Printing Leibniz's Calculus: Dating and Numbering the Editions of the Nova Methodus pro Maximis et Minimis (October 1684)

The Library ◽  
2021 ◽  
Vol 22 (2) ◽  
pp. 177-196
Author(s):  
Samuel V Lemley
Keyword(s):  
Seventeenth Century ◽  
Scientific Journal ◽  
Infinitesimal Calculus ◽  
Textual History ◽  
Multiple Copies ◽  
History Of ◽  
Printing History

Abstract The textual history of the first work on infinitesimal calculus and differentiation in print—Gottfried Wilhelm Leibniz’s ‘Nova methodus pro maximis et minimis …’ in the October 1684 instalment of the Leipzig scientific journal Acta Eruditorum—remains unstudied. Consequent to this inattention, extant copies of Leibniz’s article have been assigned to a single edition and a single press, despite evidence of substantive variation among them. This article examines the typographic and bibliographical evidence across multiple copies of the October 1684 instalment of the Acta to demonstrate that these extant copies in fact represent three separate editions printed on multiple presses over many years. This evidence, in turn, casts new light on both the complex printing history of the Acta Eruditorum in its first decade of publication (1682–93) and the distribution of learned periodicals in the seventeenth century.

The Indivisibles of the Continuum

2020 ◽  
pp. 104-122
Author(s):  
Douglas M. Jesseph
Keyword(s):  
Seventeenth Century ◽  
Internal Structure ◽  
Original Formulation ◽  
Infinitesimal Calculus ◽  
History Of ◽  
John Wallis ◽  
The Continuum

This chapter considers some significant developments in seventeenth-century mathematics which are part of the pre-history of the infinitesimal calculus. In particular, I examine the “method of indivisibles” proposed by Bonaventura Cavalieri and various developments of this method by Evangelista Torricelli, Gilles Personne de Roberval, and John Wallis. From the beginning, the method of indivisibles faced objections that aimed to show that it was either conceptually ill-founded (in supposing that the continuum could be composed of dimensionless points) or that its application would lead to error. I show that Cavalieri’s original formulation of the method attempted to sidestep the question of whether a continuous magnitude could be composed of indivisibles, while Torricelli proposed to avoid paradox by taking indivisibles to have both non-zero (yet infinitesimal) magnitude and internal structure. In contrast, Roberval and Wallis showed significantly less interest in addressing foundational issues and were content to maintain that the method could (at least in principle) be reduced to Archimedean exhaustion techniques.

Manuscript Circulation

2021 ◽  
pp. 41-68
Author(s):  
Joseph Hone
Keyword(s):  
Seventeenth Century ◽  
Political Factors ◽  
The Third ◽  
Textual History ◽  
History Of ◽  
Scribal Publication ◽  
Unknown Manuscript

This chapter challenges enduring assumptions about Pope’s early uses of scribal publication. Drawing on a wealth of famous and hitherto overlooked or unknown manuscript sources, it reconstructs the early circulation of Pope’s poems. The chapter explores the methods by which Pope’s fair copy holographs circulated among select readers and, in the second section, examine important differences between the manuscript and printed texts of his poems. The third section traces the distribution of his early poems in contemporary manuscript miscellanies. Pope’s earliest manuscript readers, it argues, viewed him as the latest addition to a grand tradition of seventeenth-century royalist poetry. The last section of the chapter investigates what remains of Pope’s juvenile epic, Alcander, Prince of Rhodes. Tracing the textual history of the Alcander manuscript from its origins in 1701 to its destruction in 1717, it argues that the poem’s non-appearance in print was probably due to political factors rather than literary ones.

scholarly journals The Paradoxes of Preaching in Print: Seeing and Believing in the Sermons of Jacques Abbadie

2016 ◽  
Vol 16 (1) ◽  
pp. 87-105
Author(s):  
Ruth Whelan
Keyword(s):  
Seventeenth Century ◽  
The Other ◽  
Social Connections ◽  
History Of ◽  
Printing History ◽  
Reformed Churches ◽  
The One ◽  
Theoretical Reflection

The boom in printed sermons in French in the latter half of the seventeenth-century is usually attributed, on the one hand, to the popularity of pulpit eloquence and, on the other, to the piety of both preacher and faithful. However, this study of the rhetorical organisation, imagery, and printing history of the sermons of Jacques Abbadie points to a more ambiguous explanation for the boom. Although the French Reformed Churches counselled their pastors against the pursuit of eloquence in their preaching, Abbadie made a display of it, and engaged in theoretical reflection to justify his practice. According to him, pulpit eloquence promotes receptivity in the faithful; but, with hindsight, it is clear that it also promotes the preacher. Publishing eloquent sermons publicised the hermeneutical and oratorical gifts of the preacher; the epistle dedicatory advertised his social connections; thus the printed sermon was also a strategy for advancing the career of the preacher.

Dating Milton's History of Britain

1993 ◽  
Vol 36 (4) ◽  
pp. 929-943 ◽  
Author(s):  
Austin Woolrych
Keyword(s):  
Seventeenth Century ◽  
Close Association ◽  
Civil Liberty ◽  
Divine Providence ◽  
Classical Approach ◽  
National History ◽  
Historical Scholarship ◽  
Textual History ◽  
History Of ◽  
Modern Form

When I had the pleasure of reviewing Nicholas von Maltzahn's study of Milton's History of Britain, I had nothing but praise for the scholarship he brought to the whole intellectual background of the work, and for his judicious placing of it in the Miltonic canon. His book gives an excellent account of the state of British historiography in the first half of the seventeenth century, and shows how Milton's essentially humanist and literary conception of what a history should be, and his exclusive interest in narrative sources, made him already out of date in his method at a time when Spelman and Selden were pioneering a recognizably modern form of historical scholarship. He carefully traces the development of Milton's ambition to write a great national history, explaining why his first conception of a verse epic, singing the heroic past, gave way to that of a lofty prose narrative that would culminate in a celebration of God's presence with his elect nation in the struggle for religious and civil liberty in his own time. He deals fully and learnedly with the influences upon the style and content of the History, from Sallust (Milton's favourite exemplar) and Tacítus through Bacon (possibly) to the preachers of the Fast Sermons before the Long Parliament. He is illuminating about the close association in Milton's mind between eloquence and virtue, and about the ways in which his beliefs about the operation of divine providence modified his predominantly classical approach to the writing of history. He is thoroughly informative about the textual history of the work, and especially about the fragment published in 1681 as Mr John Miltons Character of the Long Parliament, whose editor he convincingly identifies as the arch-Tory Roger L'Estrange.

The Art of Chinese Philosophy

2020 ◽  
Author(s):  
Paul Goldin
Keyword(s):  
Chinese Philosophy ◽  
Philosophical Tradition ◽  
Current Form ◽  
Han Feizi ◽  
Textual History ◽  
Classical Chinese ◽  
History Of ◽  
Crucial Characteristic ◽  
The Way

This book provides an unmatched introduction to eight of the most important works of classical Chinese philosophy—the Analects of Confucius, Mozi, Mencius, Laozi, Zhuangzi, Sunzi, Xunzi, and Han Feizi. The book places these works in rich context that explains the origin and meaning of their compelling ideas. Because none of these classics was written in its current form by the author to whom it is attributed, the book begins by asking, “What are we reading?” and showing that understanding the textual history of the works enriches our appreciation of them. A chapter is devoted to each of the eight works, and the chapters are organized into three sections: “Philosophy of Heaven,” which looks at how the Analects, Mozi, and Mencius discuss, often skeptically, Heaven (tian) as a source of philosophical values; “Philosophy of the Way,” which addresses how Laozi, Zhuangzi, and Sunzi introduce the new concept of the Way (dao) to transcend the older paradigms; and “Two Titans at the End of an Age,” which examines how Xunzi and Han Feizi adapt the best ideas of the earlier thinkers for a coming imperial age. In addition, the book presents explanations of the protean and frequently misunderstood concept of qi—and of a crucial characteristic of Chinese philosophy, nondeductive reasoning. The result is an invaluable account of an endlessly fascinating and influential philosophical tradition.

Muscovy and the Tatars

2020 ◽  
Vol 54 (4) ◽  
pp. 403-431
Author(s):  
Bulat R. Rakhimzianov
Keyword(s):  
Seventeenth Century ◽  
Social Institutions ◽  
The Political ◽  
East European ◽  
Central Eurasia ◽  
History Of ◽  
Mutual Relations ◽  
Forest Line ◽  
The Relationship

Abstract This article explores relations between Muscovy and the so-called Later Golden Horde successor states that existed during the fifteenth and sixteenth centuries on the territory of Desht-i Qipchaq (the Qipchaq Steppe, a part of the East European steppe bounded roughly by the Oskol and Tobol rivers, the steppe-forest line, and the Caspian and Aral Seas). As a part of, and later a successor to, the Juchid ulus (also known as the Golden Horde), Muscovy adopted a number of its political and social institutions. The most crucial events in the almost six-century-long history of relations between Muscovy and the Tatars (13–18th centuries) were the Mongol invasion of the Northern, Eastern and parts of the Southern Rus’ principalities between 1237 and 1241, and the Muscovite annexation of the Kazan and Astrakhan khanates between 1552 and 1556. According to the model proposed here, the Tatars began as the dominant partner in these mutual relations; however, from the beginning of the seventeenth century this role was gradually inverted. Indicators of a change in the relationship between the Muscovite grand principality and the Golden Horde can be found in the diplomatic contacts between Muscovy and the Tatar khanates. The main goal of the article is to reveal the changing position of Muscovy within the system of the Later Golden Horde successor states. An additional goal is to revisit the role of the Tatar khanates in the political history of Central Eurasia in the fifteenth and sixteenth centuries.

Drifting Through a Planetary System

2018 ◽  
Author(s):  
Karel Schrijver
Keyword(s):  
Seventeenth Century ◽  
Solar System ◽  
Virtual Worlds ◽  
Planetary System ◽  
System P ◽  
History Of ◽  
Or Team ◽  
Water Contents

This chapter describes how the first found exoplanets presented puzzles: they orbited where they should not have formed or where they could not have survived the death of their stars. The Solar System had its own puzzles to add: Mars is smaller than expected, while Venus, Earth, and Mars had more water—at least at one time—than could be understood. This chapter shows how astronomers worked through the combination of these puzzles: now we appreciate that planets can change their orbits, scatter water-bearing asteroids about, steal material from growing planets, or team up with other planets to stabilize their future. The special history of Jupiter and Saturn as a pair bringing both destruction and water to Earth emerged from the study of seventeenth-century resonant clocks, from the water contents of asteroids, and from experiments with supercomputers imposing the laws of physics on virtual worlds.

Hymnody and Liturgy

2019 ◽  
pp. 491-506
Author(s):  
Jonathan Hehn
Keyword(s):  
Nineteenth Century ◽  
Seventeenth Century ◽  
Sixteenth Century ◽  
North American ◽  
John Calvin ◽  
Church Of Scotland ◽  
Metrical Psalmody ◽  
History Of ◽  
The Church

This chapter outlines the history of Presbyterian worship practice from the sixteenth century to the present, with a focus on North American Presbyterians. Tracing both their hymnody and their liturgy ultimately to John Calvin, Presbyterian communions have a distinct heritage of worship inherited from the Church of Scotland via seventeenth-century Puritans. Long marked by metrical psalmody and guided by the Westminster Directory, Presbyterian worship underwent substantial changes in the nineteenth century. Evangelical and liturgical movements led Presbyterians away from a Puritan visual aesthetic, into the use of nonscriptural hymnody, and toward a recovery of liturgical books. Mainline North American and Scottish Presbyterians solidified these trends in the twentieth and twenty-first centuries; however, conservative North American denominations and some other denominations globally continue to rely heavily on the use of a worship directory and metrical psalmody.

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