The Hibeh Papyri, data analysis of n/45 derivatives.     

Presented by Bruce C. Friedman

Last edited: June 8, 2002

 

The plates and translation of the Hibeh papyrus known as Hibeh, I.27 from, "The Hibeh Papyri. Edited with translations and notes by Bernard P. Grenfell and Arthur S. Hunt". London, 1906 are expanded upon and analyzed below.  Page and line numbers from this source text translation are referenced on the right and the math content is shown on the left.

 

Additional Bibliography:

TGP = “Greek Papyri; an introduction [by] E.G. Turner”, Princeton, 1968.

 

FMPA = “The Mathematics of Plato’s Academy: a new reconstruction / D.H. Fowler.” Oxford University Press, 1987 and 1999.

 

Abbreviations used:

[E/D]: eta delta [meaning= HOURS of]

ABPT24hr: [meaning=Above pair of both daily portions totals 24 hours]

NT= Night

DY= Day

 

 

I. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

As per FMPA: 3 other missing or unmentioned months = Thoth; Phaophi; Hathyr; then CHOIAK.

[CHOIAK 1]

146,55a            Iota(10) Gamma(3) iota(10) beta(2) mu(40) epsilon(5) [E/D]

                                                                        mu epsilon=45                        NT 13+ 4/45

146,55b            Iota (10) beta(2) epsilon(5) lambda(30) qoppa(90) [E/D]

                                                                                                            DY 10+41/45

ABPT24hr

 

[CHOIAK 16], Arcturus Rises

146,56                        Iota(10) Sigma(6)                        wpwv=night                        16th

146,57a            Iota(10) Beta(2) beta(2) iota(10) epsilon(5) mu(40) epsilon(5) [E/D]

                                                                        hmepa=day                        NT 12+34/45

146,57b            Iota(10) Alpha(1) theta(9) iota(10) lambda(30)                        DY 11+ 11/45

ABPT24hr

 

[CHOIAK 26], Corona rises

146,58                        Kappa(20) Sigma(6)                        “5” = six!                        26th

146,60a            Iota(10) Beta(2) <(?) lambda(30) [E/D]                                   

                                                                        “5”=Stigma                        NT 12+ 8/15

146,60b            Iota(10) Alpha(1) gamma(3) iota(10) lambda(30)            DY 11+ 7/15

ABPT24hr                                                            Osipis=OSIRIS

 

[TUBI 5]

146,62a            Epsilon(5)                                    TvBi=Tubi                        5th

 

 

 

II. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

[TUBI 20] AN EQUINOX (spring), Feast of Phitorois

146,62b            Kappa(20)                                                                        20th

146,63a            Iota(10) Beta(2)                                                            NT 12 (hrs)

146,63b            Iota(10) Beta(2)                                                            DY 12 (hrs)

ABPT24hr

 

[TUBI 27], Pleides set in the evening

146,64                        Kappa(20) Zeta(7)                                                            27th

146,65                        Iota(10) Alpha(1) beta(2) 5(6) qoppa(90)                        NT 11+ 38/45

146,66                        Iota(10) Beta(2) iota(10) lambda(30) mu(40) epsilon(5)            DY 12 + 7/45

ABPT24hr

 

[MECHEIR 6] Sun enters Taurus, Hyades sets in the evening

146,66’                        5(6)                                                MeXeip=Mecheir            6th

146,68                        Iota(10) Alpha(1) <(?) iota(10) lambda(30) epsilon(5)           

                                                                        Tavpwi=Taurus                        NT 11 + 29/45

146,69                        Iota(10) Beta(2) gamma(3) mu(40) epsilon(5)           

                                                                        Tades=Hyades                        DY 12 + 16/45

ABPT24hr                                                            akpwvuXos=rises

 

[MECHEIR 19], Lyra rises in the evening, Assembly at Sais

146,73’                        Iota(10) Theta(9)                        ^vpa=Lyra                        19th or 16th?

146,75a            Iota(10) Alpha(1) gamma(3) iota(10) epsilon(5).__mu(40) epsilon(5) [E/D]

                                                                                                            NT 11 + 19/45

146,75b            Iota(10) Beta(2) <(?) iota(10) epsilon(5) omicron(?70)           

                                                                                                            DY 12 + 26/45

ABPT24hr

 

[MECHEIR 20+_?] Orion sets or rises?

146,79                        Kappa(20)+? [MISSING]                                                20+

146,80                        Iota(10) Alpha(1) +? [MISSING]                                                NT 11+

146,81                        Iota(10) Beta(2) Beta(2) [MISSING]                                    DY 12 + 2¼.

ABPT24hr-probably

 

[MECHEIR 27], Lyra sets in the evening, Feast of Prometheus

147,83                        Kappa(20) Zeta(7)                                                            27th

147,84a            Iota(10) Alpha(1) 5(6) qoppa(90)                                    NT 11+8/45

147,84b            Iota(10) Beta(2) Beta(2) iota(10) lambda(30) mu(40) epsilon(5)

                                                                                                            DY 12+ 37/45

ABPT24hr

 

[PHAMENOTH 4], Sun enters Gemini, Capella rises in the morning           

147,88                        Delta(4)                                                                        4th

147.89                        Iota(10) Alpha(1) epsilon(5) mu(40)                                    NT 11+1/45

147,90                        Iota(10) Beta(2) Beta(2)delta(4) kappa(20) qoppa(90)            DY 12+44/45

ABPT24hr

 

 

 

 

 

 

 

 

 

III. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

[PHAMENOTH 5], Scorpio begins to set in the morning                       

147,90                        Epsilon(5)                                                                        5th

147,91                        Iota(10) Gamma(3?)                                                            NT 11?

147,92                        Iota(10) Gamma(3)                                                            DY 13

ABPT24hr-?

 

[PHAMENOTH 9],Feast of Edu among the Egyptians

147,92                        Theta(9)                                                                        9th

 

[PHAMENOTH 12], Scorpio sets completely in the morning

147,93                        Iota(10) Beta(2)                                                            12th

147,94                        Iota(10) Beta(2) 5(6) qoppa(90)                                                NT 10+38/45

147,95                        Iota(10)Gamma(3) iota(10) lambda(30) {lambda} {{30}) mu(40) epsilon(5)                       

                                                                                                            DY 13+ 7/45

ABPT24hr

 

[PHAMENOTH 13], Pleiades rise in the morning

147,95                        Iota(10) Gamma (3)                                                            13th

 

[PARMOUTHI 3] Sun enters Cancer, Aquila rises in the morning

147,107            Gamma(3)                                                                        3rd

147,109a            Iota(10) gamma(3) lambda(30) qoppa(90) [E/D]                        NT 10+ 17/45

147,109b            Iota(10) Gamma(3)<(?) qoppa(90) mu(40) epsilon(5)            DY 13+ 28/45

ABPT24hr

 

[PARMOUTHI 11] Delphinus rises in the evening

148,110            Iota(10)Alpha(1)                                                            11th

148,111a            Iota(10)epsilon(5) [E/D]                                                            NT 10+ 1/5

148,111b            Iota(10)Gamma(3) beta(2) iota(10) {alpha}(1) lambda(30)

                                                                                                            DY 13+ 4/5

ABPT24hr

 

[PARMOUTHI 17] Orion rises in the morning

148,113            Iota(10)Zeta(7)                                                                        17th

148,114a            Iota(10) iota(10) epsilon(5) [E/D]                                                NT 10+ 1/15

148,114b            Iota(10) Gamma(3) beta(2) delta(4) xi(60)                        DY 13+ 14/15

ABPT24hr

 

[PARMOUTHI 20] The Sun rises in the same place for 3 days.

148,115            Kappa(20)                                                                        20th

148,115a            Iota(10)                                                                                    NT 10

148,115b            Iota(10) Delta(4)                                                            DY 14

ABPT24hr

148,117            Gamma(3) (nuepas)                                                            3 Days

 

 

 

 

 

 

 

 

 

 

 

IV. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

[PARMOUTHI 21]

148,117            Kappa(20) Alpha(1)                                                            21st

148,117b            Iota(10)                                                                                    NT 10

148,118            Iota(10)Delta(4)                                                            DY 14

ABPT24hr

 

[PARMOUTHI 22]

148,118            Kappa(20) Beta(2)                                                            22nd

148,118b            Iota(10)                                                                                    NT 10

148,119’            Iota(10)Delta(4)                                                            DY 14

ABPT24hr

 

[PARMOUTHI 23]

148,119            Kappa(20) Gamma(3)                                                            23rd

148,119b            Iota(10)                                                                                    NT 10

148,120            Iota(10)Delta(4)                                                            DY 14

ABPT24hr

 

[PARMOUTHI 24] Summer Solstice, the night gains upon the day by 1/45 of an hour

148,120b            Kappa(20)Delta(4)                                                            24th

148,122            mu(40) epsilon(5)                                                            1/45

148,123            Iota(10) epsilon(5) mu(40)                                                NT 10+ 1/45

148,124            Iota(10)Gamma(3) beta(2) delta(4) kappa(20) qoppa(90)           

                                                                                                            DY 13+ 44/45

ABPT24hr

 

[PARMOUTHI 25],Etesian winds begin to blow, river begins to rise

148,124            Kappa(20) Epsilon(5)                                                            25th

148,127            Iota(10) lambda(30) qoppa(90)                                                NT 10+ 2/45

148,128            Iota(10)Gamma(3)beta(2) delta(4) lambda(30) rho(100) pi(80)

                                                                                                            DY 13+ 43/45

ABPT24hr

 

[PACHON 6], Sun enters Leo, Vindemitor rises?

148,129            5(6)                                                                                    6th

148,131            Iota(10) delta(4) lambda(30) rho(100) pi(80)                        NT 10+ 13/45

148,132            Iota(10)Gamma(3) [Beta(2) lambda(30)] qoppa(90)            DY 13+ 32/45

ABPT24hr

 

[PACHON 9], Orion rises completely in the morning

148,132            Theta(9)                                                                        9th

148,134a            Iota(10) gamma(3) mu(40) [ epsilon](5)            [E/D]                        NT 10+ 16/45

148,134b            Iota(10)Gamma(3) <(?) iota(10) lambda(30) qoppa(90)            DY 13+ 29/45

ABPT24hr

 

 

 

 

 

 

 

 

 

 

 

 

V. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

[PACHON 18], Canis rises in the morning

148,135            Iota(10)Eta(8)                                    Kvwv=Canis                        18th

148,136            Iota(10) <(?) lambda(30) mu(40) epsilon(5)            [E/D]

                                                                                                            NT 10+ 5/9

149,137            Iota(10)Gamma(3) Gamma(3)delta(4)                                    DY 13+ 4/9

ABPT24hr

 

[PAUNI 4], Sun enters Virgo, Aquila sets in the morning

149,137            Delta(4)                                                                        4th

149,139            Iota(10) Beta(2) epsilon(5) lambda(30) qoppa(90) [E/D]

                                                                                                            NT 10+ 41/45

149,140            Iota(10)Gamma(3) iota(10)epsilon(5)mu(40)epsilon(5)            DY 13+ 4/45

ABPT24hr

 

[PAUNI 16], Corona sets in the morning, Feast of Bubastis                       

                                                                        Corona=Stepanos

149,141            Iota(10) 5(6)                                                                        16th

149,143            Iota(10)Alpha(1) 5(6) qoppa(90) [E/D]                                    NT 11+ 8/45

149,144            Iota(10)Beta(2)            beta(2) iota(10) lambda(30) mu(40)epsilon(5)

                                                                                                            DY 12+ 37/45

ABPT24hr

 

[PAUNI 20+_?], Delphinus sets in the morning

149,146            Kappa(20)+[missing]                                                            20+th

149,148            Iota(10)Alpha(1) gamma(3)[missing] [E/D]                        NT 11+?

149,149            Iota(10)Beta(2) ,(?) [missing]                                                DY 12+?

ABPT24hr-probably

 

[PAUNI 27], Feast of? Lyra sets in the morning

149,151            Kappa(20)Zeta(7)                                                            27th

149,152            Iota(10)Alpha(1) gamma(3) iota(10) mu(40) epsilon(5) epsilon(5)            [E/D]

                                                                                                            NT 11+ 19/45

149,153            Iota(10)Beta(2) <(?) iota(10) epsilon(5) qoppa(90)            DY 12+ 26/45

ABPT24hr

 

[PAUNI 30], Feast of _? There are indications?

149,155            Lambda(30)                                                                        30th

149,157            Iota(10) Alpha(1) gamma(3) iota(10) lambda(30) mu(40) epsilon(5)

                                                                                                            NT 11+ 22/45

149,158            Iota(10)Beta(2) <(?)qoppa(90)                                                DY 12+ 23/45

ABPT24hr

 

[EPEIPH ?], Sun enters the claws of Scorpio                                                Missing

 

 

 

 

 

 

 

 

 

 

 

 

 

VI. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

[EPEIPH 13],Arcturus rises in the morning, an assembly at Sais in honor of Athena,           

                                                                        13th is absent                        Missing

and they burn lamps throughout the country and the river gives indications of rising.

149,163            Iota(10)alpha(1)beta(2) [missing]                                    NT 11+ ?

149,164            Iota(10)Beta(2) [missing]                                                DY 12+ ?

ABPT24hr-probably

 

[EPEIPH 23], Autumnal EQUINOX, Feast of Anubis, river gives indications of rising                                                           

149,170            Kappa(20)Gamma(3)                                                            23rd

149,171            Iota(10)Beta(2)                                                                        NT 12

149,172             Iota(10)Beta(2)                                                                        DY 12

ABPT24hr

 

[EPEIPH 27], Capella rises in the evening

149,177            Kappa(20)Zeta(7)                                                            27th

149,179            Iota(10)Beta(2)            iota(10) epsilon(5) mu(40) epsilon(5)            NT 12+ 4/45

149,180            Iota(10)Alpha(1) Beta(2) epsilon(5) lambda(30) qoppa(90)

                                                                                                            DY 11+ 41/45

ABPT24hr

 

[MESORE 2], Sun enters Scorpio, Pleiades rise in the evening, Feast of Apollo

149,181            Beta(2)                                                                                    2nd

150,184            Iota(10)Beta(2)epsilon(5)                                                NT 12+ 1/5

150,185            Iota(10)Alpha(1) Beta(2)iota(10)lambda(30)                        DY 11+ 4/5

ABPT24hr

 

[MESORE 4],Corona rises in the morning

150,187            Delta(4)                                                                        4th

150,188            Iota(10)Beta(2)            epsilon(5) lambda(30) qoppa(90)            NT 12+ 11/45

150,189            Iota(10)Alpha(1) Beta(2) iota(10) epsilon(5) mu(40) epsilon(5)

                                                                                                            DY 11+ 34/45

ABPT24hr

 

[MESORE 9], Scorpio begins to set in the evening

150,190            Theta(9)                                                                        9th

149,192            Iota(10) Beta(2)gamma(3) mu(40) epsilon(5)                        NT 12+ 16/45

149,193            Iota(10)Alpha(1) <(?) iota(10) lambda(30) qoppa(90)            DY 11+ 29/45

ABPT24hr

 

[MESORE 14], Scorpio sets completely

149,194            Iota(10) Delta(4)                                                            14th

149,195            Iota(10)Beta(2) gamma(3) iota(10) lambda(30)                        NT 12+ 21/45

149,196            Iota(10)Alpha(1) <(?) lambda(30)                                    DY 11+ 24/45

ABPT24hr

 

 

 

 

 

 

 

 

 

 

 

VII. The Hibeh Papyri                                                CLUES                                    TEXT MATCH

[MESORE 17], Hyades rise in the evening

150,197            Iota(10)Zeta(7)                                                                        17th

150,199            Iota(10)Beta(2) <(?) lambda(30)                                                NT 12+ 24/45

The Day is omitted here

 

In the 5 intercalary days:

150,200            Epsilon(5) (nuepais)                                                            5 days

 

[4th intercalary day], Arcturus sets in the evening, the birthday festival of Isis

150,202            Delta(4)                                                                        4th (intercalary day)

150,203            Iota(10)Beta(2)            Beta(2) epsilon(5) lambda(30) qoppa(90)

                                                                                                            NT 12+ 41/45

150,204            Iota(10)Alpha(1) iota(10) epsilon(5) mu(40) epsilon(5)            DY 11+ 4/45

 

The balance of the original document is badly damaged:

[?Tubi 20th]

150,209            Kappa(20)                                                                        20th

150,211            Kappa(20)Gamma(3)                                                            23rd

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

PAGE EIGHT MY Notes:

 

            The above calendar includes the names of NINE months.

            None of the dates are the 30th or greater day of a month.

            Five intercalary days follow.

            I assume 12 equal months of 30 days and 5 feast days is the ANNUS VAGUS=365 days.

                        Names of months shown are bolded:

            1.      As per FMPA: Thoth

2.                   As per FMPA: Phaophi

3.                   As per FMPA: Hathyr

            4.      CHOIAK

            5.      TUBI

            6.      MECHEIR

            7.      PHAMENOTH

            8.      PARMOUTHI

            9.      PACHON

            10.      PAUNI

            11.      EPEIPH

            12.      MESORE

            13.      FIVE INTERCALARY DAYS.

            ANNUS VAGUS.

           

GIVEN THE ABOVE:

THE SPRING EQUINOX (TUBI 20), IS 183 DAYS FROM THE AUTUMNAL EQUINOX (EPEIPH 23).

ALSO,

THE SPRING EQUINOX (TUBI 20), IS 94 DAYS FROM THE SUMMER SOLSTICE (PARMOUTHI 24).

 

THE CALENDAR DESCRIBES A CHANGE IN THE LENGTH OF DAYLIGHT SET AT 1/45 AN HOUR PER DAY.

            WE ARE GIVEN A SPRING EQUINOX ON TUBI 20 WITH 12 HOURS LIGHT(DAY) AND 12 DARK(NIGHT).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[PAGE NINE] GIVEN the TUBI 20 EQUINOX, WE CAN ESTABLISH THE FOLLOWING BY FIXING ONE MONTH OF CHANGES AT 30/45 AN HOUR:

 

                                    CHOIAK

                                                So, CHOIAK 20 the night is 12 + 30/45 hours

                                                            See CHOIAK 16 CORRECT as 12 + 34/45

                                    TUBI

                                                Given TUBI 20 the night is 12 hours

                                                            Given

                                    MECHEIR

                                                So, MECHEIR 20 the night is 11 + 15/45 hours

                                                            See MECHEIR 19 INCORRECT as 11 + 19/45

                                                                        MECHEIR 19 night should equal 11 + 16/45

                                                                        A discrepancy of 3/45 or three days

                                                                        Grenfell notes this (19/45) is correct for the 16th

                                                                         I note that 16/45 would be correct for the 19th.

                                                                                    This also suggests a possible Scribal error.

                                    PHAMENOTH

                                                So, PHAMENOTH 20 the night is 10 + 30/45 hours

                                                            See PHAMENOTH 12 CORRECT as 10 + 38/45

                                    PARMOUTHI

                                                So, PARMOUTHI 20 the night is 10 hours

                                                            See PARMOUTHI 20 CORRECT as 10 hours

                                                                        The calendar notes that the “Sun rises in the same place for three days”

                                                                        No change in the length of the night is seen until PARMOUTHI 24

                                                                                    See PARMOUTHI 24 the night is 10 + 1/45 hours

                                   

                                    This explains the three day discrepancy of PACHON 18; PAUNI 16; EPEIPH 23; MESORE 17. 

                                    This also may explain the discrepancy/error of MECHEIR 19.

                                    PACHON

                                                So, PACHON 20 the night is 10 + 30/45 hours           

                                                            See PACHON 18 INCORRECT as 10 + 25/45 (5/9)

                                                                        PACHON 18 night should equal 10 + 28/45

                                                                                    A discrepancy of 3/45 or three days

                                    PAUNI

                                                So, PAUNI 20 the night is 11 + 15/45 hours

                                                            See PAUNI 16 INCORRECT as 11 + 8/45

                                                                         PAUNI 16 night should equal 11 + 11/45

                                                                                    A discrepancy of 3/45 or three days

                                   

 

 

 

[PAGE TEN]

                                    EPEIPH

                                                So, EPEIPH 20 the night is 12 hours           

                                                            See EPEIPH 23  INCORRECT as 12 hours

                                                                        EPEIPH 23  night should equal 12 + 3/45

                                                                                    A discrepancy of 3/45 or three days

                       

                                    MESORE

                                                So, MESORE 20 the night is 12 + 30/45 hours           

                                                            See MESORE 17 INCORRECT as 12 + 24/45

                                                                        MESORE 17  night should equal 12 + 27/45

                                                                                    A discrepancy of 3/45 or three days

                                   

                                   

FIVE INTERCALARY DAYS:

            The text shows the length of the night of the 4th intercalary day is 12 + 41/45 hours.

            This suggests the number of days between MESORE 17 and intercalary day 4 was 41-24=17 days.

                        This is correct if MESORE has 30 days.

 

I note the number of days between the Feast of (TUBI 20) Phitorois and (MECHEIR 27) Prometheus is 37 days.

I also note the number of days between the Feast of (PHAMENOTH 9) Edu and (PAUNI 16) Bubastis is 37 days.

No other obvious conclusions from the other feast dates.

 

The text references these astrological items:

            1.            arcturus

            2.            corona

            3.            pleiades

            4.            taurus

            5.            hyades

            6.            lyra

            7.            orion

            8.            gemini

            9.            capella

            10.            scorpio

            11.            cancer

            12.            aquila

            13.            delphinus

            14.            etesian winds?

            15.            leo

            16.            vindemitor

            17.            canis

            18.            virgo

 

 

 

 

 

 

 

[PAGE ELEVEN] FRACTIONS, Next problem is the different ways used to show the same fraction.

CHOIAK 1

The fractional part of the night is 4/45.

Shown as;

            iota beta mu epsilon

4/45 appears 3 other times as;

            iota epsilon mu epsilon

The fractional part of the day is 41/45.

Shown as;

            Beta epsilon lambda qoppa

41/45 appears 3 other times the same.

 

CHOIAK 16

The fractional part of the night is 34/45.

Shown as;

            Beta iota epsilon mu epsilon

34/45 appears 3 other times the same.

The fractional part of the day is 11/45.

Shown as;

            theta iota lambda

11/45 appears 1 other time as;

            epsilon lambda qoppa

 

CHOIAK 26

The fractional part of the night is 24/45 (8/15).

Shown as;

            <(unknown) lambda

24/45 appears 2 other times the same.

The fractional part of the day is 21/45 (7/15).

Shown as;

            Gamma iota lambda

21/45 appears 1 other time the same

 

TUBI 27

The fractional part of the night is 38/45.

Shown as;

            Beta stigma qoppa

38/45 appears 1 other time the same.

The fractional part of the day is 7/45

Shown as;

            Iota lambda mu epsilon

7/45 appears 1 other time the same.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[PAGE TWELVE] FRACTIONS           

MECHEIR 6

The fractional part of the night is 29/45.

Shown as;

            <(unknown) iota lambda epsilon

29/45 appears 2 other times as;

            <(unknown) iota lambda qoppa

The fractional part of the day is 16/45

Shown as;

            gamma mu epsilon

16/45 appears 2 other times the same.

 

MECHEIR 19

The fractional part of the night is 19/45.

Shown as;

            gamma iota epsilon mu epsilon

19/45 appears 1 other times as;

            gamma iota mu epsilon epsilon

The fractional part of the day is 26/45

Shown as;

            <(unknown) iota epsilon omicron

26/45 appears 1 other time as;

            <(unknown) iota epsilon qoppa

 

MECHEIR 27

The fractional part of the night is 8/45.

Shown as;

            Stigma qoppa

8/45 appears 1 other times the same.

The fractional part of the day is 37/45

Shown as;

            Beta iota lambda mu epsilon

37/45 appears 1 other time the same.

 

PHAMENOTH 4

The fractional part of the night is 1/45.

Shown as;

            Epsilon mu

1/45 appears 1 other time the same.

The fractional part of the day is 44/45

Shown as;

            Beta delta kappa qoppa

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[PAGE THIRTEEN]

PHAMENOTH 4 continued

44/45 appears 1 other time the same.

 

PARMOUTHI 3

The fractional part of the night is 17/45.

Shown as;

            Gamma lambda qoppa

17/45 appears 0 other times.

The fractional part of the day is 28/45

Shown as;

            <(unknown) qoppa mu epsilon

28/45 appears 0 other times.

 

PARMOUTHI 11

The fractional part of the night is 9/45 (1/5).

Shown as;

            epsilon

9/45 appears 1 other time the same.

The fractional part of the day is 36/45 (4/5).

Shown as;

            Beta iota lambda

36/45 appears 1 other time the same.

 

PARMOUTHI 17

The fractional part of the night is 3/45 (1/15).

Shown as;

            Iota epsilon

3/45 appears 0 other times.

The fractional part of the day is 42/45 (14/15).

Shown as;

            Beta delta xi

42/45 appears 0 other times.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[PAGE FOURTEEN], FRACTIONS

 

PARMOUTHI 25

The fractional part of the night is 2/45.

Shown as;

            Lambda qoppa

2/45 appears 0 other times.

The fractional part of the day is 43/45.

Shown as;

            Beta delta lambda rho pi

43/45 appears 0 other times.

 

PACHON 6

The fractional part of the night is 13/45.

Shown as;

            Delta lambda rho pi

13/45 appears 0 other times.

The fractional part of the day is 32/45.

Shown as;

            Beta lambda qoppa

32/45 appears 0 other times.

 

PACHON 18

The fractional part of the night is 25/45 (5/9).

Shown as;

            <(unknown) lambda mu epsilon

25/45 appears 0 other times.

The fractional part of the day is 20/45 (4/9).

Shown as;

            Gamma delta

20/45 appears 0 other times.

 

PAUNI 30

The fractional part of the night is 22/45.

Shown as;

            Gamma iota lambda mu epsilon

22/45 appears 0 other times.

The fractional part of the day is 23/45.

Shown as;

            <(unknown) qoppa

23/45 appears 0 other times.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FINALE fifteen

 

1/45 shown as: epsilon mu

2/45 shown as:  lambda qoppa

3/45 shown as: iota epsilon

4/45 shown as: iota beta mu epsilon OR iota epsilon mu epsilon

5/45 shown as: ABSENT

 

6/45 shown as: ABSENT

7/45 shown as: iota lambda mu epsilon

8/45 shown as: stigma qoppa

9/45 shown as: epsilon (as one fifth?)

10/45 shown as: ABSENT

 

 

11/45 shown as: theta iota lambda OR epsilon lambda qoppa

12/45 shown as: ABSENT

13/45 shown as: delta lambda rho pi

14/45 shown as: ABSENT

15/45 shown as: ABSENT

 

 

16/45 shown as: gamma mu epsilon

17/45 shown as: gamma lambda qoppa

18/45 shown as: ABSENT

19/45 shown as: gamma iota epsilon mu epsilon OR gamma iota mu epsilon epsilon

20/45 shown as: gamma delta

 

 

21/45 shown as: gamma iota lambda

22/45 shown as: gamma iota lambda mu epsilon

23/45 shown as: <(unknown) qoppa

24/45 shown as: <(unknown) lambda

25/45 shown as: <(unknown) lambda mu epsilon

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FINALE sixteen

 

26/45 shown as: <(unknown) iota epsilon omicron OR <(unknown) iota epsilon qoppa

27/45 shown as: ABSENT

28/45 shown as: <(unknown) qoppa mu epsilon

29/45 shown as: <(unknown) iota lambda epsilon OR <(unknown) iota lambda qoppa

30/45 shown as: ABSENT

 

31/45 shown as: ABSENT

32/45 shown as: beta lambda qoppa

33/45 shown as: ABSENT

34/45 shown as: beta iota epsilon mu epsilon

35/45 shown as: ABSENT

 

 

36/45 shown as: beta iota lambda

37/45 shown as: beta iota lambda mu epsilon

38/45 shown as: beta stigma qoppa

39/45 shown as: ABSENT

40/45 shown as: ABSENT

 

 

41/45 shown as: beta epsilon lambda qoppa

42/45 shown as: beta delta xi

43/45 shown as: beta delta lambda rho pi

44/45 shown as: beta delta kappa qoppa

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

HIBEH FINALE pg. SEVENTEEN

 

(Milesian accounts)

 

Whole hours or dates                        fractions

 

1=Alpha                                    In the calendar alpha’=not used

2=Beta                                                 In the calendar beta’=2/3

           

                                                In the calendar <(unknown)=1/2

 

3=Gamma                                    In the calendar gamma’=1/3

4=Delta                                                In the calendar delta’=1/4

5=Epsilon                                    In the calendar epsilon’=1/5

6=Stigma (not sigma)                        In the calendar stigma’=1/6

7=Zeta                                                In the calendar zeta’=not used

8=Eta                                                In the calendar eta’=not used

9=Theta                                    In the calendar theta’=1/9

10=Iota                                                In the calendar iota’=1/10

                                                also iota’ epsilon’=1/(10+5)=1/15

 

20=Kappa                                    In the calendar kappa’=1/20

30=Lambda                                    In the calendar lambda’=1/30

40=Mu                                                In the calendar mu’ epsilon’=1/45

50=Nu                                                In the calendar nu’=not used

60=Xi                                                In the calendar xi’=1/60

70=Omicron                                    In the calendar omicron’=1/70 is used incorrectly

80=Pi                                                In the calendar pi’ used as in

                                                            rho’ pi’=1/(100+80)=1/180

 

90=Qoppa (not Kappa)                        In the calendar qoppa’=1/90

100=Rho                                    In the calendar rho’ used as in

                                                            rho’ pi’=1/(100+80)=1/180

 

200=Sigma                                    not found in this calendar.

300=Tau                                    not found in this calendar.

400=Upsilon                                    not found in this calendar.

500=Phi                                    not found in this calendar.

600=Chi                                    not found in this calendar.

700=Psi                                    not found in this calendar.

800=Omega                                    not found in this calendar.

900=Sampi                                     not found in this calendar.