Two very challenging Late Babylonian procedure texts for constructing

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1 Mathieu Ossendrijver 12 february 2014 Two very challenging Late Babylonian procedure texts for constructing a gnomon Basic phenomenology of the gnomon equinoxes (months I, VII) N noon morning afternoon sunset W E sunrise S summer solstice (month IV) N sunset sunrise noon W morning afternoon E S winter solstice (month X) morning N afternoon noon W E S sunset sunrise 1

2 Text 1 (BM X) Copy of BM 34067: Late Babylonian Astronomical Texts 1495 (1955) Obverse 0 [... At the command of Bēl and Bēlt] ia may it remain intact/succeed 1 [...] the 4 [...] fixed on top of the position. In order for you to [...]: the top, left and right of the stone you brick up(?), on its top side 2 [...] its [...] are established/strengthened (?). The drawings which rise together, the rising(?) to the interior you draw together as? a maqtû. You take the measurement of the drawing 3 [...] left and right of your 1 cubit shadow, and all over the room which you set up you make dots/holes. From/By means of the 4 [morning?] shadow [of] month IV an equivalent/front is present, that you draw [from?] the pole of Cancer until the morning shadow. From the house of the bariṣu 5 [you...]... and that is the head of the 1 cubit shadow... Until the small pole of Cancer you measure? ( take ) with the morning shadow and, in its fullness, from the top of 6 [...]..., that is the drawing of the equinox/ equilibrium,... you put (it?) down until the transversal of the shadow. You draw the holes/dots of the transversal drawing until that of the edge?: that is the rising (and?) appearance 7 of Cancer (IV). From/By means of the holes/dot(s) that are on top, completely, until the afternoon shadow of month IV you measure?, and the holes/dots from the base of the drawings on the left and the right 8 for your 1 cubit shadow you tattalqa (and) draw/implement. From/By means of... until the times: the rising (and?) appearance of your 1 cubit shadow you subtract(?) to 1 cubit, and 9 you draw (it). In its middle you draw the middle hole/dot of the top. From/By means of the morning shadow of Cancer until the handū hu you measure with the pole, and in its fullness 10 [...]... (for the) 1 cubit shadow with the middle drawing you draw dot(s). 2

3 From/By means of the handū hu until (that of) month IV you measure with the pole of month IV, and 11 [... ] the shadow to the base of the 1 cubit shadow you mark with dot(s), to a circle you surround it with dot(s). From/By means of the afternoon shadow of month IV until the handū hu of Capricorn (X) 12 [you measure?...]... that is Libra (VII), 1 cubit... 1 cubit shadow which at the drawing ring touches the months. Until the morning shadow 13 [the...] (pl.) you draw in a thin way. That distance between the poles which is/are above the morning shadow you measure, and 14 [...].. you cover with dots/holes. You draw the dots/holes of the transversal drawings. From the pole of Cancer (IV) until the minimum within(?) the 1 cubit shadow 15 [...] its... The dots/holes of the 1 cubit shadow you put down with the drawing that proceeds to the pole, on top of 1 cubit of shadow. You put down the mouth? of the bariṣu 16 [...] your... the minimum (and?) the top. You surround it with dots/holes to a circle. (On) top of the tablet 17 [...] you draw... dots/holes of the drawings until the middle of the stone. According(?) to the stone, (to?) which the house is attached, 18 [...]... appearance of the months of your 1 cubit shadow you put down. [You measure?] the frame with the morning shadow of Capricorn (X) 19 [...] [...] you draw the morning shadow of Capricorn, its image you put down, its drawings 20 [you...] [You measure?...] the pole of Capricorn with the morning shadow beyond the triangle/wedge [...] 21 [...] 1 cubit of your shadow tattalqa, the minimum (and) the summit 22 [...]... shape to 1 cubit, this (accus) 23 [...] of the months you measure [... sha]dow? you cover with dots [...] 25 [...] triangle/wedge you draw [...] 26 [...] its... (n lines missing) Reverse (about n lines missing) 1 [...]... 2 [...]... drawing [...]... you put down. 3 [...]... of the top of the wall you put down. 4 [... sha]. dow you draw, for month V 5 [...]... you divide into 12 parts, and 6 [...]... You take the measurement of the front stylus, and 7 [...] the stylus from the... stylus, the drawing which to the frame 8 [...]... that stylus... one fourth of the morning shadow you measure, and 9 [...]... the middle drawing until the morning shadow of... the top of the wall you put down 10 [...] this (accus.), the drawing of the bariṣu of the board, you draw it with the edge/rim of the 1 cubit shadow. 11 [...] the bases of the styli which are in the front and at the back, that is the house of the bariṣu. 3

4 12 [...] you divide into [12] parts, and the holes/dots of the drawings 13 [of...]... (you do) as before, ditto. The styli of the wall which is (at) the front and the back of the frame you attach to the wall. 14 The cross bar? of the wall: whatever the drawing of the equinoxes?/equilibria? exceeds 1/4 of the total(?) of the cross bar, the wall, 15 beyond the frame you draw in red. 16 In order for you to draw the times, the... and the equinoxes?/equilibria? which are at the front and at the back of the wall of Libra (?)..., in the middle of... Text 2 (BM 34719) Copy: Late Babylonian Astronomical Texts 1494 (1955) Obverse 1 In order for you to construct a crescent. The top, left and right [...] 2 from the middle/half, that is the drawing (of?) the transversal [...] 3 the head of the stylus from the teeth(?) of the drawing of the transversal [...] 4 whatever (reaches?) half of the drawing of the transversal you measure [...] 5 You draw [...] with the frame until the afternoon shadow, that of month X. 6 You draw [...] the (sun)rise of month IV, the pole of Cancer, with the frame. You measure [...] 7 until the pole of Cancer with the shadow of (sun)rise. [...] 8 the MAR?.DU you put down, and the holes/dots of the transversal drawings for the rising (and) appearances [of ZOD. SIGN you draw...] [...] 9 with the (sun)rise you measure,... in its fullness you... [...] 10 You draw the holes/dots of the transversal drawing for the risings and appearances of Capricorn [...] 11 You measure [...] month X with the pole, and in its fullness from the middle of the draw[ing?...] 4

5 12 The bariṣu of the room completely(?) un[til?...] 13 Left and right you make dots/holes on the stone. The holes/dots of the fixed? drawings [... ] 14 the drawing of the top side completely until the afternoon shadow [...] 15 left and right (for) 1 cubit of shadow at the backside you provide dots from... [...] 16 and at the front for 1 cubit of shadow... [...] 17 [...] ka? shadow of (sun)rise until the handu hu... [...] 18 [...] Cancer you put down and mark with (a) dot(s). From/By means of the hand[u hu...] 19 [...]... Capricorn its mouth from the dot of...[...] 20 [...]... du at the front 1 cubit... [...] (n lines missing) Reverse (about n lines missing) 1... a... [...] 2 In order for you to construct the times. You draw a room, 2 cubits the height and the base, the measurement... [...] 3 The holes/dots of the transversal drawing until the end of the side(?) of the first hour of Cancer and Capricorn [...] 4 of the room which (on ) top completely until the first hour with [...] 5 of your wall with the front drawing which from the front room... [...] [...] 6 with the second drawing of which everything is the same. For Capricorn the same; the bariṣu [...] 7 top side, rising of month IV drawings and times, the top of the wall [...] Elements of the construction stone holes/dots drawings; transversal drawings; middle drawing 1 cubit shadow room shadow: 1-cubit shadow morning shadow of Cancer (month IV) afternoon shadow of month IV morning shadow of Capricorn (month X) afternoon shadow of month X pole: pole of Cancer / month IV; pole of Capricorn (month X) (a small object; part of a lock? ): of month IV handu h hu handu h hu 5

6 bariṣu; house of the bariṣu ( sparkling?) tablet frame 12 parts stylus: front stylus board/plate wall cross bar Recurring expressions: you measure? ( take, lift ) Obv2 You take the measurement of the drawing 3 [...] left and right of your 1 cubit shadow, and... 5 Until the small pole of Cancer you measure? ( take ) with the morning shadow, and... 7 From/By means of the holes/dot(s) that are on top, completely, until the afternoon shadow of month IV you measure?, and... 9 From/By means of the morning shadow of Cancer until the handū hu you measure? with the pole, and From/By means of the until (that of?) month IV you measure with the pole of month IV, and... handū hu 11 From/By means of the afternoon shadow of month IV until the of Capricorn (X) handū hu 12 [you measure?...] 13 The distance between these poles which are at the top of the morning shadow you measure, and Rev6 [...]... You take the measurement of the front stylus, and BM 34719: Obv7 Until the pole of Cancer with the shadow of (sun)rise you measure [...] 11 You measure [...of ] month X with the pole, 17 [...]... shadow of (sun)rise until the... [...] handu hu Recurring expressions: rising (and?) appearance BM 34067: 6 That is the rising (and?) appearance 7 of Cancer (IV). 8 You subtract(?) the rising (and?) appearance of your 1-cubit shadow to 1 cubit. BM 34719: 10 You draw the holes/dots of the transversal drawing for the risings and appearances of Capricorn [...] 6

7 BM Generated February 11, BM (Instruction for gnomon like instrument) Obverse 0 [xxx ina a-mat d en u ga san]- ia 2 li s-lim 1 [xxxx] 4 ina ugu man-za-za kun-nu a- na? [x]-ka mu h- hi 15 u 2.30 sa 2 na 4 tu-lab-ba-ni-i ina ugu mu h- hi- su 2 2 [xxx] x - su 2 kun-nu-u 2 gi s. hur.me s sa 2 ana a- ha- me s kur- ha sar.a ana sa 3 a- ha-mi s 2 ma-aq-ta-a te-eṣ-ṣir me s- hat gi s. hur 3 [xx 1]5 u 2.30 sa 2 1 ku s 3 gissu-ka il 2 - ma? ta zag.til.la.bi. se 3 sa 2 ku-um-ma sa 2 gar-an bur 3 ta-tak-kip ta gissu 4 [xx] iti. su mi- hi-ir-ti gal 2 - si mu.a-ti 3 x tal-lu alla en gissu se-e-ri te-eṣ-ṣir ta e 2 ba-ri-ṣa 5 [xx] x -ma sa 2 su-u 2 sag sa 2 1 ku s 3 gissu x a-di tal-lu alla tur ki gissu se-e-ri il 2 -ma diri- su 2 ta mu h- hi 6 [x] x u 4 sa 2 su-u 2 gi s. hur lal 2 x a-di pa-rik-ti gissu gar-an bur 3 gi s. hur pa-rik-ti a-di sa 2 pa-a-ti te-eṣ-ṣir su-u 2 kur? igi 7 sa 2 alla ta ti-ik-pi sa 2 ugu zag.til.la.bi. se 3 en gissu? an.ne iti. su il 2 -ma bur 3 ta su hu s gi s. hur.me s sa 2 15 u sa 2 1 ku s 3 gissu-ka ta-tal-qa ta-tak-kip ta x a-di si-man.me s kur igi sa 2 1 ku s 3 gissu-ka a-na 1 ku s 3 tu-na- sar-ma 9 gi s. hur ina murub 4 - su 2 bur 3 murub 4 mu h- hi te-eṣ-ṣir ta gissu [ se]- e -ri alla a-di it-ti tal-lu il 2 -ma diri- su 2 10 [xx]-ti 1 ku s ha-an-du h 3 gissu ki gi s. hur murub 4 -ti ta- tak? -kip ta a-di iti. su ki tal-lu iti. su il 2 -ma 11 [xx] gissu ana su hu s 1 ku s ha-an-du h 3 gissu ta-tak-kip bur 3 ana kip-pat nigin-mi ta gissu an.ne iti. su en ma s 2 12 [xx] x su-u ha-an-du h 2 rin 2 1 ku s 3 x 1 ku s 3 gissu sa 2 a- sar gi s. hur ur 5 -tu 2 iti.me s tag.tag-ut en gissu se-e-ri 13 [xxx].me s qat 2 -nu te-eṣ-ṣir bi-rit tal-lu.me s ur 5 -tu 2 sa 2 ugu gissu se-e-ri il 2 -ma 14 [xxxx] xx tu? -tak-kap bur 3 gi s. hur.me s pa-ar 2 -ki-e-ti te-eṣ-ṣir ta tal-lu alla en sup-lu sa 3 1 ku s 3 gissu 15 [xxxx] x x- su 2 bur 3 1 ku s 3 gissu it-ti gi s. hur sa 2 ana dal du mu h- hi 1 ku s 3 gissu gar-an ka ba-ri-ṣa 16 [xxxx] x -ka sup -lu mu h- hi gar-an bur 3 a-na kip-pat nigin-mi ugu i-ge-er-tu 4 17 [xxxxx] x bur 3 gi s. hur.me s a- di sa 3 -ti na 4 te-eṣ-ṣir a s 2 - su 2 na? sa 4 2 e 2 pa-da-at 18 [xxxxxxx] x igi sa 2 iti.me s sa 2 1 ku s 3 gissu-ka gar-an sip-pi ki gissu se-e-ri ma s 2 19 [xxxxxxx] gissu se-e-ri ma s 2 te-eṣ-ṣir tam- sil- su 2 gar gi s. hur.me s- su 2 20 [xxxxxxxxx] x tal-lu ma s 2 ki gissu se-e-ri al-la sag.du 3 21 [xxxxxxxxxx] 1 ku s 3 gissu- ka ta-tal-qa sup-lu ṣip-ri 22 [xxxxxxxxxxxx] x mi-nu la? a-na 1 ku s 3 su-a-ti 3 23 [xxxxxxxxxxxx] sa 2 iti.me s il 2 xx 24 [xxxxxxxxxxxxx].gi 6 tu-tak-[kip x] 25 [xxxxxxxxxxxxxx] sag.du 3 te- eṣ -[ṣir x] 26 [xxxxxxxxxxxxxxxxx] x - su 2 (n lines missing) Reverse (about n lines missing) 1 [xxxxxxxxxxxxxxxxx] xx 2 [xxxxxxxxxxxxxx] x gi s. hur [x] x gar -an 3 [xxxxxxxxxxxx]-rit sa 2 ugu a- gur-ri? gar-an 4 [xxxxxxxxxxx]. gi 6 te-eṣ-ṣir sa 2 iti.ne 5 [xxxxxxxxx] xx 12 ta.am 3 tu-za-az-ma 6 [xxxxxxxx] x me s- hat qa-an-ṭup ha.la.me s igi-u 2 il 2 -ma 7 [xxxxx qa-an]- ṭup -pi ta du x qa-an-ṭup gi s. hur sa 2 ana sip-pi 8 [xx] xxx qa-an- ṭup -pi su-a-ti 3 a- x 4- u-u 2 gissu se-e-ri GI S-ma 9 [xx] gi s. hur murub 4 -ti u a- di hi? gissu se-e-ri sa 2 x mu h - hi a-gur-ru gar-an 10 [xxxx] mu.a-ti 3 gi s. hur ba- ri -ṣi sa 2 da-ap-pi ki sap -ti 1 ku s 3 gissu te-eṣ-ṣir 11 [xxxxxx] su hu s?.me s qa-an-ṭup-pi sa 2 ina igi u egir su-u 2 e 2 ba-ri-ṣi 12 [xxxxx]. ta.am 3 tu-za-az-ma bur 3 gi s. hur.me s 13 [x] x.me s gin ha.la.me s 7 igi-u 2 kimin qa-an-ṭup. pi me s a-gur-e sa 2 igi u egir ana sip-pi ki a-gur-ru tu-kan-na 14 bar?.nun sa 2 a-gur-e ma-la mim-ma sa 2 gi s. hur lal 2.me s al-la 4- u-u 2 zag.til.la.bi. se 3 ṣa-al-pi diri- su 2 a-gur-ru 15 al-la sip-pi ṣa-rap-an-u s gi s. hur- su 2 16 si? - man me s GI S?.me s lal 2.me s sa 2 ina igi u egir a-gur rin 2 nu igi.me s ana e-ṣi-ri-ka ina murub 4 nag gal? 2 ud?

8 BM Generated February 11, BM (Construction of gnomon-like instrument) Obverse 1 1 u 4.sakar ana du 3 -ka mu h- hi 15 u [xxxxx...] 2 ta mi- sil si-i gi s. hur pa-rik- ti? [xxxxx...] 3 sag qa-an-ṭup-pi ta ka.me s gi s. hur pa- rik -[ti xxxx...] 4 ma-la mi- sil gi s. hur pa-rik-tu 4 il 2 [xxxx...] 5 ki sip-pi en gissu an.ne su-u ab te-eṣ- ṣir? [xxx...] 6 sar itu. su tal-lu 4 alla it-ti sip-pi te- eṣ -[ṣir xxx...] 7 en tal-lu 4 alla it-ti gissu sar il 2 [xxx...] 8 mar?.du gar-ma bur 3 gi s. hur pa-rik-tu 2 ana kur- ha igi- x [xx...] 9 it-ti sar il 2 [x] diri- su 2 ta-i-x u 4 [xx...] 10 bur 3 gi s. hur pa-rik-tu 4 ana kur.me s igi.me s sa 2 ma s 2 te-eṣ- ṣir [xx...] 11 iti.ab ki tal-lu 4 il 2 -ma diri- su 2 ta murub 4 gi s.[xx...] 12 ba-ri-ṣa sa 2 ku-um-ma it-ti zag.til.la.bi. se 3 a-[di xx...] u 2.30 na 4 ta-tak-kip bur 3 gi s. hur.me s gi. na [xx...] 14 gi s. hur sa 2 ugu zag.til.la.bi. se 3 a-di gissu an.ne [xx...] u ku s 3 gissu ana egir ta- tak-kip ta x [xx...] 16 u a-na pa-an sa 2 1 ku s 3 gissu ta- x -da x [xxx...] 17 [x] ka? gissu sar a-di gin ha-[an]-du h? [xxx...] 7 18 [xx] alla gar-ma ta-tak-kip ta xxx...] 19 [xx] x ma s ha-an-d[u h 2 ka- su 2 ta ti-ik-pi sa 2 x [xxx...] 20 [xx] xx -ti du a-na pa-an 1 ku s 3 x [xxxx...] (n lines missing) Reverse (about n lines missing) 1 xxxx a xxxx [xxxxxxxxxxxx...] 2 2 si-man.me s ana du 3 -ka ku-um-ma 2 ku s 3 sag u s te-eṣ-ṣir mi- si h-ti qa- x [...] 3 bur 3 gi s. hur pa-rik-ti a-di til a 2 si-man igi-u 2 sa 2 alla u ma s 2 [x...] 4 sa 2 ku-um-ma sa 2 ugu zag.til.la.bi. se 3 en si-man igi-u 2 ki [xx...] 5 sa 2 a-gur-ri-ka ki gi s. hur igi? -ti sa 2 ta ku-um igi-u 2 x [xx...] 6 ki gi s. hur 2-tu 4 sa 2 pap- si-na kimin? sa 2 ma s 2 kimin ba-ri- ṣa? [xxx...] 7 ugu a- ṣu -u 2 sa 2 su gi s. hur.me s u si-man.me s ugu a-gur-[ri xx...]

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