Hero of Alexandria

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Hero of Alexandria

From Wikipedia, the free encyclopedia

Heron


Born

c.

10 AD

Residence

Alexandria
,

Roman Egypt

Fields

Mathematics

Known

for

aeolipile

Hero

(or

Heron
)

of Alexandria

(
Greek
:

Ἥρων ὁ Ἀλεξανδρεύς
) (c. 10

70 AD) was an ancient

Greek
mathematician

and

engineer
[1]
[2]
[3]

who was a
ctive in his native city of

Alexandria
,

Roman Egypt
. He is
considered the greatest experimenter of antiquity
[1]

and his work is representative of the

H
ellenistic
scientific
tradition.
[4]

Hero published a well recognized description of a

steam
-
powered device

called an

aeolipile

(hence sometimes
called a "Hero engine"). Among his most famous inventions was a

windwheel
, constituting the earliest instance
of

wind harnessing

on land.
[5]
[6]

He is said to have been a follower of the

Atomists
. Some of his ideas were
derived from the works of

Ctesibius
.

Much of Hero's original writings and designs have be
en lost, but some of his works were preserved in Arab
manuscripts.

Contents



[
hide
]




1

Career



2

Inventions and achievements



3

Mathematics



4

Bibliography



5

Media



6

See also



7

References



8

Further Reading



9

External links

[
edit
]
Career

A number of references mention dates around 150 BC, but these are inconsistent with the dates of
his
publications and inventions. This may be due to a misinterpretation of the phrase "first century" or because
Hero was a common name.

It is almost certain that Hero taught at the

Musaeum

which included the famous

Library of Alexandria
, because
most of his writings appear as lecture notes for courses in

mathematics
,

mechanics
,
physics

and

pneumatics
.
Although the field was not formalized until the 20th century, it is thought that the work of Hero, his automated
devices in particular, represents some of the first formal research into cybernetics.
[7]

[
edit
]
Inventions and achievements



Heron's
Aeolipile



Hero described construction of the

aeolipile

(a version of which is known as

Hero's engine
) which was
a

rocket
-
like reaction engine

and the first
-
recorded steam engine (although

Vitruvius

mentioned the
aeolipile in

De Architectura

some 100 years earlier than Hero). It was created almost two millennia before
the industrial revolution. Another engine used air from a closed chamber heated

by an altar fire to displace
water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple
doors.
[8]

Some historians have conflated the two inventions to assert that the aeolipile was capable of
useful work.
[9]



Hero's wind
-
powered

organ
(reconstruction)



The first

vending machine

was also one of his constructions, when a coin was introduced via a slot on the
top of the machine, a set amount of holy water was dispensed. This was included in his list of inventions in
his book, "Mechanics and Optics". When the coin was deposited, it
fell upon a pan attached to a lever. The
lever opened up a valve which let some water flow out. The pan continued to tilt with the weight of the coin
until it fell off, at which point a counter
-
weight would snap the lever back up and turn off the valve.
[10]



A windwheel operating an organ, marking the first instance of wind powering a machine in history.
[5]
[6]



Hero also invented many mechanisms for the Greek

theater
, including an en
tirely mechanical play almost
ten minutes in length, powered by a binary
-
like system of ropes, knots, and simple machines operated by
a rotating cylindrical cogwheel. The sound of

thunder

wa
s produced by the mechanically
-
timed dropping of
metal balls onto a hidden drum.



Hero's fire
-
engine



The

force pump

was widely used in the

Roman

world, and one application was in a fire
-
engine.



A

syringe
-
like device was described by Heron to control the d
elivery of air or liquids.
[11]



The syringe



In optics, Hero formulated the

Principle of the Shortest Path of Light
: If a ray of light propagates from point
A to point B within the same medium, the path
-
length followed is the shortest possible. It was nearly 1000
years later that

Alhacen

expanded the principle to both reflection and refraction, and the principle was later
stated in this form by

Pierre de Fermat

in 1662; the most moder
n form is that the path is at an

extremum
.



A standalone fountain that operates under self
-
contained hydrostatic energy. (
Heron's fountain
)

[
edit
]
Mathematics

Hero d
escribed a method of iteratively computing the

square root
.
[12]

Today, though, his name is most
closely
associated with

Heron's Formula

for finding the area of a triangle from its side lengths.

The

imaginary number
, or

imaginary unit
, is also noted to have been first observed by Hero while c
alculating
the volume of a pyramidal frustum.
[13]

[
edit
]
Bibliography

The most comprehensive edition of Hero's works was published in 5 volumes in Leipzig by the publishing
house Teubner in 1903.

Works known to be written by Hero:



Pneumatica
, a description of machines working on

air
,

steam

or

water

pressure
, including
the

hydraulis

or

water organ
.
[14]



Automata
, a description of machines which enable wonders in temples by mechanical or pneumatical
means (e.g. automatic opening or closing of temple doors, statues that pour wine, etc.). See
Autom
aton
.



Mechanica
, preserved only in Arabic, written for

architects
, containing means to lift heavy objects.



Metrica
, a description of how to calculate

surfaces

and

volumes

of diverse objects.



On the Dioptra
, a collection of methods to measure lengths. In this work the

odometer

and the

dioptra
, an
apparatus which resembles the

theodolite
, are described.



Belopoeica
, a description of

war machines
.



Catoptrica
, about the progression of

light
,

reflection

and the use of

mirrors
.

Works which have sometimes been attributed to Hero
, but are now thought to have most likely been written by
someone else:
[15]



Geometria
, a collection of equations based on the first chapter of

Metrica
.



Stereometrica
,
examples of three dimensional calculations based on the second chapter of

Metrica
.



Mensurae
, tools which can be used to conduct measurements based on

Stereometrica

and

Metrica
.



Cheiroballistra
, about

catapults
.



Definitiones
, containing definitions of terms for geometry.

Works which are preserved only in fragments:



Geodesia



Geoponica

Latest paper on Hero:



Schellenberg, H.M.:

Anmerkungen zu Hero von Alexandria und seinem Werk über den
Geschützbau
, in:
Schellenberg, H.M./ Hirschmann, V.E./ Krieckhaus, A.(edd.): A Roman Miscellany. Essays in Honour of
Anthony R. Birley on his Seventieth Birthday, Gdansk 2008, 92
-
130 (with a huge bibliography of over 300
titles and discussion of the commun
is opinio on Hero).

[
edit
]
Media

A 2007

The

History Channel

television show

Ancient Discoveries

includes recreations of most of Heron's
devices.

A 2008 The History Channel television show

Ancient Discoveries

-

"Ancient New York" includes a short
recreation of a fountain device that made water flow
uphill.

A 1979 Soviet animated short film focuses on Heron's invention of the

aeolipile
, showing him as a plain
craftsman who invented the

turbine

accidentally.
[16]

[
edit
]
See also



Heron's formula



Heronian triangle



Heronian mean



Heron's engine

[
edit
]
References

1.

^

a

b

Research Machines plc. (2004).

The Hutchinson dictionary of scientific biography
. Abingdon, Oxon:
Helicon Publishing. pp.

546. "
Hero of Ale
xandria (lived c.

AD

60)

Greek mathematician and engineer, the
greatest experimentalist of antiquity"

2.

^

Boyer

(1968 [1991]). "Greek Trigonometry and Mensuration".

A History of Mathematics
. pp.

171

172. "At
least from the days of Alexander the Great to the close of the cla
ssical world, there undoubtedly was much
intercommunication between Greece and Mesopotamia, and it seems to be clear that the Babylonian
arithmetic and algebraic geometry continued to exert considerable influence in the Hellenistic world. This
aspect of ma
thematics, for example, appears so strongly in Heron of Alexandria (fl. ca. A.D. 100) that Heron
once was thought to be Egyptian or Phoenician rather than Greek. Now it is thought that Heron portrays a
type of mathematics that had long been present in Gree
ce but does not find a representative among the
great figures
-

except perhaps as betrayed by Ptolemy in the

Tetrabiblos
."

3.

^

Gregory A Tokaty (1994).

A History
and Philosophy of Fluid Mechanics
. Courier Dover Publications.
pp.

26.

ISBN

0
-
486
-
68103
-
3
.

Grolier Incorporated (1989).

Academic American Encyclopedia
. Grolier

University of Mich
igan
.
pp.

144.

ISBN

0
-
7172
-
2024
-
9
.

Encyclopædia Britannica Online
-

Heron of Alexandria

Israel Shatzman, Michael Avi
-
Yonah (1975).

Illustrated Encyclopedia of the Classical World
. Harper and
Row. pp.

234.

ISBN

0
-
06
-
010178
-
4
.

Gillian Clements (2005).

The Picture History of Great Inventors
. frances lincoln ltd. pp.

13.

ISBN

0
-
7112
-
1605
-
3
.

Enc. Britannica 2007, "Heron of Alexandria"

4.

^

Marie Boas, "Hero's Pneumatica: A Study of Its Transmission and Influence", Isis, Vol. 40, No. 1 (Feb.,
1949), p. 38 and supra

5.

^

a

b

A.G. Drachmann, "Heron's Windmill",

Centaurus
, 7 (1961), pp. 145
-
151

6.

^

a

b

Dietrich Lohrmann, "Von der östlichen zur westlichen Windmühle",

Archiv für Kulturgeschichte
, Vol. 77,
Issue 1 (1995), pp.1
-
30 (10f.)

7.

^

Kelly, Kevin (1994).

Out of control: the new biology of machines, social systems and the economic world
.
Boston: Addison
-
Wesley.

ISBN

0
-
201
-
48340
-
8
.

8.

^

Hero of Alexandria
; Bennet Woodcroft (trans.) (1851).

"Temple Doors opened by Fire on an
Altar"
.

Pneumatics of
Hero of Alexandria
. London: Taylor Walton and Maberly (online edition from University
of Rochester, Rochester, NY). Retrieved 2008
-
04
-
23.

9.

^

for example:

Mokyr, Joel

(2001).

Twenty
-
five centuries of technological change
. London: Routledge.
p.

11.

ISBN

0
-
415
-
26931
-
8
.
"Among the devices credited to Hero are the aeolipile, a working steam engine
used to open temple doors"

and

Wood, Chris M.; McDonald, D. Gordon (1997). "History of propulsion
devices and turbo machines".

Global Warming
. Cambridge, England: Cambridge Unive
rsity Press.
p.

3.

ISBN

0
-
521
-
49532
-
6
. "Two exhaust nozzles...were used to direct the steam with high velocity and
rotate the sphere...By attaching ropes to the axial shaft Heron used the developed power to perform tasks
such as opening temple doors"

10.

^

Humphrey, John W.; John P. Oleson, Andrew N. Sherwood (1998).

Greek and Roman technology: A
Sourcebook. Annotated translations of Greek and Latin texts and documents
. Routledge

Sourcebooks for
the Ancient World. London and New York: Routledge.

ISBN

978
-
0
-
415
-
06137
-
7
., pp.66

67

11.

^

Hero of Alexandria; Bennet Woodcroft (trans.) (1851). "No. 57. Description of a S
yringe.". Pneumatics of
Hero of Alexandria. London: Taylor Walton and Maberly (online edition from University of Rochester,
Rochester, NY).

[1]

Retrieved 2010 January 27

12.

^

Heath, Thomas (1921).

A History of Greek Mathematics, Vol. 2
. Oxford: Clarendon Press. pp.

323

324.

13.

^

Nahin, Paul."An Imaginary Tale: The story of [the square root of minus one]. Princeton University Press.
1998"

14.

^

Jamies W. McKinnon. "Hero of Alexandria and Hydraulis",

Grove Music Online
, ed. L. Macy (accessed
January 1
7 2007),

grovemusic.com

(subscription access).

15.

^

O'Connor, J.J. and E.F. Robertson.

"Heron biography"
.

The MacTutor History of Mathematics archive
.
Retrieved 2006
-
06
-
18.

16.

^

animator.ru

[
edit
]
Further Reading











Edit

3
0

59




Rene Descartes (1596
-
1650)



Introduction


Rene Descartes was a French philosopher,

mathematician,
and scientist and can be considered the father of modern
philosophy and the founder of modern mathematics. He is
best known for originating Cartesian philosophy ("I think,
therefore I am") and the Cartesian plain (coordinate plain).



Table

of Contents:

I. Biography

II. Works /Contributions to Science

III. Philosophy and Ideas

IV. Importance to the Scientific
Revolution**

V. Bibliography

VI. External Links



I.Biography


Rene Descartes was born on March 31st, 1596 in a small village called La Haye (now named Descartes
in honor of him) in France. He was the son of Joachim Descartes, a Councilor in Parliament, so Rene
enjoyed a good upbringing. However, his mother died when
he was only one. There were many things in
his life that separated him from the other people of the upper class in France. For one, his father believed
that Rene should solely focus on his studies. Because of this, his father moved him to another wing of t
he
house that isolated him from other possible distractions.(11) He got his education from the Jesuit College
of Henri IV where he studied literature, grammar, science and mathematics. Descartes proved to be the
most adept at mathematics and science. After

the Jesuit College, he went to Poitiers and earned his Law
degree, on the side he studied philosophy, theology and medicine.(11)


In 1618 while on a peaceful trip though Breda, Rene had the amazing fortune to run into what would
become one of the most fam
ous and respected philosophers of all time. While walking through Breda he
met Isaac Beckham, a renowned physicist and and extremely progressive mind during the time. When
the two met they immediately hit it off and began to have a deep conversation about
science and just life
in general. During their conversation they began to discuss physics and new age math. After talking about
this for a while, their conversations began to fall more heavily on the concept of gravity and the falling
body and objects. His

conversations with Issac Beckham would lead him to become one of the greatest
minds of our time and would direct his thinking towards " I think, therefore I am.". Descartes led a quiet life
from then on while making important philosophical, mathematical a
nd scientific discoveries. He came to
be quite famous because of his achievements. He left France for the Netherlands and stayed there for 16
years. It is there that he made his greatest discoveries and he returned to his native France for only brief
visit
s. In his later years, he was sent to Sweden to tutor Queen Christina in philosophy. However, the high
altitudes, cold weather, and early schedule proved to be too much for Descartes' health. He developed
pneumonia soon after he arrived in Sweden and died
on February 11th, 1650 at the age of 54.(11)


Rene Descartes



II.Works/ Contributions to Science


Rene Descartes' works include (5):



Compendium Musica

(1618): Descartes'

Compendium Musica

attempted to express the notion of
harmony in mathematical terms.(1)



Rules for the

Direction of the Mind

(1628): This document is a set of 21 rules set down by Descartes.
These rules state that "The aim of our studies should be to direct the mind with a view to forming true and
sound judgments about whatever comes before it."(12)



Discou
rse on the Method of Rightly Conducting the Reason, and Seeking the Truth in the
Sciences

(1637): This is arguably one of Descartes' most important works. It swept away the beliefs of
the past and set the stage for modern thought as it attempted to put hum
an knowledge on a firm
footing.(10)



La Géométrie

(1637): This document was an appendix to his previous work,

Discourse on the Method of
Rightly Conducting the Reason, and Seeking the Truth in the Sciences.

In this work, Descartes invented
what is now known

as analytical geometry. Another important contribution Descartes made in Geometry
was the invention of the Cartesian coordinates.(10)



Meditations on First Philosophy

(1641): In this document Descartes establishes modern skepticism and
rejects the Aristote
lian belief that all knowledge is gained from the senses. He also addresses the mind
-
body relationship and explains the concept of Dualism.(8)



Les Principes de la philosophie (Principles of Philosophy)

(1644): Although intended to have six parts,
this docu
ment had just four: The Principles of Human Knowledge, The Principles of Material Things, The
Visible Universe, and The Earth. In this document, Descartes took one step further in trying to create a
unified science and reject the Scholastic tradition.



The
Singing Epitaph

(1646)



Comments on a Certain Broadsheet

(1647)



The Description of the Human Body (
1647): In this document, Descartes shows the intricacies of the
human body based on his experiments and explains the importance of knowing one's own body. "Th
ere is
nothing one can more profitably occupy oneself with than with trying to know oneself." (4)



Conversation with Burman

(1648):In 1648, Descartes allowed Frans Burman to interview him. In the
interview they discussed a critical analysis of his past work
s and accomplishments. (15)



Passions of the Soul (
1649): In Descartes'

Passions of the Soul

he delves further into the Mind
-
Body
problem and in addition he gives an insight to his own personal moral philosophy.



Descartes also worked with the scholar Isaac
Beckham which enhanced his knowlegde of gravity and
mathematics. (7)



Descartes popularized the basics for Calculus and Analytical Geometry for future scholars and laid the
foundation for modern mathematics and philosophy. (15)


III.Philosophy And Ideas


Rene Descartes, also known as Cartesius, was the originator of Cartesian philosophy.(7) The quote "
Cognitus Ergo Sum" ,which in English means " I think, therefore I am",(12) sums up the philosophy of
doubt that Descartes derived, in which he stated that n
othing that he knew could be true. He said all
previously thought knowledge and his own senses could not be trusted. He then systematically eliminated
all known knowledge, beliefs and ideas. He did this by applying the rules of mathematics that he knew so
well. Like in math, he started with a strong foundation of self evident principles and then moving forward
as axioms are added to form more complex truths.(7) The only thing that could not be doubted was that
he existed, because he could think. He then beg
an to reprove all knowledge starting with the existence of
God and moving on from there. He figured that God must exist, because it was necessary for a perfect
being to set the world in motion, by defining physical laws.(7)


Another element of Cartesian ph
ilosophy is the connection between the the mind and the physical world.
He rationalized that the physical world had to be real because God would not deceive the mind with
illusions of a physical reality. However, at the same time, he believed that the phys
ical world was entirely
mechanical and the only connection between the mind and the physical world was from God.


Descartes assumed that the physical world was made up of an infinite amount of particles that were
continually moving, but not at random. He b
elieved that these "corpuscles" did not move at random, but
followed specific laws created by God. Descartes set out to discover these laws. He concluded at least
that a particle will remain at rest until otherwise pushed in a direction, and a moving parti
cle will not rest
unless deflected. This was the first unequivocal statement of the law of inertia (included inertial linearity,
unlike Galileo's thought of circularity).(7)



IV. Importance to the Scientific Revolution


Descartes played a very important role in the Scientific Revolution. Not only did he revolutionize human
knowledge and thought through skepticism, but he laid the foundation for modern philosophy and
mathematics. Before Descartes' time, many scientists who

disagreed with traditional Scholastic and
Aristotelian beliefs were afraid to oppose the Church. Although Descartes did not oppose traditional belief
as radically as Galileo, it still gave aspiring scientists and mathematicians the courage to voice their
opinions. Without Descartes' contributions to the Scientific Revolution, the world would not be where it is
today.



V.Bibliography



1) "Compedium Musica." Stanford University. 12 Sept. 2007 <
http://plato.stanford.edu/entries/descartes
-
works/>.

2) "Descartes and Cartesianism."

Encyclopedia Britannica
. 15th ed. 29 vols. Chicago: Encyclopedia
Britannica, Inc, 2001.

3) "Descartes's Passions of the Soul."

Philosophy COmpass
. Mar. 2006. 12
Sept. 2007
<
http://www.blackwell
-
compass.com/subject/philosophy/article_view?article_id=phco_articles_bpl022>.

4) Descartes, Rene. "Descart
es: the Description of the Human Body." 1647. 12 Sept. 2007

5) "Descartes, Rene, 1596
-
1650."

The University of Adelaide Library
. 16 Apr. 2007. University of
Adelaide. 11 Sept. 2007 <
http://etext.library.adelaide.edu.au/d/descartes/rene/>.

6) "Descartes, Rene."

Encyclopedia Britannica
. 15th ed. 29 vols. Chicago: Encyclopedia Britannica, Inc,
2001.

7) "Elements of Cartesian Philosophy."

InfoPlease
. 2007. The Columbia Electronic Encyclo
pedia. 12
Sept. 2007 <
http://www.infoplease.com/ce6/people/A0857735.html>.

8) "Meditations on First Philosophy."

SparkNotes
. 2006. 12 Sept. 2007
<
http://www.sparknotes.com/philosophy/meditations/section1.html>.

<
http://ww
w.philosophy.leeds.ac.uk/GMR/hmp/texts/modern/descartes/body/body.html>.

9) "Rene Descartes 1596
-
1650."

www.Yesnet.com
. 11 Sept. 2007

<
http://www.yesnet.yk.ca/schools/p
rojects/renaissance/descartes.html>.

10) "Rene Descartes." 5 Sept. 2005. 12 Sept. 2007
<
http://www.thocp.net/biographies/descartes_rene.htm>.

11) "Rene Descartes." 9 Dec. 2002. 12 Sept
. 2007 <
http://www.renedescartes.com/
>

12) "Rules for the Direction of the Mind." 12 Sept. 2007 <
http://www.hfu.edu.tw/~huangkm/ration
/RULES
-
summary.htm>.

13) Stokes, Philip.

Philosophy
-

10 Essential Thinkers
. New York: Enchanted Lion Books, 2003.

14) Tarnas, Richard.

The Passion of the Western Mind: Understanding the Ideas That Have Shaped Our
World View
. New York: Ballantine Books, 19
91.

15) "The Philosophical Review."

J Stor
. 1976. 12 Sept. 2007 <
http://links.jstor.org/sici?sici=0031
-
8108(197807)87%3A3%3C453%3ADCWB%3E2.0.CO%3
B2
-
%23>.