Wednesday, November 12, 2008

The history of Mathematics

The history of Mathematics

Every culture on earth has developed some mathematics. In some cases, this mathematics has spread from one culture to another. Now there is one predominant international mathematics, and this mathematics has quite a history. It has roots in ancient Egypt and Babylonia, then grew rapidly in ancient Greece. Mathematics written in ancient Greek was translated into Arabic. About the same time some mathematics of India was translated into Arabic. Later some of this mathematics was translated into Latin and became the mathematics of Western Europe. Over a period of several hundred years, it became the mathematics of the world.
There are other places in the world that developed significant mathematics, such as China, southern India, and Japan, and they are interesting to study, but the mathematics of the other regions have not had much influence on current international mathematics. There is, of course, much mathematics being done these and other regions, but it is not the traditional math of the regions, but international mathematics.
By far, the most significant development in mathematics was giving it firm logical foundations. This took place in ancient Greece in the centuries preceding Euclid. See Euclid's Elements. Logical foundations give mathematics more than just certainty-they are a tool to investigate the unknown.
By the 20th century the edge of that unknown had receded to where only a few could see. One was David Hilbert, a leading mathematician of the turn of the century. In 1900 he addressed the International Congress of Mathematicians in Paris, and described 23 important mathematical problems.
Mathematics continues to grow at a phenomenal rate. There is no end in sight, and the application of mathematics to science becomes greater all the time.
The History of Mathematics
Instructor: G. Donald Allen
Spring, 1997
The Origins of Mathematics
{The origins of mathematics accompanied the evolution of social systems. Many, many social needs require
· counting,
· calculations,
· measurement
· The worth of a herdsman cannot be known unless some basics facts of counting are known.
· An temple cannot be built unless certain facts about triangles, squares, and volumes are known.
· An inheritance cannot be distributed unless certain facts about division (fractions) are known.
From practical needs such as these, mathematics was born.
One view is that the core of early mathematics is based upon two simple questions.
· How many?
· How much?
This is the cardinal number viewpoint.
Ordinals
Another view is that mathematics may have an even earlier basis on ordinals used perhaps for rituals in religious practices or simply the pecking order for eating the fresh game. Such basic questions are thus:
· Who is first, etc?
· What comes first, etc?
We will take the cardinal numbers viewpoint in the following.
HOW MANY?
As indicated earlier, as society formed and organized, the need to express quantity emerged. Even at this early level, perhaps as early as 250,000 years ago, there must have begun a transition from sameness to similarity of numbers.
one wolf one sheep
two dogs wolf two rabbits
five warriors five spears
This abstraction of the concept of number was a major step toward modern mathematics.
HOW MANY?
From artifacts even more than 5,000 years old, notches on bones have been noted. Were these to count seasons, kills, children? We don't know. But the need to denote quantity must have been significant.
The English language, as others, has quantifier to indicate plurality
school of fish
pack of wolves
flock of geese
HOW MANY?
Other examples of counting and enumerations reveal just how enumeration began and proceeded.
1. The Indians of the Tamanaca on the Orinoco River.
HOW MANY?
2. The Dammara tribe in Africa (19th century). Trading of tobacco sticks for sheep. The tradesman knew the equivalence:
2 sticks = 1 sheep
However, he was unable to cipher correctly the formula:
4 sticks = 2 sheep
So, at the very early stage of counting numerical equivalences there is no such fact as two times two equals four.
3. Certain Australian aboriginal trives counted to two only, with any number larger than two called simply as much or many.
4. Other South American Indians on the tributaries of the Amazon were equally lacking in number words. They count count to six, but had no words for three, four, five, or six. For example, three was expressed as two-one.
5. The bushmen of Africa could count to ten with just two words.
ten=2+2+2+2+2+2
For larger numbers the descriptive phrases became too long.
Even earlier records
6. The earliest records of counting do not come from words but from physical evidence -- scratches on sticks or stones. Old stone age peoples had devised a system of tallyign by groups as early as 30,000 B.C. There is an example of the shinbone from a young wolf found in Czechoslovakia in 1937. It is about 7 inches long, and is engraved with 55 deeply cut notches, of about equal length, arranged in groups of 5. (Modern systems!!!)
7. There is other evidence dating from 8500 B.C on the shores of Lake Edward (in the Queen Elizabeth National Park in Uganda). An incised bone fossil contains groups of notches in three definite columns. Odd and unbalanced, it does not appear decorative. One set of is arranged in groups of 11, 21, 19 and 9 notches. Another is arranged in groups of 3, 6, 4, 8, 10, 5, 5, 7 notches. Many have conjectured on the meaning of these groups. (Lunar months, doubling, halving, ...)
Some etymology.
· The word tally comes from the French verb tailler, ``to cut", like the English word tailor. The root Latin word is tailler, talea, ``to cut". Note also the English word write comes from the Anglo-saxon writan, ``to scratch".
· Our word calculate comes from the Latin calculus, pebble.
· The English thrice, just like the Latic ter, has the double meaning: three times, and many. There is a plausible connection between the Latin tres, three, and trans, beyond. The same can be said regarding the French trés, very, and trois, three.
· Some primitive languages have words for every color but have no word for color. Others have all the number words but no word for number. The same is true for other words.
· English is very rich in native expressions for types of collections: flock, herd, set, lot, bunch, to name a few. Yet the words collection and aggregate are of foreign extraction. From Bertrand Russell we have the quote, ``It must have required many ages to discover that a brace of pheasants and a couple of days were both instances of the number two." Today we have many terms to describe the idea of two: couple, set, team, twin, brace, etc.
Tallying
Tally sticks have been used since the beginning of counting. But it was not limited to ``primitive" peoples. The acceptance of tally sticks as promissory notes or bills of exchange reached all levels of development in the British Exchequer tallies. (12 century onwards.) It took an act of parliament in 1846 to abolish the practice.
An anecdote: The double tally stick was used by the Bank of England. If someone lent the Bank money, the amount was cut on a stick and the stick was then cut in half. The piece retained by the Bank was called the foil, and the other half was called the stock. It was the receipt issued by the Bank. The holder of said became a ``stockholder" and owned ``bank stock". When the holder would return the stock was carefully checked agained the foil; if they agreed, the owner would be paid the correct amount in kind or currency. A written certificate that was presented for remittance and checked against its security later became a ``check".
Tallying on a bone or stick is both ancient and modern. A more ancient form of counting was done by means of knots tied in a cord -- though counting is carried out to this day by knots or beads. Both objects and days were so tallied. From King Darius of Persia, we have this command given to the Ionians:
The King took a leather thong and tying sixty knots in it called together the Ionian tyrants and spoke thus to them: ``Untie every day one of the knots; if I do not return before the last day to which the knots will hold out, then leave your station and return to your several homes."
Knotted cords, called quipus were also used by the Incas of Peru. The conquering Spaniards noted that each village and an official of the knots, who maintained complex accounts on knotted cords of several colors and thicknesses, and performed a function similar to today's city treasurer.
HOW MANY?
Systems of enumeration.
Primitive:
notches, sticks, stones
Egyptians:
symbols for 1, 10, 100, 1,000, ... 1,0000,000.
Babylonians:
two symbols only--cunieform
Greeks:
alphabetical denotations, plus special symbols
Roman:
Roman numerals, I,V,X,L,C,D,M..
Arabs:
Ten special symbols for numbers.
Modern:
Ten special symbols for numbers.
Methods of ciphering.
Devices:
Abacus, counting boards.
Symbolic:
Arithmetic.
HOW MANY?
Bases for numbering systems
· binary -- early
· ternary -- early
· quinary -- early
· decimal
· vigesimal
· sexigesimal
· combinations of several
A study among American Indians showed that about one third used a decimal scheme; one third used a quinary/decimal scheme; fewer than a third used a binary scheme; and about one fifth used a vegesimal system. and a ternary scheme was used by only one percent.
HOW MUCH?
When counting or asking how many, we can limit discussions to whole positive integers. When asking how much, integers no longer suffice. Examples:
Given 17 seedlings, how can they be planted in five rows?
Given 20 talons of gold, how can they be distribution to three persons?
Given 12 pounds of salt, how can it be divided into five equal containers?
When asking how much we are led directly to the need of fractions.
HOW MUCH?
Another how much question is connected with measurement.
Where?
· Construction. To build graneries, or ovens to bake bread, or pyramids, or temples we need formulas for quantity, or area or volume.
· Planting. To divide arable plots we need formulas for plane area and those for seasons.
· Astronomy. To study the motions of stars we need angular and temporal measurment.
· Taxes and commerce. To properly assess taxes, we need ways to compute percentages (fractions).
To consider questions of how much we need more advanced numbers and arithmetic; we also need concepts of geometry.

Mathematics Used by American
Indians North of Mexico
For the American Indians north of Mexico, we may say that although their bonds of superstition and lack of an adequate number symbolism limited their mathematical progress, number still played an important role in their religious beliefs. In addition, they used many geometric figures in ornamentation and construction.


Sacred Numbers.
Specific reference to the use of three, four five, seven, and thirteen in religious ceremonies is extant, with four being the more prevalent. The may be due to the four points of the compass. Here are examples.
· Five was the mystical number of some of the Pacific Coast Indians. Three and five were sacred to the Iroquois.
· Seven was used by the Zuñi, Cherokee, Creeks, and most of the Plains tribes.
Thirteen was adopted by the Hopi Pawnee, and the Zuñi. It was also widely used in Central America.
· In the Pueblo Snake Dance the Snake Men prepared eight days for the ceremony; the snakes used were of four kinds obtained from a four days' hunt in the four directions.
· An Apache prayed to his gods at least once every four days, and if possible every day, for four times a day. Apache medicine men used this number in their remedies, e.g. four roots of one herb, roots of four varieties, ...
· Suppose a member of the Potawatomi tribe was accused of murder, but that the tribal chief thought he was not guilty, a pipe bearer would bring flint and steel and attempt to light the chief's pipe. If he was successful within four strokes of the steel the man went free, otherwise the man was executed. An influential man might get away with three murders, but for four murders, nothing could save him.
· The Iroquois when smoking would take three puffs from a pipe. Only three trials were allowed in physical contests. Five days or multiple thereof must elapse between the announcement of and the beginning of a celebration.
Counting
Counting on fingers was nearly universal among Indian tribes. Sometimes the fingers were bent in during counting, other times the fingers were extended from a fist during counting.
· Usually, both hands, beginning with the left hand were used to count ten. To get the next ten, some tribes used the toes; others used the fingers again. The Zuñi counted the second ten on their knuckles.
· Tally marks (vertical strokes) were used to denote one. Grouping was not generally evident. The Dakotas used only the vertical stroke. The Creeks also used this but a cross was used for ten.
· Evidence of subtraction has been found. For example in the Bellacoola language of British Columbia we have:
16 one man less four
18 = one man less two
26 = one man and two hands less four
36 = two men less four
· Traces of multiplication can be found in the number words of the Zuñi. We have
10 all the fingers
20 = two times all the fingers
100 = the fingers all the fingers
1000 = the fingers all the fingers times all the fingers
Mounds and Other Earthworks.
Most Indian mounds have been found in the eastern United States. Most were conical. The typical pyramidal mound was a truncated quadrilateral pyramid. The largest is located in Illinois. It is one hundred feet high and has a seven hundred foot base. Mounds have also been discovered and some excavated in Minnisota, Wisconsin, Ohio, Iowa, Georgia, and Mississippi. Many of the mounds were constructed well before Europeans arrived in the new world, some as early as 1000 BCE. The practice seems to have ending in about 1300 CE.


One group of mounds found in Ohio have bases in the shapes of circles, squares, and octagons --- all being quite accurate to true figures. The angles of one measuring more than 900 feet on its base made angles differing from right angles by less than one degree. Could this have been achieved by line of sight? It is an interesting exercise to explain how a people, living in the wilderness, with no tradition of geometry and little tradition of contruction could have made not just one but four nearly right angles on so gigantic a scale. Below is the Adena Serpent mound near Locust Grove, Ohio. Constructed in the second century BCE, it measures 1336 ft (405 meters) long by about 3-6 feet high. Note the use of spirals and semicircles as a part of a quite regular wavy line.

One mound in Georgia constructed by the Etowah Indians is the tallest structure in the area (about 61 feet), and furnishes an impressive view of the Etowah River Valley. The top covers about an acre of land. Another quadrilateral pyramid was a near accurate square with sides pointing in the compass directions. Below is a picture of the terraced-pyramidal Monk's mound rising 100 feet above the surrounding lansdscape, which is a part of the Cahokia mounds in Illinois, just across the Mississippi river from St. Louis. Cahokia is the largest pyramds construction north of Mexico. At its peak it was home to 30,000-50,000 people. Depending on the elevation used it measures 954 ft in the north-south direction and 775 ft in the east-west direction.

Two purposes of these mounds emerge. They were a location of temples and dwellings for the upper crust of the tribes. These sites were clearly more defensible in the event of rather common attacks from neighboring tribes. The other purpose was for burial, and some mounds were exclusively for this purpose. Though these mounds have supplied archeologists with a steady supply of artifacts about the the customs and daily life of the tribes, there has been little by way of mathematical abilities uncovered.

Ornamentation.
Anyone who has visited New Mexico has seen the beautiful blankets still woven by the local Indians. These blankets and other objects of Indian art throughout North America have an assortment of geometrical patterns and themes. Navajo pottery, for example, exhibits opposed sets of isosceles triangles, line bordering dots, hooked spirals, double spirals, vertical and horizontal lines, and stepped figures.

Mathematics in China


Primary sources are Mikami's The Development of Mathematics in China and Japan and Li Yan and Du Shiran's Chinese Mathematics, a Concise History. See the bibliography below.

1. Numerical notation, arithmetical computations, counting rods
o Traditional decimal notation -- one symbol for each of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000, and 10000. Ex. 2034 would be written with symbols for 2,1000,3,10,4, meaning 2 times 1000 plus 3 times 10 plus 4. Goes back to origins of Chinese writing.
o Calculations performed using small bamboo counting rods. The positions of the rods gave a decimal place-value system, also written for long-term records. 0 digit was a space. Arranged left to right like Arabic numerals. Back to 400 B.C.E. or earlier.
o Addition: the counting rods for the two numbers placed down, one number above the other. The digits added (merged) left to right with carries where needed. Subtraction similar.
o Multiplication: multiplication table to 9 times 9 memorized. Long multiplication similar to ours with advantages due to physical rods. Long division analogous to current algorithms, but closer to "galley method."
2. Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.)
o Describes one of the theories of the heavens. Early Han dynasty (206 B.C.E -220 C.E.) or earlier. Book burning of 213 B.C.E..
o States and uses the Pythagorean theorem for surveying, astronomy, etc. Proof of the Pythagorean theorem.
o Calculations including with common fractions.
3. The Nine Chapters on the Mathematical Art (Jiuzhang Suanshu) (c. 100 B.C.E.-50 C.E.)
Collects mathematics to beginning of Han dynasty. 246 problems in 9 chapters. Longest surviving and most influential Chinese math book. Many commentaries.
o Ch 1, Field measurement: systematic discussion of algorithms using counting rods for common fractions including alg. for GCD, LCM; areas of plane figures, square, rectangle, triangle, trapezoid, circle, circle segment, sphere segment, annulus -- some accurate, some approximations.
o Ch 2,3,6 on proportions, Cereals, Proportional distribution, Fair taxes.
o Ch 4, What width?: given area or volume find sides. Describes usual algorithms for square and cube roots but takes advantage of computations with counting rods
o Ch 5, Construction consultations: volumes of cube, rectangular parallelepiped, prism frustums, pyramid, triangular pyramid, tetrahedron, cylinder, cone, and conic frustum, sphere -- some approximations, some use pi=3
o Ch 7, Excess and deficients: false position and double false position
o Ch 8, Rectangular arrays: Gives elimination algorithm for solving systems of three or more simultaneous linear equations. Involves use of negative numbers (red reds for pos numbers, black for neg numbers). Rules for signed numbers.
o Ch 9, Right triangles: applications of Pythagorean theorem and similar triangles, solves quadratic equations with modification of square root algorithm, only equations of the form x^2 + a x = b, with a and b positive.
4. Sun Zi (c. 250? C.E.)
Wrote his mathematical manual. Includes "Chinese remainder problem" or "problem of the Master Sun": find n so that upon division by 3 you get a remainder of 2, upon division by 5 you get a remainder of 3, and upon division by 7 you get a remainder of 2. His solution: Take 140, 63, 30, add to get 233, subtract 210 to get 23.
5. Liu Hui (c. 263 C.E.)
o Commentary on the Nine Chapters
Approximates pi by approximating circles polygons, doubling the number of sides to get better approximations. From 96 and 192 sided polygons, he approximates pi as 3.141014 and suggested 3.14 as a practical approx.
States principle of exhaustion for circles
Suggests Calvalieri's principle to find accurate volume of cylinder
o Haidao suanjing (Sea Island Mathematical Manual). Originally appendix to commentary on Ch 9 of the Nine Chapters. Includes nine surveying problems involving indirect observations.
6. Zhang Qiujian (c. 450?)
Wrote his mathematical manual. Includes formula for summing an arithmetic sequence. Also an undetermined system of two linear equations in three unknowns, the "hundred fowls problem"
7. Zu Chongzhi (429-500) Astronomer, mathematician, engineer.
o Collected together earlier astronomical writings. Made own astronomical observations. Recommended new calendar.
o Determined pi to 7 digits: 3.1415926. Recommended use 355/113 for close approx. and 22/7 for rough approx.
o With father carried out Liu Hui's suggestion for volume of sphere to get accurate formula for volume of a sphere.
8. Liu Zhuo (544-610) Astronomer
Introduced quadratic interpolation (second order difference method).
9. Wang Xiaotong (fl. 625) Mathematician and astronomer.
Wrote Xugu suanjing (Continuation of Ancient Mathematics) of 22 problems. Solved cubic equations by generalization of algorithm for cube root.
10. Translations of Indian mathematical works.
By 600 C.E., 3 works, since lost. Levensita, Indian astronomer working at State Observatory, translated two more texts, one of which described angle measurement (360 degrees) and a table of sines for angles from 0 to 90 degrees in 24 steps (3 3/4 degree) increments.
Hindu decimal numerals also introduced, but not adopted.
11. Yi Xing (683-727) tangent table.
12. Jia Xian (c. 1050)
Written work lost. Streamlined extraction of square and cube roots, extended method to higher-degree roots using binomial coefficients.
13. Qin Jiushao (c. 1202 - c. 1261)
Shiushu jiuzhang (Mathemtaical Treatise in Nine Sections), 81 problems of applied math similar to the Nine Chapters. Solution of some higher-degree (up to 10th) equations. Systematic treatment of indeterminate simultaneous linear congruences (Chinese remainder theorem). Euclidean algorithm for GCD.
14. Li Chih (a.k.a. Li Yeh) (1192-1279)
Ceyuan haijing (Sea Mirror of Circle Measurements), 12 chapters, 170 problems on right triangles and circles inscribed within or circumscribed about them. Yigu yanduan (New Steps in Computation), geometric problems solved by algebra.
15. Yang Hui (fl. c. 1261-1275)
Wrote sevral books. Explains Jiu Xian's methods for solving higher-degree root extractions. Magic squares of order up through 10.
16. Guo Shoujing (1231-1316).
Shou shi li (Works and Days Calendar). Higher-order differences (i.e., higher-order interpolation).
17. Zhu Shijie (fl. 1280-1303)
Suan xue qi meng (Introduction to Mathematical Studies), and Siyuan yujian (Precious Mirror of the Four Elements). Solves some higher degree polynomial equations in several unknowns. Sums some finite series including (1) the sum of n^2 and (2) the sum of n(n+1)(n+2)/6. Discusses binomial coefficients. Uses zero digit.
Chronology of Mathematicians and Mathematical Works

Early traditional texts
These developed in a gradual accumulation of material over centuries. The dates given are roughly when they reached their final form.
· Suan shu shu (A Book on Arithmetic) (c. 180 B.C.E.). A book of bamboo strips found in 1984 near Jiangling in Hubei province.
· Zhoubi suanjing (The Arithmetical Classic of the Gnomon and the Circular Paths of Heaven) (c. 100 B.C.E.-c. 100 C.E.)
· Jiuzhang suanshu (Nine Chapters of the Mathematical Art) (c. 100 B.C.E.-50 C.E.)
The development of mathematics
· Zhang Heng (78-139)
o Ling xian (Spiritual Constitution of the Universe)
· Liu Hong (fl. 178-187)
o Qian xiang li (Calendrical Science Based on the Celestial Appearances) (178-187)
· Wang Fan (217-257)
· Sun Zi (c. 250?)
o Sunzi suanjing (Master Sun's Mathematical Manual)
· Zhao Shuang (Jun Qing) (c. 260)
o Zhoubi suanjing zhu (Commentary on the `Zhoubi Suanjing')
· Liu Hui (c. 263)
o Jiushang suanshu zhu (Commentary on the `Nine Chapters of the Mathematical Art')
o Haidao suanjing (Sea Island Mathematical Manual)
· Xiahou Yang (c. 350?)
o Xiahou Yang suanjing (Xiahou Yang's Mathematical Manual)
· Zhang Qiujian (c. 450?)
o Zhang Qiujian suanjing (Zhang Qiujian's Mathematical Manual)
· Zu Chongzhi (Wenyuan) (429-500)
o Da ming li (Da Ming Calendar) (462)
o Zhui shu (Method of Interpolation)
o Jiuzhang shu yi zhu (Commentary on the Methods and Essence of the `Nine Chapters')
o Chong cha zhu (Commentary on Double Differences)
· Zu Geng
o Zhui shu (Method of Interpolation)
· Zhen Luan (Shuzun) (fl. 566)
o Tian he li (Tian He Calendar) (462)
o Wucao suanjing (Mathematical Manual of the Five Government Departments)
o Wujing suanshu (Arithmetic in Five Classics)
o Shushu juji (Memoir on some Traditions of Mathematical Art)
· Liu Zhuo (544-610)
o Huang ji li (Imperial Standard Calendar) (600)
· Wang Xiaotong (fl. 625)
o Xugu suanjing (Continuation of Ancient Mathematics)
· Li Chunfeng (fl. 664)
o Edited the Shibu suanjing (Ten Books of Mathematical Classics) .
This collection included the Jiuzhang suanshu (Nine Chapters of the Mathematical Art), Haidao suanjing (Sea Island Mathematical Manual), Sunzi suanjing (Master Sun's Mathematical Manual), Wucao suanjing (Mathematical Manual of the Five Government Departments), Wujing suanshu (Arithmetic in Five Classics), Zhang Qiujian suanjing (Zhang Qiujian's Mathematical Manual), Xiahou Yang suanjing (Xiahou Yang's Mathematical Manual), Zhui shu (Method of Interpolation), and Xugu suanjing (Continuation of Ancient Mathematics).
· Yi Xing (683-727)
o Da yan li (Da Yan Calendar) (727)
· Levensita (fl. 718)
o Jiu zhi li (Catching Nines Calendar) (718) translated from an Indian work
Three century interlude
followed by
The zenith of mathematical development
· Jia Xian (c. 1050)
o Jia Xian suanjing (Jia Xian's Mathematical Manual)
· Shen Kuo (1031-1095)
o Meng qu bi tan (Dream Pool Essays)
· Li Zhi (Li Ye) (Jingzhai) (1192-1279)
o Ceyuan haijing (Sea Mirror of Circle Measurements) (1248)
o Yigu yanduan (New Steps in Computation) (1259)
· Liu Yi (fl. c. 1225)
o Yigu genyuan (Discussion of the Old Sources)
· Qin Jiushao (Daogu) (c. 1202-c. 1261)
o Shiushu jiuzhang (Mathemtaical Treatise in Nine Sections) (1247)
· Guo Shoujing (1231-1316)
· Yang Hui (Qianguang) (fl. 1261-1275)
o Xiangjie jiuzhang suanfa (A Detailed Analysis of the Mathematical Methods in the `Nine Chapters') (1261)
o Riyong suan fa (Computing Methods for Daily Use) (1262)
o Yang Hui suan fa (Yang Hui's Methods of Computation) (1274)
o Fasuan qu yong ben mo (Alpha and Omega of a Selection on the Applications of Arithmetical Methods (1274)
o Xugu zhaiqi suan fa (Continuation of Ancient Mathematical Methods for Elucidating the Strange [Properties of Numbers]) (1275)
o Jiuzhang suan fa zuan lei (Reclassification of the Mathematical Methods in the `Nine Chapters')
o Tian mu bi lei cheng chu jie fa (Practical Rules of Arithmetic for Surveying) (1275)
o Cheng chu tong bian suan bao (Precious Reckoner for Variations of Multiplication and Division)
· Wang Xun (1235-1281)
· Shou shi li (Works and Days Calendar), Guo Shoujing, Wang Xun, and others. (1280).
· Zhu Shijie (Hanqing, Songting) (fl. 1280-1303)
o Suan xue qi meng (Introduction to Mathematical Studies) (1299) There is a Japanese edition of 1658.
o Siyuan yujian (Precious Mirror of the Four Elements) (1303)
The decline of mathematics
· Sha keshi (fl. 1321)
o He fang tong yi (On the Prevention of River Flooding) (1321)
· Ding Ju (fl. 1355)
o Ding ju suan fa (Ding Ju's Arithmetical Methods) (1355)
· He Pingzi (fl. 1373)
o Xiangming suan fa (Explanations of Arithmetic) (1373)
· Liu Shilong (fl. 1424)
o Jiu zhang tong ming suanfa (Methods of Calculation in the `Nine Chapters') (1424)
· Wu Jing (fl. 1450)
o Jiu zhang suan fa bi lei da quan (Complete Description of the `Nine Chapters' on Arithmetical Techniques) (1450)
· Wang Wensu (fl. 1524)
o Suan xue baojian (Precious Mirror of Mathematics) (1524)
· Xu Xinlu
o Pan zhu suan fa (Method of Calculating on an Abacus) (1573)
· Ke Sangquin (fl. 1578)
o Shu xue tong gui (Rules of mathematics) (1578)
· Matteo Ricci (1552-1610)
· Niccolo Longobardi (1559-1654)
· Xu Guangqi (Zixian, Xuanhu) (1562-1633)
· Li Zhizao (Zhenzhi) (1565-1630)
Introduction of Western Mathematics
· Cheng Dawei (Rusi, Binqu)(fl. 1592)
o Suan fa tong zong (Systematic Treatise on Arithmetic) (1592) Reprinted in Japan in 1675.
o Zhi zhi uan fa tong zong (Postscript to the Systematic Treatise on Arithmetic) (1592)
o Suan fa zuan yao (Highlights of Calculation Methods (1598)
· Huang Longyi (fl. 1604)
o Suan fa ji nan (Directory of Calculation Methods) (1604)
· Johann Terrenz Schreck (1576-1630)
o Da ce (Complete Surveying)
o Ge tu ba xian biao (Tables of Trigonometric Functions) (1631)
o Ce tian yue shuo (Brief Description of the Measurement of the Heavens)
· Li Tianjing (1579-1659)
· Translation of euclid.html">Euclid's Elements, first six books, Matteo Ricci and Xu Guangqi (1607)
· Giulio Aleni (1582-1649)
o Ji he yao fa (Essentials of Geometry)
· Johann Adam Schall von Bell (1591-1666)
· Giacomo Rho (1593-1638)
o Chou suan (Napier's Bones) (1628)
o Ce liang quan yi (Complete Theory of Surveying) (1631)
o Bi li gui jie (Manual for proportional dividers) (1631)
· Tong wen suan zhi (Treatise on European Arithmetic) an edited translation of Clavius's Epitome of Practical Arithmetic, Matteo Ricci and Li Zhizao (1631)
· Chong zhen li shu (Chong Zhen Reign Treatise on Astronomy and Calendrical Science). (1631-1634).
A collection of 137 books in five submissions edited by Xu Guanqi and Li Tianjing with support of many others. It included Aleni's Ji he yao fa (Essentials of Geometry); Terrenz's Da ce (Complete Surveying), Ge tu ba xian biao (Tables of Trigonometric Functions), and Ce tian yue shuo (Brief Description of the Measurement of the Heavens); and Rho's Ce liang quan yi (Complete Theory of Surveying), Bi li gui jie (Manual for proportional dividers), and Chou suan (Napier's Bones).
· Jean Nicolas Smogulecki (1611-1656)
· Xi yang xin fa li shu (Treatise on Astronomy and Calendrical Science According to the New Western Methods).
A collection of 100 books in 17 volumes emended by Schall von Bell from the Chong zhen li shu (Chong Zhen Reign Treatise on Astronomy and Calendrical Science) (1645)
· Xue Fengzuo (d. 1680)
· Fang Zhongtong (1633-1698)
· Li xue hui tong (Understanding Calendar Making) (1652-1654)
A collection of books published by Smogulecki and Xue Fengzuo. Included are
o Bi li si xian xin biao (New Tables for Four Logarithmic Trigonometric Functions)
o Bi li dui shu biao (Logarithm Tables with Explanations)
o San jiaofa (Essentials of Trigonometry) (1653)
· Tian bu zhen yuan (True Course of Celestial Motions) (1653)
A collection of books written by Smogulecki and Xue Fengzuo. Includes
o San jiao suan fa (Method of Trigonometrical Calculations)
· Mei Wending (Dingjiu, Wu'an) (1633-1721)
o See Mei Juecheng, Mei shi congshu jiyao (Collected Works of the Mei Family) for publication of Mei Wending's written comments on mathematics
· Shu li jing yun (Collected Basic Principles of Mathematics) (1723).
Supervised by Emperor Kang Xi (Aixinjueluo) (1654-1722), edited by Mei Juecheng, Chen Houyao, He Guozong, Ming Antu, Mei Wending, and others.
· Mei Juecheng
o In 1761, Mei Juecheng complied Mei Wending's written commentaries into the Mei shi congshu jiyao (Collected Works of the Mei Family). It included several works on mathematics: Bisuan (Pen Calculations), Chou suan (Napier's bones), Du suan shi li (Proportional Dividers), Shao guang shi yi (Supplement to `What Width'), Fang cheng lun (Theory of Rectangular Arrays), Gougu ju yu (Right-angled Triangles), Jihe tong jie (Explanations in Geometry), Ping san jiao ju yao (Elements of Plane Trigonometry), Fang yuan mi ji (Squares and Circles, Cubes and Spheres), Jihe bu bian (Supplement to Geometry), Hu san jiao ju yao (Elements of Spherical Trigonometry), Huan zhong shu chi (Geodesy), and Qiandu celiang (Surveying Solids).
Mathematics under the "Closed Door" Policy
· Chen Shiren (1676-1722)
o Shao guang bu yi (Supplement to `What Width')
· Ming Antu (d. 1765)
o Suanjing shishu (Ten Mathematical Manuals) (1773)
o Ge yuan mi lu jie fa (Quick Method for Determining Close Ratios in Circle Division) (1774)
· Jiao Xun (1763-1820)
o Da yan qiu yi shu (Technique for Finding 1 by the Great Extension)
· Ruan Yuan (1764-1849)
· Wang Lai (Xiaoying, Hengzhai) (1768-1813)
o Hengzhai suanxue (Hengzhai's Mathematics)
o Hengahai yi shu (Unpublished Works of Hengzhai) (1834, edited by Xia Xie)
· Chou ren zhuan (Biographies of Mathematicians and Astronomers) (1795-1799). Edited by Ruan Yuan.
· Li Huang (d. 1811)
o Jiuzhang suanshu xi cao tu shuo (Careful Explanation of the `Nine Chapters on the Mathematical Art')
o Haidao suanjing xi cao tu shuo (Careful Explanation of the `Sea Island Mathematical Manual')
o Xu gu suanjing kao zhu (Commentary on the `Continuation of Ancient Mathematical Methods for Elucidating the Strange [Properties of Numbers]')
· Li Rui (Shangzhi, Sixiang) (1773-1817)
o Li shi suan xue yi shu (Collected Mathematical Works of Li Rui)
· Luo Tengfeng
o Yi you lu (Records of the Art of Learning) (1815)
· Xiang Mingda (1789-1850)
o Xiang shu yi yuan (The Source of Series) (1888, edited by Dai Xu)
· Luo Shilin (1789-1853)
o Siyuan yujian xicao (Commentary on the `Precious Mirror of the Four Elements') (1836)
· Dong Youcheng (Fangli) (1791-1823)
o Ge yuan mi lu tu jie (Explanation for the `Determination of Close Ratios in Circle Division')
· Gu Guanjuang (1799-1862)
o Zhoubi suanjing xiao kan ji (A Textual Criticism of the `Zhoubi Suanjing')
· Shen Qinpei (fl. 1829)
o Siyuan yujian xicao (Commentary on the `Precious Mirror of the Four Elements') (1829)
· Zhang Dunren (fl. 1831)
o Qiu yi suan shu (Techniques of Finding 1) (1831)
· Dai Xu (1805-1860)
o Dai shu jian fa (Concise Technique of Logarithms) (1846)
International Mathematics in China
· Li Shanlan (Renshu, Qiuren) (1811-1882)
o Duo ji bi lei (Sums of Piles of Various Types)
o Fang yuan chan you (Explanation of the Square and the Circle)
o Hu shi qi mi (Unveiling the Secrets of Arc and Sagitta)
o Dui shu tan yuan (Seeking the Source of Logarithms)
o Several translations of Western mathematics (1852-1866)
· Hua Hengfan (Ruo Ting) (1833-1902)
o Xingsu xuan suan (Mathematical Papers form the Xing Su Study)
o Several translations of Western mathematics (1868-1886)
· Shi Richun
o Qiu yi shu zhi (Path to the Technique of Finding 1) (1873)
· Huang Zongxian
o Qiu yi shu tong jie (Explanation of the Technique of Finding 1) (1873)
The Origins of Mathematics.
Like every other aspect of human invention, mathematics has its origin, and like every technology, and mathematics is at least partly that, its origin is based upon needs of mankind. The particular needs are those arising from the wants of society. The more complex the society, the more complex the needs. The primitive tribe has little mathematical needs beyond counting. The complex society intent on building great temples, mustering conquering armies, or managing large capital assets has logistical problems that demand mathematics to solve.
Long before Pythagoras considered proving the famous theorem named after him, others tackled the just-as-complex operation of counting. You will see that for some the concept of two times two equals fours is advanced beyond comprehension, while for others counting past three is very complex. That counting began more than 50,000 years ago and many peoples even today and even in complex societies have trouble counting suggests that its creation was not as simple as we may.

WHAT DO CHRISTIANS BELIEVE?

Seven Things About God
1. We believe there is Only One Unique God. It is written: (Deuteronomy 6:4) Hear, O Israel; The LORD our God [is] one LORD.
2. God is Creator of everything, this vast universe. All was created by His Word. He spoke it into being. It is written: (Genesis 1:3) And God said... and it was so. His Word is powerful.
3. How can we created beings know anything about God? How can we puny creatures know anything about His thoughts?
We can - but only because God Himself has chosen to reveal something about Himself to us. He is the God of Revelation. It is written: (Deuteronomy 29:29) The secret things belong to the LORD our God; but the things that are revealed belong to us and to our children for ever, that we may do all the words of this law.
What has God revealed about Himself to us?
4. He is Holy - pure - absolutely no evil can exist in or with Him. He has nothing to do with any sin, or wrong thinking, or evil. It is written: (Habakkuk 3:11) Your eyes are too pure to look on evil; you cannot tolerate wrong.
5. He is Just - which means that all wrongdoing will be punished. Sometimes people are confused on this point. Justice is not the same as mercy. Justice means if you break the law, you pay the penalty.
God does not compromise His nature of Holiness. He punishes all wrong doing.
It is not as if God puts all our good deeds on one side of a scale, and all our bad deeds on the other side to see which is heavier. To use an example: If I were to murder your brother, would a judge be just who said, "It's OK. We can let him be free. He has done mostly good during his life." God does not close His eyes to wrong. He does not tolerate it.
But doesn't God know that we are all dust? That we are prone to make mistakes? There is no perfect man or woman. Yes, He knows. But does this mean that our mistakes don't matter to God? God is holy and just, so they matter greatly. If we understand this, then we realize that we are in a very bad situation.
If we are honest - which of us has never had a selfish or wrong thought? or never lied? Who can say that they have a pure heart before a Holy God?
And even if we were able to live without making mistakes now - what about the past? Does God have a poor memory? Does doing good erase doing wrong? No.
Each of us deserves God's judgment and Hellfire. It's not just a matter of saying a prayer, "I am sorry. I will try to do better next time." There would be no justice in that.
An example: If I drive through a red light and an officer stops me, is it any good saying, "But officer, I have been going through green lights the rest of my life!" If this argument wouldn't work with an officer, how much less with a Holy and Just God! It is written: (Romans 6:23) The payment of wrongdoing is death.
Fortunately for each one of us, this is not the end of the story.
6. God is Almighty - God can do anything He wants to. It is written: (Jeremiah 32:17) Ah Lord GOD! You have made the heavens and the earth by your great power and outstretched arm, nothing is too hard for you.
There are no limits - no bounds to His power.
God is consistent. God is not contradictory - He doesn't contradict His holiness or justice. He does not violate His law.
Let me ask a question: "How do you get to know someone?" You might be able to tell something about others from the way they look. But you can't know what they think, what's in their heart. We need to hear a person's words. Their words tell what is inside their heart, what they are thinking in their mind.
If I want to communicate my wishes to you, there are several ways of doing it. I might send you a letter, writing down my thoughts. You could read it. But you might have questions, or not understand something. A better way is to send my letter with a good friend, someone who knows me well. My friend would be able to explain something of what I am saying. Better yet, I telephone you, and you can talk with me directly. But best of all, I come to you in person, and we meet face to face.
God's Word spoke the universe into being. His Word is powerful beyond our comprehension. He wants us to know Him. God gave His written Word in the law. He sent the prophets to explain and clarify His Word. It is written: (Hebrews 1:1) In the past God spoke to our forefathers through the prophets at many times and in various ways.
God is so powerful that nothing is impossible - if God wants to, His WORD can actually come to us, face to face. His Word can become a man.
7. God is LOVE - God loves us and wants us to know Him - so His Word became a man.
It is written: (John 1:1,14) In the beginning was the Word, and the Word was with God, and the Word was God ... The Word became flesh and made His dwelling among us. We have seen His glory, the Glory of the One and Only.
Jesus is the Word of God. The pure and Holy Word of God.
Remember Abraham and his son? (Genesis 22:1-14) Abraham wanted to obey and submit to God. He took his son to sacrifice him, and on the way his son asked, "The fire and wood are here, but where is the lamb for the offering?" Abraham answered, "God himself will provide the Lamb for the offering." Abraham laid his son on the altar for sacrifice and was about to slay him when God called to him, "Abraham! Do not lay a hand on the boy!" And Abraham looked up and saw a ram God momentously provided, caught by its horns, and sacrificed it instead. His son was ransomed.
The Bible calls Jesus the Lamb of God (John 1:29) when the prophet John declared, "Behold, the Lamb of God, who takes away the sin of the world!" He ransomed us. In love, God's Word took the judgment we deserved upon Himself.
But He didn't stay dead - He could not - He rose victorious - and conquered death.

How can we know God?
How can we know God? It isn't easy - it takes humility.
It takes humility to recognize that we are dust, that we have unclean hearts, and our deeds deserve Hell.
It takes humility to receive what God has done: He washes us clean, makes us pure, and gives His Spirit to help us live lives of obedience.
There is great joy and freedom in knowing God - the One and Only God, the Creator, the One who Reveals Himself, who is Holy, Just, Almighty, and Loving.
He calls us not to be servants, but His children. Jesus says (John 15:15) I no longer call you servants, because a servant does not know his master's business. Instead I have called you friends.
It is written: (John 1:12) To all who received Him, who believed in His name, He gave power to become children of God.

WHAT THE BIBLE SAYS ABOUT MOHAMMED (PEACE BE UPON HIM) THE PROPHET OF ISLAM

WHAT THE BIBLE SAYS ABOUT MOHAMMED (PEACE BE UPON HIM) THE PROPHET OF ISLAM
A lecture by Ahmed Deedat

SAY: "DO YOU SEE ?
WHETHER THIS MESSAGE BE FROM ALLAH (God Almighty),
AND YET YOU REJECT IT,
AND A WITNESS FROM AMONG THE CHILDREN OF ISRAEL BORE
WITNESS OF ONE LIKE HIM......."
(Holy Qur'an 46:10). (see note 1)

Mr.Chairman, Ladies and Gentlemen,
The subject of this evening's talk - "What the BIBLE says about MUHAMMED" - will no doubt come as a surprise to many of you because the speaker is a Muslim. How does it come about that a Muslim happens to be expounding prophecies from the Jewish and Christian Scriptures ?
As a young man, about 30 years ago, I attended a series of religious lectures by a Chriatian theologian, a certain Rev. Hiten, at the "Theatre Royal", Durban in South Africa.
Pope or Kissinger?
This Reverend gentleman was expounding Biblical prophecies. He went on to prove that the Christian Bible foretold the rise of Soviet Russia, and the Last Days. At one stage he went to the extent of proving that his Holy Book did not leave even the Pope out of its predictions. He expatiated vigo rously in order to convince his audience that the "Beast 666" mentioned in the Book of Revelation the last book of the New Testament was the POPE, who was the Vicar of Christ on earth. It is not befitting for us Muslims to enter into this controversy between the Roman Catholics and the Protestants. By the way, the latest Christia exposition of the "Beast 666" of the Christian Bible is Dr.Henry Kissinger(2). Christian scholars are ingenious and indefatigable in their efforts to prove their case.
Rev. Hiten's lectures led me to ask that if the Bible foretold so many things - not even excluding the "Pope" and "Israel" - then surely it must have something to say about the greatest benefactor of mankind(3) , the Holy Prophet Muhammed (may the peace of Allah be upon him).
As a youngster I set out to search for an answer. I met priest after priest, attended lectures, and read everything that I could lay my hands relating to the fields of Bible prophecies. Tonight I am going to narrate to you one of these interviews with a dominee(4) of the Dutch Reformed Church.
Lucky Thirteen
I was invited to the Transvaal(5) to deliver a talk on the occasion of Birthday celebration of the Holy Prophet Muhammed. Knowing that in that province of the Republic, the Afrikaans language is widely spoken, even by my own people, I felt that I ought to acquire a smattering of this language so a s to feel a little "at home" with the people. I opened the telephone directory and began phoning the Afrikaans-speaking Churches. I indicated my purpose to the priests that I was interested in having a dialogue with them, but they all refused my request with "Plausible" excuses. No.13 was my lucky number. The thirteenth call brought me pleasure and relief. A dominee Van Heerden agreed to meet me at his home on the Saturday afternoon that I was to leave for Transvaal.
He received me on his verandah with a friendly welcome. He said if I did not mind, he would like his father-in-law from the Free State (a 70 year old man) to join us in the discussion. I did not mind. The three of us settled down in the dominee's library.
Why nothing?
I posed the question: "What does the Bible say about Muhummed?" Without hesitation he answered, "Nothing!" I asked: "Why nothing? According to your interpretation the Bible have so many things to say about the rise of Soviet Russia and about the Last Days and even about the Pope of the Roman Ca tholics?" He said, "Yes, but there was nothing about Muhummed!" I asked again, "Why nothing? Surely this man Muhummed who had been responsible for the bringing into being a world-wide community of millions of Believers who, on his authority, believe in:
(1) the miraculous birth of Jesus,
(2) that Jesus is the Messiah,(note 6)
(3) that he gave life to the dead by God's permission, and that he healed those born blind and the lepers by God's permission.
Surely this book (the Bible) must have something to say about this great Leader of men who spoke so well of Jesus and his mother Mary?"
The old man from the Free State replied. "My son, I have been reading the Bible for the past 50 years, and if there was any mention of him, I would have known it."
Not One by name!
I enquired: "According to you, are there not hundreds of prophecies regarding the coming of Jesus in the Old Testament." The dominee interjected: "Not hundreds, but thousands!" I said, "I am not going to dispute the 'thousand and one' prophecies in the Old Testament regarding the coming of Jesu s Christ, because the whole Muslim-world has already accepted him without the testimony of any Biblical prophecy. We Muslims have accepted the de facto Jesus on the authority of Muhummed alone, and there are in the world today no less than 900,000,000 followers of Muhummed who love, respect and rev ere Jesus Christ as a great Messenger of God without having the Christians to convince them by means of their Biblical dialectics. Out of the 'thousands' of prophecies referred to, can you please give me just one single prophecy where Jesus is mentioned by name? The term 'Messiah', translated as 'C hrist', is not a name but a title. Is there a single Prophecy where it says that the name of the Messiah will be JESUS, and that his mother's name will be MARY, that his supposed father will be JOSEPH THE CARPENTER; that he will be born in the reign of HEROD THE KING, etc. etc.? No! There are no su ch details! Then how can you conclude that those 'thousand' Prophecies refer to Jesus (Peace be upon him)?"
What is Prophecy?
The dominee replies: "You see, prophecies are word-pictures of something that is going to happen in the future. When that thing actually comes to pass, we see vividly in these prophecies the fulfilment of what had been predicted in the past." I said: "What you actually do is that you deduce, yo u reason, you put two and two together." He said: "Yes." I said: "If this is what you have to do with a 'thousand' prophecies to justify your claim with regards to the genuineness of Jesus, why should we not adopt the very same system for Muhummed?" The dominee agreed that it was a fair proposition , a reasonable way of dealing with the problem.
I asked him to open up Deuteronomy, chapter 18, verse 18, which he did. I read from memory the verse in Afrikaans, because this was my purpose in having a little practice with the language of the ruling race in South Africa. (8)
'N PROFEET SAL EK VIR HULLE VERWEK UIT DIE MIDDE VAN HULLE BROERS, SOOS JY IS, EN EK SAL MY WOORDE IN SY MOND LE, EN HY SY SAL AAN HULLE SE ALLE WAT EK HOM BEVEEL. Deut.18: 18.
The English translation reads as follows:-
"I will raise them up a Prophet from among their brethren,
like unto thee,
and I will put my words in his mouth;
and he shall speak unto them all that I shall command him." Deut.18:18.
Prophet Like Moses
Having recited the verse in Afrikaans, I apologised for my uncertain pronunciation, The dominee assured me that I was doing fine. I enquired: "To whom does this prophecy refer?" Without the slightest hesitation he answered: "JESUS!" I asked: "Why Jesus?... his name is not mentioned here." The domin ee replied: "Since prophecies are word-pictures of something that is going to happen in the future, we find that the wordings of this verse adequately describe him. You see the most important words of this prophecy are 'SOOS JY IS' (like unto thee), - LIKE YOU - like Moses, and Jesus is like Moses. " I questioned: "In which way is Jesus like Moses?" The answer was: "In the first place Moses was a JEW and Jesus was also a JEW; secondly, Moses was a PROPHET and Jesus was also a PROPHET - therefore Jesus is like Moses and that is exactly what God had foretold Moses - "SOOS JY IS". "Can you think of any other similarities between Moses and Jesus?" I asked. The dominee said that he could not think of any. I replied: "If these are the only two criteria for discovering a candidate for this prophecy of Deuteronomy 18:18, then in that case the criteria could fit any one of the following Biblica l personages after Moses:- Solomon, Isaiah, Ezekiel, Daniel, Hosea, Joel, Malachi, John the Baptist etc., because they were also ALL Jews as well as Prophets. Why should we not apply this prophency to any one of these prophets, and why only to Jesus? Why should we make fish of one and fowl of anoth er?" The dominee had no reply. I continued: "You see, my conclusions are that Jesus is most unlike Moses, and if I am wrong I would like you to correct me."
Three Unlikes
So staying, I reasoned with him: "In the FIRST place Jesus is not like Moses, because, according to you - 'JESUS IS A GOD', but Moses is not God. Is this true?" He said: "Yes." I said: "Therefore, Jesus is not like Moses! SECONDLY, according to you - 'JESUS DIED FOR THE SINS OF THE WORLD', but Mose s did not have to die for the sins of the world. Is this true?" He again said: "Yes." I said: "Therefore Jesus is not like Moses! THIRDLY, according to you - 'JESUS WENT TO HELL FOR THREE DAYS', but Moses did not have to go there. Is this true?" He answered meekly: "Y-e-s." I concluded: "Therefore Jesus is not like Moses!" "But dominee," I continued: "these are not hard facts, solid facts, they are mere matters of belief over which the little ones can stumble and fall. Let us discuss something very simple, very easy that if your little ones are called in to hear the discussion, would have no difficulty in following it, shall we?" The dominee was quiet happy at the suggestion.
Father and Mother
(1) "Moses had a father and a mother. Muhummed also had a father and a mother. But Jesus had only a mother, and no human father. Is this true?" He said: "Yes." I said: "DAAROM IS JESUS NIE SOOS MOSES NIE, MAAR MUHUMMED IS SOOS MOSES!" Meaning: "Therefore Jesus is not like Moses, but Muhummed is lik e Moses!" (By now the reader will realise that I was using the Afrikaans language only for practice purposes. I shall discontinue its use in this narration).
Miraculous Birth
(2) "Moses and Muhummed were born in the normal, natural course, i.e. the physical association of man and woman; but Jesus was created by a special miracle. You will recall that we are told in the Gospel of St.Matthew 1:18".....BEFORE THEY CAME TOGETHER,(Joseph the Carpenter and Mary) SHE WAS FOUND WITH CHILD BY THE HOLY GHOST.' And St.Luke tells us that when the good news of the birth of a holy son was announded to her, Mary reasoned:'.......HOW SHALL THIS BE, SEEING I KNOW NOT A MAN? AND THE ANGEL ANSWERED AND SAID UNTO HER, THE HOLY GHOST SHALL COME UPON THEE, AND THE POWER OF THE HIGHEST SHALL OVERSHADOW THEE:......'(Luke 1:35). The Holy Qur'an confirms the miraculous birth of Jesus, in nobler and sublimer terms. In answer to her logical question:
" O MY LORD! HOW SHALL I HAVE A SON WHEN NO MAN HATH TOUCHED ME? "
The angel says in reply:
"EVEN SO:
ALLAH CREATETH WHAT HE WILLETH:
WHEN HE HATH DECREED A PLAN,
HE BUT SAITH TO IT "BE,"
AND IT IS " (9) (HOLY QUR'AN, 3:47).
It is not necessary for God to plant a seed in man or animal. He merely wills it and it comes into being. This is the Muslim conception of the of birth of Jesus.
(When I compared the Qur'an and the Biblical versions of the birth of Jesus to the head of the Bible Society in our largest City, and when I enquired: "Which version would you prefer to give your daughter, the QUR'ANIC version or the BIBLICAL version?" The man bowed his head and answered: "The Qur'anic.") In short, I said to the dominee: "Is it true that Jesus was born miraculously as against the natural birth of Moses and Muhummed?"He replied proudly:"Yes!" I said:"Therefore Jesus is not like Moses, but Muhummed is like Moses. And God says to Moses in the Book of Deuteronomy 18:18 "LIKE UNTO THEE" (Like You, Like Moses) and Muhummed is like Moses."
Marriage Ties
(3) "Moses and Muhummed married and begat children, but Jesus remained a bachelor all his life. Is this true?" The dominee said: "Yes." I said: "Therefore Jesus is not like Moses, but Muhummed is like Moses."
Jesus Rejected by his People
(3) "Moses and Muhummed were accepted as prophets by their people in their very lifetime. No doubt the Jews gave endless trouble to Moses and they murmured in the wilderness, but as a nation, they acknowledged that Moses was a Messenger of God sent to them. The Arabs too made Muhummed's life imposs ible. He suffered very badly at their hands. After 13 years of preaching in Mecca, he had to emigrate from the city of his birth. But before his demise, the Arab nation as a whole accepted him as the Messenger of Allah. But according to the Bible: 'He (Jesus) CAME UNTO HIS OWN, BUT HIS OWN RECEIVED HIM NOT.' (John 1:11). And even today, ofter two thousand years, his people- the Jews, as a whole, have rejeted him. Is this true?" The dominee said: "Yes." I said: "THEREFORE JESUS IS NOT LIKE MOSES, BUT MUHUMMED IS LIKE MOSES."
"Other-Wordly" Kingdom
(5) "Moses and Muhummed were prophets as well as kings. A prophet means a man who receives Divine Revelation for the Guidance of Man and this Guidance he conveys to God's creatures as received without any addition or deletion. A king is a person who has the power of life and death over his people. It is immaterial whether the person wears a crown or not, or whether he was ever addressed as king or monarch: if the man has the prerogative of inflicting capital punishment - HE IS A KING. Moses possessed such a power. Do you remember the Israelite who was found picking up firewood on Sabbath Day , and Moses had him stoned to death? (Numbers- 15:13). There are other crimes also mentioned in the Bible for which capital punishment was inflicted on the Jews at the behest of Moses. Muhummed too, had the power of life and death over his people. There are instances in the Bible of persons who wer e given gift of prophecy only, but they were not in a position to implement their directives. Some of these holy men of God who were helpless in the face of stubborn rejection of their mesage, were the prophets lot, Jonah, Daniel, Ezra, and John the Baptist. They could only deliver the message, but could not enforce the Law. The Holy Prophet Jesus (Peace b.u.h) also belonged to this category. The Christian Gospel clearly confirms this: when Jesus was dragged before the Roman Governor, Pontius Pilate, Charged for sedition, Jesus made a convincing point in his defence to refute the false charg e: JESUS ANSWERED, "MY KINGDOM IS NOT OF THIS WORLD': IF MY KINGDOM WERE OF THIS WORLD, THEN WOULD MY SERVANTS FIGHT, THAT I SHOULD NOT BE DELIVERED TO THE JEWS; BUT NOW IS MY KINGDOM NOT FROM HENCE"(John 18:36) This convinced Pilate (A Pagan) that though Jesus might not be in full possessio n of his mental faculty, he did not strike him as being a danger to his rule. Jesus claimed a spiritual Kingdom only; in other words he only claimed to be a Prophet. Is this true?" The dominee answered:"Yes." I said:"Therefore Jesus is not like Moses but Muhummed is like Moses."
No New Laws
(6) "Moses and Muhummed brought new laws and new regulations for their people. Moses not only gave the Ten Commandments to the Israelites, but a very comprehensive ceremonial law for the guidance of his people. Muhummed comes to a people steeped in barbarism and ignorance. They married their step-m others; they buried their daughters alive; drunkenness, adultery, idolatry, and gambling were the order of the day. Gibbon describe the Arabs before Islam in his "Decline and Fall of the Roman Empire", THE HUMAN BRUTE, ALMOST WITHOUT SENSE, IS POORLY DISTINGUISHED FROM THE REST OF THE ANIMAL CREATI ON.' There was hardly anything to distinguish between the "man" and the "animal" of the time; they were animals in human form.
"From this abject barbarism, Muhummed elevated them, in the words of Thomas Carlysle, 'into torch-bearers of light and learning.' 'TO THE ARAB NATION IT WAS AS A BIRTH FROM DARKNESS INTO LIGHT. ARABIA FIRST BECAME ALIVE BY MEANS OF IT. A POOR SHEPHERD PEOPLE, ROAMING UNNOTICED IN ITS DESERTS SINCE THE CREATION OF THE WORLD. SEE, THE UNNOTICED BECOMES WORLD NOTABLE, THE SMALL HAS GROWN WORLD-GREAT. WITHIN ONE CENTURY AFTERWARDS ARABIA WAS AT GRANADA ON ONE HAND AND AT DELHI ON THE OTHER. GLANCING IN VALOUR AND SPLENDOUR, AND THE LIGHT OF GENIUS, ARABIA SHINES OVER A GREA SECTION OF THE WORLD. ...' The fact is that Muhummed gave his people a Law and Order they never had before.
"As regards Jesus, when the Jews felt suspicious of him that he might be an imposter with designs to pervert their teachings, Jesus took pains to assure them that he had not come with a new religion - no new laws and no new regulations. I quote his own words: 'THINK NOT THAT IAM COME TO DESTROY THE LAW, OR THE PROPHETS: IAM NOT COME TO DESTROY, BUT TO FULFIL. FOR VERILY I SAY UNTO YOU, TILL HEAVEN AND EARTH PASS, ONE JOT OR ONE TITLE SHALL IN NO WISE PASS FROM THE LAW, TILL ALL BE FULFILLED.'(Mathew 5:17-18). In other words he had not come with any new laws or regulation he came only to fulfil the old law. This what he gave the Jews to understand- unless he was speaking with the tongue in his cheek trying to bluff the Jews into accepting him as a man of God and by subterfuge trying to ram a new religion down their throats. No! This Messenger of God would never resort to such fo ul means to subvert the Religion of God. He himself fulfilled the laws. He observed the commandments of Moses, and he respected the Sabbath. At no time did a single Jew point a finger at him to say, 'why don't you fast' or 'why don't you wash your hands before you break bread',which charges they al wasy levied against his disciples, but never against Jesus. This is because as a good Jew he honoured the laws of the prophets who preceded him. In short, he had created no new religion and had brought no new law like Moses and Muhummed. Is this true?" I asked the dominee, and he answered: "Yes." I said:"Therefore, Jesus is not like Moses but Muhummed is like Moses."
How they Departed
(7) "Both Moses and Muhummed died natural deaths, but according to Christianity, Jesus was violently killed on the cross.(10) Is this true?" The dominee said: "Yes." I averred: "Therefore Jesus is not like Moses but Muhummed is like Moses."
Heavenly Abode
(8) "Moses and Muhummed both lie buried in earth, but according to you, Jesus in heaven. Is this true?" The dominee agreed. I said: "Therefore Jesus is not like Moses but Muhummed is like Moses."
Ishmael The First Born
Since the dominee was helplessly agreeing with every point, I said, "Dominee, so far what I have done is to prove only one point out of the whole prophecy- that is proving the phrase 'LIKE UNTO THEE' - 'Like You' 'Like Moses'. The Prophecy is much more than this single phrase which reads as follows : "I WILL RAISE THEM UP A PROPHET FROM AMONG THEIR BRETHREN LIKE UNTO THEE......." The emphasis is on the words- "From among their brethren." Moses and his people, the Jews, are here addressed as a racial entity, and as such their 'brethren' would undoubtedly be the arabs. You see, the Holy Bible s peaks of Abraham as the "Friend of God". Abraham had two wives - Sarah and Hagar. Hagar bore Abraham a son - HIS FIRST-BORN- '......And Abraham(11) called HIS SON'S name, which Hagar bare Ishmael.' (Genesis 16:15). 'And Abraham took Ishmael HIS SON......" (Genesis 17:23). 'And Ishmael HIS SON was thirteen years old, when he was circumcised in the flesh of his foreskin.'(Genesis 17:25). Up to the age of THIRTEEN Ishmael was the ONLY son and sed of Abraham, when the covenant was ratified between God and Abraham. God grants Abraham another son through Sarah, named Isaac, wh o was very much the junior to his brother Ishmael.
Arabs and Jews
If Ishmael and Isaac are the sons of the same father Abraham, then they are brothers. And so the children of the one are the BRETHREN of the children of the other. The children of Isaac are the Jews and the Children of Ishmael are the Arabs - so they are BRETHREN to one another. The Bible affirms, 'AND HE (ISHMAEL) SHALL DWELL IN THE PRESENCE OF ALL HIS BRETHREN.' (Genesis 16:12). 'AND HE (ISHMAEL) DIED IN THE PRESENCE OF ALL HIS BRETHREN.(Genesis 25:18). The children of Isaac are the brethren of the Ishmaelites. In like manner Muhummed is from among the brethren of the Israeli tes beause he was a descendant of Ishamel the son of Abraham. This exactly as the prophecy has it- 'FROM AMONG THEIR BRETHREN'.(Deut.18:18). There the prophecy distinctly mentions that the coming prophet who would be like Moses, must arise NOT from the 'children of Israel' or from 'among the mselves', but from among their brethren. MUHUMMED THEREFORE WAS FROM AMONG THEIR BRETHREN!
Words in the Mouth
"The prophecy proceeds further:'.......AND I WILL PUT MY WORDS INTO HIS MOUTH.......' What does it mean when it is said 'I will put my words in your mouth'? You see, when I asked you (the dominee) to open Deuteronomy chapter 18, verse 18, at the beginning, and if I had asked you to read, and if you had read: would I be putting my words into your mouth?" The dominee answered: "No." "But," I continued: "If I were to teach you a language like Arabic about which you have no knowledge, and if I asked you to read or repeat after me what I utter i.e.:
"SAY: HE IS ALLAH THE ONE AND ONLY;
ALLAH, THE ETERNAL ABSOLUTE;
HE BEGETTETH NOT, NOR IS HE BEGOTTEN:
AND THERE IS NONE LIKE UNTO HIM.
(Holy Qur'an 112:1-4)( I read them in Arabic )
Would I not be putting these unheard words of a foreign tongue which you utter, into your mouth?" The dominee agreed that it was indeed so. In an identical manner, I said, the words of the Holy Qur'an, the Revelation vouchsafed by the Almighty God to Muhummed, were revealed.
History tells us that Muhummed was forty years of age. He was in a cave some three miles north of the City of Mecca. It was the 27th night of the Muslim month of Ramadaan. In the cave the Archangel Gabriel commands him in his mother tongue:'IQRA' which means READ! or PROCLAIM! or RECITE! Muhummed w as terrified and in his bewilderment replied that he was not NOT LEARNED! The angel commands him a second time with the same result. For the third time the angel continues.
Now Muhummed, grasps, that what was required of him was to repeat! to rehearse! And he repeats the words as they were put into his mouth:
"READ! IN THE NAME OF THE LORD AND CHERISHER, WHO CREATED-
CREATED MAN, FROM A (MERE) CLOT OF CONGEALED BLOOD:
READ! AND THY LORD IS MOST BOUNTIFUL,-
HE WHO TAUGHT (THE USE OF) THE PEN,
TAUGHT MAN THAT WHICH HE KNEW NOT".
(Holy Qur'an 96:1-5)
These are the first five verses which were revealed to Muhummed which now occupy the beginning of the 96th chapter of the Holy Qur'an.
The Faithful Witness
Immediately the angel had departed, Muhummed rushed to his home. Terrified and sweating all over he asked his beloved wife Khadija to 'cover him up!' He lay down, and she watched by him. When he had regained his composure, he explained to her what he had seen and heard. She assured him of her faith in him and that Allah would not allow any terrible thing to happen to him. Are these the confessions of an imposter? Would imposters confess that when an angel of the Lord confronts them with a Message from on High, they get fear-stricken, terrified, and sweating all over, run home to their wives? Any critic can see that his reactions and confessions are that of an honest, sincere man, the man of Truth- 'AL-AMIN' - THE Honest, the Upright, the Truthful. During the next twenty-three years of his prophetic life, words were 'Put into his mouth', and he uttered them. They made an indeliable imp ression on his heart and mind: and as the volume of the Sacred Scripture (Holy Qur'an) grew, they were recorded on palm-leaf libre, on skins and on the shoulder-blades of animals; and in the hearts of his devoted disciples. Before his demise these words were arranged according to his instructions i n the order in which we find them to-day in the Holy Qurann.
The words (revelation) were actually put into his mouth, exactly as foretold in the prophecy under discusiion: 'AND I WILL PUT MY WORDS IN HIS MOUTH.'(Deut. 18:18).
Un-lettered Prophet
Muhummed's experience in the cave of Hira, later to be known as Jabal-un Noor - The Mountain of Light, and his response to that first Revelation is the exact fulfilment of another Biblical Prophecy. In the Book of Isaish. Chapter 29, verse 12, we read: "AND THE BOOK" (al-Kitaab,al-Quran the 'Readin g', the 'Recitation') "IS DELIVERED TO HIM THAT IS NOT LEARNED," (Isaiah 29:12) "THE UNLETTERED PROPHET " (Holy Qur'an 7:158) and the biblical verse continues : "SAYING, READ THIS, I PRAY THEE:" (the words "I pray thee", are not in the Hebrew manuscripts; compare with the Roman Cathol ics' "Douay Version and also with the "Revised Standard Versions") "AND HE SAITH, I AM NOT LEARNED." ("I am not learned." is the exact translation of the Arabic words which Muhummed uttered twice to the Holy Ghose - the Archangel Gabriel, when he was commanded : "READ!").
Let me quote the verse in full without a break as found in the "King James Version," or the "Authorised version" as it is more popularly know "AND THE BOOK IS DELIVERED TO HIM THAT IS NOT LEARNED, SAYING, READ THIS I PRAY THEE: AND HE SAITH, I AM NOT LEARNED." (Isaiah 29:12).
Important note :
It may be noted that there were no Arabic Bibles(12) in existence in the 6th Century of the Christian Era when Muhummed lived and preachedl Besides, he was absolutely unlettered and unlearned. No human had ever taught him a word. His teacher was his Creator:
"HE DOES NOT SPEAK (AUGHT), OF (HIS OWN) DESIRE:
IT IS NO LESS THAN INSPIRATION SENT DOWN TO HIM:
HE WAS TAUGHT BY ONE MIGHTY IN POWER,"
(Holy Qur'an 53:3-5).
Without any human learning, 'he put to shame the wisdom of the learned'.
Grave Warning
"See!" I told the dominee, "how the prophecies fit Muhummed like a glove. We do not have to stretch prophecies to justify their fulfilment in Muhummed."
The dominee replied, "All your expositions sound very well, but they are of no real consequence, because we Christians have Jesus Christ the "incarnate" God, who has redeemed us from the Bondage of Sin!"
I asked, "Not important?" God didn't think so! He went to a great deal of trouble to have His warnings recorded. God knew that there would be people like you who will flippantly, light-heartedly discount his words, so he followed up Deuteronomy 18:18 with a dire warning: "AND IT SHALL COME TO PASS, " (it is going to happen) "THAT WHOSOEVER WILL NOT HEARKEN UNTO MY WORDS WHICH HE SHALL SPEAK IN MY NAME, I WILL REQUIRE IT OF HIM. (in the Catholic Bible the ending words are - "I will be the revenger", I will take vengeance from him - I will take revenge!) "Does not this terrify you? God Almighty is threathening revenge! We shake in our pants if some hoodlum threathens us, yet you have no fear of God's warning?"
"Miracle of Miracles! in the verse 19 of Deuteronomy chapter 18, we have a further fulfilment of the prophecy in Muhummed! Note the words-'.....MY WORDS WHICH HE SHALL SPEAK IN MY NAME," In whose name is Muhummed speaking?" I opened Yusuf Ali's translation of the Holy Qur'an, at chapter 114- 'Sura Nas', or Mankind - the last chapter, and showed him the formula at the head of the charpter: and the meaning: "IN THE NAME OF GOD, MOST GRACIOUS, MOST MERCIFUL." And the heading of chapter 113: and the meaning: "IN THE NAME OF GOD, MOST GRACIOUS, MOST MERCIFUL". And every chapter downwards 112 , 111, 110.......was the same formula and the same meaning on every page, because the end SURAS (chapters) are short and take about a page each.
"And what did the prophecy demand?' ......WHICH HE SHALL SPEAK IN MY NAME and in whose name does Muhummed speak?'IN THE NAME OF GOD, MOST GRACIOUS MOST MERCIFUL.' The Prophecy is being fulfilled in Muhummed to the letter "Every chapter of the Holy Qur'an except the 9th begin with the formula: IN TH E NAME OF GOD, MOST GRACIOUS, MOST MERCIFUL.' The Muslim begins his every lawful act with the Holy formula. But the Christian begins: "In the name of the Father, son and holy ghost.'"(13)
Concerning Deuteronomy chapter eighteen, I have given you more than 15 reasons as to how this prophecy refers to Muhummed and NOT to Jesus.
Baptist Contradicts Jesus
In New Testament times, we find that the Jews were still expecting the fulfilment of the prophecy of 'ONE LIKE MOSES', refer John 1:19-25. When Jesus claimed to be the Messiah of the Jews,the Jews began to enquire as to where was Elias? The Jews had a parallel prophecy that before the coming of the Messiah, Elias must come first in his second coming. Jesus confirms this Jewish belief:
".......ELIAS TRULY SHALL FIRST COME, AND RESTORE ALL THINGS. BUT I SAY UNTO YOU, THAT ELIAS IS COME ALREADY, AND THEY KNEW HIM NOT,...THEN THE DISCIPLES UNDERSTOOD THAT HE SPAKE UNTO THEM OF JOHN THE BAPTIST."(Matthew 17:11-13). According to the New Testament the Jews were not the ones to s wallow the words of any would-be Messiah. In their investigations they underwent intense difficulties in order to find their true Messiah. And this the Gospel of John confirms: "AND THIS IS THE RECORD OF JOHN,"(the Baptist) "WHEN THE JEWS SENT PRIESTS AND LEVITES FROM JERUSALEM TO ASK HIM, WHO ART THOU? AND HE CONFESSED AND DENIED NOT; BUT CONFESSED, I AM NOT THE CHRIST." (This was only natural because there can't be two Messiahs (14) at the same time. If Jesus was the Christ then John couldn't be the Christ!) "AND THEY ASKED HIM, WHAT THEN? ART THOU ELIAS? AND HE SAITH, I AM NOT." (Here Joh n the Baptist contradicts Jesus! Jesus says that John is "Elias" and John denies that he is what Jesus ascribes him to be. One of the TWO (Jesus or John), God forbid!, is difinitely not speaking the TRUTH! On the testimony of Jesus himself, John the Baptist was the greatest of the Israelite prophet s:"VERILY I SAY UNTO YOU, AMOUNG THEM THAT ARE BORN OF WOMEN THERE HAS NOT RISENA GREATER THAN JOHN THE BAPTIST:... (Matthew 11:11).
We Muslims know John the Baptist as Hazrut YAHYAA Alai-his-salaam (peace be upon him). We revere him as a true prophet of Allah. The Holy Prophet Jesus known to us as Hazrut ISAA Alai-his-salaam (peace be upon him), is also esteemed as one of the mightiest messenger of the Almighty. How can we Musl ims impute lies to either of them? We leave this problem between Jesus and John for the Christians to solve, for their "sacred scriptures abound in discrepancies which they have been glossing over as the "dark sayings of Jesus"(15). We Muslims are really interested in the last questions posed to Jo hn the Baptist by the Jewish elite- "ART THOU THAT PROPHET? AND HE ANSWERED, NO."(John 1:21)
Three Questions!
Please note that three different and distinct questions were posed to John the Baptist and to which he gave three emphatic "NO'S" as answers. To recapitulate:-
1) ART THOU THE CHRIST?
2) ART THOU ELIAS?
3) ART THOU THAT PROPHET?
But the learned men of Christendom somehow only see two questions implied here. To make doubly clear that the Jews definitely had T-H-R-E-E separate prophecies in their minds when they were interogating John the Baptist, let us read the remonstrance of the Jews in the verses following:
"AND THEY ASKED HIM, AND SAID UNTO HIM, WHEY BAPTIZEST THOU THEN, IF THOU BE
a) NOT THAT CHRIST,
b) NOR ELIAS,
c) NEITHER THAT PROPHET?"
(John 1:25)
The Jews were waiting for the fulfilment of THREE distinct prophecies: One, the coming of CHRIST. Two the coming of ELIAS, and Three, the coming of THAT PROPHET.
"That Prophet"
If we look up any Bible which has a concordance or cross-references, the we will find in the marginal note where the words "the Prophet", or "that Prophet" occur in John 1:25, that these words refer to the prophecy of Deuteronomy 18:15 and 18. And that 'that prophet' - 'the prophet like Moses' - "L IKE UNTO THEE", we have proved through overwhelming evidence that he was MUHUMMED and not Jesus!
We Muslims are not denying that Jesus was the "Messiah", which word is translated as "Christ".(16) We are not contesting the "thousand and one prophecies" which the Christians claim abound in the Old Testament foretelling the coming of the Messiah. What we say is that Deuteronomy 18:18 does NOT ref er to Jesus Christ but it is an explicit prophecy about the Holy Prophet MUHUMMED!"
The dominee, very politely parted with me by saying that it was a very interesting discussion and he would like me very much to come one day and address his congregation on the subject. A decade and half has passed since then but I am still awaiting that privilege.
I believe the dominee was sincere when he made the offer, but prejudices die hard and who would like to loose his sheep?
The Acid Test
To the lambs of Christ I say, why not apply that acid test which the Master himself wanted you to apply to any would be claimant to prophethood? He had said: "BY THEIR FRUITS YE SHALL KNOW THEM. DO MEN GATHER GRAPES FROM THE THORNS, OR FIGS FROM THE THISTLES? EVERY GOOD TREE WILL BEAR GOOD FRUIT AN D EVERY EVIL TREE WILL BEAR EVIL FRUIT....BY THEIR FRUITS YE SHALL KNOW THEM. (Matthew 7:16-20).
Why are you afraid to apply this test to the teachings of Muhummed? You will find in the Last Testament of God - the Holy Qur'an - the true fulfilment of the teachings of Moses and Jesus which will bring to the world the much-needed peace and happiness. "IF A MAN LIKE MOHAMED WERE TO ASSUME THE DIC TATORSHIP OF THE MODERN WORLD, HE WOULD SUCCEED IN SOLVING ITS PROBLEMS THAT WOULD BRING IT THE MUCH NEEDED PEACE AND HAPPINESS."(George Bernard Shaw)
The Greatest!
The Weekly Newsmagazine "TIME" dated July 15, 1974, carried a selection of opinions by various historians, writers, military men, businessmen and others on the subject: "Who Were History's Great Leaders?" Some said that it was Hitler; others said-Gandhi, Buddha, Lincoln and the like. But Jules Mass erman, a United States psychoanalyst put the standards straight by giving the correct criteria wherewith to judge. He said: "LEADERS MUST FULFIL THREE FUNCTIONS:-
(1) Provide for the well-being of the led,
(2) Provide a social organization in which people feel relatively secure
and
(3) Provide them with one set of beliefs."
With the above three criteria he searches history and analyses - Hitler, Pasteur, Gaesar, Moses, Confucius and the lot, and ultimately concludes:
"PEOPLE LIKE PASTEUR AND SALK ARE LEADERS IN THE FIRST SENSE. PEOPLE LIKE GANDHI AND CONFUCIUS, ON ONE HAND, AND ALEXANDER, CAESAR AND HITLER ON THE OTHER, ARE LEADERS IN THE SECOND AND PERHAPS THE THIRD SENSE. JESUS AND BUDDHA BELONG IN THE THIRD CATEGORY ALONE. PERHAPS THE GREATEST LEADER OF ALL TIMES WAS MOHAMMED, WHO COMBINED ALL THREE FUNCTIONS. To a lesser degree, MOSES DID THE SAME."
According to the objective standards set by the Professor of the Chicago University, whome I believe to be Jewish, - JESUS and BUDDHA are now - here in the picture of the "Great Leaders of Mankind", but by a queer coincidence groups Moses and Muhummed together thus adding further weight to the argu ment that JESUS is not like MOSES, but MUHUMMED is like MOSES: Deut.18:18 "LIKE UNTO THEE" - Like MOSES!
In conclusion, I end with a quotation of a Christian Reverend the commentator of the Bible, followed by that of his Master:
"THE ULTIMATE CRITERION OF A TRUE PROPHET IS THE MORAL CHARACTER OF HIS TEACHING."(Prof.Dummelow.)
"BY THEIR FRUITS YE SHALL KNOW THEM." (Jesus Christ)

A concluding suggestion : Come let us reason together !
SAY:"O PEOPLE OF THE BOOK!
COME TO COMMON TERMS AS BETWEEN US AND YOU:
THAT WE WORSHIP NONE BUT GOD;
THAT WE ASSOCIATE NO PARTNERS WITH HIM;
THAT WE ERECT NOT, FROM AMONG OURSELVES,
LORDS AND PATRONS OTHER THAN GOD."
IF THEN THEY TURN BACK,
SAY:"BEAR WITNESS THAT WE (AT LEAST)
ARE MUSLIMS (BOWING TO GOD'S WILL)."
(Holy Qur'an 3:64)
"PEOPLE OF THE BOOK" is the respectful title given to the Jews and the Christians in the Holy Qur'an. The Muslims is here commanded to invite - "O People of the Book!" - O Learned People! O People who claim to be the recipients of Divine Revelation, of a Holy Scripture; let us gather together onto a common platform - "that we worship none but God", because none but God is worthy of worship, not because "THE LORD THY GOD IS A JEALOUS GOD VISITING THE INIQUITY OF THE FATHERS UPON THE CHILDREN UNTO THE THIRD AND FOURTH GENERATION OF THEM THAT HATE ME."(Exodus 20:25). But because He is ou r Lord and Cherisher, our Sustainer and Evolver, worthy of all praise, prayer and devotion.
In the abstract the Jews and the Christians would agree to all the three propositions contained in this Qur'anic verse. In practice they fail. Apart from doctrinal lapses from the unity of the One True God, (ALLAH_ Subha-nahu wa ta-ala) there is the question of a consecrated Priesthood (among the J ews it was hereditary also), as if a mere human being - Cohe or Pope, or Priest, or Brahuman, - could claim superiority apart from his learning and the purity of his life, or could stand between man and God in some special sense. ISLAM DOES NOT RECOGNISE PRIESTHOOD!
The Creed of Islam is given to us here in a nutshell from Holy Qur'an:
Say ye: "We believe in Allah,
And the revelation given to us,
And to Abraham, Isma'il, Isaac,
Jacob, and the Tribes,
And that given to Moses and Jesus
And that given to (all)
Prophets from their Lord:
We make no difference
Between one and another of them:
And we bow to Allah (in Islam)."
(Holy Qur'an 2:136).
The Muslim position is clear. The Muslim does not claim to have a religion peculiar to himself. Islam is not a sect or an ethnic religion. In its view all Religion is one, for the Truth is one. IT WAS THE SAME RELIGION PREACHED BY ALL THE EARLIER PROPHETS. (Holy Qur'an 42:13). It was the truth taug ht by all the inspired Books. In essence it amounts to a consciousness of the Will and Plan of God and a joyful submission to that Will and Plan. IF ANYONE WANTS A RELIGION OTHER THAN THAT, HE IS FALSE TO HIS OWN NATURE, AS HE IS FALSE TO GOD'S WILL AND PLAN. Such a one cannot expect guidance, for he has deliberately renounced guidance.

NOTES
(1) This refers to Moses. See Yusuf Ali's commentaries Nos. 4783/4 to this verse.
(2) Christian exegesists give progressive numerical values by sixes, to the English alphabet and add up to get the total 666. i.e.A=6,B=12,C=18, D=24 and so on. Progression by 6's because the number of the Beast in the Bible is "666". Try it for Dr.Kissinger.
(3) The writer has just delivered another talk in the City Hall, Durban on the 10th December, 1975 on the subject "Muhummed the Greatest".
(4) "Dominee" is the Afrikaans equivalent of priest, parson and predikant.
(5) One of the Provinces of the Republic of South Africa.
(6) The word "Messiah" comes from the Arabic and Hebrew word masaha which means to rub, to massage, to annoint. The religious significance is "the one who is anointed' - priests and kings were anointed in consecration to their offices. Messiah translated Christ does not mean God. Even the heathen C yrus is called "Christ" in the Bible, (Isaiah 45:1)
(7) Muhummed is mentioned by name in the Song of Solomn 5:16. The Hebrew word used there is Muhammuddim. The end letters IM is plural of respect majesty and grandeur. Minus "im" the name would be Muhamudd translated as "altogether lovely" in the Authorised Version of the Bible or 'The Praised One' 'the one worthy of Praise' i.e. MUHUMMED!
(8) If this lecture is translated into any language, please change the Afrikaans words into the local dialect; and do not try a free hand translation of the Biblical quotation. Obtain a Bible in the language in which translation is being made and transcribe exactly as the words occur in that Bible.
(9) Please open the Holy Qur'an 3:42 and 19:16 where the birth of Jesus is spoken about; read it with the commentry, note the high position which Jesus and his mother occupy in Islam.
(10) Write for "Was Christ Crucified?" by the writer, free on request.
(11) According to the Bible Abraham's name was Abram before it was changed by God to Abraham.
(12) There are today Arabic Bibles in Fourteen different scripts and dialects for the Arabs alone. See "The Gospels in many tongues", obtainable from the Bible Society.
(13) The Christian theologians are ignorant of even the "name of God. Because "God" is not a name, and "Father" is also not a name. What's his name? See "Muhummed-the Natural Successor to Christ", by the author, available free.
(14) The Jews were expecting a single Messiah not two.
(15) See the "TIMES" Magazine December 30th, 1974, article "How true is the Bible?" And write for your free copy of "50,000 Errors in the Bible? a reproduction from the Christian Magazine "AWAKE!" September 8, 1957.
(15) How the word Messiah was transmuted to Christ? Write for booklet above, reference 13.
END OF LECTURE