July 8, 2025 • 15 mins
Long before telescopes and satellites, Hipparchus of Nicaea looked to the skies and changed the course of scientific history. In this fascinating episode of Math Science History, Gabrielle revisits the life and legacy of the ancient astronomer whose innovations in trigonometry, geography, and star mapping still resonate today. From discovering axial precession to laying the groundwork for the astrolabe, Hipparchus helped humanity understand our place in the cosmos: mathematically, geographically, and philosophically.
Three Key Take-Aways
How Hipparchus measured the Earth's axial precession and why this was a monumental scientific discovery.
The mathematical brilliance behind his trigonometric tables and how they informed tools like the astrolabe.
How ancient astronomy evolved into cartography, influencing how we view geography and time today.
Resources & References
Griffith Observatory Astronomers Monument: https://griffithobservatory.org
Ptolemy's Almagest: Loeb Classical Library
Hipparchus in The Internet Encyclopedia of Philosophy: https://iep.utm.edu/hipparchus/
Cosimo Bartoli’s Del modo di misurare: https://archive.org/details/delmododimisurar00bart
🔗 Explore more on our website: mathsciencehistory.com
📚 To buy my book Hypatia: The Sum of Her Life on Amazon, visit https://a.co
Mark as Played
Transcript
Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
(00:00):
Welcome to Math Science History.
This summer, as we continue with our series
of reposts and stories about scientists on vacation,
I am sharing a repost about Hipparchus.
This is one of my favorite episodes.
And if you'd like visuals and resources, please
come visit me at mathsciencehistory.com.
And while you're there, remember to click on
that coffee button.
Every donation that you make keeps this podcast
(00:21):
up and running and provides a free educational
resource for all who visit the website and
listen to the podcast.
In the year 415, the infamous philosopher and
mathematician Hypatia of Alexandria, Egypt was savagely murdered
by church monks.
(00:43):
This murder shocked the Roman community and its
government leaders.
Hypatia was known far and wide as a
respected philosopher, mathematician, government advisor, and a professor.
Hypatia, the sum of her life, is a
book that I wrote that looks not just
at the circumstances surrounding her death, but also
(01:03):
at the sum of her entire life.
I weave in the details of her education,
disciples, Neoplatonic philosophies, female contemporaries, and the many
mathematics that she wrote and taught about.
There is truly more to Hypatia's life than
her death.
Hypatia, the sum of her life, written by
me, Gabriel Birchak, is now on sale on
(01:25):
Amazon.
Buy your copy today.
Space.
It's not just the final frontier.
It's not just an infinite, three-dimensional platform
where entities have position and direction.
Space is a profound reminder that we are
part of this giant construct of atoms, molecules,
(01:49):
elements, compounds, voids, masses, and gravity that work
together as a unifying body that moves us
in the universe's dance of life.
Starting with the Big Bang, we began to
exist, even though we were in the dust
scattered across the inflating universe.
Many of us examine the stars to understand
(02:09):
where we came from and where we are
going.
We observe their movement to understand the beauty
that encircles us every night as the sun
sets, and we embrace its vast magnificence while
identifying with our minuteness in this tremendously grand
structure that is the universe.
The written history of astronomical observation dates back
(02:31):
to over 2,000 years.
Observing the night sky has evolved and developed
so that we now have an extensive list
of space telescopes that bring us up close
to the beauty of our cosmos.
It is utterly amazing to think that a
little over 2,000 years ago, this data
-gathering process began to advance through the brilliant
(02:51):
work of the ancient astronomer Hipparchus.
Hipparchus was born in 190 BCE in the
Kingdom of Bithynia, which today is now known
as the region of Northern Anatolia in Turkey.
We know about Hipparchus through the writings of
ancient historians, mathematicians, and scientists, including Ptolemy, who
utilized Hipparchus' astronomical findings for his infamous work
(03:15):
Almagest.
Ptolemy admired him so much that he referred
to him as, quote, that enthusiastic worker and
lover of truth, unquote.
Hipparchus has been referenced in the works of
Strabo, who wrote Geography, and Pliny the Elder,
who wrote Natural History.
By the 4th century, Hipparchus had been referenced
by Alexandrian mathematicians Pappus, Theon, and Hypatia.
(03:40):
Unfortunately, very little of Hipparchus' works survive.
He wrote at least 14 books, which included
a star catalog and one of the first
trigonometric tables in his work called Of Lines
Inside a Circle.
This trigonometric table included several values of a
chord function, which was quite a feat considering
his work came from 200 BCE.
(04:03):
Hipparchus authored On the Length of the Year,
which were his observations on the sun's motions
and orbits.
He studied the moon's movement and determined a
period of an eclipse by comparing his data
with Babylonian data from 300 years prior.
When Hipparchus flourished as a mathematician and astronomer,
it had already been known that the moon
(04:24):
moved at varying speeds.
However, no data showed the actual size of
the orbits.
Hipparchus was the first astronomer to determine the
size of the moon's orbit.
Furthermore, as noted by the great historian Pliny
the Elder, Hipparchus was one of the first
astronomers to show that lunar eclipses occur 5
(04:47):
months apart and that solar eclipses occur 7
months apart.
He also revealed that the sun could be
hidden twice in 30 days depending on the
viewer's location.
Thus, many of our astronomical findings would not
have been realized if it were not for
the works of Hipparchus.
His systematical techniques helped him to discover and
(05:09):
measure the Earth's precession, and this discovery was
no eureka moment.
It was an extensive application of trigonometry, trigonometry
tables, and applications of spherical trigonometry and geometry.
The Earth's precession can be understood by looking
at a gyroscope or, more simply, a spinning
top.
(05:30):
The top spins on its tip.
Where one grabs it to make it spin
is called the crown.
The crown, as defined in physics, indicates the
axis of the top.
The axis is the line in which the
body of the top spins around.
However, when you spin a top, you will
notice that the axis also rotates.
(05:53):
As it speeds up, the axis makes a
smaller circular motion.
When it slows down, the axis makes a
larger circular motion.
The axis does not spin as fast as
the top.
The gravity of the Earth causes the axis
to spin, which in physics is referred to
as torque.
So, in the case of Earth, as the
(06:14):
world spins on its axis while spinning around
the sun, the axis, which is represented as
the North Pole, is also spinning, albeit very
slowly.
This spinning is the Earth's axial precession.
Historically, this was referred to as the precession
of the equinoxes.
And the Earth has two equinoxes, the spring
(06:35):
equinox and the fall equinox.
An equinox is when the sun's rays are
perpendicular to the Earth's equator, which means that
the sun's rays to the equator is zero
degrees.
Hipparchus discovered the Earth's precession by following and
measuring the movements of the stars, specifically Spica
and Regulus, two of the brightest stars in
(06:57):
our night sky.
In his observations, he measured the longitudes of
these two stars.
Then, he compared his numbers to the data
of previous scientists and astronomers.
He discovered that the bright star Spica had
moved two degrees compared to its location during
the fall equinox.
Through this calculation, he realized that the precession
(07:20):
of our equinoxes moves at a rate between
one and two degrees.
Hipparchus concluded that because the Earth's axis moves
so slowly, it would complete a rotation about
every 36,000 years.
Well, this number was further validated in Ptolemy's
work Homagest.
And what is really impressive about this discovery
(07:41):
is that Hipparchus was not that far off.
We have since realized and discovered that the
Earth's axis completes a rotation approximately every 26
,000 years.
We'll be right back after a quick word
from my advertisers.
In 398 CE, about 600 years after Hipparchus,
Senecius of Cyrene, one of Hypatia's students and
(08:03):
disciples, wrote a letter to the military leader
Pylemenes.
Along with that letter, Senecius had sent Pylemenes
an astrolabe.
Senecius' mission was to influence and encourage the
politicians of Rome to study and learn the
value of science.
So, clearly, the importance of educating politicians on
(08:24):
the value of science has been an endeavor
among scientists for thousands of years.
So, in this letter, Senecius writes, quote, the
great Ptolemy and the divine band of his
successors were content to have it as one
of their useful possession.
For the 16 stars, it made sufficient for
the night clock.
(08:44):
Hipparchus merely transposed the stars and inserted them
into the instrument, unquote.
So, here we have an early reference that
the astrolabe might have actually been Hipparchus' invention.
The astrolabe was the evolution and combination of
an armillary sphere, a celestial map, and a
dioptera.
(09:05):
An armillary sphere is a spherical frame of
rings representing the star's celestial latitude and longitude.
It often has an axis that is characterized
by an arrow.
So, if you've ever been shopping at home
goods, more than likely, you've seen a multitude
of them in the decor department, which I
(09:26):
think is kind of cool.
So, a dioptera is a measuring tube with
a protractor.
It's surveyed over far distances, which was useful
for measuring land, for building structures in aqueducts,
and for measuring the of the stars.
Heron of Alexandria in the first century referenced
the dioptera in his work called The Dioptera
(09:46):
and indicated that his instrument worked as a
general sighting tool and as a level.
So, the astrolabe, a combination of these objects,
allowed astronomers to map out the stars and
project the night sky as a celestial sphere
onto the plane of the equator.
The astrolabe eventually evolved into a flat, user
(10:08):
-friendly, portable mechanism.
Metaphorically speaking, with the astrolabe, users were then
able to hold the galaxy in the palms
of their hands.
The main body of the astrolabe is called
the mater.
The front part of the mater cradles the
parts of the astrolabe together in the womb.
At the top of the astrolabe is a
cross with 24 symbols etched around the limb
(10:29):
with an M at the bottom.
The cross represents noon and the M represents
midnight.
Etchings around the outer rim represent degrees, hours,
or even both.
The plates that sit inside the womb are
called climates.
These climates are mapped with a celestial sphere.
The climates can be interchanged depending on an
(10:49):
individual's latitude and location of the observation.
All that the user can observe in three
-dimensional space is flattened onto the astrolabe.
Thus, the final tool that is needed to
read an astrolabe is the imagination.
So, if you were to hold an astrolabe
in your hand, you would imagine the night
sky as a dome of stars above you.
(11:10):
This enormous imagined sphere is a stereographic projection.
The stereographic projection is the mapping of three
-dimensional spherical objects onto a two-dimensional plane,
which in this case is the astrolabe.
For a visual, please visit me at mathsciencehistory
.com where you can see the graphics that
I created that identify the parts of the
(11:32):
astrolabe as well as the intricacies of stereographic
projection.
Stereographic projection is essential for the astrolabe because
it preserves circles and angles.
The astrolabe assists in determining the angle at
which one can see the moon or the
stars.
It also measures altitude, latitude, and the width
(11:53):
of rivers and valleys.
It serves as a compass and helps determine
the day's hour.
However, unlike a map that provides preserved distances
or areas on a ratio scale, stereographic projection
creates a projected map of curves referenced by
inscribed angles.
Again, for a visual and instructions on how
(12:14):
to read an astrolabe, please come visit me
at mathsciencehistory.com where I provide a graphic
that explains all the intricate details of an
astrolabe.
Hipparchus, thus using this concept of stereographic projection,
created a map by imagining a perpendicular line
that connected each star to a point on
(12:35):
the plates of the astrolabe.
By using this astrolabe and observing fixed stars,
Hipparchus was also able to measure one's geographical
latitude and the time of day or night
at that geographical latitude.
And because he had such an extensive background
working with trigonometry and understanding the angles of
(12:55):
projection, using a grade grid, he was able
to assign a value of latitude and longitude
to various locations on earth.
These multiple locations of reference allowed him to
design the interchangeable plates on the astrolabe that
the viewer could change depending on where they
were located.
Also, this method of determining the latitude and
(13:16):
longitude of geography contributed to his treatise called
Against the Geography of Eratosthenes.
In this work, Hipparchus literally redefined the cartography
of the world map by correcting many of
the geographical mistakes that Eratosthenes made in his
own work, Geography.
Hipparchus was a tremendous astronomer.
(13:38):
At the Griffith Observatory in my hometown of
Los Angeles, there is a 40-foot monument
with a hollow bronze armillary sphere at the
top.
There are six great astronomers carved into this
magnificent monument.
The only one from antiquity is Hipparchus, and
rightly so.
He was one of the very first astronomers
who not only intrigued our curiosity and imagination
(14:01):
with stereographic projection, but he also defined the
earth's geography.
Additionally, he was one of the first to
not only observe, but also mathematically and trigonometrically
define his observations.
As we ride along with the stars and
the galaxies in our world, we dance among
(14:21):
our own personal atoms, molecules, voids, and gatherings.
Hipparchus's mathematical astronomy grounded us in understanding where
we are in the world and in the
universe.
He helped us to see the choreography of
the universe and showed how we move with
it.
Thus, his observations piqued our curiosity and inspired
(14:44):
us to imagine our place as we stand
on this little blue dot, moving through space
as observers and participants in this glorious dance
of the stars.
Until next time, carpe diem.
Thank you for tuning in to Math Science
History.
If you enjoyed today's episode, please leave a
(15:07):
quick rating and review.
They really help the podcast.
You can find our transcripts at mathsciencehistory.com,
and while you're there, remember to click on
that coffee button because every dollar you donate
supports a portion of our production costs and
keeps our educational website free.
Again, thank you for tuning in and until
next time, carpe diem.
Welcome to Math Science History.
This summer, as we continue with our series
of reposts and stories about scientists on vacation,
I am sharing a repost about Hipparchus.
This is one of my favorite episodes.
And if you'd like visuals and resources, please
come visit me at mathsciencehistory.com.
And while you're there, remember to click on
that coffee button.
Every donation that you make keeps this podcast
(00:21):
up and running and provides a free educational
resource for all who visit the website and
listen to the podcast.
In the year 415, the infamous philosopher and
mathematician Hypatia of Alexandria, Egypt was savagely murdered
by church monks.
(00:43):
This murder shocked the Roman community and its
government leaders.
Hypatia was known far and wide as a
respected philosopher, mathematician, government advisor, and a professor.
Hypatia, the sum of her life, is a
book that I wrote that looks not just
at the circumstances surrounding her death, but also
(01:03):
at the sum of her entire life.
I weave in the details of her education,
disciples, Neoplatonic philosophies, female contemporaries, and the many
mathematics that she wrote and taught about.
There is truly more to Hypatia's life than
her death.
Hypatia, the sum of her life, written by
me, Gabriel Birchak, is now on sale on
(01:25):
Amazon.
Buy your copy today.
Space.
It's not just the final frontier.
It's not just an infinite, three-dimensional platform
where entities have position and direction.
Space is a profound reminder that we are
part of this giant construct of atoms, molecules,
(01:49):
elements, compounds, voids, masses, and gravity that work
together as a unifying body that moves us
in the universe's dance of life.
Starting with the Big Bang, we began to
exist, even though we were in the dust
scattered across the inflating universe.
Many of us examine the stars to understand
(02:09):
where we came from and where we are
going.
We observe their movement to understand the beauty
that encircles us every night as the sun
sets, and we embrace its vast magnificence while
identifying with our minuteness in this tremendously grand
structure that is the universe.
The written history of astronomical observation dates back
(02:31):
to over 2,000 years.
Observing the night sky has evolved and developed
so that we now have an extensive list
of space telescopes that bring us up close
to the beauty of our cosmos.
It is utterly amazing to think that a
little over 2,000 years ago, this data
-gathering process began to advance through the brilliant
(02:51):
work of the ancient astronomer Hipparchus.
Hipparchus was born in 190 BCE in the
Kingdom of Bithynia, which today is now known
as the region of Northern Anatolia in Turkey.
We know about Hipparchus through the writings of
ancient historians, mathematicians, and scientists, including Ptolemy, who
utilized Hipparchus' astronomical findings for his infamous work
(03:15):
Almagest.
Ptolemy admired him so much that he referred
to him as, quote, that enthusiastic worker and
lover of truth, unquote.
Hipparchus has been referenced in the works of
Strabo, who wrote Geography, and Pliny the Elder,
who wrote Natural History.
By the 4th century, Hipparchus had been referenced
by Alexandrian mathematicians Pappus, Theon, and Hypatia.
(03:40):
Unfortunately, very little of Hipparchus' works survive.
He wrote at least 14 books, which included
a star catalog and one of the first
trigonometric tables in his work called Of Lines
Inside a Circle.
This trigonometric table included several values of a
chord function, which was quite a feat considering
his work came from 200 BCE.
(04:03):
Hipparchus authored On the Length of the Year,
which were his observations on the sun's motions
and orbits.
He studied the moon's movement and determined a
period of an eclipse by comparing his data
with Babylonian data from 300 years prior.
When Hipparchus flourished as a mathematician and astronomer,
it had already been known that the moon
(04:24):
moved at varying speeds.
However, no data showed the actual size of
the orbits.
Hipparchus was the first astronomer to determine the
size of the moon's orbit.
Furthermore, as noted by the great historian Pliny
the Elder, Hipparchus was one of the first
astronomers to show that lunar eclipses occur 5
(04:47):
months apart and that solar eclipses occur 7
months apart.
He also revealed that the sun could be
hidden twice in 30 days depending on the
viewer's location.
Thus, many of our astronomical findings would not
have been realized if it were not for
the works of Hipparchus.
His systematical techniques helped him to discover and
(05:09):
measure the Earth's precession, and this discovery was
no eureka moment.
It was an extensive application of trigonometry, trigonometry
tables, and applications of spherical trigonometry and geometry.
The Earth's precession can be understood by looking
at a gyroscope or, more simply, a spinning
top.
(05:30):
The top spins on its tip.
Where one grabs it to make it spin
is called the crown.
The crown, as defined in physics, indicates the
axis of the top.
The axis is the line in which the
body of the top spins around.
However, when you spin a top, you will
notice that the axis also rotates.
(05:53):
As it speeds up, the axis makes a
smaller circular motion.
When it slows down, the axis makes a
larger circular motion.
The axis does not spin as fast as
the top.
The gravity of the Earth causes the axis
to spin, which in physics is referred to
as torque.
So, in the case of Earth, as the
(06:14):
world spins on its axis while spinning around
the sun, the axis, which is represented as
the North Pole, is also spinning, albeit very
slowly.
This spinning is the Earth's axial precession.
Historically, this was referred to as the precession
of the equinoxes.
And the Earth has two equinoxes, the spring
(06:35):
equinox and the fall equinox.
An equinox is when the sun's rays are
perpendicular to the Earth's equator, which means that
the sun's rays to the equator is zero
degrees.
Hipparchus discovered the Earth's precession by following and
measuring the movements of the stars, specifically Spica
and Regulus, two of the brightest stars in
(06:57):
our night sky.
In his observations, he measured the longitudes of
these two stars.
Then, he compared his numbers to the data
of previous scientists and astronomers.
He discovered that the bright star Spica had
moved two degrees compared to its location during
the fall equinox.
Through this calculation, he realized that the precession
(07:20):
of our equinoxes moves at a rate between
one and two degrees.
Hipparchus concluded that because the Earth's axis moves
so slowly, it would complete a rotation about
every 36,000 years.
Well, this number was further validated in Ptolemy's
work Homagest.
And what is really impressive about this discovery
(07:41):
is that Hipparchus was not that far off.
We have since realized and discovered that the
Earth's axis completes a rotation approximately every 26
,000 years.
We'll be right back after a quick word
from my advertisers.
In 398 CE, about 600 years after Hipparchus,
Senecius of Cyrene, one of Hypatia's students and
(08:03):
disciples, wrote a letter to the military leader
Pylemenes.
Along with that letter, Senecius had sent Pylemenes
an astrolabe.
Senecius' mission was to influence and encourage the
politicians of Rome to study and learn the
value of science.
So, clearly, the importance of educating politicians on
(08:24):
the value of science has been an endeavor
among scientists for thousands of years.
So, in this letter, Senecius writes, quote, the
great Ptolemy and the divine band of his
successors were content to have it as one
of their useful possession.
For the 16 stars, it made sufficient for
the night clock.
(08:44):
Hipparchus merely transposed the stars and inserted them
into the instrument, unquote.
So, here we have an early reference that
the astrolabe might have actually been Hipparchus' invention.
The astrolabe was the evolution and combination of
an armillary sphere, a celestial map, and a
dioptera.
(09:05):
An armillary sphere is a spherical frame of
rings representing the star's celestial latitude and longitude.
It often has an axis that is characterized
by an arrow.
So, if you've ever been shopping at home
goods, more than likely, you've seen a multitude
of them in the decor department, which I
(09:26):
think is kind of cool.
So, a dioptera is a measuring tube with
a protractor.
It's surveyed over far distances, which was useful
for measuring land, for building structures in aqueducts,
and for measuring the of the stars.
Heron of Alexandria in the first century referenced
the dioptera in his work called The Dioptera
(09:46):
and indicated that his instrument worked as a
general sighting tool and as a level.
So, the astrolabe, a combination of these objects,
allowed astronomers to map out the stars and
project the night sky as a celestial sphere
onto the plane of the equator.
The astrolabe eventually evolved into a flat, user
(10:08):
-friendly, portable mechanism.
Metaphorically speaking, with the astrolabe, users were then
able to hold the galaxy in the palms
of their hands.
The main body of the astrolabe is called
the mater.
The front part of the mater cradles the
parts of the astrolabe together in the womb.
At the top of the astrolabe is a
cross with 24 symbols etched around the limb
(10:29):
with an M at the bottom.
The cross represents noon and the M represents
midnight.
Etchings around the outer rim represent degrees, hours,
or even both.
The plates that sit inside the womb are
called climates.
These climates are mapped with a celestial sphere.
The climates can be interchanged depending on an
(10:49):
individual's latitude and location of the observation.
All that the user can observe in three
-dimensional space is flattened onto the astrolabe.
Thus, the final tool that is needed to
read an astrolabe is the imagination.
So, if you were to hold an astrolabe
in your hand, you would imagine the night
sky as a dome of stars above you.
(11:10):
This enormous imagined sphere is a stereographic projection.
The stereographic projection is the mapping of three
-dimensional spherical objects onto a two-dimensional plane,
which in this case is the astrolabe.
For a visual, please visit me at mathsciencehistory
.com where you can see the graphics that
I created that identify the parts of the
(11:32):
astrolabe as well as the intricacies of stereographic
projection.
Stereographic projection is essential for the astrolabe because
it preserves circles and angles.
The astrolabe assists in determining the angle at
which one can see the moon or the
stars.
It also measures altitude, latitude, and the width
(11:53):
of rivers and valleys.
It serves as a compass and helps determine
the day's hour.
However, unlike a map that provides preserved distances
or areas on a ratio scale, stereographic projection
creates a projected map of curves referenced by
inscribed angles.
Again, for a visual and instructions on how
(12:14):
to read an astrolabe, please come visit me
at mathsciencehistory.com where I provide a graphic
that explains all the intricate details of an
astrolabe.
Hipparchus, thus using this concept of stereographic projection,
created a map by imagining a perpendicular line
that connected each star to a point on
(12:35):
the plates of the astrolabe.
By using this astrolabe and observing fixed stars,
Hipparchus was also able to measure one's geographical
latitude and the time of day or night
at that geographical latitude.
And because he had such an extensive background
working with trigonometry and understanding the angles of
(12:55):
projection, using a grade grid, he was able
to assign a value of latitude and longitude
to various locations on earth.
These multiple locations of reference allowed him to
design the interchangeable plates on the astrolabe that
the viewer could change depending on where they
were located.
Also, this method of determining the latitude and
(13:16):
longitude of geography contributed to his treatise called
Against the Geography of Eratosthenes.
In this work, Hipparchus literally redefined the cartography
of the world map by correcting many of
the geographical mistakes that Eratosthenes made in his
own work, Geography.
Hipparchus was a tremendous astronomer.
(13:38):
At the Griffith Observatory in my hometown of
Los Angeles, there is a 40-foot monument
with a hollow bronze armillary sphere at the
top.
There are six great astronomers carved into this
magnificent monument.
The only one from antiquity is Hipparchus, and
rightly so.
He was one of the very first astronomers
who not only intrigued our curiosity and imagination
(14:01):
with stereographic projection, but he also defined the
earth's geography.
Additionally, he was one of the first to
not only observe, but also mathematically and trigonometrically
define his observations.
As we ride along with the stars and
the galaxies in our world, we dance among
(14:21):
our own personal atoms, molecules, voids, and gatherings.
Hipparchus's mathematical astronomy grounded us in understanding where
we are in the world and in the
universe.
He helped us to see the choreography of
the universe and showed how we move with
it.
Thus, his observations piqued our curiosity and inspired
(14:44):
us to imagine our place as we stand
on this little blue dot, moving through space
as observers and participants in this glorious dance
of the stars.
Until next time, carpe diem.
Thank you for tuning in to Math Science
History.
If you enjoyed today's episode, please leave a
(15:07):
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