Ganita the term used in Sanskrit for mathematics; is derived from the root gana, which means to count or to enumerate. Mathematics in India has been cultivated in connection with Astronomy. Like the other streams of knowledge, the early references of mathematics, are also found in the vedic literature. The word Rashividya is used for mathematics in Chhandogya Upanishad (7.1.2). Some hymns of Shuklayajureda reveal the knowledge of odd numbers and tables (18/24,25). The Brahmana texts like ; ekaya svaha, dvabhyam svaha, tribhyah svaha reflect the vedic concept of arithmetical progressions. In Pingal sutra there is a discourse on the calculation of squares and square roots.
The concept of zero, i.e. shunya, which means void, a figure to indicate the absence of a position of number is virtually void. A round figure, symbol for zero, i.e. 0 had emerged to represent the philosophical concept of void. The Indians became familiar with the system of place value of numerals. India is the birth place of several mathematical concepts including zero, the decimal system, algebra, algorithm, square root and cube root etc. The origin of calculus was in India, even more than three centuries before Leibnitz and Newton introduced their own theorems.
Since the 5th centruay A.D., the method of graduated calculation had been introduced in India. By that time, the geometric theories were known to the Indians. We may see some displays of motifs on the walls of ancient temples. Those motifs ideally reflect the patterns available in Indian architecture, as we see the admixture of floral and wall pattern of geometric method. These concepts, were collected and developed further by the mathematicians like Aryabhata who flourished in the 5th Century A.D. His work Aryabhatiyam is equally important for Mathematics and Astronomy. The first part of the book explains the special system of writing numerals that was introduced by Aryabhata alone. The Second part gives a small anthology of mathematical teachings of Aryabhatta. He deals in his work with evolution and revolution, area and volumes, progressions and algebraic identities.
The Carakasamhita mentions about the Ancient Indians who knew how to prepare sulphuric acid, nitric acid, the oxides of copper tin and zinc, the sulphate of copper, zinc and iron and the carbonates of lead and iron. The weapons mentioned in the Mahabharata and the Ramayana were actually the products of Chemistry.
Indian chemists knew the production of gunpowder and it was called as aurbagni, which was attributed to Aurba, the preceptor of Sagara. The work called Niticintamani discusses about the ingredients and power of fire of Aurba. It says; " combining burnt wood, saltpeter and sulphur by parts gradually lessened, a terrible fire is produced by which even water and others are burnt."
Architecture and Engineering
Architecture the Vastu vidya or Sthapatya is one of the basic Arts of ancient India. The word vastu is derived from vas to reside. Thus vastu denotes all sorts of buildings. Thus architecture includes the complete science of Civil Engineering. The chief development of the Indian Architecture centres round the Hindu Temple. Specimen of different styles of Temple Architecture particularly, the Northern and Dravidian are found in the two parts of India, north and south. The Temple Architecture reflects the spiritual ideals of India. Temples are the abode of gods and goddesses on earth.
The main Sanskrit treatises on Architecture are the Mayamata, Manasara, Vishvakarma - VastuShastra, Samaranganasutradhara, Aparajita - Priccha, Manasollasa, Prasadamandana, Shilparatnam etc.
Mechanical Engineering is known as Yantra Vidya in Sanskrit Shastras. There are many references in Sanskrit literature which speak of the mechanical skills of Indians. The samarangana-sutradhara describes three classes of yantras (i) yana yantra conveyances like vimanas and chariots, (ii) udakayantra water machines variyantra and dharayantra, (iii) sangramayantra like Agneyastra, Varunastra, bhushundi, shataghni and sahasraghni etc.
Indian the medical science is popularly known as Ayurveda which means the Veda for lengthening of the span of life. The beginning of Medical Science goes back to the age of Vedas. The Vedic Indians, who wanted to live for hundred full years with prosperity and good health, developed a holistic approach in the field of healthcare and medical systems, which emphasizes the physical, mental, intellectual and spiritual aspects of a human being.
Bhaishajya-suktani of Atharvaveda reveal the knowledge of medical science in ancient India. Atanomy, embryology and hygiene were also known from the Vedic times.
Ayurveda is considered as an Upanga (subsidiary) to the Atharvaveda. It is inclusive of Achar (the life style), vichar (the thinking process) and ahar (the dietetics).
Ayurveda is divided into eight main branches such as : shalya tantra (major surgery), shalakyatantra (minor surgery), kaya chikitsa (treatment of diseases of the body), bhutavidya (demonology), kumarbhritya (paediatrics), agad tantra(toxicology), rasayana (elixir) and vajikaran (aphrodisiaca).
Atreya, Harita, Kashyapa, Agnivesha, Bhela and jivaka are the ancient scholars, who are named by traditions.
The earliest work on the Indian medicine is the Charakasamhita of Charaka in the first century A.D. It consists of eight chapters: 1)Sutrasthan, that in general describes means of healing, diet, duities of a physician etc. 2)Nidansthan, on the eight principal ailments 3)Vimansthan, on tastes, food, general pathology, and medical stadium 4)Sharirsthana, on anatomy and embryology 5) Indriyasthan, on diagnosis and prognosis 6)Chikitsasthan, on special therapy 7) Kalp and 8)Siddhant sthan, on general therapy.
Charaka, Sushruta and Vagbhata are prominent contributors to the Ayurvedic Literautre. Sushrutasamhita, of Sushruta, Ashtangsangraha of Vagbhata, Madhavanidan of Madhava, Ayurvedadipika of chakrapanidatta are some other important works in this field.
Ayurveda has a well developed school of surgery. Sushruta was most probably the first surgeon in the world to deal systematically, exhaustively and elaborately with the entire subject of surgery including gynaecology, obstetrics, eye-diseases, plastic surgery, artificial limbs etc. Surgical instruments are also described, 101 kinds of blunt instruments and 21kinds of sharp instruments. Vagbhata had classified diseases into seven distinct groups. He has given a complete list of various diseases. He has enlisted 94 eye diseases, 29 ear disorders, 18 diseases related to nose and 75 diseases related to mouth cavity.