What is Taught: The first mention of man in flight was by Roger Bacon, who drew a flying apparatus. Leonardo da Vinci also conceived of airborne transport and drew several prototypes.

What Should be Taught: Ibn Firnas of Islamic Spain invented, constructed and tested a flying machine in the 800's A.D. Roger Bacon learned of flying machines from Arabic references to Ibn Firnas' machine. The latter's invention antedates Bacon by 500 years and Da Vinci by some 700 years.

What is Taught: Glass mirrors were first produced in 1291 in Venice.

What Should be Taught: Glass mirrors were in use in Islamic Spain as early as the 11th century. The Venetians learned of the art of fine glass production from Syrian artisans during the 9th and 10th centuries.

What is Taught: Until the 14th century, the only type of clock available was the water clock. In 1335, a large mechanical clock was erected in Milan, Italy. This was possibly the first weight-driven clock.

What Should be Taught: A variety of mechanical clocks were produced by Spanish Muslim engineers, both large and small, and this knowledge was transmitted to Europe through Latin translations of Islamic books on mechanics. These clocks were weight-driven. Designs and illustrations of epi-cyclic and segmental gears were provided. One such clock included a mercury escapement. The latter type was directly copied by Europeans during the 15th century. In addition, during the 9 th century, Ibn Firnas of Islamic Spain, according to Will Durant, invented a watch-like device which kept accurate time. The Muslims also constructed a variety of highly accurate astronomical clocks for use in their observatories.

What is Taught: In the 17th century, the pendulum was developed by Galileo during his teenage years. He noticed a chandelier swaying as it was being blown by the wind. As a result, he went home and invented the pendulum.

What Should be Taught: The pendulum was discovered by Ibn Yunus al-Masri during the 10th century, who was the first to study and document its oscillatory motion. Its value for use in clocks was introduced by Muslim physicists during the 15 th century.

What is Taught: Movable type and the printing press was invented in the West by Johannes Gutenberg of Germany during the 15th century.

What Should be Taught: In 1454, Gutenberg developed the most sophisticated printing press of the Middle Ages. However, movable brass type was in use in Islamic Spain 100 years prior, and that is where the West's first printing devices were made.

What is Taught: Isaac Newton's 17th century study of lenses, light and prisms forms the foundation of the modern science of optics .

What Should be Taught: In the 1lth century al-Haytham determined virtually everything that Newton advanced regarding optics centuries prior and is regarded by numerous authorities as the "founder of optics. " There is little doubt that Newton was influenced by him. Al-Haytham was the most quoted physicist of the Middle Ages. His works were utilized and quoted by a greater number of European scholars during the 16th and 17th centuries than those of Newton and Galileo combined.

What is Taught: Isaac Newton, during the 17th century, discovered that white light consists of various rays of colored light.

What Should be Taught: This discovery was made in its entirety by al-Haytham (11th century) and Kamal ad-Din (14th century). Newton did make original discoveries, but this was not one of them.

What is Taught: The concept of the finite nature of matter was first introduced by Antione Lavoisier during the 18th century. He discovered that, although matter may change its form or shape, its mass always remains the same. Thus, for instance, if water is heated to steam, if salt is dissolved in water or if a piece of wood is burned to ashes, the total mass remains unchanged.

What Should be Taught: The principles of this discovery were elaborated centuries before by Islamic Persia's great scholar, al-Biruni (d. 1050). Lavoisier was a disciple of the Muslim chemists and physicists and referred to their books frequently.

What is Taught: The Greeks were the developers of trigonometry .

What Should be Taught: Trigonometry remained largely a theoretical science among the Greeks. It was developed to a level of modern perfection by Muslim scholars, although the weight of the credit must be given to al-Battani. The words describing the basic functions of this science, sine, cosine and tangent, are all derived from Arabic terms. Thus, original contributions by the Greeks in trigonometry were minimal.

What is Taught: The use of decimal fractions in mathematics was first developed by a Dutchman, Simon Stevin, in 1589. He helped advance the mathematical sciences by replacing the cumbersome fractions, for instance, 1/2, with decimal fractions, for example, 0.5.

What Should be Taught: Muslim mathematicians were the first to utilize decimals instead of fractions on a large scale. Al-Kashi's book, Key to Arithmetic , was written at the beginning of the 15th century and was the stimulus for the systematic application of decimals to whole numbers and fractions thereof. It is highly probably that Stevin imported the idea to Europe from al-Kashi's work.

What is Taught: The first man to utilize algebraic symbols was the French mathematician, Francois Vieta. In 1591, he wrote an algebra book describing equations with letters such as the now familiar x and y's. Asimov says that this discovery had an impact similar to the progression from Roman numerals to Arabic numbers.

What Should be Taught: Muslim mathematicians, the inventors of algebra, introduced the concept of using letters for unknown variables in equations as early as the 9th century A.D. Through this system, they solved a variety of complex equations, including quadratic and cubic equations. They used symbols to develop and perfect the binomial theorem.

What is Taught: The difficult cubic equations (x to the third power) remained unsolved until the 16th century when Niccolo Tartaglia, an Italian mathematician, solved them.

What Should be Taught: Cubic equations as well as numerous equations of even higher degrees were solved with ease by Muslim mathematicians as early as the 10th century.

What is Taught: The concept that numbers could be less than zero, that is negative numbers, was unknown until 1545 when Geronimo Cardano introduced the idea.

What Should he Taught: Muslim mathematicians introduced negative numbers for use in a variety of arithmetic functions at least 400 years prior to Cardano.

What is Taught: In 1614, John Napier invented logarithms and logarithmic tables.

What Should be Taught: Muslim mathematicians invented logarithms and produced logarithmic tables several centuries prior. Such tables were common in the Islamic world as early as the 13th century.

What is Taught: During the 17th century Rene Descartes made the discovery that algebra could be used to solve geometrical problems . By this, he greatly advanced the science of geometry.

What Should be Taught: Mathematicians of the Islamic Empire accomplished precisely this as early as the 9th century A.D. Thabit bin Qurrah was the first to do so, and he was followed by Abu'l Wafa, whose 10th century book utilized algebra to advance geometry into an exact and simplified science.

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