Last updated 12/25/05
and analysis of ancient mathematical objects:
See images and analysis of ancient mathematical objects:
IANDANAE: (Greek) papyri with accounts, math
(as per E. G. Turner) See [O_027]
P. Iand. = Papyri Iandanae, cum discipulis edidit C. Kalbfleisch, Leipzig, 1912.
Pt i, Voluminum Codicumque Fragmenta Graeca cum Amuleto Christiano, ed. E. Schaefer, 1912.
Pt. ii, Epistulae Privatae Graecae, ed. L. Eisner, 1913.
Pt iii, Instrumenta, Graeca Publica et Privata, pt. i, ed. L. Spohr, 1913.
Pt iv, Instrumenta, Graeca Publica et Privata, pt. ii, ed. G. Speiss, 1914.
Pt v, Literarische Stucke und Verwandtes, ed. J. Sprey, 1931.
Pt. vi, Greichische Privatbriefe, ed. G. Rosenberger, 1934.
Pt vii, Greichische Verwaltungsurkunden, ed. D, Curschmann, 1934.
Pt. viii, Greichische Wirtschaftsrechnungen und Verwandtes. ed. J. Hummel, 1938.
P. Iand. Inv. 653 = A Sixth Century Account of Hay, ed. T. Reekmans, Brussels, 1962.
P.Iand. 2.8. Letter from Ischyriôn to Antôninos: (Greek; Arsinoite)
P.Iand.inv. 653: A Sixth Century Account of Hay: (Greek)
With dated accounts and inventory?
CATNYP# *IC (Papyri Iandanae)
BOBST# PA3308 .P3
“Papyri Iandanae, Cum discipulis edidit C. Kalbfleisch. Fasc. 1.”
Lipsiae [Leipzig], 1912.
[O_027]=Pt I=Voluminum Codicumque Fragmenta Graeca cum Amuleto Christiano, ed. Ernestus
Schaefer accedunt IV tabulae phototypicae, 1912.
See BOBST Archive: O 1
Includes legal accounts and fragments of the Illiad by HOMER; an astrology fragment; Christian fragments
and a grammatical fragment.
A collection of papyri named “Iandanae” in honor of the publishers Karl Reinhold Janda who died 1869 and Johann Ferdinand Janda who died 1888.
These papyri were originally kept at the University of Marburg and were transferred to the University of Giessen.See plates
NO CATNYP BOBST# PA3343 .R32
“A sixth century [CE] account of hay. (P. Iand inv. 653) / Tony Reekmans.”
P. Iandanus 653 (Greek)
IBSCHER: (Greek) papyrus
(as per E. G. Turner) See P. Hamb., ed. B. Snell.
IFAO: (Greek) papyri
P.IFAO: Papyrus grecs de l'Institut Français d'Archéologie Orientale
P. IFAO 1.1. Lease of land: (Greek; AD 27; from Tebtynis)
IG: inscriptiones graecae
IGAI: (Greek studies) text
[B_436,rvw,IGAI] CATNYP# JFE 99-13015
“La Peninsula Iberica en los autores griegos : de Homero a Platon / edicion, treduccion y comentario, Elvira Gangutia Elicegui. Inscriptiones graecae antiquissimae Iberiae [IGAI] / edicion, traduccion y comentario, Helena Rodriguez Somolinos ; Julio Mangas y Domingo Placido (eds.).”
IMOUTHES: (AE) papyrus
(as per AEB) Goyon, Jean-Claude, Le Papyrus d'Imouthes Fils de Psintaes Au Metropolitan Museum of Art de New York (P. MMA 35.9.21), 1999.
INANNA: (2300 BCE, Sumerian Goddess/ Deity).
INCA: civilization of South America
See April 2002 discoveries of import.
INCIRLI: (Phoenician) Stela:from Karamanmarash, Turkey
With Phoenician inscriptions
The Incirli Stela contains a lengthy text written on all four sides of the stone in standard Phoenician of the late 8th century BCE. It is a commemorative boundary inscription marking the successful end of a territorial struggle between the kings of Cilicia (Que) and Kummuh and the various allied powers, presumably over the territory where the monument was originally erected. Since it seems clear that the monument was reused much later as a boundary stone with a Greek inscription of the Byzantine period, we cannot necessarily assume that the earlier text should be associated with the specific locale where the stone was discovered in 1993. Still, considering its size and weight, it seems unlikely that it had been moved very far from where it was first erected.
INDIAN MATHEMATICS: sprinkled throughout
6.1. Bag, Amulya Kumar. Mathematics in Ancient and Medieval India. Varanasi: Chaukhambha Orientalia, 1979.
6.2-3. Datta, Bibhutibhusan, and Avadesh Narayan Singh. History of Hindu Mathematics: A Source Book. Vol.1. Numerical Notation and Arithmetic. Vol.2. Algebra. Lahore: Motilal Banarsidass, 1935/1938. Reprinted in one vol. Bombay: Asia Publishing House, 1962.
6.4. Joseph, George Gheverghese. The Crest of the Peacock: Non-European Roots of Mathematics. London: Penguin Books, 1990. Reprinted New Delhi: Affiliated East-West Press Pvt. Ltd., 1995. [Chapters 8 and 9 only].
6.5. Juschkewitsch, A. P. Geschichte der Mathematik in Mittelalter. Leipzig: Teubner, 1964. Translated from the 2nd edition of the Russian original by V. Ziegler. [Chapter 2 only.] [You can also use the Russian original: Yushkevich, A.P. Matematika srednikh vekov, Moscow, 1961].
6.6. Pingree, David. “History of Mathematical Astronomy in India”. In: Dictionary of Scientific Biography. Vol. 15. Edited by C. C. Gillispie. New York: Charles Scribner’s Sons, 1978, 533–633.
6.7. Sen, Samarendra Nath. “Mathematics”. In A Concise History of Science in India. Edited by D. M. Bose et al. New Delhi: India National Science Academy, 1971, 136–212.
6.8. Sen, Samarendra Nath, and Amulya Kumar Bag. “Post-Vedic Mathematics”. In the science and technolog volume (vol. 6) of The Cultural Heritage of India. Edited by Priyadaranja Ray and S. N. Sen. Calcutta: Ramakrishna Mission Institute of Culture, 1986, 36–55.
6.9. Srinivas, M. D. “The Methodology of Indian Mathematics and Its Contemporary Relevance”. In: History of Science and Technology in India. Edited by G. Kuppuram and K. Kumudamani, eds., Vol. 2, 29–86.
6.10. Srinivasiengar, C. N. The History of Ancient Indian Mathematics. Calcutta: The World Press, 1967.
6.11. Bronkhorst, Johanes. “A Note on Zero and the Numerical Place-Value System in Ancient India”. Asiatische Studien 48 (4) 1994, 1039–1042.
6.12. Datta, Bibhutibhushan. “Early Literary Evidence of the Use of Zero in India”. American Mathematical Monthly 33 (1926), 449–454.
6.13. Ganguli, Saradakanta. “The Indian Origin of the Modern Place-Value Arithmetical Notation”. American Mathematical Monthly 39 (1932), 251–256, 389–393; 40 (1933), 25–31, 154–157.
6.14. Raman, Anand V. “The Katapayadi Formula and the Modern Hashing Technique”. Annals of the History of Computing 19 (4) 1997, 49–52.
6.15. Ruegg, D. S. “Mathematical and Linguistic Models in India Thought: The Case of Zero and sunyata”. Wiener Zeitschrift fur die Kunde Sudasiens 22 (1978), 171–181.
6.16. Datta, Bibhutibhushan. The Science of the Sulba: A Study in Early Hindu Geometry. Calcutta: University of Calcutta, 1932.
6.17. Seidenberg, A. “The Ritual Origin of Geometry”. Archive for History of Exact Sciences 1 (1962), 488–527.
6.18. Gupta, Radha Charan. “Circumference of the Jambudvipa in Jaina Cosmography”. Indian Journal of History of Science 10 (1975), 38–46.
6.19. Gupta, Radha Charan. “Madhavacandra’s and Other Octagonal Derivations of the Jaina Value pi = sqr (10), Indian Journal of History of Science 21 (1986), 131–139.
6.20. Datta, Bibhutibhusan. “The Science of Calculation by the Board”. American Mathematical Monthly 35 (1928), 520–529.
6.21. Mazars, Guy. “Les fractions dans l’Inde ancienne de la civilisation de l’Indus à Mahavira (IXe siècle)”. In: Histoire de fractions, fractions d’histoire. Edited by Paul Benoit, Karine Chemla, and Jim Ritter, (Science Networks. Historical Studies 10.) Basel, Boston, Berlin: Birkhauser Verlag, 1992, 209–218.
6.22. Singh, Paramanand. “The So-called Fibonacci Numbers in Ancient and Medieval India”. Historia Mathematica 12 (1985), 229–244.
6.23. Gupta, Radha Charan. “On the Volume of a Sphere in Ancient India”. Historia Scientiarum 42 (1991), 33–44.
6.24. Hayashi, Takao, Takanori Kusuba, and Michio Yano. “India Values for pi Derived from Aryabhata’s Value”. Historia Scientiarum 37 (1989), 1–16.
6.25. Pottage, John. “The Mensuratio of Quadrilaterals and the Generation of Pythagorean Triads: A Mathematical, Heuristical and Historical Study with Special Reference to Brahmagupta’s Rules”. Archive for History of Exact Sciences 12 (1974), 299–354.
6.26. Sarasvati Amma, T. Geometry in Ancient and Medieval India. New Delhi: Motilal Banarsidass, 1979.
6.27. Hayashi, Takao. “Varahamihira’s Pandiagonal Magic Square of the Order Four”. Historia Mathematica 14 (1987), 159–166.
6.28. Rosu, Arion. “Les carrés magiques indiens et l’histoire des idées en Asie”. Zeitschrift der Deutchen Morgenlaendischen Gesellschaft 139 (1989), 120–158.
6.29. Hayashi, Takao, and Takanori Kusuba. “Twent -One Algebraic Normal Forms of Citrabhanu”. Historia Mathematica 25 (1998), 1–21.
6.30. Selenius, Clas-Olof. “Rationale of the Chaklavala Process of Jayadeva and Bhaskara II”. Historia Mathematica 2 (1975), 167–184.
6.31. Gold, David, and David Pingree. “A Hitherto Unknow Sanskrit Work concerning Madhava’s Derivation of the Power Series for Sine and Cosine”. Historia Scientiarun 42 (1991), 49–65.
6.32. Gupta, Radha Charan. “Addition and Subtraction Theorems for the Sine and the Cosine in Medieval India”. Indian Journal of History of Science 9 (1974), 164–177.
6.33. Gupta, Radha Charan. “Bhaskara I’s Approximation to Sine”. Indian Journal of History of Science 2 (1967), 121–136.
6.34. Gupta, Radha Charan. “Second Order Interpolation in India Mathematics up to the Fifteenth Century”. Indian Journal of History of Science 4 (1969), 86–98.
6.35. Hayashi, Takao. “Aryabhata’s Rule and Table for Sine-Differences”. Historia Mathematica 24 (1997), 396–406.
6.36. Mukhopadhyay, A. and M. R. Adhikari. “Polygonal Approximation to Circle and Madhavacarya”. Indian Journal of History of Science 30 (1995), 35–45.
6.37. Plofker, Kim. “A Example of the Secant Method of Iterative Approximation in a Fifteenth Century Sanskrit Text”. Historia Mathematica 23 (1996), 246–256.
6.38. Rajagopal, C. T., and M. S. Ragachari. “On an Untapped Source of Medieval Keralese Mathematics”. Archive for History of Exact Sciences 18 (1978), 89–102.
6.39. Camman, Schuyler. “Islamic and Indian Magic Squares”. History of Religion 8 (1968–1969), 181–209, 271–299.
6.40. Pingree, David. “The Indian and Pseudo-Indian Passages in Greek and Latin Astronomical and Astrological Texts”. Viator: Medieval and Renaissance Studies Berkeley: University of California Press 7 (1976), 141–195.
6.41. Pingree, David. “Power Series in Medieval India Trigonometry”. In Proceedings of the South Asia Seminar. Vol. II. Pennsylvania: University of Pennsylvania (Department of South Asia Regional Studies), 1981/1982, 25–30.
6.42. Saidan, A. S. The Arithmetic of al-Uqlidisi. Dordrecht and Boston: D. Reidel Publishing Company, 1978.
6.43. van der Waerden, B. L. Geometry and Algebra in Ancient Civilizations. Berlin: Springer Verlag, 1983.
6.44. Yabuuti, Kiyosi. “Researches on the Chiu-chih li — Indian Astronomy under the T‘ang Dynasty”. Acta Asiatica 36 (1979), 7–48.
All the above and more via this link:
See also FIBONACCI; GUPTA; MAHAVIRA.
INDUS: (ancient Indian) script; INDUS VALLEY SCRIPT
Today you have brought to me from Harappa as a gift from Prof. Kenoyer, drawings of a number of new tablets from Harappa. Looking at them I find that most of them are repetitions of finds already well known and included in Parpola's volumes. So the chances of a long connected narrative seem to be slim. There is always the possibility that somewhere along the Makran coast [in Baluchistan] or even in the Middle East a bilingual seal or even a bilingual clay tablet could be found. It is known that traders from Meluhha [the Mesopotamian word for the Indus Valley] went to the Middle East and set up colonies there, but this is looking into the future. As of now all the work that has been done can only be said to be of a tentative character….
In some of the Indus Valley seals found in the Middle East, particularly the round seals which must have been locally manufactured, the order of the signs and their combination are totally dissimilar to what we find in Harappa and Mohenjo-daro., This may have been an attempt to use the Harappan script by the natives of the Indus Valley who went over to the Middle East for trade purposes, to adapt the Indus script to a local Middle Eastern language. But for this exception, within the Indus Valley itself, in all its areas and throughout the time, the language was the same as proved by the frequency of the Indus signs….
(As per V. Gupta; personal correspondence; 090104)
Please read the book review given below. There is still controversy, and not every one is buying Rajaram's interpretations, but I think it is good start.
My own thinking is that Hindus still follow most of traditions which were followed by Indus Valley people. So Indus Valley has to be a part of our heritage. It is very likely that the civilization disappeared due to heavy flooding, and not due invasion by Aryans (Indo-Europeans). Saraswati river, which was so highly adored by Rig Vedic [See RGVEDA] people, possibly also disappeared around that time. It might be due to massive earthquake which changed the course of Saraswati river leading to over-flooding in Indus. Satellite survey shows that Saraswati river did change course, and about 2500 years ago it was part of Gaghar river which flowed through Punjab and Rajas than. Now Gaghar is merely a seasonal river, and drilling at various locations in Punjab and Rajasthan has shown that water is indeed present underground all along that route discovered by satellite survey.
the Mother of All Alphabetic Scripts
-- Book Review --
The Deciphered Indus Script:
Methodology, Readings, InterpretationsbyNatwar Jha
and N. S. Rajaram (New Delhi: Aditya Prakashan, 2000
270 pages with numerous illustrations, Rs. 950)
Reviewed by C. J. S. Wallia [below]
Science historians have long acknowledged that the international numeral system (1,2, 3,), based on the concepts of placement and zero, as well as the decimal system were invented by the ancient Hindus. (Nonetheless many Western publications continue to call these numerals Arabic-- Arab historians themselves have always acknowledged the numerals' Hindu origins.)
An even more fundamental contribution to human knowledge-- the origin of alphabetic writing--must now be credited to the ancient Hindus. This claim arises from the deciphering of the ancient Indus script recently accomplished by Natwar Jha. In 1996, he published Vedic Glossary on Indus Seals, which briefly explained his methodology and presented readings of more than 100 seals. It was an English language summary of his monumental publications, Sindhu Mudra Lipi Bhasa, in Sanskrit, and Sindhu Sabhyata ki Mudraon ki Bhasa aur Lipi, in Hindi.
The Deciphered Indus Script, written in collaboration with Navaratna Rajaram, is a more comprehensive exposition of the methodology, readings, and interpretations. The decipherments are Jha's; the historical interpretations are Rajaram's. The authors summarize:
"Jha's decipherment tells us that the language of the seals is Vedic Sanskrit, while the writing itself is proto-alphabetical, representing an intermediate stage in the transition from a primitive consonantal (syllabic) system to the phonetically exact alphabetical writing which is the unique achievement of the Indian civilization.
"...The readings on the seals are overwhlemingly from the Vedic literature. The same is true of the symbolism of the images. From this we conclude that at least those seals that carry Vedic themes were created to serve as educational aids, as a combination of an index and a Vedic theme."
In the first part of Vedic Glossary on Indus Seals, Jha described his major insight into his deciphering efforts: the four- to five-thousand-years-old inscriptions were meant to serve as a link betweenVedic literature and archaeology. Jha's inspiration came from his reading about Rishi Yaska's search in the Mahabharata for Kashyapa's lost Sanskrit etymological composition. Jha wrote:
"The 'Moksa Dharm--Santiparv--chapter 343 of Mahabharat and its couplet no. 71, 72, 73, 88, 89, 92, and 93 are very important for understanding the subject matter as written on Indus seals. Where couplet 73 is clearly related with the Indus seals and couplet 92 records Aryan trend of considering Lord Vishnu in the form of unicorn (bull with one horn), called the Eksringah Nandivardhnhah in our epic and 'bull-bos indicus' called the Vrisha, Vrishakapi, Sipivisht, and Trk-kut. Similarly couplet 89 assimilates all above material information on varied forms of bulls with Nighantu -- the first generation Vedic glossary composition. We get information from couplet 73 that Nighantu was buried in the ground for certain reasons, like floods; and after some time, under the able guidance of Rishi Yaska an attempt was made to excavate the buried composition. And thus the recovered material formed the basis of composing Nirukta -- the second generation Vedic composition."
Natwar Jha, who serves as the principal of Kendriya Vidyalaya, Farraka, West Bengal, spent 20 years on the Indus Script project. He has deciphered more than half of the known seals and established the script as old Brahmi, a thousand years older than the Phoenician script, which was the supposed origin of all alphabetic writing. In detailed charts, the book shows stage-by-stage derived forms from the Indus script that include Phoenician, Aramaic of Taxila, Sabien Hemyaretic, and Greek.
Commenting on Jha's earlier work, Rajaratnamwrote (before they were acquainted): "I find the readings so decisive that I am convinced that all previous theories, readings, and formulations have been rendered irrelevant by Jha's work. Any changes, if needed, will only be refinements. ...In the Indus seals, we have in all probability the mother of alphabetic writing. This is only one of the revisions to our knowledge of history of science brought about by the decipherment of the Indus script."
The beautifully crafted 5,000-year-old Indus seals, discovered in 1921, long baffled scholars who attempted to decipher the script accompanying the images. The scholars failed largely because of the assumption under which they labored-- they uncritically assumed the inscriptions had to be pre-Vedic and Dravidian. These assumptions stemmed from the prevailing Eurocentric, colonial dogma that Sanskrit-speaking invaders came to India from the West and could not have composed the Vedas before 1200 B.C. This date was insisted upon by writers like Max Muller, who worked long and hard to deliberately distort the Vedas for their hidden agenda to persuade Hindus to convert to Christianity. Muller insisted on the very late date for the Rig Veda [See RGVEDA] to fit into the Judeo-Christian time scale, which posited that the world itself had been created in 4004 B.C.!
The Aryan invasion theory is in tatters now. No Aryan journey to the east; instead, Sanskrit speakers migrated westwards into Kassite Iran, Hittite Anatolia, Greece, and much further. N.Rajaram and David Frawley, in their acclaimed book The Vedic Aryans and the Origins of Civilization: A Literary and Scientific Analysis date the composition of the Rig Veda at 3750 B.C. They base this date, in part, on Subhash Kak's brilliant work on the astronomical code contained in the Rig Veda.
In the introductory chapter ofVedic Glossary on Indus Seals, Jha discussed how the Indus civilization ended. He cited recent Indo-French LANDSAT satellite mappings of the shifting courses of the Sarasvati river over many centuries during the third millennium B.C. The final drying up of the Sarasvati occurred in 1900 B.C. because tectonic plate movements made the mighty river lose two of its tributaries, Yamuna and Sutlej. (Noting the centrality of the Sarasvati in the civilization of Sapta Sindhu or seven rivers, from 7500 B.C. to 1900 B.C., and the repeated homage this river receives in the Rig Veda, Subhash Kak has suggested that the Indus civilization be renamed as Sarasvati civilization and the script on the seals as Sarasvati script.)
The famous Dholavira sign-board consisting of 10 large signs,
approximately 37cm by 27cm, embedded in semi-precious stones on a
wooden board is deciphered and translated by Jha and Rajaram as:
"I was a thousand times victorious over avaricious raiders desirous
of my wealth of horses." A warning to would-be horse thieves!
In the second part of Vedic Glossary on Indus Seals, Jha claimed the Indus script as "the first and the oldest scientific script of the world, which later on crossed the national boundary and went to West Asia and Europe, where it developed as Semitic and Greek." Jha presented a convincing, stage-by-stage comparative study in the next 50 pages.
Some of the main features of Jha's decipherment are: the old-Brahmi script is written from left to right, although sometimes it is also written right to left like plough lines on soil ("halayudh lekhan paddhti"); there are 61 basic signs in total comprising 55 consonants, 1 Onkar, 3 Vowels, and 2 Ayogwah (combination of vowel and consonant); there are also 162 composite signs; Phoenician is a reduced subset of 22 signs from the old-Brahmi's 61 signs; some seals are inscribed with the swastika as well as a cross without arms; a few of the signs are pictographic, but most of them are alphabetic.
The Indus/Sarasvati script or old-Brahmi developed in two divergent directions in India: Devanagari and related North Indian regional variants; and Ashokan Brahmi from which derived Bhattiprolu Brahmi in South India.
Jha also charted the evolutionary stages of the five point numeral system, shown on the reverse side of several seals, into Greco-Roman numerals. Some of the seals carry mathematical formulas. One seal is carved with the formula for the circumference to diameter ratio or p from "paridhi vyas anupati"from which derived the term pi of the Greeks. Another seal shows the formula for the circumference of a circle as 2 times p times radius.
Jha cites the work of Navaratna Rajaram and A. Seidenberg, an eminent American historian of science, for establishing the source of both Egyptian and old Babylonian mathematics in the technical manuals for the construction of complex geometrical Vedic fire altars, Sulba-Sutras.
INNSBRUCK: papyrological studies at
See GIESSEN; [B_489,rvw]
INSCRIPTIFACT: KICKS ASS
(AE; Ptolemaic;demotic; ~300 BCE) wisdom papyrus
(as per LEX) Seek OMRO Ro III, 1922.
See Harris, [B_050].
“It is in the heart of the imbecile that the work of God causes the snigger [laughter]. The life of the imbecile is a burden even for God.”
Egyptian Literature, Lichtheim, M., Vol. III, P184f.)
A man spends ten years as a child before he understands death and life, He spends another ten years acquiring the instruction by which he will be able to live. He spends another ten years earning and gaining possessions by which to live. He spends another ten years up to old age, when his heart becomes his counselor. There remain sixty years of the whole life [100 years; see TORAH for limit of Man’s lifespan to 120 years], which Thoth has assigned to the man of god.
See: Lexa, F., Papyrus Insinger, Librairie orientaliste Paul Geuthner, Paris, 1926.
Scribe named Onqsheshonq:
J. H. Insinger worked with/contributed his collections to the Leiden Museum; lived in Luxor.
INVENTORY STELA: (AE; NK)
Known by Cairo, Eg. Mus. 2091
(as per G. Reader; EEF; 030103)
Inventory Stela found by Mariette in 1858 in a 21 Dynasty temple of
Isis built into the pyramid temple of Henutsen daughter of Khufu. This
stela is one of the most abused and misunderstood documents from ancient Egypt.
It has been used by "alternative" authors to claim that the Sphinx is
older that Khufu and on the other hand has been labeled a forgery and pious
fraud by some orthodox Egyptologists. A recent book:
Sphinx, by Christiane Zivie-Coche, translated by David Lorton,
Cornell 2002 (see pages 83-90) places the stela in its proper historical
milieu as a commemorative document.<snip>
"THE STELA OF THE DAUGHTER OF CHEOPS
<snip>The style of the piece and the deities chosen illustrate it could not [have been an ]
Old Kingdom original <snip>
Another voice of caution with some new insights is Eva Lange who
lectures Old and Middle Egyptian at the Humboldt-University of
Eva Lange makes the argument that half the inscription is about Khufu and half about Amasis because of
finding the Golden Horus name of Amasis "Chosen of the Gods" on the right half of the stela. But Christiane Zivie-Coche's translation of this part of the stela is very different from other translations I have seen from Breasted on.
(as per M. Tilgner; EEF; 030203)
Mariette, Auguste, Monuments divers recueillis en Égypte et en Nubie /
Par A. Mariette-Pacha. Texte par G. Maspero. - Paris : Vieweg, 1892, p. 17,
Brugsch, Heinrich, Thesaurus inscriptionum Aegyptiacarum :
Altägyptische Inschriften / gesammelt, verglichen, übertragen, erklärt und
Autographiert von Heinrich Brugsch. - Leipzig : Hinrichs, 1883-1891, p. 1231
Photograph (Wildung: "only useful photographic reproduction")
HASSAN, Selim, The Great Sphinx and Its Secrets. Historical Studies in
The Light of Recent Excavations, Cairo, Government Press, 1953, pls. 55-56
WILDUNG, Dietrich, Die Rolle ägyptischer Könige im Bewusstsein ihrer
Nachwelt. Teil I. Posthume Quellen über die Könige der ersten vier
Dynastien, Berlin, Verlag Bruno Hessling, 1969 = Müchner Ägyptologische
Studien 17, pp. 182-184 with the references given above
(as per P. Manuelian; EEF; 030203)
Giza au premier millenaire by Christiane Zivie-Coche, Boston
MFA, 1991, pls. 39-40 for the best photos I have ever seen of the piece, and pp.218-46 for the text and translation.
(as per M. Marcolin; EEF 030203)
<snip> further ref. on the stela in question
[Cairo,Eg. Mus. 2091]
Daressy, La stele de la fille de Cheops", RecTrav XXX (1908), 1-6.
Hassan, The Great Sphinx, 113-7, fig. 80, pls. LV-I;
Zivie, Giza au premier millenaire. Autor du temple d'Isis dames des pyramides.
ISHANGO: (Pre-historic) counting bone
The Ishango bone found in Zaire/Uganda/Congo dated to 20000 to 8500 BCE. [not much clarification from carbon dating?]
With tallies. Prime numbers. [Potential] Lunar calendar uses.
See this link.
See GILGAMESH; ENUMA ANU ELISH; TORAH; JEWS
CATNYP# *KP (Eragny) (Gilgamesh. Descent of Ishtar)
“The Descent of Ishtar. By Diana White.”
Allat (a feminine underworld/Satan figure) is distraught over Ishtar’s relative success (failure to desintegrate), while Ishtar herself threatens to allow the dead to walk the Earth and devour the living as the dead are more numerous (no longer true!). This raising of the dead and Ishtar’s elimination being prevented by other divinities enfuriated Allat who then beats her breast and rents [tears] her garments. Compare to traditional Jewry and customs.
Layered removals correspond to Ishtar’s descent at these levels:
1. High Crown
4. Sumptuous ornaments from her chest
5. Gem encrusted waist belt
6. bracelets on her hands and feet [wrists and ankles]
7. Her last veil [i.e. her dignity or virginity]
This is comparable to the quest to the forests of Lebanon [See MONSTER; Hawara] made by Enkidu and Gilgamesh in the repetitive trials they encountered against the Divine forest.
ISIS: (AE) Goddess
(As per EEF; 011504)
Burden of Isis, by James Teackle Dennis, 1910
With: The Laments of Isis and Nephthys (Berlin Pap. 1425),
The Chants (BM Pap. 10188), Hymn to Osiris-Sokar.
ISIS: (AE) Scholarly Publication
CATNYP# *OAC (Isis) 1936
“On a Curious Subdivision of the Egyptian Cubit.”
Isis, Volume 25, No. 2, September 1936, pages 399-402.
Two MMA CUBIT fragments briefly discussed.
CATNYP# *OAC (Isis) 1923
“Michigan Mathematical Papyrus No. 621.”
Isis, Volume 5, No. 1, 1923, pages 20-25.
Analysis of Greek unit fractions similar to Achmim papyri.
ISIS-N: (AE) papyri; fragments?
NO CATNYP Moeller reference.
Hieratic math content. 2 BCE?
(as per Moeller) See:
Die liegenden Datumgahlen werden im Hieratischen zu Beginn der Ptolermaerzeit durch die gewohnlichen Zahlzeichen [numerals].?
(as per Y. Koenig)
Seek fragments: VF, VIII B, XXXI, and Horus fragments XXXI?
WATSONLINE Yields nothing.
5.1. Berggren, J. L Episodes in the Mathematics of Medieval Islam. New York: Springer-Verlag, 1986. [Location: Islamic Studies QA27 A67 B46 1986; Physical Sciences Engineering QA27 A67 B46 1986]
5.2. Yushkevich, Adolf P. Les mathématiques arabes (VII e –XV e siècles). Paris: J. Vrin, 1976. [Location: Islamic Studies QA23 I814; also in Phys. Eng. Sci. Library]
5.3. Rashed, R. “L’extraction de la racine nième et l’invention des fractions décimales (XI e –XIII e siècles)”. Archive for History of Exact Sciences 18 (1978), 191–243.
5.4. Rashed, R. “L’induction mathématique: al-Karaji, as-Samawal”. Archive for History of Exact Sciences 9 (1972), 1-21.
5.5. King, D. “Science in the Service of Religion: the Case of Islam”. Vol. 159. (Impact of Science on Society.) Paris: Unesco, 1990.
5.6. Sabra, A. I. “Situating Arabic Science: Locality versus Essence”. Isis 87 (1996), 645-670.
5.7. Kennedy , E. S., et al. Studies in the Islamic Exact Sciences. Edited by D. A. King, and M.-H. Kennedy. Beirut: American University of Beirut Press, 1983.
5.8. Lorch, R. Arabic Mathematical Sciences: Instruments, Texts, Transmission. Aldershot: Variorum, 1995.
5.9. Rashed, R. The Development of Arabic Mathematics: Between Arithmetic and Algebra. Dordrecht: Kluwer, 1994. (or the original French edition: Rashed, Roshdi: Entre arithmétique et algèbre. Paris: Société d'édition Les Belles lettres, 1984. Location: Islamic Studies QA27 A67 R37 1984).
5.10. Rashed, R. Optique et mathématiques. Recherches sur l’histoire de la pensée scientifique en Arabe. Aldershot: Variorum, 1992. [Location: Islamic Studies QC352 R37 1992]
5.11. Lamrabet, Driss. Introduction à l'histoire des mathématiques maghrébines. Rabat : El Maârif Al Jadida, 1994. [Location: Islamic Studies QA27 A355 L36 1994]
5.12. Mukhammad ibn Musa al-Khorezmi. Moskva: Nauka, 1983 [in Russian]. [Location: Humanities & Social Sciences McLennan Bldg Q124.95 M85 1983]
5.13. Sesiano, Jacques. Books IV to VII of Diophantus' Arithmetica in the Arabic translation attributed to Qusta ibn Luqa. New York ; Heidelberg : Springer-Verlag, 1982. [Location: Edward Rosenthall Math Stats QA22 D5623 S47 1982]
5.14. Hill, George Francis. The development of Arabic numerals in Europe. Oxford, Clarendon press, 1915. [Location: Osler Robertson QA 21 H646 1915]
5.15. Daffa', 'Ali 'Abd Allah. Studies in the exact sciences in Medieval Islam. Dhahran, Saudi Arabia : University of Petroleum and Minerals ; Chichester [West Sussex] ; New York : Wiley, 1984. [Location: Islamic Studies Q127 A5 D34 1984]
All the above and more via this link:
See AURELIUS ISODORUS
ISOSEPHIA: See GEMATRIA
ITALIAN: (Latin) papyri at Universities in Italy
P.Ital.: Die nichtliterarischen lateinischen Papyri Italiens aus der Zeit 445-700
P.Ital. 1.1.: (Latin; AD 445; from Ravenna)
Numerical content to be pursued. Math.
IZBET SARTAH: (Hebrew) shard; abecedary
contains 80 crudely written letters as an abcedary written from left to right
…Wait, wait, wait. I mean, yes, theoretically, it’s possible that there’s a single inscription in the ninth century. The Gezer calendar, in my opinion, is ninth century B.C. [not tenth, as many scholars think.—Ed.]. In the second half of the ninth century we do have inscriptions in Moab—the Mesha stela—and in Damascus—the Tel Dan stela [mentioning the “House of David”], which was written by Hazael. Why not Israel? It’s possible. We don’t have such an inscription from the Northern Kingdom yet, but we may expect one ...
See TORAH; GEZER; TELL GEZER