ARCHIMEDES (ca. 287 - 212 BC). On the Equilibrium of Planes; On Floating Bodies; The Method of Mechanical Theorems; On Spiral Lines; On the Sphere and the Cylinder; On the Measurement of the Circle; Stomachion, all in Greek. PALIMPSEST MANUSCRIPT ON VELLUM (upper text: Euchologion, in Greek, 12th century)
ARCHIMEDES (ca. 287 - 212 BC). On the Equilibrium of Planes; On Floating Bodies; The Method of Mechanical Theorems; On Spiral Lines; On the Sphere and the Cylinder; On the Measurement of the Circle; Stomachion, all in Greek. PALIMPSEST MANUSCRIPT ON VELLUM (upper text: Euchologion, in Greek, 12th century)

ARCHIMEDES (ca. 287 - 212 BC). On the Equilibrium of Planes; On Floating Bodies; The Method of Mechanical Theorems; On Spiral Lines; On the Sphere and the Cylinder; On the Measurement of the Circle; Stomachion, all in Greek. PALIMPSEST MANUSCRIPT ON VELLUM (upper text: Euchologion, in Greek, 12th century)

Byzantine Empire, probably Constantinople,third quarter of the 10th century
195 x 150 mm. 174 leaves, foliated 1-177 in a modern hand in arabic numerals (ff. 104, 123, 170 now missing, as well as approximately 60 unnumbered leaves). Collation: [12 (lacking 2 or more leaves in the middle of the quire, and at least 1 quire following 1/2) 24 36 4-58 (perhaps lacking a quire following 5/8, replaced by a later 8-leaf paper quire) 66 7-84 (lacking 8/1-2, represented by stubs) 9-168 (lacking 16/5 and 16/8+1) 17-186 198 (lacking 19/7) 20-228 236 248 258 (25/8+1, lacking 25/8) 266 (at least one subsequent quire lacking, at one time replaced by a later paper quire)]. ALMOST ALL LEAVES PALIMPSESTED, WITH THE WORKS OF ARCHIMEDES AS THE LOWER TEXT ON AT LEAST 61 BIFOLIA AND 5 SINGLE LEAVES. Archimedes: each complete leaf a bifolium of the present codex, 300 x 195 mm, double columns of 35 lines, written in minuscule script in ink that is now pale brown, no visible ruling, justification: 240 x 145 mm; book titles in capital letters, a few ornamental calligraphic initials, geometrical diagrams. Euchologion: 195 x 150 mm, 25-27 lines written below the ruled lines in minuscule script in dark brown ink, blind-ruled at right angles to the earlier writing, justification: 140 x 100 mm, rubrics in red, many ornamental initials in fine penwork, most colored red, some blue, a few decorative headpieces in red pigment and brown ink. A quire of 8 paper leaves loosely inserted after 5/8: 8o, 18 (7 a blank stub), 150 x 110 mm, 17-20 lines, justification: 115 x 85 mm, watermark: scissors, apparently 16th century. (Condition defective: first leaves and edges of bookblock scorched, most leaves with damp and mildew stains, ca. 50 leaves with holes or tears in text area, ca. 15 leaves with strips cut from blank margins, ca. 20 leaves detached and laid in loosely, ca. 10 pages with upper script retraced, 4 modern miniatures added on ff. 21r, 57r, 64v, 81r, versos of miniatures faded with traces of mounting, modern illuminated tailpiece on f. 116v). Binding: 19th-century dark brown sheepskin over wooden boards tapered at the spine edge, metal button on front cover remaining from thread-and-button closure (hole for thread at fore-edge of back cover), two leaves from canon tables of the 13th(?) century as pastedowns, edges of binding flush with those of the leaves, headcaps not raised. (Binding defective: various repairs and reinforcements to inner margins and sewing, old rebacking partially detached, recent repairs to spine.)


The manuscript in its present form is a Greek liturgical book, probably written in the second half of the twelfth or conceivably in the first half of the thirteenth century. As such it has no obvious claim to be regarded as possessing special significance, but it is also a palimpsest, i.e., a manuscript from which the first writing has been effaced so that the vellum could be reused. In this codex most of the leaves derive from a uniquely important manuscript of Archimedes, dating from the mid-tenth century. This makes the volume the most valuable surviving document for studying the thought of the greatest scientist of Antiquity and a central chapter in the history of Greek mathematics and engineering.

From late Antiquity onwards the shortage of writing material, both in the territories of the former Roman Empire and in the Byzantine world, was often severe enough to compel copyists to have recourse to the unfortunate practice of reusing parchment. Unwanted manuscripts were dismembered; the writing was scraped, or more usually washed, from the leaves; and the vellum was used for writing new texts. Many of the resulting palimpsests survive. Among those in Greek the present volume is beyond question the most important, since it brought to light a substantial text of outstanding value and at the same time preserved improved readings in some passages of the essays that were already known. The significance of the Archimedes palimpsest is thrown into relief when one compares it to two of the other best known Greek palimpsests: one is a small fragment in Paris (Bibliothque nationale, grec 107B) written in the fifth century, which yields about a hundred lines of Euripides' lost play Phaethon, while the other is a quite substantial book in Jerusalem (Library of the Greek Patriarchate, MS 36) containing parts of several known plays by Euripides and dating from the eleventh century. The former, although it reveals some charming lyric poetry, is a relatively short text, while the latter, despite being one of the earliest extant copies of Euripides and containing several hundred lines of poetic text, offers virtually no improvement. Some palimpsests of Latin texts, however, have added more to our knowledge and are thus more comparable to the Archimedes. One may cite as examples the Verona codex of an important legal treatise, Gaius' Institutes (Cathedral Library, MS XV(13)) or Cicero's De re publica (Vatican Library, MS Vat. lat. 5757). In each of these the lower text of a single palimpsest manuscript preserves the only copy of a text that would otherwise be lost.

Provenance of the Palimpsest

1. Byzantine Empire, probably Constantinople. The original Archimedes manuscript was probably written in Constantinople. Although one cannot identify intellectuals living in the capital who might have been sufficiently interested in advanced mathematics in the late tenth century to commission such a book, there is even less reason to suppose that it could have been produced in one of the far-flung provinces of the Byzantine Empire.

Where and exactly when the Archimedes text was discarded and made into a palimpsest is also obscure. In the Byzantine world the demand for biblical, theological and liturgical texts was persistent, and until paper became readily available at an affordable price, any old book written on parchment and containing texts of no immediate and obvious importance was at risk of being converted into a palimpsest. The Archimedes was an easy target for a priest in need of a new service book.

2. Palestine, Mar Saba. At some stage the service-book which resulted appears to have been in Palestine, assuming that the report by Papadopoulos-Kerameus is acccurate that an ex-libris from the Lavra of St. Saba was found in a now-lost paper quire at the end. It would be rash, however, to assert that a monastic ownership inscription is a reliable indication of the place of origin, as in the Middle Ages books often travelled with their owners. The manuscript collection of Mar Saba, a monastery in the desert south-east of Jerusalem, was incorporated along with other local collections into the library of the Patriarchate in the middle of the nineteenth century.

3. Constantinople, Metochion of the Holy Sepulchre. How the present manuscript was transferred to the library of the daughter-house of another Palestinian monastery, the one attached to the Holy Sepulchre, remains a mystery, and there is no proper documentation for the history of the collection that was at the Metochion in the nineteenth century.

The first mention of the palimpsest in modern times is in a travel book by the German biblical scholar, Constantine Tischendorf, Reise in der Orient (Leipzig 1846), translated into English by W.E. Shuckard (London 1847; see p. 274). Tischendorf visited the patriarch's library in Constantinople and found nothing of particular interest "apart from a palimpsest dealing with mathematics". However, it seems that he came away from the library with one leaf in his possession, since that leaf was among 44 fragments sold by his executors in 1876 to the University Library in Cambridge, where it is now MS Add. 1879.23 (Easterling 1962, pp. 302, 307, where the text is not identified; in fact it is from On the Sphere and the Cylinder I 35-37, ed. Heiberg, vol. I pp. 132-138, with lacunae due to the loss of one half of the original leaf). Perhaps Tischendorf had hoped to identify the text and interest potential purchasers; his complicated maneuvers in the notorious case of the Codex Sinaiticus of the Bible (described in Sevcenko 1964) are suggestive. Evidently nothing came of any such plan.

In 1899 A.I. Papadopoulos-Kerameus published a description of the volume in his catalogue of the manuscripts belonging to the Metochion of the Holy Sepulchre in Constantinople, parts IV and V of his catalogue of the Greek manuscripts belonging to the Jerusalem Patriarchate Library (Papadopoulos-Kerameus 1899, 1915; the present codex is described as MS 355 in part IV, 1899, pp. 229-331). That description came to the notice of the German scholar H. Schne, who alerted the Danish classicist J.L.Heiberg, an acknowledged expert in the history of Greek science, to the potential interest of the palimpsest. Heiberg visited Constantinople in 1906 and was able to decipher a good deal of the text, using only a magnifying glass; some leaves were photographed for him, and his results were published in Hermes, vol. 42, 1907, pp. 233-305 (with a plate of f. 41r). He acknowledged assistance from another German colleague, H.G. Zeuthen. Heiberg examined the manuscript again in 1908 and incorporated the results of his researches into the second edition of his critical text of the works of Archimedes, published in the Bibliotheca Teubneriana in 1910-1915.

4. Paris, private collection. What happened to the codex between the time when Heiberg saw it and the time when it came into the possession of a French collector is not known. The library of the Jerusalem Patriarchate in Constantinople was dissolved in the 1920s. In the 1890s Papadopoulos-Kerameus had catalogued 890 manuscripts belonging to the Metochion of the Holy Sepulchre (Papadopoulos-Kerameus 1899, 1915). Most of the 827 surviving from the library were subsequently transferred to the National Library in Athens. One, cod. 370, is now Paris, Bibliothque nationale, supplment. grec 1317; cod. 767[419] is now University of Chicago, MS 129; cod. 634 is Cleveland, Museum of Art, MS 42.152; and cod. 355 is the present Archimedes palimpsest (see Richard 1995).

Codicology of the Palimpsest

The parchment leaves of the present manuscript are almost all palimpsest. Heiberg (1907, p. 236) stated that the only exceptions were ff. 7-13, 23-26, 51-54, 73-80, 83-86, 151-152. Despite his prolonged examination of the manuscript in situ he appears to have been in error on this point, since almost all the leaves in question have vertical ruled lines that cannot have had any purpose other than to guide the lower script. It is also evident that there are traces of an earlier script on a number of other folios (e.g., ff. 8r, 11v, and 53r), although they cannot now be easily deciphered and apparently do not come from the Archimedes manuscript. Of the leaves listed by Heiberg, only ff. 73-80 do not appear to the naked eye to have been palimpsested. Even here, ultraviolet photography of f. 76v reveals a lower text written at right angles to the upper, suggesting that all the leaves may prove to have been reused from earlier manuscripts.

Most of the palimpsest leaves derive from the Archimedes codex, as detailed below. Heiberg (partly contradicting his own list of unpalimpsested leaves) noted that ff. 73, 84, 135-138, 143, 146, 173, 176 came from a different book with the text written in a single column (1907, p. 236). At least ff. 76 and 85 should be added to this list. Heiberg deciphered a phrase on f. 138v, which surprisingly has so far foiled all attempts at identification. The study of these leaves, and all the leaves not at present identified as Archimedes, remains to be undertaken and may reveal unknown texts from Antiquity.

The collation of the volume is not easy to establish, because of its condition and occasionally tight sewing. Nevertheless, its physical make-up as it has existed in the twentieth century may be represented by the formula given above, which is derived from direct examination of the volume, supplemented by information drawn from Heiberg's list of conjugate folios containing the text of Archimedes (Heiberg 1915, pp. lxxxvi-lxxxvii). Three leaves (ff. 104, 123, 170) which were present when Heiberg saw the manuscript and from which he transcribed text are now lost; the leaves conjugate to ff. 39, 40, and 100 were already missing when Heiberg examined the volume. The modern foliation of the codex, in arabic numerals in red ink, corresponds to the foliation used by Heiberg and by Papadopoulos-Kerameus.

It is impossible to determine how much has been lost from the volume. Between folios 1 and 2 something is missing (f. 1r is not legible, and ff. 2r and 2v contain the latter part of a table of contents, beginning with item 94, which does not seem to follow on from the barely legible f. 1v). Part of a lacuna between f. 2 and f. 3 is filled by the leaf now separately preserved in Cambridge University Library as MS Add. 1879.23 (first identified by N.G. Wilson [cf. Scholars of Byzantium, London 1983, p. 139n]; its correct location in the Euchologion worked out by the late R.V. Kerr of the Cambridge University Library). Some quire signatures are visible, on the lower right hand corner of the last verso. It looks as if the Greek numeral [9] was written on f. 28v, and one can read a[11] on f. 48v, b[12] on f. 56v, z[17] on f. 96v, b[22] on f. 140v. These figures suggest that if the book were originally composed of regular quaternions, there are now some forty leaves missing, probably from near the beginning; this rough calculation fails, however, to take into account all the irregularities of the present quire structure.

The paper leaves, now detached, were apparently supplied in the sixteenth century to supplement the text of the Euchologion. Papadopoulos-Kerameus (1899, pp. 329-331) described the manuscript as including two sets of paper leaves: one was a quaternion "of smaller format" found between f. 28 and f. 29; the other, according to him, comprised the final nine [sic] leaves, ff. 177-185. (Since f. 177, a numbered vellum leaf, is still present in the codex, it is likely that the printed description is in error and that the final quire consisted of a quaternion of paper leaves, ff. 178-185.) The eight paper leaves still present in the codex are evidently the quire that followed f. 28. Since Heiberg treated them as constituting ff. 178-185, even though they are not numbered, it appears that the leaves which Papadopoulos-Kerameus numbered 178-185 were lost between 1891, when Papadopoulos-Kerameus actually prepared his catalogue, and 1906, when Heiberg saw the manuscript. Heiberg repeats (1907, p. 241) the assertion made in the printed catalogue that there was an ex-libris of the Lavra of St. Saba, a famous Palestinian monastery, on f. 184v. No date was assigned to it, and it should not be regarded as proof that the prayer-book was written in or for Mar Saba, although it suggests that the paper leaves may have been supplied there.


The original Archimedes manuscript was a typical example of tenth century Byzantine book production. It exhibited a common format, measuring ca. 300 x 195 mm. with text in two columns of some 35 lines, each ca. 240 mm. in height and 65-70 mm. in width. Capital letters were used for titles. At the beginning of a new section of the text a large initial letter extended into the margin, and for the start of a new paragraph there was no indentation, but the first letter of the next line projected into the margin. On ff. 46r, 88v, 109r and 177r there are large initials with simple decoration. In all these respects the book conformed to normal practice. Diagrams accompanied the text; these had probably been transmitted as an integral part of the treatises and may be presumed to derive from the author's master copy. One respect in which the scribe differed somewhat from general practice is that he did not hesitate to use a fair number of abbreviations for common words or grammatical inflections (most copyists used them only at the end of lines, to help with justification). None of the abbreviations, however, is so unusual as to throw any light on the origin of the book.

Since the scribe who reused the vellum divided the bifolia of Archimedes at the fold, and refolded each leaf to a format half that of the original, there is now no direct evidence for the original collation. The manuscript presumably consisted of quaternions, like the great majority of Byzantine manuscripts. Indirect evidence for this may be found in the fact that in their present order the reused Archimedes leaves occur, almost without exception, in pairs of two from the same treatise (see list of contents below). This strongly suggests that each pair represents a bifolium of the original manuscript. When the list of contents is rearranged in the correct order of Archimedes' text, the pattern of leaf-pairs does indeed correspond to quires mostly of eight leaves, as marked in the second of the two contents lists below. This is clearest in the case of the treatises On Spiral Lines and On the Sphere and the Cylinder, where a number of consecutive leaves are extant, and where there are other sources to confirm the completeness of these sections of text as well as the extent and location of the lacunae found in the palimpsest in its present state. Further study of these pairings may elucidate the composition of the original manuscript and, together with their analysis in relation to the sense of the text, may aid in detecting continuity or lacunae where no other witnesses are available. Extrapolating from the tables below, and considering that about a quarter is lacking from the Archimedes texts as well as from the Euchologion manuscript, the collation of the original Archimedes codex might have read something like this: 1-68 76 8-138 (quire 1 [now missing] On the Equilibrium of Planes, quires 2-3 On Floating Bodies, quires 4-6 Method of Mechanical Theorems [with the possibility that there is a quire missing between 4 and 5 and/or between 5 and 6], quires 7-8 On Spiral Lines, quires 9-12 On the Sphere and the Cylinder, quire 13 On the Measurement of the Circle and Stomachion).

The hand is a fluent and assured script, which can be dated to the middle or second half of the tenth century. It exhibits a vague affinity with a dated manuscript of AD 988 (Patmos, Monastery of St. John 138), and a rather closer similarity to undated manuscripts of classical authors generally thought to have been produced from about AD 950 onwards, such as the illuminated Nicander in Paris (Bibliothque nationale, supplment. grec 247) or the famous Florentine Sophocles (Biblioteca Laurenziana 32.9). But it is not possible to identify the copyist or his scriptorium -- in fact the notion that he worked in a scriptorium may be misleading, as there is reason to think that some copyists may have been free-lance professionals. He was probably working in the capital of the Byzantine empire; this conclusion is an inference partly from the lack of any specific pointer to provincial origin, partly from the fact that the capital normally played a dominant role in intellectual life.


Each bifolium of the manuscript was formed from one leaf of the Archimedes manuscript, which was turned on its side and folded in half. The new lines for writing, ruled with a hard point, are therefore at an angle of 90 to the original script. This was common practice in palimpsests in order to lesson the risk of illegibility. Based on the evidence of the leaf-pairs described above, one may postulate that the scribe of the Euchologion was working with undivided palimpsested bifolia which he separated into single leaves as he prepared to use them. Corroboration of this hypothesis may be found in the fact that on ff. 165 and 168 the scribe failed to conform to his usual practice. There, instead of dividing the conjoint leaves, he retained the original orientation of the bifolium while cutting it down around the margins, perhaps because it was too damaged to produce two complete leaves. Thus, ff. 168 and 168, which are conjugate in the present manuscript, also represent a bifolium of the original Archimedes codex (although it it now upside down). On these two leaves the lines of the upper script run parallel to those of the lower script, and the original fold and sewing stations of the Archimedes manuscript are visible near the inner margin of f. 165.

The upper script is a competent if undistinguished minuscule of the middle Byzantine period; its avoidance of enlarged letters or awkward stiffness strongly suggests a date in the twelfth century. In any case it could not be later than the middle of the thirteenth century; it does not bear any resemblance to the archaising script found in quite a number of books written in the period ca. 1280-1330.

There are a few decorative headpieces (e.g., ff. 52r, 62r, 97r, 117r) and many ornamental initials in fine penwork, mainly in red with a little use of blue; epsilon is of the design with a pointing hand (e.g., ff. 13r, 31v, 132v, 158r), and a crude zoomorphic alpha is found on f. 18v and f. 97r. The liturgical instructions are in red. Occasionally the text has been re-inked by a later hand, e.g., ff. 80v, 110r. A marginal note of theological content on f. 126r, perhaps thirteenth century, is not by the scribe. A later prayer on f. 75r asks the Lord to remember the writer, who does not give his name.

Binding and Illumination

Both the binding and the sewing appear to be fairly modern, perhaps nineteenth century. The binding consists of wooden boards, which taper slightly, being thinner near the spine, and are covered in dark-stained sheepskin with a fine-grained finish. It has been suggested that a similar finish is to be seen on the bindings of various books acquired from the monastery of Mar Saba near Jerusalem by Lord Curzon and others, now in the British Library. There is no sign of the raised headcaps characteristic of Byzantine bindings. A small button on the front board near the fore-edge is matched by a hole in the back board, from which a thread was presumably attached to keep the book closed (typical late Byzantine bindings had two clasps). Each board has a parchment pastedown, consisting of a leaf taken from canon tables, i.e. a kind of concordance of the Gospels. The rather primitive decoration in blue, green and yellow is faded. These leaves may date from the thirteenth century, but the script is impossible to date accurately.

Four leaves (ff. 21, 57, 64, 81), all now detached, are illuminated with full-page portraits, presumably intended to represent the Evangelists. Some of the colors look strangely modern, e.g. the pale blue of the decorative border on f. 21, and the green of a similar border on f. 58. Neither Heiberg nor Papadopoulos-Kerameus in his description refers to them, so they must be relatively recent, presumably the result of a misguided attempt around the time of the dissolution of the Metochion to embellish the manuscript so as to enhance its value in the eyes of a prospective purchaser. The pictures have been painted over both upper and lower scripts. All four leaves are listed by Heiberg (1915, pp. lxxxvi-lxxvii) as containing text by Archimedes, and on f. 21 it is possible to see traces of a liturgical instruction in red ink showing through the gold background of the portrait.