The Growth of Algebraic Thought in Sixteenth-Century Europe

2014 ◽  
Author(s):  
Victor J. Katz ◽  
Karen Hunger Parshall
Keyword(s):  
Sixteenth Century ◽  
Fifteenth Century ◽  
Thirteenth Century ◽  
The Body ◽  
The Third ◽  
Body Of Knowledge ◽  
Algebraic Thought

This chapter traces the growth of algebraic thought in Europe during the sixteenth century. Equations of the third and fourth degrees sparked quite a few algebraic fireworks in the first half of the century. Their solutions marked the first major European advances beyond the algebra contained in Fibonacci's thirteenth-century Liber abbaci. By the end of the century, algebraic thought—through work on the solutions of the cubics and quartics but, more especially, through work aimed at better contextualizing and at unifying those earlier sixteenth-century advances—had grown significantly beyond the body of knowledge codified in Luca Pacioli's fifteenth-century compendium, the Summa de arithmetica, geometria, proportioni, e proportionalita. Algebra during this period was evolving in interesting ways.

Islamic Monuments as Christian Trophies

2017 ◽  
Author(s):  
Antonio Urquízar-Herrera
Keyword(s):  
Sixteenth Century ◽  
Fifteenth Century ◽  
Thirteenth Century ◽  
Medieval Chronicles ◽  
Late Fifteenth ◽  
Historical Accounts ◽  
Rodrigo Jimenez De Rada ◽  
The Way

Chapter 3 approaches the notion of trophy through historical accounts of the Christianization of the Córdoba and Seville Islamic temples in the thirteenth-century and the late-fifteenth-century conquest of Granada. The first two examples on Córdoba and Seville are relevant to explore the way in which medieval chronicles (mainly Rodrigo Jiménez de Rada and his entourage) turned the narrative of the Christianization of mosques into one of the central topics of the restoration myth. The sixteenth-century narratives about the taking of the Alhambra in Granada explain the continuity of this triumphal reading within the humanist model of chorography and urban eulogy (Lucius Marineus Siculus, Luis de Mármol Carvajal, and Francisco Bermúdez de Pedraza).

Anthology of texts

2018 ◽  
Author(s):  
Steven N. Dworkin
Keyword(s):  
Fifteenth Century ◽  
Fourteenth Century ◽  
Thirteenth Century ◽  
The Body ◽  
Don Juan ◽  
Alfonso X ◽  
Conde Lucanor ◽  
Lexical Items ◽  
General Estoria

This short anthology contains extracts from three Castilian prose texts, one from the second half of the thirteenth century (General estoria IV of Alfonso X the Wise), one from the first half of the fourteenth century (El conde Lucanor of don Juan Manuel), and one from near the mid-point of the fifteenth century (Atalaya de las corónicas of Alfonso Martínez de Toledo, Arcipreste de Talavera). These passages illustrate in context many of the phonological, orthographic, morphological, syntactic, and lexical features of medieval Hispano-Romance described in the body of this book. A linguistic commentary discussing relevant forms and constructions, as well as the meaning of lexical items no longer used or employed with different meanings in modern Spanish, with cross references to the appropriate sections in the five main chapters, accompanies each selection.

Blind Men Speaking of Colors: Paul's Recollection and the Self-Image of Early Thirteenth-Century Theologians

2014 ◽  
Vol 107 (4) ◽  
pp. 425-446
Author(s):  
Ayelet Even-Ezra
Keyword(s):  
Thirteenth Century ◽  
The Body ◽  
The Self ◽  
First Person ◽  
Knowledge Of God ◽  
The Third ◽  
Self Image ◽  
Third Person ◽  
The Subject ◽  
The Third Person

In the Second Epistle to the Corinthians, Paul writes: It is doubtless not profitable for me to boast. I will come to visions and revelations of the Lord: I know a man in Christ who fourteen years ago—whether in the body I do not know, or whether out of the body I do not know, God knows—such a one was caught up to the third heaven. And I know such a man—whether in the body or out of the body I do not know, God knows—how he was caught up into Paradise and heard inexpressible words, which it is not lawful for a man to utter. Of such a one I will boast; yet of myself I will not boast, except in my infirmities. (2 Cor 12:1–5 nkiv) This brief and enigmatic account is caught between multiple dialectics of power and infirmity, pride and humility, unveiling and secrecy. At this point in his letter Paul is turning to a new source of power in order to establish his authority against the crowd of boasting false apostles who populate the previous paragraphs. He wishes to divulge his intimate, occult knowledge of God, but at the same time keep his position as antihero that is prevalent throughout the epistle. These dialectics are enhanced by a sophisticated play of first and third person. The third person denotes the subject who experienced rapture fourteen years ago, while the first person denotes the narrator in the present. Only after several verses does the reader realize that these two are in fact the same person. This alienation allows Paul the intricate play of boasting, for “of such a one I will boast, yet of myself I will not boast.”

Sur les traces du De motibus / iudiciis planetarum attribué à Ptolémée

2011 ◽  
Vol 16 (6) ◽  
pp. 571-599
Author(s):  
Eduard Frunzeanu ◽  
Isabelle Draelants
Keyword(s):  
Fifteenth Century ◽  
Present Article ◽  
Thirteenth Century ◽  
Critical Edition ◽  
Northern Italy ◽  
The Third

AbstractA short astrological treatise about the properties of the planets in the zodiac, called De motibus / iudiciis planetarum and attributed to Ptolemy (inc. Sub Saturno sunt hec signa Capricornus et Aquarius et sunt eius domus), appears from the thirteenth century onwards in two distinct traditions: in the encyclopedias of Bartholomew the Englishman and Arnold of Saxony, both written around 1230–1240, and in astronomical miscellanies copied in the fifteenth century either in or around Basel and in Northern Italy. These fifteenth-century manuscripts fall into two distinct groups of astronomical texts: the first is copied together with the De signis of Michael Scot, the second together with a part of the third book of Hyginus' De astronomia. The present article aims to describe the characteristics of the distinct textual filiations of De m. / iud. pl. and gives the first critical edition of the text.

scholarly journals Two Bronze Tritons from Nicolaes Witsen’s Collection

2017 ◽  
Vol 65 (4) ◽  
pp. 340-353
Author(s):  
Ruurd Halbertsma ◽  
Frits Scholten
Keyword(s):  
Sixteenth Century ◽  
The Body ◽  
First Century ◽  
National Museum ◽  
The Third

It recently emerged that two bronze ‘doorknobs’ in the Rijksmuseum collection, decorated with Tritons blowing conch shells and with inlaid silver discs, came from the renowned collection of the Amsterdam merchant and burgomaster Nicolaes Witsen. They were listed in 1728 in the catalogue of the sale of his estate (in the Antiquiteyten section) and appear in an engraving in the third, enlarged edition of Witsen’s Noord en Oost Tartaryen of 1785. It was also possible to establish that they were not, as had long been thought, sixteenth-century objects, but Roman appliques dating from the first century AD. The pair probably came from a litter used to carry the body of a deceased to its burial place. The two pieces were recently transferred to the National Museum of Antiquities in Leiden, where they have been reunited with other antiquities from Witsen’s collection.

scholarly journals Trigonometry in Two Sixteenth Century Works; The de Revolutionibus Orbium Coelestium and the Sidra Al-Muntahā

1987 ◽  
Vol 91 ◽  
pp. 209-214
Author(s):  
Sevim Tekeli
Keyword(s):  
Sixteenth Century ◽  
Fifteenth Century ◽  
Thirteenth Century ◽  
Individual Characteristics ◽  
The West ◽  
Islamic World ◽  
The Subject

In Greece, Autolycos (4th cent. B.C.), Aristarchos of Samos (3rd cent.B.C.), Hipparchos (2nd cent.B.C.), Menelaos (1st cent. A.D.), and Ptolemaos (2nd cent. A.D.) are the forerunners of trigonometry. The Greeks used chords and prepared a table of chords.Later, the Hindus produced Siddhāntas (4th cent.A.D.). The most important feature of these works is the use of jyā instead of chords, and utkramajyā (versed sine).In Islam, al-Battānī al-Ṣābī (858-929) used the sine, cosine, tangent, and cotangent with clear consciousness of their individual characteristics.As is known, trigonometry developed as a branch of astronomy. Although in the thirteenth century Naṣīr al-Dīn al-Ṭūsī (in the Islamic world) and in the fifteenth century Regiomontanus (in the West) established trigonometry as a science independent of astronomy, the essential situation did not change, and the subject went on developing as before.

Battista Carioni da Crema (c.1460–1534) and the ‘Third Life’: Visions of Reform in Early Sixteenth-Century Italy*

2020 ◽  
Vol 135 (573) ◽  
pp. 303-336
Author(s):  
Querciolo Mazzonis
Keyword(s):  
Sixteenth Century ◽  
Fifteenth Century ◽  
Christian Life ◽  
Systematic Analysis ◽  
Religious Reform ◽  
Historical Significance ◽  
The Third ◽  
Spiritual Director ◽  
New Geography ◽  
The Church

Abstract This essay sheds new light on the spirituality and historical significance of the influential and controversial Dominican friar Battista Carioni da Crema (c.1460–1534). A popular spiritual writer, charismatic founder of devout associations such as the Barnabites, and a spiritual director of several well-known Catholic figures, including Gaetano Thiene, Battista’s significance has not yet been fully acknowledged. The essay considers his spirituality in the framework of reforming movements emerging in Italy in the first half of the sixteenth century. In dialogue with previous interpretations of Battista, the essay provides a novel and systematic analysis of his notion of perfection and concept of the Church. Synthesising ascetic and mystic spiritual influences rooted in the monastic and humanist culture of the fifteenth century, Battista presented a distinctive view of Christian life, which included an ecclesiological perspective and a new geography of the sacred. Defined as the ‘third life’ and conceived in a period of religious fluidity, it neither fitted emerging Lutheran ideas nor the orthodox Catholicism of the Roman Church. In addition, the essay argues that Battista’s proselytism can be seen as an attempt to reform society which preceded proposals for religious reform made by groups such as the Spirituali.

The English Hospice Of St. George at Sanlucar De Barrameda

1987 ◽  
Vol 18 (3) ◽  
pp. 263-276
Author(s):  
Michael E. Williams
Keyword(s):  
Sixteenth Century ◽  
Fifteenth Century ◽  
Thirteenth Century ◽  
New World ◽  
Northern Europe ◽  
Single Group ◽  
Public Office ◽  
The Mediterranean ◽  
The Town ◽  
Point Of Departure

NOT FAR from Cadiz there is an English property that has remained Catholic for close on five hundred years. Its history goes back to pre-reformation days, indeed to the thirteenth century when the port of Sanlucar de Barrameda was recaptured from the Moors by the Guzman family who later became the Dukes of Medina Sidonia. Strategically Sanlucar was an important port because it was at the mouth of the Guadalquivir and as well as capturing the Seville trade it also commanded the traffic from the Mediterranean to Northern Europe and eventually it was the point of departure for ships leaving for the New World. Among the various nations using the port the English were conspicuous and their merchants were granted various privileges by the Dukes of Medina Sidonia during the fifteenth century. By the early sixteenth century there is evidence of a sizeable colony in the town; in fact the English were the largest single group of foreigners and many English names appear in the baptismal registers as both parents and godparents. At least one of them held high public office in the town. On the accession of Henry VIII to the throne of England, the situation further improved as he abandoned the neutrality of his father and allied himself with Spain against France. So it was that in 1517 a new charter of privileges for the English merchants in Sanlucar was drafted. A grant of land by the river was made so as to provide a chapel and a burial place for Englishmen. The chapel was dedicated to St. George and it was to be looked after by a confraternity. The chaplain was to be appointed by the Bishops of London, Winchester and Exeter, since it was from these dioceses that most of the merchants came. Although there have been rebuildings, this site has remained English ever since.

scholarly journals Thomas and Scholasticism to 1870

2015 ◽  
pp. 527-550
Author(s):  
John T. Slotemaker ◽  
Ueli Zahnd
Keyword(s):  
Fifteenth Century ◽  
Present Article ◽  
Thirteenth Century ◽  
Initial Period ◽  
Thomas Aquinas ◽  
Church Reform ◽  
Summa Theologiae ◽  
The Third ◽  
Gradual Development ◽  
Theological Authority

The present article treats the life and works of Thomas Aquinas and his reception within the scholastic traditions up to 1879 (Aeterni Patris). The first two sections introduce the life and works of Thomas Aquinas, with a particular focus on the Scriptum and the Summa theologiae. The third section treats Thomas’s reception up through 1500, looking at the initial period of condemnation in the late thirteenth century. This is followed by his canonization and acceptance as a theological authority in the fourteenth century and the gradual development of the Thomist schools of the fifteenth century. The fourth and fifth sections examine the reception of Thomas’s thought in the era of Church reform and the baroque period (1500–1650), and from 1650 until Aeterni Patris (1879) respectively.

The Italian Renaissance and the Origins of the Modern Humanities

2021 ◽  
Author(s):  
Christopher S. Celenza
Keyword(s):  
Early Modern ◽  
Fifteenth Century ◽  
Human Life ◽  
Historical Context ◽  
The Body ◽  
Italian Renaissance ◽  
Reading Practices ◽  
Body Of Knowledge ◽  
The Enlightenment ◽  
Novel Reading

Christopher Celenza is one of the foremost contemporary scholars of the Renaissance. His ambitious new book focuses on the body of knowledge which we now call the humanities, charting its roots in the Italian Renaissance and exploring its development up to the Enlightenment. Beginning in the fifteenth century, the author shows how thinkers like Lorenzo Valla and Angelo Poliziano developed innovative ways to read texts closely, paying attention to historical context, developing methods to determine a text's authenticity, and taking the humanities seriously as a means of bettering human life. Alongside such novel reading practices, technology – the invention of printing with moveable type – fundamentally changed perceptions of truth. Celenza also reveals how luminaries like Descartes, Diderot, and D'Alembert – as well as many lesser-known scholars – challenged traditional ways of thinking. Celenza's authoritative narrative demonstrates above all how the work of the early modern humanist philosophers had a profound impact on the general quest for human wisdom. His magisterial volume will be essential reading for all those who value the humanities and their fascinating history.

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