#### ESCENA 1

James Gregory
(1638-1675)
Scottish mathematician
and astronomer

•Studied optics and telescopes:
published Optica Promota in 1663

#### ESCENA 2

1st reflecting telescope:Gregorian telescope

1664, went to the University of Padua:

worked on using infinite convergent
series to find the areas of the circle and hyperbola

#### ESCENA 3

Books

-Vera circuli et hyperbolae quadrature (1667)
o Tried to prove that pi and e are transcendental

-Geometriae Pars Universalis (1668)
first known proof that the method of
tangents (differentiation) was inverse to the
method of quadratures (integration)

#### ESCENA 4

SOME DRAMA WITH VERA.....

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He sent a copy of his Vera circuli et hyperbolae quadrature
to Huygens, a Dutch mathematician, in 1668,
looking forward to hearing his expert opinions

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Huygens published a review in July 1668

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He raised objections and claimed that he
himself had been the first to prove some of
Gregory’s results
Basically, Huygens accused him of stealing

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Gregory published Exercitationes Geometricae
as a counterattack on Huygens,
including series expansions and the integral of logs

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DRAMA OVER
He joined the Royal Society
and became Regius Chair of
Mathematics

#### ESCENA 10

Add an
image here

•In a letter to his friend Collins, in 1671, he describes
Taylor’s theorem (Taylor discovered it in 1715)

#### ESCENA 11

So,

he's

the bomb.com

#### ESCENA 12

MORE ACCOMPLISHMENTS:
-earliest examples of a
comparison test for convergence
-definition of the integral
-begun to realize that algebraic equations
of degree greater than four could
not be solved by radicals

www.gregory.bomb.com