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When India mathematicians did know Euclid's Elements?

Why did India miss the Great Revolution in Maths and Science?Why did mathematicians have a hard time accepting Euclid's 5th postulate as a postulate?How did Aristotle influence Euclid?Why didn't Euclid's Elements treat conic sections?What caused or contributed to Euclid's Elements and Synthetic Geometry falling into disfavor?How was the focus/directrix property of conic sections discovered?When was this projective property of an ellipse's directrix known?mathematicians attempts at proving Euclid postulateWhat's the relationship between Aristotle's theory of elements and motion and geometry?What were the typical ways students were taught the elements when it remained the prime textbook of mathematics?

2

$begingroup$

Transfer of knowledge from India to Europe (positional number system with zero) allowed Europeans to develop arithmetic. But was there also a reverse direction (probably via Arab mathematicians) when knowledge was transferred from Europe to India?

Especially I'm curious when Euclid's Elements (probably the most known ancient mathematical book) was introduced to India..

geometry euclidean-geometry ancient-india

share|improve this question

asked 2 hours ago

WidawensenWidawensen

1136

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  "Transfer of knowledge from India to Europe (positional number system with zero) allowed Europeans to develop arithmetic". This is highly doubtful and it has been discussed at length in this forum. Chinese had their own counting system, and so did the Arabs. This idea sounds like a part of recent wave of scam. BBC made a serious report on this topic bbc.com/news/world-asia-india-46778879, where statements such as "The head of a southern Indian university cited an old text as proof that stem cell research was discovered in India thousands of years ago."
  $endgroup$
  – M. Farooq
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq I have read, for example, " Hindu astronomers and mathematicians Aryabhata, born in 476, and Brahmagupta, born in 598, are both popularly believed to have been the first to formally describe the modern decimal place value system and present rules governing the use of the zero symbol." bbc.com/travel/story/20180807-how-india-gave-us-the-zero, but maybe there are some other concepts. However the question was about Euclid's Elements in India.
  $endgroup$
  – Widawensen
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This is a rather recent wave of nationalistic view of mathematical history. Such views when taken up by any culture (and then exaggerated) distort truth and history. Not all algebra was invented by Arab mathematicians, although the name al-jabr lingers today. Algorithm is an named after an Arab mathematician. Can Arabs claim they invented modern algorithms? Problem is with very old stuff, there is no primary information. I would ask where are books by Aryabhata? Where are the translations for Europeans? Even with the Euclid original work, was there a culture of learning Greek in ancient India?
  $endgroup$
  – M. Farooq
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq Yes, there are many connections between different ( also scientific) cultures and to identify all links it is not a simple task.
  $endgroup$
  – Widawensen
  1 hour ago
  

  
  
  
  

add a comment | 

2

$begingroup$

Transfer of knowledge from India to Europe (positional number system with zero) allowed Europeans to develop arithmetic. But was there also a reverse direction (probably via Arab mathematicians) when knowledge was transferred from Europe to India?

Especially I'm curious when Euclid's Elements (probably the most known ancient mathematical book) was introduced to India..

geometry euclidean-geometry ancient-india

share|improve this question

asked 2 hours ago

WidawensenWidawensen

1136

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  "Transfer of knowledge from India to Europe (positional number system with zero) allowed Europeans to develop arithmetic". This is highly doubtful and it has been discussed at length in this forum. Chinese had their own counting system, and so did the Arabs. This idea sounds like a part of recent wave of scam. BBC made a serious report on this topic bbc.com/news/world-asia-india-46778879, where statements such as "The head of a southern Indian university cited an old text as proof that stem cell research was discovered in India thousands of years ago."
  $endgroup$
  – M. Farooq
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq I have read, for example, " Hindu astronomers and mathematicians Aryabhata, born in 476, and Brahmagupta, born in 598, are both popularly believed to have been the first to formally describe the modern decimal place value system and present rules governing the use of the zero symbol." bbc.com/travel/story/20180807-how-india-gave-us-the-zero, but maybe there are some other concepts. However the question was about Euclid's Elements in India.
  $endgroup$
  – Widawensen
  2 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This is a rather recent wave of nationalistic view of mathematical history. Such views when taken up by any culture (and then exaggerated) distort truth and history. Not all algebra was invented by Arab mathematicians, although the name al-jabr lingers today. Algorithm is an named after an Arab mathematician. Can Arabs claim they invented modern algorithms? Problem is with very old stuff, there is no primary information. I would ask where are books by Aryabhata? Where are the translations for Europeans? Even with the Euclid original work, was there a culture of learning Greek in ancient India?
  $endgroup$
  – M. Farooq
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq Yes, there are many connections between different ( also scientific) cultures and to identify all links it is not a simple task.
  $endgroup$
  – Widawensen
  1 hour ago
  

  
  
  
  

add a comment | 

$begingroup$

Transfer of knowledge from India to Europe (positional number system with zero) allowed Europeans to develop arithmetic. But was there also a reverse direction (probably via Arab mathematicians) when knowledge was transferred from Europe to India?

Especially I'm curious when Euclid's Elements (probably the most known ancient mathematical book) was introduced to India..

geometry euclidean-geometry ancient-india

share|improve this question

asked 2 hours ago

WidawensenWidawensen

1136

$endgroup$

share|improve this question

asked 2 hours ago

WidawensenWidawensen

1136

share|improve this question

asked 2 hours ago

WidawensenWidawensen

1136

asked 2 hours ago

WidawensenWidawensen

1136

asked 2 hours ago

WidawensenWidawensen

1136

2 Answers
2

active

oldest

votes

3

$begingroup$

According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma:

It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration.

---

TL/DR;

Concerning Indian mathematics at about the time Euclid, according to Frits Staal, professor of Philosophy and South/Southeast Asian Studies at UC Berkley:

The ancient Greeks developed logic and a notion of rationality as deduction best exhibited by Euclid’s geometry. These discoveries contributed substantially to the development of Western science. Ancient Indian civilisation was an oral tradition and the oral transmission of the tradition became the first object of scientific inquiry.

Thus arose two human sciences, closely related to each other in their formal structure: the sciences of ritual and language.To begin with, while a number of key contributions were made by Indian mathematicians, they somehow remained in complete darkness about conic sections. These are simply the various dissections of an hourglass (or, a double cone) which are the ellipse, the parabola and the hyperbola. The importance of these curves in the history of science up to the time of Isaac Newton is unparalleled in geometry. Planets were found to move in elliptical orbits, cannonballs and projectiles fell in a parabolic arch under the influence of gravity, and shadows on sundials moved in a hyperbolic path.

The other omissions concern solid geometry, and the existence of only five Platonic solids, namely — tetrahedron, cube, octahedron, icosahedron and the dodecahedron. These five elemental solids were used since the time of Plato in pondering the structure of atoms, crystals and matter in general.

Thus, according to Staal, ancient Indian mathematicians were primarily concerned with a scientific exploration of ritual and mysticism, applying their geometry to things like the construction of elaborate altars.

Further reading: History of Geometry - wikipedia

share|improve this answer

answered 1 hour ago

Nick RNick R

3,454723

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Alexander the Great, did visit (or rather conquer) areas which are now in Pakistan. One can find remnants of Greek culture in the Northern part and even very ancient graveyards. The views of Staal and Amma seem to be close to reality rather than web-based myths.
  $endgroup$
  – M. Farooq
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq Indeed. The Silk Road established shortly after the time of Alexander, would have, for over a millenium, introduced Greek culture far beyond what is today called Pakistan.
  $endgroup$
  – Nick R
  39 mins ago
  

  
  
  
  

add a comment | 

0

$begingroup$

Not just mystecism. See my comment on planetary diameters from Surya Siddhanta which requires a knowledge of astronomy, arithmetic and physics of scaling.The postulate behind it is the solar nebula which condensed into planets.

As far as geometry is concerned Indians followed algebraic geometry such as

(a+b)^2 +(a-b)^2 = a^2 +b^2.

India followed the place value system very early in history starting in Rg vedic times.

share|improve this answer

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91

New contributor

Partha Shakkottai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, I believe that these sorts of results were from the high period of Indian mathematics, rather than Vedic India. For example, Sripati (1019-1066 CE), in his work on astronomy and arithmetic titled Siddhantasekhara, described how to add and subtract square roots. Most impressive from the high period would be Madhava and the Kerala school.
  $endgroup$
  – Nick R
  18 mins ago
  

  
  
  
  

add a comment | 

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3

$begingroup$

According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma:

It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration.

---

TL/DR;

Concerning Indian mathematics at about the time Euclid, according to Frits Staal, professor of Philosophy and South/Southeast Asian Studies at UC Berkley:

The ancient Greeks developed logic and a notion of rationality as deduction best exhibited by Euclid’s geometry. These discoveries contributed substantially to the development of Western science. Ancient Indian civilisation was an oral tradition and the oral transmission of the tradition became the first object of scientific inquiry.

Thus arose two human sciences, closely related to each other in their formal structure: the sciences of ritual and language.To begin with, while a number of key contributions were made by Indian mathematicians, they somehow remained in complete darkness about conic sections. These are simply the various dissections of an hourglass (or, a double cone) which are the ellipse, the parabola and the hyperbola. The importance of these curves in the history of science up to the time of Isaac Newton is unparalleled in geometry. Planets were found to move in elliptical orbits, cannonballs and projectiles fell in a parabolic arch under the influence of gravity, and shadows on sundials moved in a hyperbolic path.

The other omissions concern solid geometry, and the existence of only five Platonic solids, namely — tetrahedron, cube, octahedron, icosahedron and the dodecahedron. These five elemental solids were used since the time of Plato in pondering the structure of atoms, crystals and matter in general.

Thus, according to Staal, ancient Indian mathematicians were primarily concerned with a scientific exploration of ritual and mysticism, applying their geometry to things like the construction of elaborate altars.

Further reading: History of Geometry - wikipedia

share|improve this answer

answered 1 hour ago

Nick RNick R

3,454723

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Alexander the Great, did visit (or rather conquer) areas which are now in Pakistan. One can find remnants of Greek culture in the Northern part and even very ancient graveyards. The views of Staal and Amma seem to be close to reality rather than web-based myths.
  $endgroup$
  – M. Farooq
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq Indeed. The Silk Road established shortly after the time of Alexander, would have, for over a millenium, introduced Greek culture far beyond what is today called Pakistan.
  $endgroup$
  – Nick R
  39 mins ago
  

  
  
  
  

add a comment | 

3

$begingroup$

According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma:

It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration.

---

TL/DR;

Concerning Indian mathematics at about the time Euclid, according to Frits Staal, professor of Philosophy and South/Southeast Asian Studies at UC Berkley:

The ancient Greeks developed logic and a notion of rationality as deduction best exhibited by Euclid’s geometry. These discoveries contributed substantially to the development of Western science. Ancient Indian civilisation was an oral tradition and the oral transmission of the tradition became the first object of scientific inquiry.

Thus arose two human sciences, closely related to each other in their formal structure: the sciences of ritual and language.To begin with, while a number of key contributions were made by Indian mathematicians, they somehow remained in complete darkness about conic sections. These are simply the various dissections of an hourglass (or, a double cone) which are the ellipse, the parabola and the hyperbola. The importance of these curves in the history of science up to the time of Isaac Newton is unparalleled in geometry. Planets were found to move in elliptical orbits, cannonballs and projectiles fell in a parabolic arch under the influence of gravity, and shadows on sundials moved in a hyperbolic path.

The other omissions concern solid geometry, and the existence of only five Platonic solids, namely — tetrahedron, cube, octahedron, icosahedron and the dodecahedron. These five elemental solids were used since the time of Plato in pondering the structure of atoms, crystals and matter in general.

Thus, according to Staal, ancient Indian mathematicians were primarily concerned with a scientific exploration of ritual and mysticism, applying their geometry to things like the construction of elaborate altars.

Further reading: History of Geometry - wikipedia

share|improve this answer

answered 1 hour ago

Nick RNick R

3,454723

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Alexander the Great, did visit (or rather conquer) areas which are now in Pakistan. One can find remnants of Greek culture in the Northern part and even very ancient graveyards. The views of Staal and Amma seem to be close to reality rather than web-based myths.
  $endgroup$
  – M. Farooq
  1 hour ago
  
  
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  @M.Farooq Indeed. The Silk Road established shortly after the time of Alexander, would have, for over a millenium, introduced Greek culture far beyond what is today called Pakistan.
  $endgroup$
  – Nick R
  39 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

According to The Hindu Business Line, quoting the scholar TA Sarasvati Amma:

It was only in the 18th century, nearly 2,000 years after active contact of Indians with the Greeks, that Euclid’s Elements were translated into Sanskrit and even then perhaps the example of the Arabs provided the inspiration.

---

TL/DR;

Concerning Indian mathematics at about the time Euclid, according to Frits Staal, professor of Philosophy and South/Southeast Asian Studies at UC Berkley:

The ancient Greeks developed logic and a notion of rationality as deduction best exhibited by Euclid’s geometry. These discoveries contributed substantially to the development of Western science. Ancient Indian civilisation was an oral tradition and the oral transmission of the tradition became the first object of scientific inquiry.

Thus arose two human sciences, closely related to each other in their formal structure: the sciences of ritual and language.To begin with, while a number of key contributions were made by Indian mathematicians, they somehow remained in complete darkness about conic sections. These are simply the various dissections of an hourglass (or, a double cone) which are the ellipse, the parabola and the hyperbola. The importance of these curves in the history of science up to the time of Isaac Newton is unparalleled in geometry. Planets were found to move in elliptical orbits, cannonballs and projectiles fell in a parabolic arch under the influence of gravity, and shadows on sundials moved in a hyperbolic path.

The other omissions concern solid geometry, and the existence of only five Platonic solids, namely — tetrahedron, cube, octahedron, icosahedron and the dodecahedron. These five elemental solids were used since the time of Plato in pondering the structure of atoms, crystals and matter in general.

Thus, according to Staal, ancient Indian mathematicians were primarily concerned with a scientific exploration of ritual and mysticism, applying their geometry to things like the construction of elaborate altars.

Further reading: History of Geometry - wikipedia

share|improve this answer

answered 1 hour ago

Nick RNick R

3,454723

$endgroup$

share|improve this answer

answered 1 hour ago

Nick RNick R

3,454723

answered 1 hour ago

Nick RNick R

3,454723

answered 1 hour ago

Nick RNick R

3,454723

0

$begingroup$

Not just mystecism. See my comment on planetary diameters from Surya Siddhanta which requires a knowledge of astronomy, arithmetic and physics of scaling.The postulate behind it is the solar nebula which condensed into planets.

As far as geometry is concerned Indians followed algebraic geometry such as

(a+b)^2 +(a-b)^2 = a^2 +b^2.

India followed the place value system very early in history starting in Rg vedic times.

share|improve this answer

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91

New contributor

Partha Shakkottai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, I believe that these sorts of results were from the high period of Indian mathematics, rather than Vedic India. For example, Sripati (1019-1066 CE), in his work on astronomy and arithmetic titled Siddhantasekhara, described how to add and subtract square roots. Most impressive from the high period would be Madhava and the Kerala school.
  $endgroup$
  – Nick R
  18 mins ago
  

  
  
  
  

add a comment | 

0

$begingroup$

Not just mystecism. See my comment on planetary diameters from Surya Siddhanta which requires a knowledge of astronomy, arithmetic and physics of scaling.The postulate behind it is the solar nebula which condensed into planets.

As far as geometry is concerned Indians followed algebraic geometry such as

(a+b)^2 +(a-b)^2 = a^2 +b^2.

India followed the place value system very early in history starting in Rg vedic times.

share|improve this answer

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91

New contributor

Partha Shakkottai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes, I believe that these sorts of results were from the high period of Indian mathematics, rather than Vedic India. For example, Sripati (1019-1066 CE), in his work on astronomy and arithmetic titled Siddhantasekhara, described how to add and subtract square roots. Most impressive from the high period would be Madhava and the Kerala school.
  $endgroup$
  – Nick R
  18 mins ago
  

  
  
  
  

add a comment | 

$begingroup$

Not just mystecism. See my comment on planetary diameters from Surya Siddhanta which requires a knowledge of astronomy, arithmetic and physics of scaling.The postulate behind it is the solar nebula which condensed into planets.

As far as geometry is concerned Indians followed algebraic geometry such as

(a+b)^2 +(a-b)^2 = a^2 +b^2.

India followed the place value system very early in history starting in Rg vedic times.

share|improve this answer

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91

New contributor

Partha Shakkottai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|improve this answer

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91

New contributor

Partha Shakkottai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91

New contributor

Partha Shakkottai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 34 mins ago

Partha ShakkottaiPartha Shakkottai

91