The quartic curve and its inscribed configurations

»

^^

H,i.?:i

T I . J'nJ/t.odu.cJt>.on

eocitjv.iMt a^ ri^isL^ lit setv. 4-A<»>< ^^ a^d^^A^j-^JJ. . OAJticXe. '^ Q Kortv«.

cu^oL Q- . i<y<xa. u, "tie. Enc^k-Cc^iAj-/, cie;.. i^cole^^iMc/^ii^

IcrujtArCt.

3 C; Solvv^ H ij^ ),<U^ o.^^.^.

DljA^. Ifsa |, /<}tj

-J -Kit. 5u*vv crl' Sloe -^(tt-iaM. h><yU>€^tA U a. |b oiVci^ -^Cfuv^x. ^VUXT

^ iUAAli-t, CUv,-J 'tLcJt Vks. " (-..ii/i crL. \Zcm S U.cJn. 'KjS^OO-eucrn-i LcUjcX

I G,*£aL's Jcnv-v^. Bat 5<^. (i«tofj

las-.

Scif^jy^. Vju^. V- • :f«JlW.. [..17.

S<Lo\M^ . A'vwvaii. cU Mnt^^A^A (.3) i. a.(y^'Y\) \>

3o.cj.

C«A,t^ _t«.c-t>. -j-oVwN -f>€-u.-.« eUi-L/cajo/i'iJlii. 'x'^ ^^ -SU-^cLj, '^'V— ^-*-

IHi^ ?fzw«. Cw..^ a Uc o^

Mo^A^ <t.v/i G7X.VVM. Kox.e -j^m^^^jL 'He. Aj^^^txrv- i-nvu^ iliry,yyyj^rJ>. T*ut

1 Ctejaei't Jcru/i*,^. 3i. lit) (J<^(«> .

Acto. M.oMt.y^.^Jl'C^ . t. a-J. (/'J03)_fc. 3«Aitv.. TitA-uJJti. (i<]IOj .

aoL^ai-oKi Uv uTK^.eA Tii». Co*JUU.CjjZ.^^ ate. M.oJ>-crv,rJ^ ^ iA,s-^rXi-m^J, <rL.

Qi^uyii-t OiAw« VxyMtA^K A. d-cruMle. pcn^nt '^n\JL^ t^ LVL6ott<rv>_<xiL

4 ^

'^akax «...dL J. E Va/-^.

r /to^rt-wM/<Ji h ,, i. O'bta.iy'Jul. Sivn^JLoM. As^Ldtti, -&t< aXAC*-"ia^LC 'VvLi^tA.o-oLj_

IS«. alio. A.Ca^ Co^ftud^L ?r4^., Vo€ X( |,2a(. y<,<' Xll |. '^f

,

4 ViUUujpl^ |>e*ccnAo.. -fu..^^fc.«>u . C-VvvJ^-/^(."l°7) • ^- '^'^'^ ^ou^^ .

'^'^ 3( ("}o<^J .

Uui. '>\i^v,-/.i M 0,1,1,3 o-waL -rfji 'ntc»-.i«w o, i,a..- Y oAj /'v./ "L dburu}^

cL? t^ali- oA^atU-aJiJ- i^-Pa^y.^ Naur i<Ui«. St/ooijjz^, ,A.aio-l ^o^.v.v o^

0-'lA*^aVL.<jy^aA 'yrxoJn.tyx, ov. aeeoxt.»^X ^Hr— 'ti PK''. ' • (7i_ AjiJCaA'-cry\A wl^—

" ^ r. r. A = 4.S,fe, Y= O «#« ^(j'. r^r'

An^J^ Ca-^v Cavv«^c*(U^-w.Xfcv -te e-> j^A/M^ii >t.<3Ct-<rvva>f^ L-v^ t^^^vU crf Sloe

tfot 0^a^^iiU< X ;X l/v, sislii erf, ttjL fielLaJiayOi -ikA-v/ "C^Uv»-. O-vuSi/-

"t(dL Oi^oAtt He s/iattrj l/v joG^i/'... tA.a;t c/ 'JC^ (' » n = o,i. •<( ;

OA*. S? -6c>v»aA. ^-|-oA-r-^ Urfi,<^ Urtu^ tL^y^^-^M. "t. ^€Ao ^.UML '^.v.

S'A<7t>. ti.fi.y-. .

Co'i^m-iA:) cry\£L To A 'Vi«X <3ll C^cJlrt-cA ^KA^jt-t-o^ 5e/\re^v^ -Ll/xaJ. p<n-»vts U-. «.

p<wt <r(I p,5!„/. r) "Rl U- X o^ (o-^t^ ttita ccrv,^ to««,t^jiA. T* -^

A C«.i<ti. >uu. A,.. .I i O^'l') M . Wotiitt EAia-^- 'hvK^^^Xtii ;o (/8'js) .M<i^^^iJ^

" A.tfl4»<A. -i-vJU^ -^v^M. {\UH)

l'^ie^tta,.^k.u/vue ) or t/a. tka^^^i io^^v^ ai"ry '" Sewt*. G-a**. f><n^ u« C*^

a/ri<-t"jL p OT/viX urKe~^ KoAM. ,rf__ Ccl«. -O-oy^t^ p cn,-v^ <,(JL- cry^ <a_ -^>^^^Jl.

I ^^to CaUal iU iywfiU c« MiM G A.^c<r*: QunriiiAAj, J'<Twvv^Ail. VofSx^

.z De. Tc^.tSca Lor cU:

VLz S,ix^s. po&o-'L Ju^v^aA UjxM^ A«.^.-aA^ ^ o_ Cirvv<_<^ O^-t-^xL. a- C-^Jlyt-l^.

f3<n.-»^i'l uX.^ti -hCL.^ 1^ Jo^w-t. Jso^aA -Cfcv,*^ un^ ^^-Bcl^haJ- ^ ^ <Kr>-i-cc,

stkJiAtm^iaJMi^tL^ loAo-JjScZi^rvv tiAu>v<3 ox*. <<L^ Tt^ hcrv-J^ i^ LSU-<-rM. ^o-

kowA (/i< -2b/^£«. -j-Ao^v- U/Ivcc^ ^^/L ttc<A<^ CiL^ y^e. (Uju,<j*J,^

(A

''tJLOM.cJuJL ^A-<TVv, mC<-< Aje*«-fii . T/ve. fc^oi<^K e-aiva3fe<r>»-! "S"!-- "Rut. oc.o

H -Rot^-./iv T/uw i!a»»j/«v M^ sv ScA.a.. Vof 3. (J^os-; . M<«Am '^-I-

urtLcX i^j-kt.^ C-aiv-aitJ. 1o teAo/i'^-'*-

BU-M. -0<--«it O-vxji Kam. pm^^Ji

1^-t- n1 y,M^ -t-

%;^^,\ + ^.^^=^,"^^ ^ =^,^^T=^

=

L)u<v.,j;i Urtttj^ u i^v^cf^JUj. i^ a- a^t^ it^am^x. fv^^c a.^^ C/A/>t*..-icAc*<«(

N>toot(. fi. S€/t ai- 5.^ pcn^yjti ca^ &€. Juvt^AoA- uOfcj Uu^) Se-fe

OL, twu-t ayt^uViiA Si-ct*. "itLaz:'^*'*^-;l-

^*^^ '^i^A^^Cfci', -0<i-<r>v^,t„-vJt

'e ^i-i^en*^ Seii -6(4. (Tv^ o. loaxA rrjL iic*^eJ.

Narur J '^cu^

Sail. <j£ 2.U ho^M ^xMeMoy^ tfxAA Sa^-^^ pA^^c*-^, ^rvJ: Ci^^,^<^m.^JL^_

-£a<t>,. ttxi sei ^ ^4 |D<TWvfe urL^ oA^^iei -f^^a)^ HaWe's C<nup.k.^A^d:^

d.UficriL -WaJ, i4u3xovx Vhjd <X. au.a^c (Uxh^ij^ uriUrX pa4iei iliAert<-^ oM-

pcXiMvtA (^t^-voL Si^cc ~Mwi U( '_«, <r^ ai<.aAi-c C<4-p e-v^oti, ctvv <7^^^*^ WL<aZJLa^

3

3. Set, <v£»o J^aAici^'^ . Sua. n^^^J«. cA**!* AA'v-^aAo^cvWt oU. canA/t*^ eir '^''-

C<y>vcc crt- T i^nid ^.e^tLct 'to <^ CA-fc-t-c C^.

I ktu. U evt-ijA-uZ^

I oi t£a Sloe CoVi^a4 orC- "n&i_ cu^n_J^^X-:^jteAAJc. .

^VUA LwoUjC-ti^ J>. 'y^y^dLazL &V. LrL.aL A, ^uxt\i^x. i—^ Co^ -fr«_

" s uJccJAl C-j s .

ot< id poi-rJLi, otL uvJiA.44.ctoN oi. C.a'ifui^^o <T>-<JLi'^^ 'V.-^-v-^m-M <7L a. pe^^r^cKJC <r\C-

"ncrt-vCti <rn. l uAa/. Ae^^i^Lijl t,

a-i~oL So pa.V5 'tLn.rn.^ayC. ~1mjl ^<3«-<A- perW

t

a.

±

Se<^», loovvJi urL-rii -R.<w<. PQjL SOy^^a. hJloK -<A^rUA unit 7ULQA>ijL U, ^^ a-«t (-3

0*ttu Seo*v>. [3ov^ oAt I/a -OtMs. b<n^ crlL CCa V ' ' ^J {^.a/v^vJloVv^ -XL-^

Hk« seAHUv. [aot^ urL-d -Ka-^fe. "ER/L ^Q^wJ.[

oo^aa. JCo^^ju UrM^ Ab-^oj^

"t a. c<T>vtc. G^ a—oi- "^ <u>-i^c. C OML Sk-cX mLo^ tStit p<»^'»-^ Ji-~iw

arJntLofM CaJL-<^ a^iL c.<rt~'.£. civi* -fCTU-tiLfcv- CiAjjtM>.a.h^ Cicrr^a-^-Xi .

jio^ . M ^Aat-JAodjU^ls .Su>g^£Xt.<rK -9 -Rao* C<7wl '^^:^4Aii^ t£l <Uo^ G3

Taic£_ ^i*. t/»= a/vc>€v^ (acTv-Xi a^^ "t^ uJ^A-ic ofc^TK (ji-- "iLt^Lfi, bcrwi. -t>^>ri24

'Xoc C £oc!-4- (,^> ^^^ + a.1-^-^ + ^-n^^) = ^(1-;^+ :f^X <=^^'-+ S-'^TP + aA-^LOL-t- O^:,^^,

u A. C/uA^c cu/vo-e- urivcc*. ctA_o<x-4~vs c^i.-cX^ 1^*^ T?>-cci,^.vQ^ije. ai_ heJLejJi.-'-.cjL^

at aiUo hA^iai H-A.oK'jJL "tto. t<^ pcrvvJIt u^ (jTi^ci. Tiki po*«A- Cffv^c ^

OHt <ji^ wl^t. eu.oe^ po-L^JlA OvJLcJi tii b<yPulA -lu^^jl, .OUvca. "fcua. TkAt^ u^

cnVL^

C(hVaV<-oL<.voJ!- "t CW S**/*^ -0-04^ hcn^^ -TL^ iti!, I'La,.r,4-<l-CrVi~,a Xi,«>. .

(OOC^ ) ^->,

(^c^ = o.

'ttj\.eruj^ -j-o-uJL -l-uoc*J. pcrL-v^i* <tk. T^.

ViAj T^E Tuns ^^t-cr*^ j^crv^

CUvJL D/.i U^Tj) b<TVvai Uv WWciv "tua. neJfuoA. c^tv^c <rL_ ovjt_ a^-

pcru-ii o^CTC^ciJ&J co-t^ '-<'fi "fcxo ^^ci>«.v. or>viM duv^^ C^^

aA«. ot«X (rv^

(.Y^

iU<^JilU 1 JoUA^^^ .-t 6 (Ht-^O-)

. ^ "/^^

-^xiix-vv^te^ oL- iia. Co,A-^ u-LicA J0(yiiP-4r{. iLa pA^exO^ TU^

Q,ev~i^>-«J?. <iM'y.~(_c- Qi-c^^Xtc. <a-x^oL ^o kre- Tt-<i«<_ -Tta. /Le^aJAr W^-->-t

^

CTL. pe^^J.oju<j>v4 Cay^dJiijJL lyt^CAAjLeA. (av X<^ <i?^o-„^^ ot..jKKMJ:. -j-o^

"tut K«. joa^ti^-^nu (khluo^ -|^»<'>-- "^^^»^ QA^cjA^^Jkn^^ -^ QjdUc^

AW<r<u.ytti^ (xTti^ O/w-j "t.jt) ""t-" t^ St/oc_ 'Vuj:k_ch> (3X-. "&tAA-vv3t>u.,/fc" " •i

rl\ft Cai^uai-OV «L <9- «A4/>wrjC atyUijJt'-C. djlhAM^-A -pt-T*^ a. rUo&T^ ^J

^^- ( o(, - e o<^— 6 I

TL_ |io^d^ ccrwtc 0-.JL [ocT^ -2*^ <rL-. (X.Y. ^^ om^ 'h,er^

X ( oc + a.'w^ T^x ) H- Y ( 1^+ 2.'>^-f5t) -H Z- ( ^^-(- '2j>vx.a<^^

-f 2,(>c YX (v^^{^->^y^) -^ ac^^x ('w^'-zx -^Y"-)

OwiAi^C. . ThjL *«~a< X^-a. (

=-^,

Z. ^=-0 <aA«. -tkXTa^ ^,e^

/^ X ± /(. Y -± nTc "Z^ — o.

"t 'P O-nadr ov -j^oocai JD-^a^wuL i4. (^ "k™ I^OT^ Q,Q o-^

AM. IL. jjAo^tp/lo>iJ <n /4| A-, <^ llui. |><it.^ jv^ U/Ut^ A^ U

C.o\ht^cr>,Af.,>^xy To I uS A. GtTK^ a^o(_ T«uix, '^^ T\<Ufi^^% Ke_^,Xa^

(—1 = °Vase /

Jlvt C^T>>.<3L>b.<TK "fc, 'frC -5c>i^-i<(Ziit L/i, ly^idoji. ~tL<lT jLh^t^ <^L^a JUy<~J2^.

VVs. toica/v^ <^- "Ka. ~fcfc>ute. fooKM <a->,j»(, "SILj. -J-Lu*-. h^/.a^-^^aA

Tv*. cr^J!^ u*ro -^x^ cru. t!i, ctv<.MjCti<L S uaJ^-A-CJI. .

.3. A. C.a)i^.r.^ .T/.«:. ^.Tv^^i^ >^a:td S^ S€^ 2l Y«^. 7,

f,/5c» .

'o«^C<i«^ . ItK. OaX.

(J

/UwJl U>«. "t'^ -J^t't^ I^cAa ^ -^ ja^.^.^ E ^ \r««i^ <j--

-t- 'iAoi'-t -^ 36< oc-t^ -f- 'io/'^^-t -f 3p'^-t'^+ %us-i\: -f- 3')'^-t''-f- (, [=^-^t

a= ^= k = U , (Vh.^ [)- -|^- .V- , k=Q,-e^LJ-, Ot = (^ ::^ ^ -^ (^ .

X [(s-t.i,x +(«-^)x, +U-A.>o<^ +L«.-«t)'=-t -^CA-a-^gi +C^-<i)yt] + Y [(t-/.)>-^ +(i-'V^i^

4.(L.K)y^ +(^-<i)xt ^.(6-<*L)>i f(|.-/;^-(r] t ^[(S-M^^ +(C-^-)« +CS-A.V-3.

^ [ X(-.-i,)+ Y(^--v)t ^^-t^l [x(^-'^)-+- Y^i-.^] f "^^>-i)J

tL

.1. H«u4«.. A'n«i^<u* 4e«v«iv«: au Xo-*-** (i«fcO 1'^ -uiJc^ i^i.^ O'fO h^"^

'•:{.' \t ^^na ^iIitA-LtAA.tjy, oU«. e<roA.dtt~vaiu'^Xr' '*^ CnktX. A-<3X<A 'ir^Oi^ Xu«_. -C*_

CAJtoJ^Ai. ^Atr^e-v^-t.l*4 0\^aiL.4r-M. \^rJrcAfty'~£>^vJA. \°^ cta. a-MoTK.oJt^ <*<.aaAXL«.

XlyxJiJi. loovvi AI

A^ <n-. O , ^tA "ttfl. jOaVvJU U, CjliuA,

vS a Ovjzi -^ i/j;_ Lsy-JiJ C^. i- . Kj UrWcA M [jfa, JCfftit^ <rf-

ICa jiTftw <1- X, unit Ae.^,^iji,i "t ttit di^VA-t^M "">-— l^Ot.

"i^'.ai^^ S«aH>^ -P^ocifj [7«T^ ViAj -tL I^Ao^rvLrK^l <rL A^ Ac

(jovJb Q s'^cl -tU^ A, 4c QQ |ow ... ac^

tti fcr^AA. t)^ao.j!^ a^^-'T Tt<ia CaT>^<^„^^*/« j:>A-erho\t-<r>-,^ ~^

((,-c)Yi , tc-^)ZX,(^-(.^XY

. C*-^; XT , C'.-^^YT ,(c-^J* ^~r",

oLiL -^^wJi .Ua^ u- x.y z,-7- ^ u, [.^cAx . i?L

a/—-<i- \aJ^i'UUit/vX>. "- a(M'v»*.e. <u^.<iaZ^.c- iivi-tcoct . ThjL c</ovu<_ L ^^fct^^ a_

H.-

la+'xVa+f-yj+'xyi+f.')

JJ- a. Qvta-cK^a-tc COT.J-., ^-,^_ Kj^ a»vdL a. 'turnti.tL (uAj^jc rC, a*a 5 ute^

01 2.01+1 pe-v>M <Ty\. a, ^uxuMj,_ C*J)rxJC. .

1

pe-vvUflU <rt f3<r^i< -tk Kj . K/ow tLu. -L^ ^^.v^-t^L^Ji ^ A^J^d. 5 u^.^ Kg

kowv^ Kj *» «. -j-**''-^ 4-a^^ frctA*^ ji/vJL ot.A. ''Lt.(y\^^~~. ~ew M ~XutX. '*^

3-t c*>. alia -2«. -S-rtouTK "i^«i" a--M_ |o^a.»oL SecA-tjH -r^ fVg C^x^ -&<-

a-vv<)L"^ <t~^ p {/>-. ^.JL-ck JU bo^a/i. p<a-wi_ i^n,t£_ >c.^,aL>L^ "^^ O lo-Wi

-Hu. S^et^ ^ -f^ Vc4^^ SUA^C^ -k^Ur^^y A, 'X.^-^.

tiv.^ io <2^ . 'hour X>^a.^- -^^

1 KA. hi.^,JLi: ^cJi UxIUdL oJiS- 00 t^-ti^W^ 0^x*->viaX TfeA-OT-L^A "!*ie. -J

POV^ U Jly%^JUxJ^i.C^(L <W ^*^ '>»vaife<»>(. .f|_ C(rU^.-:fev^ CflTi^-tsuJ^ S.Lcg..^/I4Z7 •7>vt^

I V<uu<^ (5aAa^jt6w.c -^4'''^-«^i»^*'-^^ J^ "l^ OAS. ^^!,^<^ l^ "b^Wj M-ltys^ ^fiA*--"^ ^.,^xt«>K

a. C^. X)«ALaw«.. -Sua. ivM. JLs.*!* >it-wwa/cy<Afr^« clt Ccrwii*. et oU. iuAiaoH aPj^fcU*y<M

j-M^^AA [U^^ iU ^iliit^ l*%tiyaec/t.<r>vj ert "WuL Xoiy^-^Lt^ fe '—^ oh "fi*.

"tw.OT-^1^ ^I'^a. "Bis OL/v^<i- -Vvvs^i; i. ae^-jatAi a- SuaJ-ojul. erf. "Wol -j-'-i'tK.

OAi <j[u><y!i Oi.i^.rti<^ |o(»^^v^ iLh-cn--^ «- -^•yXJrJ- f>ar^ T Cm-^ ^^

Vtn^a-~^blci^»|^ . i.1 M- (. 3'S.

I

5^«y. Ta/.^4^~ci^ T,. tto. Ga>»^t C.,^.

iVitut- 5Uvc«. uUai^ oAx. oq CovXi.A«.A.AtffH.

TL. skaw Cc^c (..T^OUv ^&vv<A.<ctM -os^

c<^ ot-i ^ 3 imu a±. lujuL

(Tp k)ai^ ff>- '

sUU.lJL IcryJiM. UiM, itsi. 'MJinx. -irCW- hcn^<-M Out.

CijvvLC. r^. ne^ct <'^*^ S<<J2^ "teo«^ oil- h<n-^ C<JU 01,. «. OrK/uc

ML»>.<m.qA "tlju IZaXj^ -VO-ie. poiyvJ^L »y^-J~ So (A'V^^^'^irVTv^^ UvJi a. .S-eAT .T;

OJU. (kAJArcJ. -fA<T»- tL. "^ a^,v^x^-A^ c«i%/^ Ur^c^ T5v.ci. TC*. j><A~^\

C^vJiijei (xi- (Ae- "S^ Tiu-a^^ -j-A/n^ ' 5 C^ -Ki^ 0>v a. '^l/^iiS/LXi.c.

C«aak un,a. IAjuj. -6aX<a.(>wo-oU« uri^cM. -t^ ovs. C^

<iuja^tc C44Ao«. Unil T^Afi*. -&tJW1o,,,^jt;/«^ Sct^cJiJ. (Tv. t^ '^Uhjrtk

f

urUxL e = I.

u

3C - •^X ^ - xoc ->: - s^"^

Co'iAJU.ixrKJ^ Ti. a. (uJn-c, c«,vi^ U^<jvLaA. »U. -Save*,. p<Twai ([, .

J = .^+^x^ /,X -t- /, 30 — O ocu X

T^

A o«/M^ tJt^ otcv^i 0~ o:t T t^ A. dujudi^ cLJUaaj!^ -|A-e%^

"a.«. 'jp>/.-^a^J^<JL OVoL C-<>Vut4-4 <TV,J^ "t. C. tv^..<>t (o-^oi. ~fe-£^ ~^fe_

|a(. + >,-^4^^ = o (3)

= ^ i.

^/-§Z '^Y-?/ f2->]Y

tL^., X/gY-fxT+ Y(f2->,YJ"+ x/»,X-e^y = o.

X = 2 , Y - ^ ,^ - § ,

^tt -tfl^tr'-l >. its. -*<~A,!

/" Y ." t^" X = ° (.'>

c'^f^XS €'".,' Y' * c'^g'z' - (^%2<^€'*')Y^ -(^'^^%t)xx- ,\\u.gs<'')y.\ ^o_

I

,<w, •BoU»_^. tjU M*-.U._^MA.. ^1 ifjs; '/.3 fB <VA.

A Soi ffjj Oj^aJLt .xMer<n.cJiA. \3<Tt'^i i^ CpA«. -j-A-ffv,. i.JW-rX. \\Kg,(^ <,

O^fc "*« CoVvutM cri- "tti (ifc«XLfitv<r>v <rf_ -'^•eXeA.t^oe. "ttc <rKx\. •j-'o'*'^ po^,v^X^

(l, -&, 146. 2i»+ . + S) I '. -0 .^-S ,- I, S, S + r\ S, li-B

,I

,

A = &^ 5. + 2.6 S, -(- S^ =- o.

a^<.

HtA^ ?fru>«. G«<A-v«4 S««. iJ^o Q«AiiafdL. "Rawi. Po^A^-a. U^'^iJ ^ Cco^wc .R&v,J»

.

I

!

boVU* 'VUKcn-j^ ^^le poSw crfj- Tu«. "toe "Lo-wg^vii VLfum-Jbl. r "t C_j^

B ^ 4^ 2. -t- !^4 2I

+ S^ = o

M [ 6<^ . s^^., 71 =. o,

H [^if;, &+?(;, 1^-^, H [4>^ .4^'^ ' 1

^-"

-UoL fvu^iL r\jLaAi^ 1^ CD. Tlu2. J- (Avt tCtejL Axru^ <r^ - ~U^-

ddll^^v,,^,^,^^^ OrvCtx-v. o>v£j, & ^~i^ -<^3-\-t- "ttU^at. A^ji^ OrCt^u^

tfci- V^ '>\.at aJJL a-**>< -Az-t*. t JDAo-^a*. 'UU.a^^.^SliiA.

J-\- r<.S m

r-

a. Uc. Get .3 ^ft'-y. T^,eM |. a^ aos .

To S«a. "t^ jbi u* pui

V '. CLo.i-«.. -4 fV«A<X. Uv 4-Gj>^. "^ai- e«Jt>L tfi^ 'XC«A»- C-T>.^OS

urv-Ctjn Cy Uv --|-a^^A. powJi

<^_i|/ Tf>-^ 0-4

o:|_ Corxt)^^ urot Oi., cr{_ "ttii S(.ol*i oil- o-k^l <Ja^ ^C^ <3/t--c^>'^^X<i.foiuȣi,

ri-y>&-'x) ^,''^^<^a + (T^-eK4-x")T<,-Mi'u,v^ + Ct'-^Xv-X' •^r U/.to'. ^. o,\

(1)

(TL povvJ^< Un Ulv^rX Wji Sl/5<_ JoaIa^ ai.^ 'U^^iiA^i^,_. '^('•^i,, '^/''z- -*'(^l

'\LtJ: iJLs^ \Lh*J^ <it«a<r>-oJ2. YXTvJti eL ijijJL JL- wUiiT. TqJAaJa -U*. ffK lis:

rlc+lti*^ H rfl iio. fuJ)-T-c Cywv,.*^^ f^^-j_

UrU^ "TCa- -•''«:• |oa,..' V. 'ri.

lA. o-L-t-pM-»-T-N = 0,

Tlvt <UfX*.<A L.M.N OAA So /ulJ/cCtlt:i iLmi: Hi. CLy-« t<r>-J

M ± N - - . K/ ± L -- , L L M — .

C.O><^ n^.;e^x£w -i!>f- cr±— tUfi. _^crVi~^

L - 'BG.-i-A^ — . iA ^ CA+SV ^ , hf E AB ^- CD - o

ur^t'ii A . Ti , e . T) ana. -fit-^^Aax -f-u^citc^ of- "^ Or^.^'. '.

Tkt «^c|^^Ai-<7>, ail "iL. Ci/u-^vt-c cwiv*. '»->--4M. 'Vwr«-- -&<- u^-vofe- u, tCa.

Seot/TX <iX- Ttl-a C^.,'>»u<.c ru/JLacM. SU^,otejji ot-l_ ^t^/tjn^^^ H l^-^-fW:.

1. iunvrtiet'i Tffwwv-je. s«^ 4. -til" as^ (i^TlJ

\o Di -4--iu D L^ yu c^ 1. JuUf,^

-|- u^e:t<-<y>-S .

^*^ "t Sea. "t^xt u><. -^o..^ tCa. -^ orflLywWv-, ,;»4j^<:iA.ir>>^

Tivt <it,^<rj>.>.j_i* o^ ttuLj Seci^c .^ .J> L-. V Hu.v~l.tAi L.c cd:.

A eU^tM-cc cwaa^^Lc .

ci+b + C =0 ^-h^* a. X. o <y+o.-«-t-s.o ix + fi+ ')r=o "\

«+ k'+t' = O p -f-c' + o.' 5. o "fr^ «.' 4- V t x'+fl'-i. y £ o (

y*'cti a<-;. at^

2. (a. + t-tc) =0

V«.

Ol + 0+<

o(' ^ a. + cj + <o'f^'— 1'+'-' + '^' y' ^ c+ uj+w' J

uni«A<. 'Jl«.; 'vvAt.'U IJ rt-A-«/U^

_u><. <rw«:7i/.j<. uL<iir "tttAje. 'Vyvix-v-t- ve.

iWA 'Vw'.C- Q i-^*tAX* ) m>u?t<.a^^ "cua. St«Cl£.e^ pCrvUC< <ri- l^o- Or^^-<^<-^.^^-7--

o>^ v^xit^. ^ s^(ti^-t -;a^.- !<^.t ^4

V + Y -<- "W ^ -^

Xc^ L.

3^ T -i*^ ^ -(L< ic^ t^ Y^cwfeU "'i . "V, V G*^ -^

\»\- Scn-A. lU^^ He c^i-v^j^ ct -yw "hU, ^'il-i-.ic-C (J- .

[iA**-6^ Ca«. O'wjL -J^Uv^J t^l^ "t. -<>«.

aM.a.UAxi:<wM.«X a>tt inZa^^az^ un\.o\f. )p<n^ el. CcrwtAcX cAjt. '

Co^tw^i &-L Eta aij^a.cl'iJCMAeAuJL, o t*vce. wLc tt^v^. L_ i-vifiizXs | ^ ',

Six. p<rvvv'l4 it i-oC^curS lA-^t liji^uL. OAJL Sl/^ Si^oh. (m^c^M <r/ i'-UA-^cJi

01 02. 03 , 41 42- 43 iii Ca- ii.

II ija. Tjj - - 23 3 1 I" ,

M-t_ <p^ ft. cUit, . \S OUT Ini «. ~%Lc>A£^v», OouL 'fe C^-C-UC^ UmL

b(rV>U6 odt- l*aiA4CC*iuj>v oi Wot. Sl-»c baVi^ oxL &tXa*va,*«^li ^o£<y>vi t-v^j

Mtt ' t<.!, ^ i-t>-^ t-- C cr>vcA<-oU'>va, tkaX lldlAA. (X^UL. ffvdL̂I J.

^ /; "';.

...1 _<7o^oL^-Jil <rL' 'cL.fj.

. . -- ^

'^ ",

O.^ O-ac -t- k^ -f- Q £_ o

-^ " •

F.< T^ ^, C,, ol'"-*- Vl--^^§'''^ "

^ ^ t

^JL^

Si-if-^M c Cro^^.M^-u^KAJA^

a, ^„ c,.

q-H,

HF, FQ

|3, <\ ^, c,.

I.

o,

o.

k ^o 6-. ^ •

K ^o ^5 ='

-S, a, 4 c,

S:. -&, C, a.

^3 ^. '^ \-t, a, c^ ^^

tj c, e-, a,

A .

b -= <^s.^s^&^ T i, . ^, ^,, ,

', ' - ,^

Li-vtei lO^oL -tcv^v a-iUeA, Ki^^tLS yy^JuJUyi^,

13. j^ay-Ji ffjL L,{ie. O , /(A^

STj^ ^ <rt^ . S,Aj , S^cj,^ . s,|3, -ckGf , HF , .a^Q-

"r,\- +-, K ^,,.,. \'^, -fj.q , c4F is-CL

. , .;. G,H .-<JvF,

K^r

,"x. +.'^,+3^ i^ •HF

i.i)

liL ;^* ^^,.MJ/.i

lujuuA

«;' = <><« \io, T" ^'- '^\

'

4 = <^. % r- <^-i- «- *-"-

"^J= =f.. fie. r» Mx - Fx c^j|_ =- «

^' = <^3, /3., ^3. 4^* ^ ''3'^ "^ "^"^ "^

4'= °U (33, 'J^a.a|at -nCd|-tj.;u.-f cilL ^ «

c.' = ^.^ (i,^r;*

^cc + k^^ + ^i^^L = o

<- -^ (3.^ r-> ^,

.

MLl bcrvvvt OL ^ivLv4j",v^«'K oil, <X <^ tUJL So - ''*-*- Cffw^^^^jiij.

(m)

<^",

a a. —

To ito^ iU oU,, iL .

He ae.JM.eeJ. -Svi e<TK4(.fl(M-i/vjt a, SocaEoj^ <si-^ ite. ««^4rwwc ^u\2.asx~

-CiAA't <;i4A<^^o( -i^M_ Hem. -^ a/!,<»,Kj-i/v,«. rq,*,-,*wt t

'SU'-a/uLc. OiA«< MtUjiUx. p«»*i*4 ^M<7M>p*, lt<.

-: - Mljt G«HXt,-<,cllAAjyv . T(u4 <U«xaZl<•<-C CUAV<-

f 3C -t- 'V| -w -J- S

Oc -4- H^ -+ -ic^ -(- Z k 5Cv ^ = o.

.J. 5.4- [joi^Ji <rv <^ c<j>-ti_a^i,u/i,«ijfc<»^ -iLdv-t.

vCk~l)'^i^ -^CX-dtj.'^ + 'X(ft-0 xV - l^Cf^-O'^toc -4- f<.tv-()oc'^ -

d<-^^.

a,w**. CxjJtc. £U<A<X- H <'i-<i WTrlA. Tt<.fl

—

«k6m <>»A.<U</..a cA< f"

"tlUt*. 2-4- J^ov^ cu>^ ^ aAA.a,v^««JL u-t t«ji> 5«ii ^ \t>M_ a^aA^

fj^Meiiu^ -it.. laAof^dZ" "u^cU^ V ^lWi ((V) . W^ CU^ t>^

ci IL >-.. f,^ 1. ov. l^ He^^c-. K.

aw A. U-- -^

ifAi -tvv^i ^_....,_^ tWfi. co-i

IbtJ. '^.ia-^a. £<Al_ ni*<5 'Tkm. Su^,..1 '•-»*«- ^4

'U. (s'u^C-^ «/>-Kx/>.^'L^rfcov UrU^ lluAir cri^ ^ IaZuju.

(i^^"-J^

-'I't^ |?»v.-l4 <rvv ^fcL ai^i^ .TUt yvtiJ "'"6*^ '^

-flV'TX (iL^VAii4 ^OMiidU^'i hjlv^c^'M M^ah A. Mrito^-[^ ^i

^„..:, ..ilcJl €.tite/<. oM. iot (ndZltis. \t^ l^JtiJyAfjL ^>^M^rrz^ t£a. u!^

4vfcuv5u2^^ 15^ o^- (JLcL 'iy.iu^ Ae>dL (poUoh <jt- C/J^ct

.

C3"\ RjwL /iJZfliL Ipcuob <n^ "»>«- cl<y^-cc. o^vJL "T^jo yeuKi

4 tf^ W^'c^ -£l<w<. A£aQ. \poi^ <ji- CoriCbw^.

W TLjd ^'iCftfi- |3<«-wJi <rK t£j. comac ar~JL ^Wu. pa*A-i <^| ccr>-^^-J«_

i^S) Ho hiLJi[

f'<7UA. |3A*M *A;^

UrLc£. L-a<i-i. ^ Ln JJA^tw cI^Jm If H^g. Ltd 0'J\jJIm oAj <| ttr

HXULMi^^JML CO Su.o^ Cfln^c^ CUv -»C. OAuj^vjK .J'>v it-—

: r Co-, v._ ot LvigA-yg-C^ U, /^ bC^' D . A i/O/V^^^-'*- C-QVCC

AH^t/tv. ,-.... >^J- -• i«. iUA<4-«J3i. "^ .Bffi

ot= A-t

(|+>)M,x, +>i|U-^^,')

CA<i; cr^+ &H, a- |^£<va~c ~^<ru.«X. o^

a.

*^- Tt:t 1^^- ^^

J- =^

:1st

n' • <r

--Joe ' -a«, ' m't- ' -3S ~' nt-ir

M

e.

a/vj)L aZio -klrt. ttJL Co^M—^'Ot.a^

lUt. T'LOrt^^oVv^AluyK (i^ 'Vrv^Jce.j <^ *<-^^ (-k tilt (^^^z '3-^,

jj^O-^Ji CoVJU^V^ "fe -7/UtA/l/fc-C 4lt/»-*Ux<. iPu^yLo^^

Blc^^c^-^.

<^-.

•1.,w