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MATHEMATICS (MS 1-278)
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.
Achilles and Tortoise, Algebra, Composition, Continuum, Desargues GÈrard tenline theorem, Division, Equations, linear, Equations, simultaneous, Fractions, logical and mathematical Functions, graphics, graphics, topical (topics or topology), Homogeneity, Homoloids, Homoloids, dominant, Homoloids, optical, Infinitesimals, Limit, Mathematics, Mathematics textbooks, Multiplication, Nineray theorem, Number, Place, Proposition, imaginary Quantity, Ratio, anharmonic Ratio, Rational number, Singularities (see also Geometry topics), tridimensionality of Space, Surfaces (see also Geometry topics), Textbooks mathematical
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.
MATHEMATICS / MATHEMATICAL TEXTBOOKS