Preface................................... ix
Acknowledgments..................... xvii
Chapter 1. CONSTRUCTION AS THE MARK OF THE MODERN....... 1-24
I. Projection, Construction, and the Idea of Modernity...................... 1
II. "Master of Nature, So to Speak" : Consequences of
Construction in Vico and Kant ....................................................... 7
III. Two Zoroasters : A Sense of Endings ....................................... 16
Chapter 2. THE EUCLIDEAN CONTEXT :
GEOMETRIA MORE ETHICO DEMONSTRATA .............................. 25-123
I. Preamble ................................................................................. 25
II. Episodes of Prudence and Imprudence in the Elements .............. 29
i. Ratios, Multitudes, and Magnitudes ......................... 29
ii. Homogeneity ....................................................... 33
iii. Sameness of Ratios ............................................ 42
iv. Conclusions ........................................................ 48
III. The Powers and Idioms of Construction in Greek Geometry ........ 49
IV. The Establishment of the Kantian Orthodoxy ............................... 50
V. Genesis and Knowing ............................................................... 61
VI. The Perfect Imperative ............................................................. 65
VII. The Evidentiary Force of Constructions in Greek Mathematics .... 67
i. Instrumental Constructions .................................... 70
ii. Construction as Operation
(Sensory and Imaginative) ....................................... 76
iii. Noesis and "Mental" Construction ......................... 87
VIII. Constructibility and the "Existence" of Geometrical Beings ......... 91
i. Introduction .......................................................... 91
ii. Einai and Existence in Aristotle ............................. 93
iii. Hyparxis and Deixis in Stoicism ............................ 98
iv. Essence and "Existence" in the
Medieval Arabic Tradition ......................................... 103
v. Kant's Relation to Premodern
Understandings of Existence .................................... 108
IX. The Enigma of the Postulates ..................................................... 110
X. Conclusions ............................................................................... 121
Chapter 3. DESCARTES' REVOLUTIONARY PATERNITY .................. 124-205
I. Preface ....................................................................................... 124
II. The Art of Origins : Descartes' Fabulous History ............................ 126
III. Mathesis and Mathematics in Descartes' Geometry ....................... 141
i. Prelude ................................................................ 141
ii. Reading the Geometry .......................................... 142
iii. The Structure of the Geometry .............................. 144
iv. The Style of the Geometry ..................................... 148
v. Liberty and Constraints:
Why Can Problems Be Solved? ................................. 161
vi. The Roots of the Geometry :
Unity, Order, and Measure in the Rules ....................... 174
IV. Objectum Purae Matheseos: Mathematical Construction and the
Passage from Essence to Existence in Descartes' Meditations ........... 187
i. Reading Notes ....................................................... 187
ii. Pura Mathesis and Descartes' Geometry ................. 188
iii. The Principal Characteristics of Cartesian Geometry :
Recapitulation and Extensions .................................... 191
iv. Essence and Existence in
Cartesian Pura Mathesis ............................................ 197
v. Morals Par Provision .............................................. 200
Notes ............................................................................................... 206-232
Bibliography ..................................................................................... 233-250
Index ................................................................................................ 251
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