Thursday, August 23, 2012


BENJAMIN BANNEKER - Astronomer, mathematician, surveyor, almanac author and farmer was responsible for astrologically surveying the 10 mile square that Washington DC was originally built on. Andrew Ellicot also helped and surveyed using land by day. The shape a...

nd number of square represents the number 4, which Kemetically means Foundation. 16th St. was also surveyed as the meridian point. 1 plus 6 equals 7, 7 being the kemetic number of heaven. 16th St. is the street with the most enlightenment centers in DC and ends at the White House. George Washington first US President under The Constitution, also a freemason used the 10 mile Square to symbolically mean the foundation of a new nation and knew that Benjamin had the skills to use the sky to survey the land. He is said to be a descendant of the Dogon Tribe now residing in Mali which were major astrologers. Benjamin Banneker has so much more accomplishments under his belt but sadly is now buried in an unmarked grave and though there are constant petitions to honor him being that he played a key role in literally building this “great nation”, Benjamin Banneker is being forgotten and most of the time his story is never told in mainly in DC.

Benjamin Banneker Biography
Born: November 9, 1731
Baltimore County, Maryland
Died: October 9, 1806
Baltimore County, Maryland
The First African American scientist and inventor

From 1792 through 1797 Benjamin Banneker, an African American mathematician and amateur astronomer, calculated ephemerides (tables of the locations of stars and planets) for almanacs that were widely distributed and influential. Because of these works, Banneker became one of the most famous African Americans in early U.S. history.
Early life

On November 9, 1731, Benjamin Banneker was born in Baltimore County, Maryland. He was the son of an African slave named Robert, who had bought his own freedom, and of Mary Banneky, who was the daughter of an Englishwoman and a free African slave. Benjamin grew up on his father's farm with three sisters. After learning to read from his mother and grandmother, Benjamin read the bible to his family in the evening. He attended a nearby Quaker country school for several seasons, but this was the extent of his formal education. He later taught himself literature, history, and mathematics, and he enjoyed reading.

As he grew into an adult, Banneker inherited the farm left to him by his grandparents. He expanded the already successful farm, where he grew tobacco. In 1761, at the age of thirty, Banneker constructed a striking wooden clock without having ever seen a clock before (although he had examined a pocket watch). He painstakingly carved the toothed wheels and gears of the clock out of seasoned wood. The clock operated successfully until the time of his death.
Interest in astronomy

At the age of fifty-eight Banneker became interested in astronomy (the study of the universe) through the influence of a neighbor, George Ellicott, who lent him several books on the subject as well as a telescope and drafting instruments (tools used in astronomy). Without further guidance or assistance, Banneker taught himself the science of astronomy. He made projections for solar (of the Sun) and lunar (of the Moon) eclipses and computed ephemerides for an almanac. In 1791 Banneker was unable to sell his observations, but these rejections did not stop his studies.

In February 1791 Major Andrew Ellicott (1754–1820), an American surveyor (one who maps out new lands for development), was appointed to survey the 10-mile square of the Federal Territory for a new national capital. Banneker worked in the field for several months as Ellicott's scientific assistant. After the base lines and boundaries had been established and Banneker had returned home, he prepared an ephemeris for the following year, which was published in Baltimore in Benjamin Banneker's Pennsylvania, Delaware, Maryland and Virginia Almanack and Ephemeris, for the Year of Our Lord, 1792; Being Bissextile, or Leap-Year, and the Sixteenth Year of American Independence. Banneker's calculations would give the positions of the planets and stars for each day of the year, and his almanacs were published every year from 1792 until 1797.
Communications with Thomas Jefferson

Banneker forwarded a copy of his calculations to Thomas Jefferson (1743–1826), then secretary of state, with a letter criticizing Jefferson for his proslavery views and urging the abolishment (ending) of slavery of African American people. He compared such slavery to the enslavement of the American colonies by the British crown. Jefferson

acknowledged Banneker's letter and forwarded it to the Marquis de Condorcet, the secretary of the Académie des Sciences in Paris. The exchange of letters between Banneker and Jefferson was published as a separate pamphlet, and was given wide publicity at the time the first almanac was published. The two letters were reprinted in Banneker's almanac for 1793, which also included "A Plan for an Office of Peace," which was the work of Dr. Benjamin Rush (1745–1813). The abolition societies of Maryland and Pennsylvania were very helpful in the publication of Banneker's almanacs, which were widely distributed as an example of an African American's work and to demonstrate the equal mental abilities of the races.

The last known issue of Banneker's almanacs appeared for the year 1797, because of lessening interest in the antislavery movement. Nevertheless, he prepared ephemerides for each year until 1804. He also published a treatise (a formal writing) on bees and computed the cycle of the seventeen-year locust.

Banneker never married. He died on October 9, 1806, and was buried in the family burial ground near his house. Among the memorabilia preserved from his life were his commonplace book and the manuscript journal in which he had entered astronomical calculations and personal notations. Writers who described his achievements as that of the first African American scientist have kept Banneker's memory alive. Recent studies have proven Banneker's status as an extremely capable mathematician and amateur astronomer.

                                                 BANNEKER`S ALMANAC


by Florence Fasanelli, Graham Jagger, Bea Lumpkin

Benjamin Banneker's Trigonometry Puzzle The mathematical puzzles of Benjamin Banneker (1731-1806) have been of interest since he first produced them in the last half of the 18th century and the early years of the 19th. By the age of 21, he was a hero in the territory of Maryland.1 Banneker began his life-changing studies of astronomy and mathematics about 1788, the year Maryland joined the Union, when he was lent some books by his friend the surveyor, George Ellicott. Three of these are known: Charles Leadbetter's Astronomy: Or the True System of the Planets Demonstrated (1727); James Ferguson's Astronomy Explained Upon Sir Isaac Newton's Principles, and Made Easy to Those Who Have Not Studied Mathematics(1761), and a book (in Latin) which Ellicott gave his bride as a wedding present.

In one of the puzzles, "Trigonometry," Banneker demonstrates his knowledge of logarithms as he presents his solution. The question arises as to what book of logarithmic tables could Banneker have been using. The trigonometry page is reproduced from The Maryland Historical Society, Baltimore, Maryland, where Banneker's Astronomical Journal 1798, is kept.

It is clear that Banneker is using the Law of Sines:

In a triangle, the ratios of the sine of an angle to the length of its opposite side are equal. Where Banneker writes in his proportion, "logarithm base 26," or "logarithm of the hypotenuse," he is anticipating the use of logarithms for the computation. Banneker understood, as his calculations correctly show, that the ratios involved are the sine of an angle to the side opposite, not to the log of the side. In what follows, all angles are expressed in degrees.

I. To find the hypotenuse, Banneker used the Law of Sines: sin C/c = sin B/ b "Sine complement of the angle at A," is sin 60, the sine of the angle complementary to angle A. If x is the length of the hypotenuse, then sin 60/ 26 = sin 90/ x and x = 26 sin 90/sin 60. . Taking logarithms, we have log x = log 26 + log sin 90 ??- log sin 60 and, substituting values from a suitable set of tables, log x = 1.41497 +10 ­ 9.93753 = 1.47744. Notice that, for reasons we shall see later, log sin 90 = Log 1010 = 10. We now find x as the antilogarithm of 1.47744, which is very close to 30. It is unlikely that Banneker would have had access to tables of antilogarithms, a late eighteenth century invention, but would simply have used his table of logarithms in reverse.

II. To find the remaining side, Banneker uses the Law of Sines again: sin C/c = sin A/a. If x is the length of the side perpendicular to the base then sin 60/ 26 = sin 30/ x, and x = 26 sin 30/sin 60 . Taking logarithms we get log x = log 26 + log sin 30 - log sin 60 and, again substituting values from tables, log x = 1.41497 + 9.69897 - 9.93753 = 1.7641. Again, x is the antilogarithm of 1.17643, which is very close to 15.


First American Clock Inventor Benjamin Banneker by Artist Missi Lynn Boness

from Banneker's letter to Jefferson

"I AM fully sensible of the greatness of that freedom, which I take with you on the present occasion ; a liberty which seemed to me scarcely allowable, when I reflected on that distinguished and dignified station in which you stand, and the almost general prejudice and prepossession, which is so prevalent in the world against those of my complexion.

I suppose it is a truth too well attested to you, to need a proof here, that we are a race of beings, who have long labored under the abuse and censure of the world ; that we have long been looked upon with an eye of contempt ; and that we have long been considered rather as brutish than human, and scarcely capable of mental endowments.

Sir, I hope I may safely admit, in consequence of that report which hath reached me, that you are a man far less inflexible in sentiments of this nature, than many others ; that you are measurably friendly, and well disposed towards us ; and that you are willing and ready to lend your aid and assistance to our relief, from those many distresses, and numerous calamities, to which we are reduced. Now Sir, if this is founded in truth, I apprehend you will embrace every opportunity, to eradicate that train of absurd and false ideas and opinions, which so generally prevails with respect to us ; and that your sentiments are concurrent with mine, which are, that one universal Father hath given being to us all ; and that he hath not only made us all of one flesh, but that he hath also, without partiality, afforded us all the same sensations and endowed us all with the same faculties ; and that however variable we may be in society or religion, however diversified in situation or color, we are all of the same family, and stand in the same relation to him.

Sir, if these are sentiments of which you are fully persuaded, I hope you cannot but acknowledge, that it is the indispensable duty of those, who maintain for themselves the rights of human nature, and who possess the obligations of Christianity, to extend their power and influence to the relief of every part of the human race, from whatever burden or oppression they may unjustly labor under ; and this, I apprehend, a full conviction of the truth and obligation of these principles should lead all to. Sir, I have long been convinced, that if your love for yourselves, and for those inestimable laws, which preserved to you the rights of human nature, was founded on sincerity, you could not but be solicitous, that every individual, of whatever rank or distinction, might with you equally enjoy the blessings thereof ; neither could you rest satisfied short of the most active effusion of your exertions, in order to their promotion from any state of degradation, to which the unjustifiable cruelty and barbarism of men may have reduced them.

Sir, I freely and cheerfully acknowledge, that I am of the African race, and in that color which is natural to them of the deepest dye ; and it is under a sense of the most profound gratitude to the Supreme Ruler of the Universe, that I now confess to you, that I am not under that state of tyrannical thraldom, and inhuman captivity, to which too many of my brethren are doomed, but that I have abundantly tasted of the fruition of those blessings, which proceed from that free and unequalled liberty with which you are favored ; and which, I hope, you will willingly allow you have mercifully received, from the immediate hand of that Being, from whom proceedeth every good and perfect Gift.

Sir, suffer me to recal to your mind that time, in which the arms and tyranny of the British crown were exerted, with every powerful effort, in order to reduce you to a state of servitude : look back, I entreat you, on the variety of dangers to which you were exposed ; reflect on that time, in which every human aid appeared unavailable, and in which even hope and fortitude wore the aspect of inability to the conflict, and you cannot but be led to a serious and grateful sense of your miraculous and providential preservation ; you cannot but acknowledge, that the present freedom and tranquility which you enjoy you have mercifully received, and that it is the peculiar blessing of Heaven.

This, Sir, was a time when you cleary saw into the injustice of a state of slavery, and in which you had just apprehensions of the horrors of its condition. It was now that your abhorrence thereof was so excited, that you publicly held forth this true and invaluable doctrine, which is worthy to be recorded and remembered in all succeeding ages : ``We hold these truths to be self-evident, that all men are created equal ; that they are endowed by their Creator with certain unalienable rights, and that among these are, life, liberty, and the pursuit of happiness.'' Here was a time, in which your tender feelings for yourselves had engaged you thus to declare, you were then impressed with proper ideas of the great violation of liberty, and the free possession of those blessings, to which you were entitled by nature ; but, Sir, how pitiable is it to reflect, that although you were so fully convinced of the benevolence of the Father of Mankind, and of his equal and impartial distribution of these rights and privileges, which he hath conferred upon them, that you should at the same time counteract his mercies, in detaining by fraud and violence so numerous a part of my brethren, under groaning captivity and cruel oppression, that you should at the same time be found guilty of that most criminal act, which you professedly detested in others, with respect to yourselves.

I suppose that your knowledge of the situation of my brethren, is too extensive to need a recital here ; neither shall I presume to prescribe methods by which they may be relieved, otherwise than by recommending to you and all others, to wean yourselves from those narrow prejudices which you have imbibed with respect to them, and as Job proposed to his friends, ``put your soul in their souls' stead ;'' thus shall your hearts be enlarged with kindness and benevolence towards them ; and thus shall you need neither the direction of myself or others, in what manner to proceed herein. And now, Sir, although my sympathy and affection for my brethren hath caused my enlargement thus far, I ardently hope, that your candor and generosity will plead with you in my behalf, when I make known to you, that it was not originally my design ; but having taken up my pen in order to direct to you, as a present, a copy of an Almanac, which I have calculated for the succeeding year, I was unexpectedly and unavoidably led thereto."



Jefferson's response to Banneker

Philadelphia Aug. 30. 1791.


I thank you sincerely for your letter of the 19th. instant and for the Almanac it contained. no body wishes more than I do to see such proofs as you exhibit, that nature has given to our black brethren, talents equal to those of the other colours of men, & that the appearance of a want of them is owing merely to the degraded condition of their existence both in Africa & America. I can add with truth that no body wishes more ardently to see a good system commenced for raising the condition both of their body & mind to what it ought to be, as fast as the imbecillity of their present existence, and other circumstance which cannot be neglected, will admit. I have taken the liberty of sending your almanac to Monsieur de Condorcet, Secretary of the Academy of sciences at Paris, and member of the Philanthropic society because I considered it as a document to which your whole colour had a right for their justification against the doubts which have been entertained of them. I am with great esteem, Sir, Your most obedt. humble servt. Th. Jefferson.


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