{"text_format":"3","workbook":"xlsx","n_sheets":3,"sheets":["Υπολογισμός Πάσχα","Πάσχα β-β","Πληροφορίες"],"not_rendered":{"macros":1,"defined_names":1},"read":"whole","date_system":"1900"}

{"sheet":"Υπολογισμός Πάσχα","index":0,"n_rows":51,"n_cols":10,"rows_kept":51,"merged":[[0,0,0,9],[12,3,12,5],[16,2,16,5],[16,6,16,8],[17,2,17,5],[17,6,17,8],[18,2,18,5],[18,6,18,8],[19,2,19,5],[19,6,19,8],[20,2,20,5],[20,6,20,8],[21,2,21,5],[21,6,21,8],[22,2,22,5],[22,6,22,8],[23,2,23,5],[23,6,23,8],[24,2,24,5],[24,6,24,8],[25,2,25,5],[25,6,25,8],[26,2,26,5],[26,6,26,8],[27,2,27,5],[27,6,27,8],[28,2,28,5],[28,6,28,8],[29,2,29,5],[29,6,29,8],[30,2,30,5],[30,6,30,8],[31,2,31,5],[31,6,31,8],[32,2,32,5],[32,6,32,8],[33,2,33,5],[33,6,33,8],[34,2,34,5],[34,6,34,8],[35,2,35,5],[35,6,35,8],[36,2,36,5],[36,6,36,8],[37,2,37,5],[37,6,37,8],[38,2,38,5],[38,6,38,8],[39,2,39,5],[39,6,39,8],[40,2,40,5],[40,6,40,8],[41,2,41,5],[41,6,41,8],[42,2,42,5],[42,6,42,8],[43,2,43,5],[43,6,43,8],[44,2,44,5],[44,6,44,8],[45,2,45,5],[45,6,45,8],[46,2,46,5],[46,6,46,8],[47,2,47,5],[47,6,47,8],[48,2,48,5],[48,6,48,8],[49,2,49,5],[49,6,49,8],[50,2,50,5],[50,6,50,8]]}
["Υπολογισμός Ορθόδοξου Πάσχα και σχετικών γιορτών v1.00"]
[]
[]
[]
[{"$nulls":9},{"$f":"easterdate(D9)","v":37346}]
[{"$nulls":9},{"$f":"J5","v":"2002-03-31"}]
[{"$nulls":9},{"$f":"J6","v":"2002-03-31"}]
[]
[null,null,"Δώστε το έτος:",2002,"(Μεταξύ 1583 και 4099)",{"$nulls":4},{"$f":"easter(D9)","v":37346}]
[{"$nulls":9},{"$f":"J9","v":"2002-03-31"}]
[null,null,"Κλειδί υπολογισμών:",{"$f":"MOD((19*(MOD(D9,19))+16),30)+MOD((2*(MOD(D9,4))+4*(MOD(D9,7))+6*(MOD((19*(MOD(D9,19))+16),30))),7)+3","v":35},{"$nulls":5},{"$f":"J10","v":"2002-03-31"}]
[]
[null,null,"Άγιο Πάσχα:",{"$f":"DATE(D9,IF(D11>30,5,4),IF(D11>30,D11-30,D11))","v":"2002-05-05"},{"$nulls":5},{"$f":"orthodoxeaster(D9)","v":37381}]
[{"$nulls":9},{"$f":"J13","v":"2002-05-05"}]
[null,"Κινητές γιορτές εξαρτώμενες από το Πάσχα:",{"$nulls":7},{"$f":"J14","v":"2002-05-05"}]
[]
[null,"Διαφορά","Γιορτή",{"$nulls":3},"Μέρα, Ημερομηνία"]
[null,-70,"Τελώνου και Φαρισαίου - Αρχή Τριωδίου",{"$nulls":3},{"$f":"D$13+$B18","v":"2002-02-24"}]
[null,-63,"Του Ασώτου",{"$nulls":3},"2002-03-03"]
[null,-59,"Τσικνοπέμπτη ",{"$nulls":3},"2002-03-07"]
[null,-57,"Ψυχοσάββατο Α' ",{"$nulls":3},"2002-03-09"]
[null,-56,"Της Απόκρεω",{"$nulls":3},"2002-03-10"]
[null,-49,"Τυροφάγου",{"$nulls":3},"2002-03-17"]
[null,-48,"Καθαρά Δευτέρα",{"$nulls":3},"2002-03-18"]
[null,-44,"Α' Χαιρετισμοί",{"$nulls":3},"2002-03-22"]
[null,-43,"Αγίου Θεοδώρου Τήρωνος",{"$nulls":3},"2002-03-23"]
[null,-42,"Κυριακή της Ορθοδοξίας ",{"$nulls":3},"2002-03-24"]
[null,-35,"Γρηγορίου του Παλαμά ",{"$nulls":3},"2002-03-31"]
[null,-8,"Σάββατο του Λαζάρου",{"$nulls":3},"2002-04-27"]
[null,-7,"Κυριακή των Βαΐων",{"$nulls":3},"2002-04-28"]
[null,-6,"Μεγάλη Δευτέρα",{"$nulls":3},"2002-04-29"]
[null,-5,"Μεγάλη Τρίτη",{"$nulls":3},"2002-04-30"]
[null,-4,"Μεγάλη Τετάρτη",{"$nulls":3},"2002-05-01"]
[null,-3,"Μεγάλη Πέμπτη",{"$nulls":3},"2002-05-02"]
[null,-2,"Μεγάλη Παρασκευή",{"$nulls":3},"2002-05-03"]
[null,-1,"Μεγάλο Σάββατο",{"$nulls":3},"2002-05-04"]
[null,0,"Άγιο Πάσχα",{"$nulls":3},{"$f":"D$13+$B37","v":"2002-05-05"}]
[null,1,"Δευτέρα της Διακαινησίμου",{"$nulls":3},"2002-05-06"]
[null,2,"Τρίτη της Διακαινησίμου",{"$nulls":3},"2002-05-07"]
[null,3,"Τετάρτη της Διακαινησίμου",{"$nulls":3},"2002-05-08"]
[null,4,"Πέμπτη της Διακαινησίμου",{"$nulls":3},"2002-05-09"]
[null,5,"Παρασκευή της Διακαινησίμου - Ζωοδόχου Πηγής",{"$nulls":3},"2002-05-10"]
[null,6,"Σάββατο της Διακαινησίμου",{"$nulls":3},"2002-05-11"]
[null,7,"Του Θωμά",{"$nulls":3},"2002-05-12"]
[null,14,"Των Μυροφόρων",{"$nulls":3},"2002-05-19"]
[null,21,"Του Παραλύτου (Βηθεσδά)",{"$nulls":3},"2002-05-26"]
[null,39,"Της Αναλήψεως",{"$nulls":3},"2002-06-13"]
[null,48,"Ψυχοσάββατο Β' ",{"$nulls":3},"2002-06-22"]
[null,49,"Κυριακή της Πεντηκοστής",{"$nulls":3},"2002-06-23"]
[null,50,"Αγίου Πνεύματος",{"$nulls":3},"2002-06-24"]
[null,56,"Των Αγίων Πάντων",{"$nulls":3},{"$f":"D$13+$B51","v":"2002-06-30"}]

{"sheet":"Πάσχα β-β","index":1,"n_rows":42,"n_cols":28,"rows_kept":42,"merged":[[3,4,3,5],[3,10,4,11],[3,16,3,17],[3,18,3,19],[3,22,3,27],[6,4,6,5],[15,22,15,27]]}
[]
[null,"έτος",2002]
[null,"Χρυσός Αρ.",{"$f":"MOD(C2,19)+1","v":8},null,{"$f":"FLOOR(C2/100,1)","v":20},{"$f":"MOD(C2,19)","v":7}]
[null,"Αιών",{"$f":"FLOOR(C2/100,1)+1","v":21},null,"Ιουλιανό",{"$nulls":4},"Golden","Full moon",null,"Possible","Easter",null,"Epact","Full moon",null,"Possible Easter Sunday",{"$nulls":3},"WESTERN EASTER SUNDAY DATES"]
[null,"Επακτή Ιουλιανού",{"$f":"IF(MOD(11*(C3-1),30)=0,30,MOD(11*(C3-1),30))","v":17},null,"Ij",{"$f":"MOD(19*F3+15,30)","v":28},{"$nulls":3},"Number",{"$nulls":3},"Sunday",null,1,12,"April",{"$f":"IF(R5=\"April\",4,3)","v":4},{"$f":"IF(WEEKDAY(DATE($C$2,S5,Q5),1)=1,DATE($C$2,S5,Q5)+7,DATE($C$2,S5,Q5)-WEEKDAY(DATE($C$2,S5,Q5),1)+8)","v":"2002-04-14"},null,null,"15 April 1990","23 April 2000","4 April 2010","12 April 2020","21 April 2030","1 April 2040"]
[{"$nulls":4},"Jj",{"$f":"MOD(C2+FLOOR(C2/4,1)+F5,7)","v":3},{"$nulls":3},1,5,"April",{"$f":"IF(L6=\"April\",4,3)","v":4},{"$f":"IF(WEEKDAY(DATE($C$2,M6,K6),1)=1,DATE($C$2,M6,K6)+7,DATE($C$2,M6,K6)-WEEKDAY(DATE($C$2,M6,K6),1)+8)","v":"2002-04-07"},null,2,11,"April",{"$f":"IF(R6=\"April\",4,3)","v":4},{"$f":"IF(WEEKDAY(DATE($C$2,S6,Q6),1)=1,DATE($C$2,S6,Q6)+7,DATE($C$2,S6,Q6)-WEEKDAY(DATE($C$2,S6,Q6),1)+8)","v":"2002-04-14"},null,null,"31 March 1991","15 April 2001","24 April 2011","4 April 2021","13 April 2031","21 April 2041"]
[{"$nulls":4},"Γρηγοριανό",{"$nulls":4},2,25,"March",{"$f":"IF(L7=\"April\",4,3)","v":3},{"$f":"IF(WEEKDAY(DATE($C$2,M7,K7),1)=1,DATE($C$2,M7,K7)+7,DATE($C$2,M7,K7)-WEEKDAY(DATE($C$2,M7,K7),1)+8)","v":"2002-03-31"},null,3,10,"April",4,"2002-04-14",null,null,"19 April 1992","31 March 2002","8 April 2012","17 April 2022","28 March 2032","6 April 2042"]
[null,"Ηλιακή Εξισ.",{"$f":"FLOOR(3*C4/4,1)","v":15},null,"Hg",{"$f":"MOD(E3-FLOOR(E3/4,1)-FLOOR((8*E3+13)/25,1)+19*F3+15,30)","v":7},{"$nulls":3},3,13,"April",4,"2002-04-14",null,4,9,"April",4,"2002-04-14",null,null,"11 April 1993","20 April 2003","31 March 2013","9 April 2023","17 April 2033","29 March 2043"]
[null,"Εξίσ. Σελήνης",{"$f":"FLOOR((8*C4+5)/25,1)","v":6},null,"Ig",{"$f":"F8-FLOOR(F8/28,1)*(1-FLOOR(29/(F8+1),1)*FLOOR((21-F3)/11,1))","v":7},{"$nulls":3},4,2,"April",4,"2002-04-07",null,5,8,"April",4,"2002-04-14",null,null,"3 April 1994","11 April 2004","20 April 2014","31 March 2024","9 April 2034","17 April 2044"]
[null,"Επακτή Γρηγοριανού",{"$f":"C5-C8+C9+8","v":16},null,"Jg",{"$f":"MOD(C2+FLOOR(C2/4,1)+F9+2-E3+FLOOR(E3/4,1),7)","v":4},{"$nulls":3},5,22,"March",3,"2002-03-24",null,6,7,"April",4,"2002-04-14",null,null,"16 April 1995","27 March 2005","5 April 2015","20 April 2025","25 March 2035","9 April 2045"]
[{"$nulls":9},6,10,"April",4,"2002-04-14",null,7,6,"April",4,"2002-04-07",null,null,"7 April 1996","16 April 2006","27 March 2016","5 April 2026","13 April 2036","25 March 2046"]
[{"$nulls":4},"Lj",{"$f":"F5-F6","v":25},"Ιουλιανό",null,null,7,30,"March",3,"2002-03-31",null,8,5,"April",4,"2002-04-07",null,null,"30 March 1997","8 April 2007","16 April 2017","28 March 2027","5 April 2037","14 April 2047"]
[{"$nulls":4},"Lg",{"$f":"F9-F10","v":3},"Γρηγοριανό",null,null,8,18,"April",4,"2002-04-21",null,9,4,"April",4,"2002-04-07",null,null,"12 April 1998","23 March 2008","1 April 2018","16 April 2028","25 April 2038","5 April 2048"]
[{"$nulls":9},9,7,"April",4,"2002-04-14",null,10,3,"April",4,"2002-04-07",null,null,"4 April 1999","12 April 2009","21 April 2019","1 April 2029","10 April 2039","18 April 2049"]
[null,"Ιουλιανού","Γρηγοριανού",{"$nulls":6},10,27,"March",3,"2002-03-31",null,11,2,"April",4,"2002-04-07"]
["Μήνας",{"$f":"3+FLOOR((F12+40)/44,1)","v":4},{"$f":"3+FLOOR((F13+40)/44,1)","v":3},{"$nulls":6},11,15,"April",4,"2002-04-21",null,12,1,"April",4,"2002-04-07",null,null,"ORTHODOX EASTER SUNDAY DATES"]
["Ημέρα",{"$f":"F12+28-31*FLOOR(B16/4,1)","v":22},{"$f":"F13+28-31*FLOOR(C16/4,1)","v":31},{"$nulls":6},12,4,"April",4,"2002-04-07",null,13,31,"March",3,"2002-04-07",null,null,"15 April 1990","30 April 2000","4 April 2010","19 April 2020","28 April 2030","6 May 2040"]
[{"$nulls":9},13,24,"March",3,"2002-03-31",null,14,30,"March",3,"2002-03-31",null,null,"7 April 1991","15 April 2001","24 April 2011","2 May 2021","13 April 2031","21 April 2041"]
[null,{"$f":"DATE(C2,B16,B17)","v":"2002-04-22"},{"$f":"DATE(C2,C16,C17)","v":"2002-03-31"},{"$nulls":6},14,12,"April",4,"2002-04-14",null,15,29,"March",3,"2002-03-31",null,null,"26 April 1992","5 May 2002","15 April 2012","24 April 2022","2 May 2032","13 April 2042"]
[null,{"$f":"DATE(C2,B16,B17)","v":"2002-04-22"},{"$f":"DATE(C2,C16,C17)","v":"2002-03-31"},{"$nulls":6},15,1,"April",4,"2002-04-07",null,16,28,"March",3,"2002-03-31",null,null,"18 April 1993","27 April 2003","5 May 2013","16 April 2023","24 April 2033","3 May 2043"]
[null,{"$f":"WEEKDAY(B19,1)","v":2},{"$f":"WEEKDAY(C19,1)","v":1},{"$nulls":6},16,21,"March",3,"2002-03-24",null,17,27,"March",3,"2002-03-31",null,null,"1 May 1994","11 April 2004","20 April 2014","5 May 2024","9 April 2034","24 April 2044"]
[null,{"$f":"B19+8-B21","v":"2002-04-28"},{"$f":"C19+8-C21","v":"2002-04-07"},{"$nulls":6},17,9,"April",4,"2002-04-14",null,18,26,"March",3,"2002-03-31",null,null,"23 April 1995","1 May 2005","12 April 2015","20 April 2025","29 April 2035","9 April 2045"]
[null,{"$f":"WEEKDAY(B22,1)","v":1},{"$f":"WEEKDAY(C22,1)","v":1},{"$nulls":6},18,29,"March",3,"2002-03-31",null,19,25,"March",3,"2002-03-31",null,null,"14 April 1996","23 April 2006","1 May 2016","12 April 2026","20 April 2036","29 April 2046"]
[{"$nulls":9},19,17,"April",4,"2002-04-21",null,20,24,"March",3,"2002-03-31",null,null,"27 April 1997","8 April 2007","16 April 2017","2 May 2027","5 April 2037","21 April 2047"]
[{"$nulls":15},21,23,"March",3,"2002-03-24",null,null,"19 April 1998","27 April 2008","8 April 2018","16 April 2028","25 April 2038","5 April 2048"]
["α",{"$f":"MOD(C2,19)","v":7},{"$nulls":13},22,22,"March",3,"2002-03-24",null,null,"11 April 1999","19 April 2009","28 April 2019","8 April 2029","17 April 2039","25 April 2049"]
["β",{"$f":"MOD(C2,4)","v":2},{"$nulls":13},23,21,"March",3,"2002-03-24"]
["γ",{"$f":"MOD(C2,7)","v":0},{"$nulls":13},24,18,"April",4,"2002-04-21"]
["δ",{"$f":"MOD(19*B26+16,30)","v":29},{"$nulls":13},25,{"$f":"IF(C3>11,17,18)","v":18},"April",4,"2002-04-21"]
["ε",{"$f":"MOD(2*B27+4*B28+6*B29,7)","v":3},{"$nulls":13},26,17,"April",4,"2002-04-21"]
[null,{"$f":"3+B29+B30","v":35},{"$f":"IF(B31>30,\"\",\"Απριλίου\")","v":""},"Κυριακή",{"$nulls":11},27,16,"April",4,"2002-04-21"]
[null,{"$f":"IF(B31>30,B31-30,\"\")","v":5},{"$f":"IF(B31>30,\"Μαίου\",\"\")","v":"Μαίου"},"Πάσχα",{"$nulls":11},28,15,"April",4,"2002-04-21"]
[{"$nulls":15},29,14,"April",4,"2002-04-21"]
[{"$nulls":15},30,13,"April",4,"2002-04-14"]
[]
[]
[]
[{"$nulls":9},"G","is the Golden Number–1."]
[{"$nulls":9},"H","is 23–Epact (modulo 30)."]
[{"$nulls":9},"I","is the number of days from 21 March to the Paschal full moon."]
[{"$nulls":9},"J","is the weekday for the Paschal full moon (0=Sunday, 1=Monday, etc.)."]
[{"$nulls":9},"L","is the number of days from 21 March to the Sunday on or before the Paschal full moon (a number between -6 and 28)."]

{"sheet":"Πληροφορίες","index":2,"n_rows":30,"n_cols":7,"rows_kept":30}
[null,"Οδηγίες:"]
[null,"Συμπληρώστε τα κίτρινα κελιά",{"$nulls":3},"Δεδομένα"]
[]
[null,"Βρείτε τα αποτελέσματα στα γαλάζια κελιά",{"$nulls":3},"Αποτελ."]
[]
[]
[null,"Πληροφορίες:"]
[]
[null,"Το Πάσχα είναι κινητή γιορτή και γιορτάζεται την πρώτη Κυριακή που ακολουθεί την πρώτη πανσέληνο μετά"]
[null,"ή κατά την εαρινή ισημερία. Για τον καθορισμό του Ορθόδοξου Πάσχα η εαρινή ισημερία υπολογίζεται με"]
[null,"βάση το παλαιό ημερολόγιο (Ιουλιανό)."]
[]
[null,"Τρόπος υπολογισμού:"]
[]
[null,"Έστω Ε το εξεταζόμενο έτος."]
[null,"Έστω ότι το υπόλοιπο της διαίρεσης του y με το x συμβολίζεται με [y]x"]
[null,"Έστω:"]
[null,"α=[Ε]19","β=[Ε]4","γ=[Ε]7","δ=[19α+16]30",null,"ε=[2β+4γ+6δ]7  "]
[]
[null,"Τότε το κλειδί των υπολογισμών δίνεται από τη σχέση:"]
[null,"Κλειδί = 3+δ+ε"]
[]
[null,"Αν το κλειδί έχει τιμή μικρότερη ή ίση με 30, τότε η ημερομηνία του Πάσχα είναι η αντίστοιχη μέρα του"]
[null,"Απριλίου του εξεταζόμενου έτους. Αν το κλειδί έχει τιμή μεγαλύτερη από 30, τότε η ημερομηνία του Πάσχα"]
[null,"είναι η μέρα που αντιστοιχεί στην τιμή (Κλειδί-30) του Μαΐου του εξεταζόμενου έτους."]
[]
[null,"Ο υπολογισμός μπορεί να γίνει για τα έτη από 1583 έως 4099."]
[]
[null,"Προκύπτει ότι οι ημερομηνίες του ορθόδοξου Πάσχα κυμαίνονται γενικά από τις 4 Απριλίου ως τις 8 Μαΐου."]
[null,"Όλες οι ημερομηνίες στα αποτελέσματα δίνονται στο Γρηγοριανό (σύγχρονο) ημερολόγιο."]