Atlantis Online

Science & Technology => History of Science => Topic started by: Bianca on October 14, 2008, 10:12:07 pm

Title: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:12:07 pm

                                              "Abraham, Planter of Mathematics":

                          Histories of Mathematics and Astrology in Early Modern Europe

Nicholas Popper

Princeton University

Francis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created devoted to "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.

The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical."

He continued:

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:14:14 pm

"And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the

Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the

Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts,

or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their

Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings,

their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them,

and all other events concerning learning, throughout the ages of the world; I may truly affirme to be


Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:15:42 pm

Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.

Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3

The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras and Euclid, who were considered philosophers, or from useful practitioners such as Archimedes. The term itself was a source of unending confusion. A mathematician in Aristotle's time, as later generations acknowledged, did geometry and arithmetic; but, by late antiquity, Augustine and Jerome could complain that nativity-readers were vulgarly called mathematici. This confusion and distrust spread in turn to later historical understandings of [End Page 89] mathematics, and justifies considering the Renaissance histories of magic, mathematics, astrology, and astronomy, as deeply interwoven.4

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:16:53 pm

Renaissance scholars devoted serious attention to delineating the various kinds of mathematics. To help distinguish the licit from illicit, the question of origins was given a new priority in the years leading up to 1500. The debate originated with Pico della Mirandola's considerations of the orthodoxy of astrology, that most controversial of mathematical arts. Against the backdrop of a late Quattrocentro Italy bursting with astrological prediction, Pico set the grounds for debate in two considerations of the history of magic.5 The first, his Apologia, defended a rigorously narrow range of pious magic. This tract answered the papal condemnation of twelve of his famous 900 theses.6 In defense, he wrote, "I put forward magical theorems, in which I show Magic to be twofold. One side is supported by the work and authority of demons, and consists of things, by my faith, execrable and portentous; the other is nothing other, when it is well explored, than the absolute consummation of natural philosophy."7 Pico went on to claim that natural magic was necessary for faith, since it alone allowed one to distinguish miracles from simple extraordinary events. Pico did not, however, offer much support for modern practitioners of the magical arts. With few caveats, he defended the thesis that, "All the magic, [End Page 90] which is in use amongst the moderns, and which the Church has rightly banished, has no firmness, nor truth, nor support, because it is manipulated by the first enemy of truth."8 In defining contemporary magic as diabolic, Pico suggested that a legitimate natural magic had been corrupted, lost, or, he suggested, enclosed within the ancient Jewish tradition of cabala—orally transmitted and secret wisdom—that Pico firmly supported and to which he claimed unique access. Pico's dismissals of modern astrology enabled him to advertise himself as the lone point of entry to this alternative tradition that would lead to the recovery of an unimaginably potent ancient knowledge.

Pico did not construct a thorough account of the fall of magic in his Apologia, but he did towards the end of his life in his Twelve Books Against Divinatory Astrology. Unpublished in Pico's lifetime, this tract was compiled from his remaining manuscripts and published in 1496 under the close supervision of his nephew, Gianfrancesco. This younger scholar was notoriously unsympathetic to the astrological arts and the publication cemented the family anti-astrological reputation by comprehensively critiquing the philosophical, theological, and rational grounds for astrological divination.9 In the Twelfth Book, the elder Pico dismantled the historical data with which proponents of astrology supported their claims. Two of his points were particularly effective. According to Cicero, the Chaldean astrologers claimed to found their art on 470,000 years of observation. Since this claim set the beginnings of observation roughly 466,000 years before God created the universe, Pico noted, it was extremely unlikely.10 Following Ptolemy, the greatest ancient authority on both astronomy and astrology, he instead allotted relatively modern origins to astrology, an effective means of diminishing its legitimacy. Second, Pico argued that astrology's Chaldean origins did not indicate venerable antiquity. Rather the birth of astrology formed a significant part of Babylon's notorious corruption of true religion.11 Pico's devastating exposé grounded astrological criticism for the next century. [End Page 91]

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:18:01 pm

Pico's critical genealogy of Chaldean magic was not universally accepted. In the last years of the fifteenth century, two substantial works challenged Pico's claims. The first came from Polydore Vergil. An arch-humanist, Vergil argued with Erasmus over which of them had invented the modern genre of collections of sayings, and wrote a hefty history of England that discredited Geoffrey of Monmouth.12 In his 1499 De inventoribus rerum, Vergil devoted the eighteenth chapter of the first book to the origin of mathematics. He began with the proposition, expressed most famously by Proclus, that the Egyptians were the first to practice mathematics. Vergil, however, did not subscribe to this theory. Instead, he turned to the first-century Jewish general and historian, Flavius Josephus.13

According to Josephus, Adam received all knowledge available to man, wisdom he taught his son Seth. Seth's progeny, Josephus wrote,

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:20:06 pm

discovered the science of heavenly bodies and their orderly array. Moreover, to prevent their

discoveries from being lost to mankind and perishing before they became known—Adam having

predicted a destruction of the universe, at one time by a violent fire and at another by a mighty

deluge of water—they erected two pillars, one of brick and the other of stone, and inscribed

these discoveries on both; so that, if the pillar of brick disappeared at the deluge, that of

stone would remain to teach men what was graven thereon and to inform them that they had

also erected one of brick.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:21:04 pm

"It exists to this day," Josephus claimed, "in the land of Seiris."14 Vergil held Josephus in the utmost respect, and he first referred to this passage to prove that the Hebrews had invented letters, despite Greek and Latin claims to the contrary. He then used it to prove the Hebraic origins of mathematics, and finally to trace the origins of astrology. Vergil also followed Josephus in his postdiluvian histories, claiming that the mathematical arts were [End Page 92] recovered in Assyria, and that the Jewish Patriarch Abraham, an Assyrian, transported them to Egypt 430 years later. Assuming that the "science of heavenly bodies" required mathematics, Vergil yoked the history of star-gazing to the history of mathematics, and installed astrology within a sacred lineage opposed to Pico's diabolic genealogy.15

Pico too had cited Josephus's assertion that Abraham disseminated knowledge in Egypt. But for Pico, this learning amounted only to the mathematical observation of the heavens necessary to formulate a divine calendar; a form of licit, human knowledge similar to the interpretations of nature necessary for sailors, farmers, and physicians. Indeed, Pico claimed, idolatry and astrology had received a nefarious twin birth when the Chaldeans overextended this science, confusing celestial objects with divine entities. Both Pico and Vergil accepted astronomy—and therefore mathematics—as a practice of the ancient Hebrews, but Pico strenuously insisted that all arts that attributed divine agency to natural objects were corruptions of this accepted, Hebraic knowledge. His critique pursued a reformation of natural, non-revealed knowledge.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:21:59 pm

Vergil launched an extremely cautious challenge: he stated that astrology was extremely venerable, not revealed, and expressed doubts regarding its utility.16 The other response to Pico lacked any moderation. It came from another individual of immaculate humanist pedigree and possessed of a firm respect for and constant attention to Josephus. However, the Dominican Giovanni Nanni, otherwise known as Annius of Viterbo, was not possessed of a scrupulous moral fiber. Rather, he was blessed with a fanatical conviction that the ancient Romans had derived from Etruscan stock, a belief he bulwarked through a series of forgeries and planted archaeological finds.17 [End Page 93]

Annius believed that the ancient Greeks had been inveterate liars, given to taking credit for arts and practices they did not invent, and guilty of corrupting arts as they inherited them. To uncover their lies, he sketched genealogies of all peoples from the Creation onward, focusing on the aftermath of the Flood. Within these he traced the histories of various arts, showing that the sciences that the Greeks claimed to have pioneered had actually been stolen from Chaldeans, Phoenicians, Egyptians, Italians, Franks, and Jews. Annius concocted these claims in the form of commentaries on a set of ancient documents that he allegedly discovered, publishing the entire package in 1498 as Vetustissimi Auctores. . . . Though the texts were denounced as shams within a decade of their publication, for the next century and more scholars treated them as providing legitimate insight into the ancient world.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:22:57 pm

The prize piece amongst Annius's forgeries was the lost annalistic work of Berosus. The authentic Berosus, a Chaldean priest of the late fourth century BCE, was known largely via fragments quoted in Josephus. The Annian Berosus gave a complete history of the pre-Greek world, rife with proof that the Chaldeans had been notable practitioners of astrology and mathematics well before the flood. Annius made Berosus begin his first book: "Before the famous destruction of the waters in which the entire world perished, many generations went past, which we Chaldeans faithfully preserved."18 The source, as most readers would have immediately grasped, was the Pillars of Seth. Annius granted them expansive significance: "Therefore there were letters in use, and the arts of smelting, and brickwork, and prophesying, one thousand years and more before the inundation of the earth."19 But Annius was not content merely to note that such knowledge had been available at that time. Instead, he showed that the Chaldeans had absorbed this knowledge in its very first stages:

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:24:11 pm

But that letters and disciplines began and were disseminated by their first founder Adam, is proven

not only by faith alone, but also from the history of peoples and the tradition of the Chaldeans, which

asserts that they themselves knew astronomy and letters 3634 years before the monarchy of

Alexander . . . therefore [End Page 94] the conjecture and argument are firm, that Enoch received

letters from Seth the first son of Adam, in whose time, Theologians assert, letters and disciplines were

infused into Adam, and in which same time the Chaldeans affirm themselves to have grasped letters and


Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:25:10 pm

Annius thus dated the origins of Chaldean learning to around 4000 BC; within the first generation of humankind. The Chaldeans and the Patriarchs developed wisdom at the same moment, from the same fount. Indeed, the transparent implication was that Seth and Enoch developed these arts because they were themselves Chaldeans.

Annius's Berosus provided another source, alongside Moses, for the history of early time, but one that overturned the traditional theological status of Chaldeans. But this conflict with scripture did not discredit the text. While for Pico, Chaldean origins had been an incontrovertible demonstration of astrology's illicitness, Annius's forged genealogies made the Chaldeans entirely orthodox, an integral and esteemed part of the scriptural genealogy of knowledge, and Annius's Berosus presented himself as the mouthpiece of what Walter Stephens has called the "pious Chaldean." The Annian Berosus described the Chaldeans as God's first chosen people.21 And the Hebrews inherited and preserved astrology, a pure, original and divine Chaldean practice.

Pico's initial argument had relied on a particular vision of the early Assyrian empire and of Assyrian culture, and debate regarding the propriety of astrological knowledge was framed by discussion of this historical context. Scholars either approved of or denounced astrological arts by locating their origins before or after the Chaldeans abandoned true religion. The very tool that Pico used to criticize and condemn astrology, then, could be recalibrated, given a slightly different history in order to support it. Moreover, the history could also be adjusted to condemn any range of arts: one could further constrict Pico's range of acceptable mathematics by dating [End Page 95] the origins of any mathematical art to after the Chaldean lapse. While Pico had fixed the site of the debate, its terms remained plastic.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:28:37 pm

Annius provided a powerful genealogical sanction for astrology by evoking a world history that rubbed uncomfortably against the conventional historical narrative derived from scripture. Like those Neoplatonic and Neohermetic scholars who argued for their sources' legitimacy by claiming that all peoples, not just Israel, had received some divine revelation, Annius's vision of history potently suggested that Moses's books were not the only creditable sources for deep ancient history. And Annius's bookish solution, in some ways, hewed more closely to theological orthodoxy then the cabalist tradition glorified by Pico. Pico's vision described a shadowy group of initiates possessing secret, oral knowledge—a vision that displaced the Papacy from the center of the history of learning and described revealed knowledge as fundamentally unwritten. Annius's version, by contrast, rooted the lineage of divine learning in the production and custody of texts and monuments, and granted a continuous, documented history to the Church from the 4000 BC to his present. Perhaps for countering Pico's challenge, Pope Alexander VI appointed Annius Maestro del Sacro Palazzo, or official papal theologian.22

Still, scholars found Annius's claims unsettling, and over the course of the sixteenth century, more cautious commentators—often Protestant and Northern European—reclaimed the infallibility of scripture as a historical source. Rather than turning directly to the Bible, however, they used Josephus to secure the mathematical arts' linkage to the scriptural genealogy.23

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:30:09 pm

Vergil's fragmentary Josephan history met Annius's strident and expansive version in Peter Ramus's 1569 Scholae Mathematicae. From the 1540s until his murder in the St. Bartholomew's Day Massacre, Ramus spearheaded a movement to reform the curriculum of Parisian universities.24 His myriad publications included textbooks on geometry and mathematics, [End Page 96] and in his influential 1569 Scholae Mathematicae, Ramus presented an exhaustive vision of the history of mathematics. As he explained, "Aristotle judged the arts to be eternal, as the world is, but that just as stars rise and set, the arts sometimes are excited and flourish, and at other times are debased and condemned. This was the great verdict of that great philosopher: that the arts deal with eternal and immutable things; but that the knowledge of them among men is not eternal."25 Ramus's history covered more ground than his predecessors, including the entire sweep of history from creation to his present, and he incorporated all mathematical arts, from philosophy to hydraulics.

The revolutions in the fortunes of mathematics, Ramus claimed, could be analyzed by modifying the exegetical theory of the Four Monarchies for periods of mathematics. The first was the Chaldean period, lasting from Adam to Abraham. Ramus needed only the Pillars as evidence. The Abrahamic diffusion inaugurated the second era, but Ramus made clear that Abraham was hardly alone in his divine knowledge of mathematics: Diodorus Siculus, (pseudo-)Berosus, Pliny, and Cicero showed that the ancient world had recognized a general Chaldean mastery in the discipline. For Ramus this did not substantiate a uniform condemnation. Overzealous deployment of these arts was troublesome, but the arts themselves were not.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:31:05 pm

The Egyptian period that followed, Ramus noted, had witnessed increased sophistication of mathematical knowledge. Ancient Egyptians used mathematics for commercial and mercantile purposes, and for surveying flooded lands. Thales of Miletus transported mathematics from the Egyptians to the Greeks, inaugurating the third age. The final age was emerging in Ramus's time, a rehabilitation of mathematical knowledge similar to the Reformation.

Ramus, Vergil, and other humanists such as Joannes Stadius, Heinrich Rantzau, and Matthew Dresserus agreed on a history of mathematics that traced its origins to the Hebrew Fathers in ancient Assyria.26 This polemic [End Page 97] emerged in England in the last two decades of Elizabeth I's reign, when Bacon was just beginning his career in London. The orthodoxy and utility of mathematics were heavily debated in London at this time, and the issue of the origins of mathematics too faced close scrutiny.

London was a thriving metropolis, flooded with continental texts, and if Bacon did not encounter the history of mathematics from European scholars, local texts too would have offered him cogent histories of mathematics and astrology. The discussion in England surfaced early in 1583, when Richard Harvey's famous apocalyptic prognostication An Astrological Discourse appeared in London. This mathematical and astrological prophecy forecast massive upheaval and turbulence beginning that very spring. The disorder, Harvey claimed, would swell, culminating with a thunderous crescendo in 1588, after which the world would be profoundly and irrevocably altered.27

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:32:20 pm

Henry Howard, Earl of Northampton, and no friend to the Harvey family, adapted Pico's criticism later in 1583 in his weighty and learned rebuttal, A defensative against the poyson of supposed prophecies. Unlike Pico, who wanted to support true magic while condemning its corruptions, Howard brooked no art tinged by a hint of the magical. Still, Howard's criticism drew liberally from the criticism Pico had developed almost a century before. Relying heavily on scriptural condemnations of magical arts, Howard followed Pico in defending the possibility of natural philosophical knowledge that did not encroach on the domain of God. Using examples that astrology's defenders used to support the viability of their discipline, he distinguished forms of licit natural knowledge: "We reade not, that our Saviour Christ condemned those, that deemed of the weather that should follow by the rednes of the skie; nor those that gathered upon the fig trees putting forth her leaves, that Summer was at hand: for that the causes and [End Page 98] effects were tyed together, and combine in so streight a lincke of consequence, as either swerved not at all, or very seldome, from the course which kind had limitted. He rather used them as presidents of lawfull gessing & divining, by the proper causes of al things." Mariners too observed the world in an acceptable fashion. But this neither constituted prophecy, nor relied on mathematics.28

Howard maligned astrology's Chaldean origins with the standard tools of genealogical argument:

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:33:41 pm

The Latines give themselves to follow Greece. The Greeks derive theyr knowledge from Arabia, Arabia

from Egypt and Chaldea: whereas Egypt and Chaldea, by the doctrine of our greatest Rabby Ptolome,

as I sayde before, are cast off and forsaken for theyr errours. Beside, the Chaldeis were a wicked and

ungodlie kinde of men, addicted wholie to the worshipping of false gods, and studdie of unlawfull artes:

in which respect, we should detest them rather as the teachers of abuse then vouch theyr credite as a

maske of false divinitie. Indeed, they gave themselves to practise much about the Mathematicalles,

which make not any man more wise, sayth Aristotle: but more rype and pregnaunt in the skyll of


Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:34:46 pm

And yet Howard finished this section at pains to distinguish between the acceptable star-gazing of the ancients and the horrific pollutions of the Chaldeans: "We doubt not, but the Patriarches and holy Fathers of the covenant looked uppe to heaven, and praysed GOD in all his mightie workes: but that any one of them presumed to divine of thinges invisible, by Planets which they sawe, cannot be prooved by the Scripture."29

Howard admitted that Abraham possessed some astronomical knowledge, but this was not astrological, nor a product of his Assyrian context. Rather, he developed this knowledge in spite of his surroundings. Those who felt otherwise, "forgette the rule of Plato: that in all countries and Clymates under heaven, which bring foorth greater store of badde men then good, so ofte as any one applies himselfe to better menes, and degsnerateth[sic] from the comon trade, he prooveth excellent."30 The Patriarch's relationship to the Chaldeans again provided the key to understanding astrology. [End Page 99]

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:35:53 pm

Richard Harvey's brother, Gabriel, responded by deploying the Josephan history.31 Gabriel Harvey never published a work regarding the genealogy of mathematics. Nevertheless his surviving notes in his copy of Joannes Thomas Freigius's 1583 world history Mosaicus accrued evidence for this lineage. Freigius was a prominent disciple of Ramus, and Harvey read him through a Ramist filter. While Freigius casually and infrequently mentioned expertise in many arts held by the ancients, Harvey meticulously annotated the passages in Freigius's narrative that fit a Josephan history. When Freigius, in a brief passage on notable individuals between Adam and Noah, included the story of Seth's ancestors, Harvey wrote, "The two famous Mathematical columns,"32 and at the bottom of the page, "The Two Astronomical columns, erected by the progeny of Seth."33 These notes show Harvey both conflating astronomy and mathematics, and introducing a general concern with the transmission of such knowledge. The margins of the text in Freigius's chapter on Abraham were especially fertile ground. Here Harvey wrote: "Abraham was the planter of Mathematics in Egypt, and from him came, not much later, all those mathematical and physical miracles. This was also the origin of almost all natural magic."34 On the next page Harvey noted that, "The arithmetic and astronomy of the Egyptians came from Abraham, a noble professor of the mathematical arts."35 Later, he made clear that Hermes Trismegistus's knowledge of mathematics was easily explained, since Hermes was a descendant of Abraham.36 Harvey filled out his history of mathematics by noting the invention of mathematical instruments: "The Radius, a very old instrument, most excellent and commodious of all geometric instruments. It is commonly called the Jacobs Staff, 'as if it was invented then by that sacred Patriarch.' See Ramus's Geometry, book 9. Doubtless it seemed necessary to add this mathematical [End Page 100] invention of Jacob's to the earlier mathematical inventions of his grandfather Abraham."37 Harvey thus followed Ramus in grafting the history of mathematics directly to the history of the Patriarchs while studying mathematical history alongside technical texts. In so doing, he found an orthodox and honored genealogy for the mathematical arts, salvaging the propriety of his brother's prognostication, and the dignity of his family reputation.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:36:56 pm

Harvey never published a response to Northampton, and concern with the origins of mathematics faded from print for the next two decades in England. It would surface without kindling much debate, for example, in Thomas Hood's 1588 inaugural speech as Mathematical Lecturer to the City of London.38 But in the years surrounding Elizabeth's death and James's accession, the debate flared up again. The clergyman John Chamber's 1601 A Treatise against Judiciall Astrologie expressed militant abhorrence for the astrologers, augurs and figure-flingers who brimmed in the Babylonian streets of late Tudor London. Chamber claimed that Adam and Seth had held mathematical knowledge. But this did not include astrology; that diabolic practice, he claimed, originated in the later Chaldean corruption of divine knowledge. He memorably described the astrologers as, "bastards, the sons of an hedge hore, their mother was an Hittitie," and registered deep alarm: "But that is Babylon, where Babylonicall superstitions are maintained or suffered." Chamber followed Pico in attributing orthodox astronomical knowledge to the Patriarchs, that was later corrupted into astrology by the Chaldeans.39

The godly Protestant soldier Sir Christopher Heydon responded in his 1603 A Defence of Iudiciall Astrology by strenuously insisting on the Adamic origins of astrology. He conceded that Chaldean corruptions had produced heretical and idolatrous arts such as augury, but insisted that true astrology, which proceeds from natural causes to natural effects, was a divine gift from God to Adam, and had been passed along in an unbroken chain since. In illustration, he included at the end of his treatise a "Chronological Index of Astronomers from Adam," which began with the genealogy [End Page 101] from Adam to Joseph, and extended to Tycho Brahe and other contemporaries.40

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:37:57 pm

Heydon's work prompted a defense from George Carleton, future chaplain to Prince Charles. Carleton classified astrology as part of magic, and attacked Heydon's chronology. Heydon, Carleton noted, had tried to hide suspect figures like Zoroaster and Hermes Trismegistus within the genealogy by placing them after the Hebrew Patriarchs, out of chronological order. Heydon's list was also dressed up with Joseph, Homer, and others for whom no evidence of astrological interest existed. Charleton traced a muscular anti-Josephan lineage: he wrote, "The first invention of Astrology, is by many learned men attributed to the divels," and its first disseminator was Zoroaster.41

Thus, by the 1605 appearance of the Advancement of Learning, there were two well-established, yet volatile interpretations of a single, modifiable chronology for the mathematical arts. While both sides agreed that some licit mathematical art could be traced from the time of Adam, astrology provoked bitter dissension. On the one hand, Pico and his followers rooted powerful criticisms in the historical and cultural conditions of astrology's perceived origins: that of idolatrous, Baal-worshiping Assyria. On the other hand, defenders posited Assyria as the setting in which astrology and related mathematical arts had flourished, nurtured by the pious learning of the Chaldeans. When this first flourishing gave way to idolatrous corruptions, the Jewish Patriarchs remained responsible for the maintenance of the discipline. The history of the mathematical arts was less barren and wanting than Bacon led his king to believe.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:39:43 pm

Bacon's proposal, despite his protestations, did not call for the creation of a radically new discipline. In claiming that such histories of the arts did not exist, Bacon may have been reacting more to the historical methodologies with which he was familiar than to the existing state of mathematical histories. For example Jean Bodin, whom Bacon certainly had read, devoted considerable but unsystematic attention in his 1566 Methodus ad facilem [End Page 102] historiarum cognitionem to describing the conditions of learning throughout world history. He wrote,

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:41:19 pm

Not only the virtues of our men are equal to those of the ancients but also the discipline. Literature

suffers changes of fortune. First the arts arise in some places through the practice and labor of

talented men, then they develop, later they flourish for a while at a fixed level, then languish in their

old age, and finally begin to die and are buried in a lasting oblivion by the eternal calamity of wars, or

because too great abundance (an evil much to be feared in these times, of course) brings satiety to

the frivolous, or because God inflicts just punishments upon those who direct useful knowledge to the

ruin of men. Although disciplines had gradually developed among the Greeks, so that they believed

these arts reached their peak, such a change came about afterward that Greece herself, to judge from

her present predicament, seems never to have existed.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:42:39 pm

He continued, "I omit how Egypt, India, and Ethiopia teemed with many philosophers, geometrists, and astrologers; how many well-known mathematicians were in Chaldea before Greece had any literature. I come back to our times in which, after a long eclipse of letters throughout almost the entire world, suddenly such a wealth of knowledge shone forth, such fertility of talents existed, as no age ever excelled."42 Bodin shared with Bacon and Ramus a cyclical vision of the history of knowledge; but he and Bacon did not map transmissions as Ramus did. [End Page 103]

Bodin dotted his text with "small memorials," and made no great plea for a history of the sciences. But other artes historicae did contain systematic proposals for, and examples of, the sort of history Bacon desired. As Donald R. Kelley has shown, the innovative fifth chapter of Christophe Milieu's 1551 De scribenda universitatis rerum historia outlined a historia litteraria, which began with a discussion of the Pillars of Seth and charted the position of learning in societies from the Pillars to Milieu's present.43 Equally detailed was Reinier Reineck's 1583 Methodus Legendi Cognoscendique Historiam, in which a section on the historia scholarum described the Pillars as a schoolboys' primer from the time of Enoch to the Flood.44 Reineck also admiringly described both Vergil's work and Caspar Peucer's 1572 De Divinatione as exemplary instances of this kind of history.45 Bacon's plea for a history of science was only a later example of late sixteenth-century proposals for a genre that some felt already existed. The self-proclaimed novelty of his proposal was either ill-informed or disingenuous.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:43:34 pm

Through the seventeenth century the Pillars continued to play a central role in histories that located the origins of mathematics in the deep ancient world. In England, for example, Sir Walter Ralegh relied heavily on them in his 1614 History of the World. Ralegh followed Pico, discussing the history of magic within the setting of its postdiluvian corruption, but like Annius treated many of the mathematical arts—including alchemy and astrology—as predating Chaldean corruption.46 John Wallis's 1649 inaugural oration as Savilian Professor of Geometry relied heavily on the Pillars as evidence for the presence of intricate knowledge of mathematics in the ancient world. For Wallis, the astrological knowledge of the Chaldeans, corrupt as it was, proved beyond a doubt the widespread diffusion of mathematical learning.47 [End Page 104]

The Pillars thus served as crucial evidence for mathematics in the ancient world, and a history of mathematics that began almost from the Fall. To topple the Pillars was to topple this vision, a feat achieved in 1722 by William Whiston, Newton's successor as Lucasian Professor of Mathematics. But the biblical antiquarian Whiston did not debunk the attribution of these Pillars to Seth to stake a claim regarding the history of mathematical learning. Rather, the Unitarian Whiston argued that second-century Jewish redactors had corrupted the true text of scripture by introducing Trinitarian fables. Whiston claimed that Josephus had been working with the authentic Scriptures—indeed, he thought, the Temple's copy of the Bible, which Josephus may have received directly from Titus. Whiston was thus forced to explain away any incongruities within Josephus's text, and he deemed the Pillars of Seth a "strange supposition," which needed to be dismissed.48 Josephus, Whiston claimed, was simply uninformed about Egyptian history, its pharaohs and obelisks, when he attributed the pillars to Seth instead of their rightful builder, the Pharoah "Seth-os, or Sethosis, or Sesotris the Great."49 While still dating the Pillars to almost 1200 BC—easily predating the high cultures of Greece and Rome—Whiston undermined the bedrock evidence for an Annian history of science.50

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:44:30 pm

This history of histories illuminates contemporary understandings of mathematics, astrology, and astronomy from the late fifteenth to seventeenthcenturies. Consistent in all of the authors is the understanding that mathematics had a long history. Some virtue always obtained in learning Euclid or Ptolemy; nobody questioned the utility of these arts in agriculture, husbandry, navigation, and chronology. But though none of these scholars condemned all forms of sky-gazing, all agreed that they could be corrupted. The question was where and when corruptions were introduced. For individual [End Page 105] authors real differences existed between astrology and astronomy, even if there was no consensus regarding their boundaries. The issue was whether astrology properly belonged with the constellation of orthodox studies, or with the idolatrous divinatory arts of the Chaldeans.

Further, the debate was conducted entirely within ecclesiastical history. The history of mathematics was inseparable from the history of the church and the history of worship. The orthodoxy of various arts was proven neither by showing that they did not abrogate divine authority, nor by simply showing their venerable antiquity. The reputation of the communities that produced these specialized arts licensed or condemned their adoption, and their genealogies argued for or against their orthodoxy. Chamber was not being hysterical when he depicted London as a second Babylon; to him, the city swarmed with an idolatrous lay priest caste performing rites and offending the divine will, exactly as Babylon had under the sway of the erring Chaldeans. A practicing community of Hebraic astrologers in the ancient world, as described by Josephus, served the antithetical purpose. Theological and historical debate provided the terrain for justifying mathematical and astronomical activities.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:45:26 pm

Despite Bacon's claims, there was a healthy history of science in the sixteenth century. Scholars, admittedly, drew up a history of mathematics quite at odds with a progressive history of science. Their history of science was a degeneration narrative, a problem of recovery instead of invention, of cleansing rather than expansion, with a Golden Age behind rather than ahead. But it was a history, nevertheless, and one that fits neatly with the claims of Vesalius, Scaliger, and others who depicted their innovations as reformations of ancient disciplines. These scholars conjured an ancient world teeming with mathematical practice, directing them towards various forms of lost or obscured expertise.51 The narrative of their history of science may not have resembled Kepler's, but by directing attention to the ancient authorization for mathematics, they contributed to the process of legitimizing mathematical knowledge.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:46:31 pm


I would like to thank Lauren Kassell, Robert Goulding, James Byrne, Darrel Rutkin, Amy Haley, Anthony Grafton, Simon Schaffer, and Walter Stephens for their invaluable comments, suggestions and improvements. The paper was given in a slightly different form from the 2004 History of Science Society Meeting version at the 2004 Thomas Harriot Seminar, and I thank the participants of both for useful questions and suggestions.

1. Francis Bacon, The tvvoo bookes of Francis Bacon. Of the proficience and aduancement of learning, diuine and humane (London, 1605), Aa.1.r-Aa.4.v. The history of science literature on Bacon is immense. In this context see Paolo Rossi, Francis Bacon: From Magic to Science, trans. Sasha Rabinovitch (Chicago: University of Chicago Press, 1968); and Wilhelm Schmidt-Biggemann, Topica universalis: eine Modellgeschichte humanistischer und barocker Wissenschaft (Hamburg: Meiner, 1983), 212–25.

2. Bacon, Bb.3.v.

3. There are few studies devoted to the histories early modern scholars composed for various sciences. By far the most important is Nicholas Jardine's Birth of History and Philosophy of Science: Kepler's A Defence of Tycho against Ursus, with Essays on its Provenance and Significance (Cambridge: Cambridge University Press, 1984). Jardine focuses on Kepler, who was more central to the Scientific Revolution than any of the individuals in this article. Kepler's history was distinct in its discussion of, and commitment to, a history of technical advancement. But to attribute the origins of the history of science to his work, as Jardine does, requires an understanding of the discipline as fundamentally committed to a progressive narrative. See also Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution (Chicago: University of Chicago Press, 1995), 93–123; Anthony Grafton, "From Apotheosis to Analysis: Some Late Renaissance Histories of Classical Astronomy," in History and the Disciplines: The Reclassification of Knowledge in Early Modern Europe, ed. Donald R. Kelley (Rochester, N.Y.: University of Rochester Press, 1997), 261–76. D.P. Walker's, The Ancient Theology: Studies in Christian Platonism from the Fifteenth to the Eighteenth Century (London: Duckworth, 1972) is the classic work on the power of genealogies of knowledge in early modern Europe.

4. For classical and late antique attitudes towards the disciplines under consideration here, see esp. Fritz Graf, Magic in the Ancient World, trans. Franklin Philip (Cambridge: Harvard University Press, 1997), esp. 20–60. See also Jan N. Bremmer, "The Birth of the Term 'Magic'" in The Metamorphosis of Magic from Late Antiquity to the Early Modern Period, ed. Jan N. Bremmer and Jan R. Veenstra (Leuven: Peeters, 2002) 1–11 and Peter Brown, The Making of Late Antiquity (Cambridge: Harvard University Press, 1978), 19–26.

5. The classic studies of this context are Paola Zambelli (ed.), "Astrologi hallucinati": Stars and the End of the World in Luther's Time (Berlin: W. de Gruyter, 1986); and Ottavia Niccoli, Prophecy and People in Renaissance Italy, trans. Lydia G. Cochrane (Princeton: Princeton University Press, 1990).

6. See S.A. Farmer, Syncretism in the West: Pico's 900 theses (1486): The Evolution of Traditional, Religious, and Philosophical Systems: with Text, Translation, and Commentary (Phoenix: Medieval & Renaissance Texts & Studies, 1998).

7. Pico della Mirandola, Opera Omnia (Basel, 1601), 80: "Proposuimus & magica theoremata, in quibus duplicem esse Magiam significamus, quarum altera daemonum tota opere & authoritate constat, res medius fidius execranda & portentosa: altera nihil est aliud, cum bene exploratur, quam naturalis philosophiae absoluta consummatio." Recent work on Pico includes H. Darrel Rutkin, Astrology, Natural Philosophy and the History of Science, c. 1250–1700: Studies toward an Interpretation of Giovanni Pico della Mirandola's Disputationes adversus Astrologiam Divinatricem (Ph.D. Dissertation, Indiana University, 2002), esp. 230–467, with considered discussion of the various traditions of Pico scholarship; and Steven Vanden Broecke, The Limits of Influence: Pico, Louvain, and the Crisis of Renaissance Astrology (Leiden: Brill, 2003), 55–81.

8. Pico, 113. "Tota magia, quae in usu est apud modernos, & quam merito exterminat Ecclesia, nullam habet firmitatem, nullam veritatem, nullum firmamentum: quia pendet ex manu hostium primae veritatis, potestatum harum tenebrarum, quae tenebras falsitatis malae dispositis intellectibus offendunt."

9. See Anthony Grafton, Commerce with the Classics: Ancient Books and Renaissance Readers (Ann Arbor: University of Michigan Press, 1997), 93–134; and Rutkin, 338–43.

10. Pico, 483. 

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:47:36 pm

11. See books 11 and 12 of Pico della Mirandola's Disputationes adversus Astrologiam divinatricem, esp. 11.2 at 483. For Abraham's teaching, see 485.

12. For Vergil, see Denys Hay, Polydore Vergil: Renaissance Historian and Man of Letters (Oxford: Clarendon Press, 1952); Brian Copenhaver, "The Historiography of Discovery in the Renaissance: The Sources and Composition of Polydore Vergil's De inventoribus rerum, 1–111," Journal of the Warburg and Courtauld Institutes 41 (1978): 192–214; and Copenhaver's introduction to Polydore Vergil: On Discovery, ed. and trans. Brian P. Copenhaver (Cambridge: Harvard University Press, 2002) vi-xxx.

13. On Discovery, 147–49.

14. Flavius Josephus, Jewish Antiquities, trans. H. St. J. Thackeray (Cambridge, Mass.: Loeb Classical Library, 1930), I.ii.68–71. For Josephus, and his later reputation, see Josephus, the Bible, and History, ed. Louis H. Feldman and Gohei Hata (Detroit: Wayne State University Press, 1989).

15. See On Discovery 139–47. For the references in Josephus, see I.viii.166–68. For the medieval readings of Seth's Pillars, see Cora E. Lutz, "Remigius' Ideas on the Origin and the Classification of the Seven Liberal Arts," Medievalia et humanistica 10 (1956): 32–49.

16. It should be noted that Vergil expressed caveats about astrology despite his genealogy: "Such was the beginning of the art of astrology, which doubtless was devised simply to befuddle sound minds" (On Discovery, 143). This runs contrary to his enthusiasm for letters, mathematics, and other arts that shared its genealogy.

17. For Annius see Walter Stephens, "Berosus Chaldaeus: Counterfeit and Fictive Editors of the Early Sixteenth Century" (Ph.D. Dissertation, Cornell University, 1979); parts of which were integrated into his Giants in Those Days: Folklore, Ancient History, and Nationalism (Lincoln: University of Nebraska Press, 1989); and his "Livres de haulte gresse: Bibliographic Myth from Rabelais to Du Bartas," MLN 120.1 Supplement (January 2005): S60-S83. See also Anthony Grafton, Forgers and Critics: Creativity and Duplicity in Western Scholarship (Princeton: Princeton University Press, 1990).

18. I have used the 1552 Antwerp edition [Annius of Viterbo], Berosi sacerdotis Chaldaici, antiquitatum Italiae ac totius orbis libri quinque . . . (Antwerp, 1552), 41. "Ante aquarum cladem famosam qua universus periit orbis, multa praeterierunt saecula, quae a nostris Chaldaeis fideliter servata."

19. Annius, 45. "Erant igitur in usu litterae, & ars fusilis, & lateritia & vaticinia, mille annis & amplius ante inundationem terrarum."

20. Annius, 44. "Verum quod ab Adam primo condito coeperint literae & disciplinae infusae, non est ex [fide] tantum, sed etiam historia gentium & traditione Chaldaeorum qui se astronomiam & literas habuisse ante Alexandri monarchiam tribus millibus & sexcentis annis ac trigintaquator asserunt. . . . Quare coniectura & argumentum firmum est, ab ipso Atavo eius primo Adam eundem Enoch suscepisse literas & disciplinas, cuius tempore fuisse literas & disciplinas Adae infusas Theologi asserunt, & eodem tempore se cepisse literas & Astronomiam Chaldaei affirmant."

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:48:40 pm

21. Stephens, "Berosus Chaldaeus." The notion of the "pious Chaldaean" is explored in depth 57–135, while the Annian Berosus's portrayal of the piety of his sources is discussed from 136–208.

22. See Stephens, "Berosus Chaldaeus," 136–208 for Annian-focused discussion of the importance to early modern scholars of saving ancient historical texts preserved from obliteration, with special focus on the Pillars. Some of this section has been published in Stephens, "Livres de haulte gresse."

23. For the Neohermetic tradition, see Frances Yates, Giordano Bruno and the Hermetic Tradition (London: Routledge & Kegan Paul, 1964); for the Neoplatonic tradition see James Hankins, Plato in the Italian Renaissance, 2 vols. (Leiden: E.J. Brill, 1990).

24. For Ramus in general, see French Renaissance Studies, 1540–70, ed. Peter Sharratt (Edinburgh: Edinburgh University Press, 1976). For Ramus and the history of mathematics, see Reijer Hooykas, Humanisme, science et réforme: Pierre de la Ramée (1515–1572) (Leiden: E.J. Brill, 1958); and articles by Bruyère-Robinet, Vasoli, and Cifoletti in Revue des Sciences Philosophiques et Théologiques 70.1 (1986).

25. Peter Ramus, Scholae Mathematicarum, Libri Unus et Triginta (Basle, 1569), 1. "Aristoteles igitur 1.coeli & 1.meteor. artes aeternas, ut mundum, arbitratur, sed earum tanquam stellarum varios ortus & occasus esse, ut modo excitentur & floreant, modo jaceant & contemnantur. Haec magni philosophi magna prorsus sententia, artes sunt aeternarum & immutabilium rerum: at ipsarum apud homines notitia nequaquam est aeterna." Ramus is here extrapolating from Aristotle, The Complete Works of Aristotle: The Revised Oxford Translation (Princeton: Princeton University Press, 1984) [270b1], and [352b1–353a1], though Aristotle here is not referring to arts specifically, but to the vicissitudes of all phenomena in an eternal world.

26. See Joannes Stadius, Tabulae Bergenses aequabilis et adparentus motus Orbium Coelestium . . . (Cologne, 1560), 1–3; Heinrich Rantzau, Catalogus Imperatorum, Regum, ac Principium qui astrologicam artem amarunt . . . (Antwerp, 1580), esp. 19–24; Matthaeus Dresserus, Isagoges historicae pars prima . . . (Leipzig, 1593), 26–29.

27. For Howard see Linda Levy Peck, Northampton, Patronage and Policy at the Court of James I (London: Allen & Unwin, 1982); and her article on Northumberland in The Mental World of the Jacobean Court, ed. Linda Levy Peck (Cambridge: Cambridge University Press, 1991). For the astrological debates of the 1580s, see esp. Margaret Aston, "The Fiery Trigon Conjunction: an Elizabethan Astrological Prediction," Isis 61/2 (1970): 159–87; see also Walter B. Stone, "Shakespeare and the Sad Augurs," The Journal of English and Germanic Philology 52 (1953): 457–79; Don Cameron Allen, The Star-Crossed Renaissance: The Quarrel about Astrology and Its Influence in England (Durham, N.C., Duke University Press, 1941), 121–25; and Nicholas Popper, "The English Polydaedali: How Gabriel Harvey Read Late Tudor London," JHI 66 (2005): 351–81.

28. Henry Howard, A defensative against the poyson of supposed prophecies (London, 1583), G.iv.r-v.

29. Howard, O.i.v.

30. Howard, O.i.v-O.ii.r.

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:49:43 pm

31. For Gabriel Harvey, see Virginia Stern, Gabriel Harvey, His Life, Marginalia and Library (Oxford: The Clarendon Press, 1979); Anthony Grafton and Lisa Jardine, "'Studied for Action': How Gabriel Harvey Read His Livy," Past and Present 129 (Nov. 1990): 30–78.

32. Gabriel Harvey's copy of Joannes Thomas Freigius, Mosaicus: continens historiam ecclesiasticam . . . (Basle, 1583), 60. BL shelfmark C.60.f.4. "Duae famosae columnae Mathematicae."

33. Ibid., "Duae Columnae Astronomicae, a Sethi nepotibus excitatae."

34. Harvey's Freigius, 140. "Abrahamus, primus Mathematicarum plantator in Aegypto: Unde, nec ita multo post, tot Mathematica, et Physica Miracula. Hinc fere Magia omnis Naturalis."

35. Ibid., 141. "Aegiptiorum Arithmetica, et Astronomia, ab Abrahamo: Mathematicarum artium nobili professore."

36. Ibid., 158.

37. Harvey's Freigius, 166. "Radius, Instrumentum, Perantiquum, omnium Geometricorum Instrumentorum praestantissimus; vulgo Baculus Jacobi dicitur, tanquam a sancta patriarcha illo iam olim inventus sit. Ram. Geometriae lib.9. Nimirum hoc Jacobi, mathematicum inventum, superioribus avi Abrahami inventis Mathematicis addendum videbatur."

38. Thomas Hood, A Copie of the Speache: made by the Mathematicall Lecturer, unto the Worshipfull Companye of present (London, 1588), A.iiii.v-B.i.r.

39. John Chamber, A Treatise Against Iudicall Astrologie (London, 1601), 118, 121.

40. Christoper Heydon, A Defence of Iudiciall Astrology (Cambridge, 1603), Zzz.4.v

Title: Re: "Abraham, Planter of Mathematics"
Post by: Bianca on October 14, 2008, 10:51:09 pm

41. [George Carleton], AΣTPOΛOΓOMANIA: The Madnesse of ASTROLOGERS. Or an Examination of Sir Christopher Heydons Booke, Intituled A Defence of Iudiciarie Astrologie. Written nearly 20 yeares ago by G.C. (London, 1624), 56. Since there were multiple ancient figures identified with Zoroaster, it should be noted, both critics and proponents of astrology were able to claim one of them in support of their position. See Lauren Kassell's article in this volume.

42. Jean Bodin, Method for the Easy Comprehension of History, trans. Beatrice Reynolds (New York: Norton, 1969), 300. For the original, see Jean Bodin, Methodus, ad facilem historiarum cognitionem (Paris, 1566), 358–59: "Neque solum virtutes in nostris hominibus, sed etiam disciplinae pares, atque in veteribus extiterunt. est enim literarum sua quoque vicissitudo, ut primum quibusdam in locis ingeniosorum hominum experientia & labore artes oriantur, deinde incrementa suscipiant, post aliquantum in statu vigeant, tandem sua vetustate langueant, denique sensim emoriantur, & oblivione diuturna sepeliantur: vel bellorum diuturna calamitate: vel quod nimia copia (malum his temporibus valde metuendum) satietatem levissimo cuique afferre soleat: vel quod iustas Deus poenas expetit ab iis qui scientias salutares, in hominum perniciem convertunt. Nam cum disciplinae, apud Graecos sensim adolevissent, ut ad summum pervenisse crederentur, tanta mutatio postea secuta est, ut ne ipsa quidem Graecia ubi nunc est unquam extitisse videatur . . . Omitto quammultos philosophos, geometras, astrologos, peperit Aegyptus, India Aethiopia: quammulti apud Caldaeos nobiles mathematici ante fuerunt, quam ullae essent in Graecia literae: ad nostra tempora relabor, quibus multo postquam literae toto pene terrarum orbe conquierant, tantus subito scientiarum omnium splendor affulsit, tanta fertilitas extitit ingeniorum, ut nullis unquam aetatibus maior."

43. Christophe Milieu, De scribenda universitatis rerum historia (Basle, 1551). See Schmidt-Biggemann, 23–30; and Donald R. Kelley, "Writing Cultural History in Early Modern Europe: Christoph Milieu and His Project," Renaissance Quarterly 52.2 (1999): 342–65. Kelley also notes that Bacon seemed unaware of Milieu's work, though it had indeed addressed his precise concerns.

44. Reiner Reineck, Methodus Legendi Cognoscendique Historiam tam sacram tam profanam. . . . (Helmstadt, 1583), also including his oration on the dignity of mathematics. The section on the historia scholarum, is 22v-29v. For his description of the Pillars as a pedagogical tool, see within the Oratio, 36r-v.

45. Reineck, 28r.

46. Walter Ralegh, The History of the World (London, 1614), 1:199–212.

47. John Wallis, Geometriae Professoris Saviliani, Oratio Inauguralis in Auditorio Geometrico, Oxonii, habita . . . (Oxford, 1657). See b.3.r and passim. I thank Tony Mann for this reference. See also Stephens, "Livres de haulte gresse," for the continued resourcing of the Pillars through the eighteenth century.

48. William Whiston, An Essay Towards Restoring the True Text of the Old Testament; and for Vindicating the Citations made thence in the New Testament (London, 1722), clx. For Whiston, see James E. Force, William Whiston: Honest Newtonian (Cambridge: Cambridge University Press, 1985). For Whiston's biblical exegesis, and especially his study of ancient Egypt and the Near East, see John Gascoigne, "'The Wisdom of the Egyptians' and the Secularisation of History in the Age of Newton," in The Uses of Antiquity: The Scientific Revolution and the Classical Tradition, ed. Stephen Gaukroger (Dordrecht: Kluwer, 1991), 171–212.

49. Whiston; the quote is on cxxxix; his analysis is on clix-clx.

50. Others in the early eighteenth century dismissed the Pillars just as easily. For example, Vico consigned them to the "Museum of Credulity," though on the assumption that they had been attributed to Seth to exaggerate the ancient origins of the Chaldeans rather than on antiquarian criticism (see Giambattista Vico, The New Science, trans. David Marsh (London: Penguin, 2000), [49], p. 43).

51. For this point, see Anthony Grafton, Joseph Scaliger: A Study in the History of Classical Scholarship 2 vols. (Oxford: Clarendon Press, 1983–1993), 2: 253–62; and Dear, 116–19.