;iours leur centre dans <lb/>celuy de la terre comme le &longs;prit de l'hom. </s> | <s id="s.000011"><lb/>En effet il e&longs;timpo&longs;&longs;ible de gaigner la for­<lb/>ce, & le téps tout <expan abbr="ens&etilde;ble">ensemble</expan>, <expan abbr="cõme">comme</expan> il e&longs;t im­<lb/>po&longs;&longs;ible qu'vn homme iouy&longs;&longs;e des plai­<lb/>&longs;irs fola&longs;tres du monde & de ceux du <lb/>Ciel en me&longs;me temps: de &longs;orte que les <lb/>Mechaniques peuuent en &longs;eigner à bien <lb/>viure, &longs;oit en imitant les corps pe&longs;ans <lb/>quicherchent tou&longs;iours leur centre dans <lb/>celuy de la terre comme le &longs;prit de l'hom. </s> |
| <s id="s.000012"><lb/>me doit chercher le &longs;ien dans l'e&longs;&longs;ence <lb/>diuine qui e&longs;t la &longs;ource de tous les e&longs;prits <lb/>ou en &longs;e tenantdans le perpetuel èquili­<lb/>bre moral, & rai&longs;onnable qui con&longs;i&longs;te à <lb/>rendre premierement à Dieu, & puis <lb/>au prochain tout ce que luy appartient. </s> | <s id="s.000012"><lb/>me doit chercher le &longs;ien dans l'e&longs;&longs;ence <lb/>diuine qui e&longs;t la &longs;ource de tous les e&longs;prits <lb/>ou en &longs;e tenantdans le perpetuel èquili­<lb/>bre moral, & rai&longs;onnable qui con&longs;i&longs;te à <lb/>rendre premierement à Dieu, & puis <lb/>au prochain tout ce que luy appartient. </s> |
| <s id="s.000013"><lb/>L'autheurde ce traité a obmis beaucoup <lb/>de cho&longs;es, par <expan abbr="ex&etilde;ple">exemple</expan> il n'a point parlédu <lb/>coin qui e&longs;t <expan abbr="l'in&longs;trum&etilde;t">l'in&longs;trument</expan> le plus fort de touslb/>car &longs;a force en partie depend de l'incli­<lb/>nation du plan, comme Guid Vbalde <lb/>demon&longs;tre dans le traité, qu'il en a fait, <lb/>de &longs;orte que le coin entre dautant plus<emph.end type="italics"/> | <s id="s.000013"><lb/>L'autheur de ce traité a obmis beaucoup <lb/>de cho&longs;es, par <expan abbr="ex&etilde;ple">exemple</expan> il n'a point parlé du <lb/>coin qui e&longs;t <expan abbr="l'in&longs;trum&etilde;t">l'in&longs;trument</expan> le plus fort de tous <lb/>car &longs;a force en partie depend de l'incli­<lb/>nation du plan, comme Guid Vbalde <lb/>demon&longs;tre dans le traité, qu'il en a fait, <lb/>de &longs;orte que le coin entre dautant plus <emph.end type="italics"/> |
| | |
| | |
| <pb xlink:href="047/01/006.jpg"/><emph type="italics"/>ay&longs;ement qu'il e&longs;t plus e&longs;troit, & que <lb/>&longs;es co&longs;tez panchent dauantage &longs;ur l'ho­<lb/>riz on, c'e&longs;t à dire qu'ils font de moin­<lb/>dres angles. </s> | <pb xlink:href="047/01/006.jpg"/><emph type="italics"/>ay&longs;ement qu'il e&longs;t plus e&longs;troit, & que <lb/>&longs;es co&longs;tez panchent dauantage &longs;ur l'ho­<lb/>riz on, c'e&longs;t à dire qu'ils font de moin­<lb/>dres angles. </s> |
| |
| <s id="s.000022"><emph type="center"/>PREFACE AV LECTEVR.<emph.end type="center"/></s> | <s id="s.000022"><emph type="center"/>PREFACE AV LECTEVR.<emph.end type="center"/></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000023">IE &longs;eray content &longs;i ie &longs;uis cau&longs;e <lb/>que le &longs;ieur Galilée nous don­<lb/>ne toutes &longs;es &longs;peculations des <lb/>mouuemens, & de tout ce qui ap­<lb/>partientaux Mechaniques, car ce <lb/>qui viendra de &longs;a part &longs;era excel­<lb/>lent: c'e&longs;t pourquoy ie prie ceux <lb/>qui ont de la corre&longs;pondance à <lb/>Florénce, de l'exhorter par lettres <lb/>à donner au public toutes &longs;es re­<lb/>marques, comme i'e&longs;pere qu'il <lb/>fera puis qu'il a maintenant le <lb/>temps, & la commodité tres libre <lb/>dans &longs;a mai&longs;on des champs, & <lb/>qu'il a cncor a&longs;&longs;ez de force, quoy <lb/>qu'il &longs;oit plus que &longs;eptuagenaire <lb/>pour acheuer toutes &longs;es ocuures, <lb/>comme il a&longs;&longs;eure dans vne lettre <lb/>de &longs;a main que l'on m'a commu­<lb/>niquée. </s> | <s id="s.000023">IE &longs;eray content &longs;i ie &longs;uis cau&longs;e <lb/>que le &longs;ieur Galilée nous don­<lb/>ne toutes &longs;es &longs;peculations des <lb/>mouuemens, & de tout ce qui ap­<lb/>partient aux Mechaniques, car ce <lb/>qui viendra de &longs;a part &longs;era excel­<lb/>lent: c'e&longs;t pourquoy ie prie ceux <lb/>qui ont de la corre&longs;pondance à <lb/>Florénce, de l'exhorter par lettres <lb/>à donner au public toutes &longs;es re­<lb/>marques, comme i'e&longs;pere qu'il <lb/>fera puis qu'il a maintenant le <lb/>temps, & la commodité tres libre <lb/>dans &longs;a mai&longs;on des champs, & <lb/>qu'il a encor a&longs;&longs;ez de force, quoy <lb/>qu'il &longs;oit plus que &longs;eptuagenaire <lb/>pour acheuer toutes &longs;es ocuures, <lb/>comme il a&longs;&longs;eure dans vne lettre <lb/>de &longs;a main que l'on m'a commu­<lb/>niquée. </s> |
| <s id="s.000024">Or en attendant ces trai­<lb/>cez excellent, l'on peut voir les | <s id="s.000024">Or en attendant ces trai­<lb/>tez excellent, l'on peut voir les <pb xlink:href="047/01/011.jpg"/>3 liures des Mechaniques, que le <lb/>feis imprimer l'année 1626; à quoy <lb/>i'aioute maintenant la con&longs;idera­<lb/>tion des deux cercles qu'Ari&longs;tote <lb/>a propo&longs;ez dans la 24 que&longs;tion de <lb/>&longs;es Mechaniques, parce que plu­<lb/>&longs;ieurs la <expan abbr="trouu&etilde;t">trouuent</expan> admirable dau­<lb/>tant qu'ils ne l'entendent pas. </s> |
| <pb xlink:href="047/01/011.jpg"/>3 liures des Mechaniques, que le <lb/>feis imprimer l'année 1626; à quoy <lb/>i'aioute maintenant la con&longs;idera­<lb/>tion des deux cercles qu'Ari&longs;tote <lb/>a propo&longs;ez dans la 24 que&longs;tion de <lb/>&longs;es Mechaniques, parce que plu­<lb/>&longs;ieurs la <expan abbr="trouu&etilde;t">trouuent</expan> admirable dau­<lb/>tant qu'ils ne l'entendent pas. </s> | |
| <s id="s.000025"><lb/>Et pour ce &longs;ujet &longs;oit le grand cer­<lb/>cle ACB, & le moindre FGH, il <lb/><figure id="id.047.01.011.1.jpg" xlink:href="047/01/011/1.jpg"/><lb/>e&longs;t certain <lb/>que quand <lb/>le quart du <lb/>grand cercle <lb/>BD s'e&longs;t meu <lb/>iu&longs;ques au <lb/>poinct O, de <lb/>&longs;orte que le point D &longs;erencontre <lb/>au point O, que le point E du <lb/>quart du moindre cercle FE &longs;e <expan abbr="r&etilde;-cõtre">ren­<lb/>contre</expan> au point N, & <expan abbr="cõ&longs;equ&etilde;ment">con&longs;equemment</expan> <lb/>que le petit cercle fait autant de <lb/>chemin que le grand en me&longs;me | <s id="s.000025"><lb/>Et pour ce &longs;ujet &longs;oit le grand cer­<lb/>cle ACB, & le moindre FGH, il <lb/><figure id="id.047.01.011.1.jpg" xlink:href="047/01/011/1.jpg"/><lb/>e&longs;t certain <lb/>que quand <lb/>le quart du <lb/>grand cercle <lb/>BD s'e&longs;t meu <lb/>iu&longs;ques au <lb/>poinct O, de <lb/>&longs;orte que le point D &longs;erencontre <lb/>au point O, que le point E du <lb/>quart du moindre cercle FE &longs;e <expan abbr="r&etilde;-cõtre">ren­<lb/>contre</expan> au point N, & <expan abbr="cõ&longs;equ&etilde;ment">con&longs;equemment</expan> <lb/>que le petit cercle fait autant de <lb/>chemin que le grand en me&longs;me |
| <pb xlink:href="047/01/012.jpg"/>temps, pui&longs;que le plan FN &longs;ur le­<lb/>quel il &longs;e meut e&longs;t égal au plan <lb/>DO, &longs;ur lequel roule le grand. </s> | <pb xlink:href="047/01/012.jpg"/>temps, pui&longs;que le plan FN &longs;ur le­<lb/>quel il &longs;e meut e&longs;t égal au plan <lb/>DO, &longs;ur lequel roule le grand. </s> |
| </p> | </p> |
| |
| <s id="s.000030">Et lors que le petit e&longs;t meu <lb/>parle grand, vne me&longs;me partie <lb/>du petit, touche cent parties du <lb/>grand, comme l'experience fera <lb/>voir à tous ceux qui la feront en <lb/>a&longs;&longs;ez grand volume. </s> | <s id="s.000030">Et lors que le petit e&longs;t meu <lb/>parle grand, vne me&longs;me partie <lb/>du petit, touche cent parties du <lb/>grand, comme l'experience fera <lb/>voir à tous ceux qui la feront en <lb/>a&longs;&longs;ez grand volume. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000031">Les me&longs;mes erreurs arriuent en <lb/>plu&longs;ieurs autres chofes, ce qui a <lb/>donné &longs;uiect à quelques vns d'e&longs;­<lb/>crire <emph type="italics"/>derebus fal&longs;ò creditis,<emph.end type="italics"/> dont ie <lb/>donneray cncore icy vn exem­<lb/>ple. </s> | <s id="s.000031">Les me&longs;mes erreurs arriuent en <lb/>plu&longs;ieurs autres chofes, ce qui a <lb/>donné &longs;uiect à quelques vns d'e&longs;­<lb/>crire <emph type="italics"/>derebus fal&longs;ò creditis,<emph.end type="italics"/> dont ie <lb/>donneray encore icy vn exem­<lb/>ple. </s> |
| <s id="s.000032">L'on croyt que &longs;i on iette vne <lb/>pierre en haut le plus droit que <lb/>l'on peut: lors que l'on e&longs;t dans <lb/>vn nauire qui &longs;ingle à pleins voi­<lb/>les, ou dans vn carro&longs;&longs;e qui va en <lb/>po&longs;te, que la pierre tombera de­<lb/>riere le licud'ou l'on la iette, quoy <lb/>que l'experience en&longs;eigne qu'elle <lb/>retombe dans la main qui la iette | <s id="s.000032">L'on croyt que &longs;i on iette vne <lb/>pierre en haut le plus droit que <lb/>l'on peut: lors que l'on e&longs;t dans <lb/>vn nauire qui &longs;ingle à pleins voi­<lb/>les, ou dans vn carro&longs;&longs;e qui va en <lb/>po&longs;te, que la pierre tombera de­<lb/>riere le lieu d'ou l'on la iette, quoy <lb/>que l'experience en&longs;eigne qu'elle <lb/>retombe dans la main qui la iette |
| <pb xlink:href="047/01/015.jpg"/>en core que le nauire, ou le carro­<lb/>&longs;&longs;e fa&longs;&longs;e cent pas, tandis que la <lb/>pierre e&longs;t dans l'air. </s> | <pb xlink:href="047/01/015.jpg"/>en core que le nauire, ou le carro­<lb/>&longs;&longs;e fa&longs;&longs;e cent pas, tandis que la <lb/>pierre e&longs;t dans l'air. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| |
| <s id="s.000069"><emph type="center"/><emph type="italics"/>PRIVILEGE DV ROY.<emph.end type="italics"/><emph.end type="center"/></s> | <s id="s.000069"><emph type="center"/><emph type="italics"/>PRIVILEGE DV ROY.<emph.end type="italics"/><emph.end type="center"/></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000070">PAr lettres du Roy donnces à Paris <lb/>le mois d'Aou&longs;t de l'année 1629. <lb/>&longs;ignees Perrochel, & &longs;eelees du grand <lb/>&longs;ceau de cire iaune, il e&longs;t permis au <lb/>P. M. </s> | <s id="s.000070">PAr lettres du Roy donnees à Paris <lb/>le mois d'Aou&longs;t de l'année 1629. <lb/>&longs;ignees Perrochel, & &longs;eelees du grand <lb/>&longs;ceau de cire iaune, il e&longs;t permis au <lb/>P. M. </s> |
| <s id="s.000071">Mer&longs;enne Religieux Minime <lb/>de faire imprimer par tel Libraire que <lb/>bon luy &longs;emblera <emph type="italics"/>Plu&longs;ieurs Traittez de <lb/>Philo&longs;ophie, de Theologie, & de Mathema­<lb/>tique.<emph.end type="italics"/><!-- KEEP S--></s> | <s id="s.000071">Mer&longs;enne Religieux Minime <lb/>de faire imprimer par tel Libraire que <lb/>bon luy &longs;emblera <emph type="italics"/>Plu&longs;ieurs Traittez de <lb/>Philo&longs;ophie, de Theologie, & de Mathema­<lb/>tique.<emph.end type="italics"/><!-- KEEP S--></s> |
| <s id="s.000072"> Et deffences &longs;ont faites à toutes <lb/>per&longs;onnes de quelque qualité qu'ils <lb/>&longs;oient de les faire imprimer, vendre & <lb/>diftribuer pendantle temps de &longs;ix ans à <lb/>compter du iour que le&longs;dits liures &longs;e­<lb/>ront acheuez d'imprimer, comme il <lb/>e&longs;t plus amplement porté dans les let­<lb/>tres dudit Priuilege. </s> | <s id="s.000072"> Et deffences &longs;ont faites à toutes <lb/>per&longs;onnes de quelque qualité qu'ils <lb/>&longs;oient de les faire imprimer, vendre & <lb/>diftribuer pendantle temps de &longs;ix ans à <lb/>compter du iour que le&longs;dits liures &longs;e­<lb/>ront acheuez d'imprimer, comme il <lb/>e&longs;t plus amplement porté dans les let­<lb/>tres dudit Priuilege. </s> |
| </p> | </p> |
| |
| <s id="s.000074">Mer&longs;enne à con&longs;enty & con­<lb/>&longs;ent que Henry Guenon ioüi&longs;&longs;e dudit Pri­<lb/>uilege, comme il e&longs;t plus amplement decla­<lb/>ré par l'accord fait entr eux. </s> | <s id="s.000074">Mer&longs;enne à con&longs;enty & con­<lb/>&longs;ent que Henry Guenon ioüi&longs;&longs;e dudit Pri­<lb/>uilege, comme il e&longs;t plus amplement decla­<lb/>ré par l'accord fait entr eux. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000075"><emph type="center"/>Et le&longs;dits liures ont e&longs;té achenés d'imprimer le <lb/>30. Iuin 1634.<emph.end type="center"/></s> | <s id="s.000075"><emph type="center"/>Et le&longs;dits liures ont e&longs;té acheués d'imprimer le <lb/>30. Iuin 1634.<emph.end type="center"/></s> |
| </p> | </p> |
| </section> | </section> |
| <section> | <section> |
| |
| <s id="s.000078"><emph type="center"/><emph type="italics"/>Dans lequelon void la Preface quimon&longs;tre <lb/>l'vtilité des Machines.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> | <s id="s.000078"><emph type="center"/><emph type="italics"/>Dans lequelon void la Preface quimon&longs;tre <lb/>l'vtilité des Machines.<emph.end type="italics"/><emph.end type="center"/><!-- KEEP S--></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000079">AVANT que d'entrepren­<lb/>dre la &longs;peculation des in­<lb/>&longs;trumens de la Mechani­<lb/>que, il faut remarquer en <lb/>general les commoditez, & les profits <lb/>que l'on en peut tirer, afin que les arti­<lb/>&longs;ans ne croyent pas qu'ils pui&longs;&longs;ent &longs;eruir <lb/>aux operations, dontils ne &longs;ont pas ca- | <s id="s.000079">AVANT que d'entrepren­<lb/>dre la &longs;peculation des in­<lb/>&longs;trumens de la Mechani­<lb/>que, il faut remarquer en <lb/>general les commoditez, & les profits <lb/>que l'on en peut tirer, afin que les arti­<lb/>&longs;ans ne croyent pas qu'ils pui&longs;&longs;ent &longs;eruir <lb/>aux operations, dont ils ne &longs;ont pas ca-<pb pagenum="2" xlink:href="047/01/022.jpg"/>pables, & que l'on pui&longs;&longs;e leuer de <expan abbr="grãds">grands</expan> <lb/>fardeaux auec peu de force: car la na­<lb/>ture ne peut e&longs;tre trompée, ni ceder à <lb/>&longs;es droits: & nulle re&longs;i&longs;tence ne peut <lb/>e&longs;tre &longs;urmontée que par vne plus gran­<lb/>de force, comme ie feray voir apres: & <lb/>con&longs;equemment les Machines ne peu­<lb/>uent &longs;eruir à leuer de plus grands far­<lb/>deaux que ceux qu'vne force égale <lb/>peut leuer &longs;ans l'ayde d'aucun in&longs;tru­<lb/>ment: c'e&longs;t pourquoy il faut expliquer <lb/>les vrayes vtilitez des Machines, afin <lb/>que l'on ne trauaille pas en vain, & que <lb/>l'e&longs;tude que l'on fera, reü&longs;&longs;i&longs;&longs;e heureu­<lb/>&longs;ement. </s> |
| <pb pagenum="2" xlink:href="047/01/022.jpg"/>pables, & que l'on pui&longs;&longs;e leuer de <expan abbr="grãds">grands</expan> <lb/>fardeaux auec peu de force: car la na­<lb/>ture ne peut e&longs;tre trompée, ni ceder à <lb/>&longs;es droits: & nulle re&longs;i&longs;tence ne peut <lb/>e&longs;tre &longs;urmontée que par vne plus gran­<lb/>de force, comme ie feray voir apres: & <lb/>con&longs;equemment les Machines ne peu­<lb/>uent &longs;eruir à leuer de plus grands far­<lb/>deaux que ceux qu'vne force égale <lb/>peut leuer &longs;ans l'ayde d'aucun in&longs;tru­<lb/>ment: c'e&longs;t pourquoy il faut expliquer <lb/>les vrayes vtilitez des Machines, afin <lb/>que l'on ne trauaille pas en vain, & que <lb/>l'e&longs;tude que l'on fera, reü&longs;&longs;i&longs;&longs;e heureu­<lb/>&longs;ement. </s> | |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000080">Il faut doncicy con&longs;iderer 4. cho&longs;es, <lb/>à &longs;çauoir le fardeau que l'on veut tran&longs;­<lb/>porter d'vn lieu à vn autre: la force qui <lb/>le doit mouuoir; la di&longs;tance par laquel­<lb/>le &longs;e fait le mouuement; & le temps <lb/>dudit mouuement, parce qu'il &longs;ert pour <lb/>en determiner la vi&longs;te&longs;&longs;e, puis qu'elle <lb/>e&longs;t d'autant plus grande que le corps <lb/>mobile, ou le fardeau pa&longs;&longs;e par vne plus <lb/>grande di&longs;tance en me&longs;me temps: de <lb/>&longs;orte que &longs;i l'on &longs;uppo&longs;etelle re&longs;i&longs;tence, <lb/>telle force, & telle <expan abbr="di&longs;tãce">di&longs;tance</expan> determinée <lb/>que l'on voudra, il n'y anul doute que | <s id="s.000080">Il faut donc icy con&longs;iderer 4. cho&longs;es, <lb/>à &longs;çauoir le fardeau que l'on veut tran&longs;­<lb/>porter d'vn lieu à vn autre: la force qui <lb/>le doit mouuoir; la di&longs;tance par laquel­<lb/>le &longs;e fait le mouuement; & le temps <lb/>dudit mouuement, parce qu'il &longs;ert pour <lb/>en determiner la vi&longs;te&longs;&longs;e, puis qu'elle <lb/>e&longs;t d'autant plus grande que le corps <lb/>mobile, ou le fardeau pa&longs;&longs;e par vne plus <lb/>grande di&longs;tance en me&longs;me temps: de <lb/>&longs;orte que &longs;i l'on &longs;uppo&longs;e telle re&longs;i&longs;tence, <lb/>telle force, & telle <expan abbr="di&longs;tãce">di&longs;tance</expan> determinée <lb/>que l'on voudra, il n'y a nul doute que <pb pagenum="3" xlink:href="047/01/023.jpg"/>la force requi&longs;e conduira le fardeau à <lb/>la di&longs;tance donnée, quoy que ladite <lb/>force &longs;oit tre&longs;-petite, pourueu que l'on <lb/>diui&longs;e le fardeau en tant de parties que <lb/>la force en pui&longs;&longs;e mouuoir vne, car elle <lb/>les <expan abbr="trã&longs;portera">tran&longs;portera</expan> toutes les vnes apres les <lb/>autres; d'où il &longs;'en&longs;uit que la moindre <lb/>force du monde peut tran&longs;porter tel <lb/>poids que l'on voudra. </s> |
| <pb pagenum="3" xlink:href="047/01/023.jpg"/>la force requi&longs;e conduira le fardeau à <lb/>la di&longs;tance donnée, quoy que ladite <lb/>force &longs;oit tre&longs;-petite, pourueu que l'on <lb/>diui&longs;e le fardeau en tant de parties que <lb/>la force en pui&longs;&longs;e mouuoir vne, car elle <lb/>les <expan abbr="trã&longs;portera">tran&longs;portera</expan> toutes les vnes apres les <lb/>autres; d'où il &longs;'en&longs;uit que la moindre <lb/>force du monde peut tran&longs;porter tel <lb/>poids que l'on voudra. </s> | |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000081">Mais l'on ne peut dire à la fin du <expan abbr="trã&longs;-port">tran&longs;­<lb/>port</expan>, que l'on ayt remué vn grand far­<lb/>deau auec peu de force, puis qu'elle a <lb/>tou&longs;iours e&longs;té égale à chaque partie du <lb/>fardeau: de maniere que l'on ne gaigne <lb/>rien auec les in&longs;trumens, dautant que &longs;i <lb/>l'on applique vne petite force à vn <expan abbr="grãd">grand</expan> <lb/>fardeau, il faut beaucoup de temps, & <lb/>que &longs;i l'on veut le tran&longs;porter en peu de <lb/>temps, il faut vne grande force. </s> | <s id="s.000081">Mais l'on ne peut dire à la fin du <expan abbr="trã&longs;-port">tran&longs;­<lb/>port</expan>, que l'on ayt remué vn grand far­<lb/>deau auec peu de force, puis qu'elle a <lb/>tou&longs;iours e&longs;té égale à chaque partie du <lb/>fardeau: de maniere que l'on ne gaigne <lb/>rien auec les in&longs;trumens, dautant que &longs;i <lb/>l'on applique vne petite force à vn <expan abbr="grãd">grand</expan> <lb/>fardeau, il faut beaucoup de temps, & <lb/>que &longs;i l'on veut le tran&longs;porter en peu de <lb/>temps, il faut vne grande force. </s> |
| |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000176">Il faut donc conclurre de tout ce di&longs;­<lb/>cours que dans cét in&longs;trument la force | <s id="s.000176">Il faut donc conclurre de tout ce di&longs;­<lb/>cours que dans cét in&longs;trument la force |
| <pb pagenum="30" xlink:href="047/01/050.jpg"/>C ou F doit tou&longs;iours auoir me&longs;me <expan abbr="pro-portiõ">pro­<lb/>portiom</expan> auec le poids, que le &longs;emidiame <lb/>tre de l'axe BA a auec le &longs;emidiametre <lb/>de la rouë AC. </s> | <pb pagenum="30" xlink:href="047/01/050.jpg"/>C ou F doit tou&longs;iours auoir me&longs;me <expan abbr="pro-portiõ">pro­<lb/>portion</expan> auec le poids, que le &longs;emidiame <lb/>tre de l'axe BA a auec le &longs;emidiametre <lb/>de la rouë AC. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000177">Quant à la Gruë elle e&longs;t de me&longs;me <lb/>nature que le Tour, mais le Cabe&longs;tan, <lb/>le Guindax, ou l'orgene e&longs;t vn peu dif­<lb/>rent, car &longs;on axe &longs;e meut perpendicu­<lb/>laire à l'orizon, & &longs;a rouë &longs;e meut hori­<lb/>zontalement, au lieu que l'axe du Tour <lb/><figure id="id.047.01.050.1.jpg" xlink:href="047/01/050/1.jpg"/><lb/>&longs;e meut horizontale­<lb/>ment, & &longs;a rouë <expan abbr="per-pendiculairem&etilde;t">per­<lb/>pendiculairement</expan>. </s> | <s id="s.000177">Quant à la Gruë elle e&longs;t de me&longs;me <lb/>nature que le Tour, mais le Cabe&longs;tan, <lb/>le Guindax, ou l'orgene e&longs;t vn peu dif­<lb/>rent, car &longs;on axe &longs;e meut perpendicu­<lb/>laire à l'orizon, & &longs;a rouë &longs;e meut hori­<lb/>zontalement, au lieu que l'axe du Tour <lb/><figure id="id.047.01.050.1.jpg" xlink:href="047/01/050/1.jpg"/><lb/>&longs;e meut horizontale­<lb/>ment, & &longs;a rouë <expan abbr="per-pendiculairem&etilde;t">per­<lb/>pendiculairement</expan>. </s> |
| <s id="s.000178">Ce <lb/>qui e&longs;t tres-ay&longs;é à <expan abbr="cõ-prendre">con­<lb/>prendre</expan> par le moyen <lb/>de cette figure, dont <lb/>il faut s'imaginer que <lb/>l'axe DE &longs;oit <expan abbr="perp&etilde;-diculaire">perpen­<lb/>diculaire</expan> à l'horizon, & que la rouë F <lb/>CG &longs;oit parallele au me&longs;me horizon. </s> | <s id="s.000178">Ce <lb/>qui e&longs;t tres-ay&longs;é à <expan abbr="cõ-prendre">com­<lb/>prendre</expan> par le moyen <lb/>de cette figure, dont <lb/>il faut s'imaginer que <lb/>l'axe DE &longs;oit <expan abbr="perp&etilde;-diculaire">perpen­<lb/>diculaire</expan> à l'horizon, & que la rouë F <lb/>CG &longs;oit parallele au me&longs;me horizon. </s> |
| <s id="s.000179"><lb/>Or la chorde DH tirera, ou trainera le <lb/>fardeau H iu&longs;ques à l'axe B, ou iu&longs;ques <lb/>où l'on voudra, par la force d'vn hom­<lb/>me, ou d'vn cheual qui conduira le le­<lb/>uier B à l'entour de la circonference F <lb/>GC, & fera autant de tours comme il <lb/>e&longs;t nece&longs;&longs;aire pour attirer le fardeau par <lb/>le moyen de la chorde DH, qui &longs;'en- | <s id="s.000179"><lb/>Or la chorde DH tirera, ou trainera le <lb/>fardeau H iu&longs;ques à l'axe B, ou iu&longs;ques <lb/>où l'on voudra, par la force d'vn hom­<lb/>me, ou d'vn cheual qui conduira le le­<lb/>uier B à l'entour de la circonference F <lb/>GC, & fera autant de tours comme il <lb/>e&longs;t nece&longs;&longs;aire pour attirer le fardeau par <lb/>le moyen de la chorde DH, qui &longs;'en- |
| <pb pagenum="31" xlink:href="047/01/051.jpg"/>tortille à l'entour de l'e&longs;&longs;ieu DEA: <lb/>d'où il e&longs;t ay&longs;é de conclurre la fabrique <lb/>du Guindax, ou du Cabe&longs;tan. <!-- KEEP S--></s> | <pb pagenum="31" xlink:href="047/01/051.jpg"/>tortille à l'entour de l'e&longs;&longs;ieu DEA: <lb/>d'où il e&longs;t ay&longs;é de conclurre la fabrique <lb/>du Guindax, ou du Cabe&longs;tan. <!-- KEEP S--></s> |
| </p> | </p> |
| |
| <p type="main"> | <p type="main"> |
| <s id="s.000185">APres auoir con&longs;ideré les <expan abbr="in&longs;trum&etilde;s">in&longs;trumens</expan> <lb/>qui &longs;e redui&longs;ent aux contrepoids, <lb/>& à l'équilibre, comme à leur principe, <lb/><figure id="id.047.01.052.1.jpg" xlink:href="047/01/052/1.jpg"/><lb/>& à leur <lb/><expan abbr="fondem&etilde;t">fondement</expan> <lb/>il fautpar­<lb/>ler d'vne <lb/>autre &longs;or­<lb/>te de le­<lb/>uier pour entendre la nature des pou­<lb/>lies, & de beaucoup d'autres effets Me- | <s id="s.000185">APres auoir con&longs;ideré les <expan abbr="in&longs;trum&etilde;s">in&longs;trumens</expan> <lb/>qui &longs;e redui&longs;ent aux contrepoids, <lb/>& à l'équilibre, comme à leur principe, <lb/><figure id="id.047.01.052.1.jpg" xlink:href="047/01/052/1.jpg"/><lb/>& à leur <lb/><expan abbr="fondem&etilde;t">fondement</expan> <lb/>il fautpar­<lb/>ler d'vne <lb/>autre &longs;or­<lb/>te de le­<lb/>uier pour entendre la nature des pou­<lb/>lies, & de beaucoup d'autres effets Me- |
| <pb pagenum="33" xlink:href="047/01/053.jpg"/>chaniques. </s> | <pb pagenum="33" xlink:href="047/01/053.jpg"/>chaniques. </s> |
| <s id="s.000186">Or le leuier, dont nous <lb/>auons parlé, &longs;uppo&longs;e que le poids &longs;oit <lb/>à l'vne de &longs;es extremitez, & la force à <lb/>l'autre; de &longs;orte que &longs;on &longs;ou&longs;tien doit <lb/>e&longs;tie entre &longs;es deux extremitez. </s> | <s id="s.000186">Or le leuier, dont nous <lb/>auons parlé, &longs;uppo&longs;e que le poids &longs;oit <lb/>à l'vne de &longs;es extremitez, & la force à <lb/>l'autre; de &longs;orte que &longs;on &longs;ou&longs;tien doit <lb/>e&longs;tre entre &longs;es deux extremitez. </s> |
| <s id="s.000187">Mais <lb/>&longs;i l'on met le &longs;ou&longs;tien à l'extremité du <lb/>leuier, & la force à l'autre extremité C, <lb/>& que le point D &longs;oit attaché à quelque <lb/>point du milieu: par exemple, au point <lb/>B, il e&longs;t certain que &longs;i le poids e&longs;t égale­<lb/>ment éloigné des deux extremes, com­<lb/>me quand il e&longs;t au point F, que la force <lb/>quile &longs;ou&longs;tient en F &longs;era également di­<lb/>ui&longs;ée: & par con&longs;equent la moitié du <lb/>poids e&longs;t &longs;ou&longs;tenuë par C, & l'autre <lb/>moitié par A. <!-- KEEP S--></s> | <s id="s.000187">Mais <lb/>&longs;i l'on met le &longs;ou&longs;tien à l'extremité du <lb/>leuier, & la force à l'autre extremité C, <lb/>& que le point D &longs;oit attaché à quelque <lb/>point du milieu: par exemple, au point <lb/>B, il e&longs;t certain que &longs;i le poids e&longs;t égale­<lb/>ment éloigné des deux extremes, com­<lb/>me quand il e&longs;t au point F, que la force <lb/>quile &longs;ou&longs;tient en F &longs;era également di­<lb/>ui&longs;ée: & par con&longs;equent la moitié du <lb/>poids e&longs;t &longs;ou&longs;tenuë par C, & l'autre <lb/>moitié par A. <!-- KEEP S--></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| |
| <s id="s.000189"><lb/>Mais pour comprendre cecy, il faut <lb/>s'imaginer que la ligne BA &longs;oit prolon­<lb/>gee en G, & que les di&longs;tances BA, AG <lb/>&longs;oient égales, & que le fardeau &longs;oit at­<lb/>taché au point C, & qu'il &longs;oit égal au <lb/>poids D, il e&longs;t certain qu'à cau&longs;e de l'é­<lb/>galité des poids E, D, & des di&longs;tances | <s id="s.000189"><lb/>Mais pour comprendre cecy, il faut <lb/>s'imaginer que la ligne BA &longs;oit prolon­<lb/>gee en G, & que les di&longs;tances BA, AG <lb/>&longs;oient égales, & que le fardeau &longs;oit at­<lb/>taché au point C, & qu'il &longs;oit égal au <lb/>poids D, il e&longs;t certain qu'à cau&longs;e de l'é­<lb/>galité des poids E, D, & des di&longs;tances |
| <pb pagenum="34" xlink:href="047/01/054.jpg"/>AC, & BA, le mouuement du poids <lb/>D &longs;uffira pour le &longs;ou&longs;tenir, donc la for­<lb/>ce du moment égalà celuy du point E, <lb/>lequelle pourra &longs;ou&longs;tenir, &longs;uffira enco­<lb/>re pour &longs;ou&longs;tenir le poids D. <!-- KEEP S--></s> | <pb pagenum="34" xlink:href="047/01/054.jpg"/>AC, & BA, le mouuement du poids <lb/>D &longs;uffira pour le &longs;ou&longs;tenir, donc la for­<lb/>ce du moment égalà celuy du point E, <lb/>lequelle pourra &longs;ou&longs;tenir, &longs;uffira enco­<lb/>re pour &longs;ou&longs;tenir le poids D. <!-- KEEP S--></s> |
| <s id="s.000190">Mais &longs;i l'on <lb/>veut &longs;ou&longs;tenir E au point C, la force <lb/>doit e&longs;tre à E, comme GA à CA, donc <lb/>la me&longs;me force pourra &longs;ou&longs;tenir le <lb/>point D égal à E. <!-- KEEP S--></s> | <s id="s.000190">Mais &longs;i l'on <lb/>veut &longs;ou&longs;tenir E au point C, la force <lb/>doit e&longs;tre à E, comme GA à CA, donc <lb/>la me&longs;me force pourra &longs;ou&longs;tenir le <lb/>point D égal à E. <!-- KEEP S--></s> |
| <s id="s.000191">Or la proportion qui <lb/>e&longs;t de GA à EA, e&longs;t au&longs;&longs;i de BA à CA, <lb/>GA e&longs;tant égal à BA: Et parce que les <lb/>poids ED &longs;ont égaux, chacun d'eux <lb/>aura la me&longs;me <expan abbr="proportiõ">proportiom</expan> à la force mi&longs;e <lb/>en C. D'où l'on conclud que la force C <lb/>e&longs;t égale au <expan abbr="mom&etilde;t">moment</expan> D, lors qu'il a me&longs;­<lb/>me proportion que la di&longs;tance AB à <lb/>CA. <!-- KEEP S--></s> | <s id="s.000191">Or la proportion qui <lb/>e&longs;t de GA à EA, e&longs;t au&longs;&longs;i de BA à CA, <lb/>GA e&longs;tant égal à BA: Et parce que les <lb/>poids ED &longs;ont égaux, chacun d'eux <lb/>aura la me&longs;me <expan abbr="proportiõ">proportion</expan> à la force mi&longs;e <lb/>en C. D'où l'on conclud que la force C <lb/>e&longs;t égale au <expan abbr="mom&etilde;t">moment</expan> D, lors qu'il a me&longs;­<lb/>me proportion que la di&longs;tance AB à <lb/>CA. <!-- KEEP S--></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000192">Or il e&longs;t tres-ay&longs;é de conclurre de <lb/>tout ce di&longs;cours que l'on perd autant <lb/>de vi&longs;te&longs;&longs;e comme l'on acquiert de for­<lb/>ce tant auec le leuier ordinaire qu'auec <lb/>celuy-cy: car quand la force C hau&longs;&longs;e <lb/>le leuier AC, pour le <expan abbr="trã&longs;porter">tran&longs;porter</expan> en AI, <lb/>le poids &longs;e meut par l'interualle BH, <lb/>lequel e&longs;t dautant moindre que l'e&longs;pa­<lb/>ce IC, qu'a fait la force, qu'AB e&longs;t <lb/>moindre qu'AC. <!-- KEEP S--></s> | <s id="s.000192">Or il e&longs;t tres-ay&longs;é de conclurre de <lb/>tout ce di&longs;cours que l'on perd autant <lb/>de vi&longs;te&longs;&longs;e comme l'on acquiert de for­<lb/>ce tant auec le leuier ordinaire qu'auec <lb/>celuy-cy: car quand la force C hau&longs;&longs;e <lb/>le leuier AC, pour le <expan abbr="trã&longs;porter">tran&longs;porter</expan> en AI, <lb/>le poids &longs;e meut par l'interualle BH, <lb/>lequel e&longs;t dautant moindre que l'e&longs;pa­<lb/>ce IC, qu'a fait la force, qu'AB e&longs;t <lb/>moindre qu'AC. <!-- KEEP S--></s> |
| |
| <s id="s.000194">Et pour ce &longs;uiet &longs;uppo&longs;ons que <lb/>l'on ayt la poulie ABC faite de metal, <lb/>ou d'vn bois fort dur, & qu'elle pui&longs;&longs;e <lb/>tourner &longs;ur &longs;on e&longs;&longs;ieu, qui pa&longs;&longs;e par le <lb/>centre D: & puis il faut mettre à l'en­<lb/><figure id="id.047.01.055.1.jpg" xlink:href="047/01/055/1.jpg"/><lb/>tour la chorde FCBAE, <lb/>à laquelle le poids E &longs;oit at­<lb/>taché. </s> | <s id="s.000194">Et pour ce &longs;uiet &longs;uppo&longs;ons que <lb/>l'on ayt la poulie ABC faite de metal, <lb/>ou d'vn bois fort dur, & qu'elle pui&longs;&longs;e <lb/>tourner &longs;ur &longs;on e&longs;&longs;ieu, qui pa&longs;&longs;e par le <lb/>centre D: & puis il faut mettre à l'en­<lb/><figure id="id.047.01.055.1.jpg" xlink:href="047/01/055/1.jpg"/><lb/>tour la chorde FCBAE, <lb/>à laquelle le poids E &longs;oit at­<lb/>taché. </s> |
| <s id="s.000195">Quant à la force, el­<lb/>le e&longs;t à l'autre bout de la <lb/>chorde au point F, où elle <lb/>&longs;ou&longs;tient le fardeau E. <!-- KEEP S--></s> | <s id="s.000195">Quant à la force, el­<lb/>le e&longs;t à l'autre bout de la <lb/>chorde au point F, où elle <lb/>&longs;ou&longs;tient le fardeau E. <!-- KEEP S--></s> |
| <s id="s.000196">Car <lb/>&longs;i <expan abbr="l'õ">l'om</expan> &longs;'imagine deux lignes <lb/>égales tirées du centre D, <lb/>à &longs;çauoir DC, & DA, l'on <lb/>aura l'équilibre de deux <lb/><expan abbr="mom&etilde;ts">moments</expan>, ou de deux poids <lb/>égaux, également éloignez <lb/>de l'appuy D, qui e&longs;t le <lb/>point du &longs;ou&longs;tien, lequel e&longs;t <lb/>également éloigné de tous <lb/>les co&longs;tez de la <expan abbr="circõference">circonference</expan> du cercle, <lb/>ou de la poulie ABC. <!-- KEEP S--></s> | <s id="s.000196">Car <lb/>&longs;i <expan abbr="l'õ">l'om</expan> &longs;'imagine deux lignes <lb/>égales tirées du centre D, <lb/>à &longs;çauoir DC, & DA, l'on <lb/>aura l'équilibre de deux <lb/><expan abbr="mom&etilde;ts">moments</expan>, ou de deux poids <lb/>égaux, également éloignez <lb/>de l'appuy D, qui e&longs;t le <lb/>point du &longs;ou&longs;tien, lequel e&longs;t <lb/>également éloigné de tous <lb/>les co&longs;tez de la <expan abbr="circõference">circonference</expan> du cercle, <lb/>ou de la poulie ABC. <!-- KEEP S--></s> |
| <s id="s.000197">Or ces deux li­<lb/>gnes, qui &longs;ont les bras du leuiet, ou de <lb/>la balance, determinent les di&longs;tances <lb/>des deux &longs;u&longs;pen&longs;ions d'auec le centre <lb/>D: C'e&longs;t pourquoy le poids qui e&longs;t &longs;u&longs;- | <s id="s.000197">Or ces deux li­<lb/>gnes, qui &longs;ont les bras du leuier, ou de <lb/>la balance, determinent les di&longs;tances <lb/>des deux &longs;u&longs;pen&longs;ions d'auec le centre <lb/>D: C'e&longs;t pourquoy le poids qui e&longs;t &longs;u&longs;- |
| <pb pagenum="36" xlink:href="047/01/056.jpg"/>pendu du point A ne peut e&longs;tre &longs;ou&longs;te­<lb/>nu au point C que par vne égale force, <lb/>ou par vn poids égal, &longs;uiuant la nature <lb/>des poids égaux qui pendent de di&longs;tan­<lb/>ces égales. </s> | <pb pagenum="36" xlink:href="047/01/056.jpg"/>pendu du point A ne peut e&longs;tre &longs;ou&longs;te­<lb/>nu au point C que par vne égale force, <lb/>ou par vn poids égal, &longs;uiuant la nature <lb/>des poids égaux qui pendent de di&longs;tan­<lb/>ces égales. </s> |
| <s id="s.000198">Car encore que la force F <lb/>tourne à l'entour de la poulie ABC, <lb/>cela ne change nullement l'habitude, <lb/>& le rapport que le poids, & la force <lb/>ont à la di&longs;tance AD, & DC: dautant <lb/>que la poulie garde vn perpetuel équi­<lb/>libre en &longs;e tournant. </s> | <s id="s.000198">Car encore que la force F <lb/>tourne à l'entour de la poulie ABC, <lb/>cela ne change nullement l'habitude, <lb/>& le rapport que le poids, & la force <lb/>ont à la di&longs;tance AD, & DC: dautant <lb/>que la poulie garde vn perpetuel équi­<lb/>libre en &longs;e tournant. </s> |
| <s id="s.000199">D'où il faut con­<lb/>clurre qu'Ari&longs;tote &longs;e trompe lors qu'il <lb/>dit que l'on leue plus ay&longs;ément les far­<lb/>deaux auec les plus grandes poulies, car <lb/>encore que la di&longs;tance, ou le demidia­<lb/>metre de la poulie DC &longs;'augmente, ce­<lb/>la ne &longs;ert de rien à rai&longs;on que la di&longs;tan­<lb/>ce DA &longs;'augmente également. </s> | <s id="s.000199">D'où il faut con­<lb/>clurre qu'Ari&longs;tote &longs;e trompe lors qu'il <lb/>dit que l'on leue plus ay&longs;ément les far­<lb/>deaux auec les plus grandes poulies, car <lb/>encore que la di&longs;tance, ou le demidia­<lb/>metre de la poulie DC &longs;'augmente, ce­<lb/>la ne &longs;ert de rien à rai&longs;on que la di&longs;tan­<lb/>ce DA &longs;'augmente également. </s> |
| <s id="s.000200">De &longs;or­<lb/>te que l'on ne reçoit nulle commodité <lb/>de cét in&longs;trument en ce qui concerne <lb/>la <expan abbr="diminutiõ">diminutiom</expan> de la peine. </s> | <s id="s.000200">De &longs;or­<lb/>te que l'on ne reçoit nulle commodité <lb/>de cét in&longs;trument en ce qui concerne <lb/>la <expan abbr="diminutiõ">diminution</expan> de la peine. </s> |
| <s id="s.000201">Mais &longs;a com­<lb/>modité <expan abbr="cõ&longs;i&longs;te">con&longs;i&longs;te</expan> à tirer de l'eau des puits, <lb/>parce que l'on tire de haut en bas, & <expan abbr="cõ-&longs;equemment">con­<lb/>&longs;equemment</expan> le poids des bras, & du <lb/>corps &longs;eruent à cela, au lieu qu'en <expan abbr="tirãt">tirant</expan> <lb/>à force de bras de bas en haut &longs;ans l'ay­<lb/>de des poulies, le poids des bras, & du <lb/>corps nui&longs;ent, c'e&longs;t pourquoy la poulie | <s id="s.000201">Mais &longs;a com­<lb/>modité <expan abbr="cõ&longs;i&longs;te">con&longs;i&longs;te</expan> à tirer de l'eau des puits, <lb/>parce que l'on tire de haut en bas, & <expan abbr="cõ-&longs;equemment">con­<lb/>&longs;equemment</expan> le poids des bras, & du <lb/>corps &longs;eruent à cela, au lieu qu'en <expan abbr="tirãt">tirant</expan> <lb/>à force de bras de bas en haut &longs;ans l'ay­<lb/>de des poulies, le poids des bras, & du <lb/>corps nui&longs;ent, c'e&longs;t pourquoy la poulie |
| <pb pagenum="37" xlink:href="047/01/057.jpg"/>apporte de la commodité à l'applica­<lb/>tion de la force. </s> | <pb pagenum="37" xlink:href="047/01/057.jpg"/>apporte de la commodité à l'applica­<lb/>tion de la force. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000202">Mais &longs;i l'on v&longs;e d'vne autre &longs;orte de <lb/>poulie, dont on void icy la figure, l'on <lb/>pourra leuer vn fardeau auec moins de <lb/><figure id="id.047.01.057.1.jpg" xlink:href="047/01/057/1.jpg"/><lb/>force, car &longs;i la poulie BDC, <lb/>qui &longs;edoit mouuoir au tour <lb/>du centre E, e&longs;t mi&longs;e dans <lb/>&longs;a quai&longs;&longs;e, ou dans &longs;on ar­<lb/>meure D, que G &longs;oit le far­<lb/>deau, & que la chorde AB <lb/>CF pa&longs;&longs;ant à l'entour de la­<lb/>dite poulie &longs;oit arre&longs;té par <lb/>le bout à quelque cheuille, <lb/>au point ferme, & immobi­<lb/>le; & <expan abbr="finalem&etilde;t">finalement</expan> &longs;i l'on applique la force <lb/>au point C, ou F, qui &longs;e meuue en haut <lb/>vers H, & con&longs;equemment qui fa&longs;&longs;e <lb/>monter la quai&longs;&longs;e D, & quant & quant <lb/>le fardeau G, ie dy que la force mi&longs;e en <lb/>C, ou en F, n'e&longs;t que la moitió du far­<lb/>deau qu'elle &longs;ou&longs;tient, & par <expan abbr="con&longs;equ&etilde;t">con&longs;equent</expan> <lb/>que le <expan abbr="mom&etilde;t">moment</expan> en C e&longs;t &longs;ouz double du <lb/>moment en G; parce que G e&longs;t &longs;ou&longs;te­<lb/>nu, & porté par les deux parties de la <lb/>chorde AB, & CD, de &longs;orte qu'il e&longs;t <lb/>diui&longs;é en deux parties égales, parce que <lb/>le diametre BC e&longs;t &longs;emblable au fleau | <s id="s.000202">Mais &longs;i l'on v&longs;e d'vne autre &longs;orte de <lb/>poulie, dont on void icy la figure, l'on <lb/>pourra leuer vn fardeau auec moins de <lb/><figure id="id.047.01.057.1.jpg" xlink:href="047/01/057/1.jpg"/><lb/>force, car &longs;i la poulie BDC, <lb/>qui &longs;e doit mouuoir au tour <lb/>du centre E, e&longs;t mi&longs;e dans <lb/>&longs;a quai&longs;&longs;e, ou dans &longs;on ar­<lb/>meure D, que G &longs;oit le far­<lb/>deau, & que la chorde AB <lb/>CF pa&longs;&longs;ant à l'entour de la­<lb/>dite poulie &longs;oit arre&longs;té par <lb/>le bout à quelque cheuille, <lb/>au point ferme, & immobi­<lb/>le; & <expan abbr="finalem&etilde;t">finalement</expan> &longs;i l'on applique la force <lb/>au point C, ou F, qui &longs;e meuue en haut <lb/>vers H, & con&longs;equemment qui fa&longs;&longs;e <lb/>monter la quai&longs;&longs;e D, & quant & quant <lb/>le fardeau G, ie dy que la force mi&longs;e en <lb/>C, ou en F, n'e&longs;t que la moitié du far­<lb/>deau qu'elle &longs;ou&longs;tient, & par <expan abbr="con&longs;equ&etilde;t">con&longs;equent</expan> <lb/>que le <expan abbr="mom&etilde;t">moment</expan> en C e&longs;t &longs;ouz double du <lb/>moment en G; parce que G e&longs;t &longs;ou&longs;te­<lb/>nu, & porté par les deux parties de la <lb/>chorde AB, & CD, de &longs;orte qu'il e&longs;t <lb/>diui&longs;é en deux parties égales, parce que <lb/>le diametre BC e&longs;t &longs;emblable au fleau |
| <pb pagenum="38" xlink:href="047/01/058.jpg"/>d'vne balance, & le fardeau e&longs;t &longs;u&longs;pen­<lb/>du du point E: & puis le &longs;ou&longs;tien e&longs;t <lb/>au point B, & la force e&longs;t au point C, <lb/>c'e&longs;t pourquoy il y a me&longs;me rai&longs;on de <lb/>la force au fardeau, que de BE à BC, <lb/>donc elle e&longs;t la moitié du fardeau. </s> | <pb pagenum="38" xlink:href="047/01/058.jpg"/>d'vne balance, & le fardeau e&longs;t &longs;u&longs;pen­<lb/>du du point E: & puis le &longs;ou&longs;tien e&longs;t <lb/>au point B, & la force e&longs;t au point C, <lb/>c'e&longs;t pourquoy il y a me&longs;me rai&longs;on de <lb/>la force au fardeau, que de BE à BC, <lb/>donc elle e&longs;t la moitié du fardeau. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000203">Car encore que la poulie &longs;e tourne, <lb/>tandis que la force &longs;e meut vers H, <lb/>neantmoins la &longs;u&longs;dite proportion ne <lb/>change point, comme l'on void aux <lb/>points B, E, C, & le leuier BC e&longs;t rendu <lb/>perpetuel. </s> | <s id="s.000203">Car encore que la poulie &longs;e tourne, <lb/>tandis que la force &longs;e meut vers H, <lb/>neantmoins la &longs;u&longs;dite proportion ne <lb/>change point, comme l'on void aux <lb/>points B, E, C, & le leuier BC e&longs;t rendu <lb/>perpetuel. </s> |
| <s id="s.000204">Mais en recompen&longs;e le che­<lb/>min que fait la force e&longs;t double du che­<lb/>min que fait le fardeau, car quand il e&longs;t <lb/>arriué au point F, c'e&longs;t à dire <expan abbr="quãd">quand</expan> il e&longs;t <lb/>monté au&longs;&longs;i haut qu'A, la force à mon­<lb/>té deux fois autant, c'e&longs;t à dire de C en <lb/>H. <!-- KEEP S--></s> | <s id="s.000204">Mais en recompen&longs;e le che­<lb/>min que fait la force e&longs;t double du che­<lb/>min que fait le fardeau, car quand il e&longs;t <lb/>arriué au point F, c'e&longs;t à dire <expan abbr="quãd">quand</expan> il e&longs;t <lb/>monté au&longs;&longs;i haut qu'A, la force à mon­<lb/>té deux fois autant, c'e&longs;t à dire de C en <lb/>H. <!-- KEEP S--></s> |
| <s id="s.000205">Mais il arriue icy vne incommodi­<lb/>té à la force, à rai&longs;on de &longs;a pe&longs;anteur <lb/>qui la fait incliner en bas, c'e&longs;t pour­<lb/>quoy <expan abbr="l'õ">l'om</expan> y a remedié par l'ad <expan abbr="ditiõ">ditiom</expan> d'vne <lb/>autre poulie que <expan abbr="l'õ">l'om</expan> met en haut, <expan abbr="cõme">comme</expan> <lb/>l'on peut comprendre par cette figure, <lb/>quoy que renuer&longs;ée, dans laquelle il <lb/>faut con&longs;iderer la chorde IBAEF, <lb/>qui pa&longs;&longs;e à l'entour des poulies BA, & <lb/>FE, & e&longs;t attachée à l'armure du point <lb/>D de la quai&longs;&longs;e CD, qui e&longs;t attachée | <s id="s.000205">Mais il arriue icy vne incommodi­<lb/>té à la force, à rai&longs;on de &longs;a pe&longs;anteur <lb/>qui la fait incliner en bas, c'e&longs;t pour­<lb/>quoy <expan abbr="l'õ">l'on</expan> y a remedié par l'<expan abbr="additiõ">addition</expan> d'vne <lb/>autre poulie que <expan abbr="l'õ">l'on</expan> met en haut, <expan abbr="cõme">comme</expan> <lb/>l'on peut comprendre par cette figure, <lb/>quoy que renuer&longs;ée, dans laquelle il <lb/>faut con&longs;iderer la chorde IBAEF, <lb/>qui pa&longs;&longs;e à l'entour des poulies BA, & <lb/>FE, & e&longs;t attachée à l'armure du point <lb/>D de la quai&longs;&longs;e CD, qui e&longs;t attachée |
| <pb pagenum="39" xlink:href="047/01/059.jpg"/>en haut à la poûtre, ou à la pierre H, de <lb/><figure id="id.047.01.059.1.jpg" xlink:href="047/01/059/1.jpg"/><lb/>&longs;orte que la force tirant la <lb/>chorde du point B au point <lb/>I, ou du point I au point F, <lb/>fait monter le poids at­<lb/>taché au mouffle, ou à la <lb/>quai&longs;&longs;e FE. <!-- KEEP S--></s> | <pb pagenum="39" xlink:href="047/01/059.jpg"/>en haut à la poûtre, ou à la pierre H, de <lb/><figure id="id.047.01.059.1.jpg" xlink:href="047/01/059/1.jpg"/><lb/>&longs;orte que la force tirant la <lb/>chorde du point B au point <lb/>I, ou du point I au point F, <lb/>fait monter le poids at­<lb/>taché au mouffle, ou à la <lb/>quai&longs;&longs;e FE. <!-- KEEP S--></s> |
| <s id="s.000206">Or cette force <lb/>ne doit pas e&longs;tre moindre <lb/>qu'au point A, dautant <lb/>que les momens du poids, <lb/>& de la force &longs;ont égale­<lb/>ment di&longs;tans du centre G, <lb/>car BG e&longs;t égal à GA, c'e&longs;t <lb/>pourquoy la poulie BA <lb/>n'augmente pas la force. </s> | <s id="s.000206">Or cette force <lb/>ne doit pas e&longs;tre moindre <lb/>qu'au point A, dautant <lb/>que les momens du poids, <lb/>& de la force &longs;ont égale­<lb/>ment di&longs;tans du centre G, <lb/>car BG e&longs;t égal à GA, c'e&longs;t <lb/>pourquoy la poulie BA <lb/>n'augmente pas la force. </s> |
| <s id="s.000207"><lb/>Où il faut remarquer que <lb/>les Italiens appellent cét in&longs;trument <emph type="italics"/>la <lb/>Taglia,<emph.end type="italics"/> & les Grecs, & les Latins <emph type="italics"/>Tro­<lb/>chlea<emph.end type="italics"/>: mais nous le nommons en Fran­<lb/>ce <emph type="italics"/>Mouffles<emph.end type="italics"/>; ce qui com prend l'armeu­<lb/>re, ou la quai&longs;&longs;e, qui &longs;ert de boëte aux <lb/>poulies, & les poulies, & tout ce qui <lb/>&longs;ert pour la perfection de cette machi­<lb/>ne: on l'appelle au&longs;&longs;i <emph type="italics"/>écharpes armée de <lb/>poulies.<emph.end type="italics"/></s> | <s id="s.000207"><lb/>Où il faut remarquer que <lb/>les Italiens appellent cét in&longs;trument <emph type="italics"/>la <lb/>Taglia,<emph.end type="italics"/> & les Grecs, & les Latins <emph type="italics"/>Tro­<lb/>chlea<emph.end type="italics"/>: mais nous le nommons en Fran­<lb/>ce <emph type="italics"/>Mouffles<emph.end type="italics"/>; ce qui com prend l'armeu­<lb/>re, ou la quai&longs;&longs;e, qui &longs;ert de boëte aux <lb/>poulies, & les poulies, & tout ce qui <lb/>&longs;ert pour la perfection de cette machi­<lb/>ne: on l'appelle au&longs;&longs;i <emph type="italics"/>écharpes armée de <lb/>poulies.<emph.end type="italics"/></s> |
| |
| <s id="s.000209"><emph type="center"/><emph type="italics"/>LEMME.<emph.end type="italics"/><emph.end type="center"/></s> | <s id="s.000209"><emph type="center"/><emph type="italics"/>LEMME.<emph.end type="italics"/><emph.end type="center"/></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000210">Soient donc les deux lignes AB, & <lb/><figure id="id.047.01.060.1.jpg" xlink:href="047/01/060/1.jpg"/><lb/>CD, qui repre­<lb/>&longs;entent deux le­<lb/>uiers, qui ont <lb/>leurs appuis A & <lb/>C à leurs extre­<lb/>mitez, & que le <lb/>fardeau G &longs;oit <lb/>&longs;u&longs;pendu au milieu E, & F & qu'il &longs;oit <lb/>&longs;ou&longs;tenu par les deux forces B & D ap­<lb/>pliquées aux autres extrem tez des le­<lb/>uiers, le&longs;quelles ie &longs;uppo&longs;e auoir vn <lb/>moment égal, ie dy que le moment de <lb/>chacune e&longs;t égal au moment de la qua­<lb/>trie&longs;me partie du poids G, car les deux <lb/>forces B & D &longs;ou&longs;tiennent également, <lb/>& <expan abbr="con&longs;equemm&etilde;t">con&longs;equemment</expan> la force D n'e&longs;t con­<lb/>trariée que par la moitié du poids G qui | <s id="s.000210">Soient donc les deux lignes AB, & <lb/><figure id="id.047.01.060.1.jpg" xlink:href="047/01/060/1.jpg"/><lb/>CD, qui repre­<lb/>&longs;entent deux le­<lb/>uiers, qui ont <lb/>leurs appuis A & <lb/>C à leurs extre­<lb/>mitez, & que le <lb/>fardeau G &longs;oit <lb/>&longs;u&longs;pendu au milieu E, & F & qu'il &longs;oit <lb/>&longs;ou&longs;tenu par les deux forces B & D ap­<lb/>pliquées aux autres extremitez des le­<lb/>uiers, le&longs;quelles ie &longs;uppo&longs;e auoir vn <lb/>moment égal, ie dy que le moment de <lb/>chacune e&longs;t égal au moment de la qua­<lb/>trie&longs;me partie du poids G, car les deux <lb/>forces B & D &longs;ou&longs;tiennent également, <lb/>& <expan abbr="con&longs;equemm&etilde;t">con&longs;equemment</expan> la force D n'e&longs;t con­<lb/>trariée que par la moitié du poids G qui |
| <pb pagenum="41" xlink:href="047/01/061.jpg"/>e&longs;t attaché à F. <!-- KEEP S--></s> | <pb pagenum="41" xlink:href="047/01/061.jpg"/>e&longs;t attaché à F. <!-- KEEP S--></s> |
| <s id="s.000211">Mais quand la force D <lb/>&longs;ou&longs;tient la moitié du fardeau par le <lb/>moyen du leuier CD, elle a me&longs;me <lb/>proportion à G que CD à CF, c'e&longs;t à <lb/>dire &longs;ouz double, donc le <expan abbr="mom&etilde;t">moment</expan> D e&longs;t <lb/>double du moment de la moitié du <lb/>poids G qu'il &longs;ou&longs;tient, donc il e&longs;t le <lb/>quart du moment des poids entier. </s> | <s id="s.000211">Mais quand la force D <lb/>&longs;ou&longs;tient la moitié du fardeau par le <lb/>moyen du leuier CD, elle a me&longs;me <lb/>proportion à G que CD à CF, c'e&longs;t à <lb/>dire &longs;ouz double, donc le <expan abbr="mom&etilde;t">moment</expan> D e&longs;t <lb/>double du moment de la moitié du <lb/>poids G qu'il &longs;ou&longs;tient, donc il e&longs;t le <lb/>quart du moment des poids entier. </s> |
| </p> | </p> |
| |
| <s id="s.000212">L'on demon&longs;tre la me&longs;me cho&longs;e du <lb/>moment B, de &longs;orte qu'il e&longs;t rai&longs;onna­<lb/>ble que le poids e&longs;tant également &longs;ou­<lb/>&longs;tenu par les 4 poulies qui &longs;e voyent <lb/>dans cette autre figure, chacune porte <lb/>la quatrie&longs;me partie du fardeau: ce que <lb/>ie mon&longs;tre en cette maniere. </s> | <s id="s.000212">L'on demon&longs;tre la me&longs;me cho&longs;e du <lb/>moment B, de &longs;orte qu'il e&longs;t rai&longs;onna­<lb/>ble que le poids e&longs;tant également &longs;ou­<lb/>&longs;tenu par les 4 poulies qui &longs;e voyent <lb/>dans cette autre figure, chacune porte <lb/>la quatrie&longs;me partie du fardeau: ce que <lb/>ie mon&longs;tre en cette maniere. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000213">Que le poids X &longs;oit attaché au point <lb/>K par le moven du mouffle KX, ie dy <lb/>que la force égale à la quatrie&longs;me par­<lb/>tie du fardeau X, le &longs;ou&longs;tiendra, car &longs;i <lb/>l'on s'imagine que les deux diametres <lb/>BA & DE &longs;oient deux leuiers &longs;embla­<lb/>bles à ceux que nous auons expliquez <lb/>dans la figure precedente, & que le far­<lb/>deau &longs;oit &longs;u&longs;pendu aux points CEF, <expan abbr="l'õ">l'om</expan> <lb/>trouuera que les appuis, ou les &longs;upports <lb/>de&longs;dits leuiers répondent aux points D <lb/>& A, con&longs;equemment que la force ap­<lb/>pliquée en B ou en E &longs;ou&longs;tiendra le | <s id="s.000213">Que le poids X &longs;oit attaché au point <lb/>K par le moyen du mouffle KX, ie dy <lb/>que la force égale à la quatrie&longs;me par­<lb/>tie du fardeau X, le &longs;ou&longs;tiendra, car &longs;i <lb/>l'on s'imagine que les deux diametres <lb/>BA & DE &longs;oient deux leuiers &longs;embla­<lb/>bles à ceux que nous auons expliquez <lb/>dans la figure precedente, & que le far­<lb/>deau &longs;oit &longs;u&longs;pendu aux points CEF, <expan abbr="l'õ">l'on</expan> <lb/>trouuera que les appuis, ou les &longs;upports <lb/>de&longs;dits leuiers répondent aux points D <lb/>& A, con&longs;equemment que la force ap­<lb/>pliquée en B ou en E &longs;ou&longs;tiendra le |
| <pb pagenum="42" xlink:href="047/01/062.jpg"/>poids X, dont il &longs;era &longs;ousquadruple. </s> | <pb pagenum="42" xlink:href="047/01/062.jpg"/>poids X, dont il &longs;era &longs;ousquadruple. </s> |
| <figure id="id.047.01.062.1.jpg" xlink:href="047/01/062/1.jpg"/> | <figure id="id.047.01.062.1.jpg" xlink:href="047/01/062/1.jpg"/> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000214">>Et &longs;i <expan abbr="l'õ">l'on</expan> adiou&longs;te vne pou­<lb/>lie en haut, & que lachor­<lb/>de pa&longs;&longs;e par OMB, la <lb/>force L, &longs;ou&longs;tiendra le <lb/>me&longs;me poids. </s> | <s id="s.000214">>Et &longs;i <expan abbr="l'õ">l'on</expan> adiou&longs;te vne pou­<lb/>lie en haut, & que lachor­<lb/>de pa&longs;&longs;e par OMB, la <lb/>force L, &longs;ou&longs;tiendra le <lb/>me&longs;me poids. </s> |
| <s id="s.000215">Mais il <lb/>faut accommoder les 4. <lb/>chordes, <expan abbr="cõme">comme</expan> elles &longs;ont <lb/>dans ces mouffles, en &longs;or­<lb/>te qu'elles ne &longs;e me&longs;lent <lb/>point lesvnes auec les au­<lb/>tres. </s> | <s id="s.000215">Mais il <lb/>faut accommoder les 4. <lb/>chordes, <expan abbr="cõme">comme</expan> elles &longs;ont <lb/>dans ces mouffles, en &longs;or­<lb/>te qu'elles ne &longs;e me&longs;lent <lb/>point lesvnes auec les au­<lb/>tres. </s> |
| <s id="s.000216">Or il faut icy remar­<lb/>quer ce que nous auons <lb/>de&longs;ia dit plu&longs;ieurs fois, à <lb/>&longs;çauoir que <expan abbr="l'õ">l'om</expan> ne gaigne <lb/>rien auec ces in&longs;trumens, <lb/>car &longs;i l'on épargne la for­<lb/>ce, l'on augmente le <expan abbr="t&etilde;ps">temps</expan>: <lb/>de là vient qu'il faut tirer <lb/>quatre pieds de chorde <lb/>depuis O iu&longs;ques à L pour faire monter <lb/>le poids X d'vn pied de X en C: & l'on <lb/>trouuerra perpetuellement que l'on <lb/>perd autant de temps, ou que l'on e&longs;t <lb/>contraint d'allonger autant le chemin, <lb/>que l'on gaigne de force. </s> | <s id="s.000216">Or il faut icy remar­<lb/>quer ce que nous auons <lb/>de&longs;ia dit plu&longs;ieurs fois, à <lb/>&longs;çauoir que <expan abbr="l'õ">l'on</expan> ne gaigne <lb/>rien auec ces in&longs;trumens, <lb/>car &longs;i l'on épargne la for­<lb/>ce, l'on augmente le <expan abbr="t&etilde;ps">temps</expan>: <lb/>de là vient qu'il faut tirer <lb/>quatre pieds de chorde <lb/>depuis O iu&longs;ques à L pour faire monter <lb/>le poids X d'vn pied de X en C: & l'on <lb/>trouuerra perpetuellement que l'on <lb/>perd autant de temps, ou que l'on e&longs;t <lb/>contraint d'allonger autant le chemin, <lb/>que l'on gaigne de force. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000217">Si l'on veut que la force s'augmente <lb/>au &longs;extuple, il faut adiou&longs;ter vne autre | <s id="s.000217">Si l'on veut que la force s'augmente <lb/>au &longs;extuple, il faut adiou&longs;ter vne autre |
| |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000221">Or pour expliquer la maniere de | <s id="s.000221">Or pour expliquer la maniere de |
| <pb pagenum="44" xlink:href="047/01/064.jpg"/>multiplier la force &longs;elon vn <expan abbr="nõbre">nombre</expan> im­<lb/>pair: il faut encore con&longs;iderer le leuier <lb/>de la page 40. AB, dont l'appuy e&longs;t en <lb/>A, & le poids G e&longs;t attaché à E, & &longs;ou­<lb/>&longs;tenu par deux forces égales, dont l'vne <lb/>e&longs;t en D, & l'autre en B, & <expan abbr="l'õ">l'om</expan> trouuer­<lb/>ra que chaque force a vn moment égal <lb/>au tiers du poids, G, parce que la force <lb/>mi&longs;e en E &longs;ou&longs;tient vn poids qui luy e&longs;t <lb/>égal, dautant qu'elle e&longs;t dans la ligne <lb/>de la &longs;u&longs;pen&longs;ion dudit poids. </s> | <pb pagenum="44" xlink:href="047/01/064.jpg"/>multiplier la force &longs;elon vn <expan abbr="nõbre">nombre</expan> im­<lb/>pair: il faut encore con&longs;iderer le leuier <lb/>de la page 40. AB, dont l'appuy e&longs;t en <lb/>A, & le poids G e&longs;t attaché à E, & &longs;ou­<lb/>&longs;tenu par deux forces égales, dont l'vne <lb/>e&longs;t en D, & l'autre en B, & <expan abbr="l'õ">l'on</expan> trouuer­<lb/>ra que chaque force a vn moment égal <lb/>au tiers du poids, G, parce que la force <lb/>mi&longs;e en E &longs;ou&longs;tient vn poids qui luy e&longs;t <lb/>égal, dautant qu'elle e&longs;t dans la ligne <lb/>de la &longs;u&longs;pen&longs;ion dudit poids. </s> |
| <s id="s.000222">Mais la <lb/>force <expan abbr="e&longs;tãt">e&longs;tant</expan> en B &longs;ou&longs;tient deux fois au­<lb/>tant que &longs;on poids, parce que &longs;a di&longs;tan­<lb/>ce d'auec l'appuy A e&longs;t double de EA. </s> | <s id="s.000222">Mais la <lb/>force <expan abbr="e&longs;tãt">e&longs;tant</expan> en B &longs;ou&longs;tient deux fois au­<lb/>tant que &longs;on poids, parce que &longs;a di&longs;tan­<lb/>ce d'auec l'appuy A e&longs;t double de EA. </s> |
| <s id="s.000223"><lb/>Et parce que l'on &longs;uppo&longs;e que les 2. for­<lb/>ces B, & E &longs;ont egales, il s'en&longs;uit que la <lb/>partie de G &longs;ou&longs;tenuë par B e&longs;t double <lb/>de la partie que &longs;ou&longs;tient E: donc&longs;i l'on <lb/>fait deux parties du poids G, & que l'v­<lb/>ne &longs;oit double de l'autre, la plus grande <lb/>&longs;era de 2/3, & la moindre de 1/3 de G, done <lb/>le moment de la force E &longs;era égal au <lb/>tiers de G: & parce que nous auons <lb/>&longs;uppo&longs;é B égal à E, la force B e&longs;t égale <lb/>à la force E, & con&longs;equemment chacu­<lb/>ne e&longs;t égale au tiers du poids G. <!-- KEEP S--></s> | <s id="s.000223"><lb/>Et parce que l'on &longs;uppo&longs;e que les 2. for­<lb/>ces B, & E &longs;ont egales, il s'en&longs;uit que la <lb/>partie de G &longs;ou&longs;tenuë par B e&longs;t double <lb/>de la partie que &longs;ou&longs;tient E: donc &longs;i l'on <lb/>fait deux parties du poids G, & que l'v­<lb/>ne &longs;oit double de l'autre, la plus grande <lb/>&longs;era de 2/3, & la moindre de 1/3 de G, donc <lb/>le moment de la force E &longs;era égal au <lb/>tiers de G: & parce que nous auons <lb/>&longs;uppo&longs;é B égal à E, la force B e&longs;t égale <lb/>à la force E, & con&longs;equemment chacu­<lb/>ne e&longs;t égale au tiers du poids G. <!-- KEEP S--></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000224">Cecy ayant e&longs;té demon&longs;tré, il faut <lb/>l'appliquer aux mouffles qui &longs;uiuent, | <s id="s.000224">Cecy ayant e&longs;té demon&longs;tré, il faut <lb/>l'appliquer aux mouffles qui &longs;uiuent, |
| |
| <s id="s.000233">C'e&longs;t pourquoy il faut ex­<lb/>pliquer la nature, & l'origine de la viz, <lb/>& pour ce &longs;uiet ie <expan abbr="demõ&longs;tre">demon&longs;tre</expan> icy vn theo­<lb/>re&longs;me, qui &longs;emblera, peu&longs;t-e&longs;tre, fort <lb/>éloigné de ce di&longs;cours, quoy qu'il en <lb/>&longs;oit la ba&longs;e, & le fondement. </s> | <s id="s.000233">C'e&longs;t pourquoy il faut ex­<lb/>pliquer la nature, & l'origine de la viz, <lb/>& pour ce &longs;uiet ie <expan abbr="demõ&longs;tre">demon&longs;tre</expan> icy vn theo­<lb/>re&longs;me, qui &longs;emblera, peu&longs;t-e&longs;tre, fort <lb/>éloigné de ce di&longs;cours, quoy qu'il en <lb/>&longs;oit la ba&longs;e, & le fondement. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000234">Ie dy done que tous les corps pe&longs;ans | <s id="s.000234">Ie dy donc que tous les corps pe&longs;ans <pb pagenum="47" xlink:href="047/01/067.jpg"/>ont vne inclination vers le centre de la <lb/>terre, non &longs;eulement quand ils y peu­<lb/>uent de&longs;cendre perpendiculairement, <lb/>mais au&longs;&longs;i quand ils y peuuent arriuer <lb/>par vne ligne oblique, ou par vn plan <lb/>incliné: ce que l'on peut confirmer par <lb/>l'eau qui ne tombe &longs;eulement pas à <lb/>plomb de quelque lieu éminent, mais <lb/>elle coule au&longs;&longs;i &longs;ur la terre par vne li­<lb/>gne qui a fort peu d'inclination, com­<lb/>me l'on remarque aux cours des fleu­<lb/>ues, dont les eaux de&longs;cendent libre­<lb/>ment, pourueu que leur lit ayt tant &longs;oit <lb/>peu de pante. </s> |
| <pb pagenum="47" xlink:href="047/01/067.jpg"/>ont vne inclination vers le centre de la <lb/>terre, non &longs;eulement quand ils y peu­<lb/>uent de&longs;cendre perpendiculairement, <lb/>mais au&longs;&longs;i quand ils y peuuent arriuer <lb/>par vne ligne oblique, ou par vn plan <lb/>incliné: ce que l'on peut confirmer par <lb/>l'eau qui ne tombe &longs;eulement pas à <lb/>plomb de quelque lieu éminent, mais <lb/>elle coule au&longs;&longs;i &longs;ur la terre par vne li­<lb/>gne qui a fort peu d'inclination, com­<lb/>me l'on remarque aux cours des fleu­<lb/>ues, dont les eaux de&longs;cendent libre­<lb/>ment, pourueu que leur lit ayt tant &longs;oit <lb/>peu de pante. </s> | |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000235">Or ce qui arriue aux corps fluides, &longs;e <lb/>remarque, &longs;emblablement aux corps <lb/>qui &longs;ont durs, pourueu que les figures, <lb/>& les autres empe&longs;chemens acciden­<lb/>tels, & exterieurs ne les diuerti&longs;&longs;ent <lb/>point: Car &longs;i l'on prend vne bale par­<lb/>faitement ronde, & polie, &longs;oit de mar­<lb/>bre, de verre, ou d'autre matiere, qui <lb/>reçoiue vn excellent poly, & que l'on <lb/>la mette &longs;ur vn <expan abbr="plã">plam</expan> incline, qui &longs;oit au&longs;­<lb/>&longs;i parfaitement vni, & poly que la gla­<lb/>ce d'vn miroir, elle de&longs;cendra &longs;ur ledit <lb/>plan, &longs;e mouuera <expan abbr="perpetuellem&etilde;t">perpetuellement</expan> tan­<lb/>dis qu'elle trouuera la moindre inclina- | <s id="s.000235">Or ce qui arriue aux corps fluides, &longs;e <lb/>remarque, &longs;emblablement aux corps <lb/>qui &longs;ont durs, pourueu que les figures, <lb/>& les autres empe&longs;chemens acciden­<lb/>tels, & exterieurs ne les diuerti&longs;&longs;ent <lb/>point: Car &longs;i l'on prend vne bale par­<lb/>faitement ronde, & polie, &longs;oit de mar­<lb/>bre, de verre, ou d'autre matiere, qui <lb/>reçoiue vn excellent poly, & que l'on <lb/>la mette &longs;ur vn <expan abbr="plã">plan</expan> incline, qui &longs;oit au&longs;­<lb/>&longs;i parfaitement vni, & poly que la gla­<lb/>ce d'vn miroir, elle de&longs;cendra &longs;ur ledit <lb/>plan, &longs;e mouuera <expan abbr="perpetuellem&etilde;t">perpetuellement</expan> tan­<lb/>dis qu'elle trouuera la moindre inclina- |
| <pb pagenum="48" xlink:href="047/01/068.jpg"/>tion que l'on &longs;e pui&longs;&longs;e imaginer: de &longs;or­<lb/>te qu'elle ne &longs;arre&longs;tera point iu&longs;ques à <lb/>ce qu'elle rencontre vne &longs;urface qui <lb/>&longs;oit à niueau, ou équidi&longs;tante de l'ho­<lb/>rizon, comme e&longs;t celle d'vn lac, ou d'vn <lb/>e&longs;tang glacé, &longs;ur laquelle la bale &longs;e <lb/>tiendroit ferme, & immobile, mais auec <lb/>telle condition que la moindre force <lb/>l'ébranleroit, & que le plan &longs;inclinant <lb/>de la largeur d'vn cheueu, elle <expan abbr="comm&etilde;-ceroit">commen­<lb/>ceroit</expan> incontinent à &longs;e mouuoir & à <lb/>de&longs;cendre vers la partie inclinée, & <lb/>qu'au contraire elle ne pourroit e&longs;tre <lb/>meuë &longs;ans <expan abbr="viol&etilde;cevers">violencevers</expan> la partie du plan <lb/>qui monte. </s> | <pb pagenum="48" xlink:href="047/01/068.jpg"/>tion que l'on &longs;e pui&longs;&longs;e imaginer: de &longs;or­<lb/>te qu'elle ne &longs;arre&longs;tera point iu&longs;ques à <lb/>ce qu'elle rencontre vne &longs;urface qui <lb/>&longs;oit à niueau, ou équidi&longs;tante de l'ho­<lb/>rizon, comme e&longs;t celle d'vn lac, ou d'vn <lb/>e&longs;tang glacé, &longs;ur laquelle la bale &longs;e <lb/>tiendroit ferme, & immobile, mais auec <lb/>telle condition que la moindre force <lb/>l'ébranleroit, & que le plan &longs;inclinant <lb/>de la largeur d'vn cheueu, elle <expan abbr="comm&etilde;-ceroit">commen­<lb/>ceroit</expan> incontinent à &longs;e mouuoir & à <lb/>de&longs;cendre vers la partie inclinée, & <lb/>qu'au contraire elle ne pourroit e&longs;tre <lb/>meuë &longs;ans <expan abbr="viol&etilde;ce">violence</expan> vers la partie du plan <lb/>qui monte. </s> |
| <s id="s.000236">Or il e&longs;t nece&longs;&longs;aire que la <lb/>boule &longs;arre&longs;te &longs;ur vne &longs;urface parfaite­<lb/>ment équilibre, & qu'elle demeure <expan abbr="cõ-me">con­<lb/>me</expan> indifferente entre le mouuement & <lb/>le repos: de &longs;orte que la moindre force <lb/>du <expan abbr="mõde">monde</expan> &longs;uffi&longs;e pour la mouuoir, com­<lb/>me la moindre force que l'on peut &longs;i­<lb/>maginer dans l'air, &longs;u&longs;fit pour la rete­<lb/>nir. </s> | <s id="s.000236">Or il e&longs;t nece&longs;&longs;aire que la <lb/>boule &longs;arre&longs;te &longs;ur vne &longs;urface parfaite­<lb/>ment équilibre, & qu'elle demeure <expan abbr="cõ-me">com­<lb/>me</expan> indifferente entre le mouuement & <lb/>le repos: de &longs;orte que la moindre force <lb/>du <expan abbr="mõde">monde</expan> &longs;uffi&longs;e pour la mouuoir, com­<lb/>me la moindre force que l'on peut &longs;i­<lb/>maginer dans l'air, &longs;u&longs;fit pour la rete­<lb/>nir. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000237">D'où l'on peut tirer cette conclu&longs;ion, <lb/>que tout corps pe&longs;ant, tous les empe&longs;­<lb/>chemens exterieurs e&longs;tant o&longs;tez, peut <lb/>e&longs;tre meu &longs;ur vn plan horizontal par la <lb/>moindre force que ce &longs;oit, & qu'il faut | <s id="s.000237">D'où l'on peut tirer cette conclu&longs;ion, <lb/>que tout corps pe&longs;ant, tous les empe&longs;­<lb/>chemens exterieurs e&longs;tant o&longs;tez, peut <lb/>e&longs;tre meu &longs;ur vn plan horizontal par la <lb/>moindre force que ce &longs;oit, & qu'il faut |
| <pb pagenum="49" xlink:href="047/01/069.jpg"/>d'autant plus de force pour le mouuoir <lb/>&longs;ur vn plan incliné, qu'il a plus d'incli­<lb/>nation au mouuement contraire. </s> | <pb pagenum="49" xlink:href="047/01/069.jpg"/>d'autant plus de force pour le mouuoir <lb/>&longs;ur vn plan incliné, qu'il a plus d'incli­<lb/>nation au mouuement contraire. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000238">Ce qui &longs;era plus intelligible par <lb/><figure id="id.047.01.069.1.jpg" xlink:href="047/01/069/1.jpg"/><lb/>cette figure, dans <lb/>laquelle AB &longs;oit le <lb/>plan parallele à l'o­<lb/>rizon, &longs;ur lequel la <lb/>boule e&longs;t indif­<lb/>ferente au mouue­<lb/>ment, & au repos, de &longs;orte que le vent <lb/>ou la moindre force la peut faire mou­<lb/>uoir; mais il faut vne plus grande force <lb/>pour la faire mouuoit du point A au <lb/>point C &longs;ur le plan incliné AC, & en­<lb/>core vne plus grande pour la mouuoir <lb/>&longs;ur les plans AD, & AE: & finalement <lb/>l'on ne peut la leuer &longs;ur le plan perpen­<lb/>diculaire AF, que par vne force égale à <lb/>tout le poids G. <!-- KEEP S--></s> | <s id="s.000238">Ce qui &longs;era plus intelligible par <lb/><figure id="id.047.01.069.1.jpg" xlink:href="047/01/069/1.jpg"/><lb/>cette figure, dans <lb/>laquelle AB &longs;oit le <lb/>plan parallele à l'o­<lb/>rizon, &longs;ur lequel la <lb/>boule e&longs;t indif­<lb/>ferente au mouue­<lb/>ment, & au repos, de &longs;orte que le vent <lb/>ou la moindre force la peut faire mou­<lb/>uoir; mais il faut vne plus grande force <lb/>pour la faire mouuoir du point A au <lb/>point C &longs;ur le plan incliné AC, & en­<lb/>core vne plus grande pour la mouuoir <lb/>&longs;ur les plans AD, & AE: & finalement <lb/>l'on ne peut la leuer &longs;ur le plan perpen­<lb/>diculaire AF, que par vne force égale à <lb/>tout le poids G. <!-- KEEP S--></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000239">Or l'on &longs;çaura <expan abbr="cõbien">combien</expan> il faut moins de <lb/>force pour leuer le fardeau &longs;ur les plans <lb/>AE, AD, &c, &longs;i <expan abbr="l'õ">l'om</expan> tire les lignes perpen­<lb/>diculaires à l'orizon CH, DI & KE, cat <lb/>il y aura me&longs;me proportion des forces <lb/>nece&longs;&longs;aires pour éleuer le fardeau &longs;ur <lb/>cha&longs;que plan audit fardeau, que des <lb/>lignes perpendiculaires aux lignes de | <s id="s.000239">Or l'on &longs;çaura <expan abbr="cõbien">combien</expan> il faut moins de <lb/>force pour leuer le fardeau &longs;ur les plans <lb/>AE, AD, &c, &longs;i <expan abbr="l'õ">l'on</expan> tire les lignes perpen­<lb/>diculaires à l'orizon CH, DI & KE, cat <lb/>il y aura me&longs;me proportion des forces <lb/>nece&longs;&longs;aires pour éleuer le fardeau &longs;ur <lb/>cha&longs;que plan audit fardeau, que des <lb/>lignes perpendiculaires aux lignes de |
| <pb pagenum="50" xlink:href="047/01/070.jpg"/>leurs plans. </s> | <pb pagenum="50" xlink:href="047/01/070.jpg"/>leurs plans. </s> |
| <s id="s.000240">Ce que Pappus <expan abbr="Alexãdrin">Alexandrin</expan> <lb/>s'e&longs;t efforcé de mon&longs;trer dans le 8. liure <lb/>de &longs;es Collections Mathematiques, <lb/>mais il s'e&longs;t trompé, à mon aduis, en ce <lb/>qu'il a &longs;upposé vne force donnée pour <lb/>mouuoir le poids &longs;ur le plan <expan abbr="horizõtal">horizontal</expan>, <lb/>ce qui e&longs;t faux, parce qu'il ne faut nulle <lb/>force &longs;en&longs;ible, &longs;i l'on o&longs;te les empe&longs;che­<lb/>mens exterieurs. </s> | <s id="s.000240">Ce que Pappus <expan abbr="Alexãdrin">Alexandrin</expan> <lb/>s'e&longs;t efforcé de mon&longs;trer dans le 8. liure <lb/>de &longs;es Collections Mathematiques, <lb/>mais il s'e&longs;t trompé, à mon aduis, en ce <lb/>qu'il a &longs;upposé vne force donnée pour <lb/>mouuoir le poids &longs;ur le plan <expan abbr="horizõtal">horizontal</expan>, <lb/>ce qui e&longs;t faux, parce qu'il ne faut nulle <lb/>force &longs;en&longs;ible, &longs;i l'on o&longs;te les empe&longs;che­<lb/>mens exterieurs. </s> |
| <s id="s.000241">C'e&longs;t pourquoy il e&longs;t <lb/>plus à propos de chercher la force qui <lb/>meut le fardeau &longs;ur le plan vertical ou <lb/>perpendiculaire AF, laquelle e&longs;t tou­<lb/>&longs;iours égale à la pe&longs;anteur du fardeau, <lb/>que de chercher la force qui le meut <lb/>&longs;ur le plan horizontal. </s> | <s id="s.000241">C'e&longs;t pourquoy il e&longs;t <lb/>plus à propos de chercher la force qui <lb/>meut le fardeau &longs;ur le plan vertical ou <lb/>perpendiculaire AF, laquelle e&longs;t tou­<lb/>&longs;iours égale à la pe&longs;anteur du fardeau, <lb/>que de chercher la force qui le meut <lb/>&longs;ur le plan horizontal. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000242">Soit done le cercle AIC, dontle dia­<lb/><figure id="id.047.01.070.1.jpg" xlink:href="047/01/070/1.jpg"/><lb/>mettre <lb/>e&longs;t ABC, <lb/>& le cen­<lb/>tre B; & <lb/>qu'il y ait <lb/>deux for­<lb/>ces éga­<lb/>les aux <lb/>points A <lb/>& C, qui <lb/><expan abbr="repre&longs;&etilde;t&etilde;t">repre&longs;entent</expan> <lb/>vne <expan abbr="balãce">balance</expan> mobile autour du centre B, | <s id="s.000242">Soit donc le cercle AIC, dont le dia­<lb/><figure id="id.047.01.070.1.jpg" xlink:href="047/01/070/1.jpg"/><lb/>mettre <lb/>e&longs;t ABC, <lb/>& le cen­<lb/>tre B; & <lb/>qu'il y ait <lb/>deux for­<lb/>ces éga­<lb/>les aux <lb/>points A <lb/>& C, qui <lb/><expan abbr="repre&longs;&etilde;t&etilde;t">repre&longs;entent</expan> <lb/>vne <expan abbr="balãce">balance</expan> mobile autour du centre B, |
| <pb pagenum="51" xlink:href="047/01/071.jpg"/>il e&longs;t certain que le poids C &longs;era &longs;ou&longs;te­<lb/>nu par la force A. <!-- KEEP S--></s> | <pb pagenum="51" xlink:href="047/01/071.jpg"/>il e&longs;t certain que le poids C &longs;era &longs;ou&longs;te­<lb/>nu par la force A. <!-- KEEP S--></s> |
| <s id="s.000243">Mais &longs;i l'on s'imagine <lb/>que le bras de la balance BC tombe en <lb/>BF, de &longs;orte qu'il demeure tou&longs;iours <lb/>continué auec le bras AB, & qu'ils <expan abbr="ay&etilde;t">ayent</expan> <lb/>tous deux leur point fixe, ou leur appuy <lb/>en B, le moment F, ne &longs;era pas égal au <lb/>moment A, parce que la di&longs;tance <lb/>du poinct, ou du poids F d'auec la ligne <lb/>de direction BI n'e&longs;t pas egale à la di­<lb/>&longs;tance de la force, ou du poids A d'auec <lb/>la me&longs;me ligne de direction, comme <lb/>l'on demon&longs;tre par la perpendiculaire <lb/>KF, qui determine la <expan abbr="di&longs;tãce">di&longs;tance</expan> du poinct <lb/>F auec B, ou I, de &longs;orte que le <expan abbr="mom&etilde;t">moment</expan>, <lb/>ou le poids, de C porté en F e&longs;t dimi­<lb/>nué de la di&longs;tance de KC, & qu'il n'a <lb/>plus que le <expan abbr="mom&etilde;t">moment</expan> BK: c'e&longs;t pourquoy <lb/>il faut conclure que le moment d'A <lb/>&longs;urpa&longs;&longs;e celuy de F de KC. </s> | <s id="s.000243">Mais &longs;i l'on s'imagine <lb/>que le bras de la balance BC tombe en <lb/>BF, de &longs;orte qu'il demeure tou&longs;iours <lb/>continué auec le bras AB, & qu'ils <expan abbr="ay&etilde;t">ayent</expan> <lb/>tous deux leur point fixe, ou leur appuy <lb/>en B, le moment F, ne &longs;era pas égal au <lb/>moment A, parce que la di&longs;tance <lb/>du poinct, ou du poids F d'auec la ligne <lb/>de direction BI n'e&longs;t pas egale à la di­<lb/>&longs;tance de la force, ou du poids A d'auec <lb/>la me&longs;me ligne de direction, comme <lb/>l'on demon&longs;tre par la perpendiculaire <lb/>KF, qui determine la <expan abbr="di&longs;tãce">di&longs;tance</expan> du poinct <lb/>F auec B, ou I, de &longs;orte que le <expan abbr="mom&etilde;t">moment</expan>, <lb/>ou le poids, de C porté en F e&longs;t dimi­<lb/>nué de la di&longs;tance de KC, & qu'il n'a <lb/>plus que le <expan abbr="mom&etilde;t">moment</expan> BK: c'e&longs;t pourquoy <lb/>il faut conclure que le moment d'A <lb/>&longs;urpa&longs;&longs;e celuy de F de KC. </s> |
| <s id="s.000244">Il faut dire <lb/>la me&longs;me cho&longs;e du poids C tran&longs;porté <lb/>au point L, ou en tel autre point du cer­<lb/>cle que l'on voudra, car la force en A <lb/>&longs;era d'autant plus grande que la force <lb/>L, que BA, e&longs;t plus grand que BM. </s> | <s id="s.000244">Il faut dire <lb/>la me&longs;me cho&longs;e du poids C tran&longs;porté <lb/>au point L, ou en tel autre point du cer­<lb/>cle que l'on voudra, car la force en A <lb/>&longs;era d'autant plus grande que la force <lb/>L, que BA, e&longs;t plus grand que BM. </s> |
| |
| <s id="s.000247">Mais quand il e&longs;t en F, il e&longs;t en partie <lb/>&longs;ou&longs;tenu par le plan circulaire, & &longs;a <lb/>pente, ou l'inclination qu'il a vers le <lb/>centre de la terre e&longs;t autant diminuée <lb/>que BC &longs;urpa&longs;&longs;e BK: de maniere qu'il <lb/>&longs;e tient éleué &longs;ur ce plan de me&longs;me que <lb/>s'il e&longs;toit appuyé &longs;ur la tangente GFH, <lb/><expan abbr="d'autãt">d'autant</expan> que le point d'inclination F de <lb/>la circonference CI ne differe point de <lb/>l'inclination de la tangente GFH, que <lb/>par l'angle in&longs;en&longs;ible du contact. </s> | <s id="s.000247">Mais quand il e&longs;t en F, il e&longs;t en partie <lb/>&longs;ou&longs;tenu par le plan circulaire, & &longs;a <lb/>pente, ou l'inclination qu'il a vers le <lb/>centre de la terre e&longs;t autant diminuée <lb/>que BC &longs;urpa&longs;&longs;e BK: de maniere qu'il <lb/>&longs;e tient éleué &longs;ur ce plan de me&longs;me que <lb/>s'il e&longs;toit appuyé &longs;ur la tangente GFH, <lb/><expan abbr="d'autãt">d'autant</expan> que le point d'inclination F de <lb/>la circonference CI ne differe point de <lb/>l'inclination de la tangente GFH, que <lb/>par l'angle in&longs;en&longs;ible du contact. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000248">Il faut dire la me&longs;me cho&longs;e du point <lb/>L, lequel e&longs;t incliné comme s'il e&longs;toit <lb/>&longs;ur le plan de la tangeule NLO, car il <lb/>diminuë &longs;a pente, & &longs;on <expan abbr="inclinatiõ">inclinatiom</expan> qu'il <lb/>a en C en me&longs;me proportion que Bk e&longs;t <lb/>à BC, puis qu'il e&longs;t con&longs;tant par la &longs;imi- | <s id="s.000248">Il faut dire la me&longs;me cho&longs;e du point <lb/>L, lequel e&longs;t incliné comme s'il e&longs;toit <lb/>&longs;ur le plan de la tangeule NLO, car il <lb/>diminuë &longs;a pente, & &longs;on <expan abbr="inclinatiõ">inclination</expan> qu'il <lb/>a en C en me&longs;me proportion que Bk e&longs;t <lb/>à BC, puis qu'il e&longs;t con&longs;tant par la &longs;imi- |
| <pb pagenum="53" xlink:href="047/01/073.jpg"/>litude des triangles KBF & KFH, qu'il <lb/>y a me&longs;me rai&longs;on de FK à FH que de <lb/>KB à BF. D'où nous conclüons que la <lb/>proportion du moment total & ab&longs;olu <lb/>du mobile dans la perpendiculaire de <lb/>l'orizon auec le moment qu'il a &longs;ur le <lb/>plan incliné HF e&longs;t la me&longs;me que la <lb/>proportion de FH à FK. </s> | <pb pagenum="53" xlink:href="047/01/073.jpg"/>litude des triangles KBF & KFH, qu'il <lb/>y a me&longs;me rai&longs;on de FK à FH que de <lb/>KB à BF. D'où nous conclüons que la <lb/>proportion du moment total & ab&longs;olu <lb/>du mobile dans la perpendiculaire de <lb/>l'orizon auec le moment qu'il a &longs;ur le <lb/>plan incliné HF e&longs;t la me&longs;me que la <lb/>proportion de FH à FK. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| |
| <s id="s.000250">Et parce qu'il &longs;uffit <lb/>pour mouuoir le fardeau, que la force <lb/>&longs;urpa&longs;&longs;e <expan abbr="in&longs;en&longs;iblem&etilde;t">in&longs;en&longs;iblement</expan> celle qui le &longs;ou­<lb/>&longs;tient en quel que lieu que ce &longs;oit, nous <lb/><expan abbr="faisõs">faisons</expan> icy cette propo&longs;ition vniuer&longs;elle. </s> | <s id="s.000250">Et parce qu'il &longs;uffit <lb/>pour mouuoir le fardeau, que la force <lb/>&longs;urpa&longs;&longs;e <expan abbr="in&longs;en&longs;iblem&etilde;t">in&longs;en&longs;iblement</expan> celle qui le &longs;ou­<lb/>&longs;tient en quel que lieu que ce &longs;oit, nous <lb/><expan abbr="faisõs">faisons</expan> icy cette propo&longs;ition vniuer&longs;elle. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000251"><emph type="italics"/>Que &longs;ur le plan elcué la force a la me&longs;­<lb/>me proportion au poids que la perpen­<lb/>diculaire tirée de l'extremité du plan &longs;ur <lb/>l'orizon à la longueur dudit plan, c'e&longs;t à dire <lb/>que la tangente à la &longs;ecante,<emph.end type="italics"/> car FK e&longs;t la <lb/>tangente du cercle de&longs;crit &longs;ur le dia­<lb/>mettre KH, & FH e&longs;t la &longs;ecante. </s> | <s id="s.000251"><emph type="italics"/>Que &longs;ur le plan eleué la force a la me&longs;­<lb/>me proportion au poids que la perpen­<lb/>diculaire tirée de l'extremité du plan &longs;ur <lb/>l'orizon à la longueur dudit plan, c'e&longs;t à dire <lb/>que la tangente à la &longs;ecante,<emph.end type="italics"/> car FK e&longs;t la <lb/>tangente du cercle de&longs;crit &longs;ur le dia­<lb/>mettre KH, & FH e&longs;t la &longs;ecante. </s> |
| </p> | </p> |
| <pb pagenum="54" xlink:href="047/01/074.jpg"/> | <pb pagenum="54" xlink:href="047/01/074.jpg"/> |
| <p type="main"> | <p type="main"> |
| <s id="s.000252">Cecy e&longs;tant po&longs;é, ie reuiens à mon <lb/><figure id="id.047.01.074.1.jpg" xlink:href="047/01/074/1.jpg"/><lb/>premier de&longs;&longs;ein, qui con­<lb/>&longs;i&longs;te à trouuer, & à expli­<lb/>querla naturede laviz; c'e&longs;t <lb/>pour ce &longs;ubiet qu'il faut <lb/>con&longs;iderer le triangle AB <lb/>C, dans lequel AB repre&longs;ente la ligne <lb/>horizontale, BC la perpendiculaire à <lb/>l'orizon, & AC le plan eleué, & encliné <lb/>&longs;ur l'orizon, &longs;ur lequel le mobile E e&longs;t <lb/>firé & emporté par vne force d'autant <lb/>moindre que le poids E, que la ligne <lb/>BC e&longs;t moindre que CA. <!-- KEEP S--></s> | <s id="s.000252">Cecy e&longs;tant po&longs;é, ie reuiens à mon <lb/><figure id="id.047.01.074.1.jpg" xlink:href="047/01/074/1.jpg"/><lb/>premier de&longs;&longs;ein, qui con­<lb/>&longs;i&longs;te à trouuer, & à expli­<lb/>quer la nature de la viz; c'e&longs;t <lb/>pour ce &longs;ubiet qu'il faut <lb/>con&longs;iderer le triangle AB <lb/>C, dans lequel AB repre&longs;ente la ligne <lb/>horizontale, BC la perpendiculaire à <lb/>l'orizon, & AC le plan eleué, & encliné <lb/>&longs;ur l'orizon, &longs;ur lequel le mobile E e&longs;t <lb/>tiré & emporté par vne force d'autant <lb/>moindre que le poids E, que la ligne <lb/>BC e&longs;t moindre que CA. <!-- KEEP S--></s> |
| <s id="s.000253">Or quand on <lb/>veut e&longs;leuer E plus haut &longs;ur le plan fer­<lb/>me AC, c'e&longs;t me&longs;me cho&longs;e que &longs;i le tri­<lb/>angle BCA e&longs;toit pou&longs;&longs;é iu&longs;ques au <lb/><figure id="id.047.01.074.2.jpg" xlink:href="047/01/074/2.jpg"/><lb/>point H, parce que s'il &longs;e <lb/>trouuoit dans la me&longs;me <lb/>a&longs;&longs;iette que le <expan abbr="triãgle">triangle</expan> HFG, <lb/>le mobile auroit monté la <lb/>hauteur AI, & &longs;eroit en E. <!-- KEEP S--></s> | <s id="s.000253">Or quand on <lb/>veut e&longs;leuer E plus haut &longs;ur le plan fer­<lb/>me AC, c'e&longs;t me&longs;me cho&longs;e que &longs;i le tri­<lb/>angle BCA e&longs;toit pou&longs;&longs;é iu&longs;ques au <lb/><figure id="id.047.01.074.2.jpg" xlink:href="047/01/074/2.jpg"/><lb/>point H, parce que s'il &longs;e <lb/>trouuoit dans la me&longs;me <lb/>a&longs;&longs;iette que le <expan abbr="triãgle">triangle</expan> HFG, <lb/>le mobile auroit monté la <lb/>hauteur AI, & &longs;eroit en E. <!-- KEEP S--></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| |
| <s id="s.000255">Mais l'on s'e&longs;t auisé d'enuironner <lb/>le cylindre BD du me&longs;me triangle, <lb/>affin de le reduire dans vne machine <lb/>beaucoup moindre, & plus commode. </s> | <s id="s.000255">Mais l'on s'e&longs;t auisé d'enuironner <lb/>le cylindre BD du me&longs;me triangle, <lb/>affin de le reduire dans vne machine <lb/>beaucoup moindre, & plus commode. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000256">Et pour ce &longs;ubiet l'on adonné la me&longs;­<lb/>me hauteur du triangle au cylindre, <lb/>BE, & l'inclination de l'hypotenu&longs;e <lb/>CA à l'helice AE, & à toutes les autres <lb/>qui <expan abbr="&longs;uiu&etilde;t">&longs;uiuent</expan> de bas en haut, & qui <expan abbr="fõtl'he-lice">fontl'he­<lb/>lice</expan> continuë AEFGHID, laquelle on <lb/>appelle <expan abbr="ordinairem&etilde;t">ordinairement</expan> le traict de la viz. </s> | <s id="s.000256">Et pour ce &longs;ubiet l'on adonné la me&longs;­<lb/>me hauteur du triangle au cylindre, <lb/>BE, & l'inclination de l'hypotenu&longs;e <lb/>CA à l'helice AE, & à toutes les autres <lb/>qui <expan abbr="&longs;uiu&etilde;t">&longs;uiuent</expan> de bas en haut, & qui <expan abbr="fõt">font</expan> l'he­<lb/>lice continuë AEFGHID, laquelle on <lb/>appelle <expan abbr="ordinairem&etilde;t">ordinairement</expan> le traict de la viz. </s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000257">C'e&longs;t donc en cette maniere que l'in­<lb/>&longs;trument appellé par les Grecs & par <lb/>les Latins <emph type="italics"/>cochlea<emph.end type="italics"/> & que nous <expan abbr="appelliõs">appellions</expan> <emph type="italics"/>la <lb/>viz,<emph.end type="italics"/> à e&longs;té <expan abbr="inu&etilde;tée">inuentée</expan>, affin qu'en la <expan abbr="tornãt">tornant</expan> <lb/>on e&longs;léue les fardeaux <expan abbr="cõme">comme</expan> l'on feroit <lb/>&longs;ur le triangle precedent, car l'on trou­<lb/>uera tou&longs;iours dans la viz, comme &longs;ur <lb/>tel autre plan que ce &longs;oit, que la force <lb/>e&longs;t au poids po&longs;é &longs;ur vn plan incliné <lb/>comme la hauteur dudit plan à &longs;a lon­<lb/>gueur: & con&longs;equemment que la force <lb/>de la viz ABCD &longs;era multipliée &longs;elon <lb/>que toute l'helice &longs;era plus grande que <lb/>toute la hauteur du cylindre. </s> | <s id="s.000257">C'e&longs;t donc en cette maniere que l'in­<lb/>&longs;trument appellé par les Grecs & par <lb/>les Latins <emph type="italics"/>cochlea<emph.end type="italics"/> & que nous <expan abbr="appelliõs">appellions</expan> <emph type="italics"/>la <lb/>viz,<emph.end type="italics"/> à e&longs;té <expan abbr="inu&etilde;tée">inuentée</expan>, affin qu'en la <expan abbr="tornãt">tornant</expan> <lb/>on e&longs;léue les fardeaux <expan abbr="cõme">comme</expan> l'on feroit <lb/>&longs;ur le triangle precedent, car l'on trou­<lb/>uera tou&longs;iours dans la viz, comme &longs;ur <lb/>tel autre plan que ce &longs;oit, que la force <lb/>e&longs;t au poids po&longs;é &longs;ur vn plan incliné <lb/>comme la hauteur dudit plan à &longs;a lon­<lb/>gueur: & con&longs;equemment que la force <lb/>de la viz ABCD &longs;era multipliée &longs;elon <lb/>que toute l'helice &longs;era plus grande que <lb/>toute la hauteur du cylindre. </s> |
| |
| <s id="s.000259">Neant moins il <lb/>n'e&longs;t pas nece&longs;&longs;aire de me&longs;urer la lon­<lb/>gueur de toute l'helice, ny la hauteur <lb/>totale du cylindre pour congnoi&longs;tre la <lb/>force d'vne viz propo&longs;ée, car il &longs;uffit de <lb/>&longs;çauoir combien de fois l'vn des tours <lb/>de l'helice <expan abbr="conti&etilde;t">contient</expan> &longs;a hauteur, par exem­<lb/>ple, combien de fois AF e&longs;t contenu en <lb/>AE, & en EF parce qu'il y à me&longs;me <lb/>proportion de toute la hauteur CB à <lb/>toute l'helice, que de FA à A EF, que <lb/>les Italiens appellent <emph type="italics"/>verme de la vite.<emph.end type="italics"/></s> | <s id="s.000259">Neant moins il <lb/>n'e&longs;t pas nece&longs;&longs;aire de me&longs;urer la lon­<lb/>gueur de toute l'helice, ny la hauteur <lb/>totale du cylindre pour congnoi&longs;tre la <lb/>force d'vne viz propo&longs;ée, car il &longs;uffit de <lb/>&longs;çauoir combien de fois l'vn des tours <lb/>de l'helice <expan abbr="conti&etilde;t">contient</expan> &longs;a hauteur, par exem­<lb/>ple, combien de fois AF e&longs;t contenu en <lb/>AE, & en EF parce qu'il y à me&longs;me <lb/>proportion de toute la hauteur CB à <lb/>toute l'helice, que de FA à A EF, que <lb/>les Italiens appellent <emph type="italics"/>verme de la vite.<emph.end type="italics"/></s> |
| </p> | </p> |
| <p type="main"> | <p type="main"> |
| <s id="s.000260">Or apres auoir expliqué la nature de <lb/>la viz, l'on peut <expan abbr="ay&longs;em&etilde;t">ay&longs;ement</expan> &longs;çauoir toutes <lb/>&longs;es proptietez, par exemple que l'on fait <lb/>monter le poids par le moyen de &longs;a ma­<lb/>trice auec les helices concaues dans <lb/>le&longs;quelles entrele noyau de la viz auec <lb/>&longs;es helices <expan abbr="cõuexes">conuexes</expan> <expan abbr="cõme">comme</expan> il e&longs;t ay&longs;é de <lb/>remarquer aux viz dos pre&longs;&longs;oirs, & de <lb/>toutes &longs;ortes de pre&longs;&longs;es à écroux, dont <lb/>le noyau e&longs;tant tourné fait monter la­<lb/>dite matrice, & quant & quant le poids <lb/>qui y e&longs;t attaché. </s> | <s id="s.000260">Or apres auoir expliqué la nature de <lb/>la viz, l'on peut <expan abbr="ay&longs;em&etilde;t">ay&longs;ement</expan> &longs;çauoir toutes <lb/>&longs;es proprietez, par exemple que l'on fait <lb/>monter le poids par le moyen de &longs;a ma­<lb/>trice auec les helices concaues dans <lb/>le&longs;quelles entre le noyau de la viz auec <lb/>&longs;es helices <expan abbr="cõuexes">conuexes</expan> <expan abbr="cõme">comme</expan> il e&longs;t ay&longs;é de <lb/>remarquer aux viz des pre&longs;&longs;oirs, & de <lb/>toutes &longs;ortes de pre&longs;&longs;es à écroux, dont <lb/>le noyau e&longs;tant tourné fait monter la­<lb/>dite matrice, & quant & quant le poids <lb/>qui y e&longs;t attaché. </s> |
| </p> | </p> |
| <pb pagenum="57" xlink:href="047/01/077.jpg"/> | <pb pagenum="57" xlink:href="047/01/077.jpg"/> |
| <p type="main"> | <p type="main"> |
| <s id="s.000261">Mais il faut tou&longs;iours &longs;e &longs;ouuenir que <lb/><expan abbr="l'õ">l'om</expan> perd <expan abbr="autãt">autant</expan> de vi&longs;te&longs;&longs;e, & de <expan abbr="t&etilde;ps">temps</expan>, que <lb/>l'on gaigne de force, car AB e&longs;t le plan <lb/><expan abbr="horizõtal">horizontal</expan>, & AC le plan incliné, <expan abbr="dõt">dont</expan> la <lb/>hauteur e&longs;t me&longs;urée, & determinée par <lb/>la perpendiculaire CB; Or &longs;i l'on po&longs;e <lb/>vn mobile &longs;ur le plan AC, & que la <lb/>chorde EDF le tienne attaché, la force <lb/>qui e&longs;t en F ayant me&longs;me rai&longs;on auec le <lb/>poids E que BC aà CB, &longs;ou&longs;tiendra le <lb/>poids en E, & en luy aioutant la moin­<lb/>dre force du monde, il tombera en B, & <lb/>emportera le poids E en le fai&longs;ant mon­<lb/>ter vers D. <!-- KEEP S--></s> | <s id="s.000261">Mais il faut tou&longs;iours &longs;e &longs;ouuenir que <lb/><expan abbr="l'õ">l'on</expan> perd <expan abbr="autãt">autant</expan> de vi&longs;te&longs;&longs;e, & de <expan abbr="t&etilde;ps">temps</expan>, que <lb/>l'on gaigne de force, car AB e&longs;t le plan <lb/><expan abbr="horizõtal">horizontal</expan>, & AC le plan incliné, <expan abbr="dõt">dont</expan> la <lb/>hauteur e&longs;t me&longs;urée, & determinée par <lb/>la perpendiculaire CB; Or &longs;i l'on po&longs;e <lb/>vn mobile &longs;ur le plan AC, & que la <lb/>chorde EDF le tienne attaché, la force <lb/>qui e&longs;t en F ayant me&longs;me rai&longs;on auec le <lb/>poids E que BC aà CB, &longs;ou&longs;tiendra le <lb/>poids en E, & en luy aioutant la moin­<lb/>dre force du monde, il tombera en B, & <lb/>emportera le poids E en le fai&longs;ant mon­<lb/>ter vers D. <!-- KEEP S--></s> |
| <s id="s.000262">Mais F ne fera pas moins <lb/>de chemin en de&longs;cendant perpendicu­<lb/>lairement, que le poids E en montant <lb/>obliquement, c'e&longs;t pourquoy il e&longs;t ne­<lb/>ce&longs;&longs;aire que F de&longs;cende plus bas qu'il <lb/>ne fait monter le poids E, dont l'exau­<lb/>cement &longs;e me&longs;ure par la ligne per­<lb/>pendiculaire BC: de maniere que la <lb/>ligne de la de&longs;cente de F &longs;era é galé à <lb/>CA, quand il aura fait monter le poids <lb/>de B à C. <!-- KEEP S--></s> | <s id="s.000262">Mais F ne fera pas moins <lb/>de chemin en de&longs;cendant perpendicu­<lb/>lairement, que le poids E en montant <lb/>obliquement, c'e&longs;t pourquoy il e&longs;t ne­<lb/>ce&longs;&longs;aire que F de&longs;cende plus bas qu'il <lb/>ne fait monter le poids E, dont l'exau­<lb/>cement &longs;e me&longs;ure par la ligne per­<lb/>pendiculaire BC: de maniere que la <lb/>ligne de la de&longs;cente de F &longs;era é galé à <lb/>CA, quand il aura fait monter le poids <lb/>de B à C. <!-- KEEP S--></s> |
| <s id="s.000263">Car le poids ne re&longs;i&longs;te point <lb/>au mouuement parallele à l'orizon, <lb/>parce que ce mouuement ne l'éloigne <lb/>point du centre de la terre. </s> | <s id="s.000263">Car le poids ne re&longs;i&longs;te point <lb/>au mouuement parallele à l'orizon, <lb/>parce que ce mouuement ne l'éloigne <lb/>point du centre de la terre. </s> |
| <s id="s.000264">C'e&longs;t pour­<lb/>quoy il importe grandement de con- | <s id="s.000264">C'e&longs;t pour­<lb/>quoy il importe grandement de con- |
| <pb pagenum="58" xlink:href="047/01/078.jpg"/>&longs;iderer les lignes par le&longs;quelles &longs;e font <lb/><figure id="id.047.01.078.1.jpg" xlink:href="047/01/078/1.jpg"/><lb/>les mouuemens, & <lb/>particulierement <lb/>lors qu'ils &longs;e font <lb/>par des forces ina­<lb/>nimées, dont les <lb/>momens, & les re&longs;i­<lb/>&longs;tances &longs;ont en leur &longs;ouuerain degró <lb/>dans la ligne <expan abbr="perp&etilde;diculaire">perpendiculaire</expan> à l'orizon; <lb/>mais elles &longs;e <expan abbr="diminü&etilde;tà">diminüentà</expan> proportion que <lb/>la ligne &longs;e <expan abbr="pãche">panche</expan> &longs;ur le plan horizontal. </s> | <pb pagenum="58" xlink:href="047/01/078.jpg"/>&longs;iderer les lignes par le&longs;quelles &longs;e font <lb/><figure id="id.047.01.078.1.jpg" xlink:href="047/01/078/1.jpg"/><lb/>les mouuemens, & <lb/>particulierement <lb/>lors qu'ils &longs;e font <lb/>par des forces ina­<lb/>nimées, dont les <lb/>momens, & les re&longs;i­<lb/>&longs;tances &longs;ont en leur &longs;ouuerain degré <lb/>dans la ligne <expan abbr="perp&etilde;diculaire">perpendiculaire</expan> à l'orizon; <lb/>mais elles &longs;e <expan abbr="diminü&etilde;t">diminüent</expan> à proportion que <lb/>la ligne &longs;e <expan abbr="pãche">panche</expan> &longs;ur le plan horizontal. </s> |
| </p> | </p> |
| <p type="head"> | <p type="head"> |
| <s id="s.000265"><emph type="center"/>III. ADDITION.<emph.end type="center"/><!-- KEEP S--></s> | <s id="s.000265"><emph type="center"/>III. ADDITION.<emph.end type="center"/><!-- KEEP S--></s> |
![[BACK]](http://archimedes.mpiwg-berlin.mpg.de/arch/img/icons/back.gif){kind=icon}
Return to galil_mecha_047_fr_1634.xml
CVS log ![[TXT]](http://archimedes.mpiwg-berlin.mpg.de/arch/img/icons/text.gif){kind=icon}
![[DIR]](http://archimedes.mpiwg-berlin.mpg.de/arch/img/icons/dir.gif){kind=icon}
Up to [CVSROOT] / texts / archimedes / xml