सिद्धान्त शिरोमणि

यहाँ जाएँ: भ्रमण, खोज

सिद्धान्त शिरोमणि, संस्कृत में रचित गणित और खगोल शास्त्र का एक प्राचीन ग्रन्थ है। इसकी रचना भास्कर द्वितीय (या, भास्कराचार्य) ने सन ११५० के आसपास की थी।

इसके चार भाग हैं:

१) लीलावती - इसमें अंकगणित (मैथेमेटिक्स) का विवेचन किया गया है।

२) बीजगणित - इसमें बीजगणित (अल्जेब्रा) का विवेचन है।

४) गोलाध्याय

ग्रहगणिताध्याय और गोलाध्याय में खगोलशास्त्र का विवेचन है।

सिद्धान्त शिरोमणि की एक झलक

१) गुरुत्वाकर्षण—“Father, the earth on which we live, rests on which thing?”

Leelavati had asked this question hundreds of years ago to her father, Bhaskaracharya. In reply, Bhaskaracharya said, “O daughter, Leelavati! Those people who say that the earth is resting on the sheshnaag (cobra snake), the tortoise or elephant or any other thing, are wrong. If we accept that it is based on something, then the question that arises is, that thing rests on which thing? Thus, the reason and its reason…if this sequence continues, then it is known as a state of uncondition in jurisprudence.” Leelavati still insisted on asking the question. Then, Bhaskaracharya said, “Why can we not accept that the earth is not based on anything? What is wrong in saying that the earth is standing on its own strength and call it its power of retention?” At this Leelavati asked how it was possible? Then, Bhaskaracharya speaks of principles and says that the power of things is very peculiar.

मरुच्चलो भूरचला स्वभावतो।
यतो विचित्राः खलु वस्तुशक्तयः ॥

—(सिद्धान्त शिरोमणि गोलाध्याय-भुवनकोष-5)

वे पुनः कहते हैं-

आकृष्टिशक्तिश्च महि तय यत्।
खष्ठं गुरु स्वभिमुखं स्वशक्त्या ॥
आकृष्यते तत्पततीव भाति।
समेसमन्तात् क्व पतत्वियं खे ॥

—(सिद्धान्त शिरोमणि गोलाध्याय-भुवनकोष-६)

This means that the earth has the power of attraction. So, it attracts heavy things towards itself and because of the attraction, they fall to the ground. But, when an equal power or strength pulls from all directions in the sky, then how can a thing fall? This means that the planets stay in the sky without any support because the gravitational powers of the various planets maintain the balance.

Today, we say that Newton was the first to discover the gravitational power of the earth, but 550 years before him, Bhaskaracharya had spoken about it.

२) धरती गोल है—Leelavati asks her father how he can say that the earth is round when she can see only a flat surface all around?

Bhaskaracharya says that what we see is not always the truth. He says that if you draw a large circle and look at only a hundredth part of its circumference, then it will appear to be a straight line; but actually it is not so. It is curved. Similarly, we see only a small part of the sphere of this huge earth. Hence, it seems flat to us. In reality, the earth-is round.

समो यत: स्यात्परिधेह शतान्श:।
पृथी च पृथ्वी नितरां तनीयान् ॥
नरश्च तत्पृष्ठगतस्य कृत्स्ना।
समेव तस्य प्रतिभात्यत: सा ॥

—(सिद्धान्त शिरोमणि गोलाध्याय-भुवनकोष- १३)

भाष्य

स्वयं भास्कराचार्य ने सिद्धान्त शिरोमणि के पद्यात्मक गणित सिद्धान्तों को स्पष्ट करने के लिये 'वासनाभाष्य नामक टीका लिखी है।