Mathematical Geography in the Eighteenth Century: Euler, Lagrange and Lambert

Preface
Chronologies
A Note on the Translations
Contents
About the Editors
1 Introduction
Part I Essays
2 Ancient Geography: Some Markers
2.1 Introduction
2.2 On the Figure and the Measure of the Earth in Greek Antiquity
2.3 Strabo
2.4 Ptolemy's Cartography
2.5 On Ptolemy's Chorography and Topological Mappings
2.6 The Arabs
2.7 Renaissance
2.8 Chronology of Greek Authors Mentioned in this Chapter
References
3 Euler and Maupertuis on the Figure of the Earth
3.1 Introduction
3.2 Vita of Maupertuis
3.3 On the Figure of the Earth in the Eighteenth Century
3.4 The Lapland Expedition
3.5 Maupertuis' Memoir on the Figure of the Earth
3.6 On Euler's Writings in Relation with the Figure of the Earth
3.7 On the Euler–Maupertuis Correspondence
3.8 Other and Later Works
3.9 In Guise of a Conclusion
References
4 On the Duration of the Passage of a Star from an Almucantar to Another
4.1 Introduction
4.2 Terminology and Notation
4.3 The Duration of the Passage of a Star from an Almucantar to Another
Reference
5 The Differential Equations in Euler's Work on Geography
5.1 Introduction
5.2 Geographical Projections from the Sphere into the Plane
5.3 Perfect Maps
5.4 On Mercator's Maritime Chart
5.5 Projections that Preserve Angles
5.6 Projections that Preserve Area
5.7 Further Developments and Questions
References
6 Euler, Delisle and Cartography
6.1 Introduction
6.2 Joseph-Nicolas Delisle
6.3 Peter the Great's Geographical Project
6.4 Delisle at the Saint Petersburg Academy
6.5 Euler and Delisle
6.6 Euler's Atlas Geographicus
6.7 Euler on Delisle's Method
References
7 On Delisle's Geographical Projection
7.1 Introduction
7.2 Construction of Delisle's Projection
7.3 The Distorsion of Delisle's Projection
7.4 Applications of Delisle's Projection to the Map of the Russian Empire
References
8 Lagrange's Method for the Construction of Geographical Maps
8.1 Introduction
8.2 Conformal Geographical Maps and the Distortion Factor
8.3 Conformal Maps by Which the Images of the Meridians and the Parallels are Circles
8.4 Specific Conformal Geographical Maps
Conformal Maps Whose Distortion Depends Only on Latitude
Mercator Projection
Comparison of Distortion Factors
Geometric Construction of the Images of Meridians and Parallels
Stereographic Projection
References
9 Some Notes on the Impact of Lagrange's Memoir On the Construction of Geographical Maps
9.1 Introduction
9.2 Lagrange's Memoir in the Work of Darboux
9.3 Chebyshev's Theorem and Developments
9.4 Lagrange's Memoir in the Modern Literature
9.5 On Lagrange's Work and Practical Cartography
9.6 In Guise of a Conclusion
References
10 Lambert's Work on Geographic Map Projections
10.1 Introduction
10.2 Determination of Distances for the Stereographic Projection
10.3 Lambert's Conformal Conical Projections
10.4 More General Angle-Preserving Maps
10.5 Area-Preserving Maps
10.6 Spheroidal Shape of the Earth
References
Part II Sources
11 Elements of Spheroidal Trigonometry Drawn from the Method of Maxima and Minima
12 On the Representation of the Spherical Surface on the Plane
13 On the Geographical Projection of the Surface of the Sphere
14 On Delisle's Geographical Projection Used for a General Map of the Russian Empire
15 On the Construction of Geographical Maps
15.1 First Memoir
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17
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15.2 Second Memoir
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35
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42
16 Notes and Comments on the Composition of Terrestrial and Celestial Maps
16.1 Maps to Determine the Distances of Places
16.2 A More General Method to Project the Sphere Such that all Angles are Preserved
16.3 Further Extension of the Same Method
16.4 A Most General Presentation of the Same Method
16.5 An Application of the Method to a Special Case
16.6 Regular Projections of the Surface of the Earth
16.7 Projections of the Surface of the Earth with Respect to the Area of the Countries
16.8 A Projection of the Spheroidal Surface of the Earth
Index