The Reconnaissance Portugal, it is said recently, had a great impact upon the normal science in the Renaissance Europe. It is true that the Portuguese navigators, especially Duarte Pacheco Pereira (c.1460-1534) and Joao de Castro (1500-1548), had taken the ancient authorities down easily for some matters of Cosmography through their own maritime experiences. But they could not break away from the Aristotelian Paradigm, however faultfinding they might be.
The decimal place-value notation with a zero symbol (called bindu or a point) is found to be used in the Yavanajataka (A.D.269/270) of Sphujidhvaja, while the recognition of the zero as a number to be an object of mathematical operations can be attested in Var hamihira's Pancasiddhantika (ca.A.D.505). In this paper I have proposed the hypothesis that a place-value notation with a zero symbol and computation on board by using that notation, both of which existed in India in the early centuries of the Christian era, were the necessary conditions for the recognition of zero as a number.
As is well known, the famous research of Ore C. Romer, who has confirmed the finiteness of light velocity and has estimated the value of it, is a very remarkable and important work in the history of physics. However, as is seen in several articles, it seems that there have been distributed rather widely some incomplete or erroneous understandings concerning his work.
In this short note, studies are made on the investigating process of Romer on the problems of velocity of light, including some remarks of the interpretation of it in modern mathematical words.
There used to be a field called Senkyo problem or Common Part Problem in Wasan which the old
Japanese mathematicians or Wasan experts earnestly studied during the Edo period. We have already explained in some journals that Takakazu Seki (1642?-1708) was able to solve the problems without using integral calculus.
This time, we have found a new description about the missing note of T Seki in the introductory remarks and in the main body of KTangen Sanpo", which was wr ten by Shukei Irie in 1739 According to Irie's description, he called it uKongenki Enjutsu 16 Problems" And in the main body of the text Irie had cited, in order to solve a Senkyo Problem, that T.Seki had used an approximate formula to find the area of a segment of a circle.
We were able to restore this approximate formula as follows: If we let d be the chord, c the altitude of a segment of a circle, and S the area, we have,
Through research of Irie's statement, regardless of it being true or not, we obtained some new facts about T. Seki as follows:
Firstly, it is obvious that Seki studied "Sanpo Kongenki" written by Seiko Sato in 1669, from which he learned an approximate formula like the one mentioned above. We believe that this matter may create a new point of view on the study of T. Seki.
Secondly, T. Seki must have made a note called "Kongenki Enjutsu 16 Problems" immediately after "Kokon Sanpoki" by Kazuyuki Sawaguchi was published. This is because K. Sawaguchi did not solve 16 out of 150 problems in "Sanpo Kongenki", which Sato poured out as new questions for Wasan experts of that time. Thus, we are able to place the missing note in an early time of his work.
Thirdly, it is certain that Seki's successors have passed on this missing note for mathematical education and it existed until around the end of the first half of the 18th century.