ventricles of the heart and the lungs) and described the mechanism of breathing and its relation to the blood and how it nourishes on air in the lungs. Followed a "constructivist" path of the smaller circulatory system: "blood is purified in the lungs for the continuance of life and providing the body with the ability to work". During his time, the common view was that blood originates in the liver then travels to the right ventricle, then on to the organs of the body; another contemporary view was that blood is filtered through the diaphragm where it mixes with the air coming from the lungs. Ibn al-Nafis discredited all these views including ones by Galen and Avicenna (ibn Sina). At least an illustration of his manuscript is still extant. William Harvey explained the circulatory system without reference to ibn al-Nafis in 1628. Ibn al-Nafis extolled the study of comparative anatomy in his "Explaining the dissection of [Avicenna's] Al-Qanoon" which includes a preface, and citations of sources. Emphasized the rigours of verification by measurement, observation and experiment. Subjected conventional wisdom of his time to a critical review and verified it with experiment and observation, discarding errors. Fourteenth Century Astronomy 1393–1449: Ulugh Beg commissions an observatory at Samarqand in present-day Uzbekistan. Mathematics 1380–1429: al-Kashi. According to, "contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as pi. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner." Fifteenth Century Mathematics Ibn al-Banna and al-Qalasadi used symbols for mathematics "and, although we do not know exactly when their use began, we know that symbols were used at least a century before this." Astronomy and mathematics Ibn Masoud (Ghayyathuddin Jamshid ibn Mohamed ibn mas`oud, d. 1424 or 1436.) Wrote on the decimal system. Computed and observed the solar eclipses of 809AH, 810AH and 811AH, after being invited by Ulugh Beg, based in Samarqand to pursue his study of mathematics, astronomy and physics. His works include "The Key of arithmetics"; "Discoveries in mathematics"; "The Decimal point"; "the benefits of the zero". The contents of the Benefits of the Zero are an introduction followed by five essays: