Tuesday, 27 May 2008


Abraham Zacuto (Hebrew: אברהם זכות, Portuguese: Abraão ben Samuel Zacuto) (c. 1450 – c. 1510) was a Sephardi Jew astronomer, astrologer, mathematician and historian who served as Royal Astronomer in the 15th Century to King John II of Portugal. The Zagut crater on the moon is named after him.

Zacuto was born in Salamanca, Spain circa 1450. He studied astronomy at the University of Salamanca and taught there as well. He later was for a time teacher of astronomy at the universities of Zaragoza and then Cartagena. He was versed in Jewish Law, and was rabbi of his community.

With the general expulsion of the Jews from Spain in 1492, Zacuto took refuge in Lisbon, Portugal. Already famous in academic circles, he was invited to court and nominated Royal Astronomer and Historian by King João II, a position which he held until the early reign of Manuel I. He was consulted by the King on the possibility of a sea route to India, a project which he supported and encouraged. Zacuto would be one of the few who managed to flee Portugal during the forced conversions and prohibitions of departure that Manuel I enacted, in order to keep the Jews in Portugal as nominal Christians for foreign policy reasons (see History of the Jews in Portugal).

He died in the Ottoman Empire, to where he had escaped, ca. 1510.


Zacuto perfected the astrolabe, which only then became an instrument of precision, and he was the author of the highly accurate Almanach Perpetuum that were used by ship captains to determine the position of their Portuguese caravels in high seas, through calculations on data acquired with an astrolabe. His contributions were undoubtedly valuable in saving the lives of Portuguese seamen, and allowing them to reach Brazil and India.

While in Spain he wrote an exceptional treatise on astronomy/astrology in Hebrew, with the title Ha-jibbur Ha-gadol. He published in the printing press of Leiria in 1496, property of Abraão de Ortas the book Biur Luhoth, or in Latin Almanach Perpetuum, which was soon translated into Latin and Spanish. In this book were the astronomical tables (ephemerides) for the years 1497 to 1500, which were instrumental, together with the new astrolabe made of metal and not wood as before, to Vasco da Gama and Pedro Álvares Cabral in their voyages to India and Brazil respectively.

In 1504, while in Tunisia, he wrote a history of the Jewish people, Sefer Hayuhasin, since the Creation of the World until 1500, and several other astronomical/astrological treatises. The History was greatly respected and was reprinted in Cracow in 1581, at Amsterdam in 1717, and at Königsberg in 1857, while a complete edition was published by Filipowski in London in 1857.
External links


António José da Silva (8 May 170518 October 1739), was a Portuguese-Brazilian dramatist, known as "the Jew" (O Judeu). The Brazilian spelling of his first name is Antônio.


He was born in Rio de Janeiro, but came to Portugal at the age of eight.

His parents, João Mendes da Silva and Lourença Coutinho, were descended from Portuguese Jews (few of which still exist) who had emigrated to Colonial Brazil to escape the Inquisition, but in 1702 that tribunal began to persecute the Marranos in Rio, and in October 1712 Lourença Coutinho became a victim. Her husband and children accompanied her to Portugal, where she figured among the "reconciled" in the auto-da-fé of July 9, 1713, after undergoing the torment only.

Her husband, having then acquired a fixed domicile in Lisbon, settled down to advocacy with success, and he was able to send António to the University of Coimbra, where he matriculated in the faculty of law. In 1726 António was suddenly imprisoned along with his mother on August 8; on the 16th he suffered the first interrogation, and on September 23 he was put to the torment, with the result that three weeks later he could not sign his name. He confessed to having followed the practices of the Mosaic law, and this saved his life.

He went through the great auto-da-fé held on October 23 in the presence of King John V and his court, abjured his errors, and was set at liberty. His mother was only released from prison in October 1729, after she had undergone torture and figured as a penitent in another auto-da-fé.
Meanwhile António had gone back to Coimbra, and finishing his course in 1728–1729 he returned to Lisbon and became associated with his father as an advocate. He found an ignorant and corrupt society ruled by an immoral yet fanatical monarch, who wasted millions on unprofitable buildings though the country was almost without roads and the people had become the most backward in Europe. As his plays show, the spectacle struck António's observation, but he had to criticize with caution.

He produced his first play or opera in 1733, and the next year he married his cousin, D. Leonor Maria de Carvalho, whose parents had been burnt by the Inquisition, while she herself had gone through an auto-da-fé in Spain and been exiled on account of her religion. They had their first daughter in 1734, but the years of their happiness and of Silva's dramatic career were few, for on October 5, 1737 husband and wife were both imprisoned on the charge of "judaizing." A slave of theirs had denounced them to the Holy Office, and though the details of the accusation against them were trivial and even contradictory, António was condemned to death. On October 18 he was beheaded and his body burnt in an auto-da-fé; that same day one of his popular operettas was given at a Lisbon theatre.


His dramatic works, which were produced at the Bairro Alto theatre between 1733 and 1738, include the following comedies, all played by marionettes:

Vida do Grande Dom Quixote de la Mancha e do Gordo Sancho Pança (1733)

Esopaida (1734)

Os Encantos de Medea (1735)

Amphitriio (May 1736)

Labyrintho de Creta (November 1736)

Guerras do Alecrim e Mangerona (carnival of 1737)

As Variedades de Proteo (May 1737)

Precipicio de Faetonte (1738)

Slight as these sketches are, they show considerable dramatic talent and an Aristophanic wit. The characters are well drawn and the dialogue full of comic strength, the scenes knit together and the plot skilfully worked out. Moreover Silva possessed a knowledge of stagecraft, and, if he had lived, he might have emancipated the drama in Portugal from its dependence on foreign writers; but the triple licence of the Palace, the Ordinary and the Inquisition, which a play required, crippled spontaneity and freedom. Even so, he showed some boldness in exposing types of the prevailing charlatanism and follies, though his liberty of speech is far less than that of Gil Vicente. His comedies give a truthful and interesting picture of 18th century society, especially his best comedy, the Alecrim e Mangerona, in which he treats of the fidalgo pobre, a type fixed by Vicente and Francisco Manuel de Mello.

His works bear the title "operas" because, though written mainly in prose, they contain songs which Silva introduced in imitation of the true operas which then held the fancy of the public. He was also a lyric poet of real merit, combining correctness of form with a pretty inspiration and real feeling. His plays were published in the first two volumes of a collection entitled Theatro comico portuguez, which went through at least five editions in the 18th century, while the Alecrim e Mangerona appeared separately in some seven editions. This comedy and the Don Quixote have been reprinted in a critical edition with a life of Silva by Dr Mendes dos Remedios (Coimbra, 1905).

Ferdinand Denis, in his Chefs-d'œuvre du théâtre portugais (pp. 365–496, Paris, 1823), prints liberal extracts, with a French translation, from the Vida de Dom Quixote, and F. Wolf likewise gives selections from Silva's various compositions. Silva is the subject also of several laudatory poems and dramas, one or two of which were composed by Brazilian compatriots.


Teófilo Braga, História do teatro português, a baixa comedia e a opera (Oporto, 1871)
F Wolf, Dom António José da Silva (Vienna, 1860)

Ernest David, Les Operas du juif António José da Silva, 1705–1739 (Paris, 1880)

Oliveira Lima, Aspectos de litteratura colonial Brazileira (Leipzig, 1896)

Jewish Encyclopedia, vol. xi. p. 341.

GA Kohnt, "Bibliography of Works relating to António José da Silva and Bibliography of Don António's Compositions" in the Publ. Am. Jew. Hist. Soc. No. 4, p. 181.

idem, "Martyrs of the Inquisition in South America," ib. p. 135.

M Grunwald, "José da Silva" in Monatsschrift (1880), xxix. p. 241.

This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.


Pedro Nunes (pron. IPA: ['pedɾu 'nunɨʃ]; Latin, Petrus Nonius), (1502, Alcácer do SalAugust 11, 1578, Coimbra) was a Portuguese mathematician, cosmographer, and professor, born from a New Christian (of Jewish origin) family[1].
Pedro Nunes, considered to be one of the greatest mathematicians of his time, is best known for his contributions in the technical field of navigation, which was crucial to the Portuguese period of discoveries. He was the first to propose the idea of a loxodrome and was also the inventor of several measuring devices, including the nonius, named after his Latin surname.


Little is known about Nunes' early education. He studied at the University of Salamanca, maybe from 1521 until 1522, and at the University of Lisbon (this University later become the University of Coimbra) where he obtained a degree in medicine in 1525. In the 16th century medicine used astrology, so he also learned astronomy and mathematics. He continued his medical studies but held various teaching posts within the University of Lisbon, including Moral, Philosophy, Logic and Metaphysics. When, in 1537, the Portuguese University located in Lisbon returned to Coimbra, he moved to the re-founded University of Coimbra to teach mathematics, a post he held until 1562. This was a new post in the University of Coimbra and it was set up to provide instruction in the technical requirements for navigation, clearly a topic of great importance in Portugal at this period when control of sea trade was the chief source of Portuguese wealth. Mathematics became an independent post in 1544.

In addition to teaching he was appointed Royal Cosmographer in 1529 and Chief Royal Cosmographer in 1547 up to his death.

In 1531, King John III of Portugal charged Nunes with the education of his younger brothers Luís and Henry. Years later Nunes was also charged with the education of the king's grandson, and future king, Sebastian.

It's possible that while at the University of Coimbra, Christopher Clavius attended Pedro Nunes' classes, and was influenced by his works.


Pedro Nunes lived in a transition period where science was changing from valuing theoretical knowledge (and thus where the main role of a scientist/mathematician was commenting on previous authors), to providing experimental data, both as a source of information and as a method of confirming theories. Nunes was above all one of the last great commentators, as his shown by his first published work, but he also acknowledged the value of experimentation.

In his Tratado da sphera he argued for a common and universal diffusion of knowledge.[2] Accordingly he not only published works in Latin, by then science's lingua franca, aiming for an audience of European scholars, but also in Portuguese, and Spanish (Livro de Algebra).

Much of Nunes' work related to navigation. He was the first to understand why a ship maintaining a steady course would not travel along a great circle, the shortest path between two points on Earth, but would instead follow a spiral course, called a loxodrome. The later invention of logarithms allowed Leibniz to establish algebraic equations for the loxodrome.

In his Treaty defending the sea chart Nunes argued that a nautical chart should have its parallels and meridians shown as straight lines. Yet he was unsure how to solve all the problems this caused, a situation that lasted until Mercator developed Mercator projection, the system which is still used.

Nunes worked on several practical nautical problems concerning course correction as well as attempting to develop more accurate devices to determine a ship's position. He created the nonius to improve the astrolabe's accuracy. It consisted of tracing a certain number of concentric circles on an instrument and dividing each successive one with one fewer divisions than the adjacent outer circle. Thus the outermost quadrant would have 90° in 90 equal divisions, the next inner would have 89 divisions, the next 88 and so on. When an angle was measured, the circle and the division on which the alidade fell was noted. A table was then consulted to provide the exact measure. The nonius was used for a while by Tycho Brahe who, considered it too complex. The method inspired improved systems by Christopher Clavius and Jacob Curtius.[3] These were eventually superseded by verniers.

Pedro Nunes also worked on some mechanics problems, from a mathematical point of view.
He was probably the last major mathematician to make relevant improvements to the ptolemaic system (a geocentric model), however this lost importance because Copernicus heliocentric system replaced it by then. Nunes knew Copernicus' work but he only made a short reference to it in his published works with the objective of correcting some mathematical errors.

He also solved the problem of finding the day with the shortest twilight duration, for any given position, and its duration. This problem per se is not greatly important, yet it shows the geometric genius of Nunes as it was, independently, tackled by Johann and Jakob Bernoulli more than a century later with less success. They could find a solution to the problem of the shortest day but failed to determine its duration, possibly because they got lost on details of differential calculus, still a recently developed tool (at that point in time). It also shows Nunes as a pioneer in solving maxima and minima problems, which only became common in the next century using differential calculus.

Most of Nunes' achievements were possible because of his profound understanding of spherical trigonometry and his ability to transpose Ptolemy's adaptations of Euclidean geometry to it.


Pedro Nunes translated, commented and expanded some of the major works in his field, and he also published original research.

Commented and expanded translations:

Tratado da sphera com a Theorica do Sol e da Lua (Treaty about the Sphere with Theory of the Sun and the Moon), (1537). From Tractatus de Sphaera by Johannes de Sacrobosco, Theoricae novae planetarum by Georg Purbach and the Geography by Claudius Ptolemaeus.

Original work:

Tratado em defensão da carta de marear (Treatise Defending the Sea Chart), (1537).

Tratado sobre certas dúvidas da navegação (Treatise about some Navigational Doubts), (1537)

De crepusculis (About the Twilight), (1542).

De erratis Orontii Finei (About the Errors of Orontii Finei), (1546).

Petri Nonii Salaciensis Opera, (1566). Expanded, corrected and reedited as De arte adque ratione navigandi in 1573.

Livro de algebra en arithmetica y geometria (Book of Algebra in Arithmetics and Geometry), (1567).

Some modern reprints:

Obras (6 vol.), Academia das Ciências de Lisboa, Lisboa, 1940-1960 (No ISBN at the books' record at the Portuguese National Library)

Obras (3 vol.), Fundação Calouste Gulbenkian, Lisboa, 2002-?, ISBN 972-31-0985-9 and ISBN 972-31-1084-9 (more volumes are likely to be published)


The Instituto Pedro Nunes in Coimbra, a business incubator and a center of innovation and technology transfer founded by the University of Coimbra, is named after Pedro Nunes.


Mourão, Ronaldo Rogério de Freitas, Dicionário das Descobertas, Pergaminho, Lisboa, 2001, ISBN 972-711-402-4

Dias, J. S. da Silva, Os descobrimentos e a problemática cultural do século XVI (3rd ed.), Presença, Lisboa, 1988


1-^ Martins, Jorge, Portugal e os Judeus (3 vol.), Nova Vega, Lisboa, 2006, ISBN 972-699-847-6
2-^ «o bem, quanto mais comum e universal, tanto é mais excelente» quoted by Calafate, Pedro (see above)
3-^ Daumas Maurice, Scientific Instruments of the Seventeenth and Eighteenth Centuries and Their Makers, Portman Books, London 1989 ISBN 978-0713407273

Put On Your Yarmulke (Wear My Shoes)

Put On Your Yarmulke (Wear My Shoes)


When I was young I admired clever people.
Now that I am old, I admire kind people.

- Abraham Joshua Heschel

The whole world is a very narrow bridge.
And the most important thing is to not be afraid.

-Rebbe Nachman of Breslov

"The greatest thing in the world is to do somebody else a favor."

- Aish Kodesh

"As you want G*d to give you a chance,
give everyone else a chance to also begin again."

- Shlomo Carlebach

(taken from Sefer Chabbi Deepest Torah-http://seferchabibi.blogspot.com/)
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