ANALYTICAL INDEX (TABLE OF CONTENTS)

(Index Analyticus, pp. 289–293)

Preface (Praefatio)

• Preface (English) · Praefatio (Latin) · Translation Notes

Chapter I. - On the Origin of Geometric Cognition and Its Problematic

(Caput I. - De origine cognitionis geometricae et de eius problematica)

• Full Text (English) · Latin · Summary · Notes

• § 1. On the Proper Place of this Inquiry in Philosophy (De loco proprio huius indagationis in philosophia)

• § 2. On the Origin of Mathematical Notions (De origine notionum mathematicarum)

• § 3. The Twofold Fundamental Problem (Duplex problema fundamentale)

• § 4. On the Arithmetization of the Continuum (De arithmetizatione continui)

• § 5. On the Critique of Euclid’s Postulate V (De critica postulati V Euclidis)

• § 6. On So-Called Axiomatics (De axiomatica quae dicitur)

Chapter II. - On the Problem of Necessity

(Caput II. - De problemate necessitatis)

• Full Text (English) · Latin · Summary · Notes

• Preliminary Remarks (Animadversiones praeviae)

• § 1. On Certain Arithmetic Examples (De quibusdam exemplis arithmeticis)

  • 1. - On the Divisibility of a Multitude (De divisibilitate multitudinis)

  • 2. - On Prime Numbers (De numeris primis)

  • 3. - On the Beginnings of the Combinatorial Art (De initiis artis combinatoriae)

  • 4. - The Judgment on the Addition of Numbers: 7 + 5 = 12 (Judicium de additione numerorum)

    • A. The Method of Leibniz (Methodus Leibnizii)

    • B. The Method of Mercier (Methodus Mercier)

    • C. Logistic Deduction (Deductio logistica)

    • Conspectus (Conspectus)

  • 5. - Comparison of These Facts with Theories (Comparatio horum factorum cum theoriis)

  • 6. - Preliminary Judgments (Judicia praevia)

• § 2. On Necessity in Immediate Geometric Judgments (De necessitate in judiciis immediatis geometricis)

  • 1. - In Geometric Matters a Twofold Problem (In geometricis duplex problema)

  • 2. - The Extended Entity and “Space” (Extensum et « spatium »)

  • 3. - On Divisibility (De divisibilitate)

  • 4. - On the Order Among Points (De ordine inter puncta)

  • 5. - On Pasch’s Axiom (De axiomate Pasch)

  • 6. - On the Section of the Cylinder and the “Möbius Strip” (De sectione cylindri et « folii Moebii »)

• § 3. On the Doctrine Gathered from These Facts (De doctrina quae ex his factis colligitur)

  • 1. - Comparison with Physical Laws (Comparatio cum legibus physicis)

  • 2. - Again on Theories of Knowledge Relative to Experience (Iterum de theoriis cognitionis relate ad experientiam)

  • 3. - Implicit Judgments (Judicia implicita)

  • 4. - Virtual Judgments (Judicia virtualia)

• § 4. On the Material and Formal Nexus (De nexu materiali et formali)

  • 1. - On the Material and Formal Nexus Itself (De ipso nexu materiali et formali)

  • 2. - Physical Laws and Mathematical Principles (Leges physicae et principia mathematica)

  • 3. - On So-Called Formal Abstraction (De abstractione formali quae dicitur)

Chapter III. - On the Problem of Exactitude. Part I: On the Existence of Indivisibles

(Caput III. - De problemate exactitudinis. Pars I. - De existentia indivisibilium)

• Full Text (English) · Latin · Summary · Notes

• § 1. On the Statement of the Problem (De positione problematis)

  • 1. - In What the Problem Consists (In quonam consistat problema)

  • 2. - Certain Historical Matters (Quaedam historica)

    • A. Philosophers (Philosophi)

    • B. Mathematicians (Mathematici)

  • 3. - The Solution to be Sought (Solutio quaerenda)

• § 2. On the First Notions of Classical Geometry (De primis notionibus geometriae classicae)

  • 1. - On the Point, Line, Surface (De puncto linea superficie)

  • 2. - Division of the Extended Entity (Divisio entis extensi)

    • A. Surface (Superficies)

    • B. Line and Point (Linea Punctum)

    • C. On Indivisibles in the Nature of Things (De indivisibilibus in rerum natura)

  • 3. - On Dimensions (De dimensionibus)

  • 4. - On the Objection Drawn from the “Möbius Strip” (De objectione ex « folio Moebii » desumpta)

  • 5. - What is Gathered from These for General Noetics (Quae ex his colliguntur pro noetica generali)

    • A. The Theory of Aristotle (Theoria Aristotelis)

    • B. The Theory of Plato (Theoria Platonis)

    • C. The Theory of Kant (Theoria Kantii)

    • D. The Theory of Empiricism (Theoria empirismi)

  • 6. - On Infinite Divisibility (De divisibilitate in infinitum)

    • A. On Divisibility into Extended Entities (De divisibilitate in extensa)

    • B. On the Line as a “Collection of Points” (De linea ut « collectione punctorum »)

    • C. On Equations of Analytic Geometry (De aequationibus geometriae analyticae)

  • 7. - On Geometry as a Constructive Science (De geometria ut est scientia constructiva)

Chapter IV. - On the Problem of Exactitude. Part II: On Exact Figures and Relations

(Caput IV. - De problemate exactitudinis. Pars II. - De figuris et relationibus exactis)

• Full Text (English) · Latin · Summary · Notes

• Preliminary Remarks (Animadversiones praeviae)

• § 1. On the Principle of Individuation in Geometric Matters (De principio individuationis in geometricis)

• § 2. On Motion in Geometric Matters (De motu in geometricis)

• § 3. On the Congruence of Figures (De congruentia figurarum)

• § 4. On Exact Figures (De figuris exactis)

  • 1. - Preliminary Remarks (Animadversiones praeviae)

  • 2. - On the Notion of Direction (De notione directionis)

  • 3. - On the Continuum of Directions (De continuo directionum)

  • 4. - Curves and Straight Lines (Curvae et rectae)

  • 5. - On the Surface (De superficie)

  • 6. - On the Existence of Straight Line and Plane (De existentia rectae et plani)

    • A. On the Straight Line (De linea recta)

    • B. On the Plane Surface (De superficie plana)

  • 7. - On the Connections of Straight Line and Plane (De connexionibus rectae et plani)

  • 8. - Again on the Notion of Direction (Iterum de notione directionis)

  • 9. - On Direction in Euclid (De directione apud Euclidem)

• § 5. On Euclidean and Non-Euclidean Geometry (De geometria euclidica et non-euclidica)

• § 6. On Non-Euclidean Geometry Relative to Human Cognition (De geometria non-euclidica relate ad cognitionem)

• § 7. On Classical Geometry Relative to the Philosophy of Cognition (De geometria classica relate ad philosophiam cognitionis)

Chapter V. - On Axiomatics

(Caput V. - De Axiomatica)

• Full Text (English) · Latin · Summary · Notes

• § 1. On the Axiomatic Method (De methodo axiomatica)

  • 1. - On Axiomatics Strictly So Called (De axiomatica stricte dicta)

  • 2. - On the Method of Aristotle (De methodo Aristotelis)

  • 3. - On Semi-Axiomatics (De semi-axiomatica)

• § 2. On the Foundation of the Possibility of Axiomatics (De fundamento possibilitatis axiomaticae)

  • 1. - On the Syllogism Expressed in Words (De syllogismo verbis expresso)

  • 2. - On the Mental and Verbal Syllogism from a Noetic Perspective (De syllogismo mentali et verbali noetice spectato)

    • A. Syllogizing Activity is Intuitive (Activitas syllogizans est intuitiva)

    • B. Syllogizing Activity is Natural (Activitas syllogizans est naturalis)

• § 3. On the Execution of the Axiomatic Program (De executione programmatis axiomatici)

  • 1. - Preliminary Remarks (Animadversiones praeviae)

  • 2. - Intrinsic Difficulties (Difficultates intrinsecae)

    • A. Practical Difficulty (Difficultas practica)

    • B. Theoretical Difficulty (Difficultas theoretica)

• § 4. On the Appeal to the Phantasm in Other Sciences (De appellatione ad phantasma in aliis scientiis)

  • 1. - General Remarks (Animadversiones generales)

  • 2. - In Establishing First Principles (In statuendis principiis primis)

  • 3. - In Scientific Deduction (In deductione scientifica)

    • A. On Arithmetic (De arithmetica)

    • B. On Logistics (De logistica)

    • Recapitulation (Recapitulatio)

    • C. Deduction in Other Sciences (Deductio in aliis scientiis)

    • Note on Neo-Positivism (Nota de neo-positivismo)

• § 5. On the Application of Geometry (De applicatione geometriae)

  • A. On the Application of Classical Geometry (De applicatione geometriae classicae)

  • B. On the Applicability of Axiomatically Constructed Geometry (De applicabilitate geometriae axiomatice constructae)

Chapter VI. - On the Fundamental Subject of Geometry

(Caput VI. - De subjecto fundamentali geometriae)

• Full Text (English) · Latin · Summary · Notes

• § 1. Reiterated Comparison of Euclidean and Non-Euclidean Geometry (Iterata comparatio geometriae euclidicae et non-euclidicae)

• § 2. On Extension as the Fundamental Subject of Geometry (De extensione ut est subjectum fundamentale geometriae)

  • A. On the Extension of Bodies (De extensione corporum)

  • B. On Space (De spatio)

  • C. On the Relative Independence of the Notion of Extension from Experience (De independentia relativa notionis extensionis ab experientia)

• § 3. On Successive Extension (De extensione successiva)

  • 1. - On the Notion Itself and Its Proper Attributes (De ipsa notione et eius propriis)

  • 2. - Conclusions (Conclusiones)

    • A. Exactitude in Chronometric Relations (Exactitudo in relationibus chronometricis)

    • B. A Particular Specimen of Analogy (Specimen analogiae particularis)

    • C. On the Chronotope (Spacetime) (De chronotopo)

Chapter VII. - On Extension as Intelligible Matter

(Caput VII. - De extensione ut est materia intelligibilis)

• Full Text (English) · Latin · Summary · Notes

• § 1. On the Construction of Geometric Figures (De constructione figurarum geometricarum)

• § 2. On the Twofold Intelligibility of Intelligible Matter (De duplici intelligibilitate materiae intelligibilis)

  • 1. - On the Intelligibility of the Passivity of Intelligible Matter (De intelligibilitate passivitatis materiae intelligibilis)

    • A. In Arithmetic Matters (De arithmeticis)

    • B. In Geometric Matters (De geometricis)

  • 2. - On the Intelligibility of Our Activity (De intelligibilitate activitatis nostrae)

    • A. In Arithmetic Matters (In arithmeticis)

    • B. In Geometric Matters (In geometricis)

• § 3. On the Origin of General Noetics (De origine noeticae generalis)

  • 1. - General Survey (Conspectus generalis)

  • 2. - On Mathematical Cases (De casibus mathematicis)

  • 3. - On Physical Cases (De casibus physicis)

APPENDIX: On Necessary Connections Between Existential Acts

(APPENDIX: De connexionibus necessariis inter actus existentiales)

• Full Text (English) · Latin · Summary · Notes

• § 1. “It is moved, therefore it is” (« Movetur ergo est »)

• § 2. “This is moved, therefore place is” (« Hoc movetur ergo locus est »)

• § 3. “This is moved, therefore another, moving, exists” (« Hoc movetur ergo aliud, movens, existit »)

• § 4. On Finality in Motion (De finalitate in motu)

  • Recapitulation (Recapitulatio)

• § 5. Certain Other Existential Relations (Quaedam aliae relationes existentiales)

• § 6. Aristotle on the Existential Act (Aristoteles de actu existentiali)

• § 7. On the Concept of Being Itself (De conceptu ipsius esse)

  • Additions (Additiones)