file :i* includes ! orig9al illu/rations4 ,see #adgbe-;h4htm or #adgbe-;h4zip3 7https3_/_/www4gut5b]g4org_/dirs_/#a_/d_ /g_/b_/adgbe_/adgbe-;h_/#adgbe-;h4htm7 or 7https3_/_/www4gut5b]g4org_/dirs_/#a_/d_ /g_/b_/adgbe_/adgbe-;h4zip7 ,,treatise ,,on ,,light ,9 :i* are expla9$ ,! causes ( t :i* occurs ,9 ,,reflexion1 9 ,,refraction ,& p>ticul>ly ,9 ! /range ,,refraction ,,( ,,icel& ,,cry/al by ,,*ri/iaan ,,huyg5s ,r5d]$ into ,engli% by ,,silvanus ,p4 ,,?ompson ,univ]sity ( ,*icago ,press ,,preface ,i wrote ?is ,treatise dur+ my soj\rn 9 ,france twelve ye>s ago1 & ,i communicat$ x 9 ! ye> #afgh to ! le>n$ p]sons :o !n compos$ ! ,royal ,academy ( ,sci5ce1 to ! memb]%ip ( :i* ! ,k+ _h done me ! hon\r ( call+1 me4 ,sev]al ( t body :o are /ill alive w rememb] hav+ be5 pres5t :5 ,i read x1 & above ! re/ ^? among/ !m :o appli$ !mselves p>ticul>ly to ! /udy ( ,ma!matics2 ( :om ,i _c cite m ?an ! celebrat$ g5tlem5 ,cass9i1 ,rm]1 & ,de la ,hire4 ,&1 al?\gh ,i h s9ce correct$ & *ang$ "s p>ts1 ! copies :i* ,i _h made ( x at t "t may s]ve = pro( t ,i h yet add$ no?+ to x save "s conjectures t\*+ ! =mation ( ,icel& ,cry/al1 & a novel obs]vation on ! refraction ( ,rock ,cry/al4 ,i h desir$ to relate ^! p>ticul>s to make kn[n h[ long ,i h m$itat$ ! ?+s :i* n[ ,i publi%1 & n = ! purpose ( detract+ f ! m]it ( ^? :o1 )\t hav+ se5 any?+ t ,i h writt51 may be f\nd to h treat$ ( l matt]s3 z has 9 fact occurr$ to two em95t ,geometricians1 ,messieurs ,newton & ,leibnitz1 ) respect to ! ,problem ( ! figure ( glasses = collect+ rays :5 "o ( ! surfaces is giv54 ,"o may ask :y ,i h s long delay$ to br+ ?is "w to ! light4 ,! reason is t ,i wrote x r c>elessly 9 ! ,language 9 :i* x appe>s1 ) ! int5tion ( translat+ x into ,lat91 s do+ 9 ord] to obta9 great] att5tion to ! ?+4 ,aft] :i* ,i propos$ to myself to give x out along ) ano!r ,treatise on ,dioptrics1 9 :i* ,i expla9 ! effects ( ,telescopes & ^? ?+s :i* belong m to t ,sci5ce4 ,b ! pleasure ( novelty be+ pa/1 ,i h put (f f "t to "t ! execution ( ?is design1 & ,i "k n :5 ,i %all ev] come to an end if x1 be+ (t5 turn$ aside ei!r by bus9ess or by "s new /udy4 ,consid]+ :i* ,i h f9ally judg$ t x 0 bett] wor? :ile to publi% ?is writ+1 su* z x is1 ?an to let x run ! risk1 by wait+ long]1 ( rema9+ lo/4 ,!re w be se5 9 x demon/rations ( ^? k9ds :i* d n produce z great a c]titude z ^? ( ,geometry1 & :i* ev5 diff] mu* !refrom1 s9ce :]eas ! ,geomet]s prove _! ,propositions by fix$ & inconte/able ,pr9ciples1 "h ! ,pr9ciples are v]ifi$ by ! conclusions to be drawn f !m2 ! nature ( ^! ?+s n all[+ ( ?is be+ done o!rwise4 ,x is always possible to atta9 !reby to a degree ( probability :i* v (t5 is sc>cely less ?an complete pro(4 ,to wit1 :5 ?+s :i* h be5 demon/rat$ by ! ,pr9ciples t h be5 assum$ correspond p]fectly to ! ph5om5a :i* exp]im5t has br\ght "u obs]vation2 especially :5 !re are a great numb] ( !m1 & fur!r1 pr9cipally1 :5 "o c imag9e & =esee new ph5om5a :i* ought to foll[ f ! hypo!ses :i* "o employs1 & :5 "o f9ds t !re9 ! fact corresponds to our prevision4 ,b if all ^! pro(s ( probability are met ) 9 t :i* ,i propose to discuss1 z x seems to me !y are1 ?is ought to be a v /rong confirmation ( ! success ( my inquiry2 & x mu/ be ill if ! facts are n pretty mu* z ,i repres5t !m4 ,i w\ld believe !n t ^? :o love to "k ! ,causes ( ?+s & :o are able to admire ! m>vels ( ,light1 w f9d "s satisfaction 9 ^! v>i\s speculations reg>d+ x1 & 9 ! new explanation ( its fam\s prop]ty :i* is ! ma9 f\ndation ( ! con/ruction ( our eyes & ( ^? great inv5tions :i* ext5d s va/ly ! use ( !m4 ,i hope also t !re w be "s :o by foll[+ ^! beg9n+s w p5etrate mu* fur!r into ?is "q ?an ,i h be5 able to d1 s9ce ! subject mu/ be f> f be+ exhau/$4 ,?is appe>s f ! passages :i* ,i h indicat$ :]e ,i leave c]ta9 difficulties )\t hav+ resolv$ !m1 & /ill m f matt]s :i* ,i h n t\*$ at all1 su* z ,lum9\s ,bodies ( sev]al sorts1 & all t conc]ns ,col\rs2 9 :i* no "o until n[ c boa/ ( hav+ succe$$4 ,f9ally1 !re rema9s mu* m to be inve/igat$ t\*+ ! nature ( ,light :i* ,i d n pret5d to h disclos$1 & ,i %all owe mu* 9 return to him :o %all be able to supplem5t t :i* is "h lack+ to me 9 k4 ,! ,hague4 ,! #h ,janu>y #afij4 ,,note ,,by ,,! ,,translator ,consid]+ ! great influ5ce :i* ?is ,treatise has ex]cis$ 9 ! developm5t ( ! ,sci5ce ( ,optics1 x seems /range t two c5turies %\ld h pass$ be=e an ,engli% edition ( ! "w appe>$4 ,p]haps ! circum/ance is due to ! mi/ak5 zeal ) :i* =m]ly ev]y?+ t conflict$ ) ! *]i%$ ideas ( ,newton 0 d5\nc$ by 8 foll[]s4 ,! ,treatise on ,light ( ,huyg5s has1 h[ev]1 )/ood ! te/ ( "t3 & ev5 n[ ! exquisite skill ) :i* he appli$ 8 conception ( ! propagation ( waves ( light to unravel ! intricacies ( ! ph5om5a ( ! d\ble refraction ( cry/als1 & ( ! refraction ( ! atmosph]e1 w excite ! admiration ( ! /ud5t ( ,optics4 ,x is true t 8 wave !ory 0 f> f ! complete doctr9e z subsequ5tly develop$ by ,?omas ,"y & ,augu/9 ,fresnel1 & belong$ r to geometrical ?an to physical ,optics4 ,if ,huyg5s _h no conception ( transv]se vibrations1 ( ! pr9ciple ( int]f]5ce1 or ( ! exi/5ce ( ! ord]$ sequ5ce ( waves 9 tra9s1 he nev]!less atta9$ to a rem>kably cle> und]/&+ ( ! pr9ciples ( wave-propagation2 & 8 exposition ( ! subject m>ks an epo* 9 ! treatm5t ( ,optical problems4 ,x has be5 ne$ful 9 prep>+ ?is translation to ex]cise c>e le/ "o %\ld import into ! au?or's text ideas ( subsequ5t date1 by us+ words t h come to imply mod]n conceptions4 ,h5ce ! adoption ( z lit]al a r5d]+ z possible4 ,a few ( ! au?or's t]ms ne$ explanation4 ,he uses ! ^w refraction1 = example1 bo? = ! ph5om5on or process usually s d5ot$1 & = ! result ( t process3 ?us ! refract$ ray he habitually t]ms ! refraction ( ! incid5t ray4 ,:5 a wave-front1 or1 z he t]ms x1 a wave1 has pass$ f "s initial position to a subsequ5t "o1 he t]ms ! wave-front 9 its subsequ5t position ! cont9uation ( ! wave4 ,he also speaks ( ! envelope ( a set ( elem5t>y waves1 =m$ by coalesc5ce ( ^? elem5t>y wave-fronts1 z ! t]m9ation ( ! wave2 & ! elem5t>y wave-fronts he t]ms p>ticul> waves4 ,ow+ to ! circum/ance t ! ,fr5* ^w rayon possesses ! d\ble signification ( ray ( light & radius ( a circle1 he avoids its use 9 ! latt] s5se & speaks always ( ! semi-diamet]1 n ( ! radius4 ,8 speculations z to ! e!r1 8 sugge/ive views ( ! /ructure ( cry/all9e bodies1 & 8 explanation ( opacity1 slight z !y are1 w possibly surprise ! read] by _! seem+ mod]nness4 ,& none c read 8 inve/igation ( ! ph5om5a f\nd 9 ,icel& sp> )\t m>vell+ at 8 insight & sagacity4 ,s4,p4,t4 ,june1 #aiab4 ,,table ,,( ,,matt]s ,conta9$ 9 ?is ,treatise ,,*apt] ,i4 ,on ,rays ,propagat$ 9 ,/raight ,l9es4 ,t ,light is produc$ by a c]ta9 movem5t4 ,t no sub/ance passes f ! lum9\s object to ! eyes4 ,t ,light spreads sph]ically1 almo/ z ,s\nd does4 ,:e!r ,light takes "t to spread4 ,exp]i5ce seem+ to prove t x passes in/antane\sly4 ,exp]i5ce prov+ t x takes "t4 ,h[ mu* its spe$ is great] ?an t ( ,s\nd4 ,9 :at ! emission ( ,light diff]s f t ( ,s\nd4 ,t x is n ! same m$ium :i* s]ves = ,light & ,s\nd4 ,h[ ,s\nd is propagat$4 ,h[ ,light is propagat$4 ,detail$ ,rem>ks on ! propagation ( ,light4 ,:y ,rays are propagat$ only 9 /raight l9es4 ,h[ ,light com+ 9 diff]5t directions c cross itself4 ,,*apt] ,,ii4 ,on ,reflexion4 ,demon/ration ( equality ( angles ( incid5ce & reflexion4 ,:y ! incid5t & reflect$ rays are 9 ! same plane p]p5dicul> to ! reflect+ surface4 ,t x is n ne$ful = ! reflect+ surface to be p]fectly flat to atta9 equality ( ! angles ( incid5ce & reflexion4 ,,*apt] ,,iii4 ,on ,refraction4 ,t bodies may be transp>5t )\t any sub/ance pass+ ?r\gh !m4 ,pro( t ! e!real matt] passes ?r\gh transp>5t bodies4 ,h[ ?is matt] pass+ ?r\gh c r5d] !m transp>5t4 ,t ! mo/ solid bodies 9 appe>ance are ( a v loose texture4 ,t ,light spreads m sl[ly 9 wat] & 9 glass ?an 9 air4 ,?ird hypo!sis to expla9 transp>5cy1 & ! ret>dation :i* ,light suff]s4 ,on t :i* makes bodies opaque4 ,demon/ration :y ,refraction obeys ! kn[n proportion ( ,s9es4 ,:y ! incid5t & refract$ ,rays produce "o ano!r reciprocally4 ,:y ,reflexion )9 a triangul> glass prism is sudd5ly augm5t$ :5 ! ,light c no long] p5etrate4 ,t bodies :i* cause great] ,refraction also cause /rong] ,reflexion4 ,demon/ration ( ! ,!orem ( ,mr4 ,f]mat4 ,,*apt] ,,iv4 ,on ! ,refraction ( ! ,air4 ,t ! emanations ( ,light 9 ! air are n sph]ical4 ,h[ consequ5tly "s objects appe> high] ?an !y are4 ,h[ ! ,sun may appe> on ! ,horizon be=e he has ris54 ,t ! rays ( light become curv$ 9 ! ,air ( ! ,atmosph]e1 & :at effects ?is produces4 ,,*apt] ,v4 ,on ! ,/range ,refraction ( ,icel& ,cry/al4 ,t ?is ,cry/al gr[s also 9 o!r c\ntries4 ,:o fir/-wrote ab\t x4 ,description ( ,icel& ,cry/al2 its sub/ance1 %ape1 & prop]ties4 ,t x has two diff]5t ,refractions4 ,t ! ray p]p5dicul> to ! surface suff]s refraction1 & t "s rays incl9$ to ! surface pass )\t suff]+ refraction4 ,obs]vation ( ! refractions 9 ?is ,cry/al4 ,t !re is a ,regul> & an ,irregul> ,refraction4 ,! way ( measur+ ! two ,refractions ( ,icel& ,cry/al4 ,rem>kable prop]ties ( ! ,irregul> ,refraction4 ,hypo!sis to expla9 ! d\ble ,refraction4 ,t ,rock ,cry/al has also a d\ble ,refraction4 ,hypo!sis ( emanations ( ,light1 )9 ,icel& ,cry/al1 ( sph]oidal =m1 = ! ,irregul> ,refraction4 ,h[ a p]p5dicul> ray c suff] ,refraction4 ,h[ ! position & =m ( ! sph]oidal emanations 9 ?is ,cry/al c be def9$4 ,explanation ( ! ,irregul> ,refraction by ^! sph]oidal emanations4 ,easy way to f9d ! ,irregul> ,refraction ( ea* incid5t ray4 ,demon/ration ( ! oblique ray :i* trav]ses ! ,cry/al )\t be+ refract$4 ,o!r irregul>ities ( ,refraction expla9$4 ,t an object plac$ b5ea? ! ,cry/al appe>s d\ble1 9 two images ( diff]5t heights4 ,:y ! app>5t heights ( "o ( ! images *ange on *ang+ ! position ( ! eyes above ! ,cry/al4 ,( ! diff]5t sections ( ?is ,cry/al :i* produce yet o!r refractions1 & confirm all ?is ,!ory4 ,p>ticul> way ( poli%+ ! surfaces aft] x has be5 cut4 ,surpris+ ph5om5on t\*+ ! rays :i* pass ?r\gh two sep>at$ pieces2 ! cause ( :i* is n expla9$4 ,probable conjecture on ! int]nal composition ( ,icel& ,cry/al1 & ( :at figure its p>ticles are4 ,te/s to confirm ?is conjecture4 ,calculations :i* h be5 suppos$ 9 ?is ,*apt]4 ,,*apt] ,,vi4 ,on ! ,figures ( transp>5t bodies :i* s]ve = ,refraction & = ,reflexion4 ,g5]al & easy rule to f9d ^! ,figures4 ,inv5tion ( ! ,ovals ( ,mr4 ,des ,c>tes = ,dioptrics4 ,h[ he 0 able to f9d ^! ,l9es4 ,way ( f9d+ ! surface ( a glass = p]fect refraction1 :5 ! o!r surface is giv54 ,rem>k on :at happ5s to rays refract$ at a sph]ical surface4 ,rem>k on ! curv$ l9e :i* is =m$ by reflexion 9 a sph]ical concave mirror4 ,,*apt] ,i ,,on ,,rays ,,propagat$ ,,9 ,,/raight ,,l9es ,z happ5s 9 all ! sci5ces 9 :i* ,geometry is appli$ to matt]1 ! demon/rations conc]n+ ,optics are f\nd$ on tru?s drawn f exp]i5ce4 ,su* are t ! rays ( light are propagat$ 9 /raight l9es2 t ! angles ( reflexion & ( incid5ce are equal2 & t 9 refraction ! ray is b5t accord+ to ! law ( s9es1 n[ s well kn[n1 & :i* is no less c]ta9 ?an ! prec$+ laws4 ,! majority ( ^? :o h writt5 t\*+ ! v>i\s p>ts ( ,optics h cont5t$ !mselves ) presum+ ^! tru?s4 ,b "s1 m inquir+1 h desir$ to inve/igate ! orig9 & ! causes1 consid]+ ^! to be 9 !mselves wond]ful effects ( ,nature4 ,9 :i* !y advanc$ "s +5i\s ?+s1 b n h[ev] su* t ! mo/ intellig5t folk d n wi% = bett] & m satisfactory explanations4 ,:]e=e ,i "h desire to prop\nd :at ,i h m$itat$ on ! subject1 s z to contribute z mu* z ,i c to ! explanation ( ?is dep>tm5t ( ,natural ,sci5ce1 :i*1 n )\t reason1 is reput$ to be "o ( its mo/ difficult p>ts4 ,i recognize myself to be mu* indebt$ to ^? :o 7 ! fir/ to beg9 to dissipate ! /range obscurity 9 :i* ^! ?+s 7 envelop$1 & to give u hope t !y might be expla9$ by intelligible reason+4 ,b1 on ! o!r h& ,i am a/oni%$ also t ev5 "h ^! h (t5 be5 will+ to (f]1 z assur$ & demon/rative1 reason+s :i* 7 f> f conclusive4 ,= ,i d n f9d t any "o has yet giv5 a probable explanation ( ! fir/ & mo/ notable ph5om5a ( light1 namely :y x is n propagat$ except 9 /raight l9es1 & h[ visible rays1 com+ f an inf9itude ( div]se places1 cross "o ano!r )\t h9d]+ "o ano!r 9 any way4 ,i %all !re=e essay 9 ?is book1 to give1 9 accordance ) ! pr9ciples accept$ 9 ! ,philosophy ( ! pres5t day1 "s cle>] & m probable reasons1 fir/ly ( ^! prop]ties ( light propagat$ rectil9e>ly2 secondly ( light :i* is reflect$ on meet+ o!r bodies4 ,!n ,i %all expla9 ! ph5om5a ( ^? rays :i* are said to suff] refraction on pass+ ?r\gh transp>5t bodies ( diff]5t sorts2 & 9 ?is "p ,i %all also expla9 ! effects ( ! refraction ( ! air by ! diff]5t d5sities ( ! ,atmosph]e4 ,!reaft] ,i %all exam9e ! causes ( ! /range refraction ( a c]ta9 k9d ( ,cry/al :i* is br\ght f ,icel&4 ,& f9ally ,i %all treat ( ! v>i\s %apes ( transp>5t & reflect+ bodies by :i* rays are collect$ at a po9t or are turn$ aside 9 v>i\s ways4 ,f ?is x w be se5 ) :at facility1 foll[+ our new ,!ory1 we f9d n only ! ,ellipses1 ,hyp]bolas1 & o!r curves :i* ,mr4 ,des ,c>tes has +5i\sly inv5t$ = ?is purpose2 b also ^? :i* ! surface ( a glass l5s ought to possess :5 its o!r surface is giv5 z sph]ical or plane1 or ( any o!r figure t may be4 ,x is inconceivable to d\bt t light consi/s 9 ! motion ( "s sort ( matt]4 ,= :e!r "o consid]s its production1 "o sees t "h ^u ! ,e>? x is *iefly eng5d]$ by fire & flame :i* conta9 )\t d\bt bodies t are 9 rapid motion1 s9ce !y dissolve & melt _m o!r bodies1 ev5 ! mo/ solid2 or :e!r "o consid]s its effects1 "o sees t :5 light is collect$1 z by concave mirrors1 x has ! prop]ty ( burn+ z a fire does1 t is to say x disunites ! p>ticles ( bodies4 ,?is is assur$ly ! m>k ( motion1 at lea/ 9 ! true ,philosophy1 9 :i* "o conceives ! causes ( all natural effects 9 t]ms ( me*anical motions4 ,?is1 9 my op9ion1 we mu/ necess>ily d1 or else r5\nce all hopes ( ev] compreh5d+ any?+ 9 ,physics4 ,& z1 accord+ to ?is ,philosophy1 "o holds z c]ta9 t ! s5sation ( sight is excit$ only by ! impression ( "s movem5t ( a k9d ( matt] :i* acts on ! n]ves at ! back ( our eyes1 !re is "h yet "o reason m = believ+ t light consi/s 9 a movem5t ( ! matt] :i* exi/s betwe5 u & ! lum9\s body4 ,fur!r1 :5 "o consid]s ! extreme spe$ ) :i* light spreads on e side1 & h[1 :5 x comes f diff]5t regions1 ev5 f ^? directly opposite1 ! rays trav]se "o ano!r )\t h9drance1 "o may well und]/& t :5 we see a lum9\s object1 x _c be by any transport ( matt] com+ to u f ?is object1 9 ! way 9 :i* a %ot or an arr[ trav]ses ! air2 = assur$ly t w\ld too greatly impugn ^! two prop]ties ( light1 especially ! second ( !m4 ,x is !n 9 "s o!r way t light spreads2 & t :i* c lead u to compreh5d x is ! k :i* we h ( ! spread+ ( ,s\nd 9 ! air4 ,we "k t by means ( ! air1 :i* is an invisible & impalpable body1 ,s\nd spreads ar\nd ! spot :]e x has be5 produc$1 by a movem5t :i* is pass$ on successively f "o "p ( ! air to ano!r2 & t ! spread+ ( ?is movem5t1 tak+ place equally rapidly on all sides1 ought to =m sph]ical surfaces ev] enl>g+ & :i* /rike our e>s4 ,n[ !re is no d\bt at all t light also comes f ! lum9\s body to our eyes by "s movem5t impress$ on ! matt] :i* is betwe5 ! two2 s9ce1 z we h already se51 x _c be by ! transport ( a body :i* passes f "o to ! o!r4 ,if1 9 addition1 light takes "t = its passage--:i* we are n[ go+ to exam9e--x w foll[ t ?is movem5t1 impress$ on ! int]v5+ matt]1 is successive2 & consequ5tly x spreads1 z ,s\nd does1 by sph]ical surfaces & waves3 = ,i call !m waves f _! resemblance to ^? :i* are se5 to be =m$ 9 wat] :5 a /one is ?r[n into x1 & :i* pres5t a successive spread+ z circles1 ?\gh ^! arise f ano!r cause1 & are only 9 a flat surface4 ,to see !n :e!r ! spread+ ( light takes "t1 let u consid] fir/ :e!r !re are any facts ( exp]i5ce :i* c conv9ce u to ! contr>y4 ,z to ^? :i* c be made "h on ! ,e>?1 by /rik+ lights at great di/ances1 al?\gh !y prove t light takes no s5sible "t to pass ov] ^! di/ances1 "o may say ) good reason t !y are too small1 & t ! only conclusion to be drawn f !m is t ! passage ( light is extremely rapid4 ,mr4 ,des ,c>tes1 :o 0 ( op9ion t x is in/antane\s1 f\nd$ 8 views1 n )\t reason1 ^u a bett] basis ( exp]i5ce1 drawn f ! ,eclipses ( ! ,moon2 :i*1 nev]!less1 z ,i %all %[1 is n at all conv9c+4 ,i w set x =?1 9 a way a little diff]5t f 81 9 ord] to make ! conclusion m compreh5sible4 ,illu/ration ,let ,a be ! place ( ! sun1 ,,bd a "p ( ! orbit or annual pa? ( ! ,e>?3 ,,abc a /raight l9e :i* ,i suppose to meet ! orbit ( ! ,moon1 :i* is repres5t$ by ! circle ,,cd1 at ,c4 ,n[ if light requires "t1 = example "o h\r1 to trav]se ! space :i* is betwe5 ! ,e>? & ! ,moon1 x w foll[ t ! ,e>? hav+ arriv$ at ,b1 ! %ad[ :i* x ca/s1 or ! int]ruption ( ! light1 w n yet h arriv$ at ! po9t ,c1 b w only arrive !re an h\r aft]4 ,x w !n be "o h\r aft]1 reckon+ f ! mom5t :5 ! ,e>? 0 at ,b1 t ! ,moon1 arriv+ at ,c1 w be obscur$3 b ?is obscuration or int]ruption ( ! light w n rea* ! ,e>? till aft] ano!r h\r4 ,let u suppose t ! ,e>? 9 ^! two h\rs w h arriv$ at ,e4 ,! ,e>? !n1 be+ at ,e1 w see ! ,eclips$ ,moon at ,c1 :i* x left an h\r be=e1 & at ! same "t w see ! sun at ,a4 ,= x be+ immovable1 z ,i suppose ) ,cop]nicus1 & ! light mov+ always 9 /raight l9es1 x mu/ always appe> :]e x is4 ,b "o has always obs]v$1 we are told1 t ! eclips$ ,moon appe>s at ! po9t ( ! ,ecliptic opposite to ! ,sun2 & yet "h x w\ld appe> 9 arre> ( t po9t by an am\nt equal to ! angle ,,gec1 ! supplem5t ( ,,aec4 ,?is1 h[ev]1 is contr>y to exp]i5ce1 s9ce ! angle ,,gec w\ld be v s5sible1 & ab\t #cc degrees4 ,n[ accord+ to our computation1 :i* is giv5 9 ! ,treatise on ! causes ( ! ph5om5a ( ,saturn1 ! di/ance ,,ba betwe5 ! ,e>? & ! ,sun is ab\t twelve ?\s& diamet]s ( ! ,e>?1 & h5ce f\r hundr$ times great] ?an ,,bc ! di/ance ( ! ,moon1 :i* is #cj diamet]s4 ,!n ! angle ,,ecb w be ne>ly f\r hundr$ times great] ?an ,,bae1 :i* is five m9utes2 namely1 ! pa? :i* ! e>? travels 9 two h\rs along its orbit2 & ?us ! angle ,,bce w be ne>ly #cc degrees2 & likewise ! angle ,,ceg1 :i* is great] by five m9utes4 ,b x mu/ be not$ t ! spe$ ( light 9 ?is argum5t has be5 assum$ su* t x takes a "t ( "o h\r to make ! passage f "h to ! ,moon4 ,if "o supposes t = ?is x requires only "o m9ute ( "t1 !n x is manife/ t ! angle ,,ceg w only be #cc m9utes2 & if x requires only t5 seconds ( "t1 ! angle w be less ?an six m9utes4 ,& !n x w n be easy to p]ceive any?+ ( x 9 obs]vations ( ! ,eclipse2 nor1 consequ5tly1 w x be p]missible to d$uce f x t ! movem5t ( light is in/antane\s4 ,x is true t we are "h suppos+ a /range velocity t w\ld be a hundr$ ?\s& times great] ?an t ( ,s\nd4 ,= ,s\nd1 accord+ to :at ,i h obs]v$1 travels ab\t #ahj ,toises 9 ! "t ( "o ,second1 or 9 ab\t "o beat ( ! pulse4 ,b ?is supposition ought n to seem to be an impossibility2 s9ce x is n a "q ( ! transport ( a body ) s great a spe$1 b ( a successive movem5t :i* is pass$ on f "s bodies to o!rs4 ,i h !n made no difficulty1 9 m$itat+ on ^! ?+s1 9 suppos+ t ! emanation ( light is accompli%$ ) "t1 see+ t 9 ?is way all its ph5om5a c be expla9$1 & t 9 foll[+ ! contr>y op9ion ev]y?+ is incompreh5sible4 ,= x has always seem$ tome t ev5 ,mr4 ,des ,c>tes1 ^: aim has be5 to treat all ! subjects ( ,physics intelligibly1 & :o assur$ly has succe$$ 9 ?is bett] ?an any "o be=e him1 has said no?+ t is n full ( difficulties1 or ev5 inconceivable1 9 deal+ ) ,light & its prop]ties4 ,b t :i* ,i employ$ only z a hypo!sis1 has rec5tly receiv$ great seem+ness z an e/abli%$ tru? by ! +5i\s pro( ( ,mr4 ,rm] :i* ,i am go+ "h to relate1 expect+ him himself to give all t is ne$$ = its confirmation4 ,x is f\nd$ z is ! prec$+ argum5t ^u cele/ial obs]vations1 & proves n only t ,light takes "t = its passage1 b also demon/rates h[ mu* "t x takes1 & t its velocity is ev5 at lea/ six times great] ?an t :i* ,i h j /at$4 ,= ?is he makes use ( ! ,eclipses suff]$ by ! little planets :i* revolve ar\nd ,jupit]1 & :i* (t5 ent] 8 %ad[3 & see :at is 8 reason+4 ,let ,a be ! ,sun1 ,,bcde ! annual orbit ( ! ,e>?1 ,f ,jupit]1 ,,gn ! orbit ( ! ne>e/ ( 8 ,satellites1 = x is ?is "o :i* is m apt = ?is inve/igation ?an any ( ! o!r ?ree1 because ( ! quickness ( its revolution4 ,let ,g be ?is ,satellite ent]+ into ! %ad[ ( ,jupit]1 ,h ! same ,satellite em]g+ f ! %ad[4 ,illu/ration ,let x be !n suppos$1 ! ,e>? be+ at ,b "s "t be=e ! la/ quadrature1 t "o has se5 ! said ,satellite em]ge f ! %ad[2 x mu/ ne$s be1 if ! ,e>? rema9s at ! same place1 t1 aft] #db-a_/b h\rs1 "o w\ld aga9 see a simil> em]g5ce1 because t is ! "t 9 :i* x makes ! r\nd ( its orbit1 & :5 x w\ld come aga9 into opposition to ! ,sun4 ,& if ! ,e>?1 = in/ance1 7 to rema9 always at ,b dur+ #cj revolutions ( ?is ,satellite1 "o w\ld see x aga9 em]ge f ! %ad[ aft] #cj times #db-a_/b h\rs4 ,b ! ,e>? hav+ be5 c>ri$ along dur+ ?is "t to ,c1 increas+ ?us its di/ance f ,jupit]1 x foll[s t if ,light requires "t = its passage ! illum9ation ( ! little planet w be p]ceiv$ lat] at ,c ?an x w\ld h be5 at ,b1 & t !re mu/ be add$ to ?is "t ( #cj times #db-a_/b h\rs t :i* ! ,light has requir$ to trav]se ! space ,,mc1 ! diff]5ce ( ! spaces ,,*1 ,,bh4 ,simil>ly at ! o!r quadrature :5 ! e>? has come to ,e f ,d :ile approa*+ t[>d ,jupit]1 ! imm]sions ( ! ,satellite ought to be obs]v$ at ,e e>li] ?an !y w\ld h be5 se5 if ! ,e>? _h rema9$ at ,d4 ,n[ 9 quantities ( obs]vations ( ^! ,eclipses1 made dur+ t5 consecutive ye>s1 ^! diff]5ces h be5 f\nd to be v consid]able1 su* z t5 m9utes & m2 & f !m x has be5 conclud$ t 9 ord] to trav]se ! :ole diamet] ( ! annual orbit ,,kl1 :i* is d\ble ! di/ance f "h to ! sun1 ,light requires ab\t #bb m9utes ( "t4 ,! movem5t ( ,jupit] 9 8 orbit :ile ! ,e>? pass$ f ,b to ,c1 or f ,d to ,e1 is includ$ 9 ?is calculation2 & ?is makes x evid5t t "o _c attribute ! ret>dation ( ^! illum9ations or ! anticipation ( ! eclipses1 ei!r to any irregul>ity occurr+ 9 ! movem5t ( ! little planet or to its ecc5tricity4 ,if "o consid]s ! va/ size ( ! diamet] ,,kl1 :i* accord+ to me is "s #bd ?\s& diamet]s ( ! ,e>?1 "o w ackn[l$ge ! extreme velocity ( ,light4 ,=1 suppos+ t ,,kl is no m ?an #bb ?\s& ( ^! diamet]s1 x appe>s t be+ trav]s$ 9 #bb m9utes ?is makes ! spe$ a ?\s& diamet]s 9 "o m9ute1 t is #af-b_/c diamet]s 9 "o second or 9 "o beat ( ! pulse1 :i* makes m ?an #aa hundr$ times a hundr$ ?\s& toises2 s9ce ! diamet] ( ! ,e>? conta9s #b1hfe leagues1 reckon$ at #be to ! degree1 & ea* ea* league is #b1bhb ,toises1 accord+ to ! exact measurem5t :i* ,mr4 ,pic>d made by ord] ( ! ,k+ 9 #affi4 ,b ,s\nd1 z ,i h said above1 only travels #ahj toises 9 ! same "t ( "o second3 h5ce ! velocity ( ,light is m ?an six hundr$ ?\s& times great] ?an t ( ,s\nd4 ,?is1 h[ev]1 is q ano!r ?+ f be+ in/antane\s1 s9ce !re is all ! diff]5ce betwe5 a f9ite ?+ & an inf9ite4 ,n[ ! successive movem5t ( ,light be+ confirm$ 9 ?is way1 x foll[s1 z ,i h said1 t x spreads by sph]ical waves1 l ! movem5t ( ,s\nd4 ,b if ! "o resembles ! o!r 9 ?is respect1 !y diff] 9 _m o!r ?+s2 to wit1 9 ! fir/ production ( ! movem5t :i* causes !m2 9 ! matt] 9 :i* ! movem5t spreads2 & 9 ! mann] 9 :i* x is propagat$4 ,z to t :i* occurs 9 ! production ( ,s\nd1 "o kn[s t x is occasion$ by ! agitation und]gone by an entire body1 or by a consid]able "p ( "o1 :i* %akes all ! contigu\s air4 ,b ! movem5t ( ! ,light mu/ orig9ate z f ea* po9t ( ! lum9\s object1 else we %\ld n be able to p]ceive all ! diff]5t p>ts ( t object1 z w be m evid5t 9 t :i* foll[s4 ,& ,i d n believe t ?is movem5t c be bett] expla9$ ?an by suppos+ t all ^? ( ! lum9\s bodies :i* are liquid1 su* z flames1 & app>5tly ! sun & ! />s1 are compos$ ( p>ticles :i* float 9 a mu* m subtle m$ium :i* agitates !m ) great rapidity1 & makes !m /rike aga9/ ! p>ticles ( ! e!r :i* surr\nds !m1 & :i* are mu* small] ?an !y4 ,b ,i hold also t 9 lum9\s solids su* z *>coal or metal made r$ hot 9 ! fire1 ?is same movem5t is caus$ by ! viol5t agitation ( ! p>ticles ( ! metal or ( ! wood2 ^? ( !m :i* are on ! surface /rik+ simil>ly aga9/ ! e!real matt]4 ,! agitation1 moreov]1 ( ! p>ticles :i* eng5d] ! light ought to be mu* m prompt & m rapid ?an is t ( ! bodies :i* cause s\nd1 s9ce we d n see t ! tremors ( a body :i* is giv+ out a s\nd are capable ( giv+ rise to ,light1 ev5 z ! movem5t ( ! h& 9 ! air is n capable ( produc+ ,s\nd4 ,n[ if "o exam9es :at ?is matt] may be 9 :i* ! movem5t com+ f ! lum9\s body is propagat$1 :i* ,i call ,e!real matt]1 "o w see t x is n ! same t s]ves = ! propagation ( ,s\nd4 ,= "o f9ds t ! latt] is really t :i* we feel & :i* we brea!1 & :i* be+ remov$ f any place /ill leaves !re ! o!r k9d ( matt] t s]ves to convey ,light4 ,?is may be prov$ by %utt+ up a s\nd+ body 9 a glass vessel f :i* ! air is )drawn by ! ma*9e :i* ,mr4 ,boyle has giv5 u1 & ) :i* he has p]=m$ s _m beautiful exp]im5ts4 ,b 9 do+ ?is ( :i* ,i speak1 c>e mu/ be tak5 to place ! s\nd+ body on cotton or on fea!rs1 9 su* a way t x _c communicate its tremors ei!r to ! glass vessel :i* encloses x1 or to ! ma*9e2 a precaution :i* has hi!rto be5 neglect$4 ,= !n aft] hav+ exhau/$ all ! air "o he>s no ,s\nd f ! metal1 ?\gh x is /ruck4 ,"o sees "h n only t our air1 :i* does n p5etrate ?r\gh glass1 is ! matt] by :i* ,s\nd spreads2 b also t x is n ! same air b ano!r k9d ( matt] 9 :i* ,light spreads2 s9ce if ! air is remov$ f ! vessel ! ,light does n cease to trav]se x z be=e4 ,& ?is la/ po9t is demon/rat$ ev5 m cle>ly by ! celebrat$ exp]im5t ( ,torricelli1 9 :i* ! tube ( glass f :i* ! quicksilv] has )drawn itself1 rema9+ void ( air1 transmits ,light j ! same z :5 air is 9 x4 ,= ?is proves t a matt] diff]5t f air exi/s 9 ?is tube1 & t ?is matt] mu/ h p5etrat$ ! glass or ! quicksilv]1 ei!r "o or ! o!r1 ?\gh !y are bo? imp5etrable to ! air4 ,& :51 9 ! same exp]im5t1 "o makes ! vacuum aft] putt+ a little wat] above ! quicksilv]1 "o concludes equally t ! said matt] passes ?r\gh glass or wat]1 or ?r\gh bo?4 ,z reg>ds ! diff]5t modes 9 :i* ,i h said ! movem5ts ( ,s\nd & ( ,light are communicat$1 "o may suffici5tly compreh5d h[ ?is occurs 9 ! case ( ,s\nd if "o consid]s t ! air is ( su* a nature t x c be compress$ & r$uc$ to a mu* small] space ?an t :i* x ord9>ily occupies4 ,& 9 proportion z x is compress$ ! m does x ex]t an ef=t to rega9 its volume2 = ?is prop]ty along ) its p5etrability1 :i* rema9s not)/&+ its compression1 seems to prove t x is made up ( small bodies :i* float ab\t & :i* are agitat$ v rapidly 9 ! e!real matt] compos$ ( mu* small] p>ts4 ,s t ! cause ( ! spread+ ( ,s\nd is ! ef=t :i* ^! little bodies make 9 collisions ) "o ano!r1 to rega9 fre$om :5 !y are a little m squeez$ toge!r 9 ! circuit ( ^! waves ?an else:]e4 ,b ! extreme velocity ( ,light1 & o!r prop]ties :i* x has1 _c admit ( su* a propagation ( motion1 & ,i am ab\t to %[ "h ! way 9 :i* ,i conceive x mu/ occur4 ,= ?is1 x is ne$ful to expla9 ! prop]ty :i* h>d bodies mu/ possess to transmit movem5t f "o to ano!r4 ,:5 "o takes a numb] ( sph]es ( equal size1 made ( "s v h>d sub/ance1 & arranges !m 9 a /raight l9e1 s t !y t\* "o ano!r1 "o f9ds1 on /rik+ ) a simil> sph]e aga9/ ! fir/ ( ^! sph]es1 t ! motion passes z 9 an in/ant to ! la/ ( !m1 :i* sep>ates itself f ! r[1 )\t "o's be+ able to p]ceive t ! o!rs h be5 /irr$4 ,& ev5 t "o :i* 0 us$ to /rike rema9s motionless ) !m4 ,:5ce "o sees t ! movem5t passes ) an extreme velocity :i* is ! great]1 ! great] ! h>dness ( ! sub/ance ( ! sph]es4 ,b x is /ill c]ta9 t ?is progression ( motion is n in/antane\s1 b successive1 & !re=e mu/ take "t4 ,= if ! movem5t1 or ! disposition to movem5t1 if y w h x s1 did n pass successively ?r\gh all ^! sph]es1 !y w\ld all acquire ! movem5t at ! same "t1 & h5ce w\ld all advance toge!r2 :i* does n happ54 ,= ! la/ "o leaves ! :ole r[ & acquires ! spe$ ( ! "o :i* 0 pu%$4 ,moreov] !re are exp]im5ts :i* demon/rate t all ! bodies :i* we reckon ( ! h>de/ k9d1 su* z qu5*$ /eel1 glass1 & agate1 act z spr+s & b5d someh[1 n only :5 ext5d$ z rods b also :5 !y are 9 ! =m ( sph]es or ( o!r %apes4 ,t is to say !y yield a little 9 !mselves at ! place :]e !y are /ruck1 & imm$iately rega9 _! =m] figure4 ,= ,i h f\nd t on /rik+ ) a ball ( glass or ( agate aga9/ a l>ge & q ?ick ?ick piece ( ! same sub/ance :i* _h a flat surface1 slightly soil$ ) brea? or 9 "s o!r way1 !re rema9$ r\nd m>ks1 ( small] or l>g] size accord+ z ! bl[ _h be5 weak or /rong4 ,?is makes x evid5t t ^! sub/ances yield :]e !y meet1 & spr+ back3 & = ?is "t mu/ be requir$4 ,n[ 9 apply+ ?is k9d ( movem5t to t :i* produces ,light !re is no?+ to h9d] u f e/imat+ ! p>ticles ( ! e!r to be ( a sub/ance z ne>ly approa*+ to p]fect h>dness & possess+ a spr+9ess z prompt z we *oose4 ,x is n necess>y to exam9e "h ! causes ( ?is h>dness1 or ( t spr+9ess1 ! consid]ation ( :i* w\ld lead u too f> f our subject4 ,i w say1 h[ev]1 9 pass+ t we may conceive t ! p>ticles ( ! e!r1 not)/&+ _! smallness1 are 9 turn compos$ ( o!r p>ts & t _! spr+9ess consi/s 9 ! v rapid movem5t ( a subtle matt] :i* p5etrates !m f e side & con/ra9s _! /ructure to assume su* a disposition z to give to ?is fluid matt] ! mo/ ov]t & easy passage possible4 ,?is accords ) ! explanation :i* ,mr4 ,des ,c>tes gives = ! spr+1 ?\gh ,i d n1 l him1 suppose ! pores to be 9 ! =m ( r\nd holl[ canals4 ,& x mu/ n be ?\ght t 9 ?is !re is any?+ absurd or impossible1 x be+ on ! contr>y q cr$ible t x is ?is inf9ite s]ies ( diff]5t sizes ( corpuscles1 hav+ diff]5t degrees ( velocity1 ( :i* ,nature makes use to produce s _m m>vell\s effects4 ,b ?\gh we %all ignore ! true cause ( spr+9ess we /ill see t !re are _m bodies :i* possess ?is prop]ty2 & ?us !re is no?+ /range 9 suppos+ t x exi/s also 9 little invisible bodies l ! p>ticles ( ! ,e!r4 ,also if "o wi%es to seek = any o!r way 9 :i* ! movem5t ( ,light is successively communicat$1 "o w f9d none :i* agrees bett]1 ) uni=m progression1 z seems to be necess>y1 ?an ! prop]ty ( spr+9ess2 because if ?is movem5t %\ld gr[ sl[] 9 proportion z x is %>$ ov] a great] quantity ( matt]1 9 mov+ away f ! s\rce ( ! light1 x c\ld n cons]ve ?is great velocity ov] great di/ances4 ,b by suppos+ spr+9ess 9 ! e!real matt]1 its p>ticles w h ! prop]ty ( equally rapid re/itution :e!r !y are pu%$ /rongly or feebly2 & ?us ! propagation ( ,light w always g on ) an equal velocity4 ,illu/ration ,& x mu/ be kn[n t al?\gh ! p>ticles ( ! e!r are n rang$ ?us 9 /raight l9es1 z 9 our r[ ( sph]es1 b confus$ly1 s t "o ( !m t\*es sev]al o!rs1 ?is does n h9d] !m f transmitt+ _! movem5t & f spread+ x always =w>d4 ,z to ?is x is to be rem>k$ t !re is a law ( motion s]v+ = ?is propagation1 & v]ifiable by exp]im5t4 ,x is t :5 a sph]e1 su* z ,a "h1 t\*es sev]al o!r simil> sph]es ,,ccc1 if x is /ruck by ano!r sph]e ,b 9 su* a way z to ex]t an impulse aga9/ all ! sph]es ,,ccc :i* t\* x1 x transmits to !m ! :ole ( its movem5t1 & rema9s aft] t motionless l ! sph]e ,b4 ,& )\t suppos+ t ! e!real p>ticles are ( sph]ical =m 7= ,i see inde$ no ne$ to suppose !m s7 "o may well und]/& t ?is prop]ty ( communicat+ an impulse does n fail to contribute to ! a=esaid propagation ( movem5t4 ,equality ( size seems to be m necess>y1 because o!rwise !re ought to be "s reflexion ( movem5t backw>ds :5 x passes f a small] p>ticle to a l>g] "o1 accord+ to ! ,laws ( ,p]cussion :i* ,i publi%$ "s ye>s ago4 ,h[ev]1 "o w see h]eaft] t we h to suppose su* an equality n s mu* z a necessity = ! propagation ( light z = r5d]+ t propagation easi] & m p[]ful2 = x is n beyond ! limits ( probability t ! p>ticles ( ! e!r h be5 made equal = a purpose s important z t ( light1 at lea/ 9 t va/ space :i* is beyond ! region ( atmosph]e & :i* seems to s]ve only to transmit ! light ( ! ,sun & ! ,/>s4 ,i h !n %[n 9 :at mann] "o may conceive ,light to spread successively1 by sph]ical waves1 & h[ x is possible t ?is spread+ is accompli%$ ) z great a velocity z t :i* exp]im5ts & cele/ial obs]vations dem&4 ,:5ce x may be fur!r rem>k$ t al?\gh ! p>ticles are suppos$ to be 9 cont9ual movem5t 7= !re are _m reasons = ?is7 ! successive propagation ( ! waves _c be h9d]$ by ?is2 because ! propagation consi/s n[ise 9 ! transport ( ^? p>ticles b m]ely 9 a small agitation :i* !y _c help communicat+ to ^? surr\nd+1 not)/&+ any movem5t :i* may act on !m caus+ !m to be *ang+ positions among/ !mselves4 ,b we mu/ consid] /ill m p>ticul>ly ! orig9 ( ^! waves1 & ! mann] 9 :i* !y spread4 ,&1 fir/1 x foll[s f :at has be5 said on ! production ( ,light1 t ea* little region ( a lum9\s body1 su* z ! ,sun1 a c&le1 or a burn+ coal1 g5]ates its own waves ( :i* t region is ! c5tre4 ,?us 9 ! flame ( a c&le1 hav+ di/+ui%$ ! po9ts ,a1 ,b1 ,c1 conc5tric circles describ$ ab\t ea* ( ^! po9ts repres5t ! waves :i* come f !m4 ,& "o mu/ imag9e ! same ab\t e po9t ( ! surface & ( ! "p )9 ! flame4 ,illu/ration ,b z ! p]cussions at ! c5tres ( ^! waves possess no regul> succession1 x mu/ n be suppos$ t ! waves !mselves foll[ "o ano!r at equal di/ances3 & if ! di/ances m>k$ 9 ! figure appe> to be su*1 x is r to m>k ! progression ( "o & ! same wave at equal int]vals ( "t ?an to repres5t sev]al ( !m issu+ f "o & ! same c5tre4 ,aft] all1 ?is prodigi\s quantity ( waves :i* trav]se "o ano!r )\t confusion & )\t effac+ "o ano!r mu/ n be deem$ inconceivable2 x be+ c]ta9 t "o & ! same p>ticle ( matt] c s]ve = _m waves com+ f diff]5t sides or ev5 f contr>y directions1 n only if x is /ruck by bl[s :i* foll[ "o ano!r closely b ev5 = ^? :i* act on x at ! same in/ant4 ,x c d s because ! spread+ ( ! movem5t is successive4 ,?is may be prov$ by ! r[ ( equal sph]es ( h>d matt]1 spok5 ( above4 ,if aga9/ ?is r[ !re are pu%$ f two opposite sides at ! same "t two simil> sph]es ,a & ,d1 "o w see ea* ( !m reb\nd ) ! same velocity :i* x _h 9 /rik+1 yet ! :ole r[ w rema9 9 its place1 al?\gh ! movem5t has pass$ along its :ole l5g? twice ov]4 ,& if ^! contr>y movem5ts happ5 to meet "o ano!r at ! middle sph]e1 ,b1 or at "s o!r su* z ,c1 t sph]e w yield & act z a spr+ at bo? sides1 & s w s]ve at ! same in/ant to transmit ^! two movem5ts4 ,illu/ration ,b :at may at fir/ appe> full /range & ev5 incr$ible is t ! undulations produc$ by su* small movem5ts & corpuscles1 %\ld spread to su* imm5se di/ances2 z = example f ! ,sun or f ! ,/>s to u4 ,= ! =ce ( ^! waves mu/ gr[ feeble 9 proportion z !y move away f _! orig91 s t ! action ( ea* "o 9 p>ticul> w )\t d\bt become incapable ( mak+ itself felt to our sight4 ,b "o w cease to be a/oni%$ by consid]+ h[ at a great di/ance f ! lum9\s body an inf9itude ( waves1 ?\gh !y h issu$ f diff]5t po9ts ( ?is body1 unite toge!r 9 su* a way t !y s5sibly compose "o s+le wave only1 :i*1 consequ5tly1 ought to h en\gh =ce to make itself felt4 ,?us ?is inf9ite numb] ( waves :i* orig9ate at ! same in/ant f all po9ts ( a fix$ />1 big x may be z ! ,sun1 make practically only "o s+le wave :i* may well h =ce en\gh to produce an impression on our eyes4 ,moreov] f ea* lum9\s po9t !re may come _m ?\s&s ( waves 9 ! smalle/ imag9able "t1 by ! frequ5t p]cussion ( ! corpuscles :i* /rike ! ,e!r at ^! po9ts3 :i* fur!r contributes to r5d]+ _! action m s5sible4 ,illu/ration ,!re is ! fur!r consid]ation 9 ! emanation ( ^! waves1 t ea* p>ticle ( matt] 9 :i* a wave spreads1 ought n to communicate its motion only to ! next p>ticle :i* is 9 ! /raight l9e drawn f ! lum9\s po9t1 b t x also imp>ts "s ( x necess>ily to all ! o!rs :i* t\* x & :i* oppose !mselves to its movem5t4 ,s x arises t ar\nd ea* p>ticle !re is made a wave ( :i* t p>ticle is ! c5tre4 ,?us if ,,dcf is a wave emanat+ f ! lum9\s po9t ,a1 :i* is its c5tre1 ! p>ticle ,b1 "o ( ^? compris$ )9 ! sph]e ,,dcf1 w h made its p>ticul> or p>tial wave ,,kcl1 :i* w t\* ! wave ,,dcf at ,c at ! same mom5t t ! pr9cipal wave emanat+ f ! po9t ,a has arriv$ at ,,dcf2 & x is cle> t x w be only ! region ,c ( ! wave ,,kcl :i* w t\* ! wave ,,dcf1 to wit1 t :i* is 9 ! /raight l9e drawn ?r\gh ,,ab4 ,simil>ly ! o!r p>ticles ( ! sph]e ,,dcf1 su* z bb1 dd1 etc41 w ea* make its own wave4 ,b ea* ( ^! waves c be inf9itely feeble only z comp>$ ) ! wave ,,dcf1 to ! composition ( :i* all ! o!rs contribute by ! "p ( _! surface :i* is mo/ di/ant f ! c5tre ,a4 ,"o sees1 9 addition1 t ! wave ,,dcf is det]m9$ by ! di/ance atta9$ 9 a c]ta9 space ( "t by ! movem5t :i* />t$ f ! po9t ,a2 !re be+ no movem5t beyond ?is wave1 ?\gh !re w be 9 ! space :i* x encloses1 namely 9 p>ts ( ! p>ticul> waves1 ^? p>ts :i* d n t\* ! sph]e ,,dcf4 ,& all ?is ought n to seem fraught ) too mu* m9ut5ess or subtlety1 s9ce we %all see 9 ! sequel t all ! prop]ties ( ,light1 & ev]y?+ p]ta9+ to its reflexion & its refraction1 c be expla9$ 9 pr9ciple by ?is means4 ,?is is a matt] :i* has be5 q unkn[n to ^? :o hi!rto h begun to consid] ! waves ( light1 among/ :om are ,mr4 ,hooke 9 8 ,micrographia1 & ,fa!r ,p>dies1 :o1 9 a treatise ( :i* he let me see a portion1 & :i* he 0 unable to complete z he di$ %ortly aft]w>d1 _h und]tak5 to prove by ^! waves ! effects ( reflexion & refraction4 ,b ! *ief f\ndation1 :i* consi/s 9 ! rem>k ,i h j made1 0 lack+ 9 8 demon/rations2 & = ! re/ he _h op9ions v diff]5t f m9e1 z may be w appe> "s day if 8 writ+ has be5 pres]v$4 ,to come to ! prop]ties ( ,light4 ,we rem>k fir/ t ea* portion ( a wave ought to spread 9 su* a way t its extremities lie always betwe5 ! same /raight l9es drawn f ! lum9\s po9t4 ,?us ! portion ,,bg ( ! wave1 hav+ ! lum9\s po9t ,a z its c5tre1 w spread into ! arc ,,ce b\nd$ by ! /raight l9es ,,abc1 ,,age4 ,= al?\gh ! p>ticul> waves produc$ by ! p>ticles compris$ )9 ! space ,,cae spread also outside ?is space1 !y yet d n concur at ! same in/ant to compose a wave :i* t]m9ates ! movem5t1 z !y d precisely at ! circumf]5ce ,,ce1 :i* is _! common tang5t4 ,& h5ce "o sees ! reason :y light1 at lea/ if its rays are n reflect$ or brok51 spreads only by /raight l9es1 s t x illum9ates no object except :5 ! pa? f its s\rce to t object is op5 along su* l9es4 ,= if1 = example1 !re 7 an op5+ ,,bg1 limit$ by opaque bodies ,,bh1 ,,gi1 ! wave ( light :i* issues f ! po9t ,a w always be t]m9at$ by ! /raight l9es ,,ac1 ,,ae1 z has j be5 %[n2 ! p>ts ( ! p>tial waves :i* spread outside ! space ,,ace be+ too feeble to produce light !re4 ,n[1 h[ev] small we make ! op5+ ,,bg1 !re is always ! same reason caus+ ! light !re to pass betwe5 /raight l9es2 s9ce ?is op5+ is always l>ge en\gh to conta9 a great numb] ( p>ticles ( ! e!real matt]1 :i* are ( an inconceivable smallness2 s t x appe>s t ea* little portion ( ! wave necess>ily advances foll[+ ! /raight l9e :i* comes f ! lum9\s po9t4 ,?us !n we may take ! rays ( light z if !y 7 /raight l9es4 ,x appe>s1 moreov]1 by :at has be5 rem>k$ t\*+ ! feebl5ess ( ! p>ticul> waves1 t x is n ne$ful t all ! p>ticles ( ! ,e!r %\ld be equal among/ !mselves1 ?\gh equality is m apt = ! propagation ( ! movem5t4 ,= x is true t inequality w cause a p>ticle by pu%+ aga9/ ano!r l>g] "o to /rive to recoil ) a "p ( its movem5t2 b x w !reby m]ely g5]ate backw>ds t[>ds ! lum9\s po9t "s p>tial waves incapable ( caus+ light1 & n a wave comp\nd$ ( _m z ,,ce 04 ,ano!r prop]ty ( waves ( light1 & "o ( ! mo/ m>vell\s1 is t :5 "s ( !m come f diff]5t or ev5 f oppos+ sides1 !y produce _! effect across "o ano!r )\t any h9drance4 ,:5ce also x comes ab\t t a numb] ( spectators may view diff]5t objects at ! same "t ?r\gh ! same op5+1 & t two p]sons c at ! same "t see "o ano!r's eyes4 ,n[ accord+ to ! explanation :i* has be5 giv5 ( ! action ( light1 h[ ! waves d n de/roy nor int]rupt "o ano!r :5 !y cross "o ano!r1 ^! effects :i* ,i h j m5tion$ are easily conceiv$4 ,b 9 my judgem5t !y are n at all easy to expla9 accord+ to ! views ( ,mr4 ,des ,c>tes1 :o makes ,light to consi/ 9 a cont9u\s pressure m]ely t5d+ to movem5t4 ,= ?is pressure n be+ able to act f two opposite sides at ! same "t1 aga9/ bodies :i* h no incl9ation to approa* "o ano!r1 x is impossible s to und]/& :at ,i h be5 say+ ab\t two p]sons mutually see+ "o ano!r's eyes1 or h[ two tor*es c illum9ate "o ano!r4 ,,*apt] ,,ii ,,on ,,reflexion ,hav+ expla9$ ! effects ( waves ( light :i* spread 9 a homog5e\s matt]1 we w exam9e next t :i* happ5s to !m on enc\nt]+ o!r bodies4 ,we w fir/ make evid5t h[ ! ,reflexion ( light is expla9$ by ^! same waves1 & :y x pres]ves equality ( angles4 ,let !re be a surface ,,ab2 plane & poli%$1 ( "s metal1 glass1 or o!r body1 :i* at fir/ ,i w consid] z p]fectly uni=m 7res]v+ to myself to deal at ! end ( ?is demon/ration ) ! inequalities f :i* x _c be exempt71 & let a l9e ,,ac1 incl9$ to ,,ad1 repres5t a portion ( a wave ( light1 ! c5tre ( :i* is s di/ant t ?is portion ,,ac may be consid]$ z a /raight l9e2 = ,i consid] all ?is z 9 "o plane1 imag9+ to myself t ! plane 9 :i* ?is figure is1 cuts ! sph]e ( ! wave ?r\gh its c5tre & int]sects ! plane ,,ab at "r angles4 ,?is explanation w suffice once = all4 ,illu/ration ,! piece ,c ( ! wave ,,ac1 w 9 a c]ta9 space ( "t advance z f> z ! plane ,,ab at ,b1 foll[+ ! /raight l9e ,,cb1 :i* may be suppos$ to come f ! lum9\s c5tre1 & :i* 9 consequ5ce is p]p5dicul> to ,,ac4 ,n[ 9 ?is same space ( "t ! portion ,a ( ! same wave1 :i* has be5 h9d]$ f communicat+ its movem5t beyond ! plane ,,ab1 or at lea/ p>tly s1 ought to h cont9u$ its movem5t 9 ! matt] :i* is above ?is plane1 & ?is along a di/ance equal to ,,cb1 mak+ its own p>tial sph]ical wave1 accord+ to :at has be5 said above4 ,:i* wave is "h repres5t$ by ! circumf]5ce ,,snr1 ! c5tre ( :i* is ,a1 & its semi-diamet] ,,an equal to ,,cb4 ,if "o consid]s fur!r ! o!r pieces ,h ( ! wave ,,ac1 x appe>s t !y w n only h rea*$ ! surface ,,ab by /raight l9es ,,hk p>allel to ,,cb1 b t 9 addition !y w h g5]at$ 9 ! transp>5t air1 f ! c5tres ,k1 ,k1 ,k1 p>ticul> sph]ical waves1 repres5t$ "h by circumf]5ces ! semi-diamet]s ( :i* are equal to ,,km1 t is to say to ! cont9uations ( ,,hk z f> z ! l9e ,,bg p>allel to ,,ac4 ,b all ^! circumf]5ces h z a common tang5t ! /raight l9e ,,bn1 namely ! same :i* is drawn f ,b z a tang5t to ! fir/ ( ! circles1 ( :i* ,a is ! c5tre1 & ,,an ! semi-diamet] equal to ,,bc1 z is easy to see4 ,x is !n ! l9e ,,bn 7compris$ betwe5 ,b & ! po9t ,n :]e ! p]p5dicul> f ! po9t ,a falls7 :i* is z x 7 =m$ by all ^! circumf]5ces1 & :i* t]m9ates ! movem5t :i* is made by ! reflexion ( ! wave ,,ac2 & x is also ! place :]e ! movem5t occurs 9 mu* great] quantity ?an any:]e else4 ,:]e=e1 accord+ to t :i* has be5 expla9$1 ,,bn is ! propagation ( ! wave ,,ac at ! mom5t :5 ! piece ,c ( x has arriv$ at ,b4 ,= !re is no o!r l9e :i* l ,,bn is a common tang5t to all ! a=esaid circles1 except ,,bg bel[ ! plane ,,ab2 :i* l9e ,,bg w\ld be ! propagation ( ! wave if ! movem5t c\ld h spread 9 a m$ium homog5e\s ) t :i* is above ! plane4 ,& if "o wi%es to see h[ ! wave ,,ac has come successively to ,,bn1 "o has only to draw 9 ! same figure ! /raight l9es ,,ko p>allel to ,,bn1 & ! /raight l9es ,,kl p>allel to ,,ac4 ,?us "o w see t ! /raight wave ,,ac has become brok5 up into all ! ,,okl p>ts successively1 & t x has become /raight aga9 at ,,nb4 ,n[ x is app>5t "h t ! angle ( reflexion is made equal to ! angle ( incid5ce4 ,= ! triangles ,,acb1 ,,bna be+ rectangul> & hav+ ! side ,,ab common1 & ! side ,,cb equal to ,,na1 x foll[s t ! angles opposite to ^! sides w be equal1 & !re=e also ! angles ,,cba1 ,,nab4 ,b z ,,cb1 p]p5dicul> to ,,ca1 m>ks ! direction ( ! incid5t ray1 s ,,an1 p]p5dicul> to ! wave ,,bn1 m>ks ! direction ( ! reflect$ ray2 h5ce ^! rays are equally incl9$ to ! plane ,,ab4 ,b 9 consid]+ ! prec$+ demon/ration1 "o might av] t x is inde$ true t ,,bn is ! common tang5t ( ! circul> waves 9 ! plane ( ?is figure1 b t ^! waves1 be+ 9 tru? sph]ical1 h /ill an inf9itude ( simil> tang5ts1 namely all ! /raight l9es :i* are drawn f ! po9t ,b 9 ! surface g5]at$ by ! /raight l9e ,,bn ab\t ! axis ,,ba4 ,x rema9s1 !re=e1 to demon/rate t !re is no difficulty h]e93 & by ! same argum5t "o w see :y ! incid5t ray & ! reflect$ ray are always 9 "o & ! same plane p]p5dicul> to ! reflect+ plane4 ,i say !n t ! wave ,,ac1 be+ reg>d$ only z a l9e1 produces no light4 ,= a visible ray ( light1 h[ev] n>r[ x may be1 has always "s wid?1 & consequ5tly x is necess>y1 9 repres5t+ ! wave ^: progression con/itutes ! ray1 to put in/ead ( a l9e ,,ac "s plane figure su* z ! circle ,,hc 9 ! foll[+ figure1 by suppos+1 z we h done1 ! lum9\s po9t to be inf9itely di/ant4 ,n[ x is easy to see1 foll[+ ! prec$+ demon/ration1 t ea* small piece ( ?is wave ,,hc hav+ arriv$ at ! plane ,,ab1 & !re g5]at+ ea* "o its p>ticul> wave1 ^! w all h1 :5 ,c arrives at ,b1 a common plane :i* w t\* !m1 namely a circle ,,bn simil> to ,,*2 & ?is w be int]sect$ at its middle & at "r angles by ! same plane :i* likewise int]sects ! circle ,,* & ! ellipse ,,ab4 ,illu/ration ,"o sees also t ! said sph]es ( ! p>tial waves _c h any common tang5t plane o!r ?an ! circle ,,bn2 s t x w be ?is plane :]e !re w be m reflect$ movem5t ?an any:]e else1 & :i* w !re=e c>ry on ! light 9 cont9uance f ! wave ,,*4 ,i h also /at$ 9 ! prec$+ demon/ration t ! movem5t ( ! piece ,a ( ! incid5t wave is n able to communicate itself beyond ! plane ,,ab1 or at lea/ n :olly4 ,:5ce x is to be rem>k$ t ?\gh ! movem5t ( ! e!real matt] might communicate itself p>tly to t ( ! reflect+ body1 ?is c\ld 9 no?+ alt] ! velocity ( progression ( ! waves1 on :i* ! angle ( reflexion dep5ds4 ,= a slight p]cussion ought to g5]ate waves z rapid z /rong p]cussion 9 ! same matt]4 ,?is comes ab\t f ! prop]ty ( bodies :i* act z spr+s1 ( :i* we h spok5 above2 namely t :e!r compress$ little or mu* !y recoil 9 equal times4 ,equally s 9 e reflexion ( ! light1 aga9/ :atev] body x may be1 ! angles ( reflexion & incid5ce ought to be equal not)/&+ t ! body might be ( su* a nature t x takes away a portion ( ! movem5t made by ! incid5t light4 ,& exp]im5t %[s t 9 fact !re is no poli%$ body ! reflexion ( :i* does n foll[ ?is rule4 ,b ! ?+ to be above all rem>k$ 9 our demon/ration is t x does n require t ! reflect+ surface %\ld be consid]$ z a uni=m plane1 z has be5 suppos$ by all ^? :o h tri$ to expla9 ! effects ( reflexion2 b only an ev5ness su* z may be atta9$ by ! p>ticles ( ! matt] ( ! reflect+ body be+ set ne> to "o ano!r2 :i* p>ticles are l>g] ?an ^? ( ! e!real matt]1 z w appe> by :at we %all say 9 treat+ ( ! transp>5cy & opacity ( bodies4 ,= ! surface consi/+ ?us ( p>ticles put toge!r1 & ! e!real p>ticles be+ above1 & small]1 x is evid5t t "o c\ld n demon/rate ! equality ( ! angles ( incid5ce & reflexion by similitude to t :i* happ5s to a ball ?r[n aga9/ a wall1 ( :i* writ]s h always made use4 ,9 our way1 on ! o!r h&1 ! ?+ is expla9$ )\t difficulty4 ,= ! smallness ( ! p>ticles ( quicksilv]1 = example1 be+ su* t "o mu/ conceive millions ( !m1 9 ! smalle/ visible surface propos$1 arrang$ l a heap ( gra9s ( s& :i* has be5 flatt5$ z mu* z x is capable ( be+1 ?is surface !n becomes = our purpose z ev5 z a poli%$ glass is3 &1 al?\gh x always rema9s r\gh ) respect to ! p>ticles ( ! ,e!r x is evid5t t ! c5tres ( all ! p>ticul> sph]es ( reflexion1 ( :i* we h spok51 are almo/ 9 "o uni=m plane1 & t ?us ! common tang5t c fit to !m z p]fectly z is requisite = ! production ( light4 ,& ?is alone is requisite1 9 our me?od ( demon/ration1 to cause equality ( ! said angles )\t ! rema9d] ( ! movem5t reflect$ f all p>ts be+ able to produce any contr>y effect4 ,,*apt] ,,iii ,,on ,,refraction ,9 ! same way z ! effects ( ,reflexion h be5 expla9$ by waves ( light reflect$ at ! surface ( poli%$ bodies1 we w expla9 transp>5cy & ! ph5om5a ( refraction by waves :i* spread )9 & across diaphan\s bodies1 bo? solids1 su* z glass1 & liquids1 su* z wat]1 oils1 etc4 ,b 9 ord] t x may n seem /range to suppose ?is passage ( waves 9 ! int]ior ( ^! bodies1 ,i w fir/ %[ t "o may conceive x possible 9 m ?an "o mode4 ,fir/1 !n1 if ! e!real matt] _c p5etrate transp>5t bodies at all1 _! own p>ticles w\ld be able to communicate successively ! movem5t ( ! waves1 ! same z d ^? ( ! ,e!r1 suppos+ t1 l ^?1 !y are ( a nature to act z a spr+4 ,& ?is is easy to conceive z reg>ds wat] & o!r transp>5t liquids1 !y be+ compos$ ( deta*$ p>ticles4 ,b x may seem m difficult z reg>ds glass & o!r transp>5t & h>d bodies1 because _! solidity does n seem to p]mit !m to receive movem5t except 9 _! :ole mass at ! same "t4 ,?is1 h[ev]1 is n necess>y because ?is solidity is n su* z x appe>s to u1 x be+ probable r t ^! bodies are compos$ ( p>ticles m]ely plac$ close to "o ano!r & held toge!r by "s pressure f )\t ( "s o!r matt]1 & by ! irregul>ity ( _! %apes4 ,= prim>ily _! r>ity is %[n by ! facility ) :i* !re passes ?r\gh !m ! matt] ( ! vortices ( ! magnet1 & t :i* causes gravity4 ,fur!r1 "o _c say t ^! bodies are ( a texture simil> to t ( a sponge or ( light bread1 because ! heat ( ! fire makes !m fl[ & !reby *anges ! situation ( ! p>ticles among/ !mselves4 ,x rema9s !n t !y are1 z has be5 said1 assemblages ( p>ticles :i* t\* "o ano!r )\t con/itut+ a cont9u\s solid4 ,?is be+ s1 ! movem5t :i* ^! p>ticles receive to c>ry on ! waves ( light1 be+ m]ely communicat$ f "s ( !m to o!rs1 )\t _! go+ = t purpose out ( _! places or )\t d]angem5t1 x may v well produce its effect )\t prejudic+ 9 any way ! app>5t solidity ( ! comp\nd4 ,by pressure f )\t1 ( :i* ,i h spok51 mu/ n be und]/ood t ( ! air1 :i* w\ld n be suffici5t1 b t ( "s o!r m subtle matt]1 a pressure :i* ,i *anc$ ^u by exp]im5t long ago1 namely 9 ! case ( wat] fre$ f air1 :i* rema9s susp5d$ 9 a tube op5 at its l[] end1 not)/&+ t ! air has be5 remov$ f ! vessel 9 :i* ?is tube is enclos$4 ,"o c !n 9 ?is way conceive ( transp>5cy 9 a solid )\t any necessity t ! e!real matt] :i* s]ves = light %\ld pass ?r\gh x1 or t x %\ld f9d pores 9 :i* to ins9uate itself4 ,b ! tru? is t ?is matt] n only passes ?r\gh solids1 b does s ev5 ) great facility2 ( :i* ! exp]im5t ( ,torricelli1 above cit$1 is already a pro(4 ,because on ! quicksilv] & ! wat] quitt+ ! upp] "p ( ! glass tube1 x appe>s t x is imm$iately fill$ ) e!real matt]1 s9ce light passes across x4 ,b "h is ano!r argum5t :i* proves ?is ready p5etrability1 n only 9 transp>5t bodies b also 9 all o!rs4 ,:5 light passes across a holl[ sph]e ( glass1 clos$ on all sides1 x is c]ta9 t x is full ( e!real matt]1 z mu* z ! spaces outside ! sph]e4 ,& ?is e!real matt]1 z has be5 %[n above1 consi/s ( p>ticles :i* j t\* "o ano!r4 ,if !n x 7 enclos$ 9 ! sph]e 9 su* a way t x c\ld n get out ?r\gh ! pores ( ! glass1 x w\ld be oblig$ to foll[ ! movem5t ( ! sph]e :5 "o *anges its place3 & x w\ld require consequ5tly almo/ ! same =ce to impress a c]ta9 velocity on ?is sph]e1 :5 plac$ on a horizontal plane1 z if x 7 full ( wat] or p]haps ( quicksilv]3 because e body resi/s ! velocity ( ! motion :i* "o w\ld give to x1 9 proportion to ! quantity ( matt] :i* x conta9s1 & :i* is oblig$ to foll[ ?is motion4 ,b on ! contr>y "o f9ds t ! sph]e resi/s ! impress ( movem5t only 9 proportion to ! quantity ( matt] ( ! glass ( :i* x is made4 ,!n x mu/ be t ! e!real matt] :i* is inside is n %ut up1 b fl[s ?r\gh x ) v great fre$om4 ,we %all demon/rate h]eaft] t by ?is process ! same p5etrability may be inf]r$ also z relat+ to opaque bodies4 ,! second mode !n ( expla9+ transp>5cy1 & "o :i* appe>s m probably true1 is by say+ t ! waves ( light are c>ri$ on 9 ! e!real matt]1 :i* cont9u\sly occupies ! int]/ices or pores ( transp>5t bodies4 ,= s9ce x passes ?r\gh !m cont9u\sly & freely1 x foll[s t !y are always full ( x4 ,& "o may ev5 %[ t ^! int]/ices occupy mu* m space ?an ! coh]5t p>ticles :i* con/itute ! bodies4 ,= if :at we h j said is true3 t =ce is requir$ to impress a c]ta9 horizontal velocity on bodies 9 proportion z !y conta9 coh]5t matt]2 & if ! proportion ( ?is =ce foll[s ! law ( weights1 z is confirm$ by exp]im5t1 !n ! quantity ( ! con/itu5t matt] ( bodies also foll[s ! proportion ( _! weights4 ,n[ we see t wat] weighs only "o f\rte5? "p z mu* z an equal portion ( quicksilv]3 !re=e ! matt] ( ! wat] does n occupy ! f\rte5? "p ( ! space :i* its mass obta9s4 ,x mu/ ev5 occupy mu* less ( x1 s9ce quicksilv] is less heavy ?an gold1 & ! matt] ( gold is by no means d5se1 z foll[s f ! fact t ! matt] ( ! vortices ( ! magnet & ( t :i* is ! cause ( gravity pass v freely ?r\gh x4 ,b x may be object$ "h t if wat] is a body ( s great r>ity1 & if its p>ticles occupy s small a portion ( ! space ( its app>5t bulk1 x is v /range h[ x yet resi/s ,compression s /rongly )\t p]mitt+ itself to be cond5s$ by any =ce :i* "o has hi!rto essay$ to employ1 pres]v+ ev5 its entire liquidity :ile subject$ to ?is pressure4 ,?is is no small difficulty4 ,x may1 h[ev]1 be resolv$ by say+ t ! v viol5t & rapid motion ( ! subtle matt] :i* r5d]s wat] liquid1 by agitat+ ! p>ticles ( :i* x is compos$1 ma9ta9s ?is liquidity 9 spite ( ! pressure :i* hi!rto any "o has be5 m9d$ to apply to x4 ,! r>ity ( transp>5t bodies be+ !n su* z we h said1 "o easily conceives t ! waves might be c>ri$ on 9 ! e!real matt] :i* fills ! int]/ices ( ! p>ticles4 ,&1 moreov]1 "o may believe t ! progression ( ^! waves ought to be a little sl[] 9 ! int]ior ( bodies1 by reason ( ! small det\rs :i* ! same p>ticles cause4 ,9 :i* diff]5t velocity ( light ,i %all %[ ! cause ( refraction to consi/4 ,be=e do+ s1 ,i w indicate ! ?ird & la/ mode 9 :i* transp>5cy may be conceiv$2 :i* is by suppos+ t ! movem5t ( ! waves ( light is transmitt$ indiff]5tly bo? 9 ! p>ticles ( ! e!real matt] :i* occupy ! int]/ices ( bodies1 & 9 ! p>ticles :i* compose !m1 s t ! movem5t passes f "o to ! o!r4 ,& x w be se5 h]eaft] t ?is hypo!sis s]ves excell5tly to expla9 ! d\ble refraction ( c]ta9 transp>5t bodies4 ,%\ld x be object$ t if ! p>ticles ( ! e!r are small] ?an ^? ( transp>5t bodies 7s9ce !y pass ?r\gh _! int]vals71 x w\ld foll[ t !y c communicate to !m b little ( _! movem5t1 x may be repli$ t ! p>ticles ( ^! bodies are 9 turn compos$ ( /ill small] p>ticles1 & s x w be ^! second>y p>ticles :i* w receive ! movem5t f ^? ( ! e!r4 ,fur!rmore1 if ! p>ticles ( transp>5t bodies h a recoil a little less prompt ?an t ( ! e!real p>ticles1 :i* no?+ h9d]s u f suppos+1 x w aga9 foll[ t ! progression ( ! waves ( light w be sl[] 9 ! int]ior ( su* bodies ?an x is outside 9 ! e!real matt]4 ,all ?is ,i h f\nd z mo/ probable = ! mode 9 :i* ! waves ( light pass across transp>5t bodies4 ,to :i* x mu/ fur!r be add$ 9 :at respect ^! bodies diff] f ^? :i* are opaque2 & ! m s s9ce x might seem because ( ! easy p5etration ( bodies by ! e!real matt]1 ( :i* m5tion has be5 made1 t !re w\ld n be any body t 0 n transp>5t4 ,= by ! same reason+ ab\t ! holl[ sph]e :i* ,i h employ$ to prove ! smallness ( ! d5sity ( glass & its easy p5etrability by ! e!real matt]1 "o might also prove t ! same p5etrability obta9s = metals & = e o!r sort ( body4 ,= ?is sph]e be+ = example ( silv]1 x is c]ta9 t x conta9s "s ( ! e!real matt] :i* s]ves = light1 s9ce ?is 0 !re z well z 9 ! air :5 ! op5+ ( ! sph]e 0 clos$4 ,yet1 be+ clos$ & plac$ ^u a horizontal plane1 x resi/s ! movem5t :i* "o wi%es to give to x1 m]ely accord+ to ! quantity ( silv] ( :i* x is made2 s t "o mu/ conclude1 z above1 t ! e!real matt] :i* is enclos$ does n foll[ ! movem5t ( ! sph]e2 & t !re=e silv]1 z well z glass1 is v easily p5etrat$ by ?is matt]4 ,"s ( x is !re=e pres5t cont9u\sly & 9 quantities betwe5 ! p>ticles ( silv] & ( all o!r opaque bodies3 & s9ce x s]ves = ! propagation ( light x w\ld seem t ^! bodies ought also to be transp>5t1 :i* h[ev] is n ! case4 ,:5ce !n1 "o w say1 does _! opacity come8 ,is x because ! p>ticles :i* compose !m are s(t2 t is to say1 ^! p>ticles be+ compos$ ( o!rs t are small]1 are !y capable ( *ang+ _! figure on receiv+ ! pressure ( ! e!real p>ticles1 ! motion ( :i* !y !reby damp1 & s h9d] ! cont9uance ( ! waves ( light8 ,t _c be3 = if ! p>ticles ( ! metals are s(t1 h[ is x t poli%$ silv] & m]cury reflect light s /rongly8 ,:at ,i f9d to be mo/ probable h]e91 is to say t metallic bodies1 :i* are almo/ ! only really opaque ones1 h mix$ among/ _! h>d p>ticles "s s(t ones2 s t "s s]ve to cause reflexion & ! o!rs to h9d] transp>5cy2 :ile1 on ! o!r h&1 transp>5t bodies conta9 only h>d p>ticles :i* h ! faculty ( recoil1 & s]ve toge!r ) ^? ( ! e!real matt] = ! propagation ( ! waves ( light1 z has be5 said4 ,illu/ration ,let u pass n[ to ! explanation ( ! effects ( ,refraction1 assum+1 z we h done1 ! passage ( waves ( light ?r\gh transp>5t bodies1 & ! dim9ution ( velocity :i* ^! same waves suff] 9 !m4 ,! *ief prop]ty ( ,refraction is t a ray ( light1 su* z ,,ab1 be+ 9 ! air1 & fall+ obliquely ^u ! poli%$ surface ( a transp>5t body1 su* z ,,fg1 is brok5 at ! po9t ( incid5ce ,b1 9 su* a way t ) ! /raight l9e ,,dbe :i* cuts ! surface p]p5dicul>ly x makes an angle ,,cbe less ?an ,,abd :i* x made ) ! same p]p5dicul> :5 9 ! air4 ,& ! measure ( ^! angles is f\nd by describ+1 ab\t ! po9t ,b1 a circle :i* cuts ! radii ,,ab1 ,,bc4 ,= ! p]p5dicul>s ,,ad1 ,,ce1 let fall f ! po9ts ( int]section ^u ! /raight l9e ,,de1 :i* are call$ ! ,s9es ( ! angles ,,abd1 ,,cbe1 h a c]ta9 ratio betwe5 !mselves2 :i* ratio is always ! same = all incl9ations ( ! incid5t ray1 at lea/ = a giv5 transp>5t body4 ,?is ratio is1 9 glass1 v ne>ly z #c to #b2 & 9 wat] v ne>ly z #d to #c2 & is likewise diff]5t 9 o!r diaphan\s bodies4 ,ano!r prop]ty1 simil> to ?is1 is t ! refractions are reciprocal betwe5 ! rays ent]+ into a transp>5t body & ^? :i* are leav+ x4 ,t is to say t if ! ray ,,ab 9 ent]+ ! transp>5t body is refract$ into ,,bc1 !n likewise ,,cb be+ tak5 z a ray 9 ! int]ior ( ?is body w be refract$1 on pass+ out1 into ,,ba4 ,illu/ration ,to expla9 !n ! reasons ( ^! ph5om5a accord+ to our pr9ciples1 let ,,ab be ! /raight l9e :i* repres5ts a plane surface b\nd+ ! transp>5t sub/ances :i* lie t[>ds ,c & t[>ds ,n4 ,:5 ,i say plane1 t does n signify a p]fect ev5ness1 b su* z has be5 und]/ood 9 treat+ ( reflexion1 & = ! same reason4 ,let ! l9e ,,ac repres5t a portion ( a wave ( light1 ! c5tre ( :i* is suppos$ s di/ant t ?is portion may be consid]$ z a /raight l9e4 ,! piece ,c1 !n1 ( ! wave ,,ac1 w 9 a c]ta9 space ( "t h advanc$ z f> z ! plane ,,ab foll[+ ! /raight l9e ,,cb1 :i* may be imag9$ z com+ f ! lum9\s c5tre1 & :i* consequ5tly w cut ,,ac at "r angles4 ,n[ 9 ! same "t ! piece ,a w\ld h come to ,g along ! /raight l9e ,,ag1 equal & p>allel to ,,cb2 & all ! portion ( wave ,,ac w\ld be at ,,gb if ! matt] ( ! transp>5t body transmitt$ ! movem5t ( ! wave z quickly z ! matt] ( ! ,e!r4 ,b let u suppose t x transmits ?is movem5t less quickly1 by "o-?ird1 = in/ance4 ,movem5t w !n be spread f ! po9t ,a1 9 ! matt] ( ! transp>5t body ?r\gh a di/ance equal to two-?irds ( ,,cb1 mak+ its own p>ticul> sph]ical wave accord+ to :at has be5 said be=e4 ,?is wave is !n repres5t$ by ! circumf]5ce ,,snr1 ! c5tre ( :i* is ,a1 & its semi-diamet] equal to two-?irds ( ,,cb4 ,!n if "o consid]s 9 ord] ! o!r pieces ,h ( ! wave ,,ac1 x appe>s t 9 ! same "t t ! piece ,c rea*es ,b !y w n only h arriv$ at ! surface ,,ab along ! /raight l9es ,,hk p>allel to ,,cb1 b t1 9 addition1 !y w h g5]at$ 9 ! diaphan\s sub/ance f ! c5tres ,k1 p>tial waves1 repres5t$ "h by circumf]5ces ! semi-diamet]s ( :i* are equal to two-?irds ( ! l9es ,,km1 t is to say1 to two-?irds ( ! prolongations ( ,,hk d[n to ! /raight l9e ,,bg2 = ^! semi-diamet]s w\ld h be5 equal to entire l5g?s ( ,,km if ! two transp>5t sub/ances _h be5 ( ! same p5etrability4 ,n[ all ^! circumf]5ces h = a common tang5t ! /raight l9e ,,bn2 namely ! same l9e :i* is drawn z a tang5t f ! po9t ,b to ! circumf]5ce ,,snr :i* we consid]$ fir/4 ,= x is easy to see t all ! o!r circumf]5ces w t\* ! same ,,bn1 f ,b up to ! po9t ( contact ,n1 :i* is ! same po9t :]e ,,an falls p]p5dicul>ly on ,,bn4 ,x is !n ,,bn1 :i* is =m$ by small arcs ( ^! circumf]5ces1 :i* t]m9ates ! movem5t t ! wave ,,ac has communicat$ )9 ! transp>5t body1 & :]e ?is movem5t occurs 9 mu* great] am\nt ?an any:]e else4 ,& = t reason ?is l9e1 9 accordance ) :at has be5 said m ?an once1 is ! propagation ( ! wave ,,ac at ! mom5t :5 its piece ,c has rea*$ ,b4 ,= !re is no o!r l9e bel[ ! plane ,,ab :i* is1 l ,,bn1 a common tang5t to all ^! p>tial waves4 ,& if "o w\ld "k h[ ! wave ,,ac has come progressively to ,,bn1 x is necess>y only to draw 9 ! same figure ! /raight l9es ,,ko p>allel to ,,bn1 & all ! l9es ,,kl p>allel to ,,ac4 ,?us "o w see t ! wave ,,ca1 f be+ a /raight l9e1 has become brok5 9 all ! positions ,,lko successively1 & t x has aga9 become a /raight l9e at ,,bn4 ,?is be+ evid5t by :at has already be5 demon/rat$1 !re is no ne$ to expla9 x fur!r4 ,n[1 9 ! same figure1 if "o draws ,,eaf1 :i* cuts ! plane ,,ab at "r angles at ! po9t ,a1 s9ce ,,ad is p]p5dicul> to ! wave ,,ac1 x w be ,,da :i* w m>k ! ray ( incid5t light1 & ,,an :i* 0 p]p5dicul> to ,,bn1 ! refract$ ray3 s9ce ! rays are no?+ else ?an ! /raight l9es along :i* ! portions ( ! waves advance4 ,:5ce x is easy to recognize ?is *ief prop]ty ( refraction1 namely t ! ,s9e ( ! angle ,,dae has always ! same ratio to ! ,s9e ( ! angle ,,naf1 :atev] be ! incl9ation ( ! ray ,,da3 & t ?is ratio is ! same z t ( ! velocity ( ! waves 9 ! transp>5t sub/ance :i* is t[>ds ,,ae to _! velocity 9 ! transp>5t sub/ance t[>ds ,,af4 ,=1 consid]+ ,,ab z ! radius ( a circle1 ! ,s9e ( ! angle ,,bac is ,,bc1 & ! ,s9e ( ! angle ,,abn is ,,an4 ,b ! angle ,,bac is equal to ,,dae1 s9ce ea* ( !m add$ to ,,cae makes a "r angle4 ,& ! angle ,,abn is equal to ,,naf1 s9ce ea* ( !m ) ,,ban makes a "r angle4 ,!n also ! ,s9e ( ! angle ,,dae is to ! ,s9e ( ,,naf z ,,bc is to ,,an4 ,b ! ratio ( ,,bc to ,,an 0 ! same z t ( ! velocities ( light 9 ! sub/ance :i* is t[>ds ,,ae & 9 t :i* is t[>ds ,,af2 !re=e also ! ,s9e ( ! angle ,,dae w be to ! ,s9e ( ! angle ,,naf ! same z ! said velocities ( light4 ,to see1 consequ5tly1 :at ! refraction w be :5 ! waves ( light pass into a sub/ance 9 :i* ! movem5t travels m quickly ?an 9 t f :i* !y em]ge 7let u aga9 assume ! ratio ( #c to #b71 x is only necess>y to repeat all ! same con/ruction & demon/ration :i* we h j us$1 m]ely sub/itut+ ev]y:]e #c_/b in/ead ( #b_/c4 ,& x w be f\nd by ! same reason+1 9 ?is o!r figure1 t :5 ! piece ,c ( ! wave ,,ac %all h rea*$ ! surface ,,ab at ,b1 all ! portions ( ! wave ,,ac w h advanc$ z f> z ,,bn1 s t ,,bc ! p]p5dicul> on ,,ac is to ,,an ! p]p5dicul> on ,,bn z #b to #c4 ,& !re w f9ally be ?is same ratio ( #b to #c betwe5 ! ,s9e ( ! angle ,,bad & ! ,s9e ( ! angle ,,fan4 ,h5ce "o sees ! reciprocal relation ( ! refractions ( ! ray on ent]+ & on leav+ "o & ! same transp>5t body3 namely t if ,,na fall+ on ! ext]nal surface ,,ab is refract$ into ! direction ,,ad1 s ! ray ,,ad w be refract$ on leav+ ! transp>5t body into ! direction ,,an4 ,illu/ration ,"o sees also ! reason = a notewor?y accid5t :i* happ5s 9 ?is refraction3 :i* is ?is1 t aft] a c]ta9 obliquity ( ! incid5t ray ,,da1 x beg9s to be q unable to p5etrate into ! o!r transp>5t sub/ance4 ,= if ! angle ,,daq or ,,cba is su* t 9 ! triangle ,,acb1 ,,cb is equal to #b_/c ( ,,ab1 or is great]1 !n ,,an _c =m "o side ( ! triangle ,,anb1 s9ce x becomes equal to or great] ?an ,,ab3 s t ! portion ( wave ,,bn _c be f\nd any:]e1 nei!r consequ5tly c ,,an1 :i* ought to be p]p5dicul> to x4 ,& ?us ! incid5t ray ,,da does n !n pi]ce ! surface ,,ab4 ,:5 ! ratio ( ! velocities ( ! waves is z two to ?ree1 z 9 our example1 :i* is t :i* obta9s = glass & air1 ! angle ,,daq mu/ be m ?an #dh degrees #aa m9utes 9 ord] t ! ray ,,da may be able to pass by refraction4 ,& :5 ! ratio ( ! velocities is z #c to #d1 z x is v ne>ly 9 wat] & air1 ?is angle ,,daq mu/ exce$ #da degrees #bd m9utes4 ,& ?is accords p]fectly ) exp]im5t4 ,b x might "h be ask$3 s9ce ! meet+ ( ! wave ,,ac aga9/ ! surface ,,ab ought to produce movem5t 9 ! matt] :i* is on ! o!r side1 :y does no light pass !re8 ,to :i* ! reply is easy if "o rememb]s :at has be5 said be=e4 ,= al?\gh x g5]ates an inf9itude ( p>tial waves 9 ! matt] :i* is at ! o!r side ( ,,ab1 ^! waves nev] h a common tang5t l9e 7ei!r /raight or curv$7 at ! same mom5t2 & s !re is no l9e t]m9at+ ! propagation ( ! wave ,,ac beyond ! plane ,,ab1 nor any place :]e ! movem5t is ga!r$ toge!r 9 suffici5tly great quantity to produce light4 ,& "o w easily see ! tru? ( ?is1 namely t ,,cb be+ l>g] ?an #b_/c ( ,,ab1 ! waves excit$ beyond ! plane ,,ab w h no common tang5t if ab\t ! c5tres ,k "o !n draws circles hav+ radii equal to #c_/b ( ! l5g?s ,,lb to :i* !y correspond4 ,= all ^! circles w be enclos$ 9 "o ano!r & w all pass beyond ! po9t ,b4 ,n[ x is to be rem>k$ t f ! mom5t :5 ! angle ,,daq is small] ?an is requisite to p]mit ! refract$ ray ,,da to pass into ! o!r transp>5t sub/ance1 "o f9ds t ! int]ior reflexion :i* occurs at ! surface ,,ab is mu* augm5t$ 9 brightness1 z is easy to realize by exp]im5t ) a triangul> prism2 & = ?is our !ory c af=d ?is reason4 ,:5 ! angle ,,daq is /ill l>ge en\gh to enable ! ray ,,da to pass1 x is evid5t t ! light f ! portion ,,ac ( ! wave is collect$ 9 a m9imum space :5 x rea*es ,,bn4 ,x appe>s also t ! wave ,,bn becomes s mu* ! small] z ! angle ,,cba or ,,daq is made less2 until :5 ! latt] is dim9i%$ to ! limit indicat$ a little previ\sly1 ?is wave ,,bn is collect$ toge!r always at "o po9t4 ,t is to say1 t :5 ! piece ,c ( ! wave ,,ac has !n arriv$ at ,b1 ! wave ,,bn :i* is ! propagation ( ,,ac is entirely r$uc$ to ! same po9t ,b4 ,simil>ly :5 ! piece ,h has rea*$ ,k1 ! "p ,,ah is entirely r$uc$ to ! same po9t ,k4 ,?is makes x evid5t t 9 proportion z ! wave ,,ca comes to meet ! surface ,,ab1 !re occurs a great quantity ( movem5t along t surface2 :i* movem5t ought also to spread )9 ! transp>5t body & ought to h mu* re-en=c$ ! p>tial waves :i* produce ! int]ior reflexion aga9/ ! surface ,,ab1 accord+ to ! laws ( reflexion previ\sly expla9$4 ,& because a slight dim9ution ( ! angle ( incid5ce ,,daq causes ! wave ,,bn1 h[ev] great x 01 to be r$uc$ to z]o1 7= ?is angle be+ #di degrees #aa m9utes 9 ! glass1 ! angle ,,ban is /ill #aa degrees #ba m9utes1 & ! same angle be+ r$uc$ by "o degree only ! angle ,,ban is r$uc$ to z]o1 & s ! wave ,,bn r$uc$ to a po9t7 !nce x comes ab\t t ! int]ior reflexion f be+ obscure becomes sudd5ly bright1 s soon z ! angle ( incid5ce is su* t x no long] gives passage to ! refraction4 ,n[ z conc]ns ord9>y ext]nal reflexion1 t is to say :i* occurs :5 ! angle ( incid5ce ,,daq is /ill l>ge en\gh to enable ! refract$ ray to p5etrate beyond ! surface ,,ab1 ?is reflexion %\ld occur aga9/ ! p>ticles ( ! sub/ance :i* t\*es ! transp>5t body on its outside4 ,& x app>5tly occurs aga9/ ! p>ticles ( ! air or o!rs m+l$ ) ! e!real p>ticles & l>g] ?an !y4 ,s on ! o!r h& ! ext]nal reflexion ( ^! bodies occurs aga9/ ! p>ticles :i* compose !m1 & :i* are also l>g] ?an ^? ( ! e!real matt]1 s9ce ! latt] fl[s 9 _! int]/ices4 ,x is true t !re rema9s "h "s difficulty 9 ^? exp]im5ts 9 :i* ?is int]ior reflexion occurs )\t ! p>ticles ( air be+ able to contribute to x1 z 9 vessels or tubes f :i* ! air has be5 extract$4 ,exp]i5ce1 moreov]1 tea*es u t ^! two reflexions are ( ne>ly equal =ce1 & t 9 diff]5t transp>5t bodies !y are s mu* ! /rong] z ! refraction ( ^! bodies is ! great]4 ,?us "o sees manife/ly t ! reflexion ( glass is /rong] ?an t ( wat]1 & t ( diamond /rong] ?an t ( glass4 ,i w f9i% ?is !ory ( refraction by demon/rat+ a rem>kable proposition :i* dep5ds on x2 namely1 t a ray ( light 9 ord] to g f "o po9t to ano!r1 :5 ^! po9ts are 9 diff]5t m$ia1 is refract$ 9 su* wise at ! plane surface :i* jo9s ^! two m$ia t x employs ! lea/ possible "t3 & exactly ! same happ5s 9 ! case ( reflexion aga9/ a plane surface4 ,mr4 ,f]mat 0 ! fir/ to prop\nd ?is prop]ty ( refraction1 hold+ ) u1 & directly c\nt] to ! op9ion ( ,mr4 ,des ,c>tes1 t light passes m sl[ly ?r\gh glass & wat] ?an ?r\gh air4 ,b he assum$ besides ?is a con/ant ratio ( ,s9es1 :i* we h j prov$ by ^! diff]5t degrees ( velocity alone3 or r1 :at is equival5t1 he assum$ n only t ! velocities 7 diff]5t b t ! light took ! lea/ "t possible = its passage1 & !nce d$uc$ ! con/ant ratio ( ! ,s9es4 ,8 demon/ration1 :i* may be se5 9 8 pr9t$ works1 & 9 ! volume ( lett]s ( ,mr4 ,des ,c>tes1 is v long2 :]e=e ,i give "h ano!r :i* is simpl] & easi]4 ,illu/ration ,let ,,kf be ! plane surface2 ,a ! po9t 9 ! m$ium :i* ! light trav]ses m easily1 z ! air2 ,c ! po9t 9 ! o!r :i* is m difficult to p5etrate1 z wat]4 ,& suppose t a ray has come f ,a1 by ,b1 to ,c1 hav+ be5 refract$ at ,b accord+ to ! law demon/rat$ a little be=e2 t is to say t1 hav+ drawn ,,pbq1 :i* cuts ! plane at "r angles1 let ! s9e ( ! angle ,,abp h to ! s9e ( ! angle ,,cbq ! same ratio z ! velocity ( light 9 ! m$ium :]e ,a is to ! velocity ( light 9 ! m$ium :]e ,c is4 ,x is to be %[n t ! "t ( passage ( light along ,,ab & ,,bc tak5 toge!r1 is ! %orte/ t c be4 ,let u assume t x may h come by o!r l9es1 &1 9 ! fir/ place1 along ,,af1 ,,fc1 s t ! po9t ( refraction ,f may be fur!r f ,b ?an ! po9t ,a2 & let ,,ao be a l9e p]p5dicul> to ,,ab1 & ,,fo p>allel to ,,ab2 ,,bh p]p5dicul> to ,,fo1 & ,,fg to ,,bc4 ,s9ce !n ! angle ,,hbf is equal to ,,pba1 & ! angle ,,bfg equal to ,,qbc1 x foll[s t ! s9e ( ! angle ,,hbf w also h ! same ratio to ! s9e ( ,,bfg1 z ! velocity ( light 9 ! m$ium ,a is to its velocity 9 ! m$ium ,c4 ,b ^! s9es are ! /raight l9es ,,hf1 ,,bg1 if we take ,,bf z ! semi-diamet] ( a circle4 ,!n ^! l9es ,,hf1 ,,bg1 w be> to "o ano!r ! said ratio ( ! velocities4 ,&1 !re=e1 ! "t ( ! light along ,,hf1 suppos+ t ! ray _h be5 ,,(1 w\ld be equal to ! "t along ,,bg 9 ! int]ior ( ! m$ium ,c4 ,b ! "t along ,,ab is equal to ! "t along ,,oh2 !re=e ! "t along ,,( is equal to ! "t along ,,ab1 ,,bg4 ,aga9 ! "t along ,,fc is great] ?an t along ,,gc2 !n ! "t along ,,(c w be long] ?an t along ,,abc4 ,b ,,af is long] ?an ,,(1 !n ! "t along ,,afc w by j s mu* m exce$ ! "t along ,,abc4 ,n[ let u assume t ! ray has come f ,a to ,c along ,,ak1 ,,kc2 ! po9t ( refraction ,k be+ ne>] to ,a ?an ! po9t ,b is2 & let ,,cn be ! p]p5dicul> ^u ,,bc1 ,,kn p>allel to ,,bc3 ,,bm p]p5dicul> ^u ,,kn1 & ,,kl ^u ,,ba4 ,"h ,,bl & ,,km are ! s9es ( angles ,,bkl1 ,,kbm2 t is to say1 ( ! angles ,,pba1 ,,qbc2 & !re=e !y are to "o ano!r z ! velocity ( light 9 ! m$ium ,a is to ! velocity 9 ! m$ium ,c4 ,!n ! "t along ,,lb is equal to ! "t along ,,km2 & s9ce ! "t along ,,bc is equal to ! "t along ,,mn1 ! "t along ,,lbc w be equal to ! "t along ,,kmn4 ,b ! "t along ,,ak is long] ?an t along ,,al3 h5ce ! "t along ,,akn is long] ?an t along ,,abc4 ,& ,,kc be+ long] ?an ,,kn1 ! "t along ,,akc w exce$1 by z mu* m1 ! "t along ,,abc4 ,h5ce x appe>s t ! "t along ,,abc is ! %orte/ possible2 :i* 0 to be prov54 ,,*apt] ,,iv ,,on ,,! ,,refraction ,,( ,,! ,,air ,we h %[n h[ ! movem5t :i* con/itutes light spreads by sph]ical waves 9 any homog5e\s matt]4 ,& x is evid5t t :5 ! matt] is n homog5e\s1 b ( su* a con/itution t ! movem5t is communicat$ 9 x m rapidly t[>d "o side ?an t[>d ano!r1 ^! waves _c be sph]ical3 b t !y mu/ acquire _! figure accord+ to ! diff]5t di/ances ov] :i* ! successive movem5t passes 9 equal times4 ,x is ?us t we %all 9 ! fir/ place expla9 ! refractions :i* occur 9 ! air1 :i* ext5ds f "h to ! cl\ds & beyond4 ,! effects ( :i* refractions are v rem>kable2 = by !m we (t5 see objects :i* ! rotundity ( ! ,e>? ought o!rwise to hide2 su* z ,isl&s1 & ! tops ( m\nta9s :5 "o is at sea4 ,because also ( !m ! ,sun & ! ,moon appe> z ris5 be=e 9 fact !y h1 & appe> to set lat]3 s t at times ! ,moon has be5 se5 eclips$ :ile ! ,sun appe>$ /ill above ! horizon4 ,& s also ! heights ( ! ,sun & ( ! ,moon1 & ^? ( all ! ,/>s always appe> a little great] ?an !y are 9 reality1 because ( ^! same refractions1 z ,a/ronom]s "k4 ,b !re is "o exp]im5t :i* r5d]s ?is refraction v evid5t2 :i* is t ( fix+ a telescope on "s spot s t x views an object1 su* z a /eeple or a h\se1 at a di/ance ( half a league or m4 ,if !n y look ?r\gh x at diff]5t h\rs ( ! day1 leav+ x always fix$ 9 ! same way1 y w see t ! same spots ( ! object w n always appe> at ! middle ( ! ap]ture ( ! telescope1 b t g5]ally 9 ! morn+ & 9 ! ev5+1 :5 !re are m vap\rs ne> ! ,e>?1 ^! objects seem to rise high]1 s t ! half or m ( !m w no long] be visible2 & s t !y seem l[] t[>d mid-day :5 ^! vap\rs are dissipat$4 ,^? :o consid] refraction to occur only 9 ! surfaces :i* sep>ate transp>5t bodies ( diff]5t nature1 w\ld f9d x difficult to give a reason = all t ,i h j relat$2 b accord+ to our ,!ory ! ?+ is q easy4 ,x is kn[n t ! air :i* surr\nds u1 besides ! p>ticles :i* are prop] to x & :i* float 9 ! e!real matt] z has be5 expla9$1 is full also ( p>ticles ( wat] :i* are rais$ by ! action ( heat2 & x has be5 asc]ta9$ fur!r by "s v def9ite exp]im5ts t z "o m\nts up high] ! d5sity ( air dim9i%es 9 proportion4 ,n[ :e!r ! p>ticles ( wat] & ^? ( air take "p1 by means ( ! p>ticles ( e!real matt]1 9 ! movem5t :i* con/itutes light1 b h a less prompt recoil ?an ^!1 or :e!r ! enc\nt] & h9drance :i* ^! p>ticles ( air & wat] (f] to ! propagation ( movem5t ( ! e!real progress1 ret>d ! progression1 x foll[s t bo? k9ds ( p>ticles fly+ amid/ ! e!real p>ticles1 mu/ r5d] ! air1 f a great height d[n to ! ,e>?1 gradually less easy = ! spread+ ( ! waves ( light4 ,illu/ration ,:5ce ! configuration ( ! waves ought to become ne>ly su* z ?is figure repres5ts3 namely1 if ,a is a light1 or ! visible po9t ( a /eeple1 ! waves :i* />t f x ought to spread m widely upw>ds & less widely d[nw>ds1 b 9 o!r directions m or less z !y approximate to ^! two extremes4 ,?is be+ s1 x necess>ily foll[s t e l9e int]sect+ "o ( ^! waves at "r angles w pass above ! po9t ,a1 always except+ ! "o l9e :i* is p]p5dicul> to ! horizon4 ,illu/ration ,let ,,bc be ! wave :i* br+s ! light to ! spectator :o is at ,b1 & let ,,bd be ! /raight l9e :i* int]sects ?is wave at "r angles4 ,n[ because ! ray or /raight l9e by :i* we judge ! spot :]e ! object appe>s to u is no?+ else ?an ! p]p5dicul> to ! wave t rea*es our eye1 z w be und]/ood by :at 0 said above1 x is manife/ t ! po9t ,a w be p]ceiv$ z be+ 9 ! l9e ,,bd1 & !re=e high] ?an 9 fact x is4 ,simil>ly if ! ,e>? be ,,ab1 & ! top ( ! ,atmosph]e ,,cd1 :i* probably is n a well def9$ sph]ical surface 7s9ce we "k t ! air becomes r>e 9 proportion z "o asc5ds1 = above !re is s mu* less ( x to press d[n ^u x71 ! waves ( light f ! sun com+1 = in/ance1 9 su* a way t s long z !y h n rea*$ ! ,atmosph]e ,,cd ! /raight l9e ,,ae int]sects !m p]p5dicul>ly1 !y ought1 :5 !y ent] ! ,atmosph]e1 to advance m quickly 9 elevat$ regions ?an 9 regions ne>] to ! ,e>?4 ,s t if ,,ca is ! wave :i* br+s ! light to ! spectator at ,a1 its region ,c w be ! fur!/ advanc$2 & ! /raight l9e ,,af1 :i* int]sects ?is wave at "r angles1 & :i* det]m9es ! app>5t place ( ! ,sun1 w pass above ! real ,sun1 :i* w be se5 along ! l9e ,,ae4 ,& s x may occur t :5 x ought n to be visible 9 ! abs5ce ( vap\rs1 because ! l9e ,,ae enc\nt]s ! rotundity ( ! ,e>?1 x w be p]ceiv$ 9 ! l9e ,,af by refraction4 ,b ?is angle ,,eaf is sc>cely ev] m ?an half a degree because ! att5uation ( ! vap\rs alt]s ! waves ( light b little4 ,fur!rmore ^! refractions are n altoge!r con/ant 9 all wea!rs1 p>ticul>ly at small elevations ( #b or #c degrees2 :i* results f ! diff]5t quantity ( aque\s vap\rs ris+ above ! ,e>?4 ,& ?is same ?+ is ! cause :y at c]ta9 times a di/ant object w be hidd5 beh9d ano!r less di/ant "o1 & yet may at ano!r "t be able to be se51 al?\gh ! spot f :i* x is view$ is always ! same4 ,b ! reason = ?is effect w be /ill m evid5t f :at we are go+ to rem>k t\*+ ! curvature ( rays4 ,x appe>s f ! ?+s expla9$ above t ! progression or propagation ( a small "p ( a wave ( light is prop]ly :at "o calls a ray4 ,n[ ^! rays1 in/ead ( be+ /raight z !y are 9 homog5e\s m$ia1 ought to be curv$ 9 an atmosph]e ( unequal p5etrability4 ,= !y necess>ily foll[ f ! object to ! eye ! l9e :i* int]sects at "r angles all ! progressions ( ! waves1 z 9 ! fir/ figure ! l9e ,,aeb does1 z w be %[n h]eaft]2 & x is ?is l9e :i* det]m9es :at int]pos$ bodies w\ld or w\ld n h9d] u f see+ ! object4 ,= al?\gh ! po9t ( ! /eeple ,a appe>s rais$ to ,d1 x w\ld yet n appe> to ! eye ,b if ! t[] ,h 0 betwe5 ! two1 because x crosses ! curve ,,aeb4 ,b ! t[] ,e1 :i* is b5ea? ?is curve1 does n h9d] ! po9t ,a f be+ se54 ,n[ accord+ z ! air ne> ! ,e>? exce$s 9 d5sity t :i* is high]1 ! curvature ( ! ray ,,aeb becomes great]3 s t at c]ta9 times x passes above ! summit ,e1 :i* all[s ! po9t ,a to be p]ceiv$ by ! eye at ,b2 & at o!r times x is int]cept$ by ! same t[] ,e :i* hides ,a f ?is same eye4 ,illu/ration ,b to demon/rate ?is curvature ( ! rays con=mably to all our prec$+ ,!ory1 let u imag9e t ,,ab is a small portion ( a wave ( light com+ f ! side ,c1 :i* we may consid] z a /raight l9e4 ,let u also suppose t x is p]p5dicul> to ! ,horizon1 ! portion ,b be+ ne>] to ! ,e>? ?an ! portion ,a2 & t because ! vap\rs are less h9d]+ at ,a ?an at ,b1 ! p>ticul> wave :i* comes f ! po9t ,a spreads ?r\gh a c]ta9 space ,,ad :ile ! p>ticul> wave :i* />ts f ! po9t ,b spreads ?r\gh a %ort] space ,,be2 ,,ad & ,,be be+ p>allel to ! ,horizon4 ,fur!r1 suppos+ ! /raight l9es ,,fg1 ,,hi1 etc41 to be drawn f an inf9itude ( po9ts 9 ! /raight l9e ,,ab & to t]m9ate on ! l9e ,,de 7:i* is /raight or may be consid]$ z su*71 let ! diff]5t p5etrabilities at ! diff]5t heights 9 ! air betwe5 ,a & ,b be repres5t$ by all ^! l9es2 s t ! p>ticul> wave1 orig9at+ f ! po9t ,f1 w spread across ! space ,,fg1 & t f ! po9t ,h across ! space ,,hi1 :ile t f ! po9t ,a spreads across ! space ,,ad4 ,n[ if ab\t ! c5tres ,a1 ,b1 "o describes ! circles ,,dk1 ,,el1 :i* repres5t ! spread+ ( ! waves :i* orig9ate f ^! two po9ts1 & if "o draws ! /raight l9e ,,kl :i* t\*es ^! two circles1 x is easy to see t ?is same l9e w be ! common tang5t to all ! o!r circles drawn ab\t ! c5tres ,f1 ,h1 etc42 & t all ! po9ts ( contact w fall )9 t "p ( ?is l9e :i* is compris$ betwe5 ! p]p5dicul>s ,,ak1 ,,bl4 ,!n x w be ! l9e ,,kl :i* w t]m9ate ! movem5t ( ! p>ticul> waves orig9at+ f ! po9ts ( ! wave ,,ab2 & ?is movem5t w be /rong] betwe5 ! po9ts ,,kl1 ?an any:]e else at ! same in/ant1 s9ce an inf9itude ( circumf]5ces concur to =m ?is /raight l9e2 & consequ5tly ,,kl w be ! propagation ( ! portion ( wave ,,ab1 z has be5 said 9 expla9+ reflexion & ord9>y refraction4 ,n[ x appe>s t ,,ak & ,,bl dip d[n t[>d ! side :]e ! air is less easy to p5etrate3 = ,,ak be+ long] ?an ,,bl1 & p>allel to x1 x foll[s t ! l9es ,,ab & ,,kl1 be+ prolong$1 w\ld meet at ! side ,l4 ,b ! angle ,k is a "r angle3 h5ce ,,kab is necess>ily acute1 & consequ5tly less ?an ,,dab4 ,if "o inve/igates 9 ! same way ! progression ( ! portion ( ! wave ,,kl1 "o w f9d t aft] a fur!r "t x has arriv$ at ,,mn 9 su* a mann] t ! p]p5dicul>s ,,km1 ,,ln1 dip d[n ev5 m ?an d ,,ak1 ,,bl4 ,& ?is suffices to %[ t ! ray w cont9ue along ! curv$ l9e :i* int]sects all ! waves at "r angles1 z has be5 said4 ,,*apt] ,v ,,on ,,! ,,/range ,,refraction ,,( ,,icel& ,,cry/al #a4 ,!re is br\ght f ,icel&1 :i* is an ,isl& 9 ! ,nor? ,sea1 9 ! latitude ( #ff degrees1 a k9d ( ,cry/al or transp>5t /one1 v rem>kable = its figure & o!r qualities1 b above all = its /range refractions4 ,! causes ( ?is h seem$ to me to be wor?y ( be+ c>efully inve/igat$1 ! m s because among/ transp>5t bodies ?is "o alone does n foll[ ! ord9>y rules ) respect to rays ( light4 ,i h ev5 be5 "u "s necessity to make ?is rese>*1 because ! refractions ( ?is ,cry/al seem$ to ov]turn our prec$+ explanation ( regul> refraction2 :i* explanation1 on ! contr>y1 !y /rongly confirm1 z w be se5 aft] !y h be5 br\ght "u ! same pr9ciple4 ,9 ,icel& are f\nd great lumps ( ?is ,cry/al1 "s ( :i* ,i h se5 ( #d or #e p\nds4 ,b x occurs also 9 o!r c\ntries1 = ,i h _h "s ( ! same sort :i* _h be5 f\nd 9 ,france ne> ! t[n ( ,troyes 9 ,*ampagne1 & "s o!rs :i* came f ! ,isl& ( ,corsica1 ?\gh bo? 7 less cle> & only 9 little bits1 sc>cely capable ( lett+ any effect ( refraction be obs]v$4 #b4 ,! fir/ k :i* ! public has _h ab\t x is due to ,mr4 ,erasmus ,b>?ol9us1 :o has giv5 a description ( ,icel& ,cry/al & ( its *ief ph5om5a4 ,b "h ,i %all n desi/ f giv+ my own1 bo? = ! in/ruction ( ^? :o may n h se5 8 book1 & because z respects "s ( ^! ph5om5a !re is a slight diff]5ce betwe5 8 obs]vations & ^? :i* ,i h made3 = ,i h appli$ myself ) great exactitude to exam9e ^! prop]ties ( refraction1 9 ord] to be q sure be=e und]tak+ to expla9 ! causes ( !m4 #c4 ,z reg>ds ! h>dness ( ?is /one1 & ! prop]ty :i* x has ( be+ easily split1 x mu/ be consid]$ r z a species ( ,talc ?an ( ,cry/al4 ,= an iron spike effects an entrance into x z easily z into any o!r ,talc or ,alaba/]1 to :i* x is equal 9 gravity4 ,illu/ration #d4 ,! pieces ( x :i* are f\nd h ! figure ( an oblique p>allelepip$2 ea* ( ! six faces be+ a p>allelogram2 & x admits ( be+ split 9 ?ree directions p>allel to two ( ^! oppos$ faces4 ,ev5 9 su* wise1 if y w1 t all ! six faces are equal & simil> rhombuses4 ,! figure "h add$ repres5ts a piece ( ?is ,cry/al4 ,! obtuse angles ( all ! p>allelograms1 z ,c1 ,d1 "h1 are angles ( #aja degrees #eb m9utes1 & consequ5tly ! acute angles1 su* z ,a & ,b1 are ( #gh degrees #h m9utes4 #e4 ,( ! solid angles !re are two opposite to "o ano!r1 su* z ,c & ,e1 :i* are ea* compos$ ( ?ree equal obtuse plane angles4 ,! o!r six are compos$ ( two acute angles & "o obtuse4 ,all t ,i h j said has be5 likewise rem>k$ by ,mr4 ,b>?ol9us 9 ! a=esaid treatise2 if we diff] x is only slightly ab\t ! values ( ! angles4 ,he rec\nts moreov] "s o!r prop]ties ( ?is ,cry/al2 to wit1 t :5 rubb$ aga9/ clo? x attracts /raws & o!r light ?+s z d amb]1 diamond1 glass1 & ,spani% wax4 ,let a piece be cov]$ ) wat] = a day or m1 ! surface loses its natural poli%4 ,:5 aqua=tis is p\r$ on x x produces ebullition1 especially1 z ,i h f\nd1 if ! ,cry/al has be5 pulv]iz$4 ,i h also f\nd by exp]im5t t x may be heat$ to r$ness 9 ! fire )\t be+ 9 anywise alt]$ or r5d]$ less transp>5t2 b a v viol5t fire calc9es x nev]!less4 ,its transp>5cy is sc>cely less ?an t ( wat] or ( ,rock ,cry/al1 & devoid ( col\r4 ,b rays ( light pass ?r\gh x 9 ano!r fa%ion & produce ^? m>vell\s refractions ! causes ( :i* ,i am n[ go+ to try to expla92 res]v+ = ! end ( ?is ,treatise ! /atem5t ( my conjectures t\*+ ! =mation & extraord9>y configuration ( ?is ,cry/al4 #f4 ,9 all o!r transp>5t bodies t we "k !re is b "o sole & simple refraction2 b 9 ?is sub/ance !re are two diff]5t ones4 ,! effect is t objects se5 ?r\gh x1 especially su* z are plac$ "r aga9/ x1 appe> d\ble2 & t a ray ( sunlight1 fall+ on "o ( its surfaces1 p>ts itself into two rays & trav]ses ! ,cry/al ?us4 #g4 ,x is aga9 a g5]al law 9 all o!r transp>5t bodies t ! ray :i* falls p]p5dicul>ly on _! surface passes /raight on )\t suff]+ refraction1 & t an oblique ray is always refract$4 ,b 9 ?is ,cry/al ! p]p5dicul> ray suff]s refraction1 & !re are oblique rays :i* pass ?r\gh x q /raight4 ,illu/ration #h4 ,b 9 ord] to expla9 ^! ph5om5a m p>ticul>ly1 let !re be1 9 ! fir/ place1 a piece ,,abfe ( ! same ,cry/al1 & let ! obtuse angle ,,acb1 "o ( ! ?ree :i* con/itute ! equilat]al solid angle ,c1 be divid$ into two equal p>ts by ! /raight l9e ,,cg1 & let x be conceiv$ t ! ,cry/al is int]sect$ by a plane :i* passes ?r\gh ?is l9e & ?r\gh ! side ,,cf1 :i* plane w necess>ily be p]p5dicul> to ! surface ,,ab2 & its section 9 ! ,cry/al w =m a p>allelogram ,,gcfh4 ,we w call ?is section ! pr9cipal section ( ! ,cry/al4 #i4 ,n[ if "o cov]s ! surface ,,ab1 leav+ !re only a small ap]ture at ! po9t ,k1 situat$ 9 ! /raight l9e ,,cg1 & if "o exposes x to ! sun1 s t 8 rays face x p]p5dicul>ly above1 !n ! ray ,,ik w divide itself at ! po9t ,k into two1 "o ( :i* w cont9ue to g on /raight by ,,kl1 & ! o!r w sep>ate itself along ! /raight l9e ,,km1 :i* is 9 ! plane ,,gcfh1 & :i* makes ) ,,kl an angle ( ab\t #f degrees #dj m9utes1 t5d+ f ! side ( ! solid angle ,c2 & on em]g+ f ! o!r side ( ! ,cry/al x w turn aga9 p>allel to ,,jk1 along ,,mz4 ,& z1 9 ?is extraord9>y refraction1 ! po9t ,m is se5 by ! refract$ ray ,,mki1 :i* ,i consid] z go+ to ! eye at ,i1 x necess>ily foll[s t ! po9t ,l1 by virtue ( ! same refraction1 w be se5 by ! refract$ ray ,,lri1 s t ,,lr w be p>allel to ,,mk if ! di/ance f ! eye ,,ki is suppos$ v great4 ,! po9t ,l appe>s !n z be+ 9 ! /raight l9e ,,irs2 b ! same po9t appe>s also1 by ord9>y refraction1 to be 9 ! /raight l9e ,,ik1 h5ce x is necess>ily judg$ to be d\ble4 ,& simil>ly if ,l be a small hole 9 a %eet ( pap] or o!r sub/ance :i* is laid aga9/ ! ,cry/al1 x w appe> :5 turn$ t[>ds daylight z if !re 7 two holes1 :i* w seem ! wid] ap>t f "o ano!r ! great] ! ?ickness ( ! ,cry/al4 #aj4 ,aga91 if "o turns ! ,cry/al 9 su* wise t an incid5t ray ,,no1 ( sunlight1 :i* ,i suppose to be 9 ! plane cont9u$ f ,,gcfh1 makes ) ,,gc an angle ( #gc degrees & #bj m9utes1 & is consequ5tly ne>ly p>allel to ! edge ,,cf1 :i* makes ) ,,fh an angle ( #gj degrees #eg m9utes1 accord+ to ! calculation :i* ,i %all put at ! end1 x w divide itself at ! po9t ,o into two rays1 "o ( :i* w cont9ue along ,,op 9 a /raight l9e ) ,,no1 & w simil>ly pass out ( ! o!r side ( ! cry/al )\t any refraction2 b ! o!r w be refract$ & w g along ,,oq4 ,& x mu/ be not$ t x is special to ! plane ?r\gh ,,gcf & to ^? :i* are p>allel to x1 t all incid5t rays :i* are 9 "o ( ^! planes cont9ue to be 9 x aft] !y h ent]$ ! ,cry/al & h become d\ble2 = x is q o!rwise = rays 9 all o!r planes :i* int]sect ! ,cry/al1 z we %all see aft]w>ds4 #aa4 ,i recogniz$ at fir/ by ^! exp]im5ts & by "s o!rs t ( ! two refractions :i* ! ray suff]s 9 ?is ,cry/al1 !re is "o :i* foll[s ! ord9>y rules2 & x is ?is to :i* ! rays ,,kl & ,,oq belong4 ,?is is :y ,i h di/+ui%$ ?is ord9>y refraction f ! o!r2 & hav+ measur$ x by exact obs]vation1 ,i f\nd t its proportion1 consid]$ z to ! ,s9es ( ! angles :i* ! incid5t & refract$ rays make ) ! p]p5dicul>1 0 v precisely t ( #e to #c1 z 0 f\nd also by ,mr4 ,b>?ol9us1 & consequ5tly mu* great] ?an t ( ,rock ,cry/al1 or ( glass1 :i* is ne>ly #c to #b4 ,illu/ration #ab4 ,! mode ( mak+ ^! obs]vations exactly is z foll[s4 ,^u a leaf ( pap] fix$ on a ?or\ghly flat table !re is trac$ a black l9e ,,ab1 & two o!rs1 ,,c$ & ,,kml1 :i* cut x at "r angles & are m or less di/ant f "o ano!r accord+ z x is desir$ to exam9e a ray t is m or less oblique4 ,!n place ! ,cry/al ^u ! int]section ,e s t ! l9e ,,ab concurs ) t :i* bisects ! obtuse angle ( ! l[] surface1 or ) "s l9e p>allel to x4 ,!n by plac+ ! eye directly above ! l9e ,,ab x w appe> s+le only2 & "o w see t ! portion view$ ?r\gh ! ,cry/al & ! portions :i* appe> outside x1 meet toge!r 9 a /raight l9e3 b ! l9e ,,cd w appe> d\ble1 & "o c di/+ui% ! image :i* is due to regul> refraction by ! circum/ance t :5 "o views x ) bo? eyes x seems rais$ up m ?an ! o!r1 or aga9 by ! circum/ance t1 :5 ! ,cry/al is turn$ ar\nd on ! pap]1 ?is image rema9s /ation>y1 :]eas ! o!r image %ifts & moves entirely ar\nd4 ,aft]w>ds let ! eye be plac$ at ,i 7rema9+ always 9 ! plane p]p5dicul> ?r\gh ,,ab7 s t x views ! image :i* is =m$ by regul> refraction ( ! l9e ,,cd mak+ a /raight l9e ) ! rema9d] ( t l9e :i* is outside ! ,cry/al4 ,& !n1 m>k+ on ! surface ( ! ,cry/al ! po9t ,h :]e ! int]section ,e appe>s1 ?is po9t w be directly above ,e4 ,!n draw back ! eye t[>ds ,o1 keep+ always 9 ! plane p]p5dicul> ?r\gh ,,ab1 s t ! image ( ! l9e ,,cd1 :i* is =m$ by ord9>y refraction1 may appe> 9 a /raight l9e ) ! l9e ,,kl view$ )\t refraction2 & !n m>k on ! ,cry/al ! po9t ,n :]e ! po9t ( int]section ,e appe>s4 #ac4 ,!n "o w "k ! l5g? & position ( ! l9es ,,nh1 ,,em1 & ( ,,he1 :i* is ! ?ickness ( ! ,cry/al3 :i* l9es be+ trac$ sep>ately ^u a plan1 & !n jo9+ ,,ne & ,,nm :i* cuts ,,he at ,p1 ! proportion ( ! refraction w be t ( ,,en to ,,np1 because ^! l9es are to "o ano!r z ! s9es ( ! angles ,,nph1 ,,nep1 :i* are equal to ^? :i* ! incid5t ray ,,on & its refraction ,,ne make ) ! p]p5dicul> to ! surface4 ,?is proportion1 z ,i h said1 is suffici5tly precisely z #e to #c1 & is always ! same = all incl9ations ( ! incid5t ray4 #ad4 ,! same mode ( obs]vation has also s]v$ me = exam9+ ! extraord9>y or irregul> refraction ( ?is ,cry/al4 ,=1 ! po9t ,h hav+ be5 f\nd & m>k$1 z a=esaid1 directly above ! po9t ,e1 ,i obs]v$ ! appe>ance ( ! l9e ,,cd1 :i* is made by ! extraord9>y refraction2 & hav+ plac$ ! eye at ,q1 s t ?is appe>ance made a /raight l9e ) ! l9e ,,kl view$ )\t refraction1 ,i asc]ta9$ ! triangles ,,reh1 ,,res1 & consequ5tly ! angles ,,r%1 ,,res1 :i* ! incid5t & ! refract$ ray make ) ! p]p5dicul>4 #ae4 ,b ,i f\nd 9 ?is refraction t ! ratio ( ,,fr to ,,rs 0 n con/ant1 l ! ord9>y refraction1 b t x v>i$ ) ! v>y+ obliquity ( ! incid5t ray4 #af4 ,i f\nd also t :5 ,,qre made a /raight l9e1 t is1 :5 ! incid5t ray ent]$ ! ,cry/al )\t be+ refract$ 7z ,i asc]ta9$ by ! circum/ance t !n ! po9t ,e view$ by ! extraord9>y refraction appe>$ 9 ! l9e ,,cd1 z se5 )\t refraction7 ,i f\nd1 ,i say1 !n t ! angle ,,qrg 0 #gc degrees #bj m9utes1 z has be5 already rem>k$2 & s x is n ! ray p>allel to ! edge ( ! ,cry/al1 :i* crosses x 9 a /raight l9e )\t be+ refract$1 z ,mr4 ,b>?ol9us believ$1 s9ce t incl9ation is only #gj degrees #eg m9utes1 z 0 /at$ above4 ,& ?is is to be not$1 9 ord] t no "o may se>* 9 va9 = ! cause ( ! s+ul> prop]ty ( ?is ray 9 its p>allelism to ! edges m5tion$4 ,illu/ration #ag4 ,f9ally1 cont9u+ my obs]vations to discov] ! nature ( ?is refraction1 ,i le>n$ t x obey$ ! foll[+ rem>kable rule4 ,let ! p>allelogram ,,gcfh1 made by ! pr9cipal section ( ! ,cry/al1 z previ\sly det]m9$1 be trac$ sep>ately4 ,i f\nd !n t always1 :5 ! incl9ations ( two rays :i* come f opposite sides1 z ,,vk1 ,,sk "h1 are equal1 _! refractions ,,kx & ,,kt meet ! bottom l9e ,,hf 9 su* wise t po9ts ,x & ,t are equally di/ant f ! po9t ,m1 :]e ! refraction ( ! p]p5dicul> ray ,,ik falls2 & ?is occurs also = refractions 9 o!r sections ( ?is ,cry/al4 ,b be=e speak+ ( ^?1 :i* h also o!r p>ticul> prop]ties1 we w inve/igate ! causes ( ! ph5om5a :i* ,i h already report$4 ,x 0 aft] hav+ expla9$ ! refraction ( ord9>y transp>5t bodies by means ( ! sph]ical emanations ( light1 z above1 t ,i resum$ my exam9ation ( ! nature ( ?is ,cry/al1 :]e9 ,i _h previ\sly be5 unable to discov] any?+4 #ah4 ,z !re 7 two diff]5t refractions1 ,i conceiv$ t !re 7 also two diff]5t emanations ( waves ( light1 & t "o c\ld occur 9 ! e!real matt] ext5d+ ?r\gh ! body ( ! ,cry/al4 ,:i* matt]1 be+ pres5t 9 mu* l>g] quantity ?an is t ( ! p>ticles :i* compose x1 0 alone capable ( caus+ transp>5cy1 accord+ to :at has be5 expla9$ h]et(ore4 ,i attribut$ to ?is emanation ( waves ! regul> refraction :i* is obs]v$ 9 ?is /one1 by suppos+ ^! waves to be ord9>ily ( sph]ical =m1 & hav+ a sl[] progression )9 ! ,cry/al ?an !y h outside x2 :5ce proce$s refraction z ,i h demon/rat$4 #ai4 ,z to ! o!r emanation :i* %\ld produce ! irregul> refraction1 ,i wi%$ to try :at ,elliptical waves1 or r sph]oidal waves1 w\ld d2 & ^! ,i suppos$ w\ld spread indiff]5tly bo? 9 ! e!real matt] diffus$ ?r\gh\t ! cry/al & 9 ! p>ticles ( :i* x is compos$1 accord+ to ! la/ mode 9 :i* ,i h expla9$ transp>5cy4 ,x seem$ to me t ! disposition or regul> arrangem5t ( ^! p>ticles c\ld contribute to =m sph]oidal waves 7no?+ m be+ requir$ = ?is ?an t ! successive movem5t ( light %\ld spread a little m quickly 9 "o direction ?an 9 ! o!r7 & ,i sc>cely d\bt$ t !re 7 9 ?is cry/al su* an arrangem5t ( equal & simil> p>ticles1 because ( its figure & ( its angles ) _! det]m9ate & inv>iable measure4 ,t\*+ :i* p>ticles1 & _! =m & disposition1 ,i %all1 at ! end ( ?is ,treatise1 prop\nd my conjectures & "s exp]im5ts :i* confirm !m4 #bj4 ,! d\ble emission ( waves ( light1 :i* ,i _h imag9$1 became m probable to me aft] ,i _h obs]v$ a c]ta9 ph5om5on 9 ! ord9>y ,rock ,cry/al1 :i* occurs 9 hexagonal =m1 & :i*1 because ( ?is regul>ity1 seems also to be compos$ ( p>ticles1 ( def9ite figure1 & rang$ 9 ord]4 ,?is 01 t ?is cry/al1 z well z t f ,icel&1 has a d\ble refraction1 ?\gh less evid5t4 ,= hav+ _h cut f x "s well poli%$ ,prisms ( diff]5t sections1 ,i rem>k$ 9 all1 9 view+ ?r\gh !m ! flame ( a c&le or ! lead ( w9d[ panes1 t ev]y?+ appe>$ d\ble1 ?\gh ) images n v di/ant f "o ano!r4 ,:5ce ,i und]/ood ! reason :y ?is sub/ance1 ?\gh s transp>5t1 is useless = ,telescopes1 :5 !y h ev] s little l5g?4 #ba4 ,n[ ?is d\ble refraction1 accord+ to my ,!ory h]e9be=e e/abli%$1 seem$ to dem& a d\ble emission ( waves ( light1 bo? ( !m sph]ical 7= bo? ! refractions are regul>7 & ^? ( "o s]ies a little sl[] only ?an ! o!rs4 ,= ?us ! ph5om5on is q naturally expla9$1 by po/ulat+ sub/ances :i* s]ve z vehicle = ^! waves1 z ,i h done 9 ! case ( ,icel& ,cry/al4 ,i _h !n less tr\ble aft] t 9 admitt+ two emissions ( waves 9 "o & ! same body4 ,& s9ce x might h be5 object$ t 9 compos+ ^! two k9ds ( cry/al ( equal p>ticles ( a c]ta9 figure1 regul>ly pil$1 ! int]/ices :i* ^! p>ticles leave & :i* conta9 ! e!real matt] w\ld sc>cely suffice to transmit ! waves ( light :i* ,i h localiz$ !re1 ,i remov$ ?is difficulty by reg>d+ ^! p>ticles z be+ ( a v r>e texture1 or r z compos$ ( o!r mu* small] p>ticles1 betwe5 :i* ! e!real matt] passes q freely4 ,?is1 moreov]1 necess>ily foll[s f t :i* has be5 already demon/rat$ t\*+ ! small quantity ( matt] ( :i* ! bodies are built up4 #bb4 ,suppos+ !n ^! sph]oidal waves besides ! sph]ical ones1 ,i began to exam9e :e!r !y c\ld s]ve to expla9 ! ph5om5a ( ! irregul> refraction1 & h[ by ^! same ph5om5a ,i c\ld det]m9e ! figure & position ( ! sph]oids3 z to :i* ,i obta9$ at la/ ! desir$ success1 by proce$+ z foll[s4 ,illu/ration #bc4 ,i consid]$ fir/ ! effect ( waves s =m$1 z respects ! ray :i* falls p]p5dicul>ly on ! flat surface ( a transp>5t body 9 :i* !y %\ld spread 9 ?is mann]4 ,i took ,,ab = ! expos$ region ( ! surface4 ,&1 s9ce a ray p]p5dicul> to a plane1 & com+ f a v di/ant s\rce ( light1 is no?+ else1 accord+ to ! prec$5t ,!ory1 ?an ! incid5ce ( a portion ( ! wave p>allel to t plane1 ,i suppos$ ! /raight l9e ,,rc1 p>allel & equal to ,,ab1 to be a portion ( a wave ( light1 9 :i* an inf9itude ( po9ts su* z ,,rhh,c come to meet ! surface ,,ab at ! po9ts ,,akk,b4 ,!n in/ead ( ! hemisph]ical p>tial waves :i* 9 a body ( ord9>y refraction w\ld spread f ea* ( ^! la/ po9ts1 z we h above expla9$ 9 treat+ ( refraction1 ^! mu/ "h be hemi-sph]oids4 ,! axes 7or r ! major diamet]s7 ( ^! ,i suppos$ to be oblique to ! plane ,,ab1 z is ,,av ! semi-axis or semi-major diamet] ( ! sph]oid ,,svt1 :i* repres5ts ! p>tial wave com+ f ! po9t ,a1 aft] ! wave ,,rc has rea*$ ,,ab4 ,i say axis or major diamet]1 because ! same ellipse ,,svt may be consid]$ z ! section ( a sph]oid ( :i* ! axis is ,,az p]p5dicul> to ,,av4 ,b1 = ! pres5t1 )\t yet decid+ "o or o!r1 we w consid] ^! sph]oids only 9 ^? sections ( !m :i* make ellipses 9 ! plane ( ?is figure4 ,n[ tak+ a c]ta9 space ( "t dur+ :i* ! wave ,,svt has spread f ,a1 x w\ld ne$s be t f all ! o!r po9ts ,kk,b !re %\ld proce$1 9 ! same "t1 waves simil> to ,,svt & simil>ly situat$4 ,& ! common tang5t ,,nq ( all ^! semi-ellipses w\ld be ! propagation ( ! wave ,,rc :i* fell on ,,ab1 & w\ld be ! place :]e ?is movem5t occurs 9 mu* great] am\nt ?an any:]e else1 be+ made up ( arcs ( an inf9ity ( ellipses1 ! c5tres ( :i* are along ! l9e ,,ab4 #bd4 ,n[ x appe>$ t ?is common tang5t ,,nq 0 p>allel to ,,ab1 & ( ! same l5g?1 b t x 0 n directly opposite to x1 s9ce x 0 compris$ betwe5 ! l9es ,,an1 ,,bq1 :i* are diamet]s ( ellipses hav+ ,a & ,b = c5tres1 conjugate ) respect to diamet]s :i* are n 9 ! /raight l9e ,,ab4 ,& 9 ?is way ,i compreh5d$1 a matt] :i* _h seem$ to me v difficult1 h[ a ray p]p5dicul> to a surface c\ld suff] refraction on ent]+ a transp>5t body2 see+ t ! wave ,,rc1 hav+ come to ! ap]ture ,,ab1 w5t on =w>d !nce1 spread+ betwe5 ! p>allel l9es ,,an1 ,,bq1 yet itself rema9+ always p>allel to ,,ab1 s t "h ! light does n spread along l9es p]p5dicul> to its waves1 z 9 ord9>y refraction1 b along l9es cutt+ ! waves obliquely4 ,illu/ration #be4 ,inquir+ subsequ5tly :at might be ! position & =m ( ^! sph]oids 9 ! cry/al1 ,i consid]$ t all ! six faces produc$ precisely ! same refractions4 ,tak+1 !n1 ! p>allelopip$ ,,afb1 ( :i* ! obtuse solid angle ,c is conta9$ betwe5 ! ?ree equal plane angles1 & imag9+ 9 x ! ?ree pr9cipal sections1 "o ( :i* is p]p5dicul> to ! face ,,dc & passes ?r\gh ! edge ,,cf1 ano!r p]p5dicul> to ! face ,,bf pass+ ?r\gh ! edge ,,ca1 & ! ?ird p]p5dicul> to ! face ,,af pass+ ?r\gh ! edge ,,bc2 ,i knew t ! refractions ( ! incid5t rays belong+ to ^! ?ree planes 7 all simil>4 ,b !re c\ld be no position ( ! sph]oid :i* w\ld h ! same relation to ^! ?ree sections except t 9 :i* ! axis 0 also ! axis ( ! solid angle ,c4 ,consequ5tly ,i saw t ! axis ( ?is angle1 t is to say ! /raight l9e :i* trav]s$ ! cry/al f ! po9t ,c ) equal incl9ation to ! edges ,,cf1 ,,ca1 ,,cb 0 ! l9e :i* det]m9$ ! position ( ! axis ( all ! sph]oidal waves :i* "o imag9$ to orig9ate f "s po9t1 tak5 )9 or on ! surface ( ! cry/al1 s9ce all ^! sph]oids ought to be alike1 & h _! axes p>allel to "o ano!r4 #bf4 ,consid]+ aft] ?is ! plane ( "o ( ^! ?ree sections1 namely t ?r\gh ,,gcf1 ! angle ( :i* is #aji degrees #c m9utes1 s9ce ! angle ,f 0 %[n above to be #gj degrees #eg m9utes2 &1 imag9+ a sph]oidal wave ab\t ! c5tre ,c1 ,i knew1 because ,i h j expla9$ x1 t its axis mu/ be 9 ! same plane1 ! half ( :i* axis ,i h m>k$ ,,cs 9 ! next figure3 & seek+ by calculation 7:i* w be giv5 ) o!rs at ! end ( ?is disc\rse7 ! value ( ! angle ,,cgs1 ,i f\nd x #de degrees #bj m9utes4 ,illu/ration #bg4 ,to "k f ?is ! =m ( ?is sph]oid1 t is to say ! proportion ( ! semi-diamet]s ,,cs1 ,,cp1 ( its elliptical section1 :i* are p]p5dicul> to "o ano!r1 ,i consid]$ t ! po9t ,m :]e ! ellipse is t\*$ by ! /raight l9e ,,fh1 p>allel to ,,cg1 ought to be s situat$ t ,,cm makes ) ! p]p5dicul> ,,cl an angle ( #f degrees #dj m9utes2 s9ce1 ?is be+ s1 ?is ellipse satisfies :at has be5 said ab\t ! refraction ( ! ray p]p5dicul> to ! surface ,,cg1 :i* is incl9$ to ! p]p5dicul> ,,cl by ! same angle4 ,?is1 !n1 be+ ?us dispos$1 & tak+ ,,cm at #ajj1jjj p>ts1 ,i f\nd by ! calculation :i* w be giv5 at ! end1 ! semi-major diamet] ,,cp to be #aje1jcb1 & ! semi-axis ,,cs to be #ic1daj1 ! ratio ( :i* numb]s is v ne>ly #i to #h2 s t ! sph]oid 0 ( ! k9d :i* resembles a compress$ sph]e1 be+ g5]at$ by ! revolution ( an ellipse ab\t its small] diamet]4 ,i f\nd also ! value ( ,,cg ! semi-diamet] p>allel to ! tang5t ,,ml to be #ih1ggi4 ,illu/ration #bh4 ,n[ pass+ to ! inve/igation ( ! refractions :i* obliquely incid5t rays mu/ und]go1 accord+ to our hypo!sis ( sph]oidal waves1 ,i saw t ^! refractions dep5d$ on ! ratio betwe5 ! velocity ( movem5t ( ! light outside ! cry/al 9 ! e!r1 & t )9 ! cry/al4 ,= suppos+1 = example1 ?is proportion to be su* t :ile ! light 9 ! cry/al =ms ! sph]oid ,,gsp1 z ,i h j said1 x =ms outside a sph]e ! semi-diamet] ( :i* is equal to ! l9e ,n :i* w be det]m9$ h]eaft]1 ! foll[+ is ! way ( f9d+ ! refraction ( ! incid5t rays4 ,let !re be su* a ray ,,rc fall+ ^u ! surface ,,ck4 ,make ,,co p]p5dicul> to ,,rc1 & across ! angle ,,kco adju/ ,,ok1 equal to ,n & p]p5dicul> to ,,co2 !n draw ,,ki1 :i* t\*es ! ,ellipse ,,gsp1 & f ! po9t ( contact ,i jo9 ,,ic1 :i* w be ! requir$ refraction ( ! ray ,,rc4 ,! demon/ration ( ?is is1 x w be se51 entirely simil> to t ( :i* we made use 9 expla9+ ord9>y refraction4 ,= ! refraction ( ! ray ,,rc is no?+ else ?an ! progression ( ! portion ,c ( ! wave ,,co1 cont9u$ 9 ! cry/al4 ,n[ ! portions ,h ( ?is wave1 dur+ ! "t t ,o came to ,k1 w h arriv$ at ! surface ,,ck along ! /raight l9es ,hx1 & w moreov] h produc$ 9 ! cry/al ar\nd ! c5tres x "s hemi-sph]oidal p>tial waves simil> to ! hemi-sph]oidal ,,gspg1 & simil>ly dispos$1 & ( :i* ! major & m9or diamet]s w be> ! same proportions to ! l9es xv 7! cont9uations ( ! l9es ,hx up to ,,kb p>allel to ,,co7 t ! diamet]s ( ! sph]oid ,,gspg be> to ! l9e ,,cb1 or ,n4 ,& x is q easy to see t ! common tang5t ( all ^! sph]oids1 :i* are "h repres5t$ by ,ellipses1 w be ! /raight l9e ,,ik1 :i* consequ5tly w be ! propagation ( ! wave ,,co2 & ! po9t ,i w be t ( ! po9t ,c1 con=mably ) t :i* has be5 demon/rat$ 9 ord9>y refraction4 ,n[ z to f9d+ ! po9t ( contact ,i1 x is kn[n t "o mu/ f9d ,,cd a ?ird proportional to ! l9es ,,ck1 ,,cg1 & draw ,,di p>allel to ,,cm1 previ\sly det]m9$1 :i* is ! conjugate diamet] to ,,cg2 = !n1 by draw+ ,,ki x t\*es ! ,ellipse at ,i4 #bi4 ,n[ z we h f\nd ,,ci ! refraction ( ! ray ,,rc1 simil>ly "o w f9d ,ci ! refraction ( ! ray r,c1 :i* comes f ! opposite side1 by mak+ ,co p]p5dicul> to r,c & foll[+ out ! re/ ( ! con/ruction z be=e4 ,:5ce "o sees t if ! ray r,c is incl9$ equally ) ,,rc1 ! l9e ,cd w necess>ily be equal to ,,cd1 because ,ck is equal to ,,ck1 & ,cg to ,,cg4 ,& 9 consequ5ce ,ii w be cut at ,e into equal p>ts by ! l9e ,,cm1 to :i* ,,di & di are p>allel4 ,& because ,,cm is ! conjugate diamet] to ,,cg1 x foll[s t i,i w be p>allel to g,g4 ,!re=e if "o prolongs ! refract$ rays ,,ci1 ,ci1 until !y meet ! tang5t ,,ml at ,t & t1 ! di/ances ,,mt1 ,mt1 w also be equal4 ,& s1 by our hypo!sis1 we expla9 p]fectly ! ph5om5on m5tion$ above2 to wit1 t :5 !re are two rays equally incl9$1 b com+ f opposite sides1 z "h ! rays ,,rc1 rc1 _! refractions div]ge equally f ! l9e foll[$ by ! refraction ( ! ray p]p5dicul> to ! surface1 by consid]+ ^! div]g5ces 9 ! direction p>allel to ! surface ( ! cry/al4 #cj4 ,to f9d ! l5g? ( ! l9e ,n1 9 proportion to ,,cp1 ,,cs1 ,,cg1 x mu/ be det]m9$ by obs]vations ( ! irregul> refraction :i* occurs 9 ?is section ( ! cry/al2 & ,i f9d ?us t ! ratio ( ,n to ,,gc is j a little less ?an #h to #e4 ,& hav+ reg>d to "s o!r obs]vations & ph5om5a ( :i* ,i %all speak aft]w>ds1 ,i put ,n at #aef1ifb p>ts1 ( :i* ! semi-diamet] ,,cg is f\nd to conta9 #ih1ggi1 mak+ ?is ratio #h to #e-a_/bi4 ,n[ ?is proportion1 :i* !re is betwe5 ! l9e ,n & ,,cg1 may be call$ ! ,proportion ( ! ,refraction2 simil>ly z 9 glass t ( #c to #b1 z w be manife/ :5 ,i %all h expla9$ a %ort process 9 ! prec$+ way to f9d ! irregul> refractions4 #ca4 ,suppos+ !n1 9 ! next figure1 z previ\sly1 ! surface ( ! cry/al g,g1 ! ,ellipse ,,gpg1 & ! l9e ,n2 & ,,cm ! refraction ( ! p]p5dicul> ray ,,fc1 f :i* x div]ges by #f degrees #dj m9utes4 ,n[ let !re be "s o!r ray ,,rc1 ! refraction ( :i* mu/ be f\nd4 ,ab\t ! c5tre ,c1 ) semi-diamet] ,,cg1 let ! circumf]5ce g,,rg be describ$1 cutt+ ! ray ,,rc at ,r2 & let ,,rv be ! p]p5dicul> on ,,cg4 ,!n z ! l9e ,n is to ,,cg let ,,cv be to ,,cd1 & let ,,di be drawn p>allel to ,,cm1 cutt+ ! ,ellipse g,,mg at ,i2 !n jo9+ ,,ci1 ?is w be ! requir$ refraction ( ! ray ,,rc4 ,:i* is demon/rat$ ?us4 ,illu/ration ,let ,,co be p]p5dicul> to ,,cr1 & across ! angle ,,ocg let ,,ok be adju/$1 equal to ,n & p]p5dicul> to ,,co1 & let !re be drawn ! /raight l9e ,,ki1 :i* if x is demon/rat$ to be a tang5t to ! ,ellipse at ,i1 x w be evid5t by ! ?+s h]et(ore expla9$ t ,,ci is ! refraction ( ! ray ,,rc4 ,n[ s9ce ! angle ,,rco is a "r angle1 x is easy to see t ! "r-angl$ triangles ,,rcv1 ,,kco1 are simil>4 ,z !n1 ,,ck is to ,,ko1 s also is ,,rc to ,,cv4 ,b ,,ko is equal to ,n1 & ,,rc to ,,cg3 !n z ,,ck is to ,n s w ,,cg be to ,,cv4 ,b z ,n is to ,,cg1 s1 by con/ruction1 is ,,cv to ,,cd4 ,!n z ,,ck is to ,,cg s is ,,cg to ,,cd4 ,& because ,,di is p>allel to ,,cm1 ! conjugate diamet] to ,,cg1 x foll[s t ,,ki t\*es ! ,ellipse at ,i2 :i* rema9$ to be %[n4 #cb4 ,"o sees !n t z !re is 9 ! refraction ( ord9>y m$ia a c]ta9 con/ant proportion betwe5 ! s9es ( ! angles :i* ! incid5t ray & ! refract$ ray make ) ! p]p5dicul>1 s "h !re is su* a proportion betwe5 ,,cv & ,,cd or ,,ie2 t is to say betwe5 ! ,s9e ( ! angle :i* ! incid5t ray makes ) ! p]p5dicul>1 & ! horizontal int]cept1 9 ! ,ellipse1 betwe5 ! refraction ( ?is ray & ! diamet] ,,cm4 ,= ! ratio ( ,,cv to ,,cd is1 z has be5 said1 ! same z t ( ,n to ! semi-diamet] ,,cg4 #cc4 ,i w add "h1 be=e pass+ away1 t 9 comp>+ toge!r ! regul> & irregul> refraction ( ?is cry/al1 !re is ?is rem>kable fact1 t if ,,abps be ! sph]oid by :i* light spreads 9 ! ,cry/al 9 a c]ta9 space ( "t 7:i* spread+1 z has be5 said1 s]ves = ! irregul> refraction71 !n ! inscrib$ sph]e ,,bv/ is ! ext5sion 9 ! same space ( "t ( ! light :i* s]ves = ! regul> refraction4 ,illu/ration ,= we h /at$ be=e ?is1 t ! l9e ,n be+ ! radius ( a sph]ical wave ( light 9 air1 :ile 9 ! cry/al x spread ?r\gh ! sph]oid ,,abps1 ! ratio ( ,n to ,,cs w be #aef1ifb to #ic1daj4 ,b x has also be5 /at$ t ! proportion ( ! regul> refraction 0 #e to #c2 t is to say1 t ,n be+ ! radius ( a sph]ical wave ( light 9 air1 its ext5sion 9 ! cry/al w\ld1 9 ! same space ( "t1 =m a sph]e ! radius ( :i* w\ld be to ,n z #c to #e4 ,n[ #aef1ifb is to #ic1daj z #e to #c less #a_/da4 ,s t x is suffici5tly ne>ly1 & may be exactly1 ! sph]e ,,bv/1 :i* ! light describes = ! regul> refraction 9 ! cry/al1 :ile x describes ! sph]oid ,,bpsa = ! irregul> refraction1 & :ile x describes ! sph]e ( radius ,n 9 air outside ! cry/al4 ,al?\gh !n !re are1 accord+ to :at we h suppos$1 two diff]5t propagations ( light )9 ! cry/al1 x appe>s t x is only 9 directions p]p5dicul> to ! axis ,,bs ( ! sph]oid t "o ( ^! propagations occurs m rapidly ?an ! o!r2 b t !y h an equal velocity 9 ! o!r direction1 namely1 9 t p>allel to ! same axis ,,bs1 :i* is also ! axis ( ! obtuse angle ( ! cry/al4 ,illu/ration #cd4 ,! proportion ( ! refraction be+ :at we h j se51 ,i w n[ %[ t !re necess>ily foll[s !nce t notable prop]ty ( ! ray :i* fall+ obliquely on ! surface ( ! cry/al ent]s x )\t suff]+ refraction4 ,= suppos+ ! same ?+s z be=e1 & t ! ray makes ) ! same surface g,g ! angle ,,rcg ( #gc degrees #bj m9utes1 incl9+ to ! same side z ! cry/al 7( :i* ray m5tion has be5 made above72 if "o inve/igates1 by ! process above expla9$1 ! refraction ,,ci1 "o w f9d t x makes exactly a /raight l9e ) ,,rc1 & t ?us ?is ray is n deviat$ at all1 con=mably ) exp]im5t4 ,?is is prov$ z foll[s by calculation4 ,,cg or ,,cr be+1 z prec$5tly1 #ih1ggi2 ,,cm be+ #ajj1jjj2 & ! angle ,,rcv #gc degrees #bj m9utes1 ,,cv w be #bh1ccj4 ,b because ,,ci is ! refraction ( ! ray ,,rc1 ! proportion ( ,,cv to ,,cd is #aef1ifb to #ih1ggi1 namely1 t ( ,n to ,,cg2 !n ,,cd is #ag1hbh4 ,n[ ! rectangle g,,dc is to ! squ>e ( ,,di z ! squ>e ( ,,cg is to ! squ>e ( ,,cm2 h5ce ,,di or ,,ce w be #ih1cec4 ,b z ,,ce is to ,,ei1 s w ,,cm be to ,,mt1 :i* w !n be #ah1abg4 ,& be+ add$ to ,,ml1 :i* is #aa1fji 7namely ! s9e ( ! angle ,,lcm1 :i* is #f degrees #dj m9utes1 tak+ ,,cm #ajj1jjj z radius7 we get ,,lt #bg1icf2 & ?is is to ,,lc #ii1cbd z ,,cv to ,,vr1 t is to say1 z #bi1ich1 ! tang5t ( ! complem5t ( ! angle ,,rcv1 :i* is #gc degrees #bj m9utes1 is to ! radius ( ! ,tables4 ,:5ce x appe>s t ,,rcit is a /raight l9e2 :i* 0 to be prov$4 #ce4 ,fur!r x w be se5 t ! ray ,,ci 9 em]g+ ?r\gh ! opposite surface ( ! cry/al1 ought to pass out q /raight1 accord+ to ! foll[+ demon/ration1 :i* proves t ! reciprocal relation ( refraction obta9s 9 ?is cry/al ! same z 9 o!r transp>5t bodies2 t is to say1 t if a ray ,,rc 9 meet+ ! surface ( ! cry/al ,,cg is refract$ z ,,ci1 ! ray ,,ci em]g+ ?r\gh ! opposite p>allel surface ( ! cry/al1 :i* ,i suppose to be ,,ib1 w h its refraction ,,ia p>allel to ! ray ,,rc4 ,illu/ration ,let ! same ?+s be suppos$ z be=e2 t is to say1 let ,,co1 p]p5dicul> to ,,cr1 repres5t a portion ( a wave ! cont9uation ( :i* 9 ! cry/al is ,,ik1 s t ! piece ,c w be cont9u$ on along ! /raight l9e ,,ci1 :ile ,o comes to ,k4 ,n[ if "o takes a second p]iod ( "t equal to ! fir/1 ! piece ,k ( ! wave ,,ik w1 9 ?is second p]iod1 h advanc$ along ! /raight l9e ,,kb1 equal & p>allel to ,,ci1 because e piece ( ! wave ,,co1 on arriv+ at ! surface ,,ck1 ought to g on 9 ! cry/al ! same z ! piece ,c2 & 9 ?is same "t !re w be =m$ 9 ! air f ! po9t ,i a p>tial sph]ical wave hav+ a semi-diamet] ,,ia equal to ,,ko1 s9ce ,,ko has be5 trav]s$ 9 an equal "t4 ,simil>ly1 if "o consid]s "s o!r po9t ( ! wave ,,ik1 su* z h1 x w g along hm1 p>allel to ,,ci1 to meet ! surface ,,ib1 :ile ! po9t ,k trav]ses ,kl equal to hm2 & :ile ?is accompli%es ! rema9d] l,b1 !re w />t f ! po9t m a p>tial wave ! semi-diamet] ( :i*1 mn1 w h ! same ratio to l,b z ,,ia to ,,kb4 ,:5ce x is evid5t t ?is wave ( semi-diamet] mn1 & ! o!r ( semi-diamet] ,,ia w h ! same tang5t ,,ba4 ,& simil>ly = all ! p>tial sph]ical waves :i* w be =m$ outside ! cry/al by ! impact ( all ! po9ts ( ! wave ,,ik aga9/ ! surface ( ! ,e!r ,,ib4 ,x is !n precisely ! tang5t ,,ba :i* w be ! cont9uation ( ! wave ,,ik1 outside ! cry/al1 :5 ! piece ,k has rea*$ ,b4 ,& 9 consequ5ce ,,ia1 :i* is p]p5dicul> to ,,ba1 w be ! refraction ( ! ray ,,ci on em]g+ f ! cry/al4 ,n[ x is cle> t ,,ia is p>allel to ! incid5t ray ,,rc1 s9ce ,,ib is equal to ,,ck1 & ,,ia equal to ,,ko1 & ! angles ,a & ,o are "r angles4 ,x is se5 !n t1 accord+ to our hypo!sis1 ! reciprocal relation ( refraction holds good 9 ?is cry/al z well z 9 ord9>y transp>5t bodies2 z is ?us 9 fact f\nd by obs]vation4 #cf4 ,i pass n[ to ! consid]ation ( o!r sections ( ! cry/al1 & ( ! refractions !re produc$1 on :i*1 z w be se51 "s o!r v rem>kable ph5om5a dep5d4 ,let ,,abh be a p>allelepip$ ( cry/al1 & let ! top surface ,,aehf be a p]fect rhombus1 ! obtuse angles ( :i* are equally divid$ by ! /raight l9e ,,ef1 & ! acute angles by ! /raight l9e ,,ah p]p5dicul> to ,,fe4 ,! section :i* we h hi!rto consid]$ is t :i* passes ?r\gh ! l9es ,,ef1 ,,eb1 & :i* at ! same "t cuts ! plane ,,aehf at "r angles4 ,refractions 9 ?is section h ?is 9 common ) ! refractions 9 ord9>y m$ia t ! plane :i* is drawn ?r\gh ! incid5t ray & :i* also int]sects ! surface ( ! cry/al at "r angles1 is t 9 :i* ! refract$ ray also is f\nd4 ,b ! refractions :i* app]ta9 to e o!r section ( ?is cry/al h ?is /range prop]ty t ! refract$ ray always quits ! plane ( ! incid5t ray p]p5dicul> to ! surface1 & turns away t[>ds ! side ( ! slope ( ! cry/al4 ,= :i* fact we %all %[ ! reason1 9 ! fir/ place1 = ! section ?r\gh ,,ah2 & we %all %[ at ! same "t h[ "o c det]m9e ! refraction1 accord+ to our hypo!sis4 ,let !re be1 !n1 9 ! plane :i* passes ?r\gh ,,ah1 & :i* is p]p5dicul> to ! plane ,,afhe1 ! incid5t ray ,,rc2 x is requir$ to f9d its refraction 9 ! cry/al4 ,illu/ration #cg4 ,ab\t ! c5tre ,c1 :i* ,i suppose to be 9 ! int]section ( ,,ah & ,,fe1 let !re be imag9$ a hemi-sph]oid ,,qgqg,m1 su* z ! light w\ld =m 9 spread+ 9 ! cry/al1 & let its section by ! plane ,,aehf =m ! ,ellipse ,,qgqg1 ! major diamet] ( :i* ,qq1 :i* is 9 ! l9e ,,ah1 w necess>ily be "o ( ! major diamet]s ( ! sph]oid2 because ! axis ( ! sph]oid be+ 9 ! plane ?r\gh ,,feb1 to :i* ,,qc is p]p5dicul>1 x foll[s t ,,qc is also p]p5dicul> to ! axis ( ! sph]oid1 & consequ5tly ,,qcq "o ( its major diamet]s4 ,b ! m9or diamet] ( ?is ,ellipse1 ,gg1 w be> to ,qq ! proportion :i* has be5 def9$ previ\sly1 ,article #bg1 betwe5 ,,cg & ! major semi-diamet] ( ! sph]oid1 ,,cp1 namely1 t ( #ih1ggi to #aje1jcb4 ,let ! l9e ,n be ! l5g? ( ! travel ( light 9 air dur+ ! "t 9 :i*1 )9 ! cry/al1 x makes1 f ! c5tre ,c1 ! sph]oid ,,qcqg,m4 ,!n hav+ drawn ,,co p]p5dicul> to ! ray ,,cr & situate 9 ! plane ?r\gh ,,cr & ,,ah1 let !re be adju/$1 across ! angle ,,aco1 ! /raight l9e ,,ok equal to ,n & p]p5dicul> to ,,co1 & let x meet ! /raight l9e ,,ah at ,k4 ,suppos+ consequ5tly t ,,cl is p]p5dicul> to ! surface ( ! cry/al ,,aehf1 & t ,,cm is ! refraction ( ! ray :i* falls p]p5dicul>ly on ?is same surface1 let !re be drawn a plane ?r\gh ! l9e ,,cm & ?r\gh ,,k*1 mak+ 9 ! sph]oid ! semi-ellipse ,,qmq1 :i* w be giv51 s9ce ! angle ,,mcl is giv5 ( value #f degrees #dj m9utes4 ,& x is c]ta91 accord+ to :at has be5 expla9$ above1 ,article #bg1 t a plane :i* w\ld t\* ! sph]oid at ! po9t ,m1 :]e ,i suppose ! /raight l9e ,,cm to meet ! surface1 w\ld be p>allel to ! plane ,,qgq4 ,if !n ?r\gh ! po9t ,k "o n[ draws ,,ks p>allel to ,gg1 :i* w be p>allel also to ,,qx1 ! tang5t to ! ,ellipse ,,qgq at ,q2 & if "o conceives a plane pass+ ?r\gh ,,ks & t\*+ ! sph]oid1 ! po9t ( contact w necess>ily be 9 ! ,ellipse ,,qmq1 because ?is plane ?r\gh ,,ks1 z well z ! plane :i* t\*es ! sph]oid at ! po9t ,m1 are p>allel to ,,qx1 ! tang5t ( ! sph]oid3 = ?is consequ5ce w be demon/rat$ at ! end ( ?is ,treatise4 ,let ?is po9t ( contact be at ,i1 !n mak+ ,,kc1 ,,qc1 ,,dc proportionals1 draw ,,di p>allel to ,,cm2 also jo9 ,,ci4 ,i say t ,,ci w be ! requir$ refraction ( ! ray ,,rc4 ,?is w be manife/ if1 9 consid]+ ,,co1 :i* is p]p5dicul> to ! ray ,,rc1 z a portion ( ! wave ( light1 we c demon/rate t ! cont9uation ( its piece ,c w be f\nd 9 ! cry/al at ,i1 :5 ,o has arriv$ at ,k4 #ch4 ,n[ z 9 ! ,*apt] on ,reflexion1 9 demon/rat+ t ! incid5t & reflect$ rays are always 9 ! same plane p]p5dicul> to ! reflect+ surface1 we consid]$ ! bread? ( ! wave ( light1 s1 simil>ly1 we mu/ "h consid] ! bread? ( ! wave ,,co 9 ! diamet] ,gg4 ,tak+ !n ! bread? ,cc on ! side t[>d ! angle ,e1 let ! p>allelogram ,,cooc be tak5 z a portion ( a wave1 & let u complete ! p>allelograms ,,ckkc1 ,,ciic1 ,klik1 ,,okko4 ,9 ! "t !n t ! l9e ,oo arrives at ! surface ( ! cry/al at ,kk1 all ! po9ts ( ! wave ,,cooc w h arriv$ at ! rectangle ,kc along l9es p>allel to ,,ok2 & f ! po9ts ( _! incid5ces !re w orig9ate1 beyond t1 9 ! cry/al p>tial hemi-sph]oids1 simil> to ! hemi-sph]oid ,,qmq1 & simil>ly dispos$4 ,^! hemi-sph]oids w necess>ily all t\* ! plane ( ! p>allelogram ,,kiik at ! same in/ant t ,oo has rea*$ ,kk4 ,:i* is easy to compreh5d1 s9ce1 ( ^! hemi-sph]oids1 all ^? :i* h _! c5tres along ! l9e ,,ck1 t\* ?is plane 9 ! l9e ,,ki 7= ?is is to be %[n 9 ! same way z we h demon/rat$ ! refraction ( ! oblique ray 9 ! pr9cipal section ?r\gh ,,ef7 & all ^? :i* h _! c5tres 9 ! l9e ,cc w t\* ! same plane ,,ki 9 ! l9e ,ii2 all ^! be+ simil> to ! hemi-sph]oid ,,qmq4 ,s9ce !n ! p>allelogram ,ki is t :i* t\*es all ^! sph]oids1 ?is same p>allelogram w be precisely ! cont9uation ( ! wave ,,cooc 9 ! cry/al1 :5 ,oo has arriv$ at ,kk1 because x =ms ! t]m9ation ( ! movem5t & because ( ! quantity ( movem5t :i* occurs m !re ?an any:]e else3 & ?us x appe>s t ! piece ,c ( ! wave ,,cooc has its cont9uation at ,i2 t is to say1 t ! ray ,,rc is refract$ z ,,ci4 ,f ?is x is to be not$ t ! proportion ( ! refraction = ?is section ( ! cry/al is t ( ! l9e ,n to ! semi-diamet] ,,cq2 by :i* "o w easily f9d ! refractions ( all incid5t rays1 9 ! same way z we h %[n previ\sly = ! case ( ! section ?r\gh ,,fe2 & ! demon/ration w be ! same4 ,b x appe>s t ! said proportion ( ! refraction is less "h ?an 9 ! section ?r\gh ,,feb2 = x 0 !re ! same z ! ratio ( ,n to ,,cg1 t is to say1 z #aef1ifb to #ih1ggi1 v ne>ly z #h to #e2 & "h x is ! ratio ( ,n to ,,cq ! major semi-diamet] ( ! sph]oid1 t is to say1 z #aef1ifb to #aje1jcb1 v ne>ly z #c to #b1 b j a little less4 ,:i* /ill agrees p]fectly ) :at "o f9ds by obs]vation4 #ci4 ,= ! re/1 ?is div]sity ( proportion ( refraction produces a v s+ul> effect 9 ?is ,cry/al2 :i* is t :5 x is plac$ ^u a %eet ( pap] on :i* !re are lett]s or any?+ else m>k$1 if "o views x f above ) ! two eyes situat$ 9 ! plane ( ! section ?r\gh ,,ef1 "o sees ! lett]s rais$ up by ?is irregul> refraction m ?an :5 "o puts "o's eyes 9 ! plane ( section ?r\gh ,,ah3 & ! diff]5ce ( ^! elevations appe>s by comp>ison ) ! o!r ord9>y refraction ( ! cry/al1 ! proportion ( :i* is z #e to #c1 & :i* always raises ! lett]s equally1 & high] ?an ! irregul> refraction does4 ,= "o sees ! lett]s & ! pap] on :i* !y are writt51 z on two diff]5t /ages at ! same "t2 & 9 ! fir/ position ( ! eyes1 namely1 :5 !y are 9 ! plane ?r\gh ,,ah ^! two /ages are f\r times m di/ant f "o ano!r ?an :5 ! eyes are 9 ! plane ?r\gh ,,ef4 ,we w %[ t ?is effect foll[s f ! refractions2 & x w enable u at ! same "t to asc]ta9 ! app>5t place ( a po9t ( an object plac$ imm$iately "u ! cry/al1 accord+ to ! diff]5t situation ( ! eyes4 #dj4 ,let u see fir/ by h[ mu* ! irregul> refraction ( ! plane ?r\gh ,,ah ought to lift ! bottom ( ! cry/al4 ,let ! plane ( ?is figure repres5t sep>ately ! section ?r\gh ,qq & ,,cl1 9 :i* section !re is also ! ray ,,rc1 & let ! semi-elliptic plane ?r\gh ,qq & ,,cm be incl9$ to ! =m]1 z previ\sly1 by an angle ( #f degrees #dj m9utes2 & 9 ?is plane ,,ci is !n ! refraction ( ! ray ,,rc4 ,illu/ration ,if n[ "o consid]s ! po9t ,i z at ! bottom ( ! cry/al1 & t x is view$ by ! rays ,,icr1 ,icr1 refract$ equally at ! po9ts ,cc1 :i* %\ld be equally di/ant f ,d1 & t ^! rays meet ! two eyes at ,rr2 x is c]ta9 t ! po9t ,i w appe> rais$ to ,s :]e ! /raight l9es ,,rc1 rc1 meet2 :i* po9t ,s is 9 ,,dp1 p]p5dicul> to ,qq4 ,& if ^u ,,dp !re is drawn ! p]p5dicul> ,,ip1 :i* w lie at ! bottom ( ! cry/al1 ! l5g? ,,sp w be ! app>5t elevation ( ! po9t ,i above ! bottom4 ,let !re be describ$ on ,qq a semicircle cutt+ ! ray ,,cr at ,b1 f :i* ,,bv is drawn p]p5dicul> to ,qq2 & let ! proportion ( ! refraction = ?is section be1 z be=e1 t ( ! l9e ,n to ! semi-diamet] ,,cq4 ,!n z ,n is to ,,cq s is ,,vc to ,,cd1 z appe>s by ! me?od ( f9d+ ! refraction :i* we h %[n above1 ,article #ca2 b z ,,vc is to ,,cd1 s is ,,vb to ,,ds4 ,!n z ,n is to ,,cq1 s is ,,vb to ,,ds4 ,let ,,ml be p]p5dicul> to ,,cl4 ,& because ,i suppose ! eyes ,rr to be di/ant ab\t a foot or s f ! cry/al1 & consequ5tly ! angle ,,rsr v small1 ,,vb may be consid]$ z equal to ! semi-diamet] ,,cq1 & ,,dp z equal to ,,cl2 !n z ,n is to ,,cq s is ,,cq to ,,ds4 ,b ,n is valu$ at #aef1ifb p>ts1 ( :i* ,,cm conta9s #ajj1jjj & ,,cq #aje1jcb4 ,!n ,,ds w h #gj1bhc4 ,b ,,cl is #ii1cbd1 be+ ! s9e ( ! complem5t ( ! angle ,,mcl :i* is #f degrees #dj m9utes2 ,,cm be+ suppos$ z radius4 ,!n ,,dp1 consid]$ z equal to ,,cl1 w be to ,,ds z #ii1cbd to #gj1bhc4 ,& s ! elevation ( ! po9t ,i by ! refraction ( ?is section is kn[n4 ,illu/ration #da4 ,n[ let !re be repres5t$ ! o!r section ?r\gh ,,ef 9 ! figure be=e ! prec$+ "o2 & let ,,cmg be ! semi-ellipse1 consid]$ 9 ,articles #bg & #bh1 :i* is made by cutt+ a sph]oidal wave hav+ c5tre ,c4 ,let ! po9t ,i1 tak5 9 ?is ellipse1 be imag9$ aga9 at ! bottom ( ! ,cry/al2 & let x be view$ by ! refract$ rays ,,icr1 ,icr1 :i* g to ! two eyes2 ,,cr & cr be+ equally incl9$ to ! surface ( ! cry/al ,gg4 ,?is be+ s1 if "o draws ,,id p>allel to ,,cm1 :i* ,i suppose to be ! refraction ( ! p]p5dicul> ray incid5t at ! po9t ,c1 ! di/ances ,,dc1 ,dc1 w be equal1 z is easy to see by t :i* has be5 demon/rat$ 9 ,article #bh4 ,n[ x is c]ta9 t ! po9t ,i %\ld appe> at ,s :]e ! /raight l9es ,,rc1 rc1 meet :5 prolong$2 & t ?is po9t w fall 9 ! l9e ,,dp p]p5dicul> to ,gg4 ,if "o draws ,,ip p]p5dicul> to ?is ,,dp1 x w be ! di/ance ,,ps :i* w m>k ! app>5t elevation ( ! po9t ,i4 ,let !re be describ$ on ,gg a semicircle cutt+ ,,cr at ,b1 f :i* let ,,bv be drawn p]p5dicul> to ,gg2 & let ,n to ,,gc be ! proportion ( ! refraction 9 ?is section1 z 9 ,article #bh4 ,s9ce !n ,,ci is ! refraction ( ! radius ,,bc1 & ,,di is p>allel to ,,cm1 ,,vc mu/ be to ,,cd z ,n to ,,gc1 accord+ to :at has be5 demon/rat$ 9 ,article #ca4 ,b z ,,vc is to ,,cd s is ,,bv to ,,ds4 ,let ,,ml be drawn p]p5dicul> to ,,cl4 ,& because ,i consid]1 aga91 ! eyes to be di/ant above ! cry/al1 ,,bv is deem$ equal to ! semi-diamet] ,,cg2 & h5ce ,,ds w be a ?ird proportional to ! l9es ,n & ,,cg3 also ,,dp w be deem$ equal to ,,cl4 ,n[ ,,cg consi/+ ( #ih1ggh p>ts1 ( :i* ,,cm conta9s #ajj1jjj1 ,n is tak5 z #aef1ifb4 ,!n ,,ds w be #fb1afc4 ,b ,,cl is also det]m9$1 & conta9s #ii1cbd p>ts1 z has be5 said 9 ,articles #cd & #dj4 ,!n ! ratio ( ,,pd to ,,ds w be z #ii1cbd to #fb1afc4 ,& ?us "o kn[s ! elevation ( ! po9t at ! bottom ,i by ! refraction ( ?is section2 & x appe>s t ?is elevation is great] ?an t by ! refraction ( ! prec$+ section1 s9ce ! ratio ( ,,pd to ,,ds 0 !re z #ii1cbd to #gj1bhc4 ,illu/ration ,b by ! regul> refraction ( ! cry/al1 ( :i* we h above said t ! proportion is #e to #c1 ! elevation ( ! po9t ,i1 or ,p1 f ! bottom1 w be #b_/e ( ! height ,,dp2 z appe>s by ?is figure1 :]e ! po9t ,p be+ view$ by ! rays ,,pcr1 ,pcr1 refract$ equally at ! surface ,cc1 ?is po9t mu/ ne$s appe> to be at ,s1 9 ! p]p5dicul> ,,pd :]e ! l9es ,,rc1 rc1 meet :5 prolong$3 & "o kn[s t ! l9e ,,pc is to ,,cs z #e to #c1 s9ce !y are to "o ano!r z ! s9e ( ! angle ,,csp or ,,dsc is to ! s9e ( ! angle ,,spc4 ,& because ! ratio ( ,,pd to ,,ds is deem$ ! same z t ( ,,pc to ,,cs1 ! two eyes ,rr be+ suppos$ v f> above ! cry/al1 ! elevation ,,ps w ?us be #b_/e ( ,,pd4 ,illu/ration #db4 ,if "o takes a /raight l9e ,,ab = ! ?ickness ( ! cry/al1 its po9t ,b be+ at ! bottom1 & if "o divides x at ! po9ts ,c1 ,d1 ,e1 accord+ to ! proportions ( ! elevations f\nd1 mak+ ,,ae #c_/e ( ,,ab1 ,,ab to ,,ac z #ii1cbd to #gj1bhc1 & ,,ab to ,,ad z #ii1cbd to #fb1afc1 ^! po9ts w divide ,,ab z 9 ?is figure4 ,& x w be f\nd t ?is agrees p]fectly ) exp]im5t2 t is to say by plac+ ! eyes above 9 ! plane :i* cuts ! cry/al accord+ to ! %ort] diamet] ( ! rhombus1 ! regul> refraction w lift up ! lett]s to ,e2 & "o w see ! bottom1 & ! lett]s ov] :i* x is plac$1 lift$ up to ,d by ! irregul> refraction4 ,b by plac+ ! eyes above 9 ! plane :i* cuts ! cry/al accord+ to ! long] diamet] ( ! rhombus1 ! regul> refraction w lift ! lett]s to ,e z be=e2 b ! irregul> refraction w make !m1 at ! same "t1 appe> lift$ up only to ,c2 & 9 su* a way t ! int]val ,,ce w be quadruple ! int]val ,,ed1 :i* "o previ\sly saw4 #dc4 ,i h only to make ! rem>k "h t 9 bo? ! positions ( ! eyes ! images caus$ by ! irregul> refraction d n appe> directly bel[ ^? :i* proce$ f ! regul> refraction1 b !y are sep>at$ f !m by be+ m di/ant f ! equilat]al solid angle ( ! ,cry/al4 ,t foll[s1 inde$1 f all t has be5 hi!rto demon/rat$ ab\t ! irregul> refraction2 & x is p>ticul>ly %[n by ^! la/ demon/rations1 f :i* "o sees t ! po9t ,i appe>s by irregul> refraction at ,s 9 ! p]p5dicul> l9e ,,dp1 9 :i* l9e also ! image ( ! po9t ,p ought to appe> by regul> refraction1 b n ! image ( ! po9t ,i1 :i* w be almo/ directly above ! same po9t1 & high] ?an ,s4 ,b z to ! app>5t elevation ( ! po9t ,i 9 o!r positions ( ! eyes above ! cry/al1 besides ! two positions :i* we h j exam9$1 ! image ( t po9t by ! irregul> refraction w always appe> betwe5 ! two heights ( ,d & ,c1 pass+ f "o to ! o!r z "o turns "o's self ar\nd ab\t ! immovable cry/al1 :ile look+ d[n f above4 ,& all ?is is /ill f\nd con=mable to our hypo!sis1 z any "o c assure himself aft] ,i %all h %[n "h ! way ( f9d+ ! irregul> refractions :i* appe> 9 all o!r sections ( ! cry/al1 besides ! two :i* we h consid]$4 ,let u suppose "o ( ! faces ( ! cry/al1 9 :i* let !re be ! ,ellipse ,,hde1 ! c5tre ,c ( :i* is also ! c5tre ( ! sph]oid ,,hme 9 :i* ! light spreads1 & ( :i* ! said ,ellipse is ! section4 ,& let ! incid5t ray be ,,rc1 ! refraction ( :i* x is requir$ to f9d4 ,let !re be tak5 a plane pass+ ?r\gh ! ray ,,rc & :i* is p]p5dicul> to ! plane ( ! ellipse ,,hde1 cutt+ x along ! /raight l9e ,,bck2 & hav+ 9 ! same plane ?r\gh ,,rc made ,,co p]p5dicul> to ,,cr1 let ,,ok be adju/$ across ! angle ,,ock1 s z to be p]p5dicul> to ,,oc & equal to ! l9e ,n1 :i* ,i suppose to measure ! travel ( ! light 9 air dur+ ! "t t x spreads 9 ! cry/al ?r\gh ! sph]oid ,,hdem4 ,!n 9 ! plane ( ! ,ellipse ,,hde let ,,kt be drawn1 ?r\gh ! po9t ,k1 p]p5dicul> to ,,bck4 ,n[ if "o conceives a plane drawn ?r\gh ! /raight l9e ,,kt & t\*+ ! sph]oid ,,hme at ,i1 ! /raight l9e ,,ci w be ! refraction ( ! ray ,,rc1 z is easy to d$uce f t :i* has be5 demon/rat$ 9 ,article #cf4 ,illu/ration ,b x mu/ be %[n h[ "o c det]m9e ! po9t ( contact ,i4 ,let !re be drawn p>allel to ! l9e ,,kt a l9e ,,hf :i* t\*es ! ,ellipse ,,hde1 & let ?is po9t ( contact be at ,h4 ,& hav+ drawn a /raight l9e along ,,* to meet ,,kt at ,t1 let !re be imag9$ a plane pass+ ?r\gh ! same ,,* & ?r\gh ,,cm 7:i* ,i suppose to be ! refraction ( ! p]p5dicul> ray71 :i* makes 9 ! sph]oid ! elliptical section ,,hme4 ,x is c]ta9 t ! plane :i* w pass ?r\gh ! /raight l9e ,,kt1 & :i* w t\* ! sph]oid1 w t\* x at a po9t 9 ! ,ellipse ,,hme1 accord+ to ! ,lemma :i* w be demon/rat$ at ! end ( ! ,*apt]4 ,n[ ?is po9t is necess>ily ! po9t ,i :i* is s\ght1 s9ce ! plane drawn ?r\gh ,,tk c t\* ! sph]oid at "o po9t only4 ,& ?is po9t ,i is easy to det]m9e1 s9ce x is ne$ful only to draw f ! po9t ,t1 :i* is 9 ! plane ( ?is ,ellipse1 ! tang5t ,,ti1 9 ! way %[n previ\sly4 ,= ! ,ellipse ,,hme is giv51 & its conjugate semi-diamet]s are ,,* & ,,cm2 because a /raight l9e drawn ?r\gh ,m1 p>allel to ,,he1 t\*es ! ,ellipse ,,hme1 z foll[s f ! fact t a plane tak5 ?r\gh ,m1 & p>allel to ! plane ,,hde1 t\*es ! sph]oid at t po9t ,m1 z is se5 f ,articles #bg & #bc4 ,= ! re/1 ! position ( ?is ellipse1 ) respect to ! plane ?r\gh ! ray ,,rc & ?r\gh ,,ck1 is also giv52 f :i* x w be easy to f9d ! position ( ,,ci1 ! refraction correspond+ to ! ray ,,rc4 ,n[ x mu/ be not$ t ! same ellipse ,,hme s]ves to f9d ! refractions ( any o!r ray :i* may be 9 ! plane ?r\gh ,,rc & ,,ck4 ,because e plane1 p>allel to ! /raight l9e ,,hf1 or ,,tk1 :i* w t\* ! sph]oid1 w t\* x 9 ?is ellipse1 accord+ to ! ,lemma quot$ a little be=e4 ,i h inve/igat$ ?us1 9 m9ute detail1 ! prop]ties ( ! irregul> refraction ( ?is ,cry/al1 9 ord] to see :e!r ea* ph5om5on t is d$uc$ f our hypo!sis accords ) t :i* is obs]v$ 9 fact4 ,& ?is be+ s x af=ds no slight pro( ( ! tru? ( our suppositions & pr9ciples4 ,b :at ,i am go+ to add "h confirms !m aga9 m>vell\sly4 ,x is ?is3 t !re are diff]5t sections ( ?is ,cry/al1 ! surfaces ( :i*1 !reby produc$1 give rise to refractions precisely su* z !y ought to be1 & z ,i _h =ese5 !m1 accord+ to ! prec$+ ,!ory4 ,9 ord] to expla9 :at ^! sections are1 let ,,abkf be ! pr9cipal section ?r\gh ! axis ( ! cry/al ,,ack1 9 :i* !re w also be ! axis ,,ss ( a sph]oidal wave ( light spread+ 9 ! cry/al f ! c5tre ,c2 & ! /raight l9e :i* cuts ,,ss ?r\gh ! middle & at "r angles1 namely ,,pp1 w be "o ( ! major diamet]s4 ,illu/ration3 ,section ,,abkf ,n[ z 9 ! natural section ( ! cry/al1 made by a plane p>allel to two opposite faces1 :i* plane is "h repres5t$ by ! l9e ,,gg1 ! refraction ( ! surfaces :i* are produc$ by x w be gov]n$ by ! hemi-sph]oids ,,gng1 accord+ to :at has be5 expla9$ 9 ! prec$+ ,!ory4 ,simil>ly1 cutt+ ! ,cry/al ?r\gh ,,nn1 by a plane p]p5dicul> to ! p>allelogram ,,abkf1 ! refraction ( ! surfaces w be gov]n$ by ! hemi-sph]oids ,,ngn4 ,& if "o cuts x ?r\gh ,,pp1 p]p5dicul>ly to ! said p>allelogram1 ! refraction ( ! surfaces ought to be gov]n$ by ! hemi-sph]oids ,,psp1 & s = o!rs4 ,b ,i saw t if ! plane ,,nn 0 almo/ p]p5dicul> to ! plane ,,gg1 mak+ ! angle ,,ncg1 :i* is on ! side ,a1 an angle ( #ij degrees #dj m9utes1 ! hemi-sph]oids ,,ngn w\ld become simil> to ! hemi-sph]oids ,,gng1 s9ce ! planes ,,nn & ,,gg 7 equally incl9$ by an angle ( #de degrees #bj m9utes to ! axis ,,ss4 ,9 consequ5ce x mu/ ne$s be1 if our !ory is true1 t ! surfaces :i* ! section ?r\gh ,,nn produces %\ld effect ! same refractions z ! surfaces ( ! section ?r\gh ,,gg4 ,& n only ! surfaces ( ! section ,,nn b all o!r sections produc$ by planes :i* might be incl9$ to ! axis at an angle equal to #de degrees #bj m9utes4 ,s t !re are an inf9itude ( planes :i* ought to produce precisely ! same refractions z ! natural surfaces ( ! cry/al1 or z ! section p>allel to any "o ( ^? surfaces :i* are made by cleavage4 ,i saw also t by cutt+ x by a plane tak5 ?r\gh ,,pp1 & p]p5dicul> to ! axis ,,ss1 ! refraction ( ! surfaces ought to be su* t ! p]p5dicul> ray %\ld suff] !reby no deviation2 & t = oblique rays !re w\ld always be an irregul> refraction1 diff]+ f ! regul>1 & by :i* objects plac$ b5ea? ! cry/al w\ld be less elevat$ ?an by t o!r refraction4 ,t1 simil>ly1 by cutt+ ! cry/al by any plane ?r\gh ! axis ,,ss1 su* z ! plane ( ! figure is1 ! p]p5dicul> ray ought to suff] no refraction2 & t = oblique rays !re 7 diff]5t measures = ! irregul> refraction accord+ to ! situation ( ! plane 9 :i* ! incid5t ray 04 ,n[ ^! ?+s 7 f\nd 9 fact s2 &1 aft] t1 ,i c\ld n d\bt t a simil> success c\ld be met ) ev]y:]e4 ,:5ce ,i conclud$ t "o might =m f ?is cry/al solids simil> to ^? :i* are its natural =ms1 :i* %\ld produce1 at all _! surfaces1 ! same regul> & irregul> refractions z ! natural surfaces1 & :i* nev]!less w\ld cleave 9 q o!r ways1 & n 9 directions p>allel to any ( _! faces4 ,t out ( x "o w\ld be able to fa%ion pyramids1 hav+ _! base squ>e1 p5tagonal1 hexagonal1 or ) z _m sides z "o desir$1 all ! surfaces ( :i* %\ld h ! same refractions z ! natural surfaces ( ! cry/al1 except ! base1 :i* w n refract ! p]p5dicul> ray4 ,^! surfaces w ea* make an angle ( #de degrees #bj m9utes ) ! axis ( ! cry/al1 & ! base w be ! section p]p5dicul> to ! axis4 ,t1 f9ally1 "o c\ld also fa%ion out ( x triangul> prisms1 or prisms ) z _m sides z "o w\ld1 ( :i* nei!r ! sides nor ! bases w\ld refract ! p]p5dicul> ray1 al?\gh !y w\ld yet all cause d\ble refraction = oblique rays4 ,! cube is includ$ among/ ^! prisms1 ! bases ( :i* are sections p]p5dicul> to ! axis ( ! cry/al1 & ! sides are sections p>allel to ! same axis4 ,f all ?is x fur!r appe>s t x is n at all 9 ! disposition ( ! lay]s ( :i* ?is cry/al seems to be compos$1 & accord+ to :i* x splits 9 ?ree diff]5t s5ses1 t ! cause resides ( its irregul> refraction2 & t x w\ld be 9 va9 to wi% to seek x !re4 ,b 9 ord] t any "o :o has "s ( ?is /one may be able to f9d1 by 8 own exp]i5ce1 ! tru? ( :at ,i h j advanc$1 ,i w /ate "h ! process ( :i* ,i h made use to cut x1 & to poli% x4 ,cutt+ is easy by ! slic+ :eels ( lapid>ies1 or 9 ! way 9 :i* m>ble is sawn3 b poli%+ is v difficult1 & by employ+ ! ord9>y means "o m (t5 depoli%es ! surfaces ?an makes !m luc5t4 ,aft] _m trials1 ,i h at la/ f\nd t = ?is s]vice no plate ( metal mu/ be us$1 b a piece ( mirror glass made matt & depoli%$4 ,^u ?is1 ) f9e s& & wat]1 "o smoo!s ! cry/al little by little1 9 ! same way z spectacle glasses1 & poli%es x simply by cont9u+ ! "w1 b ev] r$uc+ ! mat]ial4 ,i h n1 h[ev]1 be5 able to give x p]fect cl>ity & transp>5cy2 b ! ev5ness :i* ! surfaces acquire enables "o to obs]ve 9 !m ! effects ( refraction bett] ?an 9 ^? made by cleav+ ! /one1 :i* always h "s inequality4 ,ev5 :5 ! surface is only mod]ately smoo!d1 if "o rubs x ov] ) a little oil or :ite ( egg1 x becomes q transp>5t1 s t ! refraction is disc]n$ 9 x q di/9ctly4 ,& ?is aid is specially necess>y :5 x is wi%$ to poli% ! natural surfaces to remove ! inequalities2 because "o _c r5d] !m luc5t equally ) ! surfaces ( o!r sections1 :i* take a poli% s mu* ! bett] ! less ne>ly !y approximate to ^! natural planes4 ,be=e f9i%+ ! treatise on ?is ,cry/al1 ,i w add "o m m>vell\s ph5om5on :i* ,i discov]$ aft] hav+ writt5 all ! =ego+4 ,= ?\gh ,i h n be5 able till n[ to f9d its cause1 ,i d n = t reason wi% to desi/ f describ+ x1 9 ord] to give opportunity to o!rs to inve/igate x4 ,x seems t x w be necess>y to make /ill fur!r suppositions besides ^? :i* ,i h made2 b ^! w n = all t cease to keep _! probability aft] hav+ be5 confirm$ by s _m te/s4 ,illu/ration ,! ph5om5on is1 t by tak+ two pieces ( ?is cry/al & apply+ !m "o ov] ! o!r1 or r hold+ !m ) a space betwe5 ! two1 if all ! sides ( "o are p>allel to ^? ( ! o!r1 !n a ray ( light1 su* z ,,ab1 is divid$ into two 9 ! fir/ piece1 namely into ,,bd & ,,bc1 foll[+ ! two refractions1 regul> & irregul>4 ,on p5etrat+ !nce into ! o!r piece ea* ray w pass !re )\t fur!r divid+ itself 9 two2 b t "o :i* und]w5t ! regul> refraction1 z "h ,,dg1 w und]go aga9 only a regul> refraction at ,,gh2 & ! o!r1 ,,ce1 an irregul> refraction at ,,ef4 ,& ! same ?+ occurs n only 9 ?is disposition1 b also 9 all ^? cases 9 :i* ! pr9cipal section ( ea* ( ! pieces is situat$ 9 "o & ! same plane1 )\t x be+ ne$ful = ! two neighb\r+ surfaces to be p>allel4 ,n[ x is m>vell\s :y ! rays ,,ce & ,,dg1 incid5t f ! air on ! l[] cry/al1 d n divide !mselves ! same z ! fir/ ray ,,ab4 ,"o w\ld say t x mu/ be t ! ray ,,dg 9 pass+ ?r\gh ! upp] piece has lo/ some?+ :i* is necess>y to move ! matt] :i* s]ves = ! irregul> refraction2 & t likewise ,,ce has lo/ t :i* 0 necess>y to move ! matt] :i* s]ves = regul> refraction3 b !re is yet ano!r ?+ :i* upsets ?is reason+4 ,x is t :5 "o disposes ! two cry/als 9 su* a way t ! planes :i* con/itute ! pr9cipal sections int]sect "o ano!r at "r angles1 :e!r ! neighb\r+ surfaces are p>allel or n1 !n ! ray :i* has come by ! regul> refraction1 z ,,dg1 und]goes only an irregul> refraction 9 ! l[] piece2 & on ! contr>y ! ray :i* has come by ! irregul> refraction1 z ,,ce1 und]goes only a regul> refraction4 ,b 9 all ! inf9ite o!r positions1 besides ^? :i* ,i h j /at$1 ! rays ,,dg1 ,,ce1 divide !mselves anew ea* "o into two1 by refraction 9 ! l[] cry/al s t f ! s+le ray ,,ab !re are f\r1 sometimes ( equal brightness1 sometimes "s mu* less bright ?an o!rs1 accord+ to ! v>y+ agreem5t 9 ! positions ( ! cry/als3 b !y d n appe> to h all toge!r m light ?an ! s+le ray ,,ab4 ,:5 "o consid]s "h h[1 :ile ! rays ,,ce1 ,,dg1 rema9 ! same1 x dep5ds on ! position t "o gives to ! l[] piece1 :e!r x divides !m bo? 9 two1 or :e!r x does n divide !m1 & yet h[ ! ray ,,ab above is always divid$1 x seems t "o is oblig$ to conclude t ! waves ( light1 aft] hav+ pass$ ?r\gh ! fir/ cry/al1 acquire a c]ta9 =m or disposition 9 virtue ( :i*1 :5 meet+ ! texture ( ! second cry/al1 9 c]ta9 positions1 !y c move ! two diff]5t k9ds ( matt] :i* s]ve = ! two species ( refraction2 & :5 meet+ ! second cry/al 9 ano!r position are able to move only "o ( ^! k9ds ( matt]4 ,b to tell h[ ?is occurs1 ,i h hi!rto f\nd no?+ :i* satisfies me4 ,leav+ !n to o!rs ?is rese>*1 ,i pass to :at ,i h to say t\*+ ! cause ( ! extraord9>y figure ( ?is cry/al1 & :y x cleaves easily 9 ?ree diff]5t s5ses1 p>allel to any "o ( its surfaces4 ,!re are _m bodies1 vegetable1 m9]al1 & congeal$ salts1 :i* are =m$ ) c]ta9 regul> angles & figures4 ,?us among fl[]s !re are _m :i* h _! leaves dispos$ 9 ord]$ polygons1 to ! numb] ( #c1 #d1 #e1 or #f sides1 b n m4 ,?is well des]ves to be inve/igat$1 bo? z to ! polygonal figure1 & z to :y x does n exce$ ! numb] #f4 ,rock ,cry/al gr[s ord9>ily 9 hexagonal b>s1 & diamonds are f\nd :i* occur ) a squ>e po9t & poli%$ surfaces4 ,!re is a species ( small flat /ones1 pil$ up directly ^u "o ano!r1 :i* are all ( p5tagonal figure ) r\nd$ angles1 & ! sides a little fold$ inw>ds4 ,! gra9s ( gray salt :i* are =m$ f sea wat] affect ! figure1 or at lea/ ! angle1 ( ! cube2 & 9 ! congelations ( o!r salts1 & 9 t ( sug>1 !re are f\nd o!r solid angles ) p]fectly flat faces4 ,small sn[flakes almo/ always fall 9 little />s ) #f po9ts1 & sometimes 9 hexagons ) /raight sides4 ,& ,i h (t5 obs]v$1 9 wat] :i* is beg9n+ to freeze1 a k9d ( flat & ?9 foliage ( ice1 ! middle ray ( :i* ?r[s out bran*es incl9$ at an angle ( #fj degrees4 ,all ^! ?+s are wor?y ( be+ c>efully inve/igat$ to asc]ta9 h[ & by :at artifice nature !re op]ates4 ,b x is n n[ my int5tion to treat fully ( ?is matt]4 ,x seems t 9 g5]al ! regul>ity :i* occurs 9 ^! productions comes f ! arrangem5t ( ! small invisible equal p>ticles ( :i* !y are compos$4 ,&1 com+ to our ,icel& ,cry/al1 ,i say t if !re 7 a pyramid su* z ,,abcd1 compos$ ( small r\nd$ corpuscles1 n sph]ical b flatt5$ sph]oids1 su* z w\ld be made by ! rotation ( ! ellipse ,,gh ar\nd its less] diamet] ,,ef 7( :i* ! ratio to ! great] diamet] is v ne>ly t ( #a to ! squ>e root ( #h7--;,i say t !n ! solid angle ( ! po9t ,d w\ld be equal to ! obtuse & equilat]al angle ( ?is ,cry/al4 ,i say1 fur!r1 t if ^! corpuscles 7 lightly /uck toge!r1 on break+ ?is pyramid x w\ld break along faces p>allel to ^? t make its po9t3 & by ?is means1 z x is easy to see1 x w\ld produce prisms simil> to ^? ( ! same cry/al z ?is o!r figure repres5ts4 ,! reason is t :5 brok5 9 ?is fa%ion a :ole lay] sep>ates easily f its neighb\r+ lay] s9ce ea* sph]oid has to be deta*$ only f ! ?ree sph]oids ( ! next lay]2 ( :i* ?ree !re is b "o :i* t\*es x on its flatt5$ surface1 & ! o!r two at ! edges4 ,& ! reason :y ! surfaces sep>ate %>p & poli%$ is t if any sph]oid ( ! neighb\r+ surface w\ld come out by atta*+ itself to ! surface :i* is be+ sep>at$1 x w\ld be ne$ful = x to deta* itself f six o!r sph]oids :i* hold x lock$1 & f\r ( :i* press x by ^! flatt5$ surfaces4 ,s9ce !n n only ! angles ( our cry/al b also ! mann] 9 :i* x splits agree precisely ) :at is obs]v$ 9 ! assemblage compos$ ( su* sph]oids1 !re is great reason to believe t ! p>ticles are %ap$ & rang$ 9 ! same way4 ,illu/ration3 ,pyramid & section ( sph]oids ,!re is ev5 probability en\gh t ! prisms ( ?is cry/al are produc$ by ! break+ up ( pyramids1 s9ce ,mr4 ,b>?ol9us relates t he occasionally f\nd "s pieces ( triangul>ly pyramidal figure4 ,b :5 a mass is compos$ int]iorly only ( ^! little sph]oids ?us pil$ up1 :atev] =m x may h ext]iorly1 x is c]ta91 by ! same reason+ :i* ,i h j expla9$1 t if brok5 x w\ld produce simil> prisms4 ,x rema9s to be se5 :e!r !re are o!r reasons :i* confirm our conjecture1 & :e!r !re are none :i* are repugnant to x4 ,illu/ration3 p>alleloid arrangem5t ( sph]oids ) planes ( pot5tial cleavage ,x may be object$ t ?is cry/al1 be+ s compos$1 might be capable ( cleavage 9 yet two m fa%ions2 "o ( :i* w\ld be along planes p>allel to ! base ( ! pyramid1 t is to say to ! triangle ,,abc2 ! o!r w\ld be p>allel to a plane ! trace ( :i* is m>k$ by ! l9es ,,gh1 ,,hk1 ,,kl4 ,to :i* ,i say t bo? ! "o & ! o!r1 ?\gh practicable1 are m difficult ?an ^? :i* 7 p>allel to any "o ( ! ?ree planes ( ! pyramid2 & t !re=e1 :5 /rik+ on ! cry/al 9 ord] to break x1 x ought always to split r along ^! ?ree planes ?an along ! two o!rs4 ,:5 "o has a numb] ( sph]oids ( ! =m above describ$1 & ranges !m 9 a pyramid1 "o sees :y ! two me?ods ( division are m difficult4 ,= 9 ! case ( t division :i* w\ld be p>allel to ! base1 ea* sph]oid w\ld be oblig$ to deta* itself f ?ree o!rs :i* x t\*es ^u _! flatt5$ surfaces1 :i* hold m /rongly ?an ! contacts at ! edges4 ,& besides t1 ?is division w n occur along entire lay]s1 because ea* ( ! sph]oids ( a lay] is sc>cely held at all by ! #f ( ! same lay] t surr\nd x1 s9ce !y only t\* x at ! edges2 s t x adh]es readily to ! neighb\r+ lay]1 & ! o!rs to x1 = ! same reason2 & ?is causes unev5 surfaces4 ,also "o sees by exp]im5t t :5 gr9d+ d[n ! cry/al on a r r\gh /one1 directly on ! equilat]al solid angle1 "o v]ily f9ds mu* facility 9 r$uc+ x 9 ?is direction1 b mu* difficulty aft]w>ds 9 poli%+ ! surface :i* has be5 flatt5$ 9 ?is mann]4 ,z = ! o!r me?od ( division along ! plane ,,ghkl1 x w be se5 t ea* sph]oid w\ld h to deta* itself f f\r ( ! neighb\r+ lay]1 two ( :i* t\* x on ! flatt5$ surfaces1 & two at ! edges4 ,s t ?is division is likewise m difficult ?an t :i* is made p>allel to "o ( ! surfaces ( ! cry/al2 :]e1 z we h said1 ea* sph]oid is deta*$ f only ?ree ( ! neighb\r+ lay]3 ( :i* ?ree !re is "o only :i* t\*es x on ! flatt5$ surface1 & ! o!r two at ! edges only4 ,h[ev]1 t :i* has made me "k t 9 ! cry/al !re are lay]s 9 ?is la/ fa%ion1 is t 9 a piece weigh+ half a p\nd :i* ,i possess1 "o sees t x is split along its l5g?1 z is ! above-m5tion$ prism by ! plane ,,ghkl2 z appe>s by col\rs ( ! ,iris ext5d+ ?r\gh\t ?is :ole plane al?\gh ! two pieces /ill hold toge!r4 ,all ?is proves !n t ! composition ( ! cry/al is su* z we h /at$4 ,to :i* ,i aga9 add ?is exp]im5t2 t if "o passes a knife scrap+ along any "o ( ! natural surfaces1 & d[nw>ds z x 7 f ! equilat]al obtuse angle1 t is to say f ! apex ( ! pyramid1 "o f9ds x q h>d2 b by scrap+ 9 ! opposite s5se an incision is easily made4 ,?is foll[s manife/ly f ! situation ( ! small sph]oids2 ov] :i*1 9 ! fir/ mann]1 ! knife glides2 b 9 ! o!r mann] x seizes !m f b5ea? almo/ z if !y 7 ! scales ( a fi%4 ,i w n und]take to say any?+ t\*+ ! way 9 :i* s _m corpuscles all equal & simil> are g5]at$1 nor h[ !y are set 9 su* beautiful ord]2 :e!r !y are =m$ fir/ & !n assembl$1 or :e!r !y arrange !mselves ?us 9 com+ into be+ & z fa/ z !y are produc$1 :i* seems to me m probable4 ,to develop tru?s s recondite !re w\ld be ne$$ a k ( nature mu* great] ?an t :i* we h4 ,i w add only t ^! little sph]oids c\ld well contribute to =m ! sph]oids ( ! waves ( light1 "h above suppos$1 ^! z well z ^? be+ simil>ly situat$1 & ) _! axes p>allel4 ,calculations :i* h be5 suppos$ 9 ?is ,*apt]4 ,mr4 ,b>?ol9us1 9 8 treatise ( ?is ,cry/al1 puts at #aja degrees ! obtuse angles ( ! faces1 :i* ,i h /at$ to be #aja degrees #eb m9utes4 ,he /ates t he measur$ ^! angles directly on ! cry/al1 :i* is difficult to d ) ultimate exactitude1 because ! edges su* z ,,ca1 ,,cb1 9 ?is figure1 are g5]ally worn1 & n q /raight4 ,= m c]ta9ty1 !re=e1 ,i pref]r$ to measure actually ! obtuse angle by :i* ! faces ,,cbda1 ,,cbvf1 are incl9$ to "o ano!r1 namely ! angle ,,ocn =m$ by draw+ ,,cn p]p5dicul> to ,,fv1 & ,,co p]p5dicul> to ,,da4 ,?is angle ,,ocn ,i f\nd to be #aje degrees2 & its supplem5t ,,cnp1 to be #ge degrees1 z x %\ld be4 ,illu/ration ,to f9d f ?is ! obtuse angle ,,bca1 ,i imag9$ a sph]e hav+ its c5tre at ,c1 & on its surface a sph]ical triangle1 =m$ by ! int]section ( ?ree planes :i* enclose ! solid angle ,c4 ,9 ?is equilat]al triangle1 :i* is ,,abf 9 ?is o!r figure1 ,i see t ea* ( ! angles %\ld be #aje degrees1 namely equal to ! angle ,,ocn2 & t ea* ( ! sides %\ld be ( z _m degrees z ! angle ,,acb1 or ,,acf1 or ,,bcf4 ,hav+ !n drawn ! arc ,,fq p]p5dicul> to ! side ,,ab1 :i* x divides equally at ,q1 ! triangle ,,fqa has a "r angle at ,q1 ! angle ,a #aje degrees1 & ,f half z mu*1 namely #eb degrees #cj m9utes2 :5ce ! hypot5use ,,af is f\nd to be #aja degrees #eb m9utes4 ,& ?is arc ,,af is ! measure ( ! angle ,,acf 9 ! figure ( ! cry/al4 ,illu/ration ,9 ! same figure1 if ! plane ,,cghf cuts ! cry/al s t x divides ! obtuse angles ,,acb1 ,,mhv1 9 ! middle1 x is /at$1 9 ,article #aj1 t ! angle ,,cfh is #gj degrees #eg m9utes4 ,?is aga9 is easily %[n 9 ! same sph]ical triangle ,,abf1 9 :i* x appe>s t ! arc ,,fq is z _m degrees z ! angle ,,gcf 9 ! cry/al1 ! supplem5t ( :i* is ! angle ,,cfh4 ,n[ ! arc ,,fq is f\nd to be #aji degrees #c m9utes4 ,!n its supplem5t1 #gj degrees #eg m9utes1 is ! angle ,,cfh4 ,x 0 /at$1 9 ,article #bf1 t ! /raight l9e ,,cs1 :i* 9 ! prec$+ figure is ,,*1 be+ ! axis ( ! cry/al1 t is to say be+ equally incl9$ to ! ?ree sides ,,ca1 ,,cb1 ,,cf1 ! angle ,,g* is #de degrees #bj m9utes4 ,?is is also easily calculat$ by ! same sph]ical triangle4 ,= by draw+ ! o!r arc ,,ad :i* cuts ,,bf equally1 & int]sects ,,fq at ,s1 ?is po9t w be ! c5tre ( ! triangle4 ,& x is easy to see t ! arc ,,sq is ! measure ( ! angle ,,g* 9 ! figure :i* repres5ts ! cry/al4 ,n[ 9 ! triangle ,,qas1 :i* is "r-angl$1 "o kn[s also ! angle ,a1 :i* is #eb degrees #cj m9utes1 & ! side ,,aq #ej degrees #ef m9utes2 :5ce ! side ,,sq is f\nd to be #de degrees #bj m9utes4 ,9 ,article #bg x 0 requir$ to %[ t ,,pms be+ an ellipse ! c5tre ( :i* is ,c1 & :i* t\*es ! /raight l9e ,,md at ,m s t ! angle ,,mcl :i* ,,cm makes ) ,,cl1 p]p5dicul> on ,,dm1 is #f degrees #dj m9utes1 & its semi-m9or axis ,,cs mak+ ) ,,cg 7:i* is p>allel to ,,md7 an angle ,,gcs ( #de degrees #bj m9utes1 x 0 requir$ to %[1 ,i say1 t1 ,,cm be+ #ajj1jjj p>ts1 ,,pc ! semi-major diamet] ( ?is ellipse is #aje1jcb p>ts1 & ,,cs1 ! semi-m9or diamet]1 #ic1daj4 ,let ,,cp & ,,cs be prolong$ & meet ! tang5t ,,dm at ,d & ,z2 & f ! po9t ( contact ,m let ,,mn & ,,mo be drawn z p]p5dicul>s to ,,cp & ,,cs4 ,n[ because ! angles ,,scp1 ,,gcl1 are "r angles1 ! angle ,,pcl w be equal to ,,gcs :i* 0 #de degrees #bj m9utes4 ,& d$uct+ ! angle ,,lcm1 :i* is #f degrees #dj m9utes1 f ,,lcp1 :i* is #de degrees #bj m9utes1 !re rema9s ,,mcp1 #ch degrees #dj m9utes4 ,consid]+ !n ,,cm z a radius ( #ajj1jjj p>ts1 ,,mn1 ! s9e ( #ch degrees #dj m9utes1 w be #fb1dgi4 ,& 9 ! "r-angl$ triangle ,,mnd1 ,,mn w be to ,,nd z ! radius ( ! ,tables is to ! tang5t ( #de degrees #bj m9utes 7because ! angle ,,nmd is equal to ,,dcl1 or ,,gcs72 t is to say z #ajj1jjj to #aja1agj3 :5ce results ,,nd #fc1baj4 ,b ,,nc is #gh1jgi ( ! same p>ts1 ,,cm be+ #ajj1jjj1 because ,,nc is ! s9e ( ! complem5t ( ! angle ,,mcp1 :i* 0 #ch degrees #dj m9utes4 ,!n ! :ole l9e ,,dc is #ada1bhi2 & ,,cp1 :i* is a mean proportional betwe5 ,,dc & ,,cn1 s9ce ,,md t\*es ! ,ellipse1 w be #aje1jcb4 ,illu/ration ,simil>ly1 because ! angle ,,omz is equal to ,,cdz1 or ,,lcz1 :i* is #dd degrees #dj m9utes1 be+ ! complem5t ( ,,gcs1 x foll[s t1 z ! radius ( ! ,tables is to ! tang5t ( #dd degrees #dj m9utes1 s w ,,om #gh1jgi be to ,,oz #gg1agf4 ,b ,,oc is #fb1dgi ( ^! same p>ts ( :i* ,,cm is #ajj1jjj1 because x is equal to ,,mn1 ! s9e ( ! angle ,,mcp1 :i* is #ch degrees #dj m9utes4 ,!n ! :ole l9e ,,cz is #aci1fee2 & ,,cs1 :i* is a mean proportional betwe5 ,,cz & ,,co w be #ic1daj4 ,at ! same place x 0 /at$ t ,,gc 0 f\nd to be #ih1ggi p>ts4 ,to prove ?is1 let ,,pe be drawn 9 ! same figure p>allel to ,,dm1 & meet+ ,,cm at ,e4 ,9 ! "r-angl$ triangle ,,cld ! side ,,cl is #ii1cbd 7,,cm be+ #ajj1jjj71 because ,,cl is ! s9e ( ! complem5t ( ! angle ,,lcm1 :i* is #f degrees #dj m9utes4 ,& s9ce ! angle ,,lcd is #de degrees #bj m9utes1 be+ equal to ,,gcs1 ! side ,,ld is f\nd to be #ajj1dhf3 :5ce d$uct+ ,,ml #aa1fji !re w rema9 ,,md #hh1hgg4 ,n[ z ,,cd 7:i* 0 #ada1bhi7 is to ,,dm #hh1hgg1 s w ,,cp #aje1jcb be to ,,pe #ff1jgj4 ,b z ! rectangle ,,meh 7or r ! diff]5ce ( ! squ>es on ,,cm & ,,ce7 is to ! squ>e on ,,mc1 s is ! squ>e on ,,pe to ! squ>e on ,cg2 !n also z ! diff]5ce ( ! squ>es on ,,dc & ,,cp to ! squ>e on ,,cd1 s also is ! squ>e on ,,pe to ! squ>e on g,c4 ,b ,,dp1 ,,cp1 & ,,pe are kn[n2 h5ce also "o kn[s ,,gc1 :i* is #ih1ggi4 ,lemma :i* has be5 suppos$4 ,if a sph]oid is t\*$ by a /raight l9e1 & also by two or m planes :i* are p>allel to ?is l9e1 ?\gh n p>allel to "o ano!r1 all ! po9ts ( contact ( ! l9e1 z well z ( ! planes1 w be 9 "o & ! same ellipse made by a plane :i* passes ?r\gh ! c5tre ( ! sph]oid4 ,let ,,l$ be ! sph]oid t\*$ by ! l9e ,,bm at ! po9t ,b1 & also by ! planes p>allel to ?is l9e at ! po9ts ,o & ,a4 ,x is requir$ to demon/rate t ! po9ts ,b1 ,o1 & ,a are 9 "o & ! same ,ellipse made 9 ! sph]oid by a plane :i* passes ?r\gh its c5tre4 ,illu/ration ,?r\gh ! l9e ,,bm1 & ?r\gh ! po9ts ,o & ,a1 let !re be drawn planes p>allel to "o ano!r1 :i*1 9 cutt+ ! sph]oid make ! ellipses ,,lbd1 ,,pop1 ,,qaq2 :i* w all be simil> & simil>ly dispos$1 & w h _! c5tres ,k1 ,n1 ,r1 9 "o & ! same diamet] ( ! sph]oid1 :i* w also be ! diamet] ( ! ellipse made by ! section ( ! plane t passes ?r\gh ! c5tre ( ! sph]oid1 & :i* cuts ! planes ( ! ?ree said ,ellipses at "r angles3 = all ?is is manife/ by proposition #ae ( ! book ( ,conoids & ,sph]oids ( ,ar*im$es4 ,fur!r1 ! two latt] planes1 :i* are drawn ?r\gh ! po9ts ,o & ,a1 w also1 by cutt+ ! planes :i* t\* ! sph]oid 9 ^! same po9ts1 g5]ate /raight l9es1 z ,,oh & ,,z1 :i* w1 z is easy to see1 be p>allel to ,,bm2 & all ?ree1 ,,bm1 ,,oh1 ,,z1 w t\* ! ,ellipses ,,lbd1 ,,pop1 ,,qaq 9 ^! po9ts1 ,b1 ,o1 ,a2 s9ce !y are 9 ! planes ( ^! ellipses1 & at ! same "t 9 ! planes :i* t\* ! sph]oid4 ,if n[ f ^! po9ts ,b1 ,o1 ,a1 !re are drawn ! /raight l9es ,,bk1 ,,on1 ,,ar1 ?r\gh ! c5tres ( ! same ellipses1 & if ?r\gh ^! c5tres !re are drawn also ! diamet]s ,,ld1 ,,pp1 ,,qq1 p>allel to ! tang5ts ,,bm1 ,,oh1 ,,z2 ^! w be conjugate to ! a=esaid ,,bk1 ,,on1 ,,ar4 ,& because ! ?ree ellipses are simil> & simil>ly dispos$1 & h _! diamet]s ,,ld1 ,,pp1 ,,qq p>allel1 x is c]ta9 t _! conjugate diamet]s ,,bk1 ,,on1 ,,ar1 w also be p>allel4 ,& ! c5tres ,k1 ,n1 ,r be+1 z has be5 /at$1 9 "o & ! same diamet] ( ! sph]oid1 ^! p>allels ,,bk1 ,,on1 ,,ar w necess>ily be 9 "o & ! same plane1 :i* passes ?r\gh ?is diamet] ( ! sph]oid1 &1 9 consequ5ce1 ! po9ts ,r1 ,o1 ,a are 9 "o & ! same ellipse made by ! int]section ( ?is plane4 ,:i* 0 to be prov$4 ,& x is manife/ t ! demon/ration w\ld be ! same if1 besides ! po9ts ,o1 ,a1 !re _h be5 o!rs 9 :i* ! sph]oid _h be5 t\*$ by planes p>allel to ! /raight l9e ,,bm4 ,,*apt] ,,vi ,,on ,,! ,,figures ,,( ,,! ,,transp>5t ,,bodies ,:i* s]ve = ,refraction & = ,reflexion ,aft] hav+ expla9$ h[ ! prop]ties ( reflexion & refraction foll[ f :at we h suppos$ conc]n+ ! nature ( light1 & ( opaque bodies1 & ( transp>5t m$ia1 ,i w "h set =? a v easy & natural way ( d$uc+1 f ! same pr9ciples1 ! true figures :i* s]ve1 ei!r by reflexion or by refraction1 to collect or disp]se ! rays ( light1 z may be desir$4 ,= ?\gh ,i d n see yet t !re are means ( mak+ use ( ^! figures1 s f> z relates to ,refraction1 n only because ( ! difficulty ( %ap+ ! glasses ( ,telescopes ) ! requisite exactitude accord+ to ^! figures1 b also because !re exi/s 9 refraction itself a prop]ty :i* h9d]s ! p]fect concurr5ce ( ! rays1 z ,mr4 ,newton has v well prov$ by exp]im5t1 ,i w yet n desi/ f relat+ ! inv5tion1 s9ce x (f]s itself1 s to speak1 ( itself1 & because x fur!r confirms our ,!ory ( refraction1 by ! agreem5t :i* "h is f\nd betwe5 ! refract$ ray & ! reflect$ ray4 ,besides1 x may occur t "s "o 9 ! future w discov] 9 x utilities :i* at pres5t are n se54 ,illu/ration ,to proce$ !n to ^! figures1 let u suppose fir/ t x is desir$ to f9d a surface ,,cde :i* %all reassemble at a po9t ,b rays com+ f ano!r po9t ,a2 & t ! summit ( ! surface %all be ! giv5 po9t ,d 9 ! /raight l9e ,,ab4 ,i say t1 :e!r by reflexion or by refraction1 x is only necess>y to make ?is surface su* t ! pa? ( ! light f ! po9t ,a to all po9ts ( ! curv$ l9e ,,cde1 & f ^! to ! po9t ( concurr5ce 7z "h ! pa? along ! /raight l9es ,,ac1 ,,cb1 along ,,al1 ,,lb1 & along ,,ad1 ,,db71 %all be ev]y:]e trav]s$ 9 equal times3 by :i* pr9ciple ! f9d+ ( ^! curves becomes v easy4 ,illu/ration ,s f> z relates to ! reflect+ surface1 s9ce ! sum ( ! l9es ,,ac1 ,,cb ought to be equal to t ( ,,ad1 ,,db1 x appe>s t ,,dce ought to be an ellipse2 & = refraction1 ! ratio ( ! velocities ( waves ( light 9 ! m$ia ,a & ,b be+ suppos$ to be kn[n1 = example t ( #c to #b 7:i* is ! same1 z we h %[n1 z ! ratio ( ! ,s9es 9 ! refraction71 x is only necess>y to make ,,dh equal to #c_/b ( ,,db2 & hav+ aft] t describ$ f ! c5tre ,a "s arc ,,fc1 cutt+ ,,db at ,f1 !n describe ano!r f c5tre ,b ) its semi-diamet] ,,bx equal to #b_/c ( ,,fh2 & ! po9t ( int]section ( ! two arcs w be "o ( ! po9ts requir$1 ?r\gh :i* ! curve %\ld pass4 ,= ?is po9t1 hav+ be5 f\nd 9 ?is fa%ion1 x is easy =?) to demon/rate t ! "t along ,,ac1 ,,cb1 w be equal to ! "t along ,,ad1 ,,db4 ,= assum+ t ! l9e ,,ad repres5ts ! "t :i* ! light takes to trav]se ?is same di/ance ,,ad 9 air1 x is evid5t t ,,dh1 equal to #c_/b ( ,,db1 w repres5t ! "t ( ! light along ,,db 9 ! m$ium1 because x ne$s "h m "t 9 proportion z its spe$ is sl[]4 ,!re=e ! :ole l9e ,,ah w repres5t ! "t along ,,ad1 ,,db4 ,simil>ly ! l9e ,,ac or ,,af w repres5t ! "t along ,,ac2 & ,,fh be+ by con/ruction equal to #c_/b ( ,,cb1 x w repres5t ! "t along ,,cb 9 ! m$ium2 & 9 consequ5ce ! :ole l9e ,,ah w repres5t also ! "t along ,,ac1 ,,cb4 ,:5ce x appe>s t ! "t along ,,ac1 ,,cb1 is equal to ! "t along ,,ad1 ,,db4 ,& simil>ly x c be %[n if ,l & ,k are o!r po9ts 9 ! curve ,,cde1 t ! times along ,,al1 ,,lb1 & along ,,ak1 ,,kb1 are always repres5t$ by ! l9e ,,ah1 & !re=e equal to ! said "t along ,,ad1 ,,db4 ,9 ord] to %[ fur!r t ! surfaces1 :i* ^! curves w g5]ate by revolution1 w direct all ! rays :i* rea* !m f ! po9t ,a 9 su* wise t !y t5d t[>ds ,b1 let !re be suppos$ a po9t ,k 9 ! curve1 f>!r f ,d ?an ,c is1 b su* t ! /raight l9e ,,ak falls f outside ^u ! curve :i* s]ves = ! refraction2 & f ! c5tre ,b let ! arc ,,ks be describ$1 cutt+ ,,bd at ,s1 & ! /raight l9e ,,cb at ,r2 & f ! c5tre ,a describe ! arc ,,dn meet+ ,,ak at ,n4 ,s9ce ! sums ( ! times along ,,ak1 ,,kb1 & along ,,ac1 ,,cb are equal1 if f ! =m] sum "o d$ucts ! "t along ,,kb1 & if f ! o!r "o d$ucts ! "t along ,,rb1 !re w rema9 ! "t along ,,ak z equal to ! "t along ! two p>ts ,,ac1 ,,cr4 ,consequ5tly 9 ! "t t ! light has come along ,,ak x w also h come along ,,ac & w 9 addition h made1 9 ! m$ium f ! c5tre ,c1 a p>tial sph]ical wave1 hav+ a semi-diamet] equal to ,,cr4 ,& ?is wave w necess>ily t\* ! circumf]5ce ,,ks at ,r1 s9ce ,,cb cuts ?is circumf]5ce at "r angles4 ,simil>ly1 hav+ tak5 any o!r po9t ,l 9 ! curve1 "o c %[ t 9 ! same "t z ! light passes along ,,al x w also h come along ,,al & 9 addition w h made a p>tial wave1 f ! c5tre ,l1 :i* w t\* ! same circumf]5ce ,,ks4 ,& s ) all o!r po9ts ( ! curve ,,cde4 ,!n at ! mom5t t ! light rea*es ,k ! arc ,,krs w be ! t]m9ation ( ! movem5t1 :i* has spread f ,a ?r\gh ,,dck4 ,& ?us ?is same arc w con/itute 9 ! m$ium ! propagation ( ! wave emanat+ f ,a2 :i* wave may be repres5t$ by ! arc ,,dn1 or by any o!r ne>] ! c5tre ,a4 ,b all ! pieces ( ! arc ,,krs are propagat$ successively along /raight l9es :i* are p]p5dicul> to !m1 t is to say1 :i* t5d to ! c5tre ,b 7= t c be demon/rat$ 9 ! same way z we h prov$ above t ! pieces ( sph]ical waves are propagat$ along ! /raight l9es com+ f _! c5tre71 & ^! progressions ( ! pieces ( ! waves con/itute ! rays !mselves ( light4 ,x appe>s !n t all ^! rays t5d "h t[>ds ! po9t ,b4 ,"o might also det]m9e ! po9t ,c1 & all ! o!rs1 9 ?is curve :i* s]ves = ! refraction1 by divid+ ,,da at ,g 9 su* a way t ,,dg is #b_/c ( ,,da1 & describ+ f ! c5tre ,b any arc ,,cx :i* cuts ,,bd at ,n1 & ano!r f ! c5tre ,a ) its semi-diamet] ,,af equal to #c_/b ( ,,gx2 or r1 hav+ describ$1 z be=e1 ! arc ,,cx1 x is only necess>y to make ,,df equal to #c_/b ( ,,dx1 & f-! c5tre ,a to /rike ! arc ,,fc2 = ^! two con/ructions1 z may be easily kn[n1 come back to ! fir/ "o :i* 0 %[n be=e4 ,& x is manife/ by ! la/ me?od t ?is curve is ! same t ,mr4 ,des ,c>tes has giv5 9 8 ,geometry1 & :i* he calls ! fir/ ( 8 ,ovals4 ,x is only a "p ( ?is oval :i* s]ves = ! refraction1 namely1 ! "p ,,dk1 end+ at ,k1 if ,,ak is ! tang5t4 ,z to !1 o!r "p1 ,des ,c>tes has rem>k$ t x c\ld s]ve = reflexions1 if !re 7 "s mat]ial ( a mirror ( su* a nature t by its means ! =ce ( ! rays 7or1 z we %\ld say1 ! velocity ( ! light1 :i* he c\ld n say1 s9ce he held t ! movem5t ( light 0 in/antane\s7 c\ld be augm5t$ 9 ! proportion ( #c to #b4 ,b we h %[n t 9 our way ( expla9+ reflexion1 su* a ?+ c\ld n arise f ! matt] ( ! mirror1 & x is entirely impossible4 ,illu/ration ,illu/ration ,f :at has be5 demon/rat$ ab\t ?is oval1 x w be easy to f9d ! figure :i* s]ves to collect to a po9t incid5t p>allel rays4 ,= by suppos+ j ! same con/ruction1 b ! po9t ,a inf9itely di/ant1 giv+ p>allel rays1 our oval becomes a true ,ellipse1 ! con/ruction ( :i* diff]s 9 no way f t ( ! oval1 except t ,,fc1 :i* previ\sly 0 an arc ( a circle1 is "h a /raight l9e1 p]p5dicul> to ,,db4 ,= ! wave ( light ,,dn1 be+ likewise repres5t$ by a /raight l9e1 x w be se5 t all ! po9ts ( ?is wave1 travell+ z f> z ! surface ,,kd along l9es p>allel to ,,db1 w advance subsequ5tly t[>ds ! po9t ,b1 & w arrive !re at ! same "t4 ,z = ! ,ellipse :i* s]v$ = reflexion1 x is evid5t t x w "h become a p>abola1 s9ce its focus ,a may be reg>d$ z inf9itely di/ant f ! o!r1 ,b1 :i* is "h ! focus ( ! p>abola1 t[>ds :i* all ! reflexions ( rays p>allel to ,,ab t5d4 ,& ! demon/ration ( ^! effects is j ! same z ! prec$+4 ,b t ?is curv$ l9e ,,cde :i* s]ves = refraction is an ,ellipse1 & is su* t its major diamet] is to ! di/ance betwe5 its foci z #c to #b1 :i* is ! proportion ( ! refraction1 c be easily f\nd by ! calculus ( ,algebra4 ,= ,,db1 :i* is giv51 be+ call$ a2 its undet]m9$ p]p5dicul> ,,dt be+ call$ x2 & ,,tc y2 ,,fb w be a - y2 ,,cb w be sqrt7xx aa -#b;ay yy74 ,b ! nature ( ! curve is su* t #b_/c ( ,,tc toge!r ) ,,cb is equal to ,,db1 z 0 /at$ 9 ! la/ con/ruction3 !n ! equation w be betwe5 7#b_/c7y sqrt7xx aa - #b;ay yy7 & a2 :i* be+ r$uc$1 gives 7#f_/e7;ay - yy equal to 7#i_/e7xx2 t is to say t hav+ made ,,d equal to #f_/e ( ,,db1 ! rectangle ,,dfo is equal to #i_/e ( ! squ>e on ,,fc4 ,:5ce x is se5 t ,,dc is an ellipse1 ( :i* ! axis ,,d is to ! p>amet] z #i to #e2 & !re=e ! squ>e on ,,d is to ! squ>e ( ! di/ance betwe5 ! foci z #i to #i - #e1 t is to say #d2 & f9ally ! l9e ,,d w be to ?is di/ance z #c to #b4 ,illu/ration ,aga91 if "o supposes ! po9t ,b to be inf9itely di/ant1 9 lieu ( our fir/ oval we %all f9d t ,,cde is a true ,hyp]bola2 :i* w make ^? rays become p>allel :i* come f ! po9t ,a4 ,& 9 consequ5ce also ^? :i* are p>allel )9 ! transp>5t body w be collect$ outside at ! po9t ,a4 ,n[ x mu/ be rem>k$ t ,,cx & ,,ks become /raight l9es p]p5dicul> to ,,ba1 because !y repres5t arcs ( circles ! c5tre ( :i* is inf9itely di/ant4 ,& ! int]section ( ! p]p5dicul> ,,cx ) ! arc ,,fc w give ! po9t ,c1 "o ( ^? ?r\gh :i* ! curve ought to pass4 ,& ?is op]ates s t all ! p>ts ( ! wave ( light ,,dn1 com+ to meet ! surface ,,kde1 w advance !nce along p>allels to ,,ks & w arrive at ?is /raight l9e at ! same "t2 ( :i* ! pro( is aga9 ! same z t :i* s]v$ = ! fir/ oval4 ,besides "o f9ds by a calculation z easy z ! prec$+ "o1 t ,,cde is "h a hyp]bola ( :i* ! axis ,,d is #d_/e ( ,,ad1 & ! p>amet] equal to ,,ad4 ,:5ce x is easily prov$ t ,,d is to ! di/ance betwe5 ! foci z #c to #b4 ,illu/ration ,^! are ! two cases 9 :i* ,conic sections s]ve = refraction1 & are ! same :i* are expla9$1 9 8 ,dioptrique1 by ,des ,c>tes1 :o fir/ f\nd out ! use ( ^! l9es 9 relation to refraction1 z also t ( ! ,ovals ! fir/ ( :i* we h already set =?4 ,! second oval is t :i* s]ves = rays t t5d to a giv5 po9t2 9 :i* oval1 if ! apex ( ! surface :i* receives ! rays is ,d1 x w happ5 t ! o!r apex w be situat$ betwe5 ,b & ,a1 or beyond ,a1 accord+ z ! ratio ( ,,ad to ,,db is giv5 ( great] or less] value4 ,& 9 ?is latt] case x is ! same z t :i* ,des ,c>tes calls 8 #crd oval4 ,n[ ! f9d+ & con/ruction ( ?is second oval is ! same z t ( ! fir/1 & ! demon/ration ( its effect likewise4 ,b x is wor?y ( rem>k t 9 "o case ?is oval becomes a p]fect circle1 namely :5 ! ratio ( ,,ad to ,,db is ! same z ! ratio ( ! refractions1 "h z #c to #b1 z ,i obs]v$ a long "t ago4 ,! #d? oval1 s]v+ only = impossible reflexions1 !re is no ne$ to set x =?4 ,illu/ration ,z = ! mann] 9 :i* ,mr4 ,des ,c>tes discov]$ ^! l9es1 s9ce he has giv5 no explanation ( x1 nor any "o else s9ce t ,i "k (1 ,i w say "h1 9 pass+1 :at x seems to me x mu/ h be54 ,let x be propos$ to f9d ! surface g5]at$ by ! revolution ( ! curve ,,kde1 :i*1 receiv+ ! incid5t rays com+ to x f ! po9t ,a1 %all deviate !m t[>d ! po9t ,b4 ,!n consid]+ ?is o!r curve z already kn[n1 & t its apex ,d is 9 ! /raight l9e ,,ab1 let u divide x up into an inf9itude ( small pieces by ! po9ts ,g1 ,c1 ,f2 & hav+ drawn f ea* ( ^! po9ts1 /raight l9es t[>ds ,a to repres5t ! incid5t rays1 & o!r /raight l9es t[>ds ,b1 let !re also be describ$ ) c5tre ,a ! arcs ,,gl1 ,,cm1 ,,fn1 ,,d1 cutt+ ! rays t come f ,a at ,l1 ,m1 ,n1 ,o2 & f ! po9ts ,k1 ,g1 ,c1 ,f1 let !re be describ$ ! arcs ,,kq1 ,,gr1 ,,cs1 ,,ft cutt+ ! rays t[>ds ,b at ,q1 ,r1 ,s1 ,t2 & let u suppose t ! /raight l9e ,,hkz cuts ! curve at ,k at "r-angles4 ,illu/ration ,!n ,,ak be+ an incid5t ray1 & ,,kb its refraction )9 ! m$ium1 x ne$s mu/ be1 accord+ to ! law ( refraction :i* 0 kn[n to ,mr4 ,des ,c>tes1 t ! s9e ( ! angle ,,zka %\ld be to ! s9e ( ! angle ,,hkb z #c to #b1 suppos+ t ?is is ! proportion ( ! refraction ( glass2 or r1 t ! s9e ( ! angle ,,kgl %\ld h ?is same ratio to ! s9e ( ! angle ,,gkq1 consid]+ ,,kg1 ,,gl1 ,,kq z /raight l9es because ( _! smallness4 ,b ^! s9es are ! l9es ,,kl & ,,gq1 if ,,gk is tak5 z ! radius ( ! circle4 ,!n ,,lk ought to be to ,,gq z #c to #b2 & 9 ! same ratio ,,mg to ,,cr1 ,,nc to ,,fs1 ,,( to ,,dt4 ,!n also ! sum ( all ! antec$5ts to all ! consequ5ts w\ld be z #c to #b4 ,n[ by prolong+ ! arc ,,d until x meets ,,ak at ,x1 ,,kx is ! sum ( ! antec$5ts4 ,& by prolong+ ! arc ,,kq till x meets ,,ad at ,y1 ! sum ( ! consequ5ts is ,,dy4 ,!n ,,kx ought to be to ,,dy z #c to #b4 ,:5ce x w\ld appe> t ! curve ,,kde 0 ( su* a nature t hav+ drawn f "s po9t :i* _h be5 assum$1 su* z ,k1 ! /raight l9es ,,ka1 ,,kb1 ! excess by :i* ,,ak surpasses ,,ad %\ld be to ! excess ( ,,db ov] ,,kb1 z #c to #b4 ,= x c simil>ly be demon/rat$1 by tak+ any o!r po9t 9 ! curve1 su* z ,g1 t ! excess ( ,,ag ov] ,,ad1 namely ,,vg1 is to ! excess ( ,,bd ov] ,,dg1 namely ,,dp1 9 ?is same ratio ( #c to #b4 ,& foll[+ ?is pr9ciple ,mr4 ,des ,c>tes con/ruct$ ^! curves 9 8 ,geometric2 & he easily recogniz$ t 9 ! case ( p>allel rays1 ^! curves became ,hyp]bolas & ,ellipses4 ,let u n[ return to our me?od & let u see h[ x leads )\t difficulty to ! f9d+ ( ! curves :i* "o side ( ! glass requires :5 ! o!r side is ( a giv5 figure2 a figure n only plane or sph]ical1 or made by "o ( ! conic sections 7:i* is ! re/riction ) :i* ,des ,c>tes propos$ ?is problem1 leav+ ! solution to ^? :o %\ld come aft] him7 b g5]ally any figure :atev]3 t is to say1 "o made by ! revolution ( any giv5 curv$ l9e to :i* "o mu/ m]ely "k h[ to draw /raight l9es z tang5ts4 ,let ! giv5 figure be t made by ! revolution ( "s curve su* z ,,ak ab\t ! axis ,,av1 & t ?is side ( ! glass receives rays com+ f ! po9t ,l4 ,fur!rmore1 let ! ?ickness ,,ab ( ! middle ( ! glass be giv51 & ! po9t ,f at :i* "o desires ! rays to be all p]fectly reunit$1 :atev] be ! fir/ refraction occurr+ at ! surface ,,ak4 ,i say t = ?is ! sole requirem5t is t ! outl9e ,,bdk :i* con/itutes ! o!r surface %all be su* t ! pa? ( ! light f ! po9t ,l to ! surface ,,ak1 & f !nce to ! surface ,,bdk1 & f !nce to ! po9t ,f1 %all be trav]s$ ev]y:]e 9 equal times1 & 9 ea* case 9 a "t equal to t :i* ! light employs1 to pass along ! /raight l9e ,,lf ( :i* ! "p ,,ab is )9 ! glass4 ,illu/ration ,let ,,lg be a ray fall+ on ! arc ,,ak4 ,its refraction ,,gv w be giv5 by means ( ! tang5t :i* w be drawn at ! po9t ,g4 ,n[ 9 ,,gv ! po9t ,d mu/ be f\nd su* t ,,fd toge!r ) #c_/b ( ,,dg & ! /raight l9e ,,gl1 may be equal to ,,fb toge!r ) #c_/b ( ,,ba & ! /raight l9e ,,al2 :i*1 z is cle>1 make up a giv5 l5g?4 ,or r1 by d$uct+ f ea* ! l5g? ( ,,lg1 :i* is also giv51 x w m]ely be ne$ful to adju/ ,,fd up to ! /raight l9e ,,vg 9 su* a way t ,,fd toge!r ) #c_/b ( ,,dg is equal to a giv5 /raight l9e1 :i* is a q easy plane problem3 & ! po9t ,d w be "o ( ^? ?r\gh :i* ! curve ,,bdk ought to pass4 ,& simil>ly1 hav+ drawn ano!r ray ,,lm1 & f\nd its refraction ,,mo1 ! po9t ,n w be f\nd 9 ?is l9e1 & s on z _m times z "o desires4 ,to demon/rate ! effect ( ! curve1 let !re be describ$ ab\t ! c5tre ,l ! circul> arc ,,ah1 cutt+ ,,lg at ,h2 & ab\t ! c5tre ,f ! arc ,,bp2 & 9 ,,ab let ,,z be tak5 equal to #b_/c ( ,,hg2 & ,,se equal to ,,gd4 ,!n consid]+ ,,ah z a wave ( light emanat+ f ! po9t ,l1 x is c]ta9 t dur+ ! "t 9 :i* its piece ,h arrives at ,g ! piece ,a w h advanc$ )9 ! transp>5t body only along ,,z2 = ,i suppose1 z above1 ! proportion ( ! refraction to be z #c to #b4 ,n[ we "k t ! piece ( wave :i* is incid5t on ,g1 advances !nce along ! l9e ,,gd1 s9ce ,,gv is ! refraction ( ! ray ,,lg4 ,!n dur+ ! "t t ?is piece ( wave has tak5 f ,g to ,d1 ! o!r piece :i* 0 at ,s has rea*$ ,e1 s9ce ,,gd1 ,,se are equal4 ,b :ile ! latt] w advance f ,e to ,b1 ! piece ( wave :i* 0 at ,d w h spread into ! air its p>tial wave1 ! semi-diamet] ( :i*1 ,,dc 7suppos+ ?is wave to cut ! l9e ,,df at ,c71 w be #c_/b ( ,,eb1 s9ce ! velocity ( light outside ! m$ium is to t inside z #c to #b4 ,n[ x is easy to %[ t ?is wave w t\* ! arc ,,bp at ?is po9t ,c4 ,= s9ce1 by con/ruction1 ,,fd #c_/b ,,dg ,,gl are equal to ,,fb #c_/b ,,ba ,,al2 on d$uct+ ! equals ,,lh1 ,,la1 !re w rema9 ,,fd #c_/b ,,dg ,,gh equal to ,,fb #c_/b ,,ba4 ,&1 aga91 d$uct+ f "o side ,,gh1 & f ! o!r side #c_/b ( ,,z1 :i* are equal1 !re w rema9 ,,fd ) #c_/b ,,dg equal to ,,fb ) #c_/b ( ,,bs4 ,b #c_/b ( ,,dg are equal to #c_/b ( ,,es2 !n ,,fd is equal to ,,fb ) #c_/b ( ,,be4 ,b ,,dc 0 equal to #c_/b ( ,,eb2 !n d$uct+ ^! equal l5g?s f "o side & f ! o!r1 !re w rema9 ,,cf equal to ,,fb4 ,& ?us x appe>s t ! wave1 ! semi-diamet] ( :i* is ,,dc1 t\*es ! arc ,,bp at ! mom5t :5 ! light com+ f ! po9t ,l has arriv$ at ,b along ! l9e ,,lb4 ,x c be demon/rat$ simil>ly t at ?is same mom5t ! light t has come along any o!r ray1 su* z ,,lm1 ,,mn1 w h propagat$ ! movem5t :i* is t]m9at$ at ! arc ,,bp4 ,:5ce x foll[s1 z has be5 (t5 said1 t ! propagation ( ! wave ,,ah1 aft] x has pass$ ?r\gh ! ?ickness ( ! glass1 w be ! sph]ical wave ,,bp1 all ! pieces ( :i* ought to advance along /raight l9es1 :i* are ! rays ( light1 to ! c5tre ,f4 ,:i* 0 to be prov$4 ,simil>ly ^! curv$ l9es c be f\nd 9 all ! cases :i* c be propos$1 z w be suffici5tly %[n by "o or two examples :i* ,i w add4 ,let !re be giv5 ! surface ( ! glass ,,ak1 made by ! revolution ab\t ! axis ,,ba ( ! l9e ,,ak1 :i* may be /raight or curv$4 ,let !re be also giv5 9 ! axis ! po9t ,l & ! ?ickness ,,ba ( ! glass2 & let x be requir$ to f9d ! o!r surface ,,kdb1 :i* receiv+ rays t are p>allel to ,,ab w direct !m 9 su* wise t aft] be+ aga9 refract$ at ! giv5 surface ,,ak !y w all be reassembl$ at ! po9t ,l4 ,illu/ration ,f ! po9t ,l let !re be drawn to "s po9t ( ! giv5 l9e ,,ak ! /raight l9e ,,lg1 :i*1 be+ consid]$ z a ray ( light1 its refraction ,,gd w !n be f\nd4 ,& ?is l9e be+ !n prolong$ at "o side or ! o!r w meet ! /raight l9e ,,bl1 z "h at ,v4 ,let !re !n be erect$ on ,,ab ! p]p5dicul> ,,bc1 :i* w repres5t a wave ( light com+ f ! inf9itely di/ant po9t ,f1 s9ce we h suppos$ ! rays to be p>allel4 ,!n all ! p>ts ( ?is wave ,,bc mu/ arrive at ! same "t at ! po9t ,l2 or r all ! p>ts ( a wave emanat+ f ! po9t ,l mu/ arrive at ! same "t at ! /raight l9e ,,bc4 ,& = t1 x is necess>y to f9d 9 ! l9e ,,vgd ! po9t ,d su* t hav+ drawn ,,dc p>allel to ,,ab1 ! sum ( ,,cd1 plus #c_/b ( ,,dg1 plus ,,gl may be equal to #c_/b ( ,,ab1 plus ,,al3 or r1 on d$uct+ f bo? sides ,,gl1 :i* is giv51 ,,cd plus #c_/b ( ,,dg mu/ be equal to a giv5 l5g?2 :i* is a /ill easi] problem ?an ! prec$+ con/ruction4 ,! po9t ,d ?us f\nd w be "o ( ^? ?r\gh :i* ! curve ought to pass2 & ! pro( w be ! same z be=e4 ,& by ?is x w be prov$ t ! waves :i* come f ! po9t ,l1 aft] hav+ pass$ ?r\gh ! glass ,,kakb1 w take ! =m ( /raight l9es1 z ,,bc2 :i* is ! same ?+ z say+ t ! rays w become p>allel4 ,:5ce x foll[s reciprocally t p>allel rays fall+ on ! surface ,,kdb w be reassembl$ at ! po9t ,l4 ,illu/ration ,aga91 let !re be giv5 ! surface ,,ak1 ( any desir$ =m1 g5]at$ by revolution ab\t ! axis ,,ab1 & let ! ?ickness ( ! glass at ! middle be ,,ab4 ,also let ! po9t ,l be giv5 9 ! axis beh9d ! glass2 & let x be suppos$ t ! rays :i* fall on ! surface ,,ak t5d to ?is po9t1 & t x is requir$ to f9d ! surface ,,bd1 :i* on _! em]g5ce f ! glass turns !m z if !y came f ! po9t ,f 9 front ( ! glass4 ,hav+ tak5 any po9t ,g 9 ! l9e ,,ak1 & draw+ ! /raight l9e ,,igl1 its "p ,,gi w repres5t "o ( ! incid5t rays1 ! refraction ( :i*1 ,,gv1 w !n be f\nd3 & x is 9 ?is l9e t we mu/ f9d ! po9t ,d1 "o ( ^? ?r\gh :i* ! curve ,,dg ought to pass4 ,let u suppose t x has be5 f\nd3 & ab\t ,l z c5tre let !re be describ$ ,,gt1 ! arc ( a circle cutt+ ! /raight l9e ,,ab at ,t1 9 case ! di/ance ,,lg is great] ?an ,,la2 = o!rwise ! arc ,,ah mu/ be describ$ ab\t ! same c5tre1 cutt+ ! /raight l9e ,,lg at ,h4 ,?is arc ,,gt 7or ,,ah1 9 ! o!r case7 w repres5t an incid5t wave ( light1 ! rays ( :i* t5d t[>ds ,l4 ,simil>ly1 ab\t ! c5tre ,f let !re be describ$ ! circul> arc ,,dq1 :i* w repres5t a wave emanat+ f ! po9t ,f4 ,!n ! wave ,,tg1 aft] hav+ pass$ ?r\gh ! glass1 mu/ =m ! wave ,,qd2 & = ?is ,i obs]ve t ! "t tak5 by ! light along ,,gd 9 ! glass mu/ be equal to t tak5 along ! ?ree1 ,,ta1 ,,ab1 & ,,bq1 ( :i* ,,ab alone is )9 ! glass4 ,or r1 hav+ tak5 ,,z equal to #b_/c ( ,,at1 ,i obs]ve t #c_/b ( ,,gd ought to be equal to #c_/b ( ,,sb1 plus ,,bq2 &1 d$uct+ bo? ( !m f ,,fd or ,,fq1 t ,,fd less #c_/b ( ,,gd ought to be equal to ,,fb less #c_/b ( ,,sb4 ,& ?is la/ diff]5ce is a giv5 l5g?3 & all t is requir$ is to draw ! /raight l9e ,,fd f ! giv5 po9t ,f to meet ,,vg s t x may be ?us4 ,:i* is a problem q simil> to t :i* s]v$ = ! fir/ ( ^! con/ructions1 :]e ,,fd plus #c_/b ( ,,gd _h to be equal to a giv5 l5g?4 ,9 ! demon/ration x is to be obs]v$ t1 s9ce ! arc ,,bc falls )9 ! glass1 !re mu/ be conceiv$ an arc ,,rx1 conc5tric ) x & on ! o!r side ( ,,qd4 ,!n aft] x %all h be5 %[n t ! piece ,g ( ! wave ,,gt arrives at ,d at ! same "t t ! piece ,t arrives at ,q1 :i* is easily d$uc$ f ! con/ruction1 x w be evid5t z a consequ5ce t ! p>tial wave g5]at$ at ! po9t ,d w t\* ! arc ,,rx at ! mom5t :5 ! piece ,q %all h come to ,r1 & t ?us ?is arc w at ! same mom5t be ! t]m9ation ( ! movem5t t comes f ! wave ,,tg2 :5ce all ! re/ may be conclud$4 ,hav+ %[n ! me?od ( f9d+ ^! curv$ l9es :i* s]ve = ! p]fect concurr5ce ( ! rays1 !re rema9s to be expla9$ a notable ?+ t\*+ ! uncoord9at$ refraction ( sph]ical1 plane1 & o!r surfaces3 an effect :i* if ignor$ might cause "s d\bt conc]n+ :at we h sev]al times said1 t rays ( light are /raight l9es :i* int]sect at "r angles ! waves :i* travel along !m4 ,illu/ration ,= 9 ! case ( rays :i*1 = example1 fall p>allel ^u a sph]ical surface ,,afe1 int]sect+ "o ano!r1 aft] refraction1 at diff]5t po9ts1 z ?is figure repres5ts2 :at c ! waves ( light be1 9 ?is transp>5t body1 :i* are cut at "r angles by ! conv]g+ rays8 ,= !y c n be sph]ical4 ,& :at w ^! waves become aft] ! said rays beg9 to int]sect "o ano!r8 ,x w be se5 9 ! solution ( ?is difficulty t some?+ v rem>kable comes to pass h]e91 & t ! waves d n cease to p]si/ ?\gh !y d n cont9ue entire1 z :5 !y cross ! glasses design$ accord+ to ! con/ruction we h se54 ,accord+ to :at has be5 %[n above1 ! /raight l9e ,,ad1 :i* has be5 drawn at ! summit ( ! sph]e1 at "r angles to ! axis p>allel to :i* ! rays come1 repres5ts ! wave ( light2 & 9 ! "t tak5 by its piece ,d to rea* ! sph]ical surface ,,age at ,e1 its o!r p>ts w h met ! same surface at ,f1 ,g1 ,h1 etc41 & w h also =m$ sph]ical p>tial waves ( :i* ^! po9ts are ! c5tres4 ,& ! surface ,,ek :i* all ^? waves w t\*1 w be ! cont9uation ( ! wave ,,ad 9 ! sph]e at ! mom5t :5 ! piece ,d has rea*$ ,e4 ,n[ ! l9e ,,ek is n an arc ( a circle1 b is a curv$ l9e =m$ z ! evolute ( ano!r curve ,,enc1 :i* t\*es all ! rays ,,hl1 ,,gm1 ,,fo1 etc41 t are ! refractions ( ! p>allel rays1 if we imag9e laid ov] ! convexity ,,enc a ?read :i* 9 unw9d+ describes at its end ,e ! said curve ,,ek4 ,=1 suppos+ t ?is curve has be5 ?us describ$1 we w %[ t ! said waves =m$ f ! c5tres ,f1 ,g1 ,h1 etc41 w all t\* x4 ,x is c]ta9 t ! curve ,,ek & all ! o!rs describ$ by ! evolution ( ! curve ,,enc1 ) diff]5t l5g?s ( ?read1 w cut all ! rays ,,hl1 ,,gm1 ,,fo1 etc41 at "r angles1 & 9 su* wise t ! p>ts ( !m int]cept$ betwe5 two su* curves w all be equal2 = ?is foll[s f :at has be5 demon/rat$ 9 our treatise de ,motu ,p5dulorum4 ,n[ imag9+ ! incid5t rays z be+ inf9itely ne> to "o ano!r1 if we consid] two ( !m1 z ,,rg1 ,,tf1 & draw ,,gq p]p5dicul> to ,,rg1 & if we suppose ! curve ,,fs :i* int]sects ,,gm at ,p to h be5 describ$ by evolution f ! curve ,,nc1 beg9n+ at ,f1 z f> z :i* ! ?read is suppos$ to ext5d1 we may assume ! small piece ,,fp z a /raight l9e p]p5dicul> to ! ray ,,gm1 & simil>ly ! arc ,,gf z a /raight l9e4 ,b ,,gm be+ ! refraction ( ! ray ,,rg1 & ,,fp be+ p]p5dicul> to x1 ,,qf mu/ be to ,,gp z #c to #b1 t is to say 9 ! proportion ( ! refraction2 z 0 %[n above 9 expla9+ ! discov]y ( ,des ,c>tes4 ,& ! same ?+ occurs 9 all ! small arcs ,,gh1 ,,ha1 etc41 namely t 9 ! quadrilat]als :i* enclose !m ! side p>allel to ! axis is to ! opposite side z #c to #b4 ,!n also z #c to #b w ! sum ( ! "o set be to ! sum ( ! o!r2 t is to say1 ,,tf to ,,z1 & ,,de to ,,ak1 & ,,be to ,,sk or ,,dv1 suppos+ ,v to be ! int]section ( ! curve ,,ek & ! ray ,,fo4 ,b1 mak+ ,,fb p]p5dicul> to ,,de1 ! ratio ( #c to #b is also t ( ,,be to ! semi-diamet] ( ! sph]ical wave :i* emanat$ f ! po9t ,f :ile ! light outside ! transp>5t body trav]s$ ! space ,,be4 ,!n x appe>s t ?is wave w int]sect ! ray ,,fm at ! same po9t ,v :]e x is int]sect$ at "r angles by ! curve ,,ek1 & consequ5tly t ! wave w t\* ?is curve4 ,9 ! same way x c be prov$ t ! same w apply to all ! o!r waves above m5tion$1 orig9at+ at ! po9ts ,g1 ,h1 etc42 to wit1 t !y w t\* ! curve ,,ek at ! mom5t :5 ! piece ,d ( ! wave ,,ed %all h rea*$ ,e4 ,n[ to say :at ^! waves become aft] ! rays h begun to cross "o ano!r3 x is t f !nce !y fold back & are compos$ ( two contigu\s p>ts1 "o be+ a curve =m$ z evolute ( ! curve ,,enc 9 "o s5se1 & ! o!r z evolute ( ! same curve 9 ! opposite s5se4 ,?us ! wave ,,ke1 :ile advanc+ t[>d ! meet+ place becomes abc1 :]e( ! "p ab is made by ! evolute b,c1 a portion ( ! curve ,,enc1 :ile ! end ,c rema9s atta*$2 & ! "p bc by ! evolute ( ! portion b,e :ile ! end ,e rema9s atta*$4 ,consequ5tly ! same wave becomes def1 !n ghk1 & f9ally ,,cy1 f :5ce x subsequ5tly spreads )\t any fold1 b always along curv$ l9es :i* are evolutes ( ! curve ,,enc1 increas$ by "s /raight l9e at ! end ,c4 ,!re is ev51 9 ?is curve1 a "p ,,en :i* is /raight1 ,n be+ ! po9t :]e ! p]p5dicul> f ! c5tre ,x ( ! sph]e falls ^u ! refraction ( ! ray ,,de1 :i* ,i n[ suppose to t\* ! sph]e4 ,! fold+ ( ! waves ( light beg9s f ! po9t ,n up to ! end ( ! curve ,c1 :i* po9t is =m$ by tak+ ,,ac to ,,cx 9 ! proportion ( ! refraction1 z "h #c to #b4 ,z _m o!r po9ts z may be desir$ 9 ! curve ,,nc are f\nd by a ,!orem :i* ,mr4 ,b>r[ has demon/rat$ 9 section #ab ( 8 ,lectiones ,opticae1 ?\gh = ano!r purpose4 ,& x is to be not$ t a /raight l9e equal 9 l5g? to ?is curve c be giv54 ,= s9ce x toge!r ) ! l9e ,,ne is equal to ! l9e ,,ck1 :i* is kn[n1 s9ce ,,de is to ,,ak 9 ! proportion ( ! refraction1 x appe>s t by d$uct+ ,,en f ,,ck ! rema9d] w be equal to ! curve ,,nc4 ,simil>ly ! waves t are fold$ back 9 reflexion by a concave sph]ical mirror c be f\nd4 ,let ,,abc be ! section1 ?r\gh ! axis1 ( a holl[ hemisph]e1 ! c5tre ( :i* is ,d1 its axis be+ ,,db1 p>allel to :i* ,i suppose ! rays ( light to come4 ,all ! reflexions ( ^? rays :i* fall ^u ! qu>t]-circle ,,ab w t\* a curv$ l9e ,,afe1 ( :i* l9e ! end ,e is at ! focus ( ! hemisph]e1 t is to say1 at ! po9t :i* divides ! semi-diamet] ,,bd into two equal p>ts4 ,! po9ts ?r\gh :i* ?is curve ought to pass are f\nd by tak+1 beyond ,a1 "s arc ,,ao1 & mak+ ! arc ,,op d\ble ! l5g? ( x2 !n divid+ ! *ord ,,op at ,f 9 su* wise t ! "p ,,fp is ?ree times ! "p ,,fo2 = !n ,f is "o ( ! requir$ po9ts4 ,illu/ration ,& z ! p>allel rays are m]ely p]p5dicul>s to ! waves :i* fall on ! concave surface1 :i* waves are p>allel to ,,ad1 x w be f\nd t z !y come successively to enc\nt] ! surface ,,ab1 !y =m on reflexion fold$ waves compos$ ( two curves :i* orig9ate f two opposite evolutions ( ! p>ts ( ! curve ,,afe4 ,s1 tak+ ,,ad z an incid5t wave1 :5 ! "p ,,ag %all h met ! surface ,,ai1 t is to say :5 ! piece ,g %all h rea*$ ,i1 x w be ! curves ,,hf1 ,,fi1 g5]at$ z evolutes ( ! curves ,,fa1 ,,fe1 bo? beg9n+ at ,f1 :i* toge!r con/itute ! propagation ( ! "p ,,ag4 ,& a little aft]w>ds1 :5 ! "p ,,ak has met ! surface ,,am1 ! piece ,k hav+ come to ,m1 !n ! curves ,,ln1 ,,nm1 w toge!r con/itute ! propagation ( t "p4 ,& ?us ?is fold$ wave w cont9ue to advance until ! po9t ,n has rea*$ ! focus ,e4 ,! curve ,,afe c be se5 9 smoke1 or 9 fly+ du/1 :5 a concave mirror is held opposite ! sun4 ,& x %\ld be kn[n t x is none o!r ?an t curve :i* is describ$ by ! po9t ,e on ! circumf]5ce ( ! circle ,,eb1 :5 t circle is made to roll )9 ano!r ^: semi-diamet] is ,,ed & ^: c5tre is ,d4 ,s t x is a k9d ( ,cycloid1 ( :i*1 h[ev]1 ! po9ts c be f\nd geometrically4 ,its l5g? is exactly equal to #c_/d ( ! diamet] ( ! sph]e1 z c be f\nd & demon/rat$ by means ( ^! waves1 ne>ly 9 ! same way z ! m5suration ( ! prec$+ curve2 ?\gh x may also be demon/rat$ 9 o!r ways1 :i* ,i omit z outside ! subject4 ,! area ,,aobefa1 compris$ betwe5 ! arc ( ! qu>t]-circle1 ! /raight l9e ,,be1 & ! curve ,,efa1 is equal to ! f\r? "p ( ! quadrant ,,dab4 ,,index ,ar*im$es1 #ajd4 ,atmosph]ic refraction1 #de4 ,b>r[1 ,isaac1 #abf4 ,b>?ol9us1 ,erasmus1 #ec1 #ed1 #eg1 #fj1 #ig1 #ii4 ,boyle1 ,hon4 ,rob]t1 #aa4 ,cass9i1 ,jacques1 iii4 ,cau/ic ,curves1 #abc4 ,cry/als1 see ,icel& ,cry/al1 ,rock ,cry/al4 ,cry/als1 configuration (1 #ie4 ,desc>tes1 ,rn1 #c1 #e1 #g1 #ad1 #bb1 #db1 #dc1 #aji1 #aac4 ,d\ble ,refraction1 discov]y (1 #ed1 #ha1 #ic4 ,ela/icity1 #ab1 #ad4 ,e!r1 !1 or ,e!real matt]1 #aa1 #ad1 #af1 #bh4 ,extraord9>y refraction1 #ee1 #ef4 ,f]mat1 pr9ciple (1 #db4 ,figures ( transp>5t bodies1 #aje4 ,hooke1 ,rob]t1 #bj4 ,icel& ,cry/al1 #b1 #eb sqq4 ,icel& ,cry/al1 ,cutt+ & ,poli%+ (1 #ia1 #ib1 #ih4 ,leibnitz1 ,g4,w41 vi4 ,light1 nature (1 #c4 ,light1 velocity (1 #d1 #ae4 ,molecul> texture ( bodies1 #bg1 #ie4 ,newton1 ,sir ,isaac1 vi1 #ajf4 ,opacity1 #cd4 ,ovals1 ,c>tesian1 #ajg1 #aac4 ,p>dies1 ,rev4 ,fa!r1 #bj4 ,rays1 def9ition (1 #ch1 #di4 ,reflexion1 #bb4 ,refraction1 #bh1 #cd4 ,rock ,cry/al1 #ed1 #eg1 #fb1 #ie4 ,rm]1 ,olaf1 v1 #g4 ,r\ghness ( surfaces1 #bg4 ,s9es1 law (1 #a1 #ce1 #ch1 #dc4 ,sph]es1 ela/icity (1 #ae4 ,sph]oidal waves 9 cry/als1 #fc4 ,sph]oids1 lemma ab\t1 #ajc4 ,s\nd1 spe$ (1 #g1 #aj1 #ab4 ,telescopes1 l5ses =1 #fb1 #aje4 ,torricelli's exp]im5t1 #ab1 #cj4 ,transp>5cy1 explanation (1 #bh1 #ca1 #cb4 ,waves1 no regul> succession (1 #ag4 ,waves1 pr9ciple ( wave envelopes1 #ai1 #bd4 ,waves1 pr9ciple ( elem5t>y wave fronts1 #ai4 ,waves1 propagation ( light z1 #af1 #fc4