**Joseph Raphson** was an English mathematician credited with the independent discovery of Newton's method for solving equations numerically.

- James Raphson's will is dated October, 1689, and he was buried in Pinner churchyard in Middlesex.
- Joseph's life can only be deduced from a number of pointers.
- No obituary of Raphson seems to have been written and we can now only piece together details about his life from records which exist such at University of Cambridge records and records of the Royal Society.
- It is through the University of Cambridge records that we know that Raphson graduated with an M.A. from Jesus College Cambridge in 1692 but it is almost certain that he never studied at Cambridge since the M.A. is by Royal warrant.
- Someone of the name "Joseph Raphson" was baptised in the Parish Church in Pinner, Middlesex in the 1660s and, again it cannot be proved with certainly that this is the Joseph Raphson of this biography but it does seem highly probable.
- Rather remarkably Raphson was made a member of the Royal Society in 1689 when, if our date of birth is correct, he was only 21 years of age.
- Raphson was elected a fellow at the meeting on Saturday 30 November 1689 and, four days later, he signed the Charter Book of the Society.
- Raphson's election to that Society was on the strength of work which was published in his book "Analysis aequationum universalis" Ⓣ(Universal analysis of equations) in 1690.
- This method invented by Raphson and described in his book "Analysis aequationum universalis" Ⓣ(Universal analysis of equations) is now called the Newton method (or the Newton-Raphson method) for approximating the roots of an equation.
- Although written in 1671 it was not published until 1736, so Raphson published the result nearly 50 years before Newton.
- A copy of Raphson's book was presented as "a gift from the author" to the Society on Saturday 17 January 1691.
- Raphson's relation to Newton is important but not particularly well understood.
- In 1711, Roger Cotes and William Jones arranged for Raphson to see some of Newton's papers "...
- Raphson did indeed write his History of Fluxions which did not appear until 1715, after Raphson had died, under the title Historia fluxionum.
- Certain letters which had passed between Newton and Leibniz appeared as an appendix to a reprint of Raphson's book in 1716-1718.
- This was not Raphson's only publication relating to Newton's work.
- Newton's Arithmetica universalis Ⓣ(Universal arithmetic) was translated by Raphson and was published as Universal arithmetick in 1720 after Raphson's death.
- Early in his career Raphson published a mathematical dictionary.
- In 1691, the year Raphson was elected to the Royal Society, Jacques Ozanam published Dictionnaire mathématique.
- written by J Raphson FRS.
- Raphson published a second edition of his analysis book and, at the same time, appended his article De spatio reali Ⓣ(Real space) which is an application of mathematical reasoning to theological issues.
- Raphson wrote a second theological work Demonstratio de deo Ⓣ(Demonstration of God) in 1710.
- De spatio reali Ⓣ(Real space) discusses space and in it Raphson talks of 'real space' which he thinks of as being independent of the mind that perceives it.
- Raphson's ideas of space and philosophy were based on Cabalist ideas.
- Cabala developed several basic doctrines which were strong influences on Raphson's philosophical thinking.
- In these two works by Raphson De spatio reali Ⓣ(Real space) and Demonstratio de deo Ⓣ(Demonstration of God), cosmology, natural philosophy, mathematics and his Cabalist beliefs combine.
- Newton's views of space were strongly influenced by Christian beliefs, and possible just slightly by his interaction with Raphson.
- Let us now say a little about the date of 1712 that we have given for Raphson's death.
- Cotes corresponded with Raphson in 1709 and, writing to William Jones in February 1711, he mentions Raphson whom he certainly believes to be alive at that time.
- We mentioned above that after Leibniz died in November 1716, Newton produced an appendix to Raphson's Historia fluxionum Ⓣ(History of fluxions) but, relevant to the date of Raphson's death, retained the same 1715 publication date on the work.
- Newton's appendix states clearly that Raphson had died three years earlier.
- If we assume that Newton deliberately kept the 1715 date on the book despite the appendix being added one or even two years later, then one assumes that he would write that Raphson died three years earlier if he died in 1712.
- A date of late 1712 would also be consistent with the fact that Raphson's name appears in the 1712 list of fellows of the Royal Society but not in the 1713 list.

Born 1668, Pinner, Middlesex, England. Died 1712, England.

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Ancient Indian, Origin England

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive