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r ^T^?r ^Tft^ ^ % ti3> mm%

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mofr Cr 'ft ^ ? ?^t% SI R i9rerr

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afr^r FRTor srsr ^n=| ^ a r r ^ ^ ^ "TP IT?! % r j f r ^ ^

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^ - q # 3TR^fr ^ # i5 *fT is^rqwii-fîrfoiflr SRM^

^ r , r%g3nT% sRf^ nor RW ?Tofr ?IIT aiRâ: , f^%?:, ^^rga, ^rr^û'^r^ fî^m mm %[

^ s j r a r C i ^ % qa^-qiOT s T J w g ^ q

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f^mr qj^ |e?r i % sr^n^^r 5 i ; R i f ^ s n M - a5r

gT ^ R ^ q ^ ' r iTR-fqqjî* 't 5?n?c?i *rR?rr RTR f^rarift * it8K4 3jjT RT i: r ^ ^ c r 5ii s r r ^ ^rs-=^r^1: 'rrqiafr ( Verna

*ROT 113^ccrg[ i W r arg^r?^ T^r

^ ^*fcft f % ' t % s ^ M ^ r 3T5| ^ "^^^ Cr a n -

I i?2r ^nirr w r f t r'|??rq: s r g ^ ^Cr ^rc"^ %

51 3Tq^ 5lrfcrfq^ 3?o?i2iiTH 5nfi?ir-"jl^ QTR ^ ^ Cr^^

flul^ q ? - q ? q^ ^ - ^ ^ ^ q q% |i? %^ mm^ T ?T?ir s i ^ ' ^

^3r5i f t ^ r ^ 1 1 i?Cr sRcrira ^rs-irrqr ( Lin-gua Franca ) \%r^ ir^ qr 5?nraq-i?'8jT im qfr sfr "JI ITR ^qoift ?:fC?rCr^ ^ f e ^ ^ w ^(2;;^ f ^ q ^ ^ t fr SUIT'S?!! ^ ?iiT 5fi^^?T^ r1 '^*i q | Îff^-

l q% R^^ffî ^rr f :?? !^! ^ i ^ t ^ ^ i ^ ^ i ^ \f%% f ^ q |

Tif sFsi s ? M q j % ^ r ^ r t , 1% w s r w ^ r =qT%? I

qisîrit ^?:T^^TqwT^^Jt^ 1; 1 511= ^ ^?:oT-q?5jT^ flt f i ^

aii3T ^% mm^\ m^^h 5f^-%q^r q?:d sr ' j ^=HH

STCT^ ?T%-'q35q 3Tqflf-3Tq^ ntqîrrr^ ?^r^rq?;

3Tr?jr s q ^ 11 3?:R C5R% qjf^ n ^ r ^ r ^ ^ r | %

q r = ^ Ji5-%q^ q w Cr si"? I'? ^ n i , gRr, JTRarfq; arrî-^ ^ m t i^qj j f rgsrf^ f t? ^q^Tiv | ; q?:'5^5BTi5[?T

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îTfr ftr^ I, 5irR qftqif(% q ^ # H ftr sngs ^^'I '^rs^ ^ a q ^ Cr^ 'qrr^'? 1 q^ 5 fl?T f%?iJTr 3?I?R-

. jfral, 15 ?Tr q i s ^ 1 1 q C r ^ II% IT?T ^ Tls?r%^^ "?q?iT Ci^'r ' T' "? ^ r c ?i5

' ^ # % 5r?:r ^fi mî 5ir ^ cfr 1 scoi ^ q ^ l 1 s r C f ^ l ^ ^

nr%^ I TTRT zi^^ H^f I M\ |

êr ^n'^^s ^4m^ mi% s W s t ^ 55

CT^'? I ^?r^îr[^ ^ ^ - i r f ^ ^ ofrf q; 1 %m\ q>arf^ I ^ I ?o n o 11 ^^^^ T7{î^ m %,m\ ^ 1

f^^rr^ 3T?ci?: C ^ STRF ?:?IT 1 1 m f% '^nmoi ^^WK ^^n% s f n 5fc-nt%ft C i ^ f?R^^?: 3^

^< gr^ f^^r ! 1 q?: ^1 5?rgrri%-

^ %Ei*r q R IT r%^T S'^r^ it flrri-

q^rW*ft RtT% ??IT? TT% ?I1T ^P^ PT5lff qT3^

m sTif^ sTnfg:^!^ 5^rflnk^T% SKT arri^'^?! f s R JT -

^mi ^^k^ ^5f i^r ^^^r?: ^ j ^ - t e r ? ^ ^ ^^^^ JT if 3' % 5lr^TRR^^

V3

W^î f ^ - H R , ?J^-IIR, e^-^?tt?IR3-â,

3?nt5iftr, ^ s T R - q f t : ^ , = g[Tf !T5-55iT, îfk, anf^î

^T^lfsf ^ I T T ^ I T n?ir I I 3TI%RTB qioicl ^w-

3 # ^ * - q i a ^ T % ^ % Rf^^ iîWr n | I ; "Ti: ^ ?J55 l^^Torf^ ( Plane & Spherical T r i -

gonometry), Geometry) mj &5i-Rfcr (Mensuration ) 3TTf ^ m%5lR ^ 0? t fl5^ 33Tr ( Sine ) ^rf^rsqr (Cosine) ^q^-t^r ( Tangent ), ^rf^#^^ ^^r ( Cosecant ),

( Secant), ^tf^l^ mi ( Cotangent ) ( Versed Sine ) arrf^ %ôrff(?^* f^qf^?ff ( Ratios ) % R^n-SKT ^ qjat^T ^RJT^T^qi; ^ Rî^r sr^r mx t 1 -q^ JT ^*fr

qR^ssi : , arrf^ a N: ar^^^ ^?qraqistT ^ % ^gj q j ^ f l r ^ m - ] ^

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SfRK-J?-? ( Bibl iography )

( ? ) ^-ftl5T??f

( \) 3Tr*Tfft?i 3ift^:^r^ (arr^^rs )

( ) Rf aRr ( )

( H) TO f ^ f 3 ('TR^^r^r??) ( ^ ) RT flf 3^ri^r^Riî (cr. cTP^^îr^)

( ) ^TRoft ? r f

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3. R. ( ?R - rar -qJT SOT

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3?gf^'fi^l 3[ ^ ^frfi-'H s ^ c i ^ miT ^ li^x^^^ ^'p'Trfi^T qfrfiql^^ ^ i i h c f ^ # | I

1 5 .

Cilistial Celestial ? (Day) Day)

5> Solarday Solar Day J Ddcem Decern >) u SWT i> J) Quingue Quinque

J ^\ dHHH?:*r dHHJTC% >> J) n J>

ii ^^=?% >>

Exiguvs Exiguus ? Aloysitus lilius Aloysius Lilius

JJ X

n ? WW JJ

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Trigonometrical

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n ? I '

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Kotrogade

Trigonometrical Ratios

JJ

JJ ?o / ^ ^

JJ n

JJ

J> -f Jl ?

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JJ n 3:q?:

J i i%cRr? Ascend Ascendant

J l - q q ' - n q

^ X JJ ?:T. oc \ IT.

f ?^ [ ^ ^ H L qj=q * H

H are?! are Rl:

? S o ? qw qw

( ^ ) i . ^H, RRIRTC ? % 3T?clTt ^ J ? - ^

aflrwRH ' crr 'sj ' r mH "T ^W f^^H ?ir

II ?ft: II

( n 'ft^ ( Sphere ) Stfl ( Solid Figure ) m

'im I, ^ fWT ^Rft ^ sqi^i^ jf ir 11

q ^ s q W I^lt*^^^ (Axis) ^ ^ f t t 3fR ^

^ SCT J ?*ft5 TO 3 ^ ^ ^ ( Poles ) t I

i \ ) WTt^ (Celestial Sphere) I

^ r | , ^ 3n%^ s n ^ ^ m^ ft^ 3ipqi\^l^ ^^^^ ^ ^fm i^j sn r 11 'r i^ 9;i ^T TO TO

^ ^ ^ TO 4 k P < Celestial. Poles ^ ^ Wrt^ fft ( Celestial Axis ) ^ SfTqift I

( V ) 'Sp:^^ m % mm T% J T ^ W R (Apparent ) f r T O ^ ' T O ^m 1 ^ ^ft-^ft q f i ^ ^

qf?n I , ^ 5KTf ff frT ( Ecliptic ) 11 ( ^ ) mft-fTT m ( Cilistial Equator) 1

^ ^f^q^ i^fe 'Tm t "t TO ^ ^ ^fmî^jkm |3tt

(%) ^ ^ T f % ^ ^ 1 ' f W t t ( ^ * T *lT'Ti3 it TrfJ ^ , i\ HPT^ % ( Degree ) 1 I ^*^% ^T^^ ^ nT T ( Minute ) ^ ^ i s l *TTT T f l ^ ^ (Second ) | \

( ^ ) 5Kri^-^lrT (Equinox) \ îf^cl-lrT afi^ iTf "Ht 'Û^^ ( Plane) ^ ^ f l ^ ^ f ^ ^ T T in]

^ \ ) ^T^cT-^tf^qm ( Vernal Equinox ) m ^}^^ m^V^ TO j f M ^ rT^ ( ^ ) ^ 5iKTi -n?T (Autumnal Equinox) f^% ^ TO ' tRHi^

'Tt^T^^ J l ^ I I ^ TOT^ JTfMf

(

TPT 'l^"? ( Constant) '

^ I ' T ^ F T g f ^ T ( Apparent Solar Day ) ^ f ^ t I m^ ^-^^ ^ f ^ f ^

V f^. qTr ^ ft 5TT r 111 "% 3^f^TR mmi jth >f!

JTS^ JTl^ qo^ t 3T3^K ^]%v([ ^î\X I f^^T iJTf^^^ f^^ fî{^rf^^R^

( Equation of Time) ^ I

H ' IT f T ( Mean Solarday ) qJT^r ftm f , #

11 ? mJTî 3fr q5J% ^Tsl *finî ^fif

^q&, s^^RRT^T m îmm mi^

^ ^ ^ ^ ^ irr^sr ^ ( sidereal Solar Year i

W TO ^ mm '^Tft^ I f l ^ ^ i W r q f t ( s t a n -dard ) q ^ t I

aiT'T'T-TTf^ (Equinoctial Precession ) 1''

( ^ v . ) f ^ c i ^ ^ hi\ 5pii^-qrci ^q?j^i

q i f t ^ ^ ( Tropical Solar Year ) t 1 ?^^T

11 f^??rR}% q f t ^ 3TT^^ (standard) JTHT m\t I

( n ) T^q^ ^ ^ " ^ ^ R ^ i f i M qftspm # qs^^^ f^?HT ^ J R ^Tfm tj^^^^qqspt '^TSCm^WTJI-^RreJ (Sidereal Period) ^ 1 ? ^ TO ? v s n ^ i ^ i ^ ^ | U ? ! ^ ^ ? j m S ^ ? ? m ^ f m f ^ w i ^

( \ ^ ) ^ ^ J ^ ^ ^ qft3Fm ijft

( Lunation or SynodicPeriod ) % I f T O TO ^ f T ^

TOT ^ t | - ( ^) 3TTOr, s r m ^ ^ i ^ ^ ^

Jl

w q ^ l f t ^ l ( A )

: 'm^i s^Rpfi^ qft 3Tqmqr% \^, ^JT ; ' ^ - # T ftm I , ft?T% p > f ?i& JTfRr wp^

^ ^m ^^^^ ^([ t ( H t ?r?IT 1 1 i\

( ) ^ Solar month ) I

J i q 5 K % f t ^ ^ ) m ^ wt^-mfH I i ; f f ^ J i ^ q j T T O ' n ^ ^ m T O t \ m^-mfH iti m^m ^^^^ m r '?^n^ v i ^ 11 s p i f ^ - r n f ^

f f t ^ ^ ^ T ^ mflS TO: f ^ ? l ( Fixed ) t

3?TOFrT% w g ^ ^ ? ? ^ i f r ^ at^q5t

( Phase o the Moon ) ft?fl f I ^m \\o

%o d ^ l , f ^ f ^ ^ ^^^^ TO \ \ \ ^ \

( % f ^ T ^ q ^ ^ T | , ^

f ^ f ^ \ I otv.H WW \ m^-mf^^-Wi

t , ^ ?jrRf ?T JTf qr ^^^ T

m ^ 3nn^ ^PS[qT^^ TO-^^ ^ % % ^ ^ R [ q m ^ i j ^ q r ^ r ^ r aneul mm m^ %r q ^ n t??^T^ t ^ i ^ , ^ 51% f^^if^ 1

( ^ ^ ) ^ ' T r a f ^ 5 T f T % ^ ^ 5 T T * T - H K ^ I ^ qT#-^ qffrr ^ i M , 3Tqt?l, f^^ f^^T Tn%^ q ^ ^ 1 , TOrqq^ f i t l 4 k 3Tqi'cT ^^sRRTq TO^cT f H t t , ^ ^ ^ ^ q i ^ 3TRRq^ J f qcT ^ 1 ? ^ ^ q i ^ T O - ^ ^ d ^ T l v t ^ 3?^^% q r ^ j j ^ t ^ fwq q q>t ^rqiq^qrci^ mi^^ "m^m^^mt^l^

^ mm m^^^m i ^i\^ml fq ), f q ^ (3nqTf), ^ ( " ^ m ) , % (*TTs[q ( 3TT^^ ), 3 ^ (^Tf%^), i f ^ ^ (m^^k ), ^3 ( ), q ^ ( ) , | H ( ) m ^ \ ^ { ' ^ ) i ^ \

^q#?^ ^ qnl^-qif^ #R^^T qw-cl q:Tf ?n[c ( qr^) ^ ft^t I f^Jf^R ^ T ^ ^ qr^q t q ^ qf^q^ fhrr 11

(^ ) ^ T O , ( ^ ( ) ^ s q R s , ( n ) JSI^I^

^ q ^ f - ^ q < t I qf^d \c w I I

TO i f ^ l T f f t , q^ 5 $JTTqf teTOl%

f^^rd HR 5RH:'TI^#?: I

\

fife^fTT'ft ( Christian Calendar ) I

i ^ l ^ ^ ^ S f ^ f ^ 4t ^^^^ M ( Alban Calendar )

M^ V q f R t a ^ ftcffqi^^ ^^^ (\

ff t ^ 1 qqk^qqi^ l^^K (Ddcem=^ o) % im ^ l%?J^f^(Septem=^) 3Tl ^q (Octo=

rf I TfrR qf ft ^ ^ t ^qq% q#ci f^gi^?;% q2[ 'iRqft JTHI ^ ^^TOI ^

q ^ r ^ # T qqf^r^ ^ ( College o Pontiffs) iiqi

gfsft 5iqi^r qR ?frir qi, ^T.5f%%^ 3^q^ ^ q ^

^^mqr I f^^T qft^rq qc |3TT f% f. ^ ^ ^ ^mr^^^q^ # i T ^ (SfT % M q 'JTSNT q^ qrea^ q Sf

^ q f ^ 'fti t qf^^'fe f qWc?! ^qflf ^

finqi 11 3Tq^ ^qi l^^ ^ ^ ^ f ^ q (Sosigenes) t ?^^T^q dqtq qqq ^o f ^ q % ^^^x^o=

vvv. i|CT f^qi qfq'sqS q^cfi^ q^^% ^^qfspt^^^f^q ^ ^ i ^ T , ^ ^q%qtRqTqqTf^qJ#-'?^ qft^q^q^*^ qiq: 55qt qrqqr f tfk r f^qr ^ n t e q ^ ^ q r ^ ^ qf ^xv = qi ^ f^^t ^jft^^lf^ ^ ^ ^ f ^ q ^ q ^ s q q ^ T ^ I 1^ ^qqr^ qW^rfq^fq^ (Leep year) ^fr ^r^^qr qk qR^d ^^ fa[qf r f l ^ ^fqi i ^f^q^^src

^ f^ q^R ^^tf^q sfqt^r q[q l ^ q 5ft ( Julian Calendar) qfT I qi^R m\ ( Old Style ) ql f I 3^q^5T< q W qft^ (Quintiiis)^ U q 1 # % [3n qi, ^^^r qrq Eqqrqis R i ^ i f ^ T I :#q^R dq ^^r^ 3Tq^^ ^5 qfl% (Sextilis) 4 ^ ^ a q qiqq? qr, 3^:^^^ qrq ^qqiqi^qR rq^q ^ f^qj 11 " 3T T> T T J ^ ^ ^ %q5 srq^^q^ q^^qR-

^fcrqq qfrqf^ f^qq^qjq^tz ^ m qr 3TT3fqq; qfiq'f^ qrq qr f ^ q ^ i ^ qf^q^

[ft l^Ti

^ ^ M t ^ ^ jni*rfq fan I ^ q i^rn 5 i * , 3 r ^ q f t ^ q ^ ^ 3 T q 4 t ? c - # r ^ m f t ^m m.

^rari^qfqqi dq% qHf f ^ f wm 4t ^ T f T ; q^f^^raûT^ *ft qm qff 13?;=? : 5n% 3Fq% fiô o q ^ qj^ 3 ?|{ gjt ^msffif ^T^'ft^R^

q f t ^ 3 ? ^ ( Dionysius Exi-guvs) q R ^ dft ^ K ^ l ^ ?^tfm-q^ ?jqT 3pq ^jq^q ^ q ^ q W ^fjqqT^

^ ' s p q f ^ q f ^ m^ ^qqq^ #[ir i c ^ i ^ T qjq f^tî^ sFq-îqrqqr \ OTti^f^^

^qpRT q> q irislt I ^ T ^ ^ mi^^ ^m q I^TT i f ^ q f ^ ^qq t f% ^TqHi:-

%q^%t^# 3Pq-f^^ f ^ q q ^ V q q M ^ qTrq'r t ^ T 5pq q^^q: V g;** ^ v qf^^qit f STT qpqr sqqr t q^R arn^^q ftq f^^ ;qq;^ *ft ' ^ T ^ ^ TOR^ qf ^^^f^qfer qqr ^fkm ^ \W f^qt^ qiqr ^qr \

. ^ 3TT^|f% 'l^rq ^q?flf f^q q i ^ ^ JTiq^t; ft^ ^qr ?:q% qf^f qrif^-qiTq^ qf^ ^ ^ - q ^ T l t H I V

(Aloysitus lilius) i%q^ ^ n ^ q ^ q n q ^ ^p(ft

s r f ^ f qf qff ftqi ^ - q ? i f ^ ^ %^ arf qjf ^ qqf q f t i ^ T v^oqft^^^rR ^ qij d ^ 1 voo qqtflf ^oo snxf % ^ ft arf^Tf f I f^ q^^ qtq^q(t ^HkSt 5 t q ^ ^ ^ ( Gregorial Calendar )qqT ( New Style ) q^q

qqr ^ f ^ l \ fH q#r qqr^ f^^, ^ s4-

T T ^ f ^ < q; q%qr, 3Tf

f o ^^VS^ |o ^ . %,

5 ^ fo ^vs^H m 2^4^^ f H ^^^ ^ \

5H aifPi ^ xnqt H*fl ^nrftq jpsn^

H*R ^ 3n>m ft f H ^ 4t H#sR i gpr^-" H f ^ Hk qf f;qS ^v^^^U ^qftr fhir t r a r q ; ^ Voo qflS Voox v^^^ s arqi^s^^^vs^ '^ 3rf^ %qT ^ # r ; q^ t' f ^ i ?H^ qf qjfr ^ i f t f q V o o q^^^^^.^ ^^v^ qqTS ^ ft snqqr I qifnqq qrf-HJ Ryq fo ^^^^fanqr-, aifq; fo ^0 n=\c^\^ # ^ sfeqi q ^ r I

(^)?nfRn??T^a^5^qftf% ifoH ifqhft-'rfft ^ a r ^ q ^ 5iqf n fi m^ ^ ?ft; 3Tq J ^ wm

^ TOafft m^PiaftT ar q?: \o i qtqnrfq qi*^ f ^ sjRja^ftHiqftft f f tqt qf a ^R U fl^T H ^ q^ f ft,5#rtoHo ^^^%ftHiqf tHqr ; fH W q a s T O

f t a r o ^ q f y 3 p ? R ^ - ^ f o S8oo % T ? [ ^ ^ < f i H l f l ^ W i 'Tf H ^ STpfi^ srqriHK

qr; q^qfiq-qqifHR tm qqr i a^q: n q 5n*qqqi^ aq?q ( fi) f i ^ ^ f ^ t % i t A ' r f H q ^ n ' i ^ + M t f i ' T r t ^ , ftH^ i(i

^V9oo, Xôo^ \\oo 3Tnt^^ 3 ^ ^ q i ^ ^ q ^ ^

'IRqft ^ ^fr TO HTFH fTrft 1%H& m^W^' ^ '?ft^*T q ft?n I

V ^ TO ^ f^q H sft^, qln-i^ ifkfj w l ^ -H^qr H ^zjk% Iqf w # ^ T H i f f i ^ fH^m 11 ^ sft^^ q^r^ 3 T W T O fo Ho

qt qrCt^cn: f jm**^ i ^^nr i PrwC ) i ^ôo ^ ^fT% fo ;ff ^m^ i q^ fîs^t-q^ 15f|q

\cfm ^ eift 4k i j r e , ^ f ^ " ^ I, qf( ^ fi%^?m% I3q:frqq(^)

' [ if q2T % M % qiil^T^ ^rw^ ? 1

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ITT f q ' = Tf%-f xT-, qq=JTf-q T} 9=^m-#f; q q'= ?fIT5 q= -q5 T- ?Tf; q' = spTf - ^ qf;

q ^ H= ^ I ^T-^T^ ITT I

f q T qtor qft tor qqi i -ft ^m^ q p ^ ft, ^

fqq ^ ^ T vod, v, vsvsx, Xv9, '{^o 4k svs 5^, 5^q-'=F ^ - ^ o o " q5T qiq qjq q% *ftq, fq, 5^, PIT f qj Tfa[ qp T- T ^ 4tT ^lft^-w# ft q f fq qq-fqqq qi ii T q? m q:q : qq-5i?q q; i qr qf 1 qqm qf qq qq- qqr qr

qif i qf qiajlrqqqTl I ( ) qtTO qT J- 'q I 'ift 'qcj 4tT ^W, qqT

qRT-qft fNl TO q - 4| I qf fft qqr qft ^ fft t q qq qiq T qqq q^-^ 11

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IT. it. ^ . ^ O 0 0

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Rqte q' - q BTr it \ |q f jqq%3iiqR qq RqftqR

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^ qrqq ^ qr q mt, qf qs[T sf q ft T 11 's[, P 4R q-q T qjqtqft^^ l \ %,5^ 4tT

8R4- R f% ^^^^ qj T q>qt , U sx q 3q, sqq-qj ^ V** m qjq^^ qrq

q% ^ qfg[ q- qj flfq qi iff I q H5qi?q % ft f qi I qf ft qi Rq qqi 11

TO ^ #r ftqil \ m q5'5[%

TT. X i n i V ^ I X TOT II TO gsfT TT.^ixxivxi^m ( ^TWfi^ ?rft5r 4 I Ift% JTf q i T c l ^

1 ^ TO q i . # . ^ t I 3 T f % T T T ^ ^ Xooo % J l I ^ T gq'T-'u #r ^fs^m TO^% ^ q qr. ^ ftft 11 ^.TO II ^q^qi. ^ =

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II sq: TT. Xo I U I U I II ^ II. n X^ I I XvS II q ^ t f ^ v 9 V W S K X < o = vv. o^

tffef T ^Sv9^Xooo=^fN, S^vs; |R=X+ S^vsx-0 ^ 6 = \.o\S}3; ^T^^^ ^ q? - 0{=W\S- .

ft^ q ^ ^ r sfRT f , ^ l ^ w -

^

^ ^ #nft tor f t I i ^ : f ^ f ^ i ^ ^ ^ i ^ n ^ f w sqr^ ^ r ,

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^ ^ 1 ^ fl[-*Tm ^ ^ ^ ^ ^?rT3fi% ^ ^

W I T I { % \ )

m!r 1, ^ ^ %rT-#nf^ 3?rar ^ t* i ' ^ - ^ ^ , ^ i f e q ^ ^.^T, ^ T ^ i w l ^ ^ H i ^ l f ^ ^5T^ ft^-^T'jR

^ ^ r f ^ ^ ^ % ^ 3 T O I ? ? r - f ^ ( Solstice ) mjfi 3FTf^ JT^^TIf^T

p ( t ? n & ^ f f # [ ^ T ^ 5nq "t ^4-5K!f^TO J T f ^ ^ ^ T f ^ ^ R ^ g f ^ 5ffT^ ^ - ^ F T ^ f t ^ f t ,

ft5r SRTFtl 3T^T55^ f t ^ I f ^ T ^ ^ f W ^ R ^ iTr^ ^ ^ T % fH?r f t ^ 9^?: ' J T O TÎT ft^r ^ > r - W ? T

( ^ ) ftt^TlTT ( Terrestrial Equatar ) ^

^ fTIT t , sft =^1^ ^^TJ f t * ^fm

( V ) 5[TT%Jn ( Meridian ) ^îp^^ s^lfsW ^ ^ : f ^ q w i T n ^ t , f t m H ^ ^ ^ ^ ^ f i T q^^jT^m f3TT ^ ^ p ^ liETîww^ ^ r n r r l i ^%l f ^ ^ T T ^ g [ r f ^ ^ |3Tr I f ^ ^ m m

( \ ) ( Latitude ) ^^pT^T ^ ' ^ R ^ ^ t ^ 1 ,5ft ^J^m^K a t ^ ^

^ gfxR f t ^T>T^ ^ ^ n r 5TT^ 1 1 ( ^ ) ^ ( Longitude )

Meridian ) ^ f S 5F??5T# s[Tiîn%

3 ^ ^?RT t qf^JT^ ^ ' n q i 5TTm 1 1

3?^3T JM^T g[n'^jn I i ? f % o ? ^ r ^ (Greenwich) ^ ^ XH^^'^ft f ^ % ? q t S[Tf^TOt

(

(

S ' l i ^ T - ' ^ ^ ^ ^ ^ T 3T t

u I ^ t ^ ^ 3 ' ^ ? r - ^ ^ i f ^ it

( ) ^ ^ r i ^ ( Altitude of the Pole Star ) I

^ii[% m ^m t J

( s^ ) ^1lf?lJfPld # 5 < T I

^l'^^ 3?T?t 1 I f ^ ^ % 'Tf t r ^ W T W t # T T^, 3 | ^ - 3 T ^ S S , ^ ^ ^ ^ 501 j d B -

f l ^ l y ^TJJt^T q JTT % ^ T f ^ ^ I Vo I ,

^ - T ^ ^ X = q^TT^ v v I v ^ 3 ^ iim ^-^ H X = q^T^ u I v ^ |3?n ^ # T qjT^-qi?!^ ^m* T p s t , i ^ T 9 ^ 1 ^ ^{f^^I ?T ^ ' i f ^ T qtT-qj^ q ^ n s 1 ^v q^q

wj^^'fk^ teft q l ^ t , f f t ^ TR 3Tq t?[r t I f ^ * W H ^ ^% ftfrf t ,

^ ?2 I CT a ^ ^"^oo % ^ 3T?TOT HIT 3ft ^f5[ qr^ JTTff f t , qf^ I? gj] 3 ? f ^ f t ^ %Tfg[ I T ift^^ q^ afrc f E qw f t TO 3|^n^S& TTJ q j ^ ^ ^ F i q ^ fe TR-

1 * f i , mm ^ ^ M ^ f | ^ 1

n = ^ ^ - q r ^ ^v I v ^ 13t^Tfl[ I + mr^ ^ v I v

flT^I^^ f E f ^ ^ ^ I t I

T. I U I l^rr, Tci ^ = ^ i 1 T qm f%qi

g ' t q m ^ q JTT I I3Trl ^51% %Tfe[ U I

*nT f^TT ^t ^T5^

TO qtq-qr^ m^RTm 1 ^ U i^ff, f% ^ % U^J \%m m g. 17. U |3TF I qfftqR% q J i q i tft- f^^RR I

^ q m q ^ ^ ^qt^^ q5T^^ q s i ^ ^ q q T T p f h r i t 1 ? i f ^ q [ q ^ ^ i f ^ I 5 ^ ftqi T iqt5[q ^ ^ ^ i ^ n * ^ ^ q q ^ t i snqr i f ^ T q ^ R f ^ q q j q t ^ X \ \m^vnftqi it ^qf^^^55q;i ^ 2 T f ^ q q M U I V f q ^ I f iq} ^ q q R %

gr u nzf^ ^ wt

( ) ^ ^ ^ q T * ? : ^ (Equation of Time) 1 q ^ q f t ^ -^ 3 "7E ( Apparent Solar Day ) qisqq

f^q ( Moon Solar Day) ^ ^ qq^T 3 # ^ I f ^ q ^ qrfq q q ^ ^ im-m q ^ ^ % ^^qqr ^ , ^ q i ^ f q ^ q q q q f ^ ^ r q q ^ ^ f i

I I q f qf^qq ^ q q^qi^frr q^, a ^ R ^ q - q M q w T ^ T % qqôi, qfM' q q | ^ sqqqr i q^ qRqf^^ iqq5t 2[^T fqq q ^ q i f^?r t i q ^ ^ T R S

îm t , 5ft q i ^ - f q q< T%^^F f ^ < f % q % %?S[J| q flq^^ q ^ % p q ; ? : ! I ^f^-qq (Ecliptic )

% f q m^Siqq 3ft^3#?s[qT ( Eccentricity ) % ^yôj ^ j ^ ^ . f^^ f f q ^ mj q j q ( Right Ascension ) ^ ' ^ q q ^ q % t f q ^ q i ^ V i T f t q q t q % , sft ^ ^ q ; q^-qq qiit

mH qifT pf^qq ^ % t R q j q i f r - f q t q *ftT% ^rf^^ ftqrt, q q ^% JT^TT^-frn^ ^ q ^51% q^ig^

1 1 3 T q : q | sTT^qqj q ^ | , ^ f^iq ^ ^ ^ ^ ITTIT ( Mean time ) ^ |,

^ 3 # q i r q ^ q - q ^ ( Sun-dial ) q >?t, ^ ^ - ^ T ^ ( Apparent Time ) f^j^^\ f , U q % I f T ^

qiTqi% 3T?q^^ ^T^-qjft^^^ I' I 3 T r ^ 'qqj^ T f irici f t r i , Tqs qifnsept ^ ^ q f t f ^ q r ftq^rft ar cw; | i ^ q s - ^ i ^ ^ q q 315= ?:

qqr q ^ T ^ T^qq-qii^ 3TT^T f J q f 3 p q ^ ^ ^ ^ f q ^ , ^ ^ ^ ^ q , f q q j ^ ^ ^ q t f ^ q * q i * qq ^ ^ \ q j ^ c ^ M q^q q q qqr ^ fr q w -^ q ^ si?q I t q r q i 1 1

xs

to

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4 ^ ^ ^T^-^jft^'JI^T q ^ T ^ ^ ^ ^ ^ q ^ l l ^ q e q q ^ ^

f , q i # ^ ^ q R q % qzTfc( mm ^ I v ^ I ^^'C ^ I U ^ q q f l ^ qt ^ ^ q R q % iTsqJT ^T^

1^1% s r f ^ q f ^ i % r % ^\f^ ^^

( ) ^5r^?[iqJI q t ^ q ^ T ^ ( Mean Local Time )

3 ! T q ^ * T%q 3 1 ^ qs^qi I T % qirq 3 i q T ^ -

Hn^ ^ I q q l q t q ^ ^ml ^ ft\^z %.

5 T H % sTT fr g f t ^

^ q j [ qsqq qpr^ qf^

^ a f k q ; i # ^>Tf q ^ ^ SOf^m'R %* I ^ . jTsqjT TOsrfqqjft q j i # ^ i f ^Sk qf^

f t qt q f R f , STR^T ^ f | ^ I q i T ^

m^\k ^mf^ ^ q f t ^ i 1 1

J T f T O ^J^TR ^trq^T ^ - T O q ^ q i ^ ( P . M . ) ^^T^

'R jqpT TO q ^ n ^ i 3 T f i g [ P T f q ^ ^ ^ y

( ) fqTTT?T ^T5n I ^M^'JT f ^ q q T f | , ^ m q q ^ q ^ j f i q ^ ^ ^ T i^^m sTT T I I % t

I v s n v ^ qt ffr^wR I I ^mt \ \^ ^fz^^^^\^^ f ^ ^ f t i ^ ^ w i q f q ^ q r

^ 1 I % q q i f q^qrf^ n V S n v 5Rq I qt ^

' f t e - f $ # m ^ ^ w T ^ q

1^ 1 ^ JTf f [qqjT, qr ^ % ^ q q ^ ^ ^ , 5[q5T 1 1 q f ^ ^ p : ^ R f t ^ i ^f

^ # I - T O ^ T f t 5ff TO 1 mi =q , ' ^ ^ c R ^ ^ T 5 J - q i f t ^ f q q ^ l f f ^ q ^ , q5T^% ^ m^wTR? ^ I I q ^ r ^ it qf%^ CT m^ qiqflf q l i ^ I I m^ qjft^^'iT f l qiqst ^ f ^ t * I I'Tsq-^^T qf^JT f t qt ^ s q r ' r R ^ ^ % TR^^JTiq^ ^T^^T, qf^ f t #T ^ q^T^T 'qiT'fq I T q 5 ^ ^ ^q^"q^^T% Tq#!|-^T^^ ^ # r ^ q^qjT^T^ fi^TT I f ^ ^q^-qJT^^ q^^% f^^ TO-qjft-^^'f^fqf^^Tfc^^T q^rf^^ ^TR qt-qJT-^T^sf f | q ^ q ^ ? : 3T?nq: ' ^ ^ ^ ^ ^ f ^ ^ i ^'Tf q q ^^^T ^j^^ \ m^m ^fl^q-^^T qi'^JT I; mt ^T^t% q ^ q n '^^T^?: n M o g^^Tf? t q ^ m q q . i

^ 3 ! ! ^ qt q . v v M M V ^ I^^T I q q T^ t ^ ^ n f TO-qfft^^^ I ^^=q^(r^ m ^T it \^m' q ^ I T R f ^ ^ m q q . v v M I v s f3Tr i

( ) cfJTf?rr ( Declination ) gf^^ f % ^ ^ f r T r i l r t q ( Rigbt Ascension ) | ^7ft^% ifqJC ^TIT'T a r ^ ^ frTT^t ^ t JTf%^% ft^T |3TT q r ^ - f r f ^ qq^toiq^ qjT ; ^ T f q f r n t ^ r qf 5 ! t q f - % ^ i f t ^ q T f r f T i % q r q f ^ M T , JTfq^ sRif^ci q?rr 5!T?t-fTm ^^ 3n qn^'q-sFT^qr?! ^ ^ R ^TTJ q n ^ -

I

3

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o

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mO^ ^ i^ F ^ S ^ T ^ - ^ ^ Q Q 3^?: Q F T

m-ii^ f ^ T O %qT ^ T i | q %qT i q q q RS ^o ^

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( R

( R^ q ) qftq-q?iif ^ s n ^ - ^ q r ^ t v9 % ^% PH-q>^S

^ % g q g o i q - u ^ , ^ o ^ ; ^ q ^ q i q f ^ T

( R^ ^ ) ft^qf^-qj^ ^ T q r i f ^ g f ^ q i ^ ^ ^ - s r q i ^ ^ S ' q , 5 ^ - ' ^ ^ q , ^ ^ o o o q r q ^ q q ^wnK ^

^vsV q gtq, g q q - W M^VR Jf W'^oo q i q ^ ^ q f ^ s ^ t ^ - q i ^ % T f ^ o I U f q ^ 13Tq^T f^5^t^-

q r ^ = % l ^ ^ '

( R^ =q ) f ^ q t f ^ i q f ^ - q j ^ fqq^To5 ^ ^ q K ^ f r f q ^ ^ fq^To5 ^ q i I f3ft^-7qT% qqf^q-5qT% q i f ^ q s T % q q 5 T ^ q - ' j , ^ I to f q ^q-q;^^T \ooo^ 5 ' q , j F j q - ' ^ ^ q q:TT%T ^ ^ q i ^ r q r q ^ ^ q i s f ^ s ^ t ^ r 7qT3TTqT|;%^ l ^ i t ^ ^ o 1 |q^T w f ^ q - q f i f ^ q ^ . Ro I M I qnt^q-^qi ^VV I q:[f%# Efitf ^qT J

3Tq

( RS ) ^JTFrT ^T^T I ^ l ^ f f ^ i f t -

1 ^ aqr T R M VR | q I =qq:q vso

^ mt^ 5pif^ I VV9 q ^ ^ t 13Tq%^Tfiiq5 tolT-

\ ^ f q f r f f e l qt n R M VR ^ f^qjft ?

q ^ f s RR I Rv I s f q ^ I q m ^4 i^qf^ t ; m* q f ^ q f t I

( ) ^ q ? T f%iqt?CT \ ^ ^ n ^ qft-^ goitTfi q q : % q i f ^ m f ^ i ^ t ^ - q j ^ ?T|ii ^ ^ q q m

q m ^ ^ ^ q R T 1 R^ I VR wm

^w^vt f t q % ^ROT ^ q i i\ mm J^'^ ih

( ^ q R S % ^TT 5FTR?f f^rrot q t l ^ S -qTn^ JTrfTsm^ t 3f2[rTf R^ i R ^ Ftq^q

^^m qt q m ' q i f t ^ I

% % ^#crJ5f#T 3KTf% % l f ^ RR I RV I s i f

% l f ^ RR I Vi I VR f l I

qrq?a* ^ - q ^ ^ ^i ! -^^T< ^im i^m t i%qT

=q = qm^q 5frrpq-qiq; ^ = q f - ^ ^ i ^ r qrif^q^TT; m = q^-^ f ^ f ; q = ^ m ^ ^ T ^T[ p ; ^ = 5F?iR-iTfqji ^ t r qs^R

( ) ; = q f ; ^ q = m = ^"t^; = 3 = ^ -

( ^R )qi3[j:q(Poles of the EcHptic) m 5RT^-5[TT% fxT^ qt ^ f^ i r q I 5Tt q j ^ R ^ 5!! 1

( ( Celestial Latitude) | ^^pqftJTRFHSR^ %==3[% f t q 1^ qqj q i q ^ ( ^ i sFff^q i x f ^ R - q i # q t U q =qiqq5T ^% * q f % 5 [ ^ qrif^q-iTr* w-^-1^11,5Tfq3T J ^ ^ ^ ^ ^ ^ m r l , ^fr q f ^ t 5FiRti-fTT% f ^ ^ H f

( ) 'q?^-^^3RT o5RT I 3?fT% a r ^ T qfq q R ' ^ t ; qqffiR 'q-? 4 ^ qf'IT f^ -

3T^fRcI ^fq I Tf^t =q?s[3 sfe-

t, TO ^m^. V I Ro = ^^T ft^T 1 ; mt ^ \ooo ^ m : v9o ^ ^ F -qr toqr I

I mq f^, ^T| u . ^ 1 Ro I \ 1 1

f^qr qt u . U s I R^ I I ^ ^ n v I I T'fT TqT ^t W:k^ Ih \ \ RV I S I I ^ q t ^ % F ^ \ \ \ o [ S ^

^ T ^ Rv9 I n 3TFqT I

#P t q giT gqq-qj^^ m *ft T ' ^ f ^ to

V I s ^ gqq-qj5J nRi^vi^vs JT vs ^ *rTJi f ^ q t ^ ^ ^ ^ I M \ q f qt 3TT^q (tf^ t 4t^ 3TfiT-Tff ?T^ i ^ T ^ qqq t ^ ^ l I

( ) 5TqtT T r n s ^ ^ ' q ^ ^ i : ^ ^ ^ I q ^ ( q F n ' ? q ) m * I S=^^T I ; 3T?Ft f q

T?wf 15ft^-3^T^*t gof, gqq-^^flf \ooo

I ^ 2 = ^ - - m^ ( ^ f ^ - q ^ R )= 3 ? m - q ^ q ^ X

3nqq ^ ^ q ^ ^ X m f

5 i ^ f ^ ^ ^ , ^ Jrf% 3 ? ^ - 3 ? ^ gaiT

^ it ^m^^ q q f^qq d m | i ^ c q f ^ ^ to q t ^ q f! qt TO q ^ K f q %

M h l 3 T q ! ? i ^ q q ^ q ^ % fqqqq q q f ^ q i sqqi | I ^ q t ^ q ift^ 5 ^ * ^ ^ q t ^ i q 1 I

q ^ ^ q i t I

W I V fq^qqi q i q q ^ T . M i vvs i I^rr I i q ^ s ^ s f u . R i R R l U m = a r ^ f s j ^ R i \\[ \\ I f q q p i ^ - g q * H s ^ qjof-g^qj V^R | 3TT I fq& U 3T5rq-3T^q ^ % g a j q - ^ ^ ^ o o o ^1 q r q ^ f t - q ^ R \ i \o ^ R f3q I q ^ ' M q ^ ^ ^ ' ^ q q i q r q q

q q q i ^ f f t % ^ - q ^ R q q m ^ f f t % ^ q ^ 4y |3TT I

^ q ^ q f q q q i f l i p t q ^ t - q ^ q TO

^ 3 [ T ^ ' ^ i T O ^ 'S [ n . R i ^ v i v ^ I ^ v ^ TOqq^t^-q ^ R ^ 5 % % ^ t q ^ f q ^ ^ u . R i \ v i V M R V | 3 n 1 1 ^ arqqt^r R ^ i v n v torqr, q i q q ^ . q . ^ . U ^ I V M |3q I ^ q ^ r a R I RRUo|?(^=

R I RR f3q t fq*Tfi3^?r- 'F^ qs^qf^ I 3?qj f q q j 9 < ^ q R q q .

( ^S ) 5fJTf?rT ^T^T I ^TO ^ ^ - ^ ^ i^RT q f t t o t o f f RS%S [T^q^f^qm qf^ w^-mmi 5tfl f^^T% ff qt ^^rq qf^ ^ to T ^ i % f! qt ^ i ^ ^ i TO spTf ci a r i ^ t i

^ . q . q i q q q'5[q3T l^t?^ ^\ I RR t , f^q*T 3fiTN f ^ q q RS % ?RT R^ m I VV 3Tr| I qiq-T

| q ^^'JT ^ R t # qt TO sfTTpq ( ^ ^ i f ^ R^ I U\ V V ) I u % T r ^ \\\n \ i f I qf TT qjn' q sTif 13iff ^rî ft, qff q i S ^

( Vo ) ( The Ascend or the Rising Sign ) I 5qtlli ;-3[(T# ^ q q ^ 3??^'^ J l f ^ t ; 3?^; fqq5T ^ -

qq55HT TîTR^q^ 1 1 i ; # q 5 ^ 3 n f % q %

m STR q ^ q i f , f ^ q ^ qfT qq>% 1iT?l[ fq(t firfq^ q^ 3 f t q I3TT ^^f l l* I T%qT f S T O ^ ^ T%f 3w[ 3Tn; ^JT^ t , qfT ^q ^fr 3nfr I

^ i f ^ - ^ q ^ I 3TI q->J5T SRTf^q-iq TTfr f r l * qiT ^TOS m q j T R F R qt qql uTm^m mq qqjit

^ q i t I 'R qrr^q-lrT q i ^ - l T T # \\ I R^ % m^\% M q ^r q f f t ^ i l ^rfljqfip ^q-mqq

t , it^qf ^ q q i i t îT q ^ q ^ q q i f 3?t?: isit i j c l , ^m ^^-JTR 3Tf^^ itqi 1 1 i % q T i f ^ # %'q5T%

^ ^ 3 ^ 3Ti 3 Ra^T ^TRT I , ît m 5r?m mq*^ I qf RT q-T%I%5f? I3TI f E ^ q^Mt

"sFif^^w ^H'q-3FTPcT& qr'n 5lA qt f f ^ qm qf f[qr *T TTf 3Tr it ^^ m^qq ^ it^rt i

i^WPl torn 3 ? ! ^ 1 1 % f ^ 5 H I R?qt| I

! ( ) (55fr) ^ ^?ffqjT ^'T-qrR

;r8qrf ' j ^ R S T R T I I ^ Tjt^^ik ^ *TR A qs^T?^ ^f^q qq9& iiq^q^r

ITR f ^ T O ^ & f T ^ T T O ^ ^ R %q snqr 1 1

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)ST?R n q w ^ 5JiT f i f i r q f t f^,

l^M I3TTI fq^% R R ^ T K qt qm n ^ r r o f ^ ? f t t ^ V ^ |3TT I ^^^^l fiqq S ^ i q m f l l I

( W ) f i B ^ ^ ' ' ^ ^ S ' ^ l ^ ^ H ^ ^ T f t f ^ r q R ^ T R q S^T^J^ ^ # mm qm f^^q ^ I

f r o JTR R^v I n=R^v^5ptR^ q g q t o r i q t ^ ^ v s P ! i I |qif JTR^i * n n fq^RT qt ^ ^ ^ ^ |3n i

( ) f q i : i q q qqqST fif^lojqi I TO ^ P R -

^ T O R R q^JIl^ RV^ I V=q. V I ^ I V 3TRT I ^ ymi R R ^iqq p % J T R R^vf qft q R ^ ' J ^ q sntoTT qt ^v9^^ | 3 n ^ q m ft^q% JTR K = \o^^^ fjEft S'nr T%qT tit

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