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<?xml version="1.0" encoding="UTF-8"?> <!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd"> <archimedes> <info> <author>Johann Terrenz Schreck, Zheng Wang</author> <title>Yuanxi Qiqi Tushuo Luzui</title> <date>1627</date> <place/> <editor/> <publisher/> <translator/> <lang>zh</lang> <locator>X03.xml</locator> </info> <text> <front/> <body> <chap id="N10015" n="1"> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.001.jpg"/> <p id="N10019" type="main"> <s id="N1001F"> 道光庚寅仲夏月重鐫<lb/> </s> </p> <p id="N1001D" type="main"> <s id="N10027"> 校正無訛 翻刻必究<lb/> </s> </p> <p id="N10021" type="head"> <s id="N1002F"> 奇器圖說</s> </p> <p id="N10024" type="main"> <s id="N10035"> 來鹿堂藏板</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.002.jpg"/> <lb/> <p id="N1002A" type="head"> <s id="N1003F"> 重刊王忠節公《奇器圖說》序</s> </p> <p id="N1002D" type="main"> <s id="N10045"> 《奇器圖說》，吾秦涇陽王忠節公輯也。</s> <s id="N10048">公丁明末造，<lb/> 由進士前後司理廣平、揚州，所至惠聲洋溢，上下交<lb/> 孚。</s> <s id="N1004F">比解組歸田，值流寇猖獗，所劫州縣率無完區，獨<lb/> 涇原一邑，屢出奇兵制胜，使寇不敢西向而彎弓者，<lb/> 實公一人捍禦之功。</s> <s id="N10056">惜當時葉臺山、徐元扈兩相國，<lb/> 暨李松毓、楊忠烈諸君子，以王佐才文章推薦，卒為<lb/> 權佞阻撓，未獲起用。</s> <s id="N1005D">即值鼎革，以絕粒聞。</s> <s id="N10060">至我朝<lb/> 高宗純皇帝，追謚忠節，以慰毅魄，是其忠惠大節已<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.003.jpg"/> 彪炳如日星河嶽夫！豈徒以緒餘表見哉？即以緒餘<lb/> 論其圖說之巧，率皆有關于國計民生，迥非吳夫差<lb/> 之造千石酒鍾、唐齊映之製八尺銀缾者所可埒。</s> <s id="N1006F">且<lb/> 余聞之父老云：公未通籍前，每春夏播耕時，多為木<lb/> 偶以供驅策，或舂者、簸者、汲者、炊者、操餅仗者、抽風<lb/> 箱者，機關轉捩，宛然如生。</s> <s id="N10078">至收獲時，輒製自行車以<lb/> 捆載禾束，事半功倍，鄉人多艷而效之。</s> <s id="N1007D">公所居室曾<lb/> 竅一壁，以通傳語。</s> <s id="N10082">每值冠昏葬祭事，使一人語于竅，<lb/> 則前後數十屋悉聞之，名曰空屋傳聲，亦以簡御繁<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.004.jpg"/> <lb/> 之術也。</s> <s id="N1008D">又公于甲申林下時，聞李自成寇京師，公壘<lb/> 瓦礫為內外城，如京制，繞城默祝者七晝夜。</s> <s id="N10092">適一犬<lb/> 自西南至曳城一隅圮，公知事不可為，乃仰天慟哭，<lb/> 七日不食而殉國難。</s> <s id="N10099">此非深明天時人事者能如是<lb/> 乎？吾不知天生此才，使不究其用，其生之者何心？而<lb/> 死之者又何心？抑優游歲月，俾立器盡制，以洩前賢<lb/> 未洩之蘊歟？然此書也，人多議之，謂天有常道，聖有<lb/> 常教，民有常器，何必索隱行怪，駭人耳目？余曰：不然。</s> <s id="N100A4"><lb/> 綯髮<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/01.jpg"/>首之民，剝木以戰不知耕，抱木以游不知濟。</s> <s id="N100AB"><pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.005.jpg"/> <lb/> 自神農黃帝代作，斲木為耜，揉木為耒，刳木為舟，剡<lb/> 木為楫。</s> <s id="N100B5">厥用既神，厥功斯茂。</s> <s id="N100B8">試遙想鷇飲鶉居之眾，<lb/> 有不乍見而適適然驚耶？及歷用久之，則如布帛菽<lb/> 粟之無奇矣。</s> <s id="N100BF">且不第是蜀漢諸葛武侯造木牛流馬，<lb/> 以運軍食，省物力，即以蓄民財，此軍政之最善者。</s> <s id="N100C4">然<lb/> 而後人猶議其非中庸之道者，他何論焉？今公以聰<lb/> 明天授之資，收遠西師資之益，成備物致用之書，古<lb/> 皇固不敢妄擬，其亦武侯之流亞歟？亟宜廣為流布，<lb/> 俾百姓日用而不知，萬世率由於不敝，又奚事詫橐<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.006.jpg"/> <lb/> 駝為馬腫背耶？余家居時，聞此書板片漶漫，善本難<lb/> 得，不惜重貲購得之，冀推廣公意以傳於無窮，苦於<lb/> 無暇無力，屢舉輒屢輟之。</s> <s id="N100D9">今需次錦官偶出是書，以<lb/> 授同好。</s> <s id="N100DE">見者咸謂官有資於政事，民有資於身家，盍<lb/> 重刊之以公海內？余因眾志僉同，遂詔築氏而謀之，<lb/> 并錄所聞軼事數端，以補史傳之未備云。</s> <s id="N100E5">時<lb/> </s> </p> <p id="N1008C" type="main"> <s id="N100ED">道光己丑秋八月上旬。</s> <s id="N100F0">例授承德郎、制科孝廉方<lb/> 正、辛巳恩科舉人、癸酉科拔貢、四川候補直隸州<lb/> 州判、安康張鵬翂補山氏，書於錦官雙樨精舍</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.007.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.008.jpg"/> <!-- missing pagebreak also two signs --> <lb/> <p id="N1009A" type="head"> <s id="N10103"> 陝西通志</s> </p> <p id="N1009D" type="main"> <s id="N10109"> 王徵，字良甫，號葵心，涇陽人。</s> <s id="N1010C">天啟壬戌進士，初授廣平推<lb/> 官，佑善褫奸，明允著譽，熄白蓮亂，生全萬民，開清河閘，利<lb/> 濟百世。</s> <s id="N10113">起复揚州推官，導三王駕，不苦騷擾，釋鹺使誣，弗<lb/> 拜魏璫之祠，風節凜然，特以邊才薦陞登萊監軍僉事。</s> <s id="N10118">未<lb/> 閱月，逆弁鼓噪，遂回籍。</s> <s id="N1011D">值流寇發難，倡立忠統，堵賊保民，<lb/> 涇原獲安。</s> <s id="N10122">當道疏薦王佐才，未展其用。</s> <s id="N10125">及闖賊陷秦，徵辟<lb/> 鄉曲，賊屢迫脅，佩刀自矢，竟不赴省。</s> <s id="N1012A">聞京師失守，設帝位<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.009.jpg"/> <lb/> 哭於家，七日不食，死。</s> <s id="N10133">著有《兩理略》、《奇器圖》、《了心丹》、《百子解》、<lb/> 《學庸解》、《天問辭》、《士約》、《兵約》、《元真人傳》、《歷代發蒙》、《辨道說》、《山<lb/> 居詠》諸集行世。</s> <s id="N1013A">學者私諡端節先生。</s> <s id="N1013D"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.010.jpg"/> <p id="N100B7" type="head"> <s id="N10147"> 《奇器圖》後序</s> </p> <p id="N100BA" type="main"> <s id="N1014D"> 世間非常之事，非常之人<lb/> 為之。</s> <s id="N10152">非常者，奇也。</s> <s id="N10155">小儒膽<lb/> 薄而識淺，借口中庸以文<lb/> 飾其固陋。</s> <s id="N1015C">夫中庸之不可 <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.011.jpg"/> <lb/> 能，非奇邪？<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/02.jpg"/>苑有奇文，戰<lb/> 陳有奇兵，術數有奇門，人<lb/> 倫有奇士，山海有奇物，鬼<lb/> 神有奇狀，詎於器而無奇<lb/> 也者？要亦非常之人，靈心<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.012.jpg"/> <lb/> 躍露，直以器為寄焉耳。</s> <s id="N10176">關<lb/> 西王公，司理維、揚，寬明仁<lb/> 恕，莊敬中和，政簡刑清，士<lb/> 民胥化。</s> <s id="N1017F">即正樂一事，其與<lb/> 不肖位，講明而脩舉者，亦<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.013.jpg"/> <lb/> 既洋洋大雅，追六代之遺<lb/> 矣。</s> <s id="N1018C">以位為可教也，復出其<lb/> 《奇器圖說》一書，採輯者為<lb/> 卷三，創置者為卷一，授位<lb/> 學焉。</s> <s id="N10195">蓋公膽智宏材，披天<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.014.jpg"/> <lb/> 根而漱地軸，觸類多能，其<lb/> 緒餘矣。</s> <s id="N101A0">嘗考古，善奇者，輸<lb/> 班、墨翟見用於時，有益於<lb/> 世，其最著者矣。</s> <s id="N101A7">嗣若祖沖<lb/> 之、張平子、馬鈞藝元之流，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.015.jpg"/> <lb/> 皆當世名巧，而功不集事，<lb/> 利不及民，終無取焉。</s> <s id="N101B4">獨木<lb/> 牛流馬膾炙至今，此外多<lb/> 屬假託，非其真也。</s> <s id="N101BB">乃公所<lb/> 製自行車、自行磨已足雁<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.016.jpg"/> <lb/> 行武侯，而虹吸、鶴飲之備<lb/> 旱潦，輪壺之傳刻漏，水銃<lb/> 之滅火災，連弩之禦大敵，<lb/> 代耕之省牛馬，因風趁水<lb/> 之不煩人力，其有裨於飛<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.017.jpg"/> <lb/> 輓、轉運、軍旅、農商，瑣細米<lb/> 鹽，小大悉備，逸勞相萬矣。</s> <s id="N101D6"><lb/> 昔人謂文至韓愈，詩至杜<lb/> 甫，書至顏真卿，畫至吳道<lb/> 元，天下之能事畢焉。</s> <s id="N101DE">然於<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.018.jpg"/> <lb/> 國家緩急，生民日用，曾何<lb/> 毛髮益乎？是書也，廣而公<lb/> 之，固濟世利物者一大舟<lb/> 楫也。</s> <s id="N101ED">寧止嘉惠維、揚哉？《陰<lb/> 苻》曰：“爰有奇器，是生萬象。</s> <s id="N101F2">”<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.019.jpg"/> <lb/> 位則曰：“公有奇器，實利萬<lb/> 民；則公之品，誠有用大儒；<lb/> 公之書，固非常偉業。</s> <s id="N101FF">是胡<lb/> 可以不傳也？”敬手繪而壽<lb/> 之梓。</s> <s id="N10206">時<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.020.jpg"/> <p id="N10135" type="main"> <s id="N10211">崇禎改元中秋日直隸揚<lb/> 州府儒學訓導武位中頓<lb/> 首撰并書<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.021.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.022.jpg"/> <lb/> <!-- missing page break blank page--> <lb/> </s> </p> <p id="N10144" type="head"> <s id="N1022B"> 《遠西奇器圖說錄最》</s> </p> <p id="N10147" type="main"> <s id="N10231"> 《奇器圖說》乃遠西諸儒<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/03.jpg"/>來彼<lb/> 國圖書，此其七千餘部中之一<lb/> 支。</s> <s id="N1023B">就一支中，此特其千百之什<lb/> 一耳。</s> <s id="N10240">余不敏， 竊嘗仰窺制器尚<lb/> 象之旨，而深有味乎璇璣。</s> <s id="N10245">玉衡<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.023.jpg"/> <lb/> 之作一器也，規天條地，七政咸<lb/> 在，萬祀不磨，奇哉！蔑以尚已考<lb/> 工指南，而後代不乏宗工哲匠，<lb/> 然自化人奇肱之外，巧絕弗傳。</s> <s id="N10254"><lb/> 而木牛流馬遂擅千古絕響，余<lb/> 甚慕之愛之。</s> <s id="N1025A">間嘗不揣固陋，妄<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.024.jpg"/> <lb/> 製虹吸、鶴飲、輪壺、代耕及自轉<lb/> 磨、自行車諸器，見之者亦頗稱<lb/> 奇。</s> <s id="N10267">然于余心殊未甚快也。</s> <s id="N1026A">偶讀<lb/> 《職方外紀》所載奇人、奇事，未易<lb/> 更僕，數其中一二奇器，絕非此<lb/> 中見聞所及。</s> <s id="N10273">如云多勒多城，在<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.025.jpg"/> <lb/> 山巔取山下之水，以供山上，運<lb/> 之甚艱。</s> <s id="N1027E">近百年內有巧者製一<lb/> 水器，能盤水直至山城，絕不賴<lb/> 人力，其器自能晝夜轉運也。</s> <s id="N10285">又<lb/> 云：亞而幾墨得者，天文師也，承<lb/> 國王命，造一航海極大之舶。</s> <s id="N1028C">舶<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.026.jpg"/> <lb/> 成將下之海。</s> <s id="N10295">計雖傾一國之力，<lb/> 用牛馬駱駝千萬，莫能運也。</s> <s id="N1029A">幾<lb/> 墨得營作巧法，第令王一舉手<lb/> 引之，舶如山岳轉動，須臾即下<lb/> 海矣。</s> <s id="N102A3">又造一自動渾天儀，其七<lb/> 政各有本動，凡列宿運行之遲<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.027.jpg"/> <lb/> 疾，一一與天無二。</s> <s id="N102AE">其儀以玻璃<lb/> 為之，悉可透視，真希世珍也。</s> <s id="N102B3">《職<lb/> 方外紀》，西儒艾先生所作，其言<lb/> 當不得妄，余蓋爽然自失而私<lb/> 竊嚮往，曰：“嗟乎！此等奇器何緣<lb/> 得當吾世而一睹之哉？”丙寅冬，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.028.jpg"/> <lb/> 余補銓如都，會龍精華、鄧函璞、<lb/> 湯道未三先生，以候旨修歷，<lb/> 寓舊邸中。</s> <s id="N102C8">余得朝夕晤，請教，<lb/> 益甚讙也。</s> <s id="N102CD">暇日，因述《外紀》<lb/> 所載質之，三先生笑而唯唯。</s> <s id="N102D2">且<lb/> 曰：“諸器甚多，悉著圖說，見在可<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.029.jpg"/> <lb/> 覽也，奚敢妄？”余亟索觀，簡帙不<lb/> 一，第專屬奇器之圖之說者不<lb/> 下千百餘種。</s> <s id="N102E1">其器多用小力轉<lb/> 大重，或使升高，或令行遠，或資<lb/> 修築，或運芻餉，或便泄注，或上<lb/> 下舫舶，或預防災祲，或潛禦物<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.030.jpg"/> <lb/> 害，或自舂自解，或生響生風，諸<lb/> 奇妙器無不備具。</s> <s id="N102F2">有用人力物<lb/> 力者，有用風力水力者，有用輪<lb/> 盤，有用關捩，有用空虛，有即用<lb/> 重為力者，種種妙用，令人心花<lb/> 開爽。</s> <s id="N102FD">間有數製，頗與愚見相合，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.031.jpg"/> <lb/> 閱其圖繪，精工無比。</s> <s id="N10306">然有物有<lb/> 像，猶可覽而想像之。</s> <s id="N1030B">乃其說則<lb/> 屬西文西字，雖余嚮在里中，得<lb/> 金四表先生為余指授西文字<lb/> 母字父二十五號，刻有《西儒耳<lb/> 目資》一書，亦略知其音響乎。</s> <s id="N10316">顧<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.032.jpg"/> <lb/> 全文全義則茫然其莫測也。</s> <s id="N1031F">於<lb/> 是，亟請譯以中字。</s> <s id="N10324">鄧先生則曰：<lb/> “譯是不難，第此道雖屬力藝之<lb/> 小技，然必先攷度數之學而後<lb/> 可。</s> <s id="N1032D">蓋凡器用之微，須先有度有<lb/> 數。</s> <s id="N10332">因度而生測量，因數而生計<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.033.jpg"/> <lb/> 筭，因測量、計筭而有比例，因比<lb/> 例而後可以窮物之理，理得而<lb/> 後法可立也。</s> <s id="N1033F">不曉測量、計筭，則<lb/> 必不得比例；不得比例，則此器<lb/> 圖說必不能通曉。</s> <s id="N10346">測量另有專<lb/> 書，筭指具在《同文》，比例亦大都<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.034.jpg"/> <lb/> 見《幾何原本》中。</s> <s id="N10351">”先生為余指敶，<lb/> 余習之數日，頗亦曉其梗概。</s> <s id="N10356">於<lb/> 是，取諸器圖說全帙，分類而口<lb/> 授焉。</s> <s id="N1035D">余輒信筆疾書，不次不文，<lb/> 總期簡明易曉，以便人人覽閱。</s> <s id="N10362"><lb/> 然圖說之中巧器極多，第或不<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.035.jpg"/> <lb/> 甚關切民生日用，如飛鳶、水琴<lb/> 等類，又或非國家工作之所急<lb/> 需，則不錄。</s> <s id="N10370">特錄其最切要者，器<lb/> 誠切矣。</s> <s id="N10375">乃其作法或難，如一器<lb/> 而螺絲轉太多，工匠不能如法；<lb/> 又或器之工費甚鉅，則不錄。</s> <s id="N1037C">特<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.036.jpg"/> <lb/> 錄其最簡便者，器俱切俱便矣。</s> <s id="N10385"><lb/> 而一法多種，一種多器，如水法<lb/> 一器有百十多類，或重或繁，則<lb/> 不錄。</s> <s id="N1038D">特錄其最精妙者。</s> <s id="N10390">錄既成，<lb/> 輒名之為《遠西奇器圖說錄最》<lb/> 云。</s> <s id="N10397">客有愛余者，顧而言曰：“吾子<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.037.jpg"/> <lb/> 嚮刻《西儒耳目資》，猶可謂文人<lb/> 學士所不廢也。</s> <s id="N103A2">今玆所錄，特工<lb/> 匠技藝流耳。</s> <s id="N103A7">君子不器，子何敝<lb/> 敝焉於斯？矧西儒寓我中華，我<lb/> 輩深交，固真知其賢矣。</s> <s id="N103AE">第其人<lb/> 越在遐荒萬里外，不過西鄙一<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.038.jpg"/> <lb/> 儒焉耳。</s> <s id="N103B9">奚為偏嗜篤好之若此？”<lb/> 余應之曰：“學原不問精麤，總期<lb/> 有濟於世；人亦不問中西，總期<lb/> 不違於天。</s> <s id="N103C2">玆所錄者，雖屬技藝<lb/> 末務，而實有益於民生日用、國<lb/> 家興作甚急也。</s> <s id="N103C9">”儻執不器之說<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.039.jpg"/> <lb/> 而鄙之，則尼父繫《易》，胡以又云：<lb/> “備物制用，立成器以為天下利，<lb/> 莫大乎聖人”？且夫畸人罕遘，絕<lb/> 學希聞，遇合最難，歲月不待，明<lb/> 睹其奇而不錄以傳之，余心不<lb/> 能已也。</s> <s id="N103DC">故嚮求耳目之資，今更<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.040.jpg"/> <lb/> 求為手足之資已耳，他何計焉？<lb/> 夫西儒在玆多年，士大夫與之<lb/> 遊者靡不心醉神怡。</s> <s id="N103E9">彼且不驕<lb/> 不吝，奈何當吾世而覿面失之？<lb/> 古之好學者裹糧負笈，不遠數<lb/> 千里往訪。</s> <s id="N103F2">今諸賢從絕徼數萬<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.041.jpg"/> <lb/> 里外齎此圖書以傳我輩，我輩<lb/> 反忍拒而不納歟？諸賢寥寥數<lb/> 輩，胥皆有道之儒。</s> <s id="N103FF">來賓來王，視<lb/> 昔越裳肅慎，不啻遠之遠矣。</s> <s id="N10404">正<lb/> 可昭我明聖德，來遠千古罕儷<lb/> 之盛。</s> <s id="N1040B">邇來余省新從地中掘出<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.042.jpg"/> <lb/> 一碑，額題“景教流行中國碑頌”<lb/> ，乃唐郭子儀時所鐫，千載如新，<lb/> 與今日諸賢所傳崇敬天之教<lb/> 一一若合符節。</s> <s id="N1041A">所載自唐太宗以後凡六帝，遞相崇敬甚篤也。</s> <s id="N1041D"><lb/> 在昔已然，今又何嫌忌之與？有<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.043.jpg"/> <lb/> 客又笑謂余曰：“是固然矣。</s> <s id="N10427">第就<lb/> 子言耳目有資，手足有資，而心<lb/> 獨可無資乎哉？西儒縹緗盈室，<lb/> 資心之書必多，子不之譯而獨<lb/> 譯此器書，何也？”余俯而唯唯，曰：<lb/> “有跡之器具麤可指陳，無形之<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.044.jpg"/> <lb/> 理譚猝難究竟。</s> <s id="N1043A">余小子不敏，聊<lb/> 以辦此足矣。</s> <s id="N1043F">若夫西儒義理全<lb/> 書，非木天、石渠諸大手筆，弗克<lb/> 譯也。</s> <s id="N10446">此固余小子昕夕所深願<lb/> 而力不逮者，其尚俟之異日。</s> <s id="N1044B">”客<lb/> 遂頷然而去。</s> <s id="N10450">余因併錄其言，以<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.045.jpg"/> 識歲月。</s> <s id="N10459"><lb/> </s> </p> <p id="N1028C" type="main"> <s id="N10460">時<lb/> </s> </p> <p id="N10290" type="main"> <s id="N10468">天啟七年丁卯孟春關中涇邑<lb/> 了一道人王徵謹識<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.046.jpg"/> <p id="N10298" type="head"> <s id="N10475"> 遠西奇器圖說錄最凡例</s> </p> <p id="N1029B" type="head"> <s id="N1047B">--正用</s> </p> <p id="N1029E" type="main"> <s id="N10481"> 重學<lb/> </s> </p> <p id="N102A2" type="main"> <s id="N10489"> 借資<lb/> </s> </p> <p id="N102A6" type="main"> <s id="N10491"> 窮理格物之學<lb/> </s> </p> <p id="N102AA" type="main"> <s id="N10499"> 度學<lb/> </s> </p> <p id="N102AE" type="main"> <s id="N104A1"> 數學<lb/> </s> </p> <p id="N102B2" type="main"> <s id="N104A9"> 視學<lb/> </s> </p> <p id="N102B6" type="main"> <s id="N104B1"> 呂律學<lb/> </s> </p> <p id="N102BA" type="head"> <s id="N104B9"> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.047.jpg"/>--引取</s> </p> <p id="N102BF" type="main"> <s id="N104C3"> 勾股法義<lb/> </s> </p> <p id="N102C3" type="main"> <s id="N104CB"> 圜容較義<lb/> </s> </p> <p id="N102C7" type="main"> <s id="N104D3"> 蓋憲通考<lb/> </s> </p> <p id="N102CB" type="main"> <s id="N104DB"> 泰西水法<lb/> </s> </p> <p id="N102CF" type="main"> <s id="N104E3"> 幾何原本<lb/> </s> </p> <p id="N102D3" type="main"> <s id="N104EB"> 坤輿全圖<lb/> </s> </p> <p id="N102D7" type="main"> <s id="N104F3"> 簡平儀<lb/> </s> </p> <p id="N102DB" type="main"> <s id="N104FB"> 渾天儀<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.048.jpg"/> <p id="N102E1" type="main"> <s id="N10506"> 天問略<lb/> </s> </p> <p id="N102E5" type="main"> <s id="N1050E"> 同文筭指<lb/> </s> </p> <p id="N102E9" type="main"> <s id="N10516"> 敬天實義<lb/> </s> </p> <p id="N102ED" type="main"> <s id="N1051E"> 畸人十篇<lb/> </s> </p> <p id="N102F1" type="main"> <s id="N10526"> 七克<lb/> </s> </p> <p id="N102F5" type="main"> <s id="N1052E"> 自鳴鐘說<lb/> </s> </p> <p id="N102F9" type="main"> <s id="N10536"> 望遠鏡說<lb/> </s> </p> <p id="N102FD" type="main"> <s id="N1053E"> 職方外紀<lb/> </s> </p> <p id="N10301" type="main"> <s id="N10546"> 西學或問<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.049.jpg"/> <p id="N10307" type="main"> <s id="N10551"> 西學凡<lb/> </s> </p> <p id="N1030B" type="head"> <s id="N10559">--制器器</s> </p> <p id="N1030E" type="main"> <s id="N1055F"> 度數尺<lb/> </s> </p> <p id="N10312" type="main"> <s id="N10567"> 驗地平尺<lb/> </s> </p> <p id="N10316" type="main"> <s id="N1056F"> 合用分方分圓尺</s> </p> <n>(兩端即兩規矩)</n> <lb/> <p id="N1031C" type="main"> <s id="N10578"> 闔闢分方分圓各由一分起至十分尺<lb/> </s> </p> <p id="N10320" type="main"> <s id="N10580"> 規矩<lb/> </s> </p> <p id="N10324" type="main"> <s id="N10588"> 兩足規矩<lb/> </s> </p> <p id="N10328" type="main"> <s id="N10590"> 三足規矩<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.050.jpg"/> <p id="N1032E" type="main"> <s id="N1059B"> 兩螺絲轉闔闢定用規矩<lb/> </s> </p> <p id="N10332" type="main"> <s id="N105A3"> 單螺絲轉闔闢任用規矩<lb/> </s> </p> <p id="N10336" type="main"> <s id="N105AB"> 畫銅鐵規矩<lb/> </s> </p> <p id="N1033A" type="main"> <s id="N105B3"> 畫紙規矩<lb/> </s> </p> <p id="N1033E" type="main"> <s id="N105BB"> 作雞蛋形規矩<lb/> </s> </p> <p id="N10342" type="main"> <s id="N105C3"> 作螺絲轉形規矩<lb/> </s> </p> <p id="N10346" type="main"> <s id="N105CB"> 移遠畫近規矩<lb/> </s> </p> <p id="N1034A" type="main"> <s id="N105D3"> 寫字以大作小，以小作大規矩<lb/> </s> </p> <p id="N1034E" type="main"> <s id="N105DB"> 螺絲轉母<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.051.jpg"/> <p id="N10354" type="main"> <s id="N105E6"> 活鋸<lb/> </s> </p> <p id="N10358" type="main"> <s id="N105EE"> 雙翼鑽<lb/> </s> </p> <p id="N1035C" type="main"> <s id="N105F6"> 螺絲轉鐵鉗<lb/> </s> </p> <p id="N10360" type="head"> <s id="N105FE">--記號</s> </p> <p id="N10363" type="main"> <s id="N10604"> 號必用西字者，西字號初似難記，然正因<lb/> 其難記，欲覽者怪而尋索，必求其得耳。</s> <s id="N10609">況<lb/> 號止二十，形象各異，又不甚煩，不甚難乎。</s> <s id="N1060E"><lb/> 今將西字總列于左，即以中字並列釋之，<lb/> 以便觀覽。</s> <s id="N10614">且欲知西字止二十號耳，可括<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.052.jpg"/> 萬音萬字之用。</s> <s id="N1061D"><lb/> </s> </p> <p id="N10373" type="main"> <s id="N10624">a e i o u c ch k p t j v f g l m n s x h<lb/> </s> </p> <p id="N10377" type="main"> <s id="N1062C">丫額衣阿午則者格百德日物弗額勒麥搦色石黑<lb/> </s> </p> <p id="N1037B" type="main"> <s id="N10634"> 以上記號蓋因圖中諸器多端，須用標記，<lb/> 而後說中指其記號，一一可詳解耳，用之<lb/> 不盡不論也。</s> <s id="N1063B">圖之簡明易知者，則不用。</s> <s id="N1063E"><lb/> </s> </p> <p id="N10383" type="head"> <s id="N10645">--每所用物名目</s> </p> <p id="N10386" type="main"> <s id="N1064B"> 柱<lb/> </s> </p> <p id="N1038A" type="main"> <s id="N10653"> 長柱<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.053.jpg"/> <p id="N10390" type="main"> <s id="N1065E"> 短柱<lb/> </s> </p> <p id="N10394" type="main"> <s id="N10666"> 梁<lb/> </s> </p> <p id="N10398" type="main"> <s id="N1066E"> 橫梁<lb/> </s> </p> <p id="N1039C" type="main"> <s id="N10676"> 側梁<lb/> </s> </p> <p id="N103A0" type="main"> <s id="N1067E"> 架<lb/> </s> </p> <p id="N103A4" type="main"> <s id="N10686"> 高架<lb/> </s> </p> <p id="N103A8" type="main"> <s id="N1068E"> 方架<lb/> </s> </p> <p id="N103AC" type="main"> <s id="N10696"> 短架<lb/> </s> </p> <p id="N103B0" type="main"> <s id="N1069E"> 槓杆<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.054.jpg"/> <p id="N103B6" type="main"> <s id="N106A9"> 軸<lb/> </s> </p> <p id="N103BA" type="main"> <s id="N106B1"> 立軸<lb/> </s> </p> <p id="N103BE" type="main"> <s id="N106B9"> 平軸<lb/> </s> </p> <p id="N103C2" type="main"> <s id="N106C1"> 斜軸<lb/> </s> </p> <p id="N103C6" type="main"> <s id="N106C9"> 觚軸<lb/> </s> </p> <p id="N103CA" type="main"> <s id="N106D1"> 輪<lb/> </s> </p> <p id="N103CE" type="main"> <s id="N106D9"> 立輪<lb/> </s> </p> <p id="N103D2" type="main"> <s id="N106E1"> 攪輪<lb/> </s> </p> <p id="N103D6" type="main"> <s id="N106E9"> 平輪<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.055.jpg"/> <p id="N103DC" type="main"> <s id="N106F4"> 斜輪<lb/> </s> </p> <p id="N103E0" type="main"> <s id="N106FC"> 飛輪<lb/> </s> </p> <p id="N103E4" type="main"> <s id="N10704"> 行輪<lb/> </s> </p> <p id="N103E8" type="main"> <s id="N1070C"> 星輪<lb/> </s> </p> <p id="N103EC" type="main"> <s id="N10714"> 鼓輪<lb/> </s> </p> <p id="N103F0" type="main"> <s id="N1071C"> 齒輪<lb/> </s> </p> <p id="N103F4" type="main"> <s id="N10724"> 輻輪<lb/> </s> </p> <p id="N103F8" type="main"> <s id="N1072C"> 觚輪<lb/> </s> </p> <p id="N103FC" type="main"> <s id="N10734"> 燈輪<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.056.jpg"/> <p id="N10402" type="main"> <s id="N1073F"> 水輪<lb/> </s> </p> <p id="N10406" type="main"> <s id="N10747"> 風輪<lb/> </s> </p> <p id="N1040A" type="main"> <s id="N1074F"> 十字立輪<lb/> </s> </p> <p id="N1040E" type="main"> <s id="N10757"> 十字平輪<lb/> </s> </p> <p id="N10412" type="main"> <s id="N1075F"> 半規斜輪<lb/> </s> </p> <p id="N10416" type="main"> <s id="N10767"> 木板立輪<lb/> </s> </p> <p id="N1041A" type="main"> <s id="N1076F"> 木板平輪<lb/> </s> </p> <p id="N1041E" type="main"> <s id="N10777"> 鋸齒輪<lb/> </s> </p> <p id="N10422" type="main"> <s id="N1077F"> 半規鋸齒輪<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.057.jpg"/> <p id="N10428" type="main"> <s id="N1078A"> 上下相錯鋸齒輪<lb/> </s> </p> <p id="N1042C" type="main"> <s id="N10792"> 左右相錯鋸齒輪<lb/> </s> </p> <p id="N10430" type="main"> <s id="N1079A"> 曲柄<lb/> </s> </p> <p id="N10434" type="main"> <s id="N107A2"> 左右對轉曲柄<lb/> </s> </p> <p id="N10438" type="main"> <s id="N107AA"> 上下立轉曲柄<lb/> </s> </p> <p id="N1043C" type="main"> <s id="N107B2"> 單轆轤<lb/> </s> </p> <p id="N10440" type="main"> <s id="N107BA"> 雙轆轤<lb/> </s> </p> <p id="N10444" type="main"> <s id="N107C2"> 滑車<lb/> </s> </p> <p id="N10448" type="main"> <s id="N107CA"> 推車<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.058.jpg"/> <p id="N1044E" type="main"> <s id="N107D5"> 曳車<lb/> </s> </p> <p id="N10452" type="main"> <s id="N107DD"> 駕車<lb/> </s> </p> <p id="N10456" type="main"> <s id="N107E5"> 玉衡車<lb/> </s> </p> <p id="N1045A" type="main"> <s id="N107ED"> 龍尾車<lb/> </s> </p> <p id="N1045E" type="main"> <s id="N107F5"> 升車<lb/> </s> </p> <p id="N10462" type="main"> <s id="N107FD"> 索<lb/> </s> </p> <p id="N10466" type="main"> <s id="N10805"> 曳索<lb/> </s> </p> <p id="N1046A" type="main"> <s id="N1080D"> 垂索<lb/> </s> </p> <p id="N1046E" type="main"> <s id="N10815"> 轉索<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.059.jpg"/> <p id="N10474" type="main"> <s id="N10820"> 纏索<lb/> </s> </p> <p id="N10478" type="main"> <s id="N10828"> 水戽<lb/> </s> </p> <p id="N1047C" type="main"> <s id="N10830"> 水杓<lb/> </s> </p> <p id="N10480" type="main"> <s id="N10838"> 連珠戽<lb/> </s> </p> <p id="N10484" type="main"> <s id="N10840"> 鶴膝轉軸<lb/> </s> </p> <p id="N10488" type="main"> <s id="N10848"> 風蓬<lb/> </s> </p> <p id="N1048C" type="main"> <s id="N10850"> 風扇<lb/> </s> </p> <p id="N10490" type="main"> <s id="N10858"> 活輥木<lb/> </s> </p> <p id="N10494" type="main"> <s id="N10860"> 活地平<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.060.jpg"/> <p id="N1049A" type="main"> <s id="N1086B"> 活桔槔<lb/> </s> </p> <p id="N1049E" type="head"> <s id="N10873">--諸器所用</s> </p> <p id="N104A1" type="main"> <s id="N10879"> 用器<lb/> </s> </p> <p id="N104A5" type="main"> <s id="N10881"> 用人<lb/> </s> </p> <p id="N104A9" type="main"> <s id="N10889"> 用馬<lb/> </s> </p> <p id="N104AD" type="main"> <s id="N10891"> 用風<lb/> </s> </p> <p id="N104B1" type="main"> <s id="N10899"> 用水<lb/> </s> </p> <p id="N104B5" type="main"> <s id="N108A1"> 用空<lb/> </s> </p> <p id="N104B9" type="main"> <s id="N108A9"> 用重<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.061.jpg"/> <p id="N104BF" type="main"> <s id="N108B4"> 用槓<lb/> </s> </p> <p id="N104C3" type="main"> <s id="N108BC"> 用輪<lb/> </s> </p> <p id="N104C7" type="main"> <s id="N108C4"> 用龍尾<lb/> </s> </p> <p id="N104CB" type="main"> <s id="N108CC"> 用螺絲<lb/> </s> </p> <p id="N104CF" type="main"> <s id="N108D4"> 用秤杆<lb/> </s> </p> <p id="N104D3" type="main"> <s id="N108DC"> 用滑車<lb/> </s> </p> <p id="N104D7" type="main"> <s id="N108E4"> 用攪<lb/> </s> </p> <p id="N104DB" type="main"> <s id="N108EC"> 用轉<lb/> </s> </p> <p id="N104DF" type="main"> <s id="N108F4"> 用推<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.062.jpg"/> <p id="N104E5" type="main"> <s id="N108FF"> 用曳<lb/> </s> </p> <p id="N104E9" type="main"> <s id="N10907"> 用揭<lb/> </s> </p> <p id="N104ED" type="main"> <s id="N1090F"> 用墜<lb/> </s> </p> <p id="N104F1" type="main"> <s id="N10917"> 用薦<lb/> </s> </p> <p id="N104F5" type="main"> <s id="N1091F"> 用提<lb/> </s> </p> <p id="N104F9" type="main"> <s id="N10927"> 用小力<lb/> </s> </p> <p id="N104FD" type="main"> <s id="N1092F"> 用大力<lb/> </s> </p> <p id="N10501" type="main"> <s id="N10937"> 用一器<lb/> </s> </p> <p id="N10505" type="main"> <s id="N1093F"> 用數器<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.063.jpg"/> <p id="N1050B" type="main"> <s id="N1094A"> 用相等之器<lb/> </s> </p> <p id="N1050F" type="main"> <s id="N10952"> 用相勝之器<lb/> </s> </p> <p id="N10513" type="main"> <s id="N1095A"> 用相通之器<lb/> </s> </p> <p id="N10517" type="main"> <s id="N10962"> 用相輔之器<lb/> </s> </p> <p id="N1051B" type="head"> <s id="N1096A">--諸器能力</s> </p> <p id="N1051E" type="main"> <s id="N10970"> 能以小力勝大重<lb/> </s> </p> <p id="N10522" type="main"> <s id="N10978"> 能使重者升高<lb/> </s> </p> <p id="N10526" type="main"> <s id="N10980"> 能使重者行遠<lb/> </s> </p> <p id="N1052A" type="main"> <s id="N10988"> 能使在下者遞上而不窮<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.064.jpg"/> <p id="N10530" type="main"> <s id="N10993"> 能使不動者常動而不息<lb/> </s> </p> <p id="N10534" type="main"> <s id="N1099B"> 能使不鳴者自鳴<lb/> </s> </p> <p id="N10538" type="main"> <s id="N109A3"> 能使不吹者自吹<lb/> </s> </p> <p id="N1053C" type="main"> <s id="N109AB"> 能使大者小<lb/> </s> </p> <p id="N10540" type="main"> <s id="N109B3"> 能使小者大<lb/> </s> </p> <p id="N10544" type="main"> <s id="N109BB"> 能使近者遠<lb/> </s> </p> <p id="N10548" type="main"> <s id="N109C3"> 能使遠者近<lb/> </s> </p> <p id="N1054C" type="head"> <s id="N109CB">--諸器利益</s> </p> <p id="N1054F" type="main"> <s id="N109D1"> 省大力<lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.065.jpg"/> <p id="N10555" type="main"> <s id="N109DC"> 免大勞<lb/> </s> </p> <p id="N10559" type="main"> <s id="N109E4"> 解大苦<lb/> </s> </p> <p id="N1055D" type="main"> <s id="N109EC"> 釋大難<lb/> </s> </p> <p id="N10561" type="main"> <s id="N109F4"> 節大費<lb/> </s> </p> <p id="N10565" type="main"> <s id="N109FC"> 長大識<lb/> </s> </p> <p id="N10569" type="main"> <s id="N10A04"> 增大智<lb/> </s> </p> <p id="N1056D" type="main"> <s id="N10A0C"> 致一切難致之物平易而無危險<lb/> </s> </p> <p id="N10571" type="head"> <s id="N10A14">--全器圖說</s> </p> <p id="N10574" type="main"> <s id="N10A1A"> 起重圖說</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.066.jpg"/> <lb/> <p id="N1057A" type="main"> <s id="N10A24"> 引重圖說<lb/> </s> </p> <p id="N1057E" type="main"> <s id="N10A2C"> 轉重圖說<lb/> </s> </p> <p id="N10582" type="main"> <s id="N10A34"> 取水圖說<lb/> </s> </p> <p id="N10586" type="main"> <s id="N10A3C"> 轉磨圖說<lb/> </s> </p> <p id="N1058A" type="main"> <s id="N10A44"> 解木圖說<lb/> </s> </p> <p id="N1058E" type="main"> <s id="N10A4C"> 解石圖說<lb/> </s> </p> <p id="N10592" type="main"> <s id="N10A54"> 轉碓圖說<lb/> </s> </p> <p id="N10596" type="main"> <s id="N10A5C"> 轉書輪圖說<lb/> </s> </p> <p id="N1059A" type="main"> <s id="N10A64"> 水轉日晷圖說</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.067.jpg"/> <lb/> <p id="N105A0" type="main"> <s id="N10A6E"> 代耕圖說<lb/> </s> </p> <p id="N105A4" type="main"> <s id="N10A76"> 水銃圖說<lb/> </s> </p> <p id="N105A8" type="main"> <s id="N10A7E"> 取力水圖說<lb/> </s> </p> <p id="N105AC" type="main"> <s id="N10A86"> 書架圖說<lb/> </s> </p> <p id="N105B0" type="main"> <s id="N10A8E"> 人飛圖說</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.068.jpg"/> <lb/> <p id="N105B6" type="head"> <s id="N10A98"> 遠西奇器圖說錄最卷第一</s> </p> <p id="N105B9" type="main"> <s id="N10A9E"> 西海耶穌會士鄧玉函 口授<lb/> </s> </p> <p id="N105BD" type="main"> <s id="N10AA6"> 關西景教後學王 徵 譯繪<lb/> </s> </p> <p id="N105C1" type="main"> <s id="N10AAE"> 金陵後學武位中 較<lb/> </s> </p> <p id="N105C5" type="main"> <s id="N10AB6"> 安康張鵬翂 梓<lb/> </s> </p> <p id="N105C9" type="main"> <s id="N10ABE"> 《奇器圖說》，譯西庠文字而作者也。</s> <s id="N10AC1">西庠，凡學，各有<lb/> 本名。</s> <s id="N10AC6">此學本名原是力藝。</s> <s id="N10AC9">力藝之學，西庠首有表<lb/> 性言，且有解，所以表此學之內美好。</s> <s id="N10ACE">次有表德言，<lb/> 所以表此學之外美好。</s> <s id="N10AD3">今悉譯其原文本義，兩列<lb/> 於左。</s> <s id="N10AD8"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.069.jpg"/> <lb/> <p id="N105D7" type="head"> <s id="N10AE1"> 力藝<n>(原名)</n> </s> </p> <p id="N105DC" type="head"> <s id="N10AEA"> 表性言</s> </p> <p id="N105DF" type="main"> <s id="N10AF0"> 力藝，重學也。</s> <s id="N10AF3"><lb/> </s> </p> <p id="N105E3" type="main"> <s id="N10AFA"> 力，是氣力、力量。</s> <s id="N10AFD">如人力、馬力、水力、風力之類。</s> <s id="N10B00">又用<lb/> 力、加力之謂。</s> <s id="N10B05">如用人力、用馬力、用水風之力之類。</s> <s id="N10B08"><lb/> 藝，則用力之巧法、巧器，所以善用其力，輕省其力<lb/> 之總名也。</s> <s id="N10B0E">重學者，“學”乃公稱，“重”則私號。</s> <s id="N10B11">蓋文學、理<lb/> 學、筭學之類，俱以“學”稱，故曰公。</s> <s id="N10B16">而此力藝之學，其<lb/> 取義本專屬重，故獨私號之曰“重學”云。</s> <s id="N10B1B"><lb/> </s> </p> <p id="N105F1" type="head"> <s id="N10B22"> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.070.jpg"/> 原解表性言</s> </p> <p id="N105F6" type="head"> <s id="N10B2C"> 蓋此重學，其總司維一，曰運重。</s> <s id="N10B2F"/> </p> <p id="N105F9" type="main"> <s id="N10B34"> 凡學，各有所司。</s> <s id="N10B37">如醫學所司者，治人病疾；筭學<lb/> 所司者，計數多寡。</s> <s id="N10B3C">而此力藝之學，其所司，不論<lb/> 土、水、木、石等物，則總在運重而已。</s> <s id="N10B41"><lb/> </s> </p> <p id="N10601" type="head"> <s id="N10B48"> 其分所有二：一本所，在內，曰明悟；一借所，在外，曰<lb/> 圖籍。</s> <s id="N10B4D"/> </p> <p id="N10606" type="main"> <s id="N10B52"> 人之神，有三司：一明悟，二記含，三愛欲。</s> <s id="N10B55">凡學者，<lb/> 所取外物、外事，皆從明悟而入藏於記含之內。</s> <s id="N10B5A"><lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.071.jpg"/> 異日明悟，愛之而欲用之，直從記含中取之，足<lb/> 矣。</s> <s id="N10B64">此學之本所在內者也。</s> <s id="N10B67">至古人已成之器之<lb/> 法，載在圖籍，則又吾學之借所也，故曰在外。</s> <s id="N10B6C"><lb/> </s> </p> <p id="N10614" type="head"> <s id="N10B73"> 其造詣有三：一由師傳，一由式樣，一由看多、想多、<lb/> 做多。</s> <s id="N10B78"/> </p> <p id="N10619" type="main"> <s id="N10B7D"> 凡學，皆須由此三者而成。</s> <s id="N10B80">而此力藝之學，賴此<lb/> 三者更亟。</s> <s id="N10B85">不得師傳，不會做；不有式樣，亦不能<lb/> 憑空自做。</s> <s id="N10B8A">兩者皆有矣，而眼看不熟，心想不細，<lb/> 手做不勤，終亦不能精此學。</s> <s id="N10B8F">蓋大匠能與人規<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.072.jpg"/> 矩，不能使人巧，巧必從習熟而後得也。</s> <s id="N10B98">故曰習<lb/> 慣如自然。</s> <s id="N10B9D">三者並重，而第三尤為切近，何也？師<lb/> 傳易明，但師不克常在則難。</s> <s id="N10BA2">式樣最便，然亦有<lb/> 有式樣而不能便惺然者。</s> <s id="N10BA7">故自已看多、想多、做<lb/> 多，尤切近也。</s> <s id="N10BAC"><lb/> </s> </p> <p id="N1062F" type="head"> <s id="N10BB3"> 其作用有四：一為物理，二為權度，三為運動，四為<lb/> 致物。</s> <s id="N10BB8"/> </p> <p id="N10634" type="main"> <s id="N10BBD"> 理，如木之有根本也。</s> <s id="N10BC0">木有根本，則千枝萬實，皆<lb/> 從此生。</s> <s id="N10BC5">故人能窮物之理，則自能明物之性；一<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.073.jpg"/> 理通，而眾理可通；一法得，而萬法悉得矣。</s> <s id="N10BCE">窮理<lb/> 原為學者之急務，而於此力藝之學，尤為當務<lb/> 之首。</s> <s id="N10BD5">理既窮矣，假如兩理，不知誰重誰輕，則必<lb/> 權之度之。</s> <s id="N10BDA">理因相比，而可較然其自分也。</s> <s id="N10BDD">故權<lb/> 度次之。</s> <s id="N10BE2">夫理窮而權度亦既審矣，夫然後遇物<lb/> 之重者，舉人力所不能運、所不能動者，以此力<lb/> 藝學之法之器而運動之，無難也。</s> <s id="N10BE9">故運動又次<lb/> 之。</s> <s id="N10BEE">顧運動何為？總欲致其物耳。</s> <s id="N10BF1">假如人生，有飢、<lb/> 有寒，則思致飲食、致衣服諸物。</s> <s id="N10BF6">避風、避雨，則思<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.074.jpg"/> <lb/> 致城郭致宮室諸物。</s> <s id="N10BFF"> 防物害、防敵攻，則又思致<lb/> 干戈、致火器諸物。</s> <s id="N10C04">凡此諸物，非此力藝之學莫<lb/> 能致之。</s> <s id="N10C09">故以致物終之者，正以明此學大用之<lb/> 終竟耳。</s> <s id="N10C0E">四用似有先後，而實皆相聯。</s> <s id="N10C11">假如欲致<lb/> 物，不得運動法，則不能致。</s> <s id="N10C16">欲運動，不得權度，則<lb/> 運動無法。</s> <s id="N10C1B">而權度不根諸窮理，則將孰權孰度<lb/> 焉？故四者相須，總為此學之大用。</s> <s id="N10C20"><lb/> </s> </p> <p id="N1065E" type="head"> <s id="N10C27"> 其所傳授，因起則有五：一、始祖遞傳；二、窘迫生心；<lb/> 三、觸物起見；四、偶悟而得；五、思極而通。</s> <s id="N10C2C"><pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.075.jpg"/> </s> </p> <p id="N10665" type="main"> <s id="N10C35"> 相授之原，從人之始祖亞當受之造物主，以後<lb/> 遞相傳於子孫，然特傳其耕作器耳。</s> <s id="N10C3A">至後將近<lb/> 四千年有一大人，名亞希默得，新造龍尾車、小<lb/> 螺絲轉等器，又能記萬器之所以然。</s> <s id="N10C41">今時巧人<lb/> 之最能明萬器所以然之理者，一名未多，一名<lb/> 西門。</s> <s id="N10C48">又有繪圖刻傳者，一名耕田，一名剌墨里。</s> <s id="N10C4B"><lb/> 此皆力藝學中傳授之人也。</s> <s id="N10C4F"> 其云窘迫生心者，<lb/> 如因饑寒所迫，則思作飲食、作衣服；因風雨所<lb/> 迫，則思作城郭、作宮室；因物害敵攻所迫，則思<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.076.jpg"/> 作干戈、作火器之類是也。</s> <s id="N10C5C">觸物起見者，如觸於<lb/> 魚之搖尾水中，則因之作柁；觸於魚之以翅左<lb/> 右，則因之作櫓；觸於松鼠之伏板豎尾渡水，則<lb/> 因之作帆之類是也。</s> <s id="N10C65">偶悟而得者，如一國王以<lb/> 純金，命一匠作器。</s> <s id="N10C6A">匠潛以銀雜之，王欲廉其弊，<lb/> 弗得也。</s> <s id="N10C6F">亞希默得因浴而偶悟焉，謂金與銀分<lb/> 兩等，而體段大小不等；金重而小，銀重而大；以<lb/> 器入水，驗其所留之水，誰多誰寡，則金與銀辨<lb/> 矣，遂明其弊，而匠自服罪之類是也。</s> <s id="N10C78">思極而通<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.077.jpg"/> <lb/> 者，人能常思常慮，則心機自然細密，明悟自然<lb/> 開發。</s> <s id="N10C83">所謂思之思之，又重思之，思之不得，鬼神<lb/> 將通之者是也。</s> <s id="N10C88">此數者，雖不由傳授，然有因而<lb/> 起，故統系傳授之下而另列之為因起云。</s> <s id="N10C8D"><lb/> </s> </p> <p id="N10697" type="head"> <s id="N10C94"> 論其料，曰理，曰法，縱千百其無盡。</s> <s id="N10C97"/> </p> <p id="N1069A" type="main"> <s id="N10C9C"> 料者，力藝學中之材料也。</s> <s id="N10C9F">如一重物難起，或用<lb/> 人力，或用馬力，或用關<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/04.jpg"/>，或用輪盤。</s> <s id="N10CA7">一法不足，<lb/> 百法助之。</s> <s id="N10CAC">其機種種不同，其材料不越理法兩<lb/> 端，隨人明悟，相度取用，可千變萬化而不窮也。</s> <s id="N10CB1"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.078.jpg"/> <p id="N106A9" type="head"> <s id="N10CBB"> 核其模，有體，有制，實次第而相承。</s> <s id="N10CBE"/> </p> <p id="N106AC" type="main"> <s id="N10CC3"> 模，即體制。</s> <s id="N10CC6">蓋有材料，而不有體制作模，則必不<lb/> 能成一器。</s> <s id="N10CCB">然體制雖或千百不同，而其實則各<lb/> 各次第相承而不紊。</s> <s id="N10CD0">譬如自鳴鐘，大輪小輪，其<lb/> 中名目甚多，必一一次第相聯，而後可以自鳴<lb/> 也。</s> <s id="N10CD7">一紊其序，則不成其用矣。</s> <s id="N10CDA"><lb/> </s> </p> <p id="N106B8" type="head"> <s id="N10CE1"> 所正資而常不相離者，度數之學。</s> <s id="N10CE4"/> </p> <p id="N106BB" type="main"> <s id="N10CE9"> 造物主生物，有數，有度，有重，物物皆然。</s> <s id="N10CEC">數即筭<lb/> 學，度乃測量學，重則此力藝之重學也。</s> <s id="N10CF1">重有重<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.079.jpg"/> 之性理，以此重較彼重之多寡，則資筭學。</s> <s id="N10CFA">以此<lb/> 重之形體較彼重之形體、大小，則資測量學。</s> <s id="N10CFF">故<lb/> 數學、度學，正重學之所必須。</s> <s id="N10D04">蓋三學均從性理<lb/> 而生，如兄弟內親，不可相離者也。</s> <s id="N10D09"><lb/> </s> </p> <p id="N106CB" type="head"> <s id="N10D10"> 所借資而間可相輔者，視學及律呂之學。</s> <s id="N10D13"/> </p> <p id="N106CE" type="main"> <s id="N10D18"> 夫重學，本用在手足；而視學，則目司之；律呂學，<lb/> 則耳司之；似若不甚關切者。</s> <s id="N10D1D">然離視學，則方、圓、<lb/> 平、直不可作；離律呂學，則輕、重、疾、徐、甘、苦、高、下<lb/> 之節不易協；況夫生風、生吹、自鳴等器，皆借之<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.080.jpg"/> 律呂。</s> <s id="N10D2A">故兩學於重學，雖非內親乎，而實益友，可<lb/> 相輔而不可少也。</s> <s id="N10D2F"><lb/> </s> </p> <p id="N106DE" type="head"> <s id="N10D36"> 此其取精也既厚，則其奏效也必宏。</s> <s id="N10D39">故能力甚大，<lb/> 其所裨益於人世者良多也，命曰重學。</s> <s id="N10D3E">學者其可<lb/> 忽諸。</s> <s id="N10D43"/> </p> <p id="N106E5" type="main"> <s id="N10D48"> 夫此重學，既從度數諸學而來，其學可謂博而<lb/> 約矣。</s> <s id="N10D4D">原非一蹴而成功，自可隨奏而輒效。</s> <s id="N10D50">只就<lb/> 起重一節言之。</s> <s id="N10D55">假如有重於此，數百千人方能<lb/> 起，或猶不能起，而精此學者，止用二三人即能<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.081.jpg"/> 起之。</s> <s id="N10D60">此其能力何如也？既省多力，又節大費，且<lb/> 平實而不致險危。</s> <s id="N10D65">其裨益於人世也又何如？故<lb/> 名以重學，雖專為運重而立名，亦以見此學關<lb/> 繫至重。</s> <s id="N10D6C">有志於經世務者，不宜輕視之耳。</s> <s id="N10D6F"><lb/> </s> </p> <p id="N106F9" type="main"> <s id="N10D76"> 或問：表性言一句耳，而解奚為如此之多？曰：此<lb/> 學最奇，亦最深。</s> <s id="N10D7B">不詳解，不能遽曉此中之妙、之<lb/> 法、之性理，故解已詳。</s> <s id="N10D80">而余復為詳注之者，總期<lb/> 人人之易曉也。</s> <s id="N10D85"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.082.jpg"/> <lb/> <p id="N10705" type="head"> <s id="N10D8E"> 力藝內性圖</s> </p> <table id="N10708" xlink:href="http://archimedes/docuserver/images/arch2/schreck/char/TG1.jpg"> <lb/> </table> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.083.jpg"/> <lb/> <!-- added page break; page break missing after table --> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.084.jpg"/> <lb/> <!-- added page break; blank page --> <lb/> <p id="N10716" type="head"> <s id="N10DA5"> 力藝</s> </p> <p id="N10719" type="head"> <s id="N10DAB"> 表德言</s> </p> <p id="N1071C" type="main"> <s id="N10DB1"> 前所表者，重學之內性耳，玆復表其外德。</s> <s id="N10DB4"><lb/> </s> </p> <p id="N10720" type="head"> <s id="N10DBB"> 是重學也，最確當而無差</s> </p> <p id="N10723" type="main"> <s id="N10DC1"> 天下之學，或有全美，或有半美。</s> <s id="N10DC4">不差者固多，差<lb/> 之者亦不少也。</s> <s id="N10DC9">惟筭數、測量，毫無差謬。</s> <s id="N10DCC">而此力<lb/> 藝之學根於度數之學，悉從測量、筭數而作，種<lb/> 種皆有理有法。</s> <s id="N10DD3">故最確當而毫無差謬者，惟此<lb/> 學為然。</s> <s id="N10DD8">非如他學，此或以為可，彼或以為否；此<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.085.jpg"/> 或見以為是，彼復駁以為非者比。</s> <s id="N10DE1">蓋人同具明<lb/> 悟，知其所以然，自不得不是之，非強也。</s> <s id="N10DE6">間有差，<lb/> 亦非此學之差，則器之材質或有差；不，則人之<lb/> 所作如法與不如法耳。</s> <s id="N10DED"><lb/> </s> </p> <p id="N10739" type="head"> <s id="N10DF4"> 至易簡而可作</s> </p> <p id="N1073C" type="main"> <s id="N10DFA"> 蓋器之公者，止有一；器之所以然，亦止有一。</s> <s id="N10DFD">且<lb/> 至為明白，不依賴於多體。</s> <s id="N10E02">況其體相聯不多，如<lb/> 通一體，則他體可以相推。</s> <s id="N10E07">但一留心，自可通曉。</s> <s id="N10E0A"><lb/> 不似他學，費盡心力，而猶或不易曉也。</s> <s id="N10E0E">其理易<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.086.jpg"/> 明，其法有<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/05.jpg"/>而易見，其器又悉有成式而可擬。</s> <s id="N10E1A"><lb/> 故此學至易至簡，而人人可作。</s> <s id="N10E1E"><lb/> </s> </p> <p id="N1074F" type="head"> <s id="N10E25"> 然奇古可怪，聞者似多驚詫非常</s> </p> <p id="N10752" type="main"> <s id="N10E2B"> 人多勝多，或人多而勝寡，不怪也。</s> <s id="N10E2E">人寡能勝人<lb/> 多，則可怪。</s> <s id="N10E33">如以大力運大重，奚足怪？今用小小<lb/> 機器，輒能舉大重，使之升高，使之行遠，有不驚<lb/> 詫為非常者鮮矣。</s> <s id="N10E3A">然能通此學，知機器之所以<lb/> 然，則怪亦平常事也。</s> <s id="N10E3F">試觀千鈞之弩，惟用一寸<lb/> 之機；萬斛之舟，祗憑一尋之柁，豈不可怪？而世<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.087.jpg"/> 因常常用之，則亦視為日用家常物耳。</s> <s id="N10E4A"><lb/> </s> </p> <p id="N10764" type="head"> <s id="N10E51"> 而精妙難言，見之自當喜慰無量</s> </p> <p id="N10767" type="main"> <s id="N10E57"> 饑得餐，渴得漿，則自生喜慰。</s> <s id="N10E5A">而此精妙之器，乃<lb/> 吾人明悟之美味也。</s> <s id="N10E5F">同具明悟者，寧能不喜？況<lb/> 有大重於此，用大力多力不能起者，一旦用小<lb/> 力而大重自起，見之有不喜慰者乎？故器之精<lb/> 妙，筆舌難盡形容。</s> <s id="N10E68">但人一見器之精妙，未有不<lb/> 歡欣慰悅者也。</s> <s id="N10E6D">昔亞希默得，欲辯金與銀雜之<lb/> 故，不得。</s> <s id="N10E72">偶因沐浴而悟得其故，則歡慰之極，至<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.088.jpg"/> <lb/> 於忘其衣著赤身報王是一證也。</s> <s id="N10E7D"><lb/> </s> </p> <p id="N1077C" type="head"> <s id="N10E84"> 堪為工作之督府</s> </p> <p id="N1077F" type="main"> <s id="N10E8A"> 凡工匠皆有二等，一在上，一在下。</s> <s id="N10E8D">下者奉上之<lb/> 命，躬作諸務，有同僕役。</s> <s id="N10E92">上者指示方略，而不親<lb/> 操斧鑿者也。</s> <s id="N10E97">自有此學，總百工之在上者亦皆<lb/> 在下，而此學獨在其上。</s> <s id="N10E9C">蓋百工之在上者，非此<lb/> 宗工，無所取法，無所稟承。</s> <s id="N10EA1">其尊貴有五：一能授<lb/> 諸器於百工，二能顯諸器之用，三能明示諸器<lb/> 之所以然，四能於從來無器者自創新器，五能<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.089.jpg"/> 以成法輔助工作之所不及。</s> <s id="N10EAE">故曰督府云。</s> <s id="N10EB1"><lb/> </s> </p> <p id="N10793" type="head"> <s id="N10EB8"> 可開利益之美源</s> </p> <p id="N10796" type="main"> <s id="N10EBE"> 民生日用，飲食、衣服、宮室，種種利益，為人世急<lb/> 需之物，無一不為諸器所致。</s> <s id="N10EC3">如耕田求食，必用<lb/> 代耕等器；如水乾田，乾水田，必用升、龍尾、轆<lb/> 轤等器；如榨酒，榨油，必用螺絲轉等器；如織裁<lb/> 衣服，必用機車、剪刀等器；如欲從遠方運取衣<lb/> 食諸貨物，必用舟車等器；如欲作宮室，所需金、<lb/> 石、土、木諸物，必用起重、引重等器。</s> <s id="N10ED0">人世急需之<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.090.jpg"/> 物，何者不從此力藝之學而得？故即稱為眾美<lb/> 之源可也。</s> <s id="N10EDB">不寧惟是，即救大災，捍大患。</s> <s id="N10EDE">如防水<lb/> 害，則運大石以築堤；防火災，則用吹筒以灑水；<lb/> 遇猛獸，則用弓、弩、刀、鎗；遇大敵，則用拂郎大銃。</s> <s id="N10EE5"><lb/> 就中以寡勝眾之妙，不能盡述。</s> <s id="N10EE9">則夫通此學者，<lb/> 寧非濬開萬用之美源也哉？推而廣之，如鑿礦<lb/> 砂，采取金鐵，資貿易兵甲之書；製風琴，自奏音<lb/> 響，佐清廟明堂之盛；自鳴鐘，自報時刻，濟日晷<lb/> 晴陰之窮。</s> <s id="N10EF4">諸般奇器，不但裕民間日用之常經，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.091.jpg"/> <lb/> 抑可裨國家政治之大務，其利益無窮，學者當<lb/> 自識取之耳。</s> <s id="N10EFF"><lb/> </s> </p> <p id="N107C0" type="head"> <s id="N10F06"> 公用，則萬國攸同</s> </p> <p id="N107C3" type="main"> <s id="N10F0C"> 夫文物之邦，無器不用，固矣。</s> <s id="N10F0F">乃窮荒絕徼，如綠<lb/> 頭國人，在北極，出地七十多度之下，無城郭、州<lb/> 縣，可謂至僻之地，至野之國矣，亦知用皮船取<lb/> 水族，用弓矢取鳥獸。</s> <s id="N10F18">然則器用之公，普大地無<lb/> 不同然，何其廣耶？<lb/> </s> </p> <p id="N107CF" type="head"> <s id="N10F22"> 創垂，則千古不異<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.092.jpg"/> </s> </p> <p id="N107D4" type="main"> <s id="N10F2C"> 造物主當有天地以後。</s> <s id="N10F2F">至洪水時，人民眾多。</s> <s id="N10F32">有<lb/> 一國王，是女主，名塞密剌密，造一大府，名巴必<lb/> 暖。</s> <s id="N10F39">其城周六萬步，高二十丈，廣厚五丈，周造城<lb/> 樓二百五十座，用役一百三十萬人，一年造完。</s> <s id="N10F3E"><lb/> 彼時無器不有，無器不用。</s> <s id="N10F42">傳至於今，新新不已。</s> <s id="N10F45"><lb/> 豈不千古如常也哉。</s> <s id="N10F49"><lb/> </s> </p> <p id="N107E2" type="head"> <s id="N10F50"> 制器之初，本於人祖</s> </p> <p id="N107E5" type="main"> <s id="N10F56"> 造物主，參贊天地，即稱生人之始祖，名亞當者，<lb/> 與其妻名厄襪者，置之地堂良和之處。</s> <s id="N10F5B">其初，人<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.093.jpg"/> 無病疾，亦無老死。</s> <s id="N10F64">五穀、果木等類，皆大地自然<lb/> 生成，不勞人力。</s> <s id="N10F69">其中一切鳥獸聽命於人，無有<lb/> 毒害。</s> <s id="N10F6E">自亞當與厄襪不遵主命，犯誡得罪以後，<lb/> 遂爾五穀難生，鳥獸毒害，有饑有寒，有病有死。</s> <s id="N10F73"><lb/> 男子，則罰其耕田勞苦；女子，則罰其生育艱辛。</s> <s id="N10F77"><lb/> 於是，亞當始作耕田等器，自求衣食。</s> <s id="N10F7B">故器用皆<lb/> 從始祖創制，蓋亦繼天而立極，半從人力，半從<lb/> 天巧而得之者也。</s> <s id="N10F82"><lb/> </s> </p> <p id="N107FD" type="head"> <s id="N10F89"> 立法之妙，合乎天然<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.094.jpg"/> </s> </p> <p id="N10802" type="main"> <s id="N10F93"> 天下之物，皆天然自生自成。</s> <s id="N10F96">而此器之法，乃因<lb/> 物理而生而成。</s> <s id="N10F9B">所謂有物必有則者，此也。</s> <s id="N10F9E">然法<lb/> 雖由於造作，而比於生成之物，則或有相似、有<lb/> 相幫、有相勝、有相笑者，非一端也。</s> <s id="N10FA5">譬如天體晝<lb/> 夜自行運旋，而器之自轉磨、自行車、自鳴鐘等<lb/> 類，輒能一一與天相似。</s> <s id="N10FAC">人之耳目手足，自視、自<lb/> 聽、自行、自持，而器之製成人像者，輒又手能自<lb/> 持自起，足能自行自止，目能自閉自張，一一與<lb/> 人相似。</s> <s id="N10FB5">不謂巧擬化工矣乎？間有物力、人力不<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.095.jpg"/> 能及者，或以螺絲、龍尾、轆轤、輪盤，或用風、用水、<lb/> 用空，皆可使之助其不及，是為相幫。</s> <s id="N10FC0">所云參贊<lb/> 輔相，殆亦此義歟！至於以小力起大重，運大重，<lb/> 轉大重，雖至重之物，悉足勝之無難。</s> <s id="N10FC7">是天地間<lb/> 無有勝過此器者矣。</s> <s id="N10FCC">且重之性原在下，而此器<lb/> 不特勝之，更能使重者自上而不覺。</s> <s id="N10FD1">如龍尾取<lb/> 水，水止知其已下也，而不知其已上也，豈不可<lb/> 笑也哉？有此數端，故云立法之妙，合乎天然。</s> <s id="N10FD8">詎<lb/> 曰小道之可觀，實為大學之急務。</s> <s id="N10FDD">然此特撮其<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.096.jpg"/> <lb/> 梗概，下文方細為敷敶。</s> <s id="N10FE6"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.097.jpg"/> <p id="N10830" type="head"> <s id="N10FF0"> 力藝外德圖</s> </p> <table id="N10833" xlink:href="http://archimedes/docuserver/images/arch2/schreck/char/TG2.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.098.jpg"/> <lb/> <!-- added page break ; 2 missing page breaks after table --> <lb/> <p id="N1083B" type="head"> <s id="N11000"> 力藝</s> </p> <p id="N1083E" type="head"> <s id="N11006"> 四解</s> </p> <p id="N10841" type="main"> <s id="N1100C"> 前內性外德，特總括此學之大略耳。</s> <s id="N1100F">其詳解更<lb/> 有四端，列為四卷如左。</s> <s id="N11014"><lb/> </s> </p> <p id="N10847" type="head"> <s id="N1101B">第一卷 重解</s> </p> <p id="N1084A" type="main"> <s id="N11021"> 此學總為運重而設。</s> <s id="N11024">儻無重，何必運？且將何運？<lb/> 故重之解，列為一卷。</s> <s id="N11029"><lb/> </s> </p> <p id="N10850" type="head"> <s id="N11030">第二卷 器解</s> </p> <p id="N10853" type="main"> <s id="N11036"> 重不得起，須用器而起，器不一而足也。</s> <s id="N11039">器之中<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.099.jpg"/> 又求最巧之器。</s> <s id="N11042">故器之解，列為一卷。</s> <s id="N11045"><lb/> </s> </p> <p id="N1085B" type="head"> <s id="N1104C">第三卷 力解</s> </p> <p id="N1085E" type="main"> <s id="N11052"> 巧器用以起重、引重、轉重，固矣。</s> <s id="N11055">然器必借力而<lb/> 運，或人力馬力，或風力水力，或即借重物之力，<lb/> 故力之解，列為一卷。</s> <s id="N1105C"><lb/> </s> </p> <p id="N10866" type="head"> <s id="N11063">第四卷 動解</s> </p> <p id="N10869" type="main"> <s id="N11069"> 有重於此，或欲升之高，或欲致之遠，或欲令其<lb/> 轉旋往來而不已。</s> <s id="N1106E">此皆運動法也。</s> <s id="N11071">或薦，或揭，或<lb/> 推，或曳，或手轉足躡，種種不同。</s> <s id="N11076">故動之解，列為<lb/> 一卷。</s> <s id="N1107B"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.100.jpg"/> <p id="N10875" type="head"> <s id="N11085"> 遠西奇器圖說重解卷第一</s> </p> <p id="N10878" type="main"> <s id="N1108B"> 款凡六十一<lb/> </s> </p> <p id="N1087C" type="head"> <s id="N11093"> 第一款 最重無過於地。</s> <s id="N11096">地在天之下，必在中<lb/> 心。</s> <s id="N1109B"/> </p> <p id="N10881" type="main"> <s id="N110A0"> 試觀上圖。</s> <s id="N110A3">a、e、i、o 為星天，u為大<lb/> 地，o、i為地平。</s> <s id="N110A8">人常見者，自o至a<lb/> 至i為半天，故知地在天之下中心<lb/> 也。</s> <s id="N110AF">儻使地或在c，則其徑特為少半，<lb/> 而星在o i上者，不得見矣。</s> <s id="N110B4"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.101.jpg"/> <p id="N1088F" type="head"> <s id="N110BE"> 第二款 次重無過於海。</s> <s id="N110C1">海附於地，合為一球。</s> <s id="N110C4"/> </p> <p id="N10892" type="main"> <s id="N110C9"> 試觀上圖。</s> <s id="N110CC">a為日輪，e為地海，i為<lb/> 月，o為日影。</s> <s id="N110D1">日在地下，月在天上，日<lb/> 過地則有影，影遇月則為月食。</s> <s id="N110D6">惟地<lb/> 與海合為圓球，其影亦圓。</s> <s id="N110DB">故月食漸<lb/> 漸如半規也。</s> <s id="N110E0">觀第二圖自見。</s> <s id="N110E3">儻地形<lb/> 是方，則其影亦方，月食當截然如直<lb/> 線之形，不作半規形矣。</s> <s id="N110EA">詳具天文書<lb/> 中。</s> <s id="N110EF"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.102.jpg"/> <p id="N108A6" type="head"> <s id="N110F9"> 第三款 重之廣大，無過地球。</s> <s id="N110FC">其面與其心，相<lb/> 距一萬餘里。</s> <s id="N11101"/> </p> <p id="N108AB" type="main"> <s id="N11106"> 每圓界三百六十度，所以地球圓界<lb/> 亦有三百六十度。</s> <s id="N1110B">每度有二百五十<lb/> 里，所以相乘得九萬里。</s> <s id="N11110">因圓界a i <lb/> o u 有九萬里，所以a至i徑，用二<lb/> 十二與七比例，得二萬八千六百三<lb/> 十三里。</s> <s id="N11119">自a至e，半之，得一萬四千<lb/> 三百十六里餘。</s> <s id="N1111E">故云：地球之面與其<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.103.jpg"/> 心，相距一萬餘里也。</s> <s id="N11127">何以知一度有<lb/> 二百五十里耶？假如杭州，北極出地<lb/> 三十度十三分；上海，北極出地三十<lb/> 一度十三分，是相距為一度矣。</s> <s id="N11130">上海<lb/> 雖在東北，但與蘇州、太湖東西相封，<lb/> 所以南北同度，計曲路三百餘里，正<lb/> 路則止有二百五十里耳。</s> <s id="N11139">第二圖自<lb/>明。</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.104.jpg"/> <lb/> <p id="N108CF" type="head"> <s id="N11145"> 第四款 重何物？每體直下，必欲到地心者是。</s> <s id="N11148"/> </p> <p id="N108D2" type="main"> <s id="N1114D"> 試觀上圖。</s> <s id="N11150">圓為地球，a為地球中心。</s> <s id="N11153"><lb/> e、i、u皆重物，各體各欲直下，至地<lb/> 心方止。</s> <s id="N11159">蓋重性就下，而地心乃其本<lb/> 所故耳。</s> <s id="N1115E">譬如磁石吸鐵，鐵性就石，不<lb/> 論石之在上、在下、在左、在右，而鐵必<lb/> 就之者，其性然也。</s> <s id="N11165">重物有二：一，本性<lb/> 就下；一，體有斤兩。</s> <s id="N1116A"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.105.jpg"/> <p id="N108E4" type="head"> <s id="N11174"> 第五款 物之本重。</s> <s id="N11177"/> </p> <p id="N108E7" type="main"> <s id="N1117C"> 本重者，如金重於銀，銀重於鐵之類<lb/> 是也。</s> <s id="N11181">蓋金與銀體段一樣，而金重銀<lb/> 輕，是金之質原本重於銀也，非以一<lb/> 兩金與十兩銀相較之重。</s> <s id="N11188">故曰本重<lb/> 云。</s> <s id="N1118D"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.106.jpg"/> <p id="N108F5" type="head"> <s id="N11197"> 第六款 重之體，必定自有點、線、面、形。</s> <s id="N1119A"/> </p> <p id="N108F8" type="main"> <s id="N1119F"> 內有容，外有限，曰形。</s> <s id="N111A2">其中點為形心，<lb/> 有直線過心兩邊不出限者為徑線。</s> <s id="N111A7"><lb/> 形有二：一 面形，一體形。</s> <s id="N111AB">假如上圖，點<lb/> 線之外，a平圓，e長形，i三角，o方<lb/> 形等，俱是面形。</s> <s id="N111B2">體形有三度，或長，或<lb/> 闊，或厚。</s> <s id="N111B7">如上u、c等體是也。</s> <s id="N111BA"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.107.jpg"/> <p id="N10908" type="head"> <s id="N111C4"> 第七款 重之心。</s> <s id="N111C7">重繫於心，則不動。</s> <s id="N111CA"/> </p> <p id="N1090B" type="main"> <s id="N111CF"> 假如有重於此，以線繫之，果在其心<lb/> 如a，則不偏不動。</s> <s id="N111D4">儻不在心如e，則<lb/> 必偏且垂下矣。</s> <s id="N111D9"><lb/> </s> </p> <p id="N10913" type="head"> <s id="N111E0"> 第八款 每重各有其心。</s> <s id="N111E3"/> </p> <p id="N10916" type="main"> <s id="N111E8"> 假如有重於此，兩邊重相等，則重心<lb/> 必在其中無疑也。</s> <s id="N111ED">每重但有一重心。</s> <s id="N111F0"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.108.jpg"/> <p id="N1091E" type="head"> <s id="N111FA"> 第九款 有直線過重心不出兩限者，為重之<lb/> 徑。</s> <s id="N111FF"/> </p> <p id="N10923" type="main"> <s id="N11204"> 假如a三角形，重之心在中點。</s> <s id="N11207">直線<lb/> 從e至i過中心，則為重之徑也。</s> <s id="N1120C">諸<lb/> 重皆然。</s> <s id="N11211">如上立方圖，三徑皆從重心<lb/> 直過，故重之徑無窮盡也。</s> <s id="N11216"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.109.jpg"/> <lb/> <p id="N1092F" type="head"> <s id="N1121F"> 第十款 有重線過地心，交於地平，作兩直角<lb/> 者為重之垂徑。</s> <s id="N11224"/> </p> <p id="N10934" type="main"> <s id="N11229"> 假如上圖。</s> <s id="N1122C">圓為地球，中有地心，橫有<lb/> 地平線。</s> <s id="N11231">上有方重，其線過地心，交於<lb/> 地平線，作兩直角。</s> <s id="N11236">故其立線為重之<lb/> 垂徑也。</s> <s id="N1123B"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.110.jpg"/> <lb/> <p id="N10940" type="head"> <s id="N11244"> 第十一款 有重體，不論正斜，皆有徑線。</s> <s id="N11247">從徑線<lb/> 分破，其側面即為重之徑面。</s> <s id="N1124C"/> </p> <p id="N10945" type="main"> <s id="N11251"> 假如上圓圖，徑線a e。</s> <s id="N11254">從徑線開之，<lb/> 即作兩半球。</s> <s id="N11259">半球平面，即重之徑面<lb/> 也。</s> <s id="N1125E">又如上方圖，i o u為外周徑線<lb/> 分之，則兩半方形。</s> <s id="N11263">其分開之內兩平<lb/> 面，即重之徑面也。</s> <s id="N11268">如從c、ch 徑線開<lb/> 之，則兩側面即重之徑面也。</s> <s id="N1126D">因徑面<lb/> 常過重心，所以兩分相等。</s> <s id="N11272"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.111.jpg"/> <lb/> <p id="N10957" type="head"> <s id="N1127B"> 第十二款 有三角形，從角至對線，於中作一直<lb/> 線，直線內有重之心。</s> <s id="N11280"/> </p> <p id="N1095C" type="main"> <s id="N11285"> 假如從a角至e i對線，作一直線，<lb/> 於o分兩平分，必定a o之內有重<lb/> 心也。</s> <s id="N1128C">e至u亦然。</s> <s id="N1128F"><lb/> </s> </p> <p id="N10964" type="head"> <s id="N11296"> 第十三款 有三角形，其重心與形心同所。</s> <s id="N11299"/> </p> <p id="N10967" type="main"> <s id="N1129E"> 假如上三角形，a為形心，亦為重心。</s> <s id="N112A1"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.112.jpg"/> <lb/> <p id="N1096D" type="head"> <s id="N112AA"> 第十四款 求三角形重心。</s> <s id="N112AD"/> </p> <p id="N10970" type="main"> <s id="N112B2"> 法曰：有三角形，各分兩分。</s> <s id="N112B5">起線各至<lb/> 角為一直線，相遇十字交處便是重<lb/> 心。</s> <s id="N112BC">假如上a與e，中分有i，i至o<lb/> 為一直線。</s> <s id="N112C1">次o與e，中分有u，u至<lb/> a為一直線。</s> <s id="N112C6">兩直線相遇十字於心，<lb/> 即得所求。</s> <s id="N112CB"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.113.jpg"/> <lb/> <p id="N10980" type="head"> <s id="N112D4"> 第十五款 有三角形，每直線從過角重心到對<lb/> 線，其分不等，為二倍比例。</s> <s id="N112D9"/> </p> <p id="N10985" type="main"> <s id="N112DE"> 假如上圖，a e從角過心到u i對<lb/> 線為兩分。</s> <s id="N112E3">a c線大於c e線二倍，<lb/> 其i c線亦二倍大於c o線。</s> <s id="N112E8"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.114.jpg"/> <lb/> <p id="N1098F" type="head"> <s id="N112F1"> 第十六款 有法四邊形，其重心分兩平分為徑。</s> <s id="N112F4"/> </p> <p id="N10992" type="main"> <s id="N112F9"> 假如上圖，四邊有法長方形，其重心<lb/> 是a，其徑e i 為一線。</s> <s id="N112FE">ou、c ch各<lb/> 一線，各線每徑長短不同，俱兩平分。</s> <s id="N11303"><lb/> </s> </p> <p id="N1099A" type="head"> <s id="N1130A"> 第十七款 有法多邊形，其重心形心同所。</s> <s id="N1130D"/> </p> <p id="N1099D" type="main"> <s id="N11312"> 假如上六角形，其角等，其邊亦等，是<lb/> 名有法多邊。</s> <s id="N11317">其重心與形心摠是一<lb/> 心。</s> <s id="N1131C"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.115.jpg"/> <lb/> <p id="N109A7" type="head"> <s id="N11325"> 第十八款 平圓與雞子圓形，其重心形心亦同<lb/> 所。</s> <s id="N1132A"/> </p> <p id="N109AC" type="main"> <s id="N1132F"> 圓界與多邊形相似，故其心皆同。</s> <s id="N11332">其<lb/> 雞子形與平圓形亦相似，故其心亦<lb/> 同。</s> <s id="N11339"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.116.jpg"/> <lb/> <p id="N109B6" type="head"> <s id="N11342"> 第十九款 求直線平形之重心。</s> <s id="N11345"/> </p> <p id="N109B9" type="main"> <s id="N1134A"> 假如上無法四邊形，先分作兩三角<lb/> 形。</s> <s id="N1134F">從對角打兩垂線到分線上，a與<lb/> e分既成兩三角形。</s> <s id="N11354">用前十四款求<lb/> 三角形重心法，既得i、o兩心。</s> <s id="N11359">i與<lb/> o作直線。</s> <s id="N1135E">次用比例法，uc大垂線<lb/> 與ch k小垂線比例等於ip與p<lb/> o比例。</s> <s id="N11365">p乃所求之重心也。</s> <s id="N11368"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.117.jpg"/> <lb/> <p id="N109CB" type="head"> <s id="N11371"> 第二十款 每多稜有法柱，其重心在內徑中。</s> <s id="N11374"/> </p> <p id="N109CE" type="main"> <s id="N11379"> 假如上立方六稜柱，其重心在方徑<lb/> 內心。</s> <s id="N1137E">a至i為內徑，就是其軸。</s> <s id="N11381">e之<lb/> 內心，乃其重心也。</s> <s id="N11386"><lb/> </s> </p> <p id="N109D6" type="head"> <s id="N1138D"> 第二十一款 每多稜有法體，其重心、形心俱同所。</s> <s id="N11390"/> </p> <p id="N109D9" type="main"> <s id="N11395"> 假如上八稜有法柱，a e i是其內<lb/> 軸，e即其重心、形心是也。</s> <s id="N1139A"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.118.jpg"/> <lb/> <p id="N109E1" type="head"> <s id="N113A3"> 第二十二款 有體求其重心。</s> <s id="N113A6"/> </p> <p id="N109E4" type="main"> <s id="N113AB"> 假如上無法之面，欲求重心。</s> <s id="N113AE">先於上<lb/> 作平線繫a。</s> <s id="N113B3"> 次於e垂一直線緊靠<lb/> 一邊，又次於i亦作一垂線緊靠一<lb/> 邊。</s> <s id="N113BA">即從a上往下，以墨直點作線。</s> <s id="N113BD">e<lb/> 至o，i至u兩線，是徑之面。</s> <s id="N113C2">復轉繫<lb/> 體，再如e o、i u，作兩線如前，就得<lb/> 第二徑之面。</s> <s id="N113C9">即向上端下端看兩線，<lb/> 十字交處，即得重之徑也。</s> <s id="N113CE">又將繫體<lb/> 橫轉，從c處繫於a上，求徑線至ch，<lb/> 亦向十字交處看之，則得k，是重心也。</s> <s id="N113D5"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.119.jpg"/> <lb/> <p id="N109FC" type="head"> <s id="N113DE"> 第二十三款 每重不在其所，則必下俯地心，作正<lb/> 垂線。</s> <s id="N113E3"/> </p> <p id="N10A01" type="main"> <s id="N113E8"> 天下之物各有本所，物之性亦各喜<lb/> 得本所。</s> <s id="N113ED">每物不在其所，則必與性相<lb/> 反，且別物得以攻之。</s> <s id="N113F2">故各就本所乃<lb/> 各物之所喜向也。</s> <s id="N113F7">假如火本炎上，使<lb/> 之入水，則非本所，便就滅息。</s> <s id="N113FC">重之性<lb/> 下，水土其本所也。</s> <s id="N11401">且物性直捷，重之<lb/> 垂下，不作迂曲。</s> <s id="N11406">況天下之物性最巧，<lb/> 直線之途必短。</s> <s id="N1140B">迂曲之線，其途甚長。</s> <s id="N1140E"><lb/> 物喜短捷之便，故不肯拂性而迂曲也。</s> <s id="N11412"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.120.jpg"/> <lb/> <p id="N10A17" type="head"> <s id="N1141B"> 第二十四款 每體重之更重，必在重之心。</s> <s id="N1141E"/> </p> <p id="N10A1A" type="main"> <s id="N11423"> 假如重物，長短、厚薄、方圓為體不一，<lb/> 而每體必有更重者，為重之心。</s> <s id="N11428">譬人<lb/> 身之內有心，一家之內有長，為一體<lb/> 中之主，故也。</s> <s id="N1142F"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.121.jpg"/> <lb/> <p id="N10A26" type="head"> <s id="N11438"> 第二十五款 重下墜，其心常在垂線。</s> <s id="N1143B"/> </p> <p id="N10A29" type="main"> <s id="N11440"> 如上圖，三角形心墜下，必在直線。</s> <s id="N11443">不<lb/> 然必左傾右倒，不能直下矣。</s> <s id="N11448">所以重<lb/> 物在空，更重者雖在上，亦必先轉向<lb/> 下。</s> <s id="N1144F"><lb/> </s> </p> <p id="N10A33" type="head"> <s id="N11456"> 第二十六款 有重繫空，或高或低，其重常等。</s> <s id="N11459"/> </p> <p id="N10A36" type="main"> <s id="N1145E"> 如上圖。</s> <s id="N11461">或在a、在i、在o，其重之斤<lb/> 兩常等。</s> <s id="N11466"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.122.jpg"/> <lb/> <p id="N10A3E" type="head"> <s id="N1146F"> 第二十七款 每垂線相距似常相等。</s> <s id="N11472"/> </p> <p id="N10A41" type="main"> <s id="N11477"> 每重直線引長必到地心，所以每垂<lb/> 線之末必與地心相合。</s> <s id="N1147C">前第三款之<lb/> 圖已明。</s> <s id="N11481">此垂線非平行線也。</s> <s id="N11484">但如後<lb/> 旁圖，長短四樣三角形，最近則兩直<lb/> 線之尖相合亦最大，最遠則兩直線<lb/> 之尖相合最小。</s> <s id="N1148D">而直線初分，祗覺其<lb/> 平行，不見其末之相合，故以為相距<lb/> 似也。</s> <s id="N11494"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.123.jpg"/> <lb/> <p id="N10A55" type="main"> <s id="N1149D"> 以上止明一重之理，今又以兩重相<lb/> 比言之。</s> <s id="N114A2"><lb/> </s> </p> <p id="N10A5B" type="head"> <s id="N114A9"> 第二十八款 每重徑面分兩平分。</s> <s id="N114AC"/> </p> <p id="N10A5E" type="main"> <s id="N114B1"> 兩平分者，既從重心之徑面分，自然<lb/> 兩重相等，為兩平分也。</s> <s id="N114B6"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.124.jpg"/> <lb/> <p id="N10A66" type="head"> <s id="N114BF"> 第二十九款 有兩體，其重等，其容亦等，為同類之<lb/> 重。</s> <s id="N114C4"/> </p> <p id="N10A6B" type="main"> <s id="N114C9"> 假如上兩圓球，其體俱是鉛，其大等，<lb/> 其重自等。</s> <s id="N114CE"> 所以名為同類之重。</s> <s id="N114D1"><lb/> </s> </p> <p id="N10A71" type="head"> <s id="N114D8"> 第三十款 同類之重，有重容之比例等。</s> <s id="N114DB"/> </p> <p id="N10A74" type="main"> <s id="N114E0"> 假如上大方圖八倍於小方圖，其重<lb/> 為十六斤；則小方圖之容自八倍小<lb/> 於大方圖之容，其重當為二斤也。</s> <s id="N114E7"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.125.jpg"/> <lb/> <p id="N10A7E" type="head"> <s id="N114F0"> 第三十一款 有兩重，其容等，其重不等，為異類之<lb/> 重。</s> <s id="N114F5"/> </p> <p id="N10A83" type="main"> <s id="N114FA"> 假如上有兩體，形相等；但一是金，一<lb/> 是銀，其重自不相等。</s> <s id="N114FF">何也？金之體殆<lb/> 將二倍於銀，所以各為異類之重。</s> <s id="N11504">或<lb/> 問：金何以重於銀將近二倍也？曰：金<lb/> 之體最密而稠。</s> <s id="N1150B">試觀作金箔者，一兩<lb/> 金可作數萬張，銀則不及，故耳。</s> <s id="N11510"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.126.jpg"/> <lb/> <p id="N10A93" type="head"> <s id="N11519"> 第三十二款 重之類有二：曰乾，曰溼。</s> <s id="N1151C"/> </p> <p id="N10A96" type="main"> <s id="N11521"> 乾，如金、石、土、木之類，不流者是。</s> <s id="N11524">溼，如<lb/> 水、油、酒、漿或銀水之類，但能流者是。</s> <s id="N11529"><lb/> </s> </p> <p id="N10A9C" type="head"> <s id="N11530"> 第三十三款 每乾重，繫於直線。</s> <s id="N11533">而想直線有兩德：<lb/> 一無重，一不破。</s> <s id="N11538"/> </p> <p id="N10AA1" type="main"> <s id="N1153D"> 想者，未有直線，而先有無形直線之<lb/> 想也。</s> <s id="N11542">故無重，故不破。</s> <s id="N11545"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.127.jpg"/> <lb/> <p id="N10AA9" type="head"> <s id="N1154E"> 第三十四款 有重插於直線，或在上，或在下，但在<lb/> 垂線中者不動。</s> <s id="N11553">不，則必動而轉下。</s> <s id="N11556"/> </p> <p id="N10AAE" type="main"> <s id="N1155B"> 假如上圖。</s> <s id="N1155E">a為直線不動之一端，重<lb/> 在e，是正在垂線之上而居中者也，<lb/> 不動。</s> <s id="N11565">重在i，是正在垂線之下而居<lb/> 中者也，不動。</s> <s id="N1156A">或o，或u，則必動而轉<lb/> 下，作圓觚線。</s> <s id="N1156F"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.128.jpg"/> <lb/> <p id="N10ABC" type="head"> <s id="N11578"> 第三十五款 水搏不得。</s> <s id="N1157B"/> </p> <p id="N10ABF" type="main"> <s id="N11580"> 假如有銅球於此，水已滿其中矣。</s> <s id="N11583">欲<lb/> 再強加別水，必不得。</s> <s id="N11588">雖銅球分裂，亦<lb/> 必不能再加。</s> <s id="N1158D">何也？水體最密最稠，再<lb/> 搏不去，故也。</s> <s id="N11592"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.129.jpg"/> <lb/> <p id="N10ACB" type="head"> <s id="N1159B"> 第三十六款 水面平。</s> <s id="N1159E"/> </p> <p id="N10ACE" type="main"> <s id="N115A3"> 水隨地流。</s> <s id="N115A6">地為大圓。</s> <s id="N115A9">水附於地，其面<lb/> 亦圓。</s> <s id="N115AE"><lb/> </s> </p> <p id="N10AD4" type="main"> <s id="N115B5"> 前第二款已言之矣，而玆復云水面<lb/> 平者何？蓋大圓不見其圓，祗見其長，<lb/> 故亦祗見其平面耳。</s> <s id="N115BC"><lb/> </s> </p> <p id="N10ADC" type="main"> <s id="N115C3"> 假如地平之上，有低凹處，四周水來，<lb/> 必滿凹處，與地相平而後流焉。</s> <s id="N115C8">故水<lb/> 隨地而圓，亦隨地而平也。</s> <s id="N115CD"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.130.jpg"/> <lb/> <p id="N10AE6" type="head"> <s id="N115D6"> 第三十七款 有水在器，被迫則必旁去。</s> <s id="N115D9"/> </p> <p id="N10AE9" type="main"> <s id="N115DE"> 其所以然，已見三十五款“水搏不得”<lb/> 之下。</s> <s id="N115E3">此又明其一所不容兩體，故他<lb/> 體一入，此體被迫，而必旁溢去也。</s> <s id="N115E8"><lb/> </s> </p> <p id="N10AF1" type="head"> <s id="N115EF"> 第三十八款 天下水皆同類。</s> <s id="N115F2"/> </p> <p id="N10AF4" type="main"> <s id="N115F7"> 江河溪海，水性無不同者。</s> <s id="N115FA">但水之鹹<lb/> 者，則其體微為重耳。</s> <s id="N115FF"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.131.jpg"/> <lb/> <p id="N10AFC" type="head"> <s id="N11608"> 第三十九款 有水之重，求其大。</s> <s id="N1160B"/> </p> <p id="N10AFF" type="main"> <s id="N11610"> 假如壺中有水十三斤，不知其大為幾<lb/> 斗或幾升，或幾合也？<lb/> </s> </p> <p id="N10B05" type="main"> <s id="N1161A"> 法曰：一尺立方，容水六十五斤，今用<lb/> 三率法。</s> <s id="N1161F"><lb/> </s> </p> <p id="N10B0B" type="main"> <s id="N11626">一 六十五斤 一尺壺中容水<lb/> </s> </p> <p id="N10B0F" type="main"> <s id="N1162E">二 十寸 就如一尺之容<lb/> </s> </p> <p id="N10B13" type="main"> <s id="N11636">三 十三斤 壺中有水<lb/> </s> </p> <p id="N10B17" type="main"> <s id="N1163E">四 二寸 原壺之大</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.132.jpg"/> <lb/> <p id="N10B1D" type="head"> <s id="N11648"> 第四十款 有定體，其本重與水重等，則其在水<lb/> 不浮、不沉，上端與水面準。</s> <s id="N1164D"/> </p> <p id="N10B22" type="main"> <s id="N11652"> 如上圖，e為水庫之容，a為定體之<lb/> 重。</s> <s id="N11657">定體與水重既等，則定體上端必<lb/> 平與水面相準也。</s> <s id="N1165C"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.133.jpg"/> <lb/> <p id="N10B2C" type="head"> <s id="N11665"> 第四十一款 有定體，其本重輕于水。</s> <s id="N11668">則其在水，不<lb/> 全沉，一在水面之上，一在水面之下。</s> <s id="N1166D"/> </p> <p id="N10B31" type="main"> <s id="N11672"> 如上圖，e為水庫之容，a為定體之<lb/> 重。</s> <s id="N11677">定體既輕于水，則半沉半浮。</s> <s id="N1167A">蓋因<lb/> 水更重，所以驅定體而少上焉耳。</s> <s id="N1167F"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.134.jpg"/> <lb/> <p id="N10B3B" type="head"> <s id="N11688"> 第四十二款 有定體，其本重重于水，則其在水必<lb/> 沉至底而後止。</s> <s id="N1168D"/> </p> <p id="N10B40" type="main"> <s id="N11692"> 如上圖自明，或有乾板，薄而寬大；或<lb/> 是金或是鉛，但平平徐置水面，則亦<lb/> 不沉。</s> <s id="N11699">何也？薄而寬大，則板上之氣與<lb/> 板體相合，氣與水面相逼，故雖金、鉛<lb/> 本重而不致沉也。</s> <s id="N116A0">但有小隙上水，則<lb/> 必沉矣。</s> <s id="N116A5"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.135.jpg"/> <lb/> <p id="N10B50" type="head"> <s id="N116AE"> 第四十三款 有定體，本輕于水，其全體之重與本<lb/> 體在水之內者所容水同重。</s> <s id="N116B3"/> </p> <p id="N10B55" type="main"> <s id="N116B8"> 假如上水內立方是木，a浮水外，i<lb/> 沉水內。</s> <s id="N116BD">a、i全重只以沉水多半體<lb/> 為則，多半體所占是水重，即是本體<lb/> 重。</s> <s id="N116C4"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.136.jpg"/> <lb/> <p id="N10B61" type="head"> <s id="N116CD"> 第四十四款 有定體在水，即其沉入之大，求其全<lb/> 體之重。</s> <s id="N116D2"/> </p> <p id="N10B66" type="main"> <s id="N116D7"> 假如ai是全體，在水內外。</s> <s id="N116DA">但知i<lb/> 在水內之容為一萬尺。</s> <s id="N116DF">求其全體a、<lb/> i之重。</s> <s id="N116E4">用三率法，一尺容當六十五<lb/> 斤，則知全體該六十五萬斤重也。</s> <s id="N116E9"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.137.jpg"/> <lb/> <p id="N10B72" type="head"> <s id="N116F2"> 第四十五款 兩水，或重或輕。</s> <s id="N116F5">有兩體，同類相等。</s> <s id="N116F8"> 其<lb/> 重水與輕水之比例，即兩體沉多沉<lb/> 少相反之比例。</s> <s id="N116FF"/> </p> <p id="N10B79" type="main"> <s id="N11704"> 假如一是海水，一是河水，海水自重<lb/> 于河水。</s> <s id="N11709">但看上兩體俱同，而a沉入<lb/> 之多，與e沉入之少，則輕重之比例<lb/> 見矣。</s> <s id="N11710">如a入水，視e之入水為二倍，<lb/> 則海水必重于河水二倍也。</s> <s id="N11715"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.138.jpg"/> <lb/> <p id="N10B87" type="head"> <s id="N1171E"> 第四十六款 凝體在水輕於在空，視所占之水多<lb/> 少，即其所減之輕多少。</s> <s id="N11723"/> </p> <p id="N10B8C" type="main"> <s id="N11728"> 假如上空中立方銅體，重十六兩。</s> <s id="N1172B">即<lb/> 以同大有水立方形較之，水可二兩。</s> <s id="N11730"><lb/> 則在水立方銅體，十六減二，輕於在<lb/> 空之體，為十四兩重也。</s> <s id="N11736"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.139.jpg"/> <lb/> <p id="N10B98" type="head"> <s id="N1173F"> 第四十七款 兩體同類、同重，但不同形。</s> <s id="N11742">在水其重<lb/> 等。</s> <s id="N11747"/> </p> <p id="N10B9D" type="main"> <s id="N1174C"> 假如上圓球與立方，其體皆銅，其重<lb/> 皆五兩，則其沉水之重常相等也。</s> <s id="N11751"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.140.jpg"/> <lb/> <p id="N10BA5" type="head"> <s id="N1175A"> 第四十八款 有兩體，其大等，但一是凝體，一是流<lb/> 體。</s> <s id="N1175F">已有凝重，求流重。</s> <s id="N11762"/> </p> <p id="N10BAA" type="main"> <s id="N11767"> 假如有鉛球二十三斤，水球等於鉛<lb/> 球，該重若干？<lb/> 法曰：將鉛球以馬尾線，繫於天平一<lb/> 端，沉之水中。</s> <s id="N11770">於天平一端加權度，至<lb/> 平準而止，則鉛球止得二十一斤。</s> <s id="N11775">以<lb/> 二十三斤在空之重，減在水之重二<lb/> 十一，留二斤，即為水<lb/> 球之重也。</s> <s id="N1177E">其證<lb/> 見前四十六款。</s> <s id="N11783"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.141.jpg"/> <lb/> <p id="N10BC0" type="head"> <s id="N1178C"> 第四十九款 有凝體、流體相等。</s> <s id="N1178F">已有流重，求凝重。</s> <s id="N11792"/> </p> <p id="N10BC3" type="main"> <s id="N11797"> 假如流體是水，為一百斤，求鉛體相<lb/> 等之重。</s> <s id="N1179C"><lb/> </s> </p> <p id="N10BC9" type="main"> <s id="N117A3"> 法曰：將鉛體，其重二十三斤；用水與<lb/> 鉛體同等，其重得二斤。</s> <s id="N117A8">就用比例法：<lb/> 二與二十三比例即為一百與一千<lb/> 一百五十斤比例，則得鉛體之重一<lb/> 千一百五十斤。</s> <s id="N117B1"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.142.jpg"/> <lb/> <p id="N10BD7" type="head"> <s id="N117BA"> 第五十款 有凝、流兩體之重相等。</s> <s id="N117BD">已有凝容，求<lb/> 流容。</s> <s id="N117C2"/> </p> <p id="N10BDC" type="main"> <s id="N117C7"> 假如有鉛球大十寸，水球重與鉛球<lb/> 等，求其大若干？<lb/> </s> </p> <p id="N10BE2" type="main"> <s id="N117D1"> 法曰：將鉛體二十三斤，與水體大等，<lb/> 得水重二斤。</s> <s id="N117D6">就用比例法：二與二十<lb/> 三就是十與一百十五比例，得流容<lb/> 一百十五寸也。</s> <s id="N117DD"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.143.jpg"/> <lb/> <p id="N10BEE" type="head"> <s id="N117E6"> 第五十一款 有凝、流兩體之重相等。</s> <s id="N117E9">已有流容，求<lb/> 凝容。</s> <s id="N117EE"/> </p> <p id="N10BF3" type="main"> <s id="N117F3"> 假如水容為一百十五寸，鉛重與水<lb/> 容同大，求鉛容若干？<lb/> </s> </p> <p id="N10BF9" type="main"> <s id="N117FD"> 法曰：將鉛體二十三斤，得水二斤。</s> <s id="N11800">就<lb/> 用比例法：二十三與二為一百十五<lb/> 寸與十寸比例，得鉛容十寸也。</s> <s id="N11807"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.144.jpg"/> <lb/> <p id="N10C03" type="head"> <s id="N11810"> 第五十二款 有兩凝體相等。</s> <s id="N11813">已有彼重，求此重。</s> <s id="N11816"><lb/> </s> </p> <p id="N10C07" type="main"> <s id="N1181D"> 假如鉛球，其重一千一百五十斤，求<lb/> 錫球同等之重若干？<lb/> </s> </p> <p id="N10C0D" type="main"> <s id="N11827"> 法曰：將鉛、錫兩體同重者相較，又將<lb/> 兩水體，一箇等於鉛，一箇等於錫。</s> <s id="N1182C">一<lb/> 球水重七十四斤，一球水重一百十<lb/> 五斤。</s> <s id="N11833">用比例法：一百十五與七十四<lb/> 為一千一百五十與七百四十斤比<lb/> 例，就得錫體之重七百四十斤也。</s> <s id="N1183A"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.145.jpg"/> <lb/> <p id="N10C1D" type="head"> <s id="N11843"> 第五十三款 兩凝體重相等。</s> <s id="N11846">已有彼容，求此容。</s> <s id="N11849"/> </p> <p id="N10C20" type="main"> <s id="N1184E"> 假如鉛體容為七百四十寸，錫體等<lb/> 重，求容若干？<lb/> 法曰：將鉛體重一百十五斤以錫體<lb/> 相等重，得七十四斤。</s> <s id="N11857">用比例法：七十<lb/> 四與一百十五比例為七百四十與<lb/> 一千一百五十比例，則得錫容一千<lb/> 一百五十寸也。</s> <s id="N11860"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.146.jpg"/> <lb/> <p id="N10C32" type="head"> <s id="N11869"> 第五十四款 兩流體相等。</s> <s id="N1186C">已有彼重，求此重。</s> <s id="N1186F"/> </p> <p id="N10C35" type="main"> <s id="N11874"> 假如油體重五百五十斤，水體與油體<lb/> 相等，求重若干？<lb/> </s> </p> <p id="N10C3B" type="main"> <s id="N1187E"> 法曰：取鉛體與水體等大者，得水之<lb/> 重，或是十二斤。</s> <s id="N11883">亦取鉛體與油體等<lb/> 大者，得其重為十一斤。</s> <s id="N11888">就用比例法：<lb/> 十一與十二則為五百五十與六百，<lb/> 則得水重為六百斤也。</s> <s id="N1188F"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.147.jpg"/> <lb/> <p id="N10C49" type="head"> <s id="N11898"> 第五十五款 兩流體相等。</s> <s id="N1189B">已有彼容，求此容。</s> <s id="N1189E"/> </p> <p id="N10C4C" type="main"> <s id="N118A3"> 假如油容為六百寸，水之體與油體<lb/> 同大，求其容若干？<lb/> </s> </p> <p id="N10C52" type="main"> <s id="N118AD"> 法曰：將鉛體與水體相等，得水重十<lb/> 二斤。</s> <s id="N118B2">將鉛體與油容等，得其重為十<lb/> 一斤。</s> <s id="N118B7">用比例法：十二與十一為六百<lb/> 與五百五十比例，則得水容為五百<lb/> 五十寸也。</s> <s id="N118BE"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.148.jpg"/> <lb/> <p id="N10C60" type="head"> <s id="N118C7"> 第五十六款 球分本輕，浮於水，其底在上。</s> <s id="N118CA">球之軸<lb/> 必在垂線中。</s> <s id="N118CF"/> </p> <p id="N10C65" type="main"> <s id="N118D4"> 假如有木球如上，其平底在水中，必<lb/> 在上，必不偏倚。</s> <s id="N118D9">其軸ai必在垂線<lb/> 之中，如ai之在eo也。</s> <s id="N118DE">儻強斜之，<lb/> 彼必自反正矣。</s> <s id="N118E3"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.149.jpg"/> <lb/> <p id="N10C71" type="head"> <s id="N118EC"> 第五十七款 水力壓物，其重止是水柱。</s> <s id="N118EF">餘在旁多<lb/> 水，皆非壓重。</s> <s id="N118F4"/> </p> <p id="N10C76" type="main"> <s id="N118F9"> 求水壓物重處，止於所壓物底之平<lb/> 面。</s> <s id="N118FE">求周圍垂線，於水上面，如水中之<lb/> 柱。</s> <s id="N11903">柱乃壓物之重，如上水中柱圖。</s> <s id="N11906">下<lb/> 面口底甚小，從底口垂線，直至上面。</s> <s id="N1190B"><lb/> 中間水柱為壓重。</s> <s id="N1190F">餘水皆無干也。</s> <s id="N11912"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.150.jpg"/> <lb/> <p id="N10C84" type="head"> <s id="N1191B"> 第五十八款 水來平衝於閘。</s> <s id="N1191E">求其衝勢之重若何？</s> </p> <p id="N10C87" type="main"> <s id="N11924"> 如上求水柱法，止以所衝閘面高低，<lb/> 作a e垂線。</s> <s id="N11929"> 垂線平行，至i相等。</s> <s id="N1192C">即<lb/> 從垂線上面之a，斜行至i，則是水<lb/> 衝半柱之重。</s> <s id="N11933">其餘多水，俱無干也。</s> <s id="N11936"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.151.jpg"/> <lb/> <p id="N10C93" type="head"> <s id="N1193F"> 第五十九款 有兩體容之比例，本重之比例。</s> <s id="N11942">已有<lb/> 此重，求彼重。</s> <s id="N11947"/> </p> <p id="N10C98" type="main"> <s id="N1194C"> 假如a、e兩容，其比例a三倍於e。</s> <s id="N1194F"><lb/> 本重a為銀，e為金，其比例為一與<lb/> 二。</s> <s id="N11955">已得a重六斤，求e重若干？<lb/> </s> </p> <p id="N10CA0" type="main"> <s id="N1195D"> 法曰：以銀三分之一，等與e。</s> <s id="N11960">銀三分<lb/> 全為六斤，三分之一為二斤。</s> <s id="N11965">用比例<lb/> 法：一與二比例就是二斤與四斤比<lb/> 例，則得e為四斤重也。</s> <s id="N1196C"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.152.jpg"/> <lb/> <p id="N10CAC" type="head"> <s id="N11975"> 第六十款</s> </p> <p id="N10CAF" type="main"> <s id="N1197B"> 一 三 為比率之大數<lb/> </s> </p> <p id="N10CB3" type="main"> <s id="N11983"> 二 一 為比率之小數<lb/> </s> </p> <p id="N10CB7" type="main"> <s id="N1198B"> 三 二十四 為a之所容之數<lb/> </s> </p> <p id="N10CBB" type="main"> <s id="N11993"> 四 八 為e之所求之容<lb/> </s> </p> <p id="N10CBF" type="main"> <s id="N1199B">有兩體。</s> <s id="N1199E">已有本重之比例，已有其重，<lb/> 已有此容，求彼容。</s> <s id="N119A3"><lb/> </s> </p> <p id="N10CC5" type="main"> <s id="N119AA"> 假如a重六斤，大二十四尺，e重四<lb/> 斤。</s> <s id="N119AF">其本重比例為一與二，今欲求e<lb/> 之大為若干？<lb/> </s> </p> <p id="N10CCD" type="main"> <s id="N119B9"> 法曰：先要a、e所容之比率，而後方<lb/> 可得e之所容。</s> <s id="N119BE">其六斤與四斤比率，<lb/> 乘於a、e本重之比率，此比率乃是<lb/> 一與二也。</s> <s id="N119C5">則用乂字架法乘之，卻不<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.153.jpg"/> 用正乘法也。</s> <s id="N119CE">六與二乘得十二，其四<lb/> 與一乘得四。</s> <s id="N119D3">所以新來之比率十二<lb/> 與四，即是約而為三倍之比率也。</s> <s id="N119D8">所<lb/> 以a三倍於e。</s> <s id="N119DD">今用三率法。</s> <s id="N119E0"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.154.jpg"/> <p id="N10CE3" type="head"> <s id="N119EA"> 第六十一款 有兩體，已有其重，已有其大之比率，<lb/> 求本重之比率。</s> <s id="N119EF"/> </p> <p id="N10CE8" type="main"> <s id="N119F4"> 假如a、e兩重為六與四，其大比率<lb/> 為三倍，要求銀與金之比率。</s> <s id="N119F9"><lb/> </s> </p> <p id="N10CEE" type="main"> <s id="N11A00"> 法曰：以兩所有之數，用乂字架相乘，<lb/> 則兩者之比率為本重之比率。</s> <s id="N11A05">六、一<lb/> 相乘得六，其四、三相乘為十二。</s> <s id="N11A0A">所以<lb/> 有六與十二之比率，約之，則為二分<lb/> 之一也。</s> <s id="N11A11">故銀體之輕與金體相比，則<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.155.jpg"/> 自然差一半矣。</s> <s id="N11A1A"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.156.jpg"/> </chap> <chap id="N10D00" n="2"> <lb/> <p id="N10D03" type="head"> <s id="N11A28">遠西奇器圖說錄最卷第二</s> </p> <p id="N10D06" type="main"> <s id="N11A2E"> 西海耶穌會士鄧玉函 口授<lb/> </s> </p> <p id="N10D0A" type="main"> <s id="N11A36"> 關西景教後學王 徵 譯繪<lb/> </s> </p> <p id="N10D0E" type="main"> <s id="N11A3E"> 金陵後學武位中較 安康張鵬翂 梓<lb/> </s> </p> <p id="N10D12" type="main"> <s id="N11A46"> 款凡九十三<lb/> </s> </p> <p id="N10D16" type="head"> <s id="N11A4E">第一款 凡匠人器皿原多，若人欲解此器皿<lb/> 之運重，其釘與繩等物俱可用也。</s> <s id="N11A53">但<lb/> 其本用則可助運重之便，非可助器<lb/> 用者也。</s> <s id="N11A5A">故不解說釘繩等物之理。</s> <s id="N11A5D"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.157.jpg"/> <lb/> <p id="N10D22" type="head"> <s id="N11A66"> 輪 圖</s> </p> <table id="N10D25" xlink:href="http://archimedes/docuserver/images/arch2/schreck/char/TG3.jpg"> <lb/> </table> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.158.jpg"/> <lb/> <table id="N10D2C" xlink:href="http://archimedes/docuserver/images/arch2/schreck/char/TG3.jpg"> <lb/> </table> <lb/> <!-- added pagebreak; blank page--> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.159.jpg"/> <lb/> <p id="N10D35" type="main"> <s id="N11A80"> 力藝所用諸具，總名強運重之器。</s> <s id="N11A83"><lb/> 此力藝學所用器具，總為運重而設。</s> <s id="N11A87"><lb/> 重本在下，強之使上，故總而名之曰<lb/> 強運重之器也。</s> <s id="N11A8D"><lb/> </s> </p> <p id="N10D3F" type="head"> <s id="N11A94">第二款 器之用有三：一、用小力運大重；二、凡<lb/> 一切人所難用力者用器為便；三、用<lb/> 物力、水力、風力以代人力。</s> <s id="N11A9B"/> </p> <p id="N10D46" type="main"> <s id="N11AA0"> 假如一重物，百人方可運動；而此器<lb/> 止以一人運之，故為小力運大重也。</s> <s id="N11AA5"><lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.160.jpg"/> 又若海船之內底有小隙，日日澀水，<lb/> 人如不取，舟必沉矣。</s> <s id="N11AAF">故必用氣管探<lb/> 下取之，則水從此管中取出，而取桶、<lb/> 杓所不能取者，是器為用實便也。</s> <s id="N11AB6">其<lb/> 用物力、水力、風力以代人力，諸器中<lb/> 有明載者，不贅。</s> <s id="N11ABD"><lb/> </s> </p> <p id="N10D5A" type="head"> <s id="N11AC4">第三款 器之質不一種，大都用木、用銅、用鐵<lb/> 居多。</s> <s id="N11AC9"/> </p> <p id="N10D5F" type="main"> <s id="N11ACE"> 木必用堅者，如榆、槐、桑、檀、馬栗等木，<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.161.jpg"/> 總之，要有筋絲、有橫力，不受變者為<lb/> 佳。</s> <s id="N11AD9">塗木時宜用核桃油或芝麻油、菜<lb/> 油，綿花油更妙，不可用脂油也。</s> <s id="N11ADE">脂油<lb/> 性熱，易燒木，且易磨有聲耳。</s> <s id="N11AE3">鐵要煉<lb/> 到，銅則紅者為佳，黃者性脆故耳。</s> <s id="N11AE8"><lb/> </s> </p> <p id="N10D6F" type="head"> <s id="N11AEF">第四款 器之模不一式：一直線，一輥圓，一藤<lb/> 線。</s> <s id="N11AF4"/> </p> <p id="N10D74" type="main"> <s id="N11AF9"> 器有形象。</s> <s id="N11AFC">直線者，杆、槓、柱、梁之類是<lb/> 也。</s> <s id="N11B01">輥圓者，滑車、輥木、轆轤、車輪之類<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.162.jpg"/>是也。</s> <s id="N11B08">藤線，則螺絲、龍尾等類。</s> <s id="N11B0B"><lb/> </s> </p> <p id="N10D7D" type="head"> <s id="N11B12">第五款 器之能力最大、最多，然自不能用；或<lb/> 止受人之力，以得所求；或必待人用<lb/> 之而後能力可顯。</s> <s id="N11B19"/> </p> <p id="N10D84" type="main"> <s id="N11B1E"> 假如等子類，受人金銀等物，乃可以<lb/> 權輕重。</s> <s id="N11B23">又如斧能劈木，斧自不能劈<lb/> 也，人用斧而後劈木之能力顯矣。</s> <s id="N11B28">每<lb/> 器之公者皆然。</s> <s id="N11B2D"><lb/> </s> </p> <p id="N10D8E" type="head"> <s id="N11B34">第六款 運重之器與所運之重各各相稱，有<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.163.jpg"/> <lb/> 比例。</s> <s id="N11B3D"/> </p> <p id="N10D95" type="main"> <s id="N11B42"> 假如金銀，少者可用等子權度。</s> <s id="N11B45">多至<lb/> 千兩萬兩，則等子不足用矣，故必天<lb/> 平之大者，方可權度之耳。</s> <s id="N11B4C">諸如此類，<lb/> 比例各各有等，難以盡述，能者、明者<lb/> 當自解之。</s> <s id="N11B53"><lb/> </s> </p> <p id="N10DA1" type="head"> <s id="N11B5A">第七款 器之能力最大者，其用時必多。</s> <s id="N11B5D"/> </p> <p id="N10DA4" type="main"> <s id="N11B62"> 假如有石重萬斤，百人運之止可一<lb/> 刻。</s> <s id="N11B67">以一人用器運之，則為時必待數<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.164.jpg"/> <lb/> 刻而後可。</s> <s id="N11B70"><lb/> </s> </p> <p id="N10DAE" type="head"> <s id="N11B77">第八款 器之總類有六：一、天平；二、等子；三、槓<lb/> 杆；四、滑車；五、圓輪；六、藤線。</s> <s id="N11B7C"/> </p> <p id="N10DB3" type="main"> <s id="N11B81"> 天平、等子、槓杆皆直線之類；滑車、輪<lb/> 皆輥圓之類；藤線，有類蛇盤，皆螺絲、<lb/> 龍尾之類。</s> <s id="N11B88">上五者皆為權度之器之<lb/> 象。</s> <s id="N11B8D">如以一端用手、用力，譬如等子小<lb/> 權下加手之圖，則五者又皆運動之<lb/> 器之象也。</s> <s id="N11B94">藤線亦可權度，但用以轉</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.165.jpg"/> <lb/> <p id="N10DC3" type="main"> <s id="N11B9E">運，其用更多，故不設權云。</s> <s id="N11BA1"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.166.jpg"/> <lb/> <p id="N10DC9" type="head"> <s id="N11BAA"> 天平解</s> </p> <p id="N10DCC" type="head"> <s id="N11BB0">第九款 天平之物有三：橫梁一，指針一，垂準<lb/> 一。</s> <s id="N11BB5"/> </p> <p id="N10DD1" type="main"> <s id="N11BBA"> 橫梁分左右兩分。</s> <s id="N11BBD">其中曰心。</s> <s id="N11BC0">心，連于<lb/> 梁而不動者也。</s> <s id="N11BC5">其左右兩盡頭處曰<lb/> 端。</s> <s id="N11BCA">指針者，兩端平，則指針垂線如一。</s> <s id="N11BCD"><lb/> 垂準者，重垂之線也。</s> <s id="N11BD1">平則準。</s> <s id="N11BD4">但兩端<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.167.jpg"/> 略輕略重，則指針必偏左偏右不準<lb/> 矣。</s> <s id="N11BDF"><lb/> </s> </p> <p id="N10DE1" type="head"> <s id="N11BE6">第十款 天平用法有三：其重或即在兩端盡<lb/> 處，或繫于兩端，或盛于盤中，如後三<lb/> 圖。</s> <s id="N11BED"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.168.jpg"/> <lb/> <p id="N10DEB" type="head"> <s id="N11BF6">第十一款 天平針心有三在：或在梁之上邊，或<lb/> 在梁之下邊，或在梁之居中，如後三<lb/> 圖。</s> <s id="N11BFD"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.169.jpg"/> <lb/> <p id="N10DF5" type="head"> <s id="N11C06">第十二款 天平梁，其心在上，其兩端加重各等。</s> <s id="N11C09"><lb/> 一端用手扶起，手離則必自動至平<lb/> 而後止。</s> <s id="N11C0F"/> </p> <p id="N10DFC" type="main"> <s id="N11C14"> 如上斜起者，是扶起一端之圖。</s> <s id="N11C17">兩平<lb/> 者，是自動必至于平之象也。</s> <s id="N11C1C"><lb/> </s> </p> <p id="N10E02" type="head"> <s id="N11C23">第十三款 天平梁，其心在下，其兩端加重各等，<lb/> 梁準地平則不動。</s> <s id="N11C28">倘或一端斜起，則<lb/> 斜下者必翻轉一過而後止。</s> <s id="N11C2D"/> </p> <p id="N10E09" type="main"> <s id="N11C32"> 如上第一圖。</s> <s id="N11C35">有“地平”字者，既與地平<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.170.jpg"/> 準，則常平不動。</s> <s id="N11C3E">倘如第二圖斜起者，<lb/> 則必翻轉一過，針心必反而在上矣。</s> <s id="N11C43"><lb/> 所以必反之者，重之心在下故也。</s> <s id="N11C47"><lb/> </s> </p> <p id="N10E15" type="head"> <s id="N11C4E">第十四款 天平梁，其心在中，其兩端加重各等。</s> <s id="N11C51"><lb/> 與地平準者固不動，即或左斜、右斜，<lb/> 亦不動。</s> <s id="N11C57"/> </p> <p id="N10E1C" type="main"> <s id="N11C5C"> 兩平不動，人知之矣。</s> <s id="N11C5F">斜之而亦不動<lb/> 者，何也？因兩重相等，故不動。</s> <s id="N11C64">倘使一<lb/> 端略加些須，則動矣。</s> <s id="N11C69"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.171.jpg"/> <lb/> <p id="N10E26" type="head"> <s id="N11C72">第十五款 天平正立重</s> </p> <p id="N10E29" type="main"> <s id="N11C78"> 天平右端垂線聯于重板中徑如e，<lb/> 板下支角如i。</s> <s id="N11C7D">板在i尖上不動。</s> <s id="N11C80">板<lb/> 因天平左端加重則垂線自起，至平<lb/> 而準。</s> <s id="N11C87">是名天平正立重。</s> <s id="N11C8A">正立者，因垂<lb/> 線而為名者也。</s> <s id="N11C8F"><lb/> <lb/> </s> </p> <p id="N10E36" type="head"> <s id="N11C98"> 等子解</s> </p> <p id="N10E39" type="head"> <s id="N11C9E">第十六款 等子之物有二：一橫梁，一提繫。</s> <s id="N11CA1"/> </p> <p id="N10E3C" type="main"> <s id="N11CA6"> 橫梁與天平之梁同，但提繫不在中，<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.172.jpg"/> 微不同耳。</s> <s id="N11CAF">提繫者，垂準之換體也。</s> <s id="N11CB2"><lb/> </s> </p> <p id="N10E44" type="head"> <s id="N11CB9">第十七款 有兩重不同，左右繫于等之橫梁。</s> <s id="N11CBC">橫<lb/> 梁與地平準，則兩重名為準等。</s> <s id="N11CC1"/> </p> <p id="N10E49" type="main"> <s id="N11CC6"> 假如a一斤，繫于右；e四斤，繫于左。</s> <s id="N11CC9"><lb/> 橫梁兩平，兩重名為準等。</s> <s id="N11CCD">蓋別于相<lb/> 等之等也。</s> <s id="N11CD2"><lb/> </s> </p> <p id="N10E51" type="head"> <s id="N11CD9">第十八款 有兩重相等、相似，一繫橫梁一端之<lb/> 下，一橫附于橫梁。</s> <s id="N11CDE">附橫梁者，其重心<lb/> 必在橫梁一端盡處，則橫梁平。</s> <s id="N11CE3"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.173.jpg"/> <lb/> <p id="N10E5B" type="main"> <s id="N11CEC"> 假如a重繫于橫梁一端之下，其重<lb/> 與o重相等，其形與o形相似。</s> <s id="N11CF1">而o<lb/> 重則平附橫梁，其重心在i。</s> <s id="N11CF6">i e端<lb/> 與e u端相等，則等梁自兩平也。</s> <s id="N11CFB">所<lb/> 以然者，a重心直在u下，o重心橫<lb/> 在i下，故必相準。</s> <s id="N11D02"><lb/> </s> </p> <p id="N10E69" type="head"> <s id="N11D09">第十九款 此款乃重學之根本也，諸法皆取用<lb/> 于此。</s> <s id="N11D0E"/> </p> <p id="N10E6E" type="main"> <s id="N11D13"> 有兩係重是準等者，其大重與小重<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.174.jpg"/> 之比例就為等梁長節與短節之比<lb/> 例，又為互相比例。</s> <s id="N11D1E"><lb/> </s> </p> <p id="N10E78" type="main"> <s id="N11D25"> 假如e大重八斤，與a小重二斤為<lb/> 準等，其比例為四倍；則橫梁長節從<lb/> 提繫到u為四分，短節從提繫到i<lb/> 但有一分，其比例亦是四倍。</s> <s id="N11D2E">所以兩<lb/> 比例等，其兩比例又是互相比例法。</s> <s id="N11D33"><lb/> </s> </p> <p id="N10E84" type="head"> <s id="N11D3A">第二十款 重在提繫長節一端愈遠愈重，其垂<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.175.jpg"/> <lb/> 下愈速。</s> <s id="N11D43"/> </p> <p id="N10E8B" type="main"> <s id="N11D48"> 假如上a二斤，其重e八斤，其梁愈<lb/> 長二斤，則o為十四斤矣。</s> <s id="N11D4D"><lb/> </s> </p> <p id="N10E91" type="head"> <s id="N11D54">第二十一款 有兩重相等，係于等子，為準等于權。</s> <s id="N11D57"><lb/> 其重比例，視遠比例。</s> <s id="N11D5B"/> </p> <p id="N10E96" type="main"> <s id="N11D60"> 假如等梁為kp，其長為十二分，其<lb/> 紐i在第三分之上。</s> <s id="N11D65">其一重係ch下<lb/> 者為e，重六斤，準等于a重之在k<lb/> 下者。</s> <s id="N11D6C">一重為c，重六斤；在e下者準<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.176.jpg"/> 等于o。</s> <s id="N11D75">a、o之重比例，視等梁i p<lb/> 與i ch之比例。</s> <s id="N11D7A">假如用數i p九分，<lb/> i ch二分，其名四倍半比例。</s> <s id="N11D7F">o十八<lb/> 斤與a四斤，亦是四倍半比例。</s> <s id="N11D84"><lb/> </s> </p> <p id="N10EAA" type="head"> <s id="N11D8B">第二十二款 有兩重不等，係于等子，為準等于權。</s> <s id="N11D8E"><lb/> 其重比例，視遠比例。</s> <s id="N11D92"/> </p> <p id="N10EAF" type="main"> <s id="N11D97"> 假如等梁為十六分，i小重為三斤，<lb/> 係o下，遠于紐心十二分。</s> <s id="N11D9C">a大重十<lb/> 八斤，係e下，距紐心二分。</s> <s id="N11DA1">i小重準<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.177.jpg"/> 等于ch九斤。</s> <s id="N11DAA">a大重準等于k九斤，<lb/> a重十八斤與i重三斤為六倍比<lb/> 例，ou十二分與eu二分亦為六<lb/> 倍比例。</s> <s id="N11DB3"><lb/> </s> </p> <p id="N10EC1" type="head"> <s id="N11DBA">第二十三款 有等梁是重體，另有重係一端下。</s> <s id="N11DBD">其<lb/> 係紐不定，可近可遠，到梁準等于重。</s> <s id="N11DC2"><lb/> 其比例為後一、二、三、四之兩比例。</s> <s id="N11DC6"/> </p> <p id="N10EC8" type="main"> <s id="N11DCB">一 重為六十斤 六十<lb/> </s> </p> <p id="N10ECC" type="main"> <s id="N11DD3">二 等梁全體，假如重四十斤 四十</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.178.jpg"/> <lb/> <p id="N10ED2" type="main"> <s id="N11DDD">三 梁左長端八分，與右短端二分之<lb/> 差為六 六<lb/> </s> </p> <p id="N10ED8" type="main"> <s id="N11DE7">四 右短端二分，二倍為四分 四<lb/> </s> </p> <p id="N10EDC" type="head"> <s id="N11DEF">第二十四款 有等梁是重體，另有重係一端下。</s> <s id="N11DF2">若<lb/> 係紐定一所在，得前一、二、三、四率之<lb/> 兩比例，自然梁之重與係重準等。</s> <s id="N11DF9"/> </p> <p id="N10EE3" type="main"> <s id="N11DFE"> 覽上二十三款圖自明。</s> <s id="N11E01"><lb/> </s> </p> <p id="N10EE7" type="head"> <s id="N11E08">第二十五款 等子便，天平準。</s> <s id="N11E0B"/> </p> <p id="N10EEA" type="main"> <s id="N11E10"> 等子與天平相較，等子人用最便。</s> <s id="N11E13">為<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.179.jpg"/> 止一權，且隨物重輕，皆可用也。</s> <s id="N11E1C">然而，<lb/> 天平則更準。</s> <s id="N11E21">何也？等子紐前一端最<lb/> 短，故間有不準。</s> <s id="N11E26">天平兩端皆長，故更<lb/> 準于等子云。</s> <s id="N11E2B"><lb/> </s> </p> <p id="N10EF8" type="head"> <s id="N11E32">第二十六款 有兩重係等梁兩端，求係紐之定位<lb/> 于準等。</s> <s id="N11E37"/> </p> <p id="N10EFD" type="main"> <s id="N11E3C"> a重六斤，在o一端。</s> <s id="N11E3F">e重二斤，在u<lb/> 一端。</s> <s id="N11E44">等梁全體四分，要知係紐宜在<lb/> 何分。</s> <s id="N11E49">法曰：a、e相加為八，就用比例：</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.180.jpg"/> <lb/> <p id="N10F07" type="main"> <s id="N11E53">一 八 為兩重總數<lb/> </s> </p> <p id="N10F0B" type="main"> <s id="N11E5B">二 二 為e重之數<lb/> </s> </p> <p id="N10F0F" type="main"> <s id="N11E63">三 四 為梁體全數<lb/> </s> </p> <p id="N10F13" type="main"> <s id="N11E6B">四 一 為o i端數 紐宜i分之上<lb/> </s> </p> <p id="N10F17" type="head"> <s id="N11E73">第二十七款 有等子重體，有其重，亦有其分，亦有<lb/> 一重係一端下，求係紐之定位于準<lb/> 等。</s> <s id="N11E7A"/> </p> <p id="N10F1E" type="main"> <s id="N11E7F"> 等子之重為十二斤。</s> <s id="N11E82">全梁六分。</s> <s id="N11E85">係重<lb/> a二十四斤，要知紐宜何分？法曰：平<lb/> 分等梁為兩分，自e至u是等子重<lb/> 心，則想u為十二斤，加于a二十四<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.181.jpg"/> 斤，為三十六斤。</s> <s id="N11E94"> 就用比例：<lb/> </s> </p> <p id="N10F2C" type="main"> <s id="N11E9C">一 三十六斤 為兩重總數<lb/> </s> </p> <p id="N10F30" type="main"> <s id="N11EA4">二 十二斤 為等梁重數<lb/> </s> </p> <p id="N10F34" type="main"> <s id="N11EAC">三 三分 為i u之分數<lb/> </s> </p> <p id="N10F38" type="main"> <s id="N11EB4">四 一分 為i o之分數 紐宜o分之上<lb/> </s> </p> <p id="N10F3C" type="head"> <s id="N11EBC">第二十八款 有等子重體，有其重，有其分；亦有一<lb/> 重，但係一端少內，求係紐之定位于<lb/> 準等。</s> <s id="N11EC3"/> </p> <p id="N10F43" type="main"> <s id="N11EC8"> 等梁重為二十四斤，全分十八。</s> <s id="N11ECB">係重<lb/> 之a為十二斤，係于i分之下。</s> <s id="N11ED0">要知<lb/> 紐宜何分？法曰：得重心徑在u，想u<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.182.jpg"/> 下所繫二十四等重。</s> <s id="N11EDB">u至i為六分，<lb/> 在兩重之中。</s> <s id="N11EE0">兩重相加為三十六，就<lb/> 用比例：<lb/> </s> </p> <p id="N10F53" type="main"> <s id="N11EEA">一 三十六斤 總數<lb/> </s> </p> <p id="N10F57" type="main"> <s id="N11EF2">二 十二斤 係重<lb/> </s> </p> <p id="N10F5B" type="main"> <s id="N11EFA">三 六分 兩重中梁<lb/> </s> </p> <p id="N10F5F" type="main"> <s id="N11F02">四 二分 從i到ci。</s> <s id="N11F05">紐宜c分之上<lb/> </s> </p> <p id="N10F63" type="head"> <s id="N11F0D">第二十九款 有等子重，有其分，但兩係重在內不<lb/> 在兩端，求係紐之定位于準等。</s> <s id="N11F12"/> </p> <p id="N10F68" type="main"> <s id="N11F17"> 等子重十二斤，其全分十八。</s> <s id="N11F1A">a大重<lb/> 為十八斤，e小重為六斤。</s> <s id="N11F1F">要知紐宜<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.183.jpg"/> 何分？法曰：依法二十八款，用比率：<lb/> </s> </p> <p id="N10F72" type="main"> <s id="N11F2D">一 十八 為梁之全分<lb/> </s> </p> <p id="N10F76" type="main"> <s id="N11F35">二 六 為e重數<lb/> </s> </p> <p id="N10F7A" type="main"> <s id="N11F3D">三 六 為i至o之分數<lb/> </s> </p> <p id="N10F7E" type="main"> <s id="N11F45">四 二 為從i至u之分數<lb/> </s> </p> <p id="N10F82" type="main"> <s id="N11F4D">每用比率：<lb/> </s> </p> <p id="N10F86" type="main"> <s id="N11F55">一 三十六 為兩重總數<lb/> </s> </p> <p id="N10F8A" type="main"> <s id="N11F5D">二 十八 為u下之重數<lb/> </s> </p> <p id="N10F8E" type="main"> <s id="N11F65">三 十個 為o至u之分數<lb/> </s> </p> <p id="N10F92" type="main"> <s id="N11F6D">四 五個 為o至c之分數<lb/> </s> </p> <p id="N10F96" type="main"> <s id="N11F75">所以，c為紐<lb/> 線，則兩重為<lb/> 等體之重俱<lb/> 是準等。</s> <s id="N11F7E"><lb/> </s> </p> <p id="N10FA0" type="head"> <s id="N11F85">第三十款 有兩重準等，有定係紐位，已得此重，<lb/> 求彼重。</s> <s id="N11F8A"/> </p> <p id="N10FA5" type="main"> <s id="N11F8F"> a重為八斤，等梁為六分，係紐在二<lb/> 分之i，求e重若干。</s> <s id="N11F94">法曰：用第十九<lb/> 款比例：<lb/> </s> </p> <p id="N10FAD" type="main"> <s id="N11F9E">一 四分 梁數長端<lb/> </s> </p> <p id="N10FB1" type="main"> <s id="N11FA6">二 二分 短端</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.184.jpg"/> <lb/> <p id="N10FB7" type="main"> <s id="N11FB0">三 八斤 a重，當為八斤<lb/> </s> </p> <p id="N10FBB" type="main"> <s id="N11FB8">四 四斤 e重，當為四斤<lb/> </s> </p> <p id="N10FBF" type="head"> <s id="N11FC0">第三十一款 有繫重，有等梁重，以準等求係紐之<lb/> 位。</s> <s id="N11FC5"/> </p> <p id="N10FC4" type="main"> <s id="N11FCA"> 假如等梁之重為四十斤，其分有十。</s> <s id="N11FCD"><lb/> 係重為六十斤。</s> <s id="N11FD1">求係紐之位在何分？<lb/> 法曰：梁重心在o，從o到e為五分，<lb/> 用比例法：<lb/> </s> </p> <p id="N10FCE" type="main"> <s id="N11FDD">一 一百斤 為梁重、係重總數<lb/> </s> </p> <p id="N10FD2" type="main"> <s id="N11FE5">二 六十斤 為係重之數<lb/> </s> </p> <p id="N10FD6" type="main"> <s id="N11FED">三 五分 為o e之分<lb/> </s> </p> <p id="N10FDA" type="main"> <s id="N11FF5">四 三分 為從o到u係紐之位分</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.185.jpg"/> <lb/> <p id="N10FE0" type="head"> <s id="N11FFF">第三十二款 有兩重準等，已有此端梁之長，求彼<lb/> 端梁之長。</s> <s id="N12004"/> </p> <p id="N10FE5" type="main"> <s id="N12009"> 假如a重九斤，e重三斤，係兩端之<lb/> 下，已得i至u二分之長，求u至o<lb/> 長之分數。</s> <s id="N12010">法曰：依第十九款比例：<lb/> </s> </p> <p id="N10FED" type="main"> <s id="N12018">一 三斤 為小重<lb/> </s> </p> <p id="N10FF1" type="main"> <s id="N12020">二 九斤 為大重<lb/> </s> </p> <p id="N10FF5" type="main"> <s id="N12028">三 二分 為梁之小端<lb/> </s> </p> <p id="N10FF9" type="main"> <s id="N12030">四 六分 為梁大端之分數<lb/> </s> </p> <p id="N10FFD" type="head"> <s id="N12038">第三十三款 有等梁重，不用權，權物之重。</s> <s id="N1203B"/> </p> <p id="N11000" type="main"> <s id="N12040"> 梁重有四十斤，分作十分。</s> <s id="N12043">不知係重<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.186.jpg"/> 多少，但那移係紐至準等，得其定位。</s> <s id="N1204C"><lb/> </s> </p> <p id="N11008" type="main"> <s id="N12053"> 假如從重到係位是二分，則大端為<lb/> 八，相減為六，就是差數。</s> <s id="N12058">用三率法：<lb/> </s> </p> <p id="N1100E" type="main"> <s id="N12060">一 四分 為小端二倍<lb/> </s> </p> <p id="N11012" type="main"> <s id="N12068">二 六分 為大小端差數<lb/> </s> </p> <p id="N11016" type="main"> <s id="N12070">三 四十斤 為梁之重<lb/> </s> </p> <p id="N1101A" type="main"> <s id="N12078">四 六十斤 為係重之重<lb/> </s> </p> <p id="N1101E" type="head"> <s id="N12080"> 槓杆解</s> </p> <p id="N11021" type="head"> <s id="N12086">第三十四款 槓杆有三名：一曰頭，一曰柄，一曰定<lb/> 所。</s> <s id="N1208B">外有依賴所，曰支磯。</s> <s id="N1208E"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.187.jpg"/> <lb/> <p id="N11029" type="head"> <s id="N12097">第三十五款 槓杆之類有三，總以薦起其物者也。</s> <s id="N1209A"><lb/> 一、支磯在中，力在柄，重在頭，其名曰<lb/> 揭。</s> <s id="N120A0">二、支磯在頭，重在中，力亦在柄，其<lb/> 名曰挑。</s> <s id="N120A5">三、支磯在頭，力在中，重在柄，<lb/> 其名曰提。</s> <s id="N120AA"/> </p> <p id="N11034" type="head"> <s id="N120AF">第三十六款 揭槓平在支磯之上，頭有重，柄有力。</s> <s id="N120B2"><lb/> 重與力之比例為兩端長短互相之<lb/> 比例。</s> <s id="N120B8"/> </p> <p id="N1103B" type="main"> <s id="N120BD"> 假如揭槓之長為九分，支磯在u，短<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.188.jpg"/> 端三分，長端六分。</s> <s id="N120C6">a之重四十斤，e<lb/> 力必定二十斤。</s> <s id="N120CB">依第十九款比例，a<lb/> 與e二倍，長端與短端亦二倍。</s> <s id="N120D0"><lb/> </s> </p> <p id="N11047" type="head"> <s id="N120D7">第三十七款 挑槓平在支磯之上，頭在磯，重在中，<lb/> 力在柄之比例。</s> <s id="N120DC"/> </p> <p id="N1104C" type="main"> <s id="N120E1"> 從a重到支磯是槓之分與挑槓比<lb/> 例，就是力與重等。</s> <s id="N120E6">假如i至o九分，<lb/> u至o三分，是為三分之一。</s> <s id="N120EB">所以重<lb/> 六十斤，力止二十斤也。</s> <s id="N120F0">蓋係重愈近<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.189.jpg"/> 于支磯，用力愈可少，故挑槓常常省<lb/> 力。</s> <s id="N120FB"><lb/> </s> </p> <p id="N1105C" type="head"> <s id="N12102">第三十八款 有挑槓之分十尺，其本體重四百斤，<lb/> 上另有千斤之重，得槓之重徑、重之<lb/> 中徑，求挑力。</s> <s id="N12109"/> </p> <p id="N11063" type="main"> <s id="N1210E"> 法曰：o u與o i比例要等四百與<lb/> 一千比例。</s> <s id="N12113">假如e o為二尺，就用比<lb/> 例，十尺與二尺比例，為一千四百斤。</s> <s id="N12118"><lb/> 兩重之于二百八十斤比例。</s> <s id="N1211C"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.190.jpg"/> <lb/> <p id="N1106F" type="head"> <s id="N12125">第三十九款 提槓頭平在支磯上，柄有重、力在中<lb/> 之比例。</s> <s id="N1212A"/> </p> <p id="N11074" type="main"> <s id="N1212F"> 全槓ou與從支磯到力ei分數<lb/> 比例等于力、重之比例。</s> <s id="N12134">假如ou為<lb/> 十二分，ei為四分，是三倍比例。</s> <s id="N12139">力<lb/> 六十斤與重二十斤亦是三倍。</s> <s id="N1213E">係重<lb/> 力常要倍于重，故少用。</s> <s id="N12143"><lb/> </s> </p> <p id="N11080" type="head"> <s id="N1214A">第四十款 力用槓子挑重，其比率等與槓兩分。</s> <s id="N1214D"><lb/> 一分從支磯到點垂線，從心來到槓<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.191.jpg"/> <lb/> 所；二分從支磯到力所。</s> <s id="N12157"/> </p> <p id="N11089" type="main"> <s id="N1215C"> 假如ea為槓子，i為支磯。</s> <s id="N1215F">能力在<lb/> e為三百斤，ao重為九百斤，所以<lb/> 比率是三分之一。</s> <s id="N12166">今從o中心打垂<lb/> 線到槓上，到u點，就u到i長與i<lb/> 到e長比率亦是三分之一。</s> <s id="N1216D"> 若ui<lb/> 為兩分，則ie為六分，是三分之一<lb/> 明矣。</s> <s id="N12174"><lb/> </s> </p> <p id="N11099" type="main"> <s id="N1217B"> 第二圖，ao重係槓下，與a、c二處<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.192.jpg"/> 只用u、o垂線，則不用a、c兩點。</s> <s id="N12184">其<lb/> 後萬法皆然。</s> <s id="N12189"><lb/> </s> </p> <p id="N110A3" type="head"> <s id="N12190">第四十一款 能力挑重中心，在地平槓上。</s> <s id="N12193">起重愈<lb/> 高，則用能愈少；若重愈低，則用能力<lb/> 愈多。</s> <s id="N1219A"/> </p> <p id="N110AA" type="main"> <s id="N1219F"> 假如ea槓子在i上，地平的；其垂<lb/> 線為oa，起重在上，則用能力在e。</s> <s id="N121A4"><lb/> 從垂線o點到u，其u到i短于a<lb/> 到i之長，故用四十款之能力少也。</s> <s id="N121AA"><lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.193.jpg"/> 若重在地平之下，則從垂線為o到<lb/> f，[f]i與ai長，所用前款，力在于g，<lb/> 故力多。</s> <s id="N121B6"><lb/> </s> </p> <p id="N110BC" type="head"> <s id="N121BD">第四十二款 揭槓在平，重心在上。</s> <s id="N121C0">重心起愈高，能<lb/> 力愈少。</s> <s id="N121C5"/> </p> <p id="N110C1" type="main"> <s id="N121CA"> 如上圖。</s> <s id="N121CD">重心起高，垂線到a。</s> <s id="N121D0">視下平<lb/> 重，去支磯愈近，故用力愈少也。</s> <s id="N121D5"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.194.jpg"/> <lb/> <p id="N110C9" type="head"> <s id="N121DE">第四十三款 重心在揭槓頭內，槓杆或平或斜，其<lb/> 能力等。</s> <s id="N121E3"/> </p> <p id="N110CE" type="main"> <s id="N121E8"> 如上圖。</s> <s id="N121EB">重心在平、在斜，去支磯皆等，<lb/> 故其能力亦相等也。</s> <s id="N121F0"><lb/> </s> </p> <p id="N110D4" type="head"> <s id="N121F7">第四十四款 有重係槓頭上，支磯在內，槓柄用力。</s> <s id="N121FA"><lb/> 從平向下相距之所與槓頭係重向<lb/> 上相距之所比例等于槓杆兩端之<lb/> 比例。</s> <s id="N12202"/> </p> <p id="N110DD" type="main"> <s id="N12207"> 假如上支磯前相距小端與支磯後<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.195.jpg"/> 相距大端為三分之一，蓋小端與大<lb/> 端亦為三分之一也。</s> <s id="N12212">後挑槓亦然。</s> <s id="N12215"><lb/> </s> </p> <p id="N110E7" type="head"> <s id="N1221C">第四十五款 有重，有槓杆，有力運重，求支磯所。</s> <s id="N1221F"/> </p> <p id="N110EA" type="main"> <s id="N12224"> 假如a重百斤，力十斤，槓杆二十二<lb/> 分，求支磯所在。</s> <s id="N12229">用比例法：<lb/> </s> </p> <p id="N110F0" type="main"> <s id="N12231">一 一百十斤 為能力與重之數<lb/> </s> </p> <p id="N110F4" type="main"> <s id="N12239">二 二十二分 為槓長之分數<lb/> </s> </p> <p id="N110F8" type="main"> <s id="N12241">三 十斤 為能力之分數<lb/> </s> </p> <p id="N110FC" type="main"> <s id="N12249">四 二分 為支磯之所<lb/> </s> </p> <p id="N11100" type="head"> <s id="N12251">第四十六款 有幾重，有支磯，有槓杆之長。</s> <s id="N12254">求能力<lb/> 幾何？</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.196.jpg"/> <lb/> <p id="N11108" type="main"> <s id="N12260"> 假如有三重：a四十八斤在頭，e二<lb/> 十四斤在九分界，i十二斤在三十<lb/> 八分界。</s> <s id="N12267">支磯在二十一分界。</s> <s id="N1226A">槓杆共<lb/> 長六十分。</s> <s id="N1226F">求能力宜用幾何？法曰：a<lb/> e中，槓為九分，求兩重支磯，得小端<lb/> 三分為u。</s> <s id="N12276">自u至c槓有三十五分，<lb/> 用比例，又得五分為ch。</s> <s id="N1227B">第三次，支磯<lb/> 到力o為三十九分；從支磯到ch為<lb/> 十三分。</s> <s id="N12282">比例等于三，重八十四斤與<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.197.jpg"/> 力為二十八斤。</s> <s id="N1228B"><lb/> </s> </p> <p id="N11120" type="head"> <s id="N12292">第四十七款 有幾重，有槓長之數，有能力之數。</s> <s id="N12295">求<lb/> 支磯所。</s> <s id="N1229A"/> </p> <p id="N11125" type="main"> <s id="N1229F"> 法：即用上四十六款之圖。</s> <s id="N122A2">先求準等<lb/> 如ch為八分，自ch至力為五十二分<lb/> 也。</s> <s id="N122A9">用比例法：<lb/> </s> </p> <p id="N1112D" type="main"> <s id="N122B1">一 一百十二斤 為a、e、i、o三重與力之數<lb/> </s> </p> <p id="N11131" type="main"> <s id="N122B9">二 二十八斤 為能力之數<lb/> </s> </p> <p id="N11135" type="main"> <s id="N122C1">三 五十二分 為槓長短之分<lb/> </s> </p> <p id="N11139" type="main"> <s id="N122C9">四 十三分 為從ch重心到支磯所之分<lb/> </s> </p> <p id="N1113D" type="head"> <s id="N122D1">第四十八款 有重物，有重體槓杆，有支磯所。</s> <s id="N122D4">求能<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.198.jpg"/> <lb/> 力幾何？</s> </p> <p id="N11144" type="main"> <s id="N122E0"> 假如ch重為二千斤，其心為i；槓杆<lb/> 兩端為o、c，其體重四百斤，其重心<lb/> 在g。</s> <s id="N122E7">槓杆斜起在支磯e上，ae是<lb/> 其定所。</s> <s id="N122EC">重徑為ik，kg為六分，f<lb/> c為十二分。</s> <s id="N122F1">c用能力宜幾何？法曰：<lb/> 先求重物與槓體之重心。</s> <s id="N122F6">用比例法：<lb/> </s> </p> <p id="N11152" type="main"> <s id="N122FE">一 二千四百斤 為重與槓兩重之數<lb/> </s> </p> <p id="N11156" type="main"> <s id="N12306">二 四百斤 為槓重之數<lb/> </s> </p> <p id="N1115A" type="main"> <s id="N1230E">三 六分 為從k重心到g重心之數<lb/> </s> </p> <p id="N1115E" type="main"> <s id="N12316">四 一分 為從k到u之分數。</s> <s id="N12319">所以ug為五分<lb/> </s> </p> <p id="N11162" type="main"> <s id="N12321">再用比例法：</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.199.jpg"/> <lb/> <p id="N11168" type="main"> <s id="N1232B">一 十二分 為力c到支磯f之分數<lb/> </s> </p> <p id="N1116C" type="main"> <s id="N12333">二 一分 為uf之分數<lb/> </s> </p> <p id="N11170" type="main"> <s id="N1233B">三 二千四百斤 為兩重之全數<lb/> </s> </p> <p id="N11174" type="main"> <s id="N12343">四 二百斤 為能力之數<lb/> </s> </p> <p id="N11178" type="head"> <s id="N1234B"> 滑車解</s> </p> <p id="N1117B" type="head"> <s id="N12351">第四十九款 滑車，體全是輪。</s> <s id="N12354">輪周之側面，兩旁高，<lb/> 中則凹。</s> <s id="N12359">無輻，無齒，無軸，而有軸之眼<lb/> 空。</s> <s id="N1235E"/> </p> <p id="N11182" type="main"> <s id="N12363"> 輪小而厚亦不多。</s> <s id="N12366">兩旁高而中凹，以<lb/> 容繩轉其中者也。</s> <s id="N1236B">自身無軸，止有容<lb/> 軸之空眼。</s> <s id="N12370">另有架安軸，而此輪貫于<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.200.jpg"/> 軸上。</s> <s id="N12379">其滑最利繩轉，故名為滑車。</s> <s id="N1237C">南<lb/> 中呼為羊頭搰轆者，此也。</s> <s id="N12381">如上a為<lb/> 小輪，其中有空眼。</s> <s id="N12386">e為轉繩，從凹槽<lb/> 中上下者也。</s> <s id="N1238B">o乃其架。</s> <s id="N1238E">i則其所貫<lb/> 之軸耳。</s> <s id="N12393"><lb/> </s> </p> <p id="N11196" type="head"> <s id="N1239A">第五十款 滑車亦是天平之類，所以能力與重<lb/> 相等。</s> <s id="N1239F"/> </p> <p id="N1119B" type="main"> <s id="N123A4"> 天平兩重相等則平；一重一輕則必<lb/> 偏而下矣。</s> <s id="N123A9">此滑車之力所以常常與<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.201.jpg"/> 重相等，或云：ei一轉則不平矣。</s> <s id="N123B2">何<lb/> 以云是天平？曰：ei徑線，周圍悉是，<lb/> 則轉轉都是天平。</s> <s id="N123B9">無天平之名，而有<lb/> 天平之實，故謂與天平同類。</s> <s id="N123BE"><lb/> </s> </p> <p id="N111AB" type="head"> <s id="N123C5">第五十一款 滑車大與小，能力皆同。</s> <s id="N123C8"><lb/> 槓杆等器皿愈大，其能力亦愈大。</s> <s id="N123CC">滑<lb/> 車不然，或大或小，其力皆一。</s> <s id="N123D1">為何？兩<lb/> 徑相等故耳。</s> <s id="N123D6"/> </p> <p id="N111B4" type="head"> <s id="N123DB">第五十二款 滑車不甚省人力，但最便人用。</s> <s id="N123DE"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.202.jpg"/> <lb/> <p id="N111BA" type="main"> <s id="N123E7"> 如人從井提水，則臂力易疲。</s> <s id="N123EA">有此滑<lb/> 車在上，而人從下挽之，雖不甚省人<lb/> 力乎，而手挽視手提，則必有分矣。</s> <s id="N123F1"><lb/> </s> </p> <p id="N111C2" type="head"> <s id="N123F8">第五十三款 滑車之繩，一端向上，一端向下。</s> <s id="N123FB">其向<lb/> 下之力與向上之重相距常等，其為<lb/> 時刻亦等。</s> <s id="N12402"/> </p> <p id="N111C9" type="head"> <s id="N12407">第五十四款 滑車之繩，兩端在上，一端係重，一端<lb/> 用力，力半可起重全。</s> <s id="N1240C"/> </p> <p id="N111CE" type="main"> <s id="N12411"> 假如繩定于a，從io至e用力。</s> <s id="N12414">架<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.203.jpg"/> 之下端係重一百斤如c。</s> <s id="N1241D">從e用力<lb/> 起之，五十斤力可起百斤之重。</s> <s id="N12422">為何？<lb/> ai繩子不動，所以oi似挑槓，i<lb/> 似支磯。</s> <s id="N12429">因係重在中u之下，用挑槓<lb/> 比例，iu與io比例常為半徑與<lb/> 全徑之比例。</s> <s id="N12430"> 故半力足起全重也。</s> <s id="N12433"><lb/> </s> </p> <p id="N111E0" type="head"> <s id="N1243A">第五十五款 滑車之繩兩端在上，一端係重，一端<lb/> 用力。</s> <s id="N1243F">用力雖則一半，為時則須二倍。</s> <s id="N12442"><lb/> 且繩之向上相距之所必倍于係重<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.204.jpg"/> 相距之所。</s> <s id="N1244C">覽上圖自明。</s> <s id="N1244F"/> </p> <p id="N111EB" type="head"> <s id="N12454"> 輪盤解</s> </p> <p id="N111EE" type="head"> <s id="N1245A">第五十六款 圓體有三種：一、球；<lb/> 二、尖圓；三、長圓。</s> <s id="N1245F"/> </p> <p id="N111F3" type="main"> <s id="N12464"> 輪之物三：其全體，一；其在中曰軸，一；<lb/> 其在外曰輞，一。</s> <s id="N12469"><lb/> </s> </p> <p id="N111F9" type="head"> <s id="N12470">第五十七款 有輪，其軸兩旁長出，與輪相粘。</s> <s id="N12473">軸有<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.205.jpg"/> <lb/> 係重。</s> <s id="N1247C">人在輞邊平處用力。</s> <s id="N1247F">其重與能<lb/> 力，有輪半徑與軸半徑之比例。</s> <s id="N12484"/> </p> <p id="N11202" type="main"> <s id="N12489"> 如上圖。</s> <s id="N1248C">輪之半徑為ai，軸之半徑<lb/> 為ae，ai要平行。</s> <s id="N12491">i下有力或重<lb/> 如o。</s> <s id="N12496">軸上纏索係重為u。</s> <s id="N12499">因ai四<lb/> 分，ae一分，兩半徑有四倍之比例。</s> <s id="N1249E"><lb/> 所以u重為八百斤，能力止用二百<lb/> 斤即相準也。</s> <s id="N124A4">再加少力，則重起矣。</s> <s id="N124A7"><lb/> </s> </p> <p id="N11210" type="head"> <s id="N124AE">第五十八款 輪即等子類，如滑車即天平之類。</s> <s id="N124B1"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.206.jpg"/> <lb/> <p id="N11216" type="main"> <s id="N124BA"> 看上圖。</s> <s id="N124BD">ic平線為等子之梁，a即<lb/> 等不動所。</s> <s id="N124C2">力與重準等，即第十九款<lb/> 比例，故輪即等子類也。</s> <s id="N124C7"><lb/> </s> </p> <p id="N1121E" type="head"> <s id="N124CE">第五十九款 用輪常常省力。</s> <s id="N124D1"/> </p> <p id="N11221" type="main"> <s id="N124D6"> 因輪半徑常大于軸半徑，故係重之<lb/> 起常常省力。</s> <s id="N124DB">其軸倘更細，則用力愈<lb/> 更省也。</s> <s id="N124E0"><lb/> </s> </p> <p id="N11229" type="head"> <s id="N124E7">第六十款 輪半徑線不平，係重于線，其比例亦<lb/> 不同。</s> <s id="N124EC"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.207.jpg"/> <lb/> <p id="N11231" type="main"> <s id="N124F5"> 如上圖。</s> <s id="N124F8">有ao不平半徑線，其柄在<lb/> o上，下係重為c，其垂線從o到u，<lb/> 在ai平線上。</s> <s id="N124FF">軸之係重三百斤，如<lb/> ch，與力c比例是au與ae比例。</s> <s id="N12504"><lb/> 因au為三，ae為一，所以三百斤<lb/> 用力一百斤也。</s> <s id="N1250A">若不用重而用手，則<lb/> 在o與在i省力常等。</s> <s id="N1250F">蓋因攀而斜<lb/> 下，其垂線常在輪之周也。</s> <s id="N12514">倘必欲用<lb/> 重，則于輪周加一滑車，其重之係索<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.208.jpg"/> 從滑車而轉，則亦力省矣。</s> <s id="N1251F"><lb/> </s> </p> <p id="N11249" type="head"> <s id="N12526">第六十一款 輪周攀索之下與軸係重之上比例<lb/> 為兩半徑之比例。</s> <s id="N1252B"/> </p> <p id="N1124E" type="main"> <s id="N12530"> 假如ae為四丈與io等。</s> <s id="N12533">人在e<lb/> 所，攀a而下，到e即有四丈；而o重<lb/> 之起但能到u，止得一丈。</s> <s id="N1253A">蓋因ac<lb/> 為四分，ci為一分，故比例為四倍<lb/> 也。</s> <s id="N12541"><lb/> </s> </p> <p id="N1125A" type="head"> <s id="N12548">第六十二款 輪之用，省力而費時，比例。</s> <s id="N1254B"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.209.jpg"/> <lb/> <p id="N11260" type="main"> <s id="N12554"> 假如不用輪法，欲起千斤之重，其費<lb/> 時止一刻耳。</s> <s id="N12559"> 若用此輪法，則費時當<lb/> 須四刻。</s> <s id="N1255E">蓋用力則省，而為時則多也。</s> <s id="N12561"><lb/> </s> </p> <p id="N11268" type="head"> <s id="N12568">第六十三款 有重有力，欲用輪起。</s> <s id="N1256B">求輪法。</s> <s id="N1256E"/> </p> <p id="N1126B" type="main"> <s id="N12573"> 有重為六十斤，能力十斤。</s> <s id="N12576">用ae直<lb/> 線為軸與輪兩半徑。</s> <s id="N1257B">用比例法：<lb/> </s> </p> <p id="N11271" type="main"> <s id="N12583">一 六十斤 為重與力之總數<lb/> </s> </p> <p id="N11275" type="main"> <s id="N1258B">二 十斤 為力之數<lb/> </s> </p> <p id="N11279" type="main"> <s id="N12593">三 十四分 為ae直線之分數<lb/> </s> </p> <p id="N1127D" type="main"> <s id="N1259B">四 二分 為ec之分數，即得軸之半徑，所以ca十<lb/> </s> </p> <p id="N11281" type="main"> <s id="N125A3"> 二分為輪之半徑也。</s> <s id="N125A6">依賴前五十八款a<lb/> </s> </p> <p id="N11285" type="main"> <s id="N125AE"> 力準等于e係重，故得此法。</s> <s id="N125B1"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.210.jpg"/> <lb/> <p id="N1128B" type="head"> <s id="N125BA">第六十四款 輪勢多端，論其輞有長有側。</s> <s id="N125BD"/> </p> <p id="N1128E" type="main"> <s id="N125C2">輞輪有四，第一長者如a，<lb/> </s> </p> <p id="N11292" type="main"> <s id="N125CA">第二長者如e，<lb/> </s> </p> <p id="N11296" type="main"> <s id="N125D2">第三側者如i，<lb/> </s> </p> <p id="N1129A" type="main"> <s id="N125DA">第四側者如o。</s> <s id="N125DD"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.211.jpg"/> <lb/> <p id="N112A0" type="head"> <s id="N125E6">第六十五款 論輞之物，或牙齒，或波浪，或觚稜，或<lb/> 光輞，或輞外加板，或輞是燈輪；或周<lb/> 圍另安雙角，或另安水筒，或另安風<lb/> 扇。</s> <s id="N125EF">如後圖。</s> <s id="N125F2"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.212.jpg"/> <lb/> <!-- missing page with image ; adding pb --> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.213.jpg"/> <lb/> <p id="N112B1" type="head"> <s id="N12601">第六十六款 論軸有三，或無軸，止有軸眼，滑車之<lb/> 類是；或有軸甚細，自鳴鐘之類是；或<lb/> 圍圓廣厚，以便轉索，如轆轤之類是。</s> <s id="N12608"/> </p> <p id="N112B8" type="head"> <s id="N1260D">第六十七款 論輪體，有板輪，有有輻之輪。</s> <s id="N12610"/> </p> <p id="N112BB" type="head"> <s id="N12615">第六十八款 論置輪位，有平輪，有斜輪，有立輪。</s> <s id="N12618"/> </p> <p id="N112BE" type="head"> <s id="N1261D">第六十九款 論輪之物，有全，有不全者。</s> <s id="N12620">不全者，或<lb/> 缺一，或缺二。</s> <s id="N12625"/> </p> <p id="N112C3" type="main"> <s id="N1262A"> 但有輞，無軸，無體，如a。</s> <s id="N1262D">若有軸，其輞<lb/> 半輪，如e。</s> <s id="N12632">或為四分之一，如i；或止<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.214.jpg"/> 一觚，如o；但是一線，或軸外為柄如<lb/> u；或軸中作曲柄如c。</s> <s id="N1263D"><lb/> </s> </p> <p id="N112CF" type="main"> <s id="N12644"> 有軸，有體，無輞，其類亦多。</s> <s id="N12647">軸有一徑<lb/> 為天平如f，或幾徑為轆轤如ch，或<lb/> 止半徑一個或幾個如k。</s> <s id="N1264E"><lb/> </s> </p> <p id="N112D7" type="head"> <s id="N12655">第七十款 論輪之體，有相合而為用。</s> <s id="N12658"/> </p> <p id="N112DA" type="main"> <s id="N1265D"> 相合者，有二種。</s> <s id="N12660"> 有全輪兩個在內、在<lb/> 外者，如a。</s> <s id="N12665">有不全兩輪，但同軸，有兩<lb/> 半徑而無輞，如e。</s> <s id="N1266A">此皆相須為用者<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.215.jpg"/> 也。</s> <s id="N12673"><lb/> </s> </p> <p id="N112E6" type="head"> <s id="N1267A">第七十一款 輪子所多用者，有八種：</s> </p> <p id="N112E9" type="main"> <s id="N12680">一、行輪</s> </p> <n>(或人或獸行于輪內，以轉他重)</n> <lb/> <p id="N112EF" type="main"> <s id="N12689">二、攪輪</s> </p> <n>(或人或獸在輞外，或推或曳)</n> <lb/> <p id="N112F5" type="main"> <s id="N12692">三、踏輪</s> </p> <n>(止是人用足踏)</n> <lb/> <p id="N112FB" type="main"> <s id="N1269B">四、攀輪</s> </p> <n>(止是人用手攀)</n> <lb/> <p id="N11301" type="main"> <s id="N126A4">五、水輪</s> </p> <n>(水力激之而轉)</n> <lb/> <p id="N11307" type="main"> <s id="N126AD">六、風輪</s> </p> <n>(風力鼓之而轉)</n> <lb/> <p id="N1130D" type="main"> <s id="N126B6">七、齒輪</s> </p> <n>(齒與他輪齒遞相轉)</n> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.216.jpg"/> <lb/> <p id="N11315" type="main"> <s id="N126C2">八、飛輪</s> </p> <n> <s id="N126C6">(前七輪受力而不加力。</s> <s id="N126C9">飛輪受力而又以己之重，能加其力者也)</s> </n> <lb/> <p id="N1131B" type="head"> <s id="N126D0"> 藤線解</s> </p> <p id="N1131E" type="head"> <s id="N126D6">第七十二款 有線稜從圓體周圍迤<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/06.jpg"/>而上，曰藤<lb/> 線器。</s> <s id="N126DE"> 如藤蔓依樹周圍而上，或瓜蔓<lb/> 與葡萄枝攀纏他木，皆是其類、其象。</s> <s id="N126E3"/> </p> <p id="N11328" type="head"> <s id="N126E8">第七十三款 藤線之物有三：一、圓體；二、圓體<lb/> 之軸；三、藤線。</s> <s id="N126ED"/> </p> <p id="N1132D" type="main"> <s id="N126F2"> 如上o為圓體，其內有ae直線為<lb/> 其軸。</s> <s id="N126F7">外線棱周圍迤<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/06.jpg"/>而上，乃依賴 <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.217.jpg"/> <lb/> 于圓體并其軸者也。</s> <s id="N12703"><lb/> </s> </p> <p id="N1133A" type="head"> <s id="N1270A">第七十四款 藤線器有三類：一、柱螺絲轉；二、球螺<lb/> 絲轉；三、尖螺絲鑽。</s> <s id="N1270F"/> </p> <p id="N1133F" type="main"> <s id="N12714"> 蓋因圓體有三：一、柱圓；二、球圓；三、尖<lb/> 圓。</s> <s id="N12719"> 故藤線依賴而上，遂成三類：柱圓，<lb/> 用以起重；球圓，天文家所必須；至尖<lb/> 圓，乃開堅深入之器，工匠頗多用。</s> <s id="N12720">而<lb/> 此重學所常用者，柱圓而已。</s> <s id="N12725"><lb/> </s> </p> <p id="N1134B" type="head"> <s id="N1272C">第七十五款 前諸器皆有妙用，而此器之用更大、<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.218.jpg"/> <lb/> 更妙。</s> <s id="N12735"/> </p> <p id="N11352" type="main"> <s id="N1273A"> 何以見此器更妙于前諸器也？為其<lb/> 用最廣，其能力又最大耳。</s> <s id="N1273F">假如水閘<lb/> 木重且長，人力不能起者，用螺絲轉<lb/> 則不難起。</s> <s id="N12746">又如長大木，其尖為鐵，入<lb/> 地甚深，人力不能起者，用螺絲轉則<lb/> 能起之。</s> <s id="N1274D">又或欲壓有水有汁之物，他<lb/> 重物不能壓，即壓不能盡其汁與水<lb/> 者，惟此螺絲轉為能壓之盡；且令物<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.219.jpg"/> 之糟粕、渣滓、浮石不能比其乾也。</s> <s id="N1275A">西<lb/> 庠印書亦用螺絲轉，故其書濃淡淺<lb/> 深曲盡款畫之致。</s> <s id="N12761">至于定置諸物，不<lb/> 拘銅、鐵、金、木之器，其釘一入，便自安<lb/> 穩堅定，又不費力，抑且可開卸也。</s> <s id="N12768">況<lb/> 別器有大能力者，須用長、用大。</s> <s id="N1276D">此器<lb/> 即最短、最小，無不可作，器愈小而愈<lb/> 有能力，可怪也。</s> <s id="N12774">試觀天象，如日，一年<lb/> 一周，從冬至到夏至，也只是一個球<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.220.jpg"/> <lb/> 螺絲轉。</s> <s id="N1277F">又如雨風陡遇盤旋擊搏，即<lb/> 大木、大石可挾而上。</s> <s id="N12784">又如波中洄漩<lb/> 之水，能吸人物下墜。</s> <s id="N12789">草木如藤、如瓜、<lb/> 如豆、如葡萄之類，百種不一，皆具此<lb/> 象。</s> <s id="N12790">海中水族，如螺絲之類者，不可勝<lb/> 數。</s> <s id="N12795">故此物最貴重。</s> <s id="N12798">南人以之作貝代<lb/> 金銀也。</s> <s id="N1279D">此蓋天地顯以大用、妙用，托<lb/> 示物象，以詔人用者。</s> <s id="N127A2">不獨運重之學，<lb/> 不可離此。</s> <s id="N127A7">即如人間日用、繩索微物，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.221.jpg"/> <lb/> 及弓弩琴瑟等弦諸用，匪此旋轉交<lb/> 結之法便不得成。</s> <s id="N127B2">故其德，方之前六<lb/> 器中，此器為更妙也。</s> <s id="N127B7">又況其製簡便，<lb/> 長大者之堅固不待言，即甚小者亦<lb/> 甚堅固而絕無危險。</s> <s id="N127BE">所以亞希默得<lb/> 常常多用此器，蓋取其奇耳。</s> <s id="N127C3">能通其<lb/> 所以然之妙，凡天下之器都無難作<lb/> 者矣。</s> <s id="N127CA">細心之人，不難曉解。</s> <s id="N127CD"><lb/> </s> </p> <p id="N1139E" type="head"> <s id="N127D4">第七十六款 有立三角形，其底與地平。</s> <s id="N127D7">每交上各<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.222.jpg"/> 有一球，平繫于鉤。</s> <s id="N127E0">兩球相等，右交與<lb/> 左交之比例為右球與左球之比例。</s> <s id="N127E5"/> </p> <p id="N113A7" type="main"> <s id="N127EA"> 假如右交一半與左交，所以右球與<lb/> 左球其位亦是一半。</s> <s id="N127EF">其三角形兩旁<lb/> 為斜立面，如三稜柱狀。</s> <s id="N127F4"><lb/> </s> </p> <p id="N113AF" type="head"> <s id="N127FB">第七十七款 有立三角形，其底與地平，右交為半<lb/> 于左交。</s> <s id="N12800">每交上亦各有一球，平係于<lb/> 鉤，但右球為半于左球，必定兩球為<lb/> 準等。</s> <s id="N12807"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.223.jpg"/> <lb/> <p id="N113BB" type="main"> <s id="N12810"> 若三角形下是直角形，其右交左交<lb/> 就是股弦之比例，等于右左兩球之<lb/> 比例。</s> <s id="N12817">直立曰股，斜行曰弦，下底曰勾。</s> <s id="N1281A">直立與下底相交，即名勾股。</s> <s id="N1281D"><lb/> </s> </p> <p id="N113C3" type="head"> <s id="N12824">第七十八款 有三角形同前，但不繫于鉤，依賴滑<lb/> 車而過，垂重向下。</s> <s id="N12829">垂重與斜重比例<lb/> 亦是股弦之比例。</s> <s id="N1282E"/> </p> <p id="N113CA" type="main"> <s id="N12833"> 鉤與滑車似不同類，然重從鉤內過<lb/> 與從滑車之外過則同一行也，故其<lb/> 比例亦同。</s> <s id="N1283A"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.224.jpg"/> <lb/> <p id="N113D4" type="head"> <s id="N12843">第七十九款 滑車，一邊係重，一邊有懸空係重在<lb/> 支磯尖上，名斜立重。</s> <s id="N12848"/> </p> <p id="N113D9" type="main"> <s id="N1284D"> 假如o重板有重徑斜行線。</s> <s id="N12850">一點不<lb/> 動者，定于i支磯上。</s> <s id="N12855">一點如p，係于<lb/> 繩，斜行而上過滑車。</s> <s id="N1285A">有垂重為a，所<lb/> 懸重板不上不下。</s> <s id="N1285F">因pu直線是斜<lb/> 行者，所以a重名為斜立重也。</s> <s id="N12864"><lb/> </s> </p> <p id="N113E5" type="head"> <s id="N1286B">第八十款 三角形兩旁兩重皆係于角上，亦如<lb/> 天平、等子之用。</s> <s id="N12870">但其梁不是橫平，而<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.225.jpg"/> <lb/> 是有角。</s> <s id="N12879">如後圖。</s> <s id="N1287C"/> </p> <p id="N113EE" type="head"> <s id="N12881">第八十一款 或從斜面上運重，或用斜面起重，理<lb/> 皆同。</s> <s id="N12886"/> </p> <p id="N113F3" type="main"> <s id="N1288B"> 有斜面，欲于其面運重。</s> <s id="N1288E">或從面下邊<lb/> 薦重使之上，或從面上邊提重使之<lb/> 上，此兩者斜面不動。</s> <s id="N12895">或有重球在地，<lb/> 將斜面尖斜入球下，移進使重自上，<lb/> 此又動斜面以起重法也。</s> <s id="N1289C">其義與前<lb/> 二者同理。</s> <s id="N128A1">假如上第二圖，重球在地<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.226.jpg"/> 如a，前有所阻如e。</s> <s id="N128AA">用斜面尖入球<lb/> 下如i，用力推進，其球自起至o矣。</s> <s id="N128AF"><lb/> </s> </p> <p id="N11407" type="head"> <s id="N128B6">第八十二款 斜面轉行圓柱上，即藤線形。</s> <s id="N128B9"/> </p> <p id="N1140A" type="main"> <s id="N128BE"> 用斜面形起重有不便者，其體必長<lb/> 故也。</s> <s id="N128C3">故即以斜面之長轉纏圓柱之<lb/> 上，作藤線之器，以約其長。</s> <s id="N128C8">如上斜面<lb/> aoi弦。</s> <s id="N128CD">其體甚長，與柱之藤線等。</s> <s id="N128D0"><lb/> 股au與柱之高等，勾ui與柱之<lb/> 圓界等，則知斜面必用長體，而圓線<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.227.jpg"/> 迤<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/06.jpg"/>而上，不必長也。</s> <s id="N128DF"><lb/> </s> </p> <p id="N1141F" type="head"> <s id="N128E6">第八十三款 重與能力比例，就是藤長與高之比<lb/> 例等。</s> <s id="N128EB"/> </p> <p id="N11424" type="main"> <s id="N128F0"> 如上，弦為二倍于股；重依賴七十八<lb/> 款亦是二倍于力。</s> <s id="N128F5">今弦為藤線之長，<lb/> 股即藤線之高，所以與重之比例等。</s> <s id="N128FA"><lb/> </s> </p> <p id="N1142C" type="head"> <s id="N12901">第八十四款 藤線愈密，其能力愈大。</s> <s id="N12904"/> </p> <p id="N1142F" type="main"> <s id="N12909"> 假如上三角形，藤線之長與前三角<lb/> 形等，而股止一半之高，則弦上之重<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.228.jpg"/> 四斤；能力前用二斤者，此只用一斤<lb/> 足矣。</s> <s id="N12916"><lb/> </s> </p> <p id="N1143B" type="head"> <s id="N1291D">第八十五款 兩柱不等，藤線高等，柱大則能力亦<lb/> 大。</s> <s id="N12922"/> </p> <p id="N11440" type="main"> <s id="N12927"> 假如a柱小、e柱大，藤線高相等。</s> <s id="N1292A"><lb/> 而大柱之弦四倍于股，小柱之弦二倍<lb/> 于股。</s> <s id="N12930">所以大柱四斤之重止用一斤<lb/> 之力，視小柱四斤之重須用二斤之<lb/> 力者不同也，與藤線密義同。</s> <s id="N12937"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.229.jpg"/> <lb/> <p id="N1144E" type="head"> <s id="N12940">第八十六款 藤線用力最省，其費時必相反。</s> <s id="N12943"><lb/> 藤線之弦二倍于股，用力一半足矣，<lb/> 但費時必二倍于垂線。</s> <s id="N12949">如上圖，用力<lb/> 在o，一垂重至u，一重斜至a。</s> <s id="N1294E">一時<lb/> 用力，u重到o，a重止可到p。</s> <s id="N12953">再費一<lb/> 時，方得到o。</s> <s id="N12958">然a重用力止可二斤，<lb/> u重則須用力四斤。</s> <s id="N1295D">所以用力一半<lb/> 者，路必二倍，故費時與省力相反也。</s> <s id="N12962"/> </p> <p id="N1145F" type="head"> <s id="N12967">第八十七款 藤線器之料有三：鋼一，木一，銅一，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.230.jpg"/> <lb/> 以不致彎曲。</s> <s id="N12970">用鋼，須要平滑一律，無<lb/> 滯為妙。</s> <s id="N12975">欲其行之利，宜用油。</s> <s id="N12978">油又可<lb/> 令其不縮也。</s> <s id="N1297D">小藤線器牡者用鋼，牝<lb/> 者可用紅銅。</s> <s id="N12982">蓋銅與鋼相合，不致縮<lb/> 澀故耳。</s> <s id="N12987">然大器則必用鋼而後可，木<lb/> 須用堅，已見前解。</s> <s id="N1298C"/> </p> <p id="N11470" type="head"> <s id="N12991">第八十八款 有柱徑，亦有藤線之斜，作藤線器。</s> <s id="N12994"/> </p> <p id="N11473" type="main"> <s id="N12999"> 假如ai是aei柱之徑，亦有角。</s> <s id="N1299C"><lb/> 定藤線斜上之形，要作藤線之器。</s> <s id="N129A0">法<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.231.jpg"/> 曰：先打直線a至c，用規矩取ai<lb/> 柱徑之長。</s> <s id="N129AB">按直線ai等于徑要三<lb/> 個再加七分之一，為uo，就有ae<lb/> i柱之圓界。</s> <s id="N129B2">又用規矩，從ai處作<lb/> 一角形，等于斜角形。</s> <s id="N129B7">o上打垂線，遇<lb/> 角上斜線至p，就有三角形。</s> <s id="N129BC">ao為<lb/> 柱底圓界一周，則ap為藤線之一<lb/> 周矣。</s> <s id="N129C3">移a角之尖到p，接轉而上，<lb/> 可至無窮。</s> <s id="N129C8"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.232.jpg"/> <p id="N1148E" type="head"> <s id="N129D0">第八十九款 有藤線、高線之比例，求其角。</s> <s id="N129D3"/> </p> <p id="N11491" type="main"> <s id="N129D8"> 假如藤線之長八分，其高線一分，要<lb/> 求其角，有數法，有線法。</s> <s id="N129DD">數法用比例：<lb/> </s> </p> <p id="N11497" type="main"> <s id="N129E5">一 八分 藤線之長<lb/> </s> </p> <p id="N1149B" type="main"> <s id="N129ED">二 一分 藤線之高<lb/> </s> </p> <p id="N1149F" type="main"> <s id="N129F5">三 十萬 圓徑半界<lb/> </s> </p> <p id="N114A3" type="main"> <s id="N129FD">四 一萬二千五百 為半弦，其角為七度十一分，如所求。</s> <s id="N12A00"><lb/> </s> </p> <p id="N114A7" type="main"> <s id="N12A07"> 線法：有ae直線分兩分于i。</s> <s id="N12A0A">以i<lb/> 為心，以a為界，作半圓形如aue。</s> <s id="N12A0F"><lb/> 因ae為八分，取一分從a到o，在<lb/> 圓界線上為ao直線。</s> <s id="N12A15">o與e作直<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.233.jpg"/> 線，則aeo角如所求。</s> <s id="N12A1E"><lb/> </s> </p> <p id="N114B5" type="head"> <s id="N12A25">第九十款 有藤線之器，求其角。</s> <s id="N12A28"/> </p> <p id="N114B8" type="main"> <s id="N12A2D"> 有柱，徑三分，其高八分周。</s> <s id="N12A30">要知藤線<lb/> 斜行之角。</s> <s id="N12A35"> 法曰：以柱徑求其圓界為<lb/> ei，上打垂線等于柱高，分八分，e<lb/> o為一分。</s> <s id="N12A3C">從o到打直線，就得ei<lb/> o角，如所求。</s> <s id="N12A41">更有約法：若從ei線<lb/> 上打垂線，其高等于藤線一周之高，<lb/> 為eo。</s> <s id="N12A48">相連于i，亦得所求。</s> <s id="N12A4B"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.234.jpg"/> <lb/> <p id="N114CA" type="head"> <s id="N12A54">第九十一款 有藤線器，求其力。</s> <s id="N12A57"/> </p> <p id="N114CD" type="main"> <s id="N12A5C"> 如用上法得其角矣，用八十四款比<lb/> 例則得所求。</s> <s id="N12A61">如上圖。</s> <s id="N12A64">ao一分，a至<lb/> i為八分，則八分止用一分之能力<lb/> 矣。</s> <s id="N12A6B"><lb/> </s> </p> <p id="N114D7" type="head"> <s id="N12A72">第九十二款 有重，有力，求藤線器運。</s> <s id="N12A75"/> </p> <p id="N114DA" type="main"> <s id="N12A7A"> 假如有重一千斤，人力一百斤，用何<lb/> 等藤線之器可運？法曰：用十分比例，<lb/> 如上ao垂線，十分內取一分為a<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.235.jpg"/> i。</s> <s id="N12A85">用規矩，取十分。</s> <s id="N12A88">按直線上，從i到<lb/> u，則得aiu三角形。</s> <s id="N12A8D">用此三角形<lb/> 作藤線器，則人力百斤可起重千斤<lb/> 也。</s> <s id="N12A94"/> </p> </chap> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.236.jpg"/> <chap id="N114EC" n="3"> <lb/> <p id="N114EF" type="head"> <s id="N12AA0">遠西奇器圖說錄最卷第三</s> </p> <p id="N114F2" type="main"> <s id="N12AA6"> 西海耶穌會士鄧玉函 口授 <lb/> </s> </p> <p id="N114F6" type="main"> <s id="N12AAE"> 關西景教後學王 徵 譯繪<lb/> </s> </p> <p id="N114FA" type="main"> <s id="N12AB6"> 金陵後學武位中 較梓<lb/> </s> </p> <p id="N114FE" type="main"> <s id="N12ABE"> 安康張鵬翂補山 重梓</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.237.jpg"/> <lb/> <p id="N11504" type="head"> <s id="N12AC8">起重第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.238.jpg"/> <lb/> <p id="N1150A" type="head"> <s id="N12AD2">第一圖說</s> </p> <p id="N1150D" type="main"> <s id="N12AD8">起重<lb/> </s> </p> <p id="N11511" type="main"> <s id="N12AE0">說<lb/> </s> </p> <p id="N11515" type="main"> <s id="N12AE8"> 假如有石，重五百斤，欲起之使高。</s> <s id="N12AEB">先用立架<lb/> 一具，如圖中之a。</s> <s id="N12AF0">次於橫梁之e，繫繫秤之索如<lb/> i。</s> <s id="N12AF5">秤頭之o為舉重之索，秤尾之u為人墜之<lb/> 索。</s> <s id="N12AFA">秤杆長十有一尺，秤頭至c為一尺，秤頭過<lb/> c至ch為十尺。</s> <s id="N12AFF">k為人力，p為石重。</s> <s id="N12B02">夫o至c<lb/> 既為一尺，是為一分；o至ch既為十尺，是為十<lb/> 分。</s> <s id="N12B09">以十分而舉一分，故一人之力可起五百斤也。</s> <s id="N12B0C"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.239.jpg"/> <lb/> <p id="N11527" type="head"> <s id="N12B15">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.240.jpg"/> <lb/> <p id="N1152D" type="head"> <s id="N12B1F">第二圖說</s> </p> <p id="N11530" type="main"> <s id="N12B25">說<lb/> </s> </p> <p id="N11534" type="main"> <s id="N12B2D"> 假如途次，猝無立架，止用直木三根或四根，以<lb/> 索緊縛一頭。</s> <s id="N12B32">豎之三根作三足形，四根作四足<lb/> 形。</s> <s id="N12B37">以秤杆中心繫索，繫在上端中央。</s> <s id="N12B3A">以秤杆前<lb/> 端一尺者繫重物， 以後端十尺盡處繫人用力<lb/> 之索，更便也。</s> <s id="N12B41"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.241.jpg"/> <lb/> <p id="N11542" type="head"> <s id="N12B4A">第三圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.242.jpg"/> <lb/> <p id="N11548" type="head"> <s id="N12B54">第三圖說</s> </p> <p id="N1154B" type="main"> <s id="N12B5A">說<lb/> </s> </p> <p id="N1154F" type="main"> <s id="N12B62"> 假如有石若干重，欲起之。</s> <s id="N12B65">先作三足形立架，上<lb/> 收下開。</s> <s id="N12B6A">上端收處，平安短鐵橫梁，梁上繫滑車<lb/> 一具。</s> <s id="N12B6F">下繫滑車一具，緊鉗石上。</s> <s id="N12B72">用索一端，從上<lb/> 滑車轉垂而下，即從下滑車內轉輪而上，復過<lb/> 上滑車而下。</s> <s id="N12B79">或即用人力曳之，可矣。</s> <s id="N12B7C">如石太重，<lb/> 則滑車上下各加一具，或加二具，亦無不可。</s> <s id="N12B81">愈<lb/> 多、愈輕，人力愈可少也。</s> <s id="N12B86">如石仍太重難起，即於<lb/> 兩豎架上，安一轆轤在內。</s> <s id="N12B8B">轆轤兩<lb/> 端，各十字相反安四樁木。</s> <s id="N12B90">用人力轉其滑車內<lb/> 所轉之索更便，且力甚勁也。</s> <s id="N12B95">兩法總具上圖中。</s> <s id="N12B98"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.243.jpg"/> <lb/> <p id="N11567" type="head"> <s id="N12BA1">第四圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.244.jpg"/> <lb/> <p id="N1156D" type="head"> <s id="N12BAB">第四圖說</s> </p> <p id="N11570" type="main"> <s id="N12BB1">說<lb/> </s> </p> <p id="N11574" type="main"> <s id="N12BB9"> 假如有石太重，即用六滑車并十字轆轤法，仍<lb/> 或不起，則以轆轤改作大輪，如上圖。</s> <s id="N12BBE">用人轉輪，<lb/> 重可起也。</s> <s id="N12BC3"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.245.jpg"/> <lb/> <p id="N1157E" type="head"> <s id="N12BCC">第五圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.246.jpg"/> <lb/> <p id="N11584" type="head"> <s id="N12BD6">第五圖說</s> </p> <p id="N11587" type="main"> <s id="N12BDC">說<lb/> </s> </p> <p id="N1158B" type="main"> <s id="N12BE4"> 假如石為鉅重難起，即用六滑車并轆轤，改作<lb/> 大輪矣，或仍不起，則從傍再置一架，平安十字<lb/> 大輪，用四人遞轉架上立安大輪所轉之索，其<lb/> 力愈大，斷無不起之理矣。</s> <s id="N12BED"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.247.jpg"/> <lb/> <p id="N11597" type="head"> <s id="N12BF6">第六圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.248.jpg"/> <lb/> <p id="N1159D" type="head"> <s id="N12C00">第六圖說</s> </p> <p id="N115A0" type="main"> <s id="N12C06">說<lb/> </s> </p> <p id="N115A4" type="main"> <s id="N12C0E"> 假如照前有四足架，上用滑車繫其重，兩傍架<lb/> 上各安轆轤一具。</s> <s id="N12C13">其轉轆轤之柄，卻在架外。</s> <s id="N12C16">繫<lb/> 重兩索俱從滑車上轉垂而下，分纏兩轆轤上，<lb/> 以人力各相轉動，重自起矣。</s> <s id="N12C1D"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.249.jpg"/> <lb/> <p id="N115B0" type="head"> <s id="N12C26">第七圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.250.jpg"/> <lb/> <p id="N115B6" type="head"> <s id="N12C30">第七圖說</s> </p> <p id="N115B9" type="main"> <s id="N12C36">說<lb/> </s> </p> <p id="N115BD" type="main"> <s id="N12C3E"> 假如作屋作墻，起運磚、石、泥、土之物。</s> <s id="N12C41">即不太重，<lb/> 然或桶、或框，一人可運五六框、桶。</s> <s id="N12C46">其法：上用夜<lb/> 乂平架，兩頭各安滑車一具。</s> <s id="N12C4B">每滑車貫長索一<lb/> 根，其兩索各一端定縛長杆一根。</s> <s id="N12C50">將所用框、桶<lb/> 諸物鉤懸杆上。</s> <s id="N12C55"> 下用兩轆轤，各將前垂長索一<lb/> 端繫定，安置架上。</s> <s id="N12C5A">如物力不太重、不太多，則人<lb/> 轉轆轤足矣。</s> <s id="N12C5F">倘物或太多太重，則于兩轆轤中<lb/> 而更安一大輪。</s> <s id="N12C64">大輪另有索，旁繫一轆<lb/> 轤上。</s> <s id="N12C69">其轆轤另是一架。</s> <s id="N12C6C">一人轉此單轆轤，曳動<lb/> 大輪之索，則雙轆轤自轉，諸物俱運上矣。</s> <s id="N12C71"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.251.jpg"/> <lb/> <p id="N115D5" type="head"> <s id="N12C7A">第八圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.252.jpg"/> <lb/> <p id="N115DB" type="head"> <s id="N12C84">第八圖說</s> </p> <p id="N115DE" type="main"> <s id="N12C8A">說<lb/> </s> </p> <p id="N115E2" type="main"> <s id="N12C92"> 用一長架，有橫桄，如梯狀。</s> <s id="N12C95">兩頭各安兩立柱，下<lb/> 端安一滑車樣大榾轆，上端安一轆轤。</s> <s id="N12C9A">但轆轤<lb/> 之製分作四分，如南瓜瓣樣。</s> <s id="N12C9F">其中相架梯長短<lb/> 作戽子，不拘多少，一如水車戽子之製。</s> <s id="N12CA4">戽子中，<lb/> 實以土泥諸物。</s> <s id="N12CA9">一人用力，轉動上端瓜瓣轆轤，<lb/> 則諸戽可以流水而上矣。</s> <s id="N12CAE"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.253.jpg"/> <lb/> <p id="N115F2" type="head"> <s id="N12CB7">第九圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.254.jpg"/> <lb/> <p id="N115F8" type="head"> <s id="N12CC1">第九圖說</s> </p> <p id="N115FB" type="main"> <s id="N12CC7">說<lb/> </s> </p> <p id="N115FF" type="main"> <s id="N12CCF"> 長架同前。</s> <s id="N12CD2">或不用戽子，止用桶相聯而轉，上用<lb/> 螺絲轉法如上圖，亦便。</s> <s id="N12CD7"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.255.jpg"/> <lb/> <p id="N11607" type="head"> <s id="N12CE0">第十圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.256.jpg"/> <lb/> <p id="N1160D" type="head"> <s id="N12CEA">第十圖說</s> </p> <p id="N11610" type="main"> <s id="N12CF0">說<lb/> </s> </p> <p id="N11614" type="main"> <s id="N12CF8"> 先作一行輪。</s> <s id="N12CFB">行輪者，人從輪中行而不止，以動<lb/> 他輪者也。</s> <s id="N12D00">行輪本軸安銅輪，有齒如a，以轉有<lb/> 齒大輪如e。</s> <s id="N12D05">大輪本軸則有或銅或鐵螺絲轉<lb/> 如i。</s> <s id="N12D0A">其i螺絲轉緊靠亦是螺絲轉如o。</s> <s id="N12D0D">但o<lb/> 螺絲轉大于i螺絲轉數倍，為牝。</s> <s id="N12D12">而i乃其牡<lb/> 耳。</s> <s id="N12D17">o螺絲轉兩端，各繫起重之索如u。</s> <s id="N12D1A">其索各<lb/> 上繫于傍架滑車如c。</s> <s id="N12D1F">上端滑車並懸兩旁、兩<lb/> 層，共是四個，如ch。</s> <s id="N12D24">下端滑車並懸兩個如k。</s> <s id="N12D27">有<lb/> 重石如p，繫置滑車，直貫至牝螺絲轉兩端。</s> <s id="N12D2C">則<lb/> 以一人如f行于大輪之內，而石自起矣。</s> <s id="N12D31"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.257.jpg"/> <lb/> <p id="N1162C" type="head"> <s id="N12D3A">第十一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.258.jpg"/> <lb/> <p id="N11632" type="head"> <s id="N12D44">第十一圖說</s> </p> <p id="N11635" type="main"> <s id="N12D4A">說<lb/> </s> </p> <p id="N11639" type="main"> <s id="N12D52"> 先作一大架如a。</s> <s id="N12D55">次作一十字攪輪如e。</s> <s id="N12D58">上安<lb/> 小輪， 周有長齒如i，安架之一邊。</s> <s id="N12D5D">於對邊架上<lb/> 安大平輪，周有齒，與小輪周之長齒相合如o。</s> <s id="N12D62"><lb/> 大平輪立軸上端，亦安小輪，齒橫安如u。</s> <s id="N12D66">又於<lb/> 架之上、橫梁中，安一大輪，有齒，與立軸小輪橫<lb/> 齒相合如c。</s> <s id="N12D6D">即於橫梁大輪軸上，繫起重之索<lb/> 一端如ch。</s> <s id="N12D72">其一端從架上別安滑車上轉貫而<lb/> 過如k。</s> <s id="N12D77">直<lb/> 至於重如p。</s> <s id="N12D7C">以人力各攪轉十字輪如f，則重<lb/> 起矣。</s> <s id="N12D81">儻滑車平定一遠架上，又可作引重法也。</s> <s id="N12D84"> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.259.jpg"/> <lb/> <p id="N11651" type="head"> <s id="N12D8E">引重第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.260.jpg"/> <lb/> <p id="N11657" type="head"> <s id="N12D98">第一圖說</s> </p> <p id="N1165A" type="main"> <s id="N12D9E">引重<lb/> </s> </p> <p id="N1165E" type="main"> <s id="N12DA6">說<lb/> </s> </p> <p id="N11662" type="main"> <s id="N12DAE"> 先為方架如a，次用轆轆，一人轉之如e。</s> <s id="N12DB1">但此<lb/> 轆轆如瓜瓣樣，有六齒。</s> <s id="N12DB6">緊靠轆轆齒，立安大輪，<lb/> 輪周有齒與轆轆之齒相合如i。</s> <s id="N12DBB">大輪之軸，斜<lb/> 安鐵螺絲轉如o。</s> <s id="N12DC0">緊靠此螺絲轉，豎一立軸。</s> <s id="N12DC3">軸<lb/> 下端亦平安斜鐵螺絲轉如u，上端安小輪有<lb/> 齒如c。</s> <s id="N12DCA">小輪緊靠有平安大輪如ch，周有齒與<lb/> 小輪齒相合。</s> <s id="N12DCF">大輪同軸<lb/> 下端有小滑車，如轆轆狀。</s> <s id="N12DD4">上纏索三迴，如k。</s> <s id="N12DD7">以<lb/> 一端繫重，以一端用一人曳之如p，則重行矣。</s> <s id="N12DDC"> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.261.jpg"/> <lb/> <p id="N11678" type="head"> <s id="N12DE6">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.262.jpg"/> <lb/> <p id="N1167E" type="head"> <s id="N12DF0">第二圖說</s> </p> <p id="N11681" type="main"> <s id="N12DF6">說<lb/> </s> </p> <p id="N11685" type="main"> <s id="N12DFE"> 先為方架如a，架之前端安立軸如e。</s> <s id="N12E01">中有大<lb/> 輪如i。</s> <s id="N12E06">輪周有螺絲轉齒如o。</s> <s id="N12E09">輪上有立齒如<lb/> u。</s> <s id="N12E0E">立軸下端有星輪如c。</s> <s id="N12E11">緊靠星輪兩旁，各有<lb/> 立柱，亦各安星輪如ch。</s> <s id="N12E16">兩旁星輪上有纏索之<lb/> 搰轆如k。</s> <s id="N12E1B">緊靠螺絲轉大輪，安立輪如p。</s> <s id="N12E1E">立輪<lb/> 之齒與大輪上立齒相合。</s> <s id="N12E23">立輪之軸有長螺絲<lb/> 轉如<lb/> t。</s> <s id="N12E2A">其長螺絲轉緊靠有大立輪，亦是螺絲轉齒<lb/> 如j。</s> <s id="N12E2F">立輪兩旁，繫繫重之索如a。</s> <s id="N12E32">前端立軸大<lb/> 輪之外，有螺絲轉之柄如f。</s> <s id="N12E37">以一人轉之，則重<lb/> 行矣。</s> <s id="N12E3C">凡重之下， 有長輥木如g，遞輥遞支而前。</s> <s id="N12E3F"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.263.jpg"/> <lb/> <p id="N1169F" type="head"> <s id="N12E48">第三圖并圖說</s> </p> <p id="N116A2" type="main"> <s id="N12E4E">說<lb/> </s> </p> <p id="N116A6" type="main"> <s id="N12E56"> 先為大平車，下有活安<lb/> 長輥木如a。</s> <s id="N12E5B">車前端兩<lb/> 旁安有斜柱，上有軸，兩<lb/> 端各有十字木樁如e。</s> <s id="N12E62"><lb/> 於其前再為兩車，各如<lb/> 其製，如i、如o。</s> <s id="N12E68">但其前<lb/> 兩空車，用時暫柅不動，<lb/> 待載重之車至近，然後<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.264.jpg"/> 起而移之前也。</s> <s id="N12E75"><pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.265.jpg"/> <lb/> </s> </p> <p id="N116BE" type="head"> <s id="N12E80">第四圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.266.jpg"/> <lb/> <p id="N116C4" type="head"> <s id="N12E8A">第四圖說</s> </p> <p id="N116C7" type="main"> <s id="N12E90">說<lb/> </s> </p> <p id="N116CB" type="main"> <s id="N12E98"> 為大輪，一軸兩輪並列。</s> <s id="N12E9B">軸之中繫大桶，或繫別<lb/> 重。</s> <s id="N12EA0">以長杆繫軸上，軸不轉而兩輪轉。</s> <s id="N12EA3">一人肩杆<lb/> 而曳之， 或於杆頭安橫桄，一人推之，皆可行也。</s> <s id="N12EA8"><lb/> </s> </p> <p id="N116D3" type="main"> <s id="N12EAF">說<lb/> </s> </p> <p id="N116D7" type="main"> <s id="N12EB7"> 為兩小輪，中有軸繫杆木，杆之中懸大桶或別<lb/> 重。</s> <s id="N12EBC"> 一人肩而曳之，或用橫桄推之，皆可。</s> <s id="N12EBF"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.267.jpg"/> <lb/> <p id="N116DF" type="head"> <s id="N12EC8">轉重第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.268.jpg"/> <lb/> <p id="N116E5" type="head"> <s id="N12ED2">第一圖說</s> </p> <p id="N116E8" type="main"> <s id="N12ED8">轉重<lb/> </s> </p> <p id="N116EC" type="main"> <s id="N12EE0">說<lb/> </s> </p> <p id="N116F0" type="main"> <s id="N12EE8"> 先為立柱。</s> <s id="N12EEB">中央作方曲拐形如a。</s> <s id="N12EEE">立柱上下直<lb/> 對要正，旁拐立枝為手所轉處。</s> <s id="N12EF3">中為小軸，外貫<lb/> 木筒或竹筒，便可轉也。</s> <s id="N12EF8">或於下端作輪，或於上<lb/> 端作輪，以為轉他重之機。</s> <s id="N12EFD">惟人所作。</s> <s id="N12F00">立柱兩端<lb/> 盡處各為鐵鑽，安於架之鐵臼中，則其轉也，無<lb/> 不利矣。</s> <s id="N12F07"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.269.jpg"/> <lb/> <p id="N11700" type="head"> <s id="N12F10">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.270.jpg"/> <lb/> <p id="N11706" type="head"> <s id="N12F1A">第二圖說</s> </p> <p id="N11709" type="main"> <s id="N12F20">說<lb/> </s> </p> <p id="N1170D" type="main"> <s id="N12F28"> 先為大輪，有齒如a，安兩柱中。</s> <s id="N12F2B">次為轆轤，周圍<lb/> 有齒，與大輪齒相合，如e。</s> <s id="N12F30">一人在柱外轉其柄，<lb/> 則重可轉也。</s> <s id="N12F35">或人力不勝，則於轆轤一端近柱<lb/> 處，安飛輪一具如i。</s> <s id="N12F3A">飛輪者，已似無用，而實能<lb/> 以重助他人之力者也。</s> <s id="N12F3F">故轆轤轉之不足，加一<lb/> 飛輪，則人力必大勝矣。</s> <s id="N12F44"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.271.jpg"/> <lb/> <p id="N1171D" type="head"> <s id="N12F4D">取水第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.272.jpg"/> <lb/> <p id="N11723" type="head"> <s id="N12F57">第一圖說</s> </p> <p id="N11726" type="main"> <s id="N12F5D">取水<lb/> </s> </p> <p id="N1172A" type="main"> <s id="N12F65">說<lb/> </s> </p> <p id="N1172E" type="main"> <s id="N12F6D"> 先為大立輪，中藏水戽如a，轉水至槽池中如<lb/> e。</s> <s id="N12F72">大立輪同軸又有次立輪，有齒如i。</s> <s id="N12F75">再為龍<lb/> 尾車三具，以次而上，如o、如u、如c。</s> <s id="N12F7A">第一龍尾<lb/> 車下端有小鼓輪，亦有齒如ch，與次立輪之齒<lb/> 相合。</s> <s id="N12F81">上端又有旁齒小輪如k，則於第二龍尾<lb/> 車下端輪齒相合。</s> <s id="N12F86">第二龍尾車上端與第三龍<lb/> 尾車下端輪齒各以次相合，則水自上矣。</s> <s id="N12F8B"><lb/> </s> </p> <p id="N1173E" type="main"> <s id="N12F92">龍尾車之製，詳具《泰西水法》中。</s> <s id="N12F95"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.273.jpg"/> <lb/> <p id="N11744" type="head"> <s id="N12F9E">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.274.jpg"/> <lb/> <p id="N1174A" type="head"> <s id="N12FA8">第二圖說</s> </p> <p id="N1174D" type="main"> <s id="N12FAE">說<lb/> </s> </p> <p id="N11751" type="main"> <s id="N12FB6"> 先為大立輪。</s> <s id="N12FB9">層累而上，為三有齒之輪，與三龍<lb/> 尾車上端輪齒各相合。</s> <s id="N12FBE">柱下為平輪。</s> <s id="N12FC1">輪之齒，各<lb/> 以立板作之，外端彎曲如杓樣，向水勢衝處。</s> <s id="N12FC6">水<lb/> 衝其杓，杓杓相推，則大立柱自轉，而三龍尾車<lb/> 自然依次而上水矣。</s> <s id="N12FCD">但龍尾車各從池水槽中<lb/> 轉旋，恐漏水不便。</s> <s id="N12FD2">故於池中先作空筒，上下各<lb/> 長於槽，嚴安槽中。</s> <s id="N12FD7">龍尾車自筒中旋轉， 庶不致<lb/> 已貯之水下漏，為微妙耳。</s> <s id="N12FDC"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.275.jpg"/> <lb/> <p id="N11765" type="head"> <s id="N12FE5">第三圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.276.jpg"/> <lb/> <p id="N1176B" type="head"> <s id="N12FEF">第三圖說</s> </p> <p id="N1176E" type="main"> <s id="N12FF5">說<lb/> </s> </p> <p id="N11772" type="main"> <s id="N12FFD"> 先為飛輪之架。</s> <s id="N13000">次於飛輪軸之兩端，各安一鐵<lb/> 曲柄，但一端向上，則一端向下，必使相反。</s> <s id="N13005">故以<lb/> 一端繫於恒升車取水竿頂可上可下之木。</s> <s id="N1300A">以<lb/> 一端用人力轉之，則水升矣。</s> <s id="N1300F">飛輪者，助人用力<lb/> 之輪也。</s> <s id="N13014"><lb/> </s> </p> <p id="N1177E" type="main"> <s id="N1301B"> 恒升車之製，亦詳具《泰西水法》中。</s> <s id="N1301E"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.277.jpg"/> <lb/> <p id="N11784" type="head"> <s id="N13027">第四圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.278.jpg"/> <lb/> <p id="N1178A" type="head"> <s id="N13031">第四圖說</s> </p> <p id="N1178D" type="main"> <s id="N13037">說<lb/> </s> </p> <p id="N11791" type="main"> <s id="N1303F"> 井中水不能上。</s> <s id="N13042">先作風車以代人畜。</s> <s id="N13045">風車有軸<lb/> 即在井上，以轉井中取水之戽者也。</s> <s id="N1304A">但此圖水<lb/> 戽之製，非此中常用之戽，乃是長筒直貫井底。</s> <s id="N1304F"><lb/> 筒底有軸。</s> <s id="N13053">筒中有索貫諸皮球如雞子樣，上下<lb/> 俱小，以便筒中上下。</s> <s id="N13058">狀若聯珠。</s> <s id="N1305B">其數不拘多少，<lb/> 惟視索垂井底水中，折轉從筒中而上，直至井<lb/> 上池中，<lb/> 環連不絕為度。</s> <s id="N13064">蓋以風輪轉軸，軸轉皮球之索<lb/> 從筒底軸遞轉而上，遞塞其水，直從筒中遞湧<lb/> 而上，而後吐之井上池中也。</s> <s id="N1306B">其作球作筒之法，<lb/> 詳如圖旁散形。</s> <s id="N13070">風車之製多端，詳後轉磨諸圖中。</s> <s id="N13073"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.279.jpg"/> <lb/> <p id="N117AB" type="head"> <s id="N1307C">第五之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.280.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.281.jpg"/> <p id="N117B3" type="head"> <s id="N13089">第五圖說</s> </p> <p id="N117B6" type="main"> <s id="N1308F">說<lb/> </s> </p> <p id="N117BA" type="main"> <s id="N13097"> 為長槽，前寬後窄。</s> <s id="N1309A">于其中平安一軸。</s> <s id="N1309D">其前端安<lb/> 一木杓。</s> <s id="N130A2">杓上有環，繫槽前上端橫木上。</s> <s id="N130A5">槽前下<lb/> 端有小長板如a。</s> <s id="N130AA">杓入水則滿，至高處則因下<lb/> 端小長板所靠，不得不倒而吐矣。</s> <s id="N130AF"><lb/> </s> </p> <p id="N117C4" type="main"> <s id="N130B6"> 嚮余曾自作一引水器，一名鶴飲，一名活桔<lb/> 槔，其製一一與此相合。</s> <s id="N130BB">但此前端用杓更為<lb/> 妙耳。</s> <s id="N130C0"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.282.jpg"/> <lb/> <p id="N117CE" type="head"> <s id="N130C9">第六圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.283.jpg"/> <lb/> <p id="N117D4" type="head"> <s id="N130D3">第六圖說</s> </p> <p id="N117D7" type="main"> <s id="N130D9">說<lb/> </s> </p> <p id="N117DB" type="main"> <s id="N130E1"> 先為四方立架，視天平杆兩端水筒所至高處<lb/> 覆水為度，如a。</s> <s id="N130E6">其下于架之中央水中，用方石<lb/> 安鐵窠如e。</s> <s id="N130EB">中為立柱，下有鐵鑽。</s> <s id="N130EE">立柱下端安<lb/> 立板大輪如i。</s> <s id="N130F3">少上， 安半規斜輪，一角漸次而<lb/> 下，一角漸次而上如o。</s> <s id="N130F8">于半規輪之上，另有樞<lb/> 軸在下半規輪軸中央如u。</s> <s id="N130FD">其樞軸少上，中開<lb/> 長孔，橫安轉軸如c，以貫天平杆之中心，使之<lb/> 可上可下。</s> <s id="N13104">樞軸上端，則安在架之上梁，勿令動<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.284.jpg"/> 也， 如ch。</s> <s id="N1310D">再于天平杆兩畔，近半規輪上弦行處，<lb/> 護以圓木如k或護竹皮，使其滑澤無滯。</s> <s id="N13112">其天<lb/> 平杆兩盡頭處，各安戽筒如p。</s> <s id="N13117">但須于杆旁橫<lb/> 安小杆，繫筒如t，始無<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/07.jpg"/>于杆身。</s> <s id="N1311F">而覆水槽中<lb/> 之為便耳。</s> <s id="N13124"> <lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.285.jpg"/> <p id="N117FE" type="head"> <s id="N1312F">第七圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.286.jpg"/> <lb/> <p id="N11804" type="head"> <s id="N13139">第七圖說</s> </p> <p id="N11807" type="main"> <s id="N1313F">說<lb/> </s> </p> <p id="N1180B" type="main"> <s id="N13147"> 先為兩立柱之架如a。</s> <s id="N1314A">立柱上端有軸。</s> <s id="N1314D">次為大<lb/> 木杓如e，旁有兩耳，中貫橫木如i。</s> <s id="N13152">其杓柄為<lb/> 水出之槽，即貫在立柱架上軸內，可以轉旋上<lb/> 下如o。</s> <s id="N13159">耳中所貫橫木有索繫于旁。</s> <s id="N1315C">立桔槔之<lb/> 前端。</s> <s id="N13161">後端有垂木，中鑿多孔便安木柄，隨人高<lb/> 低，可用力也。</s> <s id="N13166">此器取水甚多。</s> <s id="N13169">桔槔杆另立巧法，<lb/> 任人意為之。</s> <s id="N1316E"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.287.jpg"/> <lb/> <p id="N1181D" type="head"> <s id="N13177">第八圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.288.jpg"/> <lb/> <p id="N11823" type="head"> <s id="N13181">第八圖說</s> </p> <p id="N11826" type="main"> <s id="N13187">說<lb/> </s> </p> <p id="N1182A" type="main"> <s id="N1318F"> 先為行輪，人行其中如a。</s> <s id="N13192">行輪中軸兩端，各安<lb/> 曲拐，一邊曲在上，一邊曲在下，如e。</s> <s id="N13197">曲拐方孔<lb/> 之中杆上，安滑車如i。</s> <s id="N1319C">于滑車貫處為立圈，下<lb/> 端定在恒升車取水杆頭如o。</s> <s id="N131A1">行輪轉動，兩邊<lb/> 自然一低一昂，水可遞引而上矣。</s> <s id="N131A6"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.289.jpg"/> <lb/> <p id="N11838" type="head"> <s id="N131AF">第九圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.290.jpg"/> <lb/> <p id="N1183E" type="head"> <s id="N131B9">第九圖說</s> </p> <p id="N11841" type="main"> <s id="N131BF">說<lb/> </s> </p> <p id="N11845" type="main"> <s id="N131C7"> 先為星輪如a。</s> <s id="N131CA">星輪者，輪周作大圓齒，間中與<lb/> 齒相等；亦作圓孔，與大星光芒四射相似，故名<lb/> 星輪。</s> <s id="N131D1">星輪之外，作鼓廂如e。</s> <s id="N131D4">鼓廂者，上下總一<lb/> 圓圈，兩旁以木板廂之，其形似鼓，故名鼓廂。</s> <s id="N131D9">鼓<lb/> 廂下面底中，開一小孔，入水如i。</s> <s id="N131DE">鼓廂上面開<lb/> 一方孔如o。</s> <s id="N131E3">方孔中，安一方屑，上方下圓。</s> <s id="N131E6">方屑<lb/> 兩旁，各安小滑車，使方屑易上易下也，如u。</s> <s id="N131EB">其<lb/> 安鼓廂及安方屑上下之架如c。</s> <s id="N131F0">于方屑方孔<lb/> 之前，開孔向上，斜安孔筒如ch，以便出水。</s> <s id="N131F5">先將<lb/> 星輪安置鼓廂之中，務使星輪兩旁與輪周齒<lb/> 輪圓處緊靠鼓廂圈板為則。</s> <s id="N131FC">其星輪之軸直出<lb/> 兩旁架外，有曲柄如k，便人運也。</s> <s id="N13201">或另作水轉<lb/> 之輪，以轉此星輪，亦無不可。</s> <s id="N13206">蓋鼓廂之架安置<lb/> 水中。</s> <s id="N1320B">下面小孔自然入水，乃以星輪遞轉而上，<lb/> 至方屑圓頭垂處，水不能再過而前，則惟有從<lb/> 斜孔筒中出水而已。</s> <s id="N13212"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.291.jpg"/> <lb/> <p id="N11869" type="head"> <s id="N1321B">轉磨第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.292.jpg"/> <lb/> <p id="N1186F" type="head"> <s id="N13225">第一圖說</s> </p> <p id="N11872" type="main"> <s id="N1322B">轉磨<lb/> </s> </p> <p id="N11876" type="main"> <s id="N13233">說<lb/> </s> </p> <p id="N1187A" type="main"> <s id="N1323B"> 為大輪，周有齒，中有輻條，如a。</s> <s id="N1323E">惟有車軸斜安，<lb/> 則輪自然斜轉矣。</s> <s id="N13243">次于斜輪兩旁立架頂上，安<lb/> 一橫梁如e。</s> <s id="N13248">以一人手攀其梁，而足踏輻條之<lb/> 上，欲上不能， 而輪則必自轉也，如i。</s> <s id="N1324D">輪外另安<lb/> 小輪，有齒與大輪之齒相合。</s> <s id="N13252">小輪之軸連于轉<lb/> 磨之樞，齒各相得，磨則無不轉也。</s> <s id="N13257">用力少而人<lb/> 不大勞，此其一種。</s> <s id="N1325C"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.293.jpg"/> <lb/> <p id="N1188C" type="head"> <s id="N13265">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.294.jpg"/> <lb/> <p id="N11892" type="head"> <s id="N1326F">第二圖說</s> </p> <p id="N11895" type="main"> <s id="N13275">說<lb/> </s> </p> <p id="N11899" type="main"> <s id="N1327D"> 為大行輪一具。</s> <s id="N13280">行輪之說已見于前。</s> <s id="N13283">第此輪極<lb/> 大， 可容兩人並行耳。</s> <s id="N13288">行輪兩旁，各安有齒小輪，<lb/> 遞轉樞， 則兩磨可俱轉也。</s> <s id="N1328D">一見自明，故不細贅。</s> <s id="N13290"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.295.jpg"/> <lb/> <p id="N118A3" type="head"> <s id="N13299">第三圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.296.jpg"/> <lb/> <p id="N118A9" type="head"> <s id="N132A3">第三圖說</s> </p> <p id="N118AC" type="main"> <s id="N132A9">說<lb/> </s> </p> <p id="N118B0" type="main"> <s id="N132B1"> 磨中之樞，下安鐵曲拐如a。</s> <s id="N132B4">樞下端，再安十字<lb/> 木杆，杆末各安鉛柁如e。</s> <s id="N132B9">樞下安鐵鑽，入鐵窠<lb/> 中如i。</s> <s id="N132BE">于曲拐中，安木桄，兩端各為轉環如o。</s> <s id="N132C1"><lb/> 一端轉環安人手曳桄上如u。</s> <s id="N132C5">其人手所曳之<lb/> 桄上端安于架上。</s> <s id="N132CA">立桄亦有轉軸如c。</s> <s id="N132CD">一人斜<lb/> 曳其手中之木，可前可後。</s> <s id="N132D2">而樞端下面十字鉛<lb/> 柁為之助力，則磨自可轉矣。</s> <s id="N132D7">倘或磨重，于對旁<lb/> 再增一曲拐，再用一人對曳如前法，尤有餘力。</s> <s id="N132DC"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.297.jpg"/> <lb/> <p id="N118C4" type="head"> <s id="N132E5">第四圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.298.jpg"/> <lb/> <p id="N118CA" type="head"> <s id="N132EF">第四圖說</s> </p> <p id="N118CD" type="main"> <s id="N132F5">說<lb/> </s> </p> <p id="N118D1" type="main"> <s id="N132FD"> 磨悉如常。</s> <s id="N13300">惟旁有立柱，安大立轆轤，繫纏垂重<lb/> 之索，如a。</s> <s id="N13305">轆轤之上安平輪，周有懸齒，以轉轉<lb/> 磨樞之立輪，如e。</s> <s id="N1330A">下有十字杆，待重垂下至地，<lb/> 用人力推杆，則重可復上，如i。</s> <s id="N1330F">于立柱之旁，另<lb/> 有立架，上橫以梁如o。</s> <s id="N13314">橫梁中開長孔，安三小<lb/> 滑車如u。</s> <s id="N13319">垂重之上有小立框，中安兩小滑車<lb/> 如c。</s> <s id="N1331E">立柱大轆轤所纏之索，平轉從旁立小架<lb/> 滑車之下而過如ch，從而上之。</s> <s id="N13323">過梁上第一在<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.299.jpg"/> 左之滑車折轉而下。</s> <s id="N1332C">又從小立框下一滑車之<lb/> 下折轉而上，過梁上第二在右之滑車，折轉而<lb/> 下。</s> <s id="N13333">又從小立框上一滑車而下，折轉而上，過梁<lb/> 上第三在中之滑車，折轉而下，始繫定于小立<lb/> 框上端小梁上如k。</s> <s id="N1333A">小立框下端小梁有環，垂<lb/> 重之上有鉤，鉤于環內如p。</s> <s id="N1333F">重下，則磨自轉矣。</s> <s id="N13342"><lb/> 所以必用此許多小滑車者，總令垂重遲遲而<lb/> 下， 不易到地，其磨可多轉耳。</s> <s id="N13348">垂重下又加小重<lb/> 者，欲人視之多寡自為增損云爾。</s> <s id="N1334D"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.300.jpg"/> <p id="N118F9" type="main"> <s id="N13357"> 此自轉磨也，嚮余曾臆想作此試之，甚便。</s> <s id="N1335A">今<lb/> 得此，實先得我心之同然。</s> <s id="N1335F">但此遲遲垂重之<lb/> 法初則夢想不及也。</s> <s id="N13364"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.301.jpg"/> <lb/> <p id="N11903" type="head"> <s id="N1336D">第五之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.302.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.303.jpg"/> <p id="N1190B" type="head"> <s id="N1337A">第五圖說</s> </p> <p id="N1190E" type="main"> <s id="N13380">說<lb/> </s> </p> <p id="N11912" type="main"> <s id="N13388"> 蓋或人多遠行，此磨載之車上，如上圖。</s> <s id="N1338B">兩磨安<lb/> 於兩頭，中安一大立柱，下安平輪有齒如a。</s> <s id="N13390">其<lb/> 輪軸下端有鐵鑽，安車中平木中央鐵窠內。</s> <s id="N13395">輪<lb/> 齒兩旁，各安有齒小輪，平轉兩邊磨中之樞。</s> <s id="N1339A">其<lb/> 立柱於平輪之上，平安橫木。</s> <s id="N1339F">中央開孔而上，上<lb/> 端安有橫梁如e。</s> <s id="N133A4">橫梁兩頭長過於車，各安下<lb/> 垂立柱如i。</s> <s id="N133A9">以馬轉兩立柱，則兩磨可自轉也。</s> <s id="N133AC"><lb/> 其車行，兼可載他輜重，故甚便之。</s> <s id="N133B0"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.304.jpg"/> <lb/> <p id="N11926" type="main"> <s id="N133B9"> 余意橫梁若作十字，則用四風扇，或直豎車上，<lb/> 或亦周垂車外，又可作風磨也。</s> <s id="N133BE"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.305.jpg"/> <lb/> <p id="N1192E" type="head"> <s id="N133C7">第六圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.306.jpg"/> <lb/> <p id="N11934" type="head"> <s id="N133D1">第六圖說</s> </p> <p id="N11937" type="main"> <s id="N133D7">說<lb/> </s> </p> <p id="N1193B" type="main"> <s id="N133DF"> 為大輪，外周安橫桄如a。</s> <s id="N133E2">內有長軸。</s> <s id="N133E5">兩端安兩<lb/> 立輪，各有齒轉兩磨立樞燈輪之齒如e。</s> <s id="N133EA">用三<lb/> 人手攀橫梁，足踏輪周橫桄，則兩磨轉矣。</s> <s id="N133EF">儻止<lb/> 用一磨，則一人足矣。</s> <s id="N133F4">在人酌而為之耳。</s> <s id="N133F7"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.307.jpg"/> <lb/> <p id="N11947" type="head"> <s id="N13400">第七圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.308.jpg"/> <lb/> <p id="N1194D" type="head"> <s id="N1340A">第七圖說</s> </p> <p id="N11950" type="main"> <s id="N13410">說<lb/> </s> </p> <p id="N11954" type="main"> <s id="N13418"> 大輪轉兩磨燈輪之樞如a，總用常法：惟大輪<lb/> 軸為大立柱，柱下端有鐵鑽，入地臼窠中；柱半<lb/> 身處，安大木平架。</s> <s id="N1341F">中開圓孔，柱從孔中透出上<lb/> 去，以轉動便利為度如e；柱上半身，安十字兩<lb/> 層橫桄，各有立檔如i。</s> <s id="N13426">四立檔外，各掛一大方<lb/> 布框如o。</s> <s id="N1342B">布框可展可收，向風吹處則自然展<lb/> 開，受風過則自收。</s> <s id="N13430">遞展而遞相受風，故兩磨可<lb/> 自轉也。</s> <s id="N13435">布框每面有兩索斜繫如u者，恐風大<lb/> 布力不能當，易至損耳。</s> <s id="N1343A"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.309.jpg"/> <lb/> <p id="N1196A" type="head"> <s id="N13443">第八之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.310.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.311.jpg"/> <p id="N11972" type="head"> <s id="N13450">第八圖說</s> </p> <p id="N11975" type="main"> <s id="N13456">說<lb/> </s> </p> <p id="N11979" type="main"> <s id="N1345E"> 其下悉是常法。</s> <s id="N13461">惟是大輪齒不得遽及磨樞燈<lb/> 輪之齒，故各再加兩燈輪。</s> <s id="N13466">立軸上，再安有齒之<lb/> 輪，庶易及磨樞耳。</s> <s id="N1346B">其上風扇則為長三角形如<lb/> a，兩面以薄木板為之， 更易受風，其力尤大也。</s> <s id="N13470"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.312.jpg"/> <lb/> <p id="N11985" type="head"> <s id="N13479">第九圖并說</s> </p> <p id="N11988" type="main"> <s id="N1347F">說<lb/> </s> </p> <p id="N1198C" type="main"> <s id="N13487"> 餘皆同<lb/> 前。</s> <s id="N1348C">惟方<lb/> 板風扇<lb/> 垂在輪<lb/> 下，上以<lb/> 四斜棖<lb/> <char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/08.jpg"/>輪，為<lb/> 少異耳。</s> <s id="N1349E"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.313.jpg"/> <p id="N119A2" type="head"> <s id="N134A8">第十圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.314.jpg"/> <lb/> <p id="N119A8" type="head"> <s id="N134B2">第十圖說</s> </p> <p id="N119AB" type="main"> <s id="N134B8">說<lb/> </s> </p> <p id="N119AF" type="main"> <s id="N134C0"> 餘悉同。</s> <s id="N134C3">止是立柱平安十字，周作輪形如a。</s> <s id="N134C6">於<lb/> 輪上周圍，以木板作方風扇如e。</s> <s id="N134CB">每扇一面，各<lb/> 有一索繫緊，風來則板直立，受其吹而自轉。</s> <s id="N134D0">然<lb/> 有索繫，則又不能前去。</s> <s id="N134D5">過風則又自然少垂，不<lb/> 阻風也。</s> <s id="N134DA"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.315.jpg"/> <lb/> <p id="N119BD" type="head"> <s id="N134E3">第十一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.316.jpg"/> <lb/> <p id="N119C3" type="head"> <s id="N134ED">第十一圖說</s> </p> <p id="N119C6" type="main"> <s id="N134F3">說<lb/> </s> </p> <p id="N119CA" type="main"> <s id="N134FB"> 餘悉常法。</s> <s id="N134FE">惟是上層周圍有墻，每面少開一方，<lb/> 以受風入如a。</s> <s id="N13503">其立柱則上至屋頂。</s> <s id="N13506">轉樞柱安<lb/> 十字木板上，下長橫少弱耳。</s> <s id="N1350B"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.317.jpg"/> <lb/> <p id="N119D4" type="head"> <s id="N13514">第十二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.318.jpg"/> <lb/> <p id="N119DA" type="head"> <s id="N1351E">第十二圖說</s> </p> <p id="N119DD" type="main"> <s id="N13524">說<lb/> </s> </p> <p id="N119E1" type="main"> <s id="N1352C"> 餘如常。</s> <s id="N1352F">止立柱上安八風扇為異，其風更大也。</s> <s id="N13532"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.319.jpg"/> <lb/> <p id="N119E7" type="head"> <s id="N1353B">第十三圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.320.jpg"/> <lb/> <p id="N119ED" type="head"> <s id="N13545">第十三圖說</s> </p> <p id="N119F0" type="main"> <s id="N1354B">說<lb/> </s> </p> <p id="N119F4" type="main"> <s id="N13553"> 餘俱如常。</s> <s id="N13556">惟於轉磨樞燈輪之立輪安長鐵軸<lb/> 於架外，作曲拐方形如a。</s> <s id="N1355B">於鐵軸盡處，定安十<lb/> 字木，兩頭悉是鉛柁，使重而易轉以助人力，有<lb/> 如飛輪。</s> <s id="N13562">於曲拐方形轉處貫以鐵環，兩端各繫<lb/> 以索。</s> <s id="N13567">其索一端繫木杆中環上如e。</s> <s id="N1356A">其杆下端，<lb/> 則定在地上，有環可轉如i。</s> <s id="N1356F">兩人封曳其杆，一<lb/> 來一往，則飛輪助力，磨之轉甚便，且省力也。</s> <s id="N13574">視<lb/> 人周行磨外，節勞不啻數倍矣。</s> <s id="N13579"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.321.jpg"/> <lb/> <p id="N11A08" type="head"> <s id="N13582">第十四圖 <n>(覽圖自明，不更立說)</n> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.322.jpg"/> <lb/> <p id="N11A10" type="head"> <s id="N1358F">第十五圖 <n>(覽圖自明，不更立說)</n> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.323.jpg"/> <lb/> <p id="N11A18" type="head"> <s id="N1359C">解木第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.324.jpg"/> <lb/> <p id="N11A1E" type="head"> <s id="N135A6">第一圖說</s> </p> <p id="N11A21" type="main"> <s id="N135AC">解木<lb/> </s> </p> <p id="N11A25" type="main"> <s id="N135B4">說<lb/> </s> </p> <p id="N11A29" type="main"> <s id="N135BC"> 先為水輪並架如a。</s> <s id="N135BF">水輪軸一端出架外，連以<lb/> 曲拐如e。</s> <s id="N135C4">曲拐之上連有立鐵杆，兩頭有環。</s> <s id="N135C7">下<lb/> 端環貫曲拐之末，上端環貫鋸之下檔木上。</s> <s id="N135CC">鋸<lb/> 齒居中，兩旁連檔立柱則各上下兩立槽中如<lb/> i。</s> <s id="N135D3">外水輪轉，則曲拐一上一下，而鋸齒亦隨之<lb/> 一上一下矣。</s> <s id="N135D8">此解法也，但能使木來就鋸則其<lb/> 中尤有巧法，須細詳之。</s> <s id="N135DD"><char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/09.jpg"/>木置架上，架兩頭有<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.325.jpg"/> 四立柱之夾木如o。</s> <s id="N135E8">架又總安一長槽中，下有<lb/> 小圓輥木數個如u。</s> <s id="N135ED">木之未解左端盡處，有索<lb/> 繫于架下斜齒鐵輪之軸如c。</s> <s id="N135F2">旁有長杆，尖頭<lb/> 有鐵乂以起斜齒之齒如ch者，則又定在遠旁<lb/> 大轉木之下端如k。</s> <s id="N135F9">大轉木上端，有小杆，亦斜<lb/> 連于鋸下檔之下如p。</s> <s id="N135FE">鋸一上，則帶轉木上端<lb/> 小杆亦上，轉木亦必少少斜轉，而上有鐵乂之<lb/> 長杆勢必起一斜齒而自出其上矣。</s> <s id="N13605">鋸一下，轉<lb/> 木亦必少少斜轉而下，則乂杆又入第二齒下<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.326.jpg"/> <lb/> 矣。</s> <s id="N13610">以此起齒，即以此纏軸之索，故木自來就鋸<lb/> 也。</s> <s id="N13615">又恐斜輪齒上而復回，則又以短乂小鐵杆<lb/> 緊隨而疾阻之如t。</s> <s id="N1361A">此皆微機，妙不容言。</s> <s id="N1361D"><pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.327.jpg"/> <lb/> </s> </p> <p id="N11A5A" type="head"> <s id="N13628">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.328.jpg"/> <lb/> <p id="N11A60" type="head"> <s id="N13632">第二圖說</s> </p> <p id="N11A63" type="main"> <s id="N13638">說<lb/> </s> </p> <p id="N11A67" type="main"> <s id="N13640"> 先為立柱架，安大水輪如a。</s> <s id="N13643">水輪同軸另安有<lb/> 齒之輪如e。</s> <s id="N13648">一邊齒轉燈輪，燈輪助以飛輪如<lb/> i。</s> <s id="N1364D">飛輪與燈輪同軸。</s> <s id="N13650">軸之一端有鐵曲拐，上連<lb/> 曳鋸之木如o。</s> <s id="N13655">又水輪有齒之輪，一邊轉小燈<lb/> 輪。</s> <s id="N1365A">同軸又有小燈輪遞轉，旁安有齒小輪如u。</s> <s id="N1365D"><lb/> 有齒小輪遞轉上小燈輪。</s> <s id="N13661">小燈輪同軸有鋸齒<lb/> 鐵輪如c。</s> <s id="N13666">鋸齒鐵輪之軸，則繫轉木就鋸之索<lb/> 者也。</s> <s id="N1366B">其阻齒勿回之乂，則以鋸上端之木，旁轉<lb/> 而上下之如ch，其消息與第一圖略相同。</s> <s id="N13670"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.329.jpg"/> <lb/> <p id="N11A7D" type="head"> <s id="N13679">第三圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.330.jpg"/> <lb/> <p id="N11A83" type="head"> <s id="N13683">第三圖說</s> </p> <p id="N11A86" type="main"> <s id="N13689">說<lb/> </s> </p> <p id="N11A8A" type="main"> <s id="N13691"> 安鋸置木之架，圖自分明，不細贅。</s> <s id="N13694">惟是架中兩<lb/> 旁，各有長輻條之大輪如a。</s> <s id="N13699">其輻條盡頭，須各<lb/> 挨入人攪大輪之輞少許，使人攪輪上旁安之<lb/> 小木樁，易掛轉也。</s> <s id="N136A0">兩輪通為一軸，軸纏轉木之<lb/> 索，使木來就鋸。</s> <s id="N136A5">其人攪兩輪亦通貫一軸，但軸<lb/> 之中作曲鐵拐，貫兩長鐵杆，直貫于轉鋸上下<lb/> 之長橫梁上如e。</s> <s id="N136AC">兩軸外各安曲柄相對，兩人<lb/> 攪之，鋸自可轉。</s> <s id="N136B1">而每輪一周，木樁可轉一輻條，<lb/> 木亦自來就鋸也。</s> <s id="N136B6"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.331.jpg"/> <lb/> <p id="N11AA0" type="head"> <s id="N136BF">第四圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.332.jpg"/> <lb/> <p id="N11AA6" type="head"> <s id="N136C9">第四圖說</s> </p> <p id="N11AA9" type="main"> <s id="N136CF">說<lb/> </s> </p> <p id="N11AAD" type="main"> <s id="N136D7"> 解法用人如常。</s> <s id="N136DA">第架上後端，立兩有力之竹弓<lb/> 如a，則省人力多多矣。</s> <s id="N136DF">覽圖自明，無容多解。</s> <s id="N136E2"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.333.jpg"/> <lb/> <p id="N11AB5" type="head"> <s id="N136EB">解石之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.334.jpg"/> <lb/> <p id="N11ABB" type="head"> <s id="N136F5">解石圖說</s> </p> <p id="N11ABE" type="main"> <s id="N136FB">解石<lb/> </s> </p> <p id="N11AC2" type="main"> <s id="N13703">說<lb/> </s> </p> <p id="N11AC6" type="main"> <s id="N1370B"> 假如有石，欲解成幾板，則有架如a。</s> <s id="N1370E">于架近一<lb/> 頭處，安立軸，上安有齒平輪如e。</s> <s id="N13713">平輪轉旁燈<lb/> 輪如i。</s> <s id="N13718">燈輪又轉小立輪上如o。</s> <s id="N1371B">小立輪軸外<lb/> 有曲拐如u。</s> <s id="N13720">曲拐之端貫直鐵杆，兩端有環如<lb/> c。</s> <s id="N13725">一端環貫曲拐之末，一端之環則貫曳鋸之<lb/> 長木杆下端。</s> <s id="N1372A">長木杆<lb/> 上端有軸可轉。</s> <s id="N1372F">木杆立貫鋸于兩頭活滑車榾<lb/> 轆中如ch。</s> <s id="N13734">鋸或二或三，俱精鐵為之，第無齒耳。</s> <s id="N13737"><lb/> 兩曳鋸長木杆下端，連以鐵杆，兩端有環如k。</s> <s id="N1373B"><lb/> 以一馬轉立軸平輪，則曲拐往來，鋸自行矣。</s> <s id="N1373F"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.335.jpg"/> <lb/> <p id="N11ADE" type="head"> <s id="N13748">轉碓之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.336.jpg"/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.337.jpg"/> <p id="N11AE5" type="head"> <s id="N13754">轉碓圖說</s> </p> <p id="N11AE8" type="main"> <s id="N1375A">轉碓<lb/> </s> </p> <p id="N11AEC" type="main"> <s id="N13762">說<lb/> </s> </p> <p id="N11AF0" type="main"> <s id="N1376A"> 先為架，安碓或一、或二、或三、或四如a，下各以<lb/> 臼承之如e。</s> <s id="N1376F">次為飛輪，中大外小，共三輪如i。</s> <s id="N13772"><lb/> 飛輪長軸兩旁各出架外，安曲柄如o。</s> <s id="N13776">軸之兩<lb/> 旁，安小鐵樁，相錯上下如u。</s> <s id="N1377B">其鐵樁相對，每碓<lb/> 各有擒碓枝之桔槔小杆如k。</s> <s id="N13780">一碓兩碓，一人<lb/> 從一旁轉輪，則碓自然上下。</s> <s id="N13785">如碓多，則兩旁兩<lb/> 人轉之自足也。</s> <s id="N1378A"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.338.jpg"/> <lb/> <p id="N11B02" type="head"> <s id="N13793">書架圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.339.jpg"/> <lb/> <p id="N11B08" type="head"> <s id="N1379D">書架圖說</s> </p> <p id="N11B0B" type="main"> <s id="N137A3">書架<lb/> </s> </p> <p id="N11B0F" type="main"> <s id="N137AB">說<lb/> </s> </p> <p id="N11B13" type="main"> <s id="N137B3"> 先為大輪，外形同鼓廂如a。</s> <s id="N137B6">內為有齒之輪，相<lb/> 等者共九輪，八面各一，中央一輪。</s> <s id="N137BB">又于八輪之<lb/> 內，各安相等八小輪，俱有齒，中央輪動則八小<lb/> 輪自轉，而八大輪隨之。</s> <s id="N137C2">其詳旁有散圖如e。</s> <s id="N137C5">其<lb/> 書安置八大輪一旁軸上，有座、有軸，其詳亦旁<lb/> 有散圖如i。</s> <s id="N137CC">大輪安置架上如o。</s> <s id="N137CF">欲看某書，大<lb/> 輪一轉則某書自來就人。</s> <s id="N137D4">而餘書雖巳轉過，仍<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.340.jpg"/> 各上下自如，不隨輪而顛倒也。</s> <s id="N137DB"><lb/> </s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.341.jpg"/> <p id="N11B28" type="head"> <s id="N137E5">水日晷圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.342.jpg"/> <lb/> <p id="N11B2E" type="head"> <s id="N137EF">水日晷說</s> </p> <p id="N11B31" type="main"> <s id="N137F5">日晷<lb/> </s> </p> <p id="N11B35" type="main"> <s id="N137FD">說<lb/> </s> </p> <p id="N11B39" type="main"> <s id="N13805"> 先以小缸盛水，於底鑽一小孔，徐徐出水。</s> <s id="N13808">上安<lb/> 小榾轆長轉軸出墻外。</s> <s id="N1380D">榾轆上纏以索，下端繫<lb/> 重木如a， 然亦不必太重。</s> <s id="N13812">上端繫小重如e。</s> <s id="N13815">墻<lb/> 外軸端，定安日晷如i。</s> <s id="N1381A">水徐徐下，則重木亦必<lb/> 徐徐下，而日晷以時轉矣。</s> <s id="N1381F">此省便法也。</s> <s id="N13822"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.343.jpg"/> <lb/> <p id="N11B47" type="head"> <s id="N1382B">代耕之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.344.jpg"/> <lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.345.jpg"/> <p id="N11B4F" type="head"> <s id="N13838">代耕圖說</s> </p> <p id="N11B52" type="main"> <s id="N1383E">代耕<lb/> </s> </p> <p id="N11B56" type="main"> <s id="N13846">說<lb/> </s> </p> <p id="N11B5A" type="main"> <s id="N1384E"> 先為兩轆轤架如a。</s> <s id="N13851">兩轆轤係兩長索，貫犁其<lb/> 中如e。</s> <s id="N13856">兩人遞轉轆轤之索，一人扶犁往來，自<lb/> 可耕也。</s> <s id="N1385B"><lb/> </s> </p> <p id="N11B62" type="main"> <s id="N13862"> 嚮余在計部觀政時，曾以臆想作此，不期與<lb/> 此圖甚相合也。</s> <s id="N13867">可謂先得我心之同然矣。</s> <s id="N1386A"/> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.346.jpg"/> <lb/> <p id="N11B6A" type="head"> <s id="N13873">水銃第一圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.347.jpg"/> <lb/> <p id="N11B70" type="head"> <s id="N1387D">第二圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.348.jpg"/> <lb/> <p id="N11B76" type="head"> <s id="N13887">第三圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.349.jpg"/> <lb/> <p id="N11B7C" type="head"> <s id="N13891">第四之圖</s> </p> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.350.jpg"/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.351.jpg"/> <p id="N11B83" type="head"> <s id="N1389D">水銃圖說</s> </p> <p id="N11B86" type="main"> <s id="N138A3">水銃<lb/> </s> </p> <p id="N11B8A" type="main"> <s id="N138AB">圖</s> </p> <n>(凡三)</n> <lb/> <p id="N11B90" type="main"> <s id="N138B4">說</s> </p> <n>(從散形圖為之說者)</n> <lb/> <p id="N11B96" type="main"> <s id="N138BD"> 先鑄兩銅筒如a、A。</s> <s id="N138C0">其容之廣，從二寸或至十寸，<lb/> 任人意為之。</s> <s id="N138C5">其高少或一尺，多或一尺有半。</s> <s id="N138C8">內<lb/> 容務上下相等。</s> <s id="N138CD">其底要最堅厚。</s> <s id="N138D0">其氣眼如b、B，有<lb/> <char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/10.jpg"/>，或在旁， 或在底，或在底旁少許，但在底更便。</s> <s id="N138D8"><lb/> 旁安管，少彎曲向上如i、I，各有小<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/10.jpg"/>如o、E。</s> <s id="N138DF">上有<lb/> 兩乂總管如u，緊壓合於兩彎管上，無絲毫漏<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.352.jpg"/> <lb/> 隙為則。</s> <s id="N138EA"><char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/10.jpg"/>共四個氣眼，入水處兩個，彎管出入<lb/> 處兩個。</s> <s id="N138F1">另有柁二具如c、u，其柄以鐵為之，其柁<lb/> 則銅。</s> <s id="N138F6">柁用兩層銅。</s> <s id="N138F9">柁周圍以滿銅筒之容為度。</s> <s id="N138FC"><lb/> 銅柁兩層中間，用<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/11.jpg"/>皮數層擠實為則。</s> <s id="N13903">兩銅筒<lb/> 俱安一銅鍋內，要極穩，勿動為則。</s> <s id="N13908">鍋底要平。</s> <s id="N1390B">如<lb/> 無銅鍋，堅大木桶亦可。</s> <s id="N13910">於兩銅筒之上，安橫梁<lb/> 如ch、e。</s> <s id="N13915">兩旁中央安兩鐵孔，是兩柁所由上下者。</s> <s id="N13918"><lb/> 居中有鐵天平立柱。</s> <s id="N1391C">其柱頂頭有小轉軸眼，上<lb/> 橫安天平長木擔。</s> <s id="N13921">於兩柁上下處，用環連於擔<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.353.jpg"/> <lb/> 上。</s> <s id="N1392A">兩端多設平木樁，以便多人攀舉。</s> <s id="N1392D">又有直角<lb/> 小管如ko，貫於總管出水上口之外。</s> <s id="N13932">要最嚴密，<lb/> 又要可周旋轉動，使之四面八方去也。</s> <s id="N13937">就中，有<lb/> 小圓槽，施以短釘，務令可轉而不可上。</s> <s id="N1393C">其必用<lb/> 槽用釘者，水力最大；不，則衝之去矣。</s> <s id="N13941">此管上又<lb/> 有直角管，但其嘴少長於ko，為PH。</s> <s id="N13946">其長少亦三<lb/> 尺，愈長其出愈遠。</s> <s id="N1394B">但嘴必少弱於管身，為出水<lb/> 之勢耳。</s> <s id="N13950">直角長管與短管相貫處，亦必用槽用<lb/> 釘，如前法。</s> <s id="N13955">此管則一人用手可轉，或上、或下、或<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.354.jpg"/> <lb/> 正、或斜，皆可向有火處施放之也。</s> <s id="N1395E">此器有二種，<lb/> 或定在一處，如第一圖；或用船、車無輪者，如第<lb/> 二圖。</s> <s id="N13965">其法皆同。</s> <s id="N13968">又有一種，其器同，但在有輪車<lb/> 上，不用橫梁，止用槓子天平，如第三圖。</s> <s id="N1396D">任人意<lb/> 消詳作之耳。</s> <s id="N13972">其運水之法，排定多人，人人可接<lb/> 遞皮袋之水至於盛筒鍋內，周轉無窮。</s> <s id="N13977">必用皮<lb/> 袋運水者，視他器便且不破壞耳。</s> <s id="N1397C"><lb/> </s> </p> <p id="N11BE7" type="main"> <s id="N13983"> 此水銃可以滅火，可以禦火，可以防火，乃新<lb/> 有之器。</s> <s id="N13988">其能力最便、最大、最奇，諸器所難比<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.355.jpg"/> 其功用者也。</s> <s id="N13991">蓋倉卒之際，火力正勝，人不可<lb/> 近。</s> <s id="N13996">但有此器，則五六人可代數百人之用。</s> <s id="N13999">又<lb/> 不空費一滴之水。</s> <s id="N1399E">不拘多高、 多遠，皆可立到。</s> <s id="N139A1"><lb/> 有似大雨噴空，無處不霑。</s> <s id="N139A5">不但可滅已燄之<lb/> 火，仍可預防未燃之火。</s> <s id="N139AA">況有圖、有說，作此不<lb/> 難；工力價直且不甚費。</s> <s id="N139AF">凡城邑村坊，悉當置<lb/> 此二三具。</s> <s id="N139B4">其於捍患禦災最有裨也。</s> <s id="N139B7">已作小<lb/> 樣試之，良驗。</s> <s id="N139BC">有志於仁民者，其尚廣為傳造<lb/> 焉。</s> <s id="N139C1"/> </p> </chap> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.356.jpg"/> <chap id="N11C02" n="4"> <lb/> <p id="N11C05" type="head"> <s id="N139CD">新製諸器圖小序</s> </p> <p id="N11C08" type="main"> <s id="N139D3"> 甕叟抱樸，驚掊渾<lb/> 帝，化人奇肱，巧絕<lb/> 弗傳，懼滋朅來人<lb/> <pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.357.jpg"/> 心之幻耳。</s> <s id="N139E0">然人心之幻<lb/> 滋甚，彌難方物，初不<lb/> 盡識破<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/12.jpg"/>之。</s> <s id="N139EA">然而民<lb/> 生日用之常，漸有輕<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.358.jpg"/> <lb/> 捷省便之法，<char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/13.jpg"/>多滯<lb/> 泥罔通。</s> <s id="N139FA">似於千古尚象<lb/> 制器之旨，不無少拘。</s> <s id="N139FF"><lb/> <char xlink:href="http://141.14.236.86/docuserver/images/arch2/schreck/char/14.jpg"/>彼大圜，輪輪遞轉，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.359.jpg"/> <lb/> 匪一輯以自斡，疇万<lb/> 象之更新而顧為是<lb/> 拘拘者耶？不揣固陋，<lb/> 妄有所作，見之者頗<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.360.jpg"/> <lb/> 謂裨益民生日用。</s> <s id="N13A18">有<lb/> 已造而行之者，有未<lb/> 造而儀其必可行者，<lb/> 繪集為圖為說，間<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.361.jpg"/> <lb/> 為之銘，自解其嘲而識<lb/> 之。</s> <s id="N13A29">若此其他自動風<lb/> 翣，与活棍木、活地平，<lb/> 及用小力運鉅重之器，<pb xlink:href="http://archimedes.fas.harvard.edu:8080/docuserver/digitallibrary/digilib.jsp?X03-01-pageimg/X03.01.362.jpg"/> <lb/> 尚有多种，為其關<lb/> 民生之未甚急也，玆<lb/> 不具載。</s> <s id="N13A3A"><lb/> </s> </p> <p id="N11C52" type="main"> <s id="N13A41">時<lb/> </s> &n