IT IS ABOUT MATHEMATICIAN'S HISTORY AND ABOUT HOW THEY SOLVE THE PROBLEM .

1. Life History of MATHEMATICIANS
OF Egypt and England
MADE BY:-
Vansh

2. Contents
 WHAT IS A MATHAMETICS ?
 HISTORY OF MATHEMATICS.
 MATHEMATICIANS OF ENGLAND.
 Life History of MATHEMATICIANS
OF ENGLAND.
 MATHEMATICIANS OF EGYPT.
 Life History of MATHEMATICIANS OF EGYPT.

3. WHAT IS A MATHEMATHICS ?
ANS Mathematics is the abstract science of
numbers, quantity and space.
Mathematics is the body of knowledge
centered on such concepts as quantity,
structure, space and change, and also the
academic discipline that studies them.

4. HISTORY OF MATHEMATHICS
• This section is on the history of mathematicians. For a history of
mathematics in general, see History of mathematics.
• In 1938 in the United States, mathematicians were desired as teachers,
calculating machine operators, mechanical engineers, accounting auditor
bookkeepers, and actuary statisticians.
• One of the earliest known mathematicians was Thales of Miletus (c. 624–
c.546 BC); he has been hailed as the first true mathematician and the first
known individual to whom a mathematical discovery has been attributed.]
He is credited with the first use of deductive reasoning applied to
geometry, by deriving four corollaries to Thales' Theorem.
• The number of known mathematicians grew when Pythagoras of Samos
(c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it
was that mathematics ruled the universe and whose motto was "All is
number". The number of known mathematicians grew when Pythagoras
of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose
doctrine it was that mathematics ruled the universe and whose motto was
"All is number".

5. MATHEMATICIANS of ENGLAND
NAME Famous mathematician of ENGLAND
1) John Laden
2) John Coach Adams
3) George Boole

6. HISTORY OF JOHN LANDEN
(MATHEMATICIAN OF ENGLAND)
• Life
• He was born at Peakirk, near Peterborough in
Northamptonshire, on 28 January 1719. He was
brought up to the business of a surveyor, and acted as
land agent to Earl Fitzwilliam, from 1762 to 1788.
Cultivating mathematics during his leisure hours, he
became a contributor to the Ladies' Diary in 1744,
published Mathematical Lucubrations in 1755, and
from 1754 onwards communicated to the Royal Society
valuable investigations on points connected with the
fluxionary calculus.

7. WORK OF JOHN LANDEN
WORKS
• The Ladies' Diary, various communications (1744-1760)
• papers in the Phil. Trans. (1754, 1760, 1768, 1771,
1775, 1777, 1785)
• Mathematical Lucubrations (1755)
• A Discourse concerning the Residual Analysis (1758)
• The Residual Analysis, book i. (1764)
• Animadversions on Dr Stewarts Method of computing
the Sun's Distance from the Earth (1771)
• Mathematical Memoirs (1780, 1789

8. JOHN COACH ADAMS
• Born 5 June 1819
Laneast, Launceston, Cornwall, United Kingdom Died
21 January 1892 (aged 72)
Cambridge Observatory
Cambridgeshire, England Nationality British Fields
Mathematics
Astronomy Institutions University of St. Andrews
University of Cambridge Academic advisors John
Hymers Notable awards Smith's Prize (1843)
Copley Medal (1848)
Gold Medal of the Royal Astronomical Society (1866}
•

9. GEORGE BOOLE
• Born 2 November 1815
Lincoln, Lincolnshire, England Died 8 December 1864
(aged 49)
Ballintemple, County Cork, Ireland Nationality British Religion
Unitarian Era 19th-century philosophy Region Western
Philosophy School Mathematical foundations of computing
• Main interests
• Mathematics, Logic, Philosophy of mathematics
• Notable ideas
• Boolean algebra
•

10. EARLY LIFE OF GEROGE BOOLE
• Early life
• Boole was born in Lincolnshire, England. His father, John Boole
(1779–1848), was a tradesman in Lincoln and gave him lessons. He
had a primary school education, but little further formal and
academic teaching. William Brooke, a bookseller in Lincoln, may
have helped him with Latin, which he may also have learned at the
school of Thomas Bainbridge. He was self-taught in modern
languages. At age 16 Boole became the breadwinner for his
parents and three younger siblings, taking up a junior teaching
position in Doncaster at Heigham's School. He taught briefly in
Liverpool.
• Boole participated in the local Mechanics Institute, the Lincoln
Mechanics' Institution, which was founded in 1833.Edward
Bromhead, who knew John Boole through the institution, helped
George Boole with mathematics books and he was given the
calculus text of Sylvestre François Lacroix by the Rev. George
Stevens Dickson of St Swithin's Lincoln. Without a teacher, it took
him many years to master calculus.

11. HONOURS AND AWARDS
• Boole was awarded the Keith Medal by the
Royal Society of Edinburgh in 1855 and was
elected a Fellow of the Royal Society in 1857.
He received honorary degrees of LL.D. from
the University of Dublin and Oxford University.

12. ALBERT EDWARD INGHAM
MAIN DEATAILS
ALBERT EDWARD INGHAM WAS BORN ON
3 APRIL 1900.HE WAS BORN IN NORTHAMPTON,
ENGLAND.
HE DIED AT 6 SEPTEMBER 1967 IN CHAMONIX,
FRANCE.

13. About ALBERT EDWARD INGHAM
EARLY LIFE
Albert Ingham’s father was Albert Edward Ingham
( born about 1875 in Northampton) who was a
foreman in a boot manufacturing factory . His
mother was Annie Gertrude Ingham (born about
1876 in Northampton) Albert Edward Ingham
(our mathematician) had an older brother
Christopher Augustus (born about 1897), and two
younger sister Phyllis Gertrude ( born about
1904) and Lilian Grace ( born about 1910)

14. SCHOOL LIFE OF ALBERT EDWARD INGHAM
Albert Ingham was educated at Stafford Grammar
School, and from there he won a scholarship to Trinity
College, Cambridge, in December 1917. After spending
a few months in the army towards the end of World
war I, he began his studies in January 1919. An
outstanding undergraduate career saw him awarded
distinction in the mathematical Tripos and win a
Smith’s prize and the highest honours. In 1922 he was
elected to a fellowship at Trinity for a dissertation on
the zeta function and his next four years were
occupied only with research, a few months of which
were spent at Gottingen. During this time Ingham was
greatly influenced by Littlewood who gave him the
advice to:-
….. Work at a hard problem: you may not solve it but
you’ll solve another one.

15. COLLEGE LIFE OF ALBERT EDWARD
INGHAM
In 1926 Ingham was appointed a Reader at
Leeds University but four years later returned
to Cambridge as a university lecturer and a
Fellow of King’s College, on the death of
Ramsey, and remained there for the rest of his
life. He was elected a Fellow of the Royal
Society in 1945 and became a Reader in
Mathematical Analysis in 1953.

16. HOW HE DIED?
He died while on a walking holiday in the
mountains. He and his wife Rose Marie Tuper-
Carey whom he married in 1932 , had taken
his type of holiday every summer for many
years.

17. DAVID GEORGE KENDALL
MAIN DETAILS
David George Kendall was born on 15 January
1918 in Ripon, Yorkshire, England.
He died on 23 October 2007 in Cambridge,
England.

18. Early life of David George Kendall
David Kendall attended Ripon Grammar School
and then entered Queen’s College, Oxford. He
was awarded his M.A. in 1943 but he had
already been involved in war work. During
these this year of World War II Kendall worked
as an Experimental Officer with the Ministry
of Supply from 1940 until the end of the war
in 1945.Other mathematicians such as Rogers
also held similar posts with the Ministry of
Supply.

19. College Life of David George Kendall
In 1946 Kendall was elected a fellow of Magdalen College,
Oxford and appointed a lecturer in Mathematics. He
spent the Academic Year 1952-53 in the United States
as a visiting lecture at Princeton University. Then in
1962 Kendall was appointed as Professor of
Mathematical Statics at the University of Cambridge. At
the same time he was elected a fellow of Churchill
College Cambridge. Kendall held this chair of
Mathematical Statistics until he retired in 1985 and
which time he became professor emeritus. He also
became an Emeritus Fellow of Magdalen College,
Oxford in 1989.

20. WORKS OF DAVID GEORGE KENDALL
Kendall is a leading authority on applied
probability and data analysis . He has written
on stochastic geometry and its applications,
and the statistical theory of shape . His recent
work includes two articles How to look at
object in a five-dimensional shape space
(1994-95) and The Riemannian structure of
Euclidean shape spaces: a novel environment
for statistics (1993).

21. EDWARD FOYLE COLLONGWOOD
MAIN DETAILS
He was born on 17 January 1900 in Alnwick,
Northumberland, England.
He died at 25 October 1970 in Alnwick ,
Norththumberland ,England .

22. EARLY LIFE OF EDWARD FOYLE
COLLINGWOOD
Edward Collingwood’s parents were Dorothy Fawcett and
Colonel Cuthbert George Collingwood .Colonel
Collingwood had a career in the army ,commanding the
Lancashire-Fusiliers in the battle the Anglo –Egyptian
force commanded by Kitchener defected the Mahdists
and established British dominance in Sudan . Colonel
Collingwood retired from army in 1899, the year before
his son Edward was born on the family of Lilburn Tower.
The estate is in Northumberland in the north of England
about 7 km from Wooler on the road to Alnwick (which is
about 20 KM to the south east). Edward was the oldest
of his parents four children, all boys, and he was brought
up on the family estate enjoying.

23. EDUCATION OF EDWARD FOYLE
COLLINGWOOD
Collingwood was educated at the Royal Naval
College Osborne , which he entered in 1913
moving to Dartmouth in the following year. He
joined the Navy and became a midshipman in
1915 on the ship HMS Collingwood. This ship
was named after Vice- Admiral Cuthbert
Collingwood who was Nelson’s second in
command at the battle of Trafalgar. Vice-
Admiral Collingwood was the brother of
Edward.

24. BIOGRAPHY OF COLLINGWOOD
Collingwood’s great – grandfather , and it was no
coincidence that Collingwood served on HMS
Collingwood for special arrangements had been
made for this to happen. However Collingwood’s
naval career came to an end when he fell down a
hatchway on board ship, broke his wrist and
damaged his knee, just before the battle of
Jutland. He was transferred to the hospital ship,
then invalided out of the Navy. Attempting to go
to Woolwich he failed to the medical examination
so, in 1918 , he entered Trinity College ,
Cambridge to study mathematics.

25. BIOGRAPHY OF COLLINGWOOD
• Collingwood became involved with hospital boards in Newcastle, being a
founder member of the Newcastle Regional Hospital Board and its
chairmen from 1953 to 1968, then later he was involved with medical
affairs on a national and international level. He was vice-president of the
International Hospital Federation from 1959 to 1967, a member of the
medical research council from 1960 to 1968, and he served on the royal
commission on medical education from 1965 to 1968. He was chairman of
the Council of Durham University for most of the 1950's and 1960's.
• He was elected to a fellowship of the Royal Society in 1965. He also served
the London Mathematical Society in many ways, as a member of the
Council and as Treasurer. He wrote an article in 1951 to mark the
centenary of the Society. He was knighted in 1962.
• Despite these numerous activities Collingwood still found time for various
hobbies. In particular he had a fine collection of eighteenth century
paintings, and a collection of Chinese porcelain. As with all his activities
Collingwood made a deep study of his hobbies and became a recognized
expert on Chinese porcelain.

26. HOW EDWARD FOYLE COLLINGWOOD
MADE MATHEMATICIANS.
Collingwood was influenced by his advisor of studies,
Hardy at Cambridge and decided early on that he
would undertake research in mathematics . He was
also influenced by Littlewood ,but his examination
performance was relatively poor and he obtained only
a Second Class degree in 1922. Although there were
many others in Collingwood‘s year at Cambridge like
Burkill Ingham and Newman, he seems to have had
little contact with them .A friend, Gilbert Ashton
,writing of these days ,wrote that Collingwood was:-
…always known by his friends and cotemporaries of
Trinity as ‘The Admircal’… I remember The Admircal as
a quiet , reserved and rather shy person…

27. WORKS OF EDWARD FOYLE
COLLINGWOOD
• He was in charge of the Sweeping Division in 1943, then Chief Scientist
in the Admiralty Mine Design Department in 1945. For his war work he
was awarded the C.B.E. and received the Legion of Merit from the USA
in 1946.
• After the war he returned to his researches on meromorphic functions,
publishing an important paper in 1949. He then undertook research
work with Mary Cartwright on the theory of cluster sets. Mary
Cartwright writes:-
• I tried to contribute what I could to this paper ... my impression is that
it was much less than his contribution. I also collaborated in one later
paper published in 1961 on an allied topic. ... I found myself quite
unable to grasp the deep results in the theory of sets of points on which
much of Collingwood's later work in this field depended.

28. HOW IS CHARACTER IS DESCRIBED?
Collingwood was loved and admired both for his
achievements and for the delight of his company.
... he had great intellectual powers which enabled
him to achieve excellence in diverse activities
conducted in parallel and not in series. Born in
Glendale in Northumberland he remained a
countrymen at heart with practical knowledge of
forestry, farming and gardening. ... He remained
a bachelor to the grief of the many dancing
partners who had been entranced by his waltzing!

29. Honours awarded to Edward
Collingwood
• Fellow of the Royal Society of Edinburgh 1954
BMC morning speaker 1956 Fellow of the
Royal Society 1965 LMS President1969 - 1970

30. Alfred Goldie
• Alfred William Goldie (December 10, 1920, Coseley, Staffordshire –
October 8, 2005, Barrow-in-Furness, Cumbria) was an English
Mathematician.
• Goldie was educated at Wolverhampton Grammar School and then read
Mathematics at St John's College, Cambridge. His studies were interrupted
by war work on ballistics with the Armament Research Department of the
Ministry of Supply, eventually taking his BA in 1942 and MA in 1946.
• Goldie became an Assistant Lecturer at the University of Nottingham in
1946. In 1948 he was appointed Lecturer in Pure Mathematics at what
was then King's College, Durham (and has been the University of
Newcastle upon Tyne since 1963) where he was promoted to Senior
Lecturer in 1958 and Reader in Algebra in 1960.
• In 1963 Goldie was appointed Professor of Pure Mathematics at the
University of Leeds. He retired from his chair in 1986 with the title
Emeritus Professor.

31. ABOUT Alfred Goldie
• Goldie won the 1970 Senior Berwick Prize from the London
Mathematical Society, where he also became Vice-
President from 1978-80.
• Goldie worked in ring theory where he introduced the
notion of the uniform dimension of a module, and the
reduced rank of a module. He is well known for Goldie's
theorem, which characterizes right Goldie rings. Indeed, his
Independent obituary described him as the "Lord of the
Rings".
• Goldie married Mary Kenyon in 1944. They had one son,
John, and two daughters, Isobel and Helen. Mary died in
1995 and in 2002 he married Margaret Turner who survived
him.

32. Alfred Goldie's father
Worked as a skilled fitter at Austin Motors, the car
manufacturers. The factory employed 1 500
skilled workers serving 15 000 unskilled labourers.
The former were responsible for preparing the
brass templates used for the accurate positioning
of the holes for the screws that held together the
various parts of the car. Templates were prepared
for new models every two years, and had to be
accurate to one thousandth of an inch. The skilled
workers often had little work to do, as the actual
drilling was done by the unskilled employees.

33. SCHOOL LIFE OF Alfred Goldie
• Alfred attended Wolverhampton Grammar School where he won a scholarship to
St John's College, Cambridge. He entered Cambridge in 1939 just days after World
War II began. His scholarship allowed him to complete the usual three year degree
in only two years and, indeed, he obtained a First in Part II of the mathematical
tripos in 1941. During these two years at Cambridge he was in the Officers Training
Corps, and he also took an interest in politics taking a left wing Communist
position.
• Because of the war, Goldie did not continue to Part III of the tripos but instead was
interviewed for a military position by C P Snow, the novelist, who was acting as
scientific adviser to the British Government. Snow realized that, despite Goldie's
training in the Officers Training Corps, he would make a more valuable
contribution to the war effort using his mathematical skills in Ballistic Research. He
was sent to work under C A Clemmow in Cambridge, but soon the Ballistic
Research team moved to Shrewsbury. He also spent time at a military base near
Glasgow, then towards the end of the war he was sent to the Woolwich Arsenal in
London. In October 1944 he married Mary Kenyon; they had one son and two
daughters. As the war drew to a close he began to think about restarting his
mathematical education

34. HOW HE CHARACTER IS DESCRIBED
He was a vivid personality with an individual mind, full of
opinions and strongly argued positions on mathematics
but also on the wider world, including politics, where
his views moved rightwards over the years - starting
with Communism whilst a student at Cambridge, and
ending well within traditional Conservatism. ... Alfred
Goldie was a very practical man, particularly enjoying
working with wood. He also had a love of the outdoors,
which he shared with his first wife, Mary, a geographer.
Despite somewhat incompatible personalities, they still
managed to give their three children a stable and
happy upbringing.

35. John Wallis
MAIN DETAILS OF JOHN WALLIS
He was born on 23 November 1616 in Ashford,
Kent, England.
He died on 28 October 1703 in Oxford, England.

36. EARLY LIFE OF JOHN WALLIS
• John Wallis's father was the Reverend John Wallis who
had become a minister in Ashford in 1602. He was a
highly respected man known widely in the area. The
Reverend Wallis married Joanna Chapman, who was
his second wife, in 1612 and John was the third of their
five children. When young John was about six years old
his father died.
• John went to school in Ashford but an outbreak of the
plague in the area led to his mother to decide that it
would be best for him to move away. He went to James
Movat's grammar school in Tenterden, Kent, in 1625
where he first showed his great potential as a scholar.
Writing in his autobiography, Wallis comments

37. SCHOOL LIFE OF JOHN WALLIS
However he spent 1631-32 at Martin Holbeach's
school in Felsted, Essex, where he became
proficient in Latin, Greek and Hebrew. He also
studied logic at this school but mathematics was
not considered important in the best schools of
the time, so Wallis did not come in contact with
that topic at school. It was during the 1631
Christmas holidays that Wallis first came in
contact with mathematics when his brother
taught him the rules of arithmetic. Wallis found
that mathematics .

38. COLLEGE LIFE OF JOHN WALLIS
• From school in Felsted he went to Emmanual College Cambridge,
entering around Christmas 1632. He took the standard bachelor of
arts degree and, since nobody at Cambridge at this time could
direct his mathematical studies, he took a range of topics such as
ethics, metaphysics, geography, astronomy, medicine and
anatomy. Although never intending to follow a career in medicine,
he defended his teacher Francis Glisson's revolutionary theory of
the circulation of the blood in a public debate, being the first
person to do so.
• In 1637 Wallis received his BA and continued his studies receiving
his Master's Degree in 1640. In the same year he was ordained by
the bishop of Winchester and appointed chaplain to Sir Richard
Darley at Butterworth in Yorkshire. Between 1642 and 1644 he
was chaplain at Hedingham, Essex and in London. It was during
this time that the first of two events which shaped Wallis's future
took place:-

39. Honours awarded to John Wallis
Fellow of the Royal Society
Biography in Aubrey's Brief Lives
Popular biographies list

40. MATHEMATICIAMS OF EGYPT
• ABU KAMIL SHUJA
• HYSPSICLES
• EUCLID
• SERENUS

41. ABU KAMIL SHUJA
MAIN DETAILS OF ABU KAMIL SHUJA
He born on about 850 in (possibly) Egypt
He died about 930

42. ABOUT ABU KAMIL SHUJA
• Abu Kamil Shuja is sometimes known as al-Hasib al-Misri, meaning the
calculator from Egypt. Very little is known about Abu Kamil's life -
perhaps even this is an exaggeration and it would be more honest to say
that we have no biographical details at all except that he came from
Egypt and we know his dates with a fair degree of certainty.
• The Fihrist (Index) was a work compiled by the bookseller Ibn an-Nadim
around 988. It gives a full account of the Arabic literature which was
available in the 10th century and it describes briefly some of the authors
of this literature. The Fihrist includes a reference to Abu Kamil and
among his works listed there are: (i) Book of fortune, (ii) Book of the key
to fortune, (iii) Book on algebra, (vi) Book on surveying and geometry, (v)
Book of the adequate, (vi) Book on omens, (vii) Book of the kernel, (viii)
Book of the two errors, and (ix) Book on augmentation and diminution.
Works by Abu Kamil which have survived, and will be discussed below,
include Book on algebra, Book of rare things in the art of calculation, and
Book on surveying and geometry.

43. ABOUT ABU KAMIL SHUJA
• Although we know nothing of Abu Kamil's life we do understand
something of the role he plays in the development of algebra. Before
al-Khwarizmi we have no information of how algebra developed in
Arabic countries, but relatively recent work by a number of historians
of mathematics as given a reasonable picture of how the subject
developed after al-Khwarizmi. The role of Abu Kamil is important here
as he was one of al-Khwarizmi's immediate successors. In fact Abu
Kamil himself stresses al-Khwarizmi's role as the "inventor of algebra".
He described al-Khwarizmi as (see for example [4] or [5]):-
• ... the one who was first to succeed in a book of algebra and who
pioneered and invented all the principles in it.
• Again Abu Kamil wrote:-
• I have established, in my second book, proof of the authority and
precedent in algebra of Muhammad ibn Musa al-Khwarizmi, and I have
answered that impetuous man Ibn Barza on his attribution to Abd al-
Hamid, whom he said was his grandfather.

44. ABOUT ABU KAMIL SHUJA
Abu Kamil had begun to understand what we would
write in symbols as xnxm = xn+m. For example he
uses the expression "square square root" for x5
(i.e. x2.x2.x), "cube cube" for x6 (i.e. x3.x3), "square
square square square" for x8 (i.e. x2.x2.x2.x2). In
fact Abu Kamil works easily with the powers up to
x8 which appear in the text. The algebra contains
69 problems which include many of the 40
problems considered by al-Khwarizmi, but with a
rather different approach to them.

45. WORKS OF ABU KAMIL SHUJA
The work also deals with circles and here Abu Kamil
takes π = 22/7. A whole section is devoted to
calculating the area of the segment of a circle.
The final part of the work gives rules for
calculating the side of regular polygons of 3, 4, 5,
6, 8, and 10 sides either inscribed in, or
circumscribed about, a circle of given diameter.
For the pentagon and decagon the rules which
Abu Kamil gives, although without proof in this
work, were fully proved in his algebra book.

46. Hypsicles of Alexandria
MAIN DETAILS OF Hypsicles of Alexandria
He was born on about 190 BC in Alexandria,
Egypt.
He died on about 120 BC.

47. About Hypsicles of Alexandria
• Hypsicles of Alexandria wrote a treatise on regular polyhedra. He is
the author of what has been called Book XIV of Euclid's Elements, a
work which deals with inscribing regular solids in a sphere.
• What little is known of Hypsicles' life is related by him in the
preface to the so-called Book XIV. He writes that Basilides of Tyre
came to Alexandria and there he discussed mathematics with
Hypsicles' father. Hypsicles relates that his father and Basilides
studied a treatise by Apollonius on a dodecahedron and an
icosahedron in the same sphere and decided that Apollonius's
treatment was not satisfactory.
• In the so-called Book XIV Hypsicles proves some results due to
Apollonius. He had clearly studied Apollonius's tract on inscribing a
dodecahedron and an icosahedron in the same sphere and clearly
had, as his father and Basilides before him, found it poorly
presented and Hypsicles attempts to improve on Apollonius's
treatment.

48. About Hypsicles of Alexandria
• Arab writers also claim that Hypsicles was involved with the so-
called Book XV of the Elements. Bulmer-Thomas writes in [1] that
various aspects are ascribed to him, claiming that either:-
• ... he wrote it, edited it, or merely discovered it. But this is clearly
a much later and much inferior book, in three separate parts, and
this speculation appears to derive from a misunderstanding of the
preface to Book XIV.
• Diophantus quotes a definition of polygonal number due to
Hypsicles (see either [1] or [2]):-
• If there are as many numbers as we please beginning from 1 and
increasing by the same common difference, then, when the
common difference is 1, the sum of all the numbers is a triangular
number; when 2 a square; when 3, a pentagonal number [and so
on]. And the number of angles is called after the number which
exceeds the common difference by 2, and the side after the
number of terms including 1.
• This says that, in modern notation, the nth m-agonal number is
• n [2 + (n - 1) (m - 2)]/2.

49. WORK OF Hypsicles of Alexandria
• The work which involves arithmetic progressions is
Hypsicles' On the Ascension of Stars. In this work he was the
first to divide the Zodiac into 360°. He says (see [1] or [2]):-
• The circle of the zodiac having been divided into 360 equal
arcs, let each of the arcs be called a spatial degree, and
likewise, if the time taken by the zodiac circle to return from
a point to the same point is divided into 360 equal times, let
each of the times be called a temporal degree.
• Hypsicles considers two problems in this work [2]:-.
• (i) Given the ratio of the longest to the shortest day at any
place, how long does it take any given sign of the zodiac to
rise there?
(ii) How long does it take any given degree in a sign to rise?

50. MISTAKES OF Hypsicles of Alexandria
The mistake which Hypsicles makes is to assume
that the rising times form an arithmetical
progression. Having made this assumption his
results are correct and Neugebauer certainly
values this work much more highly than Heath
does. In fact without the aid of the sine
function and trigonometry it is hard to see
how Hypsicles could have done better.

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