she-philosopher.com: Looking forward (the LIBRARY section)

This little tract, written for Samuel Hartlib in 1639 and published by Hartlib in 1650, was approved not only by Hartlib, but also by Mersennes and Descartes. Indeed, Robert Hooke would record this early model of peer review, conducted by way of correspondence, by reprinting Pell’s Idea Mathesos along with

· Mersenne’s “his Censure of this Idea” (dated 1639),

· Pell’s “Answer to this Censure” (dated 1639),

· Mersenne’s very short “Reply thereunto, and his full approbation thereof” (dated 1639),

· and Descartes’ “Judgment and Approbation ... of this Idea” (dated 1640),

in No. 5 (1682) of his Philosophical Collections, a scientific journal which filled the 6-year void in publication of the Philosophical Transactions of the Royal Society of London (between vol. 12 and vol. 13) after Henry Oldenburg (publisher of the Transactions) died in 1677.

“[B]eing a common friend to them all,” the German refugee Theodore Haak, F.R.S. had been sent copies of all 4 letters on Pell’s Idea, which he had kept among his papers. It was Haak who passed the correspondence to Hooke for formal publication in 1682.

Pell’s scheme for making mathematical knowledge more generally available centered on his proposal for

a library which would contain not only all the mathematical books that were published but all mathematical instruments besides, while specially compiled compendiums and epitomes would be at the disposal of the young student, besides a well-informed librarian.

It was an idea which resonated with the members of the Hartlib circle studying the pedagogical reforms of Comenius, who had visited England in 1642. Their Comenian program had many followers in England, and was an important influence on Royal Society founders and fellows alike. Pell was elected a Fellow of the Royal Society in 1663.

Pell, who showed great early promise which he did not always live up to, trained with the rector of the academy at Albury (hence, sometime tutor in the earl of Arundel’s family), William Oughtred. Oughtred was a brilliant mathematician who invented trigonometrical abbreviations and introduced the multiplication and proportion signs. Pell would himself discover the division sign (the line with a dot above and below), and would move in most all the overlapping social circles associated with the new science during his lifetime. As a member of the Cavendish circle, e.g., he collaborated with Charles Cavendish (Margaret’s brother-in-law) on mathematical matters; extending their research to optics, the two men together designed a new type of lens for a perspective glass.

Aubrey records that Pell was an accomplished linguist: “before he went first out of England, he understood” Latin, Greek, Hebrew, Arabic, Italian, French, Spanish, High-Dutch, and Low-Dutch. Like Oughtred, Pell “did believe that he solved some questions non sine divino auxilio.” And he told Aubrey that his mathematical genius ran throughout body and soul:

... when he solves a question he straines every nerve about him, and that now in his old age it brings him to a looseness.

Pell was also the brother-in-law of Bathsua Makin. Makin, who was governess and tutor to the children of Charles I and Henrietta Maria for about 10 years, later ran at least one school for young “gentlewomen” in which they were taught the “experimental philosophy” (knowledge of things and arts), as well as foreign languages (French, Latin, Greek, Hebrew, Italian and Spanish), oratory, logic, philosophy and mathematics, geography, history, and astronomy. The comprehensive and innovative curriculum, with its concentration on science, was perhaps the earliest implementation of Comenian pedagogy aimed at girls.

As with her brother-in-law, Makin’s ties to new science circles extended beyond that of Hartlib and Comenius, in her case encompassing medical professionals as well. According to her modern biographer, Fran Teague, Makin’s “work as a healer was well-known: she had received Sir Walter Raleigh’s chemical and alchemical recipes from his widow, for example, and was a friend to several prominent members of the Royal College of Physicians.”

RELATES TO: various ISSUES webessays and IN BRIEF topics on the gendering of science and women’s aptitude for mathematics; the GALLERY exhibit on Chambers’ Cyclopædia, with its discussion of Petty’s reformed “Gymnasium Mechanicum or a Colledge of Trades-men”; references to Comenius and the Hartlib/Comenian educational reform movement scattered throughout the site (e.g., the feature on “The Booksellers Shop” on the LIBRARY page, and the discussion of Prudentia as figured in Comenius’ primer, Orbis Pictus, in the GALLERY exhibit on the Athenian Society emblem); references to Bathsua Makin scattered throughout the site (e.g., the introductory webessay on Margaret Cavendish in the PLAYERS section and the GALLERY exhibit, Portraits of Melancholy — III)


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Search this site		© August 2005 revised 26 June 2008
	*John Pell’s An Idea of Mathematics* (1650)** This little tract, written for Samuel Hartlib in 1639 and published by Hartlib in 1650, was approved not only by Hartlib, but also by Mersennes and Descartes. Indeed, Robert Hooke would record this early model of peer review, conducted by way of correspondence, by reprinting Pell’s Idea Mathesos along with · Mersenne’s “his Censure of this Idea” (dated 1639), · Pell’s “Answer to this Censure” (dated 1639), · Mersenne’s very short “Reply thereunto, and his full approbation thereof” (dated 1639), · and Descartes’ “Judgment and Approbation ... of this Idea” (dated 1640), in No. 5 (1682) of his Philosophical Collections, a scientific journal which filled the 6-year void in publication of the Philosophical Transactions of the Royal Society of London (between vol. 12 and vol. 13) after Henry Oldenburg (publisher of the Transactions) died in 1677. “[B]eing a common friend to them all,” the German refugee Theodore Haak, F.R.S. had been sent copies of all 4 letters on Pell’s Idea, which he had kept among his papers. It was Haak who passed the correspondence to Hooke for formal publication in 1682. Pell’s scheme for making mathematical knowledge more generally available centered on his proposal for a library which would contain not only all the mathematical books that were published but all mathematical instruments besides, while specially compiled compendiums and epitomes would be at the disposal of the young student, besides a well-informed librarian. It was an idea which resonated with the members of the Hartlib circle studying the pedagogical reforms of Comenius, who had visited England in 1642. Their Comenian program had many followers in England, and was an important influence on Royal Society founders and fellows alike. Pell was elected a Fellow of the Royal Society in 1663. Pell, who showed great early promise which he did not always live up to, trained with the rector of the academy at Albury (hence, sometime tutor in the earl of Arundel’s family), William Oughtred. Oughtred was a brilliant mathematician who invented trigonometrical abbreviations and introduced the multiplication and proportion signs. Pell would himself discover the division sign (the line with a dot above and below), and would move in most all the overlapping social circles associated with the new science during his lifetime. As a member of the Cavendish circle, e.g., he collaborated with Charles Cavendish (Margaret’s brother-in-law) on mathematical matters; extending their research to optics, the two men together designed a new type of lens for a perspective glass. Aubrey records that Pell was an accomplished linguist: “before he went first out of England, he understood” Latin, Greek, Hebrew, Arabic, Italian, French, Spanish, High-Dutch, and Low-Dutch. Like Oughtred, Pell “did believe that he solved some questions non sine divino auxilio.” And he told Aubrey that his mathematical genius ran throughout body and soul: ... when he solves a question he straines every nerve about him, and that now in his old age it brings him to a looseness. Pell was also the brother-in-law of Bathsua Makin. Makin, who was governess and tutor to the children of Charles I and Henrietta Maria for about 10 years, later ran at least one school for young “gentlewomen” in which they were taught the “experimental philosophy” (knowledge of things and arts), as well as foreign languages (French, Latin, Greek, Hebrew, Italian and Spanish), oratory, logic, philosophy and mathematics, geography, history, and astronomy. The comprehensive and innovative curriculum, with its concentration on science, was perhaps the earliest implementation of Comenian pedagogy aimed at girls. As with her brother-in-law, Makin’s ties to new science circles extended beyond that of Hartlib and Comenius, in her case encompassing medical professionals as well. According to her modern biographer, Fran Teague, Makin’s “work as a healer was well-known: she had received Sir Walter Raleigh’s chemical and alchemical recipes from his widow, for example, and was a friend to several prominent members of the Royal College of Physicians.” RELATES TO: various ISSUES webessays and IN BRIEF topics on the gendering of science and women’s aptitude for mathematics; the GALLERY exhibit on Chambers’ Cyclopædia, with its discussion of Petty’s reformed “Gymnasium Mechanicum or a Colledge of Trades-men”; references to Comenius and the Hartlib/Comenian educational reform movement scattered throughout the site (e.g., the feature on “The Booksellers Shop” on the LIBRARY page, and the discussion of Prudentia as figured in Comenius’ primer, Orbis Pictus, in the GALLERY exhibit on the Athenian Society emblem); references to Bathsua Makin scattered throughout the site (e.g., the introductory webessay on Margaret Cavendish in the PLAYERS section and the GALLERY exhibit, Portraits of Melancholy — III)
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