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Last updated 12/25/05

 

 

See images and analysis of ancient mathematical objects: IMAGE GRID

HALENSIS: (Greek) papyri

See DIKAIOMATA; [O_026] and see SAMMLUNG

 

HALLE: (Greek) papyri at University of

(as per E. G. Turner) AKA P. HALLE.

P. Hal. = Dikaiomata: Auszuge aus Alexandrinischen Gesetzen und Verordnungen in einem Papyrus des philologischen Seminars der Universitat Halle mit einem Anhang weiterer Papyri derselben Sammlung, ed. By the Graeca Halensis Berlin, 1913.

 

P.Hal. 1.: (Greek; after 256 bce; from Apollonopolite Magna?)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0127

 

See DIKAIOMATA; [O_026] and see SAMMLUNG; HALENSIS

 

HAMA: publication

 

See KESKINTO; see alt interpretation of the Keskinto inscription

VERY different; still no source image.

[B_535,SIBL,8.5,IMG,NO KESKINTO IMG]

History of Ancient Mathematical Astronomy

By O. Neugebauer

3 volumes; 1975 reprint; springer-verlag

CATNYP# JSE 76-844 (3 volumes) “HAMA”

Copies from v. 1:

698-705: See KESKINTO!

“In 1893 a Greek from Lindos on the Island of Rhodes accidentally discovered in nearby Keskinto [ancient Lartos; ~7 [or 8!] Km west of Lindos; the text does not come from a systematic excavation] a fragmentary astronomical inscription of which he made a squeeze that was sent to Athens and then to Hiller v. Gaertringen in Berlin.  The stone itself was later transported to the museum in Berlin.”

Source images referred to: [fragment roughly 76 x 28 centimeters]

1. Herz [1894], p. 1144 (upside down) [in SBAW or similar]

2. Tannery, Mem. Sci. 15, p. 119

3. Prof. Derek Price [AKA Derek John de Solla Price [1922-1983] of Yale University] obtained a new squeeze after World War II [Item was not destroyed by an act of war].

4. Preliminary notice [indirectly by Hiller von Gaertringen]: Archaeologischer Anzeiger 1894, No. 3, p. 125 =KESKINTO; [B_540]

[See HAMA]

“the last line of the text (preceeding the dedication) contains the statement

…] the circle (contains) 360 degrees (moipwv) 720 “points”

(stigmwv) of the circle [a drawn circle]. One degree contains [2] points.”

My note to readers: see how this differs from the IG analysis!

[9720 points and 27 sub-points!]

Neugebauer [Henceforth O.N.] states the planets are ordered thusly:

[Venus]-Mercury-Mars-Jupiter-Saturn; i.e. the same order found with Archimedes.

[O.N.] For each one of the outer planets are listed four sets of integers, called, respectively,

*kata mnkos lwdiakoi [zodiacal longitutes=L]

*kata platos tropikoi [latitudinal variations=B]

*kata bados peridpomai [rotations in depth=G]

*kata oxnma diesodoi [returns in phase=A]

*Note my approximation of the Greek is only for recognition purposes and is NOT phonetically viable. I wish to avoid inserting a Greek font into this website. Persons requiring scans may contact me: brucefriedmandcg@aol.com

p. 700:

Mars

n                      l0 n

L          [1]74[9]2                       174920

B          [17]436                         174360

G          [ ]                                 491680

A          [ ]                                 136480

 

Jupiter

n                      l0 n

L          [2157]                           21570

B          [215]6                           21560

G          24260                           242600

A          26690                           26[6900]

Saturn

n                      l0 n

L          [ ]                                 [ ]

B          [ ]                                 9810

G          [2]7176                         [27]1760

A          [2]8148                         2[8]1480

 

[O.N.] 1. In any planetary theory the revolutions of the planet in longitude (L) and the number of corresponding phases (A) should satisfy the following identity

number of sidereal rotations + number of synodic periods =

number of sidereal years

Consequently we should expect L + A = N0

With probably the same value N0 for all planets. This assumption is easily tested. We know, e.g., from the Babylonian “Goal-year texts” how many synodic periods S correspond to N years:

Mars: N=79   Jupiter: N=71  Saturn: N=59

          S=37                S=65               S=57

Hence we should expect that in our text

A*(N/S)~=N0

This is indeed nearly the case

Pages 715-725 discuss the “Anaphorikos” [”On Rising Times] by Hypsicles!

Note HAMA references to Hibeh parapegmata and Hypsicles; “Anaphorikos”

O.N. v. 3 includes these plates:

1. Marc. Gr. 325, fol 105v

2. [p. 1448] Cuneiform astronomy sketch

2. [p. 1449] Cuneiform astronomy sketch

3. [p. 1450] Cuneiform astronomy sketch

4. Cuneiform astronomy fragments; ACT 122

5. Cuneiform astronomy fragments

6. Cuneiform astronomy fragments; BM 34629+

7. Greek papyrus zodiac

8. [p. 1454] Vat. Gr. 204, fol 61 verso

8. [p. 1455] Vat. Gr. 204, fol 62 recto

9. Vat. Gr. 211, fol 116 recto

Volume three includes this reference to the source image text.

See squeeze source: Herz, Norbert

See [B_537]; KESKINTO

 

HAMBURGER: (Greek) papyri at University of

See also IBSCHER.

 

(as per E. G. Turner) P. Hamb. = Greichische Papyrusurkunden der Hamburger Staats- und Universitatsbibliothek, i, (in 2 parts), ed. P. M. Meyer, Liepzig-Berlin, 1911-24.

 

A new series begins with Greichische Papyrusurkunden der Hamburger Staats- und Universitatsbibliothek, mit einingen Stucken aus der Sammlung Hugo Ibscher, ed. B. Snell et al. Hamburg, 1954.

 

P.Hamb. 1.1. Unselbständige Girobankbescheinigung aus Alexandria:

(Greek; AD 59)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0128

 

 

HAMMURABI: (OK; Babylonian) historical ruler, Law code of

Follow these links to a tr. of the Code of Hammurabi=Hammurapi.

http://www.yale.edu/lawweb/avalon/hammenu.htm

 

http://www.fordham.edu/halsall/ancient/hamcode.html

 

(as per Y. Muffs) See [W_012], ELEPHANTINE.

See G. Dossin, “L’article 142/143 du code de Hammurabi, “ RA, 42 (1948), pp. 113-24.

 

See Sennacherib, [B_290].

 

See the archive of MARI.

 

See LAW.

 

http://www.varchive.org/ce/hammurabi.html

 

See METROLOGY.

In the code of Hammurabi the salary for a farm laborer is set at 6 “she” [SHEH] of silver per day.

 

 

HAPI-ANKH: (AE)papyrus of

See hieroglyphic Berlin P. 13603

 

 

HAPSHETSUT: (MK; AE) Female Pharaoh ~1500 BCE. A tireless Educator.

[W_051,rvw] WATSON# 532K15 L52. "L'aile nord do pylone d'Amenophis III a Karnak / par MM. Georges Legrain et Edouard Naville" Paris, 1902.

 

See SENENMUT.

 

(as per EEF; Egypt Online)

Hatshepsut's renovated temple reopens October , 2001.

http://www.uk.sis.gov.eg/online/html4/o030921g.htm

 

 

HARAGEH: (MK; AE; literary) papyrus

http://www.casa.ucl.ac.uk/digital_egypt/literature/sanehat/sources.html

Middle Kingdom: Papyrus Harageh 1 (UC 32773). At Petrie Museum.

 

(as per LEX) See P. Harageh 3 in JEA 27, 1941, see Smither?

 

See also SINUHE; SANEHAT; Wadi Khargeh?

"A tax assessors journal of Middle Kingdom" in JEA 27, 74sq.

 

 

HAREM: (AE) the conspiracy

Study the Ramses III Harem Conspiracy.

Those caught were forced to commit suicide.

 

This may be related to Sethnakhte.

 

 

HARHOTPE: AE papyri

Viewed at the MET, 4/24/02.

A ration list.

Found at THEBES.

11th-12th Dynasty; ~2009-1900 BCE.

Hieratic math content.

See also HEKANAKHTE; MEKUTRA; WATSON.

 

 

HARKNESS: (demotic) papyrus

See CHICAGO.

Magical?

 

[B_079,rvw]

CATNYP# *OAC (Studies in ancient oriental civilization, no. 39),

"Studies in honor of George R. Hughes : January 12, 1977. Chicago 1976.

 

WATSONLINE Yields nothing.

 

 

HARRASSOWITZ VERLAG WEISBADEN: publisher of near east studies

[B_332; 2002 catalog on file with]

 

 

HARRIS: (Author; Collector; AE; Greek); papyri

James Rendel Harris 1852-1941.

(funerary; magical; *135 feet long; a Harper’s song).

 

[B_050,IGNR,HPB] CATNYP# OBR (Blok, H. P. Beide volksverhalen van Papyrus Harris 500 verso), "De beide volksverhalen van Papyrus Harris 500 verso / door Henri Peter Blok", Leiden 1925.

As per the above text:

Seek (Author) Theophore Personennamen Hoffman?

Seek also:

P. Bremner 22

P. Insinger

Codex Hammurabi

Patrick. Boylan (Author)

P. Golenischeff (G:3)=

No copies made.

(as per EEF; S. ElSabaie; 011004)
Text above has details on "The Taking of Joppa" and "The Doomed Prince"

 

(as per LEX) P. Harris I=P. Hier, Work by Budge, 2, Series.

 

(as per Y. Koenig) refers to Harris magical Papyrus (501) and lists:

"Der Magische P. Harris", 49, 4 (m); 44, 9; Moeller, pa1.II, p. 34 note 4?

 

(as per Y. Koenig) see Bibliotheca Aegyptiaca V, 3, 3.

 

(as per EEF) Relates to ELEPHANTINE Stele and mentions family of Sethnakhte.

 

(as per EEF) KV14 was begun by Tawosret and completed by Setnakht.

 

See SETHNAKHT.

 

(as per T.E. Peet,[B_041b], ABBOTT)

The Harris P. was commisioned by Ramses IV to record his father's benefactions to the Priesthood of Amun. Father = Ramses III.

Harris P. 500=BM 10060 contains:

The Capture of Joppa

The Foredoomed Prince

Love Songs.

 

Harris P. 501=B.M. 10042= Magical.

H.P. 499=B.M. 10052=(as per LEX)=P. Harris C.

Harris A.=B.M. 10053

Harris= B.M. 10054, the distribution of grain. Math.

 

(as per AEB 84.1130) Bibe, Celia, Numerologia Egipcia I, Aegyptus Antiqua, Buenos Aires 5 (1984), 5-12.

Specifies alternate to glyph for 1 million. Math.

See also:

(AEB 87.1008) Bibe, Celia, Nouveaux recherches sur la mathematique pharaonique, partie II..., GM 100 (1987), 19-22. See MATH prior to 1601.

 

(as per AEB) Bommas, Martin, Hie Heidelberger fragmente des Magischen P. Harris, Heidelberg, Universitatsverlag C. Winter, 1998.

 

(as per F. Chabas) P. Mag. Harris mentions the Monster, Makou,

the Son of Set.

 

(as per E. G. Turner) P. Harris = The Rendel Harris Papyri of Woodbrooke College, Birmingham, ed. J. E. Powell. Cambridge, 1936.

 

(as per S. Katary, [B_100]) P. Harris I mentions herds of cattle as gifts from Ramses III.

 

(as per L. Bailey; excerpted from Hornung) See P. Harris:

“If the one on the water (the crocodile) opens his mouth,

If he shakes with his two arms,

I shall cause the earth to go down into the primal water.

And the south will be the north

And the earth will turn around.”

 

P.Harr.: The Rendel Harris Papyri of Woodbrooke College, Birmingham

P.Harr. 1.57.: (Greek)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0129

 

 

[B_448=O_013,IMG,8.5]

CATNYP# *OBR + (Chabas, F. J. Papyrus Magique Harris)

BOBST# PJ1681 .H35 C4 Oversize

“Le Papyrus Magique Harris. Traduction analytique et commentee d’un manuscrit egyptien; comprenant le text hieratique publie pour la premiere fois, un tableau phonetique et un glossaire. Par F. Chabas (Vice-President de la Societe d’Histoire et d’Archeologie de Chalon-sur-Saone / Associe-Correspondant de la Societe imperiale des Antiquaires de France, etc.) Chalon-sur-Saone,1860.”

See BOBST Archive: O 1

Minor math content and SETHNAKHTE reference?

Volume includes plates.

 

(as per E. G. Turner) See (GREEK) [B_478=O_048,rvw]

[B_478=O_048,rvw]

CATNYP# *OBKQ (Selly Oak colleges, Birmingham, Eng. Woodbrooke college. Rendel Harris papyri of Woodbrooke college, Birmingham)

BOBST# PA3304 .W6

“The Rendel Harris Papyri of Woodbrooke College, Birmingham, edited with translation and notes by J. Enoch Powell, with a portrait and five plates.”

Cambridge, 1936.

Studies include Greek Papyri. See plates.

James Rendel Harris, [1852-1941].

 

[B_338,rvw,LB] CATNYP# Sc 913.32-H

John Richard Harris, editor.

“The legacy of Egypt; edited by J. R. Harris. Second edition.”

Oxford, Clarendon Press, 1971.

See “The Calendars and Chronology.”

See also [B_338b,rvw]

 

[B_338b,rvw] CATNYP# Sc 913.32-H

See “Mathematics and Astronomy.” By G. J. Toomer.

(as per D. Meeks) seek Smither's "A tax assessors journal of Middle Kingdom" in JEA 27, 74sq.

See also HARAGEH.

(as per T. Sagrillo; EEF; 011003)

The standard hieroglyphic transcription (no translation) remains:

Erichsen, W. 1933. _Papyrus Harris I: hieroglyphische Transkription_.

BiAeg 5. Brussel: Fondation égyptologique reine Élisabeth.

The most recent study and translation (with photos of the entire

papyrus) is:

Grandet, P. 1994. _La papyrus Harris I (BM 9999)_. 2 vols. BiEtud

109/1-2. Cairo: IFAO.

Grandet has also produced a 3rd volume of glossary for the papyrus:

1999. _La papyrus Harris I: Glossaire_. BiEtud 129. Cairo: IFAO.

From The Papyri, vol. 2, London, 1895, pp. 1-12
http://www.bookrags.com/ebooks/7413/3.html
http://nefertiti.iwebland.com/texts/the_taking_of_joppa.htm
-- English translation: William Kelly Simpson (ed.), The Literature of
Ancient Egypt, 3rd ed., New Haven and London, 2003, pp. 72-74
-- French translation: Gaston Maspero, Les contes populaires de
l'Egypte ancienne, 4th ed., Paris, [1911], pp. 115-122
http://visualiseur.bnf.fr/Visualiseur?Destination=Gallica&O=NUMM-36147

HATNOUB: (AE) Stele of

See work by G. Posener:

“Un Stele de Hatnoub.”

See JEA 54 (1968), 67-70.

 

 

HAUNIENSIS: (Greek) papyri

 

(as per Duke Univ.)

I, Literarische Texte und ptolemäische Urkunden, ed. T. Larsen. Copenhagen 1942. Nos. 1-12. [Rp. CG] Documentary texts reprinted as SB VI 9422-9245. Five additional texts were published in Cahiers de l'Institut du Moyen-Age Grec et Latin, Copenhagen 1971, by A. Bülow-Jacobsen and S. Ebbesen. [o.e. CIU] Reprinted as SB XIV 11355-11358 and 11714.

 

II, ed. A. Bülow-Jacobsen. Bonn 1981. (Pap.Texte Abh. XXIX). Nos. 13-44. [o.e. RH]

 

III, ed. T. Larsen and A. Bülow-Jacobsen. Bonn 1985. (Pap.Texte Abh. XXXVI). Nos. 45-69. [o.e. RH]

 

(as per ZPE, D. Fowler) Seek (Greek) P. Haun iii 49, 200 BCE.

Tables of squares, math content.

 

(as per E. G. Turner) P. Haun. = Papyri Graecae Hauniensis, fasc. i,

ed T. Larsen, Copenhagen, 1942.

 

[B_180b, 8.5, IMG, v. 2] CATNYP# *OBQ+ 73-2731 t. 82, “Hommages Serge Sauneron, Cairo, 1979. See volume two (of two).

Image of P. Haun. (inv. 318), 500 CE. Plate One.

 

http://adam.igl.ku.dk/~bulow/PHaun.html

 

P.Haun. 1.9. Letter concerning violent assault:

(Greek; ~240 bce?; Arsinoite?)

http://perseus.csad.ox.ac.uk/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.05.0130

 

 

HAUSWALDT: (demotic) papyrus

(as per CATNYP) Hauswaldt P. ~250 CE.

 

[B_153,rvw] CATNYP# *OBKQ 98-7647, “The Hauswaldt papyri: a third century B.C. family dossier from Edfu / transcription, translation and commentary by Joseph Gilbert Manning.” Sommerhausen : G. Zauzich, 1997.

 

[B_154,rvw] CATNYP# *OBS+++ (Spiegelberg, Wilhelm. Demotischen papyri Hauswaldt), “Die Demotischen papyri Hauswaldt, vertrage der ersten halfte der Ptolemaerzeit (Ptolemaios II-IV) aus Apollinopolis (Edfu) hrsg. Und ubers. Von Wilhelm Spiegelberg, mit einem rechtsgeschichtlichen beitrag von Josef Partsch; dazu 26 lichtdrucktafeln in besonderem grossfolio-umschlag.”

Liepzig, 1913.

 

(as per D. Meeks) seek Dem. P. Hauswaldt. Seek Hauswaldt XVI re Edfu.

 

(as per Duke Univ.)

The Hauswaldt Papyri, ed. J. Manning. [B_153] Sommerhausen 1997. [o.e. Gisela Zauzich Verlag] Nos. 1-25. There are Greek dockets to nos. 2a and b, 8a and b, and 9a and b. This edition replaces a quasi-edition of the same texts, [B_154] Die Hauswaldt-Papyri, ed. W. Spiegelberg with a "Rechtsgeschichtliche Beiträge" by J. Partsch. Leipzig 1913 with a separate elephant-folio volume of plates. While the Spiegelberg edition does not transcribe or translate many of the texts, the plate volume is essential. Manning only provides plates of nos. 10, 16, and 17 and nos. 4 and 6 are no longer extant. The numeration of the texts is the same in both volumes.

 

 

HAWARA: (Greek) papyri

(as per E. G. Turner) Seek “Hawara, Biahmu and Arsinoe, p. 24-36,

by W. M. Flinders Petrie, London 1899.

See also: J.G. Milne, Archiv, v, 1913, p.378-397.

 

See P. Arsinoe

 

http://www.oi.uchicago.edu/OI/DEPT/PUB/CATALOG/OIP113.html

 

http://lhpc.arts.kuleuven.ac.be/purchases.html

See Lugduno-Batava; [B_447=O_012,NO IMG,8.5]

 

HAWASS: modern Egyptian

[2003] Secretary General of the Supreme Council of Antiquities, Zahi Hawass
Director of the Giza Pyramids Excavation

http://www.guardians.net/hawass/index.htm

 

 

HEARST: (AE; medicinal) papyrus

(as per AEMT) The tr. states AE used cloth strips, soaked in plaster, to produce casts for fractured bones.

See a 5th Dynasty mummy with such a cast (Smith & Dawson, 1924).

See also work by Wreszinski, Liepzig, 1912.

 

See also Ebers.

 

(as per LEX) Walter Wreszinski, Der Londoner Medizenische P. und der Pap. Hearst, Leipzig, 1912.

 

[B_155,rvw] CATNYP# QBM+(California. University. Publications.

Egyptian Archaeology. V. 1)

“The Hearst medical papyrus; hieratic text in 17 fascimile plates in collotype, with introduction and vocabulary, by George A. Reisner.” Leipzig, 1905.

 

 

HEBREW CALENDAR: obscure functions; Venus considerations?

See CALENDAR; ENUMA ANU ENLIL; GEZER

The names of the months in the Hebrew calendar are of Babylonian origin, the returnees from the Babylonian exile brought them to the Land of Israel. Only four of the original Hebrew names survived: the month of Aviv - Spring (Nissan), the month of Ziv (Iyar), the month of Bul (Marcheshvan) and the month of Eitanim (Tishrei). In the excavations at Gezer an ancient clay tablet was found on which names of months are engraved in ancient Hebrew script. These months have direct agricultural links: Assif-the harvest month, Zera-the month of planting, Lekesh-the month of Spring grain, Ktzir Pishtan - the flax harvest month, Ktzir Seorim- the barley harvest month, Ktzir Col- the month of general harvest, Zamir-pruning month and Kayitz-the month of Summer.

 

In Biblical times and in the time of the Second Temple it was customary to call the months by their numerical order - the First Month (Nissan), the Third Month (Sivan), the Seventh Month (Tishrei) and so forth.

http://www.biu.ac.il/ICJI/Competition/chapter7/703.htm

 

See these citations!

the Hebrew months have been designated in the course of Jewish history by two sets of names. Of the former set--going back probably to Chanaanite times--only four names have survived in the Hebrew Bible. These are: 'Abhîbh (A.V. Ex. 13:4, 23:15; Deut. 16:1), subsequently the first month; Zíw (III K. 6:1), subsequently the second month; 'Ethanîm (III K. 8:2), subsequently the seventh month; and Bûl (III K. 6:38), subsequently the eighth month. The latter set of names, certainly of Babylonian origin, began to be used after the Exile. Of its twelve names now found in the Jewish calendar only seven occur in the Hebrew text, but the whole twelve appear as the main divisions of the Megillath Ta'anith (Scroll of Fasting), which in its original form is referred to a date before the Christian Era. These twelve names are as follows:

Nîsan (Nehem. 2:1; Esth. 3:7)

'Iyyar (not named in Scripture)

Sîwan (Esth. 8:9; Baruch 1:8)

Támmûz (Cf. A.V. Ezek. 8:14)

'Abh (not named in Scripture)

'Elûl (Nehem. 6:15; I Mach. 14:27)

Tíshrî (not named in Scripture)

Márhéshwan, or simply Héshwan (not named in Scripture)

Kíslew (Zach. 7:1; Nehem. 1:1)

Tebeth (Esth. 2:16)

Shebhat (Zach. 1:7, I Mach. 16:14)

'Adar (I Esdras 6:15; Esth. 3:7, 8:12, etc.)

http://www.newadvent.org/cathen/03166a.htm

 

Israel adopted all twelve months of the Babylonian calendar as their civil calendar, but not all of the twelve months are listed in the Bible. The seven that occur are: Nisan, the first month; Sivan, the third month; Elul, the sixth month; Kislev, the ninth month; Tevet, the tenth month; Shevat, the eleventh month; and Adar, the twelfth month.

http://biblicalholidays.com/Excerpts/hebrew_calendar.htm

 

Holidays that occur in the month of Adar (such as Purim) are celebrated in Adar 2 in a leap year. The same rule is applied to birthdays, anniversaries and other personal events.

http://www.rtlsoft.com/hebrew/calendar/about.html

 

Years are counted since the creation of the world, which is assumed to have taken place in 3761 BC[E]. In that year, AM 1 started (AM = Anno Mundi = year of the world).

In the year AD 2001 we have witnessed the start of Hebrew year AM 5762.

 

http://www.tondering.dk/claus/cal/node4.html

Note these references from the preface:

1. See Canonical Celestial Omens by Francesca Rothberg in JAOS 108 (1987), pages 51-62. [See also ABCD]

2. See Otto Neugebauer in JAOS 63 (1943), p. 116-126.

RLIN notes from NYPL ANNEX request made on 5/14/02 on file in index.

See UHN: p. 217: According to Hebrew calendar analysis, the act of Creation began: Monday, 7 October 3761 BCE.

See GEZER.

 

HEBREW CUBITS: pursuing the obvious

See CUBITS; METROLOGY; TALMUD; TORAH.

Study these Old Testament and New Testament portions until they are familiar!:

1. Genesis 6:15

2. Genesis 6:16

3. Genesis 7:20

4. Exodus 25:10

5. Exodus 25:17

6. Exodus 25:23

7. Exodus 26:2

8. Exodus 26:8

9. Exodus 26:13

10. Exodus 26:16

11. Exodus 27:1

12. Exodus 27:9

13. Exodus 27:11

14. Exodus 27:12

15. Exodus 27:13

16. Exodus 27:14

17. Exodus 27:15

18. Exodus 27:16

19. Exodus 27:18

20. Exodus 30:2

21. Exodus 36:9

22. Exodus 36:15

23. Exodus 36:21