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The algebra of logic
Capitel I: Die rationalen Curven
edited-book
Publication date
(Print):
1883
Publisher:
F. Fues
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Hogrefe Medicine
Author and book information
Book Chapter
Publication date (Print):
1883
Pages
: 1-42
DOI:
10.3792/chmm/1424377267
SO-VID:
326aca1a-b8d2-4faf-9fc3-81c53a7dfb08
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Book chapters
pp. 1
Introduction
pp. 1
Introduzione
pp. 1
Capitel I: Die rationalen Curven
pp. 3
1: Introduction
pp. 3
2: The two interpretations of the logical calculus
pp. 3
Chapter I. The resultant
pp. 4
3: Relation of inclusion
pp. 6
4: Definition of equality
pp. 8
5: Principle of identity
pp. 8
6: Principle of the syllogism
pp. 9
7: Multiplication and addition
pp. 11
8: Principles of simplification and composition
pp. 12
9: The laws of tautology and of absorption
pp. 14
10: Theorems on multiplication and addition
pp. 15
11: The first formula for transforming inclusions into equalities
pp. 16
12: The distributive law
pp. 17
13: Definition of o and i
pp. 18
Chapter II. The resolvent
pp. 20
14: The law of duality
pp. 21
15: Definition of negation
pp. 23
16: The principles of contradiction and of excluded middle
pp. 24
17: Law of double negation
pp. 25
18: Second formula for transforming inclusions into equalities
pp. 26
19: Law of contraposition
pp. 27
20: Postulate of existence
pp. 28
21: The developments of o and of i
pp. 29
23: Logical functions
pp. 29
22: Properties of the constituents
pp. 29
Capitolo I: Limiti e derivate geometriche
pp. 29
Chapter III. General properties of modules
pp. 30
24: The law of development
pp. 32
25: The formulas of De Morgan.
pp. 34
27: Properties of developed functions
pp. 34
26: Disjunctive sums
pp. 37
28: The limits of a function
pp. 38
29: Formula of Poretsky
pp. 39
30: Schroder's theorem
pp. 41
31: The resultant of elimination
pp. 42
Abschnitt I: Die Normcurven (speciell der Ebene und des Raumes)
pp. 43
32: The case of indetermination
pp. 44
33: Sums and products of functions
pp. 46
34: The expression of an inclusion by means of an indeterminate
pp. 48
35: The expression of a double inclusion by means of an indeterminate
pp. 50
36: Solution of an equation involving one unknown quantity
pp. 53
37: Elimination of several unknown quantities
pp. 55
38: Theorem concerning the values of a function
pp. 57
Capitolo II: Curve piane
pp. 57
40: Solution of equations containing several unknown quantities
pp. 57
39: Conditions of impossibility and indetermination
pp. 59
41: The problem of Boole
pp. 61
42: The method of Poretsky
pp. 62
43: The law of forms
pp. 63
44: The law of consequences
pp. 64
Chapter IV. The inverse system and modular equations
pp. 67
45: The law of causes
pp. 69
46: Forms of consequences and causes
pp. 70
47: Example: Venn's problem
pp. 73
48: The geometrical diagrams of Venn
pp. 75
49: The logical machine of Jevons
pp. 76
50: Table of consequences
pp. 77
51: Table of causes
pp. 79
52: The number of possible assertions
pp. 80
53: Particular propositions
pp. 81
54: Solution of an inequation with one unknown
pp. 83
55: System of an equation and an inequation
pp. 84
56: Formulas peculiar to the calculus of propositions
pp. 84
Abschnitt II: Die binäre biquadratische Form $f$ und ihre Apolaritätsverhältnisse auf den Normcurven zweiter, dritter und vierter Ordnung
pp. 85
57: Equivalence of an implication and an alternative
pp. 88
58: Law of importation and exportation
pp. 90
59: Reduction of inequalities to equalities
pp. 92
Conclusion
pp. 94
Index, and back pages
pp. 94
Capitolo III: Curve nello spazio e superficie
pp. 101
Note on the theory of ideals
pp. 131
Capitolo IV: Funzioni della posizione d'un punto
pp. 152
Capitolo V: Grandezze geometriche
pp. 194
Abschnitt III: Die binäre Form sechsten Grades $f$ und die biquadratische Involution und ihre Apolaritätsverhältnisse auf den Normcurven zweiter, dritter und vierter Ordnung
pp. 260
Capitolo VI: Della curvatura
pp. 272
Abschnitt IV: Die biquadratische Involution auf der cubischen Raumcurve. Zweiter Theil
pp. 302
Capitolo VII: Figure variabili; inviluppi
pp. 336
Errata-corrige
pp. 348
Capitel III: Verallgemeinerungen
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