1. On the Simplest Possible Branch of Mathematics
A. MS., n.p., [c.1903?], pp. 1-9, 13, 17-33.
Brief discussion of paradisaical logic, i.e., system
of logic in which only one value is supposed, provided
another value (or other values) is not positively denied.
The simplest kind of mathematics referred to, however,
is a two-valued system of which Boole's algebra of
logic is regarded as a special case. Inadequacies of
Boolean algebra and some merits of secundal notation.
Rules and examples for common mathematical operations
in CSP's dyadic system.
2. On the Simplest Branch of Mathematics (SM)
A. MS., n.p., [c.1903?], pp. 1-2; 1-5, incomplete, with
an alternative p. 5.
The pure mathematics of existential graphs, alpha and
beta parts, with definitions and permissions of transformation.
See MS. 512 for more of MS. 2.
3. On Dyadics: the Simplest Possible Mathematics (D)
A. MS., n.p., [c.1903?], pp. s-2, incomplete.
Intended as the first of a series of four memoirs, with
plans for further memoirs on the application of mathematical
theory to deductive logic. The doctrine of multitude
and a working definition of "continuity."
See MS. 511.
4. Sketch of Dichotomic Mathematics (DM)
A. MS., n.p., [c.1903?], pp. 1-52 (p. 25 missing), with
11 pp. of variants.
Nominal and real definitions; definition of terms, e.g.,
"postulate," "axiom," "corrollary,"
"theorem," which are employed in mathematical
or geometrical demonstration; canon of demonstration.
Long digression which begins with recognition of seven
schools of philosophy each determined by the emphasis
placed upon one or more of the following concepts:
form, matter, and entelechy. The relationship of these
schools to the realist-nominalist controversy, with
special attention given to the Aristotelian position.
The nature of signs: sign and related notions, especially
form, law, habit and entelechy; sign as having its
being in the power, not act, of determining matter;
sign as entelechy.
5. Dichotomic Mathematics (DM)
A. MS., n.p., [c.1903?], pp. 1-4, 1-3, 2-9, 6-11, 6-8,
10, 16-7, 45-46, with 22 pp. belonging to other drafts.
Similar in content to MS. 4, but without any of the
digressions.
6. [Dyadic Value System]
A. MS., n.p., n.d., 2 pp.
The simplest of value systems serves as the foundation
for mathematics and, indeed, for all reasoning, because
the purpose of reasoning is to establish the truth
or falsity of our beliefs, and the relationship between
truth and falsity is precisely that of a dyadic value
system.
7. On the Foundations of Mathematics (Foundations)
A. MS., n.p., [c.1903?], pp. 1-16, with 3 rejected pages;
17-19 of another draft. Mathematics as dealing essentially
with signs. The MSS. below (Nos. 8-11) are drafts of
this one, and all are concerned with the nature of
signs.
8. On the Foundations of Mathematics (Foundations)
A. MS., n.p., [c.1903?], pp. 1-4, 3-4; 4-8 of another
draft.
9. [Foundations of Mathematics]
A. MS., n.p. [c.1903?], pp. 1-5, with rejected pages.
Vagueness, generality, and singularity.
10. [Foundations of Mathematics]
A. MS., n.p., [c.1903?], pp. 1-2.
11. [Foundations of Mathematics]
A. MS., n.p., [c.1903?], pp. 1-2, incomplete.
12. Notes Preparatory to a Criticism of Bertrand Russell's
Principles of Mathematics (B. Russell)
A. MS., n.p., February 5, 1912, pp. 1-14.
The comments on Russell's work are as follows: ".
. . true in the main" and "throughout, however,
he betrays insufficient reflection on the fundamental
conceptions of the subject," with the "primary
difficulty . . . his not having begun with a thorough
examination of the elements; . . . the ultimate analytic
of thought." The major part of the manuscript
concerns CSP's own analytic of thought (theory of signs).
13. On the Logic of Quantity (L of Q)
A. MS., n.p., [c.1895], pp. 1-13; 7-12, with an alternative
p. 8 of another draft.
The principal questions raised are these: Why mathematics
always deals with a system of quantity, what the different
systems of quantity are and how they are characterized,
and what the logical nature of infinity is. The relationship
of logic and metaphysics to the three categories of
Firstness, Secondness, and Thirdness. Singular, dual,
and plural fasts. Chaldean metaphysics; chaos to determinacy;
the evolutionary process. Postulates of mathematical
logic (pp. 7-12).
14. On Quantity, with special reference to Collectional
and Mathematical Infinity (Quantity)
A. MS., n.p., [c.1895], pp. 1-34.
The nature of mathematics, pure and applied. In general,
mathematics is concerned with the substance of hypotheses,
drawing necessary conclusions from them; pure mathematics
is concerned only with those hypotheses which contain
nothing not relevant to the forms of deduction. The
nature of quan-tity (real, rational, and imaginary).
System of quaternions as an enlargement of the system
of imaginary quantity. Possible grades of multitude.
Spatial and temporal continuity. Common sense notions
of continua, especially with regard to the flow of
time. "Continuum" defined as "a whole
composed of parts, with the parts of the whole comprising
a series, such that, taking any multitude whatever,
a collection of those parts can be discovered the multitude
of which is greater than the given multitude."
Lastly, reasons are given for thinking that continuity
exists beyond the evidence afforded by our natural
beliefs in the continuity of space and time.
15. On Quantity, with special reference to Collectional
and Mathematical Infinity (Quantity)
A. MS., n.p., [c.1895], pp. 1-29, incomplete.
Same questions raised as in MS. 14. "Mathematics"
defined, with extended comments on the divisions of
the sciences.
16. On the Logic of Quantity, and especially of Infinity
(Logic of Quantity)
A. MS, n.p., [c.1895], pp. 1, 5-9, 7-18, 18-20.
Several definitions of "mathematics," including
Aristotle's and CSP's. Mathematical proof and probable
reasoning; the system and scale of quantity; the importance
of quantity for mathematics. But to grasp the nature
of mathematics is to grasp the three elements, which,
with regard to consciousness, are feeling, consciousness
of opposition, and consciousness of the clustering
of ideas into sets. Recognition of the three elements
in the three kinds of signs logicians employ. An analysis
of the syllogism.
17. On the Logic of Quantity (Logic of Quantity)
A. MS., n.p., [c.1895], pp. 1-9; 7-10 of another draft.
This manuscript should be compared with MS. 16, to which
it bears a special similarity. See also MS. 250 where
CSP defines "mathematics" as "the tracing
out of the consequences of an hypothesis." Five
definitions of "mathematics." Benjamin Peirce's
definition found acceptable with modification. "Science"
defined in terms of the activity of scientists, not
in terms of its content or "truths." Probable
inference and certain features of mathematical proof
(pp. 7-10).
18. (Logic of Quantity)
A. MS., n.p., n.d., pp. 3-4.
Defense of a modified version of Benjamin Peirce's definition
of "mathematics." Cf. MS. 78.
19. Logic of Quantity (Logic of Quantity)
A. MS., n.p., n.d., pp. 1-12.
Several theorems demonstrated, e.g., that every relation
included under a preference is itself a preference.
Solution is offered to the following problem: Required
that property which a collection must have to prevent
it from proceeding from any collection of which it
forms a part.
20. Logic of Quantity (Logic of Quantity)
A. MS., n.p., n.d., pp. 1-5; 1-4, 3-5; plus a single-page
table of contents ("Contents") and 3 rejected
pages.
Definitions, corollaries, theorems, and problems. The
theorems and problems differ from those in MS. 19.
21. Memoire sur la Logique de la Quantite. Deuxieme
Partie.
A. MS., n.p., n.d.. pp. 1-16, with 5 rejected pages.
The application of the logic of relations to quantity.
22. Systems of Quantity
A. MS., n.p., n.d., 5 pp.
Definitions of "relation," "relationship,"
"ring-relationship," and "quantity."
Systems of logical, collectional, and total quantity
distinguished.
23. [Logic of Number]
TS., n.p., n.d., pp. 2-7.
A draft of G-1881-7 (for annotated reprint of, see MS.
38). Unlimited and limited discrete simple quantity.
24. The Theory of Multitude (Multitude)
A. MS., n.p., [c.1903], pp. 1-3; 3-4 of another draft.
"Multitude" defined in terms of collection,
followed by a pragmatistic definition of "collection."
25. Multitude and Number (Multitude)
A. MS., G-1897-1, pp. 1-82, with rejected or alternative
pages running brokenly from p. 7 to p. 71.
Most of manuscript was published (4.170-226, except
187n1) but omitted were several illustrations (pp.
21-24; 34) and several proofs of theorems, among which
are the following: That the collection of possible
sets of units which can be taken from discrete collections
is always greater than the collection of units (pp.
12-13), that the sum of an enumerable collection of
enumerable multitudes is an enumerable multitude (pp.
29-32), and that there is a vast collection of indefinitely
divident relations between the units of any denumerable
collection (pp. 40-54).
26. On Multitude (On Multitude)
A. MS., n.p., [c.1897], pp. 1-24, with 24 pp. of rejects
and/or alternatives.
An inquiry into what grades of multitude of collections
are mathematically possible. This is a logical inquiry
because both a strict logica utens and the principles
of logica docens are required. Collection is explained
but not precisely defined. Provided are three axioms
relating to collections and several theorems. The inquiry
concludes with a discussion of the general method of
drawing conclusions by means of the above system.
27. Considerations concerning the Doctrine of Multitude
A. MS., n.p., [c.1905-07?], pp. 1-5; 23, 24, 27, 29,
30.
The nature of definition; "collection" defined;
first- and second-intentional collection.
28. [On Multitudes]
A. MS., n.p., [c.1897?], pp. 23-48.
Abnumeral collection; first, second, and third denumeral
multitude; princi, secundo, and tertio post-numeral
multitude. Continuity and the doctrine of limits.
29. [On Multitudes]
A. MS., n.p., n.d., 10 pp.
Innumerable and inenumerable multitude. Generality and
infinity.
30. Note on the Doctrine of Multitude
A. MS., n.p., [November 1903], pp. 1-6; 1-2.
Doctrine of multitude is developed in terms of dog-names
and boy-names. See CSP - Josiah Royce correspondence,
11/13/03, and the CSP-E. H. Moore correspondence, 12/16/03.
31. On the theory of Collections and Multitude
A. MS., n.p., [c.1905-07?], 2 pp.; plus 1 p. (p. 2)
("Note on Collections").
32. [On Collections]
A. MS., n.p., n.d., pp. 1-2, incomplete.
"Collection" defined; collection and quota
distinguished.
33. [On Collections and Multitudes]
A. MS., n.p., n.d., pp. 4-8.
34. [Collections and the Fermatian Inference]
A. MS., n.p., n.d., 26 pp. of discontinuous fragments
(nn. except for 67).
35. [Fermatian Inference]
A. MS., n.p., n.d., 5 pp.
36. [Fragments on Collections]
A. MS., n.p., n.d., 14 pp.
37. On the Number of Forms of Sets
A. MS., n.p., n.d., pp. 1-3.
Explanation of form and formality in terms of plurality
and diversity of sets. Table of formalities.
38. On the Logic of Number Reprints, G-1881-7.
One of the two reprints is annotated. Undated revisions
in the form of marginal notes.
39. Logic of Number
A. MS., n.p., n.d., 18 pp.
Fundamental premises concerning number.
40. Axioms of Number
A. MS., n.p., [C.1881?], 4 pp.
Fifteen axioms (or assumptions) of arithmetic which
provide a definition of "positive, discrete number"
and from which, CSP thought, every proposition of the
theory of numbers may be deduced by formal logic. Definitions
of "addition" and "multiplication."
41. The Axioms of Number
TS., n.p., n.d., 2 pp.
42. [Cardinal and Ordinal Number]
A. MS., n.p., n.d., 10 pp.
43. [Cardinal Number]
A. MS., n.p., n.d., pp. 36-38.
Mathematical calculations on the versos of these pages.
44. First Definition of Ordinals (Topics)
A. MS., G-c.1905-3 [G-1904-3], pp. 26-49, with 10 pp.
of rejects and/or alternatives.
Published, in part, as 4.331-340. Omitted: an attempt
to define formally a secundal system of enumeration
(pp. 38-39) and a second example (pp. 46-49).
*45, [Second Definition of Ordinals]
A. MS., n.p., [1904], pp. 4-6; 19-22; and 1 p. (the
number of which is missing).
Parenthetically: "As for the whole existing race
of philosophers, say John Dewey, to mention a relatively
superior man whom you see, why they are the sort of
trash who are puzzled by Achilles and the Tortoise!
Think of trying to drive any exact thought through
such skulls! Royce is the only philosopher I know of
real power of thought now living."
46. [Ordinals]
A. MS., n.p., n.d., pp. 6-7.
Second definition of "ordinals," and first
and second ordinal definition of "addition."
Also multitudinal definition of "addition."
47. Proof of the Fundamental Proposition of Arithmetic
A. MS., n.p., [1890?], pp. 1-4.
The proposition to be proved: ". . . that the order
of sequence in which the things of any collection are
counted makes no difference is [in] the result, provided
there can be any order of counting in which the count
can be completed. "
48. Numeration (Num)
A. MS., n.p., n.d., pp. 1-20, with 44 pp., some of which
belong to different drafts but many of which are rejected
pages.
Definitions of "number" and "series."
The distinction between precise and definite; vague
and indefinite. Abstraction, or ens rationis. In what
sense can it be said that entia rationis are real?
These pages were probably intended for an arithmetic.
49. An Illustration of Dynamics (Illustration)
A. MS., n.p., [c.1901-02?], pp. 1-20, with 3 pp. of
variants.
Setting out from two problems of dynamics both of which
require for their solution the method of infinitesimals,
CSP attempts an explanation of the method of infinitesimals,
which requires, in turn, an explanation of collections
and multiplicity. In addition, there is a discussion
of the different modes of being, followed by a discussion
of the distinction between reality and existence (for
the purpose of showing that although nothing unreal
can exist, something may be non-existent without being
unreal).
50. (Attraction)
A. MS., n.p., [c.1901-02?], pp. 1-12, with a rejected
p. 10.
Contents are similar to those of previous manuscript,
but without the discussions of existence and reality
and of collections.
NUMERICAL NOTATION AND ANALYSIS
51. On the Ways of Thinking of Mathematics (W of T)
A. MS., n.p., [c.1901-02?], pp. 1-4, with a rejected
p. 3.
On the decimal and secundal systems of enumeration.
52. Notes on Numerical Notation
A. MS., n.p., [c.1910?], pp. 1-10, plus a rejected p.
2.
The notion of "elegance" in mathematics. The
secundal system.
53. Secundal Computation
A. MS., n.p., [c.1912?], pp. 1-6, with 2 other attempts
to write p. 2.
The notion of "elegance" in mathematics. The
secundal system. Modes of reality.
54. Secundal Computation, Rules
A. MS., n.p., [early 1912], 8 pp., with 3 rejected pages;
plus 1 folded sheet ("rules for addition and subtraction").
Notational explanation and accompanying statement of
the rules for multiplication, division, addition, and
subtraction. The extraction of square roots.
55. Computations for a Table of Secundal Antilogarithms
A. MS., n.p., n.d., pp. 2-4.
56. Calculation of I.V.I. and Secundal Expression
A. MS., n.p., n.d., pp. 1-2; plus a folded sheet ("Calc.
of Table of Secundal Logarithms").
57. Essay on Secundal Augrim (SA)
A. MS., n.p., [c. February 1905?], pp. 1-9.
Dedicated to James Mills Peirce and concerned with the
same material as MS. 54.
58. Secundal Augrim
A. MS., n.p., n.d., 1 p.
Calculation of fundamental antilogs by additive method.
Calculation of (10)01.
59. Secundal Augrim. Calculation of 10-01 by additive
method continued
A. MS., n.p., n.d., 1 p.
60. Secundal Augrim. Sheet 1
A. MS., n.p., n.d., 1 p.
61. Secundal Numerical Notation (Secundals)
A. MS., n.p., n.d., pp. 1-12, with variant pages 7 and
9.
The four distinguishing characteristics of the system
of secundals. CSP's version of the secundal system,
with its several rules and examples of their application.
62. [Notes on Secundal Numeration]
A. MS., n.p., [c.1905?], 1 p., with 64 pp. of secundal
calculations.
63. [Secundal Notation Employed in Finding Factors]
A. MS., n.p., n.d., 11 pp.
64. Notes for my treatise on Arithmetic
A. MS., notebook, n.p., n.d.
Mostly on secundals. Versos contain calculations pertinent
to pendulum experiment, and two of these pages are
dated Paris 1876.
65. The Binary Numerical Notation
A. MS., n.p., n.d., pp. 1-2; 1-2 ("The Binary System
of Numerical Notation").
66. Mathematics as it is to be treated in my Logic treated
as Semiotics
A. MS., n.p., [c.1892-94?], pp. 1-5.
Binary system of notation.
67. Sextal Numeration
A. MS., notebook, n.p., n.d.
Transformation of an integer from decimal or sextal
to secundal expression and back again to the decimal
expression. Synthemes.
68. Note on a Series of Numbers (Series)
A. MS., n.p., [c.1903?], pp. 1-12, with variants (pp.
7, 8-12).
The series investigated is that whose first two dozen
members are 2 S 3 S 3 S 4 S 5 S 5 S 4 S 5 S 7 S 8 S
7 S 7 S 8 S 7 S 5 S 6 S 9 S 11 S 10 S 11 S 13 S 12
S 9 S 9 S
69. Numerical Equations
A. MS., n.p., n.d., 1 folded sheet (2 pp.).
Method of getting all the roots when their moduli are
all different.
70. Analysis of some Demonstrations concerning definite
Positive Integers (N)
A. MS., G-1905-6, pp. 1-20, with 50 pp. of variants
and notes.
See notes for an explanation of existential graphs.
The versos of some pages contain notes for dictionary.
In addition there is a draft of a letter in reply to
an advertisement appearing in the New York Herald.
71. Of the Unordered Combinations of Six Things (6 Things)
A. MS., n.p., [c.1899], pp. 1-8.
The symmetrics of combinations of six things.
72. On the Combinations of Six Things
A. MS., n.p., n.d., 1 p.
73. A Problem of Trees
A. MS., n.p., n.d., 4 pp. (incomplete or unfinished).
The problem for which a solution is offered is to find
how many distinct forms there are for a row of a given
number of letters (separated into two parts by a punctuation
mark, and each part not consisting of a single letter
into two parts by a subordinate punctuation mark,
and so on until all letters are separated).
*74. On the Number of Dichotomous Divisions: a problem
in permutations
A. MS., n.p., n.d., pp. 1-10 (p. 7 missing); plus 17
pp. of another draft.
In the calculus of logic, a proposition is separated
by its copula into two parts. The two parts may again
be separated in a like manner, and so on indefinitely.
One may inquire how many such propositional forms with
a given number of copulas there are. Similar problem
in algebra.
ALGEBRA
75. Notes on Associative Multiple Algebra
A. MS., n.p., n.d., 23 pp.
"The main proposition of this note was presented
to the American Academy of Arts and Sciences, May 11,
1875; and is published in the Proceedings of the Academy
on p. 392." It is clear that this manuscript and
the following two (76 and 77) belong together. See
G-1875-2 and 3.150-151.
76. II. On the Relative Forms of the Algebras
A. MS., n.p., n.d., pp. 1-7.
A draft of G-1881-10 (Addendum 2).
77. III. On the Algebras in which division is unambiguous
A. MS., n.p., n.d., pp. 8-14.
A draft of G-1881-10 (Addendum 3).
78. Notes on B. Peirce's Linear Associative Algebra
(LAA)
A. MS., n.p., n.d., pp. 1-5.
A defense of Benjamin Peirce's definition of "mathematics":
Six possible objections noted and countered. Cf. G-1881-10
and MS. 18.
79. Nilpotent Algebras
A. MS., n.p., n.d., 1 p.
Double and triple algebras.
80. Nilpotent Algebras
A. MS., n.p., n.d., 3 pp.
81. Notes on the Fundamentals of Algebra
A. MS., n.p., n.d., 2 pp.
Copula. Ligations, both simple and branching.
82. On the Application of Logical Analysis to Multiple
Algebra
A. MS., n.p., n.d., pp. 1, 3-4.
See G-1875-2.
83. Index to Jordan's "Substitutions"
A. MS., n.p., n.d., 8 pp.
84. [Algebraical Problems]
A. MS., n.p., n.d., 3 pp.
Drafts of corresponding pages of MS. 165.
85. An Algebraical Excursus
A. MS., n.p., n.d., pp. 1-2.
86. On the Quadratic Equation (QE)
A. MS., n.p., n.d., pp. 1-5.
On the real, equal, or imaginary roots of quadratic
equations.
87. Rough Sketch of Suggested Prolegomena to your [i.e.,
James Mills Peirce's] First Course in Quaternions
A. MS., n.p., [c.1905?], pp. 1-20, 16-19, 17-26, and
20 pp. of variants.
The mathematician's threefold task involves substituting
hypotheses for less definite descriptions of real or
imaginary states of affairs, then developing a point
of view for making those hypotheses as comprehensible
as possible, and finally employing that point of view
for the purpose of solving problems. Mathematical theory
is the discovery of methods of treating a broad class
of problems from one general point of view. Quaternions
as a particular theory of tridimensional space. Analysis
of spatial and temporal relations. Listing Numbers.
88. Quaternions Applied to Probabilities
A. MS., n.p., [1860's, early 1870?] 1 folded sheet (4
pp.).
89. Quaternions Theory of Functions
A. MS., n.p., n.d., 7 pp.
90. [Quaternions]
A. MS., n.p., [c.1876], 2 pp.
Quaternion algebra. Hamilton's and Benjamin Peirce's
forms interpreted geometrically.
CALCULUS OF FINITE DIFFERENCES
91. A Treatise on the Calculus of Differences (Calc.
Diff.)
A. MS., n.p., [1903-04?], pp. 1-25, with twice as many
pages from other drafts.
For "calculus of differences" CSP preferred
"calculus of successions." He planned to
divide treatise into four parts, but the manuscript
only gets into the first part which, treating the subject
generally without regard to the na-ture of known quantities,
is occupied mainly with equations of differences. The
distinction between logical and mathematical functions.
Features of mathematical functionality. Definitions
of "value," "universe of values."
"quantity." Notational rules.
92. Note on the Notation of the Calculus of Finite Differences
(NFD)
A. MS., n.p., [1903-04?], pp. 1-4.
The calculus of finite differences and the differential
calculus compared, especially with respect to the notion
of function.
93. Calculus of Finite Differences
A. MS., n.p., n.d., pp. 1-2, with 2 pp. (of two other
starts); 1 p. ("The Logic of Finite Differences");
3 pp. ("Equations of Finite Differences");
a notebook ("Promiscuous Notes").
The notebook from p. 17 onward is devoted to Boole's
Finite Differences and related topics (Tagalog is the
major subject of the first part of notebook).
BRANCHES AND FOUNDATIONS OF GEOMETRY
94. New Elements of Geometry by Benjamin Peirce, rewritten
by his sons, James Mills Peirce and Charles Sanders
Peirce.
A. MS., n.p., n.d., pp. 1-6, 1-4 ("Preface"),
2 pp. ("Nota Bene"), pp. 1-398, (pp. 7, 31-33,
35, 69-70, 74-76, 78, 92-94, 166-168, 175, 182-183,
235 missing), with pp. xvi, xvii, xviii, xix, and pp.
37-150 from Benjamin Peirce's Plane and Solid Geometry
mounted and ready for revision.
Rewritten are books II-V concerned with the fundamental
properties of space, topology, graphics, metrics.
95. [The Branches of Geometry; Ordinals]
A. MS., notebook, G-1904-3 and sup(1) G-c.1905-3, pp.
1-34.
An address delivered to the National Academy of Sciences.
There is no indication of publication under G-1904-3,
but this is G-c.1905-3 which is a mistake. see sup(1)
G-c.1905-3.
*96. [The Branches of Geometry; Existential Graphs]
A. MS., n.p., [c.1904-05?], 11 pp.
97. [The Branches of Geometry]
A. MS., n.p., n.d., pp. 9-16, with 5 pp. of variants.
98. The Axioms of Geometry
A. MS., n.p., [c.1870-71?], 2 pp., with 3 pp. of other
starts.
99. The Axioms of Geometry. Attempt at enumerating them
A. MS., n.p., [c.1875-76], l p.
100. First Attempt at a Geometry Logically Correct
A. MS., notebook, n.p., September 21, 1874.
101. [Six Fundamental Properties of Space]
A. MS., n.p., n.d., 2 pp.
CSP's intention is to explain imaginaries in a new way,
bringing them into the orbit of synthetic geometry
by means of the principle of continuity.
ANALYTIC GEOMETRY
102. Promptuarium of Analytic Geometry
A. MS., n.p., n.d., 5 pp. and 4 pp. of different drafts.
103. Syllabus of Plane Analytic Geometry
A. MS., n.p., n.d., 5 pp.
104. On Real Curves
A. MS., n.p., n.d., pp. 1-5, with variant p. 4.
105. On Real Curves. First Paper
A. MS., n.p., n.p., n.d., 13 pp.
*106. Four Systems of Coordinates
A. MS., n.p., n.d., 16 pp.
EUCLIDEAN AND NON EUCLIDEAN GEOMETRY
107. Synopsis of Euclid
A. MS., n.p., n.d., 2 pp.
108. [Euclid's Elements; Properties of the Number 2;
the Meaning of "Rational"]
A. MS., n.p., n.d., pp. 1-4.
109. Pythagorean Triangles (Pyth. Tri)
A. MS., n.p., [c.1901?], pp. 1-4.
110. Note on Pythagorean Triangles
A. MS., n.p., n.d., 1 p.
111. Formulae for Plane Triangles
A. MS., n.p., n.d., 1 sheet.
112. Notes on Klein Icosahedron
A. MS., n.p., n.d., 12 PP.
*113. Icosahedron (Icosahedron)
A. MS., n.p., n.d., 16 pp.
114. On Hyperbolic Geometry (Hyp. Geom)
A. MS., n.p., [c.1901?], pp. 1-6, 16-20, with rejected
pages.
Formulae required for the projection of the hyperbolic
plane upon the Euclidean. Definitions of "individual,"
"independence of individuals," and "collection."
Fundamental theorem of multitude. (Cantor's demonstration
of this theorem is thought to be fallacious.)
115. Newton's Enumeration of Cubic Curves
A. MS., n.p., n.d., 7 pp.
Hyperbolic geometry.
116. Brocardian Geometry
A. MS., n.p., n.d., 1 p.
117. The Non-Euclidean Geometry made Easy
A. MS., G-undated-7, pp. 1-8.
Published, in part, as 8.97-99. Unpublished (pp. 3-8).
Denial of either the first or second of the two "natural
propositions," noted in that part of manuscript
which was published, leads to a non-Euclidean geometry.
Both of the corresponding kinds of non-Euclidean geometry
are intelligible, and a consideration of plane geometry
will suffice to show this.
118. Reflections on Non-Euclidean Geometry
A. MS., n.p., n.d., pp. 1-5.
119. Non-Euclidean Geometry
A. MS., n.p., [c.1883 or later], 1 p. and 1 p. ("Notes
on Non-Euclidean Geometry") .
The purpose of this memoir is to find some way of treating
geometry metrically by introducing the absolute synthetically.
The attempt is restricted to plane non-Euclidean geometry:
"Solid non-Euclidean geometry is a trifle too
hard for me."
120. The Elements of Non-Euclidean Geometry. Preface
A. MS., n.p., n.d., 3 pp., plus 3 pp. which may be part
of the same draft.
121. [On Non-Euclidean Geometry]
A. MS., G-undated-6, pp. 2-11; plus 4 pp. of an earlier
draft.
Probably manuscript of an address to the New York Mathematical
Society, November 24, 1894. Published, in part, as
8.93 n2. Was Euclid a non-Euclidean geometer? Probably!
Properties of space. Evidence for thinking there is
an absolute which is a real quadric surface. Newton's
argument that space is an entity and its bearing on
non-Euclidean Geometry. On back of p. 11: "Professor
Fiske" [i.e., Thomas S. Fiske].
122. Non-Euclidean Geometry. Sketch of a Synthetic Treatment
A. MS., n.p., n.d., 32 pp. (several attempts with different
titles).
123. Lobachevski's Geometry
A. MS., n.p., n.d., 3 pp.
124. Formulae
A. MS., notebook, n.p., n.d.
Notes on non-Euclidean geometry, existential graphs,
and Laurent's probabilities. Solution of quadratic
equation. The "formulae" of the title refers
to trigonometrical formulae and formulae of analytic
geometry.
PROJECTIVE GEOMETRY
125. Geometry. Book 1. Projective Geometry
A. MS., n.p., n.d., pp. 1-4.
Definitions: Geometry, Body, Surface, Line, Point.
126. A Geometrico-Logical Discussion
A. MS., n.p., n.d., pp. 1-10, with 28 pp. of other drafts.
Four-ray problem (How many rays cut four given rays?)
as offering best apercus into nature of projective
geometry. The impossibility of exact ideas, even in
mathematics. Idea of a person; idea of a species of
animal. Reality and entia rationis. Brief note on verso
of one of the pages is dated September 16, 1906, and
reads as follows: "11 1/4 P.M. Fell asleep standing
and dreamed something about a tablet in a church In
memory of my mother."
127. [Fragments on Projective Geometry]
A. MS., n.p., n.d., 61 pp.
128. [Mathematical Notion of Projection]
Amanuensis, with corrections in CSP's hand, n.p., n.d.,
pp. 11-12.
METRICAL GEOMETRY
129. Metrical Geometry
A. MS., n.p., n.d., pp. 1-39, with variant pages, and
155 pp. of other drafts.
Drafts for MS. 94 or 165. Foundations of linear and
angular measurement. Signate, imaginary and quaternional
measurement. Concept of a metron. Definitions, theorems,
and demonstrations.
130. Metrical Geometry
A. MS., n.p., n.d., 27 pp.
Drafts for MS. 94 or 165. On the nature of spatial measurement.
131. [Metrical Geometry]
A. MS., n.p., n.d., 12 pp.
Drafts for MS. 94 or 165. On propositions holding true
for all kinds of systems of measurement.
132. Plan of Geometry
A. MS., n.p., n.d., 28 pp.
133. [Metrical Geometry]
A. MS., n.p., n.d., pp. 1, 14-l5, 17-19
Much of the content, however, is projective geometry
which is thought of as requisite for metrics.
134. [Metrical Geometry]
A. MS., n.p., n.d., pp. 27-39, plus 4 pp. of variants.
Drafts for MS. 94 or 165.
135. [Metrical Geometry]
A. MS., n.p., n.d., pp. 56-62, plus a variant p. 58.
Drafts for MS. 94 or 165.
136. [Metrical Geometry]
A. MS., G-undated-12 (Space), 1 p.
TOPICAL GEOMETRY
137. Topical Geometry (Topics)
A. MS., n.p., [1904], pp. 1-29, plus a confusion of
partial drafts with pages running as high as p. 40,
but with no continuous or final draft.
It is not evident that the title page goes with rest
of the manuscript, which was written for Popular Science
Monthly. The branches of geometry and their mutual
relations. The branches of topics. Topics presupposes
time, and time presupposes the doctrine of multitude.
The topical properties of time; the hypothetically
defined time of topics a true continuum; true continuity
opposed to the pseudo-continuity (of the calculus).
Instances of time, with the multitude of instances
defined with the aid of the secundal system of enumeration.
Points as possibilities, not actualized until something
occurs to mark them. The dividing point between green
and white is both green and white. Law of contradiction
does not apply to potentialities. Census Theorem, Census
Number, and Listing Numbers. On general words (signs).
138. Analysis of Time
A. MS., notebook, n.p., begun c.1904-05 with two entries
dated August 13, 1908.
Four given rays may be crossed by how many rays? The
analysis of the Four-ray problem requires a consideration
of continuity which in its primitive, i.e., simple,
sense has the form of time. Time as a determination
of actuality (later see annotation CSP dissents).
Definition of terms, e.g., instant, gradations. "I
will not take up more of this book with the subject
of discrete quantity But I refer to a similar book
labelled 'All Pure Quantity merely ordinal' [MS. 224]
for more about it."
139. On synectics, otherwise called Topology or Topic
A. MS., n.p., n.d., 4 pp., incomplete.
Synectics as the science of spatial connections; pure
synectics as the science of the connection of the parts
of true continua.
140. A Treatise on General Topics (General Topics)
A. MS., n.p., n.d., pp. 1-4, plus 1 p., dated December
26, 1913, on what it means to say that a line is continuous.
141. On Topical Geometry, in General (T)
A. MS., G-undated-12, pp. 1-14, 4-8, 4-7, 5-7, 5, 9,
13.
Published, in part, as 7.524-538, except 534n4 and 535n6.
Omitted from publication is a discussion of the Kainopythagorean
Categories centering in the view that there are but
three and that there can be no element in experience
not included in the three.
142. Notes on Topical Geometry
A. MS., G-undated-16 [c.1899-1900?], 6 pp., plus 2 pp.
each of two other drafts having the same title as above.
Published, in part, as 8.368n23. Omitted from publication
are definitions of "thing" and "collection,"
and a discussion of signs, especially icon, index,
and symbol.
143. Topic (Topic)
A. MS., n.p., n.d., pp. 1-4.
Point-figures and line-figures.
144. On General Topic (Topic)
A. MS., n.p., n.d., pp. 1-3, incomplete.
General and special topic distinguished. Properties
of a continuum.
*145. An Attempt to state systematically the Doctrine
of the Census in Geometrical Topics or Topical Geometry,
more commonly called "Topologie" in German
books; Being A Mathematical-Logical Recreation of C.
S. Peirce following the lead of J. B. Listing's paper
in the "G^ttinger Abhandlungen"
A. MS., n.p., n.d., 12 pp.
146. On Space-Logic
A. MS., n.p., November 13, 1895, pp. 1-2 (with a second
p. 2), incomplete.
Notation. Topical singularity of a line.
147. On Space-Logic
A. MS., n.p., November 14, 1895, 1 p.
Notation only.
148. Topics of Surfaces
A. MS., n.p., n.d., 1 p.
149. Ch. 2. Topical Geometry
A. MS., n.p., n.d., 1 p.
Definitions of "space," "place,"
"point," "particle," "line,"
"filament," "surface," "film,"
"solid," "body."
150. [Topical Geometry]
A. MS., n.p., n.d., 45 pp.
Draft of MS. 94 or 165. Also material on graphics (projective
geometry).
151. Topics. Chapter I. Singular Systems
A. MS., n.p., n.d., 3 pp.
Firstness, or qualities, are positive albeit vague determinations.
Vagueness and generality discriminated.
152. Section 4. Of Topical Geometry
A. MS., n.p., n.d., pp. 6-12; 7-8.
Kinds of multitude: numerable, innumerable, enumerable,
inenumerable.
153. On the Problem of Coloring a Map (4 Colors)
A. MS., n.p., n.d., pp. 1-17, plus variants.
154. On the Problem of Map-Coloring and on Geometrical
Topics, in General (MC, PMC, Map)
A. MS., n.p., [1899-1900], pp. 1-10, plus variants and
many other attempts (82 pp. in all), none going beyond
p. 10.
The problem of map-coloring is stated as follows: "To
determine demonstratively the smallest number of colors
that will suffice so as to color any map whatever which
can be drawn on a given surface, that no two confine
regions (that is, two regions having a common boundary-line)
shall have the same color." See CSP W. E. Story
correspondence, 12/29/00.
155. Studies in map Coloring as Starting-point for Advance
into Geomet-rical Topics
A. MS., notebook, n.p., [c.1897-1900?].
The first part of the notebook, the date of which is
c.1870, deals with physical constants.
156. Map Coloring Vol. IV
A. MS., small notebook, n.p., n.d., plus another notebook
("Map Coloring Vol. V"), n.p., n.d.
Study of the Census Number.
157. [Link Coloring]
A. MS., n.p., [c.1897-1900?], 16 pp.
In how many ways, with c colors, can a simple chain
of 1 links be colored, no two adjacent links being
colored alike? In how may ways, with c + l colors,
can a simple chain of I + l links be colored so that
all adjacent links are colored differently?
158. [Fragments on Map-Coloring]
A. MS., n.p., n.d., 32 pp. and 3 pp.
159. Notes on Listing
A. MS., n.p., [1897?], pp. 1-7.
160. A Study of Listing Numbers (Listing Numbers)
A. MS., n.p., February 3, 1897, pp. 1-5, plus 1 p. which
apparently belongs here.
161. [Listing Numbers; The Census-Number; The Census
Theorem]
A. MS., n.p., n.d., 5 pp.
162. [Fragments on Listing Numbers and the Census-Number]
A. MS., n.p., n.d., 8 pp.
163. [Topology; Real Curves; Astronomy; Archeology;
Assorted Mathematical Notes]
A. MS., notebook, n.p., 1895 (p. 45 is dated July 1895).
MATHEMATICAL TEXTBOOKS
164. New Elements of Mathematics
A. MS., n.p., [c.1895], title page and 2 pp. ("Preface").
An introduction to a book which is designed to give
the educated man all the mathematics he needs to know
and which could serve as preparation for the study
of higher mathematics. Brief account of the recent
history of mathematics, followed by an examination
of the branches of geometry.
165. Elements of Mathematics
A. MS., n.p., [c.1895], pp. 1-357 (pp. 61, 77, 93, 213,
259-273, 276-294 missing), with 23 pp. of a well-detailed
"Table of Contents" and "Subject Index"
and 18 pp. of another draft of Article 2, Scholium
2, of Chapter I.
Chapter I "Introduction" (pp. 1-39): Elementary
account of the nature of mathematics; analysis of the
game of tit-tat-too as an illustration of the process
of deducing the consequences of hypotheses; definitions
and the etymology of important terms. See MS. 1525
for possible early drafts of some of this material.
Chapter II "Sequences" (pp. 40-76, with p.
61 missing): Sequences, both simple and complex. Chapter
III "The Fundamental Operations in Algebra"
(pp. 78-92, with pp. 77 and 93 missing): Fundamental
operations in algebra; explicit and implicit functions;
functions of several variables. Chapter IV "Factors"
(pp. 94-106): Parts, divisors, and factors; prime factors;
greatest common divisor of several numbers; multiples,
dividends, and products; least common multiple; fundamental
theorem of composition. Chapter V "Negative Numbers"
(pp. 107 116): Definition and historical data. Chapter
VI "Fractional Quantities" (pp. 117-130):
Rational number explained; the system of rational numbers
as including the values of all rational fractions except
o/o. Chapter VII "Simple Equations" (pp.
131-173): Solution of linear equations; systems of
simultaneous equations. Chapter VIII "Ratios and
Proportions" (pp. 174-188): Ratios, proportions,
anharmonic ratio. Chapter IX "Surds" (pp.
189-222, with p. 213 missing): Possibility and importance
of surds; definition of "limit"; Achilles
and the tortoise (p. 196); imaginary quantities; exercises
and problems. Chapter X "Topical Geometry"
(pp. 223-275, with pp. 259-273, 276-293 missing): Topical
geometry explained; continuum; homo-geneity; tridimensionality
of space; singularities; topical classes of surfaces;
the topical census. Long footnote on the intelligibility
of infinitesimals. Chapter XI "Perspective"
(pp. 294-357): Graphics; homoloidal system of plates;
dominant (optical) homoloids; projection; Desarques'
Ten-Line theorem; the Nine-Ray theorem.
166. Elements of Mathematics
A. MS., n.p., [c.1895], pp. 44-320, with many gaps and
variant pages.
Another draft of MS. 165.
167. Practical Arithmetic
A. MS., n.p., n.d., pp. 1-29 (pp. 26-27 missing), plus
2 pp.
Maxims for attaining accuracy and speed in handling
numbers. Counting and measuring. The decimal names
of numbers. The arabic notation.
168. Practical Arithmetic
TS. (corrected), n.p., n.d., 21 pp. of two drafts.
169. Factotal Augrim (A) (B)
A. MS., n.p., n.d., pp. 1-18 (A), 5-18 (A), plus variants;
1-4 (B).
Terminology: augrim, arithmetic, vulgar arithmetic,
practical arithmetic, ciphering, and algorithm. Elementary
and composite augrims. On number, including a long
footnote on collections.
170. Rough List of Works Consulted for Arithmetic
A. MS., n.p., [1890-91?], 3 pp.
171. CSP's Small Inventions in Arithmetic and Logic
A. MS., n.p., n.d., 8 pp.
The arrangement of all the rational fractions, not negative,
in the order of their values and without calculation.
172. Examples in Arithmetic
A. MS., n.p., n.d., 8 pp.
173. A System of Arithmetic
A. MS., n.p., n.d., 3 pp.
Rule for addition.
174. Rule for Division
A. MS., n.p., n.d., pp. 1-28 (pp. 2, 13, 15-16, 23-26
missing), plus variants and several unnumbered pages.
175. Exercises in Arithmetic
A. MS., notebook, n.p., n.d.
176. [Elementary Arithmetic]
A. MS., n.p., n.d., 15 pp.
Rule for addition. Counting by threes, fours, fives,
etc.
177. The Practice of Vulgar Arithmetic
A. MS., notebook, n.p., n.d.
Addition, multiplication, squaring a number, solving
algebraic equations, Rule of False.
178. C. S. Peirce's Vulgar Arithmetic: Its Chief Features
A. MS., notebook, n.p., [c.1890].
Draft of a book, outlining its chief features. Shortcuts
in the teaching of arithmetic.
179. Peirce's Primary Arithmetic Upon the Psychological
Method
A. MS., n.p-, [1893], 52 pp.
Teaching numeration. Addition. Multiplication.
180. Plan of the Primary Arithmetic
A. MS., n.p., n.d., pp. 1-3.
The contents of seventeen chapters are noted.
181. Primary Arithmetic
A. MS., n.p., n.d., 31 pp.
Six lessons concerned with counting.
182. Primary Arithmetic. Suggestions to Teachers
A. MS., n.p., n.d., 12 pp.
A teaching manual on counting.
183. Mugling Arithmetic
A. MS., n.p., n.d., pp. 1-2.
184. [On Counting]
A. MS., n.p., n.d., 4 pp.
185. Chapter IV. Addition
A. MS., n.p., n.d., 6 pp.
186. Familiar Letters about the Art of Reasoning
A. MS., n.p., May 15, 1890, pp. 1-22, plus title page
and 2 pp. (unnumbered).
In the form of a letter to Barbara (of the mnemonical
verses). Card-playing as a pedagogical instrument,
useful in teaching the art of reasoning.
187. [Assorted Notes for an Elementary Arithmetic]
A. MS., n.p., n.d., 6 pp. (not all in CSP's hand).
188. [Introduction to Practical Arithmetic]
A. MS., n.p., n.d., 2 pp.
Discussion is somewhat advanced and may not be part
of a primary or vulgar arithmetic.
189. Lydia's Peirce's Primary Arithmetic
A. MS., notebook, n.p., [1904-05], with 65 pp. of drafts.
"Grandmother" Lydia teaches counting, making
use of children's nonsense rhymes like "eeny-meeny-mony-meye,"
but pointing up the numerical limitations of gibberish.
190. [Notes on Square Roots, Long Division, Addition,
Cyclic Numeration]
A. MS., n.p., n.d., 9 pp.
191. [Balance and Scales]
A. MS., n.p., n.d., 13 pp.
Part of a proposed book for children.
192. [On Algebra]
A. MS., n.p., n.d., pp. 2-15.
An elementary discussion possibly for a textbook.
193. Syllabus of the Elements of Trigonometry
A. MS., n.p., n.d., 4 pp., representing three different
starts.
194. [Fragments on Trigonometry]
A. MS., n.p., n.d., over 100 pp.
195. Trigonometry
A. MS., n.p., n.d., pp. 1-2, plus 13 pp.
196. Sketch of a Proposed Treatise on Trigonometry
A. MS., n.p., n.d., 20 pp.
197. Elements of Geometry
A. MS., n.p., n.d., 1 p.
198. [Geometry Exercises]
A. MS., n.p., n.d., 14 pp.
MATHEMATICAL RECREATIONS
199. The Third Curiosity (MM/D)
A. MS., n.p., [1907], pp. 1-76, plus 53 rejected pages.
Numeration with a base other than 10. Sextal and secundal
systems. The rules of arithmetic, e.g., rule of algebraic
summation and the rule of "direct division."
200. The Fourth Curiosity (MM/E)
A. MS., G-1908-1e, pp. 1-186, plus 161 pp. (running
brokenly to p. 186).
Omitted from publication in the Collected Papers: further
discussion of the relationships of the Aristotelian
pattern; definition of "pure mathematics";
numbers as entia rationis; first valid argument for
pragmatism involves the denial of the Absolute. Kind,
class, and collection. Signs and predication.
201. A Contribution to the Amazes of Mathematics (MM)
A. MS., n.p., [c.1908], 210 pp., most of which are numbered
with the numbered pages running as high as p. 164 (many
pages missing, however).
Rationale for two card "tricks" [The First
(?) and Second Curiosities]. Abstract real (not imaginary)
numbers viewed pragmatistically. Cantorian system.
Cyclical system of numbers. The Fourth Curiosity. Secundal
arithmetic. Reference to Elements of Mathematics (MS.
165), with bitter note on publishers of textbooks.
202. Some Amazements of Mathematics (Cu)
A. MS., n.p., [c.1908], pp. 1-53, plus 26 pp. of variants.
This paper begins with an analysis of the peculiarity
of the number 142857. Lengthy discussion of infinitesimals.
Fermat's theorem, Polynomial theorem, Rule of "direct
division." Card "trick" (same as one
of the two card "tricks" of MS. 201).
203. Addition (Add)
A. MS., n.p., May 24, 1908, pp. 1-5.
Alternate draft of 4.642. Does the collective system
of irrational and rational quantity constitute a continuum
or a pseudo-continuum? CSP says "pseudo-continuum"
as against the opinions of both Cantor and Dedekind.
204. Supplement (A)
A. MS., G-1908-1b, pp. 1-17, incomplete, with variants.
The exact date of this manuscript is May 24, 1908. It
was published, in part, as 7.535n6. Unpublished: Whether
mathematicians generally, including Cantor and Dedekind,
are correct in their views as to what constitutes a
true continuum. The three universes of ideas, i.e.,
arbitrary possibilities, physical things, and minds.
Reality and existence; perfect and imperfect continua.
205. Recreations in Reasoning (RR)
A. MS., G-c.1897-4, pp. 1-35, plus 22 pp. probably from
another draft.
Published as 4.153-169, with the proofs of several theorems
omitted.
206. Recreative Exercises in Reasoning (R)
A. MS., n.p., n.d., pp. 1-4.
Solution of the following exercise: "Required to
arrange all the rational fractions (whose denominators
do not exceed a given number and whose numerators do
not exceed a given number of times the denominator)
in the order of their values, in a horizontal row with
< or = interposed between each successive two to
state their relation of value."
207. Recreations in Reasoning (R)
A. MS., n.p., n.d., pp. 1-24, 2-5 with one rejected
page and 14 pp. of variants; plus 11 pp. of notes.
Three distinguishing marks of numerical multitude. The
ordering of fractions and the simplest method for calculating
circulating decimals.
208. Recreations of Reasoning (RR)
A. MS., n.p., [c.1897], pp. 1, 21, 32; and 1 p.
209. Knotty Points in the Doctrine of Chances
A. MS., n.p., [c.1899], pp. 1-16.
Problem in probabilities: mathematics of the roulette
table. CSP concludes whimsically: "That in an
even game, say an honest roulette without zeros, all
the players might make it a rule to leave off only
when they had netted a winning equal to a single bet,
and were their fortunes or backing unlimited, every
man of them would be sure of success, while the bank,
though it would not win anything, would never lose!"
Now "let U.S. lend to each citizen ..." and
then allow the winnings to be taxed.
210. A Corner for Pythagoreans. Mathematical Recreations
No. 1 by Pico di Sablonieri (pseudonym)
A. MS., n.p., [c.1895], pp. 1-11; plus 12 pp. and 5
pp. of other drafts.
A problem in probabilities. Content is similar to that
of the preceding manuscript.
211. A Brief Preliminary and Hasty Syllabus of a book
to be entitled Calculations of Chances
A. MS., n.p., n.d., 38 pp.; plus pp. 8, 11-18.
COMPUTATIONS AND FRAGMENTS
212. A Trade Secret (Trade Secret)
A. MS., n.p., n.d., pp. 1-4, with a variant p. 1.
The computing of values of a function from an infinite
series: a dodge generally known among professional
computers.
213. Notes of a Computer
A. MS., n.p., n.d., pp. 1-3, plus 1 p. ("A Device
of Computation") and 1 p. ("A Computer's
Device").
214. Note on o(inf)
TS., n.p., n.d., 3 pp.
215. Integer Negative Powers of 2
A. MS., n.p., "checked and found correct by CSP
1911, Oct. 8," 2 pp.
216. Practical Comments on Namur's Tables of Logarithms
A. MS., n.p., n.d., 1 p.
217. Calc. of Nat. Log. 10
A. MS., n.p., n.d., 1 sheet.
218. A Short Table of Reciprocals
A. MS., n.p., n.d., 1 sheet.
219. Computation of the excess of 5/10 over 1
A. MS., n.p., n.d., 1 p.
220. Calculation of the fractional part of 5/10
A. MS., n.p., n.d., 2 pp.
221. Hints toward the invention of a Scale-Table
A. MS., n.p., n.d., pp. 1-6; 1-3; and 9 pp. of fragments.
Table of antilogarithms and a logarithmic scale.
222. Dedekind's Dirichlet #23
A. MS., n.p., n.d., pp. 1-3, plus 5 pp. of two other
starts.
The object of this paper is to describe a notation which
reveals clearly the elementary constitution and properties
of the functions connected with the GCD algorithm.
223. Gibb's Papers. Vol. II. p. 30
A. MS., n.p., n.d., 3 pp.
Probably a draft of G-1883-5d.
224. All Pure Quantity merely ordinal
A. MS., notebook, August 16, 1908.
Notes for a memoir whose purpose is "to prove that
every system of signs of abstract quantities signifies
nothing but that one sign denotes an object later in
one or more sequences (or later in one and earlier
in another, etc.) than an object denoted by another."
A study of two systems: (a) additive scheme of rational
values, (b) numerative scheme of positive fractions.
Ens rationis and feeling (monadic experience contrasted
with dyadic experience, or "reaction").
225. Memorandum of How to Do Things
A. MS., notebook, n.p., n.d.
Various formulae of computation. Certain kinds of problems,
e.g., drawing the best algebraic curve of a given order
through any number of points, finding times of moon's
rising and setting, etc., and their solutions.
226. Note to p. 378 of [Benjamin] Peirce's Analytic
Mechanics
A. MS., n.p., n.d., 4 pp.
227. Theorems of Numbers
A. MS., n.p., n.d., 2 pp., incomplete.
228. Notes
A. MS., n.p., n.d., 9 pp.
Distributions of the theorems of mathematics throughout
the various branches of the discipline. In addition,
the notes are concerned with the theory of equations,
equal roots, symmetric functions, different kinds of
ratios.
229. [Logic of Number] (Lefevre)
A. MS., n.p., n.d., pp. 2-7, 16, 18, 20-21.
Definition of "mathematics" as "the science
of hypotheses."
230. [Analytic Geometry]
A. MS., notebook, n.p., n.d.
Includes, in addition to the material on analytic geometry,
a personal expense account, covering several days,
but with no indication of the year.
231. Studies of Laws of Frequency of Occurrence of Numbers
A. MS., n.p., n.d., 1 p.
These studies are based on population figures for 1900.
232. Note on the Mouse Trap Problem
A. MS., n.p., n.d., 1 p.
233. Gauss's Rule for Easter improved
A. MS., n.p., n.d., 1 p.
234. [Arithmetical Calculations]
A. MS., notebook, n.p., n.d.
235. [Fragment on Quantity]
A. MS., n.p., n.d., pp. 15-16.
236. [Fermat's Theorem]
A. MS., n.p., n.d., 4 pp.
Draft of a postscript to an unidentified letter.
237. Formulae for Repeated Differentiations (Repeated
Differentiations)
A. MS., n.p., n.d., pp. 1-2; plus 2 pp. (Dn).
238. An Apology for the Method of Infinitesimals (Apology)
A. MS., n.p., n.d., pp. 1-15.
An attempt at justifying a remark (see Century Dictionary
s.v. limit) that the method of infinitesimals is more
in harmony with advances in mathematics (1883) than
the method of limits.
239. Infinitesimals
Corrected proofs, G-1900-1.
240. A Mathematical Suggestion
A. MS., n.p., n.d., 1 folded sheet (4 pp.).
241. A Mathematical Discussion
A. MS., n.p., n.d., l folded sheet (4 pp.).
242. [Computation of Ordinates for Points on a Probability
Curve]
A. MS., n.p., n.d., 1 p.
243. The Theta Function of Probabilities
A. MS., n.p., n.d., 1 p., with 5 sheets of calculations.
* 244. [A Problem in Probabilities]
A. MS., notebook, n.p., n.d.
Solution of algebraic problems. Venn Diagrams. Calculation
of the asymptotic axis of the larger atomic weights.
245. Illustrative Problem in Probabilities
A. MS., n.p., n.d., 16 pp.
246. Reflections on the Logic of Science
A. MS., n.p., January 1-7, 1889, pp. 2-22
Evidently for a book on the philosophy of physics. The
relationship between mathematics and physical theory.
The Rule of False. MSS. 247-249 are presumably continuations
of this one.
247. Chapter II. The Doctrine of Chances
A. MS., n.p., January 8, 1889, pp. 23-29, plus another
p. 27.
248. Chapter II. Mathematics
A. MS., n.p., January 9-17, 1889, pp. 23-29.
249. Ordinal Geometry
A. MS., n.p., January 18-19, 1889, 40 pp., representing
several starts.
250. Notes for Chapter of Mathematics
A. MS., n.p., November 24-25, 1901, pp. 1-4.
251. Topics of Mathematics
A. MS., n.p., n.d., 1 p.
252. [On Mathematical Reasoning]
A. MS., n.p., n.d., 22 pp.
Mathematical reasoning illustrated by means of the game
tit-tat-too. The advantage, in general, of studying
mathematics.
253. Logical Analysis of Some Demonstrations in High
Arithmetic (D)
A. MS., n.p., June 11, 1905, pp. 1-20, incomplete, with
an alternate p. 20.
Reference is made to a paper published in The American
Journal of Mathematics (G-1881-7). Demonstrations of
Fermat's and Wilson's theorems.
254. Of the Nature of Measurement
A. MS., G-undated-4, pp. 1-26, plus 6 pp. rejected.
Published, in part, as 7.280-312. Omitted are the demonstration
and scholium in connection with the theorem on hyperbolic
motion (pp. 13-17) and the corollary of the definition
occurring on p. 21 and published as 7.312 (pp. 22-26).
255. Of the Nature of Measurement
A. MS., n.p., n.d., pp. 1-8, plus variants.
256. Properties of Space
A. MS., n.p., n.d., 11 pp. (fragmentary).
257. [On the Properties of Space]
A. MS., n.p., n.d., 6 pp. and 5 pp. of another draft.
The three classes of spatial properties: intrinsic,
metrical, and optical.
258. [On the Properties of Mathematical Space]
A. MS., n.p., n.d., 2 pp.
Space is tri-dimensional and unlimited; its points are
continuous; and it has the same properties everywhere,
and in all directions.
259. Note on the Analytic Representation of Space as
a Section of a Higher Dimensional Space
A. MS., n.p., n.d., 1 p.
260. Note on the Utility of considering Space as a Section
of a Space of more than 3 Dimensions
A. MS., n.p., n.d., 4 pp.
261. Notes on Geometry of Plane Curves without Imaginaries
A. MS., n.p., n.d., pp. 1-5, plus 6 pp.
262. On the Real Qualitative Characters of Plane Curves
TS., n.p., n.d., 12 pp. of several drafts.
*263. Singularities of Pairs of Terminals
A. MS., n.p., n.d., 2 pp.
264. On the Real Singularities of Plane Curves
A. MS., n.p., n.d., 9 pp.
265. Topical Singularities
A. M.S., n.p., n.d., 3 pp.
266. [Worksheets on the Nine-Ray Theorem]
A. MS., notebook, n.p., n.d.
267. [Points, Lines, and Surfaces]
A. MS., notebook, n.p., n.d.
268. Euclid Easy. Chapter I. A Talk on Continuity
A. MS., n.p., n.d., pp. 1-4.
An imaginary conversation between Thomas J. Jeffers
and Euclid Easy, preparatory to a full scale discussion
of the logic of continuity.
269. Notes for Theorems
A. MS., notebook, n.p., n.d.
Various topics are listed with reference both to standard
works and other writings. Topology and the four-color
problem.
270. Test-Example of Mathematical Reasoning
A. MS., n.p., n.d., 6 pp.
An inquiry which presupposes points, rays, planes, and
a relation called "containing."
271. Pythagorean
A. MS., n.p., n.d., 1 p.
272. Remarkable points of a triangle
A. MS., n.p., n.d., 2 pp., and 4 pp. ("Triangle").
273. [Homoloids]
A. MS., n.p., n.d., 8 pp.
Discussion of the four-ray problem.
274. The Dodecanes
A. MS., n.p., n.d., 26 pp,
275. On a Geometrical Notation
TS., n.p., n.d., 2 pp., with 2 pp. of TS. (corrected)
on "Notation."
276. Miscellaneous Journal
A. MS., notebook, dated entries for February 9, 11,
14-15, 20, 25, 28, 1910.
Secundal arithmetic. Probability. Petersburg problem.
Justification for asserting a proposition. Analysis
of the predicate "positive." Also a draft
of a letter apparently to Mrs. O. H. P. Belmont.
277. The Prescott Book
A. MS., n.p., begun May 1907 and continued June 8, 1907-September
13, 1910.
On singularities, Petersburg problem, Ten-Point theorem,
continuity, existential graphs. An analysis of signs,
notes on phaneroscopy, and an outline of a paper for
the Hibbert Journal on "a little known 'Argument'
for the Being of God."
*278. [Unidentified Fragments]
A. MS., n.p., n.d., over 1400 pp.