This exciting Greenvill Collins biography is about seventeenth century navigation, focusing for the first time on mathematics practised at sea. This monograph argues the Restoration kings’, Charles II and James II, promotion of cartography for both strategy and trade. It is aimed at the academic, cartographic and larger market of marine enthusiasts. Through shipwreck and Arctic marooning, and Dutch and Spanish charts, Collins evolved a Prime Meridian running through Charles’s capital. After John Ogilby’s successful Britannia, Charles set Collins surveying his kingdom’s coasts, and James set John Adair surveying in Scotland. They triangulated at sea. Subsequently, Collins persuaded James to sustain his dead brother’s ambition. This, the British coast’s first survey took six years. After James’s flight, and William III’s invasion, Collins lead the royal yacht squadron for six years more, garnering funds to publish Great Britain’s Coasting Pilot. The Admiralty and civic institutions subsidised what became his own pilot. Collins aided Royal Society members in their investigations, and his new guide remained vital to navigators through the century following. Charles’s cartographic promotion bloomed the most spectacularly in the atlases of Ogilby, Collins and John Flamsteed for roads, harbours, and stars.

This exciting Greenvill Collins biography is about seventeenth century navigation, focusing for the first time on mathematics practised at sea. This monograph argues the Restoration kings’, Charles II and James II, promotion of cartography for both strategy and trade. It is aimed at the academic, cartographic and larger market of marine enthusiasts. Through shipwreck and Arctic marooning, and Dutch and Spanish charts, Collins evolved a Prime Meridian running through Charles’s capital. After John Ogilby’s successful Britannia, Charles set Collins surveying his kingdom’s coasts, and James set John Adair surveying in Scotland. They triangulated at sea. Subsequently, Collins persuaded James to sustain his dead brother’s ambition. This, the British coast’s first survey took six years. After James’s flight, and William III’s invasion, Collins lead the royal yacht squadron for six years more, garnering funds to publish Great Britain’s Coasting Pilot. The Admiralty and civic institutions subsidised what became his own pilot. Collins aided Royal Society members in their investigations, and his new guide remained vital to navigators through the century following. Charles’s cartographic promotion bloomed the most spectacularly in the atlases of Ogilby, Collins and John Flamsteed for roads, harbours, and stars.

1. Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century p. 8 1.1 The Quaestio de Certitudine Mathematicarum p. 10 1.2 The Quaestio in the Seventeenth Century p. 15 1.3 The Quaestio and Mathematical Practice p. 24 2. Cavalieri's Geometry of Indivisibles and Guldin's Centers of Gravity p. 34 2.1 Magnitudes, Ratios, and the Method of Exhaustion p. 35 2.2 Cavalieri's Two Methods of Indivisibles p. 38 2.3 Guldin's Objections to Cavalieri's Geometry of Indivisibles p. 50 2.4 Guldin's Centrobaryca and Cavalieri's Objections p. 56 3. Descartes' Geometrie p. 65 3.1 Descartes' Geometrie p. 65 3.2 The Algebraization of Mathematics p. 84 4. The Problem of Continuity p. 92 4.1 Motion and Genetic Definitions p. 94 4.2 The "Causal" Theories in Arnauld and Bolzano p. 100 4.3 Proofs by Contradiction from Kant to the Present p. 105 5. Paradoxes of the Infinite p. 118 5.1 Indivisibles and Infinitely Small Quantities p. 119 5.2 The Infinitely Large p. 129 6. Leibniz's Differential Calculus and Its Opponents p. 150 6.1 Leibniz's Nova Methodus and L'Hopital's Analyse des Infiniment Petits p. 151 6.2 Early Debates with Cluver and Nieuwentijt p. 156 6.3 The Foundational Debate in the Paris Academy of Sciences p. 165 Appendix Giuseppe Biancani's De Mathematicarum Natura p. 178 Notes p. 213 References p. 249 Index p. 267.

The early modern map has come to mark the threshold of modernity, cutting through the layered customs of Medieval parochialism with its clean, expansive geometries. Re-thinking the role played by mathematics and cartography in the English seventeenth century, this book argues that the cultural currency of mathematics was as unstable in the period as that of England's controversial enclosures and plantations. Reviewing evidence from a wide range of literary and scientific; courtly and pragmatic texts, Edwards suggests that its unstable currency rendered mathematics necessarily rhetorical: subject to constant re-negotiation. Yet he also finds a powerful flexibility in this weakness. Mathematized texts from masques to maps negotiated a contemporary ambivalence between Calvinist asceticism and humanist engagement. Their authors promoted themselves as artful guides between virtue and profit; the study and the marketplace. This multi-disciplinary work will be of interest to all disciplines affected by the recent 'spatial turn' in early modern cultural studies, and particularly to students and researchers in literature, history and geography.

What was the basis for the adoption of mathematics as the primary mode of discourse for describing natural events by a large segment of the philosophical community in the seventeenth century? In answering this question, this book demonstrates that a significant group of philosophers shared the belief that there is no necessary correspondence between external reality and objects of human understanding, which they held to include the objects of mathematical and linguistic discourse. The result is a scholarly reliable, but accessible, account of the role of mathematics in the works of (amongst others) Galileo, Kepler, Descartes, Newton, Leibniz, and Berkeley. This impressive volume will benefit scholars interested in the history of philosophy, mathematical philosophy and the history of mathematics.

What was the basis for the adoption of mathematics as the primary mode of discourse for describing natural events by a large segment of the philosophical community in the seventeenth century? In answering this question, this book demonstrates that a significant group of philosophers shared the belief that there is no necessary correspondence between external reality and objects of human understanding, which they held to include the objects of mathematical and linguistic discourse. The result is a scholarly reliable, but accessible, account of the role of mathematics in the works of (amongst others) Galileo, Kepler, Descartes, Newton, Leibniz, and Berkeley. This impressive volume will benefit scholars interested in the history of philosophy, mathematical philosophy and the history of mathematics.

This work counters historiographies that search for the origins of modern science within the experimental practices of Europe’s first scientific institutions, such as the Cimento. It proposes that we should look beyond the experimental rhetoric found in published works, to find that the Cimento academicians were participants in a culture of natural philosophical theorising that existed throughout Europe.