Ebook: From Discrete to Continuous: The Broadening of Number Concepts in Early Modern England
Author: Katherine Neal (auth.)
- Tags: History, History of Mathematical Sciences, Mathematics Education, Algebra
- Series: Australasian Studies in History and Philosophy of Science 16
- Year: 2002
- Publisher: Springer Netherlands
- Edition: 1
- Language: English
- pdf
In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways.
This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.
In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways.
This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.
In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways.
This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.
Content:
Front Matter....Pages i-ix
Transformation of the Number Concept....Pages 1-11
The Ancient Sources....Pages 12-27
The Contemporary Influences....Pages 28-45
Early Modern English Algebra....Pages 46-79
The Development of the Logarithms....Pages 80-114
Isaac Barrow....Pages 115-137
John Wallis....Pages 138-156
Conclusion....Pages 157-162
Back Matter....Pages 163-175
In the early modern period, a crucial transformation occurred in the classical conception of number and magnitude. Traditionally, numbers were merely collections of discrete units that measured some multiple. Magnitude, on the other hand, was usually described as being continuous, or being divisible into parts that are infinitely divisible. This traditional idea of discrete number versus continuous magnitude was challenged in the early modern period in several ways.
This detailed study explores how the development of algebraic symbolism, logarithms, and the growing practical demands for an expanded number concept all contributed to a broadening of the number concept in early modern England. An interest in solving practical problems was not, in itself, enough to cause a generalisation of the number concept. It was the combined impact of novel practical applications together with the concomitant development of such mathematical advances as algebraic notation and logarithms that produced a broadened number concept.
Content:
Front Matter....Pages i-ix
Transformation of the Number Concept....Pages 1-11
The Ancient Sources....Pages 12-27
The Contemporary Influences....Pages 28-45
Early Modern English Algebra....Pages 46-79
The Development of the Logarithms....Pages 80-114
Isaac Barrow....Pages 115-137
John Wallis....Pages 138-156
Conclusion....Pages 157-162
Back Matter....Pages 163-175
....