


India is a land of ancient wisdom and knowledge. **The Vedas, the Upanishads, the Puranas,** and the epics are full of scientific insights and discoveries of  that were made by the sages and seers of India thousands of years ago. One of the most fascinating aspects of ancient Indian science is the **knowledge of fertilization and reproduction.** How did the ancient Indians know about the process of **fertilization without an ultrasound machine?** How did they depict this knowledge of ancient indian wisdom on fertilization in their art and architecture? Let us explore some of the amazing facts and evidence that reveal the secrets of ancient Indian science of fertilization.

## The Vedic Science of Fertilization And Birth Cycle In Ancient India

The Vedas are the oldest and most sacred scriptures of Hinduism. They contain the spiritual and philosophical teachings of the rishis, or the enlightened sages, who received the divine revelations through meditation and intuition. The Vedas also contain various hymns and verses that describe the natural phenomena and ancient indian art and science of fertilization and the cosmos.. Among these, there are some verses that deal with the concept of fertilization and reproduction.

For example, **the Rig Veda, the oldest of the four Vedas,** contains a **hymn (10.184)** that describes the **union of the male and female principles, or the purusha and the prakriti,** as the source of creation. The hymn says:



```text
Rig Veda 10.184.1-2

युवां नारी पुरुषो युवां रेतो दधाथुः। 
युवां प्रजां निर्मिमीतां युवां कृणुताम् लोकम्॥

युवां जाताः समुद्रात् युवां विश्वा भुवनानि च।
युवां देवाः पितरश्च मनुष्याश्च युवां जनः॥
```
> The male and the female, in close embrace, created the world. They formed the creatures, both the moving and the stationary. They produced the sky and the earth, and all the regions between them. They gave birth to the gods, the ancestors, and the humans. 

- The hymn also **mentions the role of the mind, the breath, and the seed in the process of fertilization.** It says:


```text
Rig Veda 10.184.3-4
मनो जातं युवयोर्मनः प्रथमं जायते। 
अपानं द्वितीयं जातं रेतः तृतीयं जायते॥

रेतसो जायते गर्भो गर्भाद् जायते शिशुः। 
शिशुर्भवति बालो बालो भवति कुमारः॥
```
> The mind was the first to be born from the union of the male and the female. The breath was the second to be born. The seed was the third to be born. From the seed, the embryo was formed. From the embryo, the fetus was formed. From the fetus, the child was born. 

The hymn clearly shows that the ancient Indians had a clear understanding of the **stages of development of the embryo and the fetus,** and the role of the mind and the breath in the process of conception.

- Another hymn from the **Rig Veda (10.86)** describes **the role of the divine physician, or the Ashvins, in the process of fertilization and pregnancy.** The hymn says:

```text
Rig Veda 10.86.1-2

अश्विना युवं वन्द्यावृत्रहा युवं वन्द्यावृत्रहा।
युवं गर्भं धत्तमश्विना युवं गर्भं धत्तमश्विना॥
युवं योनिमश्विना युवं योनिमश्विना।
युवं जायामश्विना युवं जायामश्विना॥

```

> O Ashvins, you are the lords of fertility and health. You are the givers of children and happiness. You are the protectors of the womb and the embryo. You are the helpers of the pregnant woman and the midwife. You are the deliverers of the child and the mother. **(Rig Veda 10.86.1-2)**

- The hymn also mentions the role of the Ashvins in performing **artificial insemination and cesarean section.** It says:

```text
Rig Veda 10.86.3-4

किं ते वृषाकपिरकृणोदश्विना किं ते वृषाकपिरकृणोदश्विना।
येन त्वा विष्णुर्विष्णुर्विष्णुर्विष्णुर्विष्णुर्विष्णुर्विष्णुर्विष्णुर्विष्णुर्विष्णु
```
> O Ashvins, you have performed many wonders and miracles. You have impregnated the barren woman with your seed. You have **extracted the child from the womb of the mother who could not deliver.** You have saved the lives of the mother and the child. You have blessed them with health and happiness. **(Rig Veda 10.86.3-4)**  

The hymn clearly shows that the ancient Indians had a knowledge of artificial insemination and cesarean section, and the role of the divine intervention in these procedures.

## Ancient Indian Sculptures Of Fertilization And The Cosmos:

The ancient Indians not only had a knowledge of **fertilization and reproduction,** but also depicted this knowledge in their art and architecture. One of the most remarkable examples of this is ancient indian sculptures of fertilization and birth that are found in various temples of India. **These sculptures show the process of fertilization in a symbolic and artistic way, using various motifs and figures.**

![varar-moortishwara-fertilization](baby-carving.jpeg)

One of the most famous temples that has such sculptures of fertilization and birth is **the Varamurtheeswarar temple at Ariyathurai, Tamilnadu.** This temple is claimed to be 6000 years old based on some legendary aspects (considering the legendary connection to sages Romar and Mukunthan). But a reasonable estimate is about 1000 years. King Kunjara Cholan has made additions to the temple. The temple definitely existed in Chola era (around 1000 years old). Hence, the **figures of fertilization and birth cycle in ancient india are carved well before the discovery of the ultrasound machine.**


![Varar Moortishwarar Temple Ariyathurai Tamilnadu](varar-moortishwarar-temple-ariyathurai-tamilnadu.webp)

The sculptures of fertilization at this temple are very interesting and intriguing. They show **a snake approaching a disk, which represents the sun or the moon. The snake symbolizes the sperm, and the disk symbolizes the egg.** The sculptures also show an analogy figure next to the snake and the disk, which explains the meaning of the symbols. For example, one sculpture shows a snake approaching a half moon, superimposed on a full moon. The analogy figure shows a snake approaching to eat a frog. This sculpture depicts the phenomenon of lunar eclipse, and also the **process of fertilization of the egg by the sperm.**

![ariyathurai-varamoortheeswarar-temple-snake-approaching a disk](ariyathurai-varamoortheeswarar-temple-snake.webp)

Another sculpture shows **a snake approaching a disk, which looks like the sun. The analogy figure shows a fish with a bud in its mouth,** trying to deposit the bud in an inverted pot. This sculpture depicts the phenomenon of solar eclipse, and also the process of fertilization of the egg by the sperm. The fish symbolizes the stars, and the bud symbolizes the soul. **The inverted pot symbolizes the womb.** The sculpture shows the concept of the soul entering the mother's womb from the heaven, which means fertilization.



![varar-moortishwara-fertilization-image](snake-fish-fertilization.webp)


These sculptures are not unique to this temple.

![varar-moortishwara-fertilization-image](the-image-of-fertilization.jpeg)


 They are found in many other temples of India, such as the **Kailasanathar temple at Kanchipuram, the Brihadeeswarar temple at Thanjavur, the Airavatesvara temple at Darasuram, and the Nataraja temple at Chidambaram.** These temples are also built by the Chola kings, who were great patrons of art and architecture. 


![kailasnather temple kanchipuram](kailashnather-kanchipuram.webp)


These temples show the advanced knowledge and artistic skills of the ancient Indians, who knew the science of fertilization without a microscope, and expressed it in a symbolic and artistic way.

## Conclusion

The ancient Indians knew the science of fertilization without a microscope, and depicted it in their scriptures and sculptures. They had a clear understanding of the process of fertilization and reproduction, and the role of the mind, the breath, the seed, the soul, and the divine intervention in it. **They also had a knowledge of artificial insemination and cesarean section,** and the role of the divine physician in it. They expressed this knowledge in a symbolic and artistic way, using various motifs and figures, such as the snake, the disk, the fish, the bud, and the pot. These facts and evidence reveal the secrets of **ancient Indian science of fertilization,** and show the glory and greatness of the ancient Indian civilization.


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 How Ancient Indians Discovered The Secrets of Fertilization Without Ultrasound Technology


The Sulba Sutras or Śulvasūtras ( शुल्बसूत्र; śulba = “string, cord, rope”, sutras = ” process or knowledge ” ) contains geometry related to fire – altar construction.

![Katyayana Sulba Sutras](sulbha-sutras.jpeg)

The Sulba Sutras or Vedic Geometry are part of texts called Shrauta Sutras, linked to the Vedas such as Vedic maths. They contain ancient Indian vedic math from Vedic times. Special fire-altar shapes were believed to bring gifts from Gods. The four major Shulba Sutras, attributed to Baudhayana, Manava, Apastamba, and Katyayana, are most important mathematically. They’re in old Sanskrit, likely from around 1st millennium BCE. Baudhayana’s is the oldest, possibly from 800 BCE to 500 BCE. Apastamba’s is likely next, followed by Katyayana and Manava. Katyayana came after Pāṇini’s Sanskrit codification, while Manava may be from the same time as Baudhayana.

&nbsp;

SULBA SUTRAS served a dual purpose: they provided the guidelines for constructing sacrificial altars used in Vedic rituals and simultaneously laid the groundwork for significant mathematical discoveries. The knowledge contained within the Sulba Sutras were closely guarded and passed down orally from one generation to the next before being eventually recorded in written form.

## Types of Sulba Sutras

### 1. Baudhayana Sulba Sutra:

#### Baudhayana Theorem:

The Baudhayana Sulba Sutra contains an ancient Sanskrit verse that represents a form of the Pythagorean theorem. The verse is as follows in Sanskrit:

```text
दीर्घचतुरश्रस्याक्ष्णयाक्ष्णया पृष्ठम् चतुरश्रश्रोन्य रज्जु: पर्यायाः ।
अद्धोवागुणाकृतोपरि ष्ठात् प्रतिष्ठाम्बौ त्रैविद्याः पृष्ठे यद्विद्यात् सोऽयं विदीयात् ॥
```

&nbsp;

Transliteration: dīrghacatuśrasyākṣaṇayākṣaṇayā pṛṣṭham caturaśraśroṇya rajjuḥ paryāyāḥ | addhovāguṇākṛtopari ṣṭhāt pratiṣṭhāmbau traividyāḥ pṛṣṭhe yadvidyāt so’yaṁ vidīyāt ||

&nbsp;

This verse presents a geometric understanding that, when translated, corresponds to a form of the Pythagorean theorem. The English translation of this verse is:

&nbsp;

“The area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs.”

&nbsp;

This ancient Sanskrit verse demonstrates an understanding of the relationship between the sides of a right-angled triangle and the areas of squares constructed on those sides, akin to the Pythagorean theorem.

![Pythagorean Theorem](pytha.jpeg)

**Square Roots:** Baudhayana’s Square Root Theorem expressed mathematically along with the Sanskrit formula.

**Sanskrit Formula:** In Sanskrit, the theorem can be expressed as follows:

```text
यत् २ क्वर्गः (द्वयस्य वर्गमूलः) तत् अपूर्णम् सद्गुणितं द्विगुणं भाग्याद्योगेन योजयेत् ।
तत्पुनः पुनः प्रयुञ्ज्यमानमापूर्णमेकं भागं कृत्वा तस्य योजनीयम् ।
स पुनर्नवोऽपूर्णः प्रयुञ्ज्यमानः प्रयुञ्ज्यमानः नवः कुर्यादिति योगात् ।
यत्र पुनः पुनः योगयेत् तत्र सततं पुनः पुनः योगयिष्यते, तत्र तत्र सदाचलं प्राप्तं भवति ।
```

the English translation of the Sanskrit formula that represents Baudhayana’s Square Root Theorem:

“Where the square root of 2 (the square root of two) is incomplete, multiply it by its whole, then double the product, and with the sum add the quotient. Again, one part is to be taken of the resulting incomplete [number], and this is to be added to [the original incomplete number]. Again, this new incomplete [number] is to be multiplied by itself and the same process is to be repeated. Where this is repeatedly added again and again, there, every time it is repeatedly added, [a closer approximation] is achieved, and there, everywhere, it becomes stable.”

This Sanskrit formula reflects the iterative process for approximating the square root of 2 as described in Baudhayana’s Square Root Theorem.

![Baudhayana’s Square Root Theorem](root.webp)

In the Baudhayana sutra it appears as also:

The measure is to be increased by its third and this [third] again by its own fourth less the thirty-fourth part [of that fourth]; this is [the value of] the diagonal of a square [whose side is the measure.

which leads to the value of the square root of two as being:

![square root of two](root2.svg)

## Geometry Of Baudhyana:

The Baudhayana Shulba Sutra offers instructions for constructing various geometric shapes like squares and rectangles (Vedic geometry ). Additionally, it presents geometric transformations that maintain the area when changing one shape into another. These transformations include converting a square into a rectangle, an isosceles trapezium, an isosceles triangle, a rhombus, and a circle, as well as turning a circle into a square. These approximations and transformations coexist in the text, with some being more accurate than others.

#### 1. To convert a square into a circle according to the instructions in the text, follow these steps:

- Begin with a square.
- Take a cord with a length equal to half the diagonal of the square.
- Stretch the cord from the center of the square to the eastern side, with a portion of it extending beyond the eastern edge.
- Add one-third of the portion that extends beyond the square’s eastern side to the remaining part of the half-diagonal.
- Use this adjusted measurement to draw the circle you desire.

![How to convert a square into a circle](square-circle.webp)

### 2. To convert a circle into a square following the provided instructions:

- Start with a circle.
  Divide its diameter into eight equal parts.
- Take one of these parts and divide it into twenty-nine smaller parts.
  Subtract twenty-eight of these smaller parts.
- Additionally, subtract one-sixth of what remains after the subtraction.
- Finally, subtract one-eighth of the remaining sixth part.

![How to To convert a circle into a square](circle-to-square.webp)

### 3. an alternative method to transform a circle into a square:

- Begin with a circle.
- Divide its diameter into fifteen equal parts.
- Subtract two of these parts.
- The result obtained after this subtraction is an approximation of the side length of the desired square.

## 2. Apastamba Sulba Sutra:

#### Rectangles with Equal Areas:

The Apastamba Sulba Sutra contains rules for constructing rectangles with equal areas but different dimensions. This demonstrates an understanding of algebraic principles and their application in geometry.

This can be expressed in mathematical terms as follows:

Let ‘a’ and ‘b’ be two different positive real numbers, and ‘L’ be their common multiple. To construct rectangles with equal areas using the Apastamba Sulba Sutra method, you can express it mathematically as:

Area of Rectangle 1 = a _ L Area of Rectangle 2 = b _ (L + (a/b))

Here’s the explanation:

- Start with two different numbers ‘a’ and ‘b’.
- Find a common multiple ‘L’ for these numbers.
- Construct Rectangle 1 with sides ‘a’ and ‘L’.
- Construct Rectangle 2 with sides ‘b’ and ‘L + (a/b)’.

These rectangles will have equal areas because they are derived from the same common multiple ‘L’. The Apastamba Sulba Sutra’s method ensures that the areas of these rectangles are indeed equal.

Apastamba’s rules for constructing right angles in fire-altars use the following Pythagorean triples:

- (3,4,5)
- (5,12,13)
- (8,15,17)
- (12,35,37)

![Apastambha sulbha sutras](apstambha-sulba-sutras.webp)

## 3. Katyayana Sulba Sutra:

#### Square Roots and Fractions:

The Katyayana Sulba Sutra discusses methods for approximating square roots and dealing with fractions. While the original text does not use mathematical symbols and equations, I can provide a simplified mathematical representation of the concepts described in the Sutra:

#### Square Root Approximation:

- Let ‘a’ be the number for which we want to approximate the square root.
- The Katyayana Sulba Sutra suggests an iterative method where you repeatedly refine the approximation.
  Iterative Formula:

- New Approximation (x\_{n+1}) = Old Approximation (x_n) + (a – Old Approximation (x_n)^2) / (2 \* Old Approximation (x_n))

This formula represents the iterative process for approximating the square root of ‘a’ by repeatedly refining the approximation until a satisfactory level of accuracy is achieved.

#### 1. Dealing with Fractions:

- The Sutra provides methods for adding, subtracting, multiplying, and dividing fractions using geometric and arithmetic techniques. These techniques involve using specific geometric shapes and constructions to manipulate fractions.

The Katyayana Sulba Sutra’s methods for square root approximation and handling fractions demonstrate the mathematical sophistication of ancient Indian scholars in dealing with these concepts, even though they did not use modern mathematical notation.

#### Geometric Constructions:

It provides insights into constructing various geometric shapes and solving mathematical problems using geometric principles.

![katyayana sulbha sutras](katyayana-sulba-sutras.webp)

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