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Papyrus

1. Papyrus Moscow

Mathematics of Papyrus Moscow have been noted since year 1850 BC, time of Abraham V.S Golenishchev obtain ; got it at 1893 and brought it to Moscow. This Papyrus is high fairish 8cm and wide 540cm and contained 25 problems and its solution. Most interesting problems in Mathematics of Moscow Papyrus was problem of concerning volume calculation from a limas. If the limas was limas with the pallet of square and its pallet side is connective a and a line of pallet with the pallet top is side b and if height is h, hence volume limas is h (a²+ab+b²)

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If b=0, we will express the formula of volume limas with the pallet of square that is a²xh

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2.Papyrus Rhind

A sheet papyrus highly 33cm and wide 565cm have been found in Egypt. This Sheet Papyrus have been bought by a market in Luxor at 1858 by Scotlandian 25 years old, Alexander of Henry Rhind. After its death at 30 years old, this found sheets was placed in Museum English in London at 1864. This Sheet Papyrus is often referred as Papyrus of Mathematics Rhind.

Mathematics of Papyrus Rhind copied from a so called writer of Ahmes Year 1650 BC. Mathematics of Rhind Papyrus exposed to promise the reader about this following sentence " By learning those good everything, all knowledge will be exist and knowledge from hidden secret will be expressed. Mostly the problem of Papyrus of Mathematics Rhind took form of the arithmetical puzzle. One of them is : Seven house contained seven cat, each ; each of cat killed seven mouse, each of mouse ate seven items of rice field, each ; each item of rice field produced seven bunch of grist. How many totalizing from all that?

Mathematic of Papyrus Rhind contained the problems connected with trigonometry. Besides, it showed knowledge of linier similarity solving one ordo, the arithmetical addition, and the perfect number. The other problem in the Papyrus Rihnd was about algebra and geometry.

Mathematics of Papyrus Rhind showed us about how the Egyptian divided, done the square root and solved the linear similarity using formula π x r² to calculate the area of circle. For example, it have been claimed by that half from circling pyramid pallet by dividing based the height or as proportion with 3,14. So, we assume that the Egyptian had known the value π until 2 numbers of behind the comma.

3. Papyrus Rollin

Nowadays Papyrus Rollin is looked after in Louvre, contained some detailed calculation about the prices bread and showed the using of big numbers during that period.

4. Papyrus Harris

A document arranged by Rameses IV, when he abdicated. This document elaborated the works from his father, Rameses III. Registration of the temple properties during that period exemplified the best something about practical bookkeeping had come until to us and the ancient Egypt.

Invention of Number Irrational

The integer numbers was the abstraction of arising out in calculating limited objects. To answer the demand of this measurement, not only required by the integer, but also the fraction. The rational number can be interpreted with the simple geometry that was marked by a contour line with the point 0 and 1 ( point 0 located on the left of point 1 ). Here the negative numbers shown at the point on the left of point 0, the integer number (for example: p) located on the right of point 1, while fraction ( for example : q ) can be expressed with the points dividing every set of difference from same shares of q. By this way, it arise the difference that there are the point at that line that did not deputize whatever the rational number. This invention was one of result from brotherhood Pythagoras. All follower Pythagoras indicated that there was no rational number expressing of point p in that line a parting from 0 or 0p equal to diagonal or square with the side of equal to 1 set of.

So, it necessary to create a new number to express that number. Here was the source of the irrational number. To prove that that diagonal length is not deputized by the irrational number, it is same to prove? 2 it is irrational number. Something we required in this case take an example √2 rational number, its meaning √ 2=a? b, where a and b as prima integer, so :

√ 2=a √b

a=b?2 or a²=2b²

Because a= multiple 2 of an integer number, so a² even so that even a also. Taking example a=2c so the similarity become: 4c²=2b²

2c²=b²

So that b² even and also b. But this not possible because a and b not possible are even because representing relative primus number.

So, the assumption that ? 2 having the character of that rational was wrong. We open the other; dissimilar verification having the character of geometric by indicating that side and diagonal square don't have set of same size. Now we take example on the contrary. According to this example, there will be similar segment AP in such a way so, that diagonal of AC and side AB from square ABCD represent the circular multiplication from AP, its meaning that AC and B have set of same size AP. At AC, measure the CB1=AB and draw the B1C1 vertical with CA. It’s easy to proved that C1B=C1B1=AB1, so AC1=AB – AB1 and AB1 will have less equal set with AP. But AC1 and AB1 are diagonal and the sizes of square that smaller than the original square side. Being repeating this way, finally we will find a square with the diagonal of ACN and side ABN which can be measured by AP, while ACN.

Euclid

A few information a Mathematics professor at University Iskandaria and become the founder from School of Mathematics Iskandaria.It possible that he got material of mathematic at Platonic school in Athena. Long years later, that time he compared Euclid with Appolonius, Pappus praised Euclid because he was kind gentle. He put a story in Eudemian Summari-Nya, story about Euclid answer to Ptolomeus question can be given by a practical solution ; ‘’there is no roadway in geometry". The same story narrated about Manaechmus when he worked as a teacher to Iskandaria. Other story narrated by Stobaeus, a student which learn the geometry below Euclid, asking what will get by learning the science. Euclid commanded a slave to give a currency to the student “because he had to get the advantage from what learned".

1. Euclid equipments

It’s important to comprehend the subject of any kind of we which can do with the ruler and expect. With our ruler, we can paint a straight line which unlimited length passing 2 different points, while with our meter we can paint a circle with a certain point as center and passing each every the certain second point.

Because postulate - postulate from masterpiece Euclid limited the using of ruler and expect pursuant to above order, so the used equipment become famous as a means of Euclid equipment.

2. Euclid element book

Euclid became famous because of his The Element book. In the reality marvelous masterpiece immediately and perfection can overcome all previous Element : in fact there was no secondhand which left behind from antecedent efforts.

Actually it was not found by copy Element from that real Euclid correctness have date from life spans its author. Modern printing; mould from Element relied on a renewal compiled by Theon from Iskandaria almost 700 years after original masterpiece write. Recently, start of century 19th found by an older copy was library Vatikan.

Complete first Latin Translation from Element was not made of a Greek but Arab Language. And in year 1120 a so called English master of Adolard Of Both, making Latin translation from Element among other things that the old man Arab translation. Other Latin translation made in Arab Language by Gherard from Cremona ( 1140-1187). Complete first English translation from Element translation Billingsley published in year 1570.

3. Fill of the Euclid element book

Book of Element Euclid besides studying Geometry explanation of theory of elementary algebra and number.

Book I

Learning postulates and axiom, there are 48 theorems. 26 first theorem study the nature of trilateral and theorem congruency. Theorem 27-32 placing theory base mark with lines similar and prove that trilateral sum from the aspect of its equal to right angle; right corner. While at theorem 47 studying theorem Pythagoras.

Book II

Studying elementary change algebra and Madzab Pythagoras. In this book is we meet the geometric equivalent from a number of algebra identity. Last two Theorem place the generalizing base from theorem Pythagoras, what now we know as the “law cosines".

Book III

Studying about circle, bow string, pertinent tangent measurement and from that connected corner.

Book IV

There are solution about Pythagoras, with the ruler and expect about triangle.

Book V

Explanation from Eudexus of about proportion. Theories which can be recognized at this size measure have solved the “logic scandal" created by invention Pythagoras of concerning number of irrational and definition two ratios. Size measure told to have the first same ratio to third and second to fourth if ever from the first and the third taken by random, the second and the fourth taken same also. So it will have the excess, same insuffiency or equality. Equally if A, B, C, D, representing sign element do not A and B of its inclusive of same type ( the two shares mark with lines the, angle ; corner, wide / volume) thereby ratio A:B = C:D.

Book VI

Settling proportion theory of area geometry expressing that trilateral to bisector from the aspect of cut the side which looks out on in proportionate shares two other sides. To show of verification difference of according to Pythagoras and Eudexus about a theorem which is concerning proportion explained by that triangle wide highly is same proportional with its pallet Book VII, VIII, IX

Loading entirely 102 theorem and study the elementary number theory. Book VII, starting by to divide the biggest federation from 2 integer or more which nowadays known as Algorithm Euclid and use it as tester two number primus relative.

Book VIII

Studying comparison partake and pertinent row of measure.

While at book IX explain about all integer of larger ones from n, can be expressed by as result multiply from primus ( number do not be divisible ) with and only one way of Book X.

Studying problems irrational, cutting - incommensurable line cutting with the certain other line cutting.

Book XI, XII, XIII

Studying about solid geometry. Start theorem ( XI ) representing base from way of later Exhaustion used in book XII , if a size measure lessened with the shares which is not less than as half as in the end will be left behind by a size measure which is smaller than all size measure of a kind determined. Definitions of theorem about line and area in space and theorems about all of Lelelipod there are in book XIII.