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Roshdi Rashed
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Thabit ibn Qurra (826a "901) was one of historya (TM)s most
original thinkers and displayed expertise in the most difficult
disciplines of this time: geometry, number theory, and astronomy as
well as ontology, physics, and metaphysics. Approximately a dozen
of this shorter mathematical and philosophical writings are
collected in this volume. Critically edited with accompanying
commentary, these writings show how Thabit Ibn Qurra developed and
reconceived the intellectual inheritance of ancient Greece in all
areas of knowledge.
Despite its importance in the history of Ancient science, Menelaus'
Spherics is still by and large unknown. This treatise, which lies
at the foundation of spherical geometry, is lost in Greek but has
been preserved in its Arabic versions. The reader will find here,
for the first time edited and translated into English, the
essentials of this tradition, namely: a fragment of an early Arabic
translation and the first Arabic redaction of the Spherics composed
by al-Mahani /al-Harawi, together with a historical and
mathematical study of Menelaus' treatise. With this book, a new and
important part of the Greek and Arabic legacy to the history of
mathematics comes to light. This book will be an indispensable
acquisition for any reader interested in the history of Ancient
geometry and science and, more generally, in Greek and Arabic
science and culture.
In this unique insight into the history and philosophy of
mathematics and science in the mediaeval Arab world, the eminent
scholar Roshdi Rashed illuminates the various historical, textual
and epistemic threads that underpinned the history of Arabic
mathematical and scientific knowledge up to the seventeenth
century. The first of five wide-ranging and comprehensive volumes,
this book provides a detailed exploration of Arabic mathematics and
sciences in the ninth and tenth centuries. Extensive and detailed
analyses and annotations support a number of key Arabic texts,
which are translated here into English for the first time. In this
volume Rashed focuses on the traditions of celebrated polymaths
from the ninth and tenth centuries 'School of Baghdad' - such as
the Banu Musa, Thabit ibn Qurra, Ibrahim ibn Sinan, Abu Jafar
al-Khazin, Abu Sahl Wayjan ibn Rustam al-Quhi - and
eleventh-century Andalusian mathematicians like Abu al-Qasim ibn
al-Samh, and al-Mu'taman ibn Hud. The Archimedean-Apollonian
traditions of these polymaths are thematically explored to
illustrate the historical and epistemological development of
'infinitesimal mathematics' as it became more clearly articulated
in the eleventh-century influential legacy of al-Hasan ibn
al-Haytham ('Alhazen'). Contributing to a more informed and
balanced understanding of the internal currents of the history of
mathematics and the exact sciences in Islam, and of its adaptive
interpretation and assimilation in the European context, this
fundamental text will appeal to historians of ideas,
epistemologists, mathematicians at the most advanced levels of
research.
Theory of Conics, Geometrical Constructions and Practical Geometry:
A History of Arabic Sciences and Mathematics Volume 3, provides a
unique primary source on the history and philosophy of mathematics
and science from the mediaeval Arab world. The present text is
complemented by two preceding volumes of A History of Arabic
Sciences and Mathematics, which focused on founding figures and
commentators in the ninth and tenth centuries, and the historical
and epistemological development of 'infinitesimal mathematics' as
it became clearly articulated in the oeuvre of Ibn al-Haytham. This
volume examines the increasing tendency, after the ninth century,
to explain mathematical problems inherited from Greek times using
the theory of conics. Roshdi Rashed argues that Ibn al-Haytham
completes the transformation of this 'area of activity,' into a
part of geometry concerned with geometrical constructions, dealing
not only with the metrical properties of conic sections but with
ways of drawing them and properties of their position and shape.
Including extensive commentary from one of world's foremost
authorities on the subject, this book contributes a more informed
and balanced understanding of the internal currents of the history
of mathematics and the exact sciences in Islam, and of its adaptive
interpretation and assimilation in the European context. This
fundamental text will appeal to historians of ideas,
epistemologists and mathematicians at the most advanced levels of
research.
This volume provides a unique primary source on the history and
philosophy of mathematics and science from the mediaeval Arab
world. The fourth volume of A History of Arabic Sciences and
Mathematics is complemented by three preceding volumes which
focused on infinitesimal determinations and other chapters of
classical mathematics. This book includes five main works of the
polymath Ibn al-Haytham (Alhazen) on astronomy, spherical geometry
and trigonometry, plane trigonometry and studies of astronomical
instruments on hour lines, horizontal sundials and compasses for
great circles. In particular, volume four examines: the increasing
tendency to mathematize the inherited astronomy from Greek sources,
namely Ptolemy's Almagest; the development of celestial kinematics;
new research in spherical geometry and trigonometry required by the
new kinematical theory; the study on astronomical instruments and
its impact on mathematical research. These new historical materials
and their mathematical and historical commentaries contribute to
rewriting the history of mathematical astronomy and mathematics
from the 11th century on. Including extensive commentary from one
of the world's foremost authorities on the subject, this
fundamental text is essential reading for historians and
mathematicians at the most advanced levels of research.
This volume provides a unique primary source on the history and
philosophy of mathematics and the exact sciences in the mediaeval
Arab world. The second of five comprehensive volumes, this book
offers a detailed exploration of Arabic mathematics in the eleventh
century as embodied in the legacy of the celebrated polymath
al-Hasan ibn al-Haytham. Extensive analyses and annotations from
the eminent scholar, Roshdi Rashed, support a number of key Arabic
texts from Ibn al-Haytham's treatises in infinitesimal mathematics,
translated here into English for the first time. Rashed shows how
Ibn al-Haytham's works demonstrate a remarkable mathematical
competence in mathematical subjects like the quadrature of the
circle and of lunes, the calculation of the volumes of paraboloids,
the problem of isoperimetric plane figures and solid figures with
equal surface areas, along with the extraction of square and cubic
roots. The present text is complemented by the first volume of A
History of Arabic Sciences and Mathematics, which focused on
founding figures and commentators in the ninth and tenth centuries
Archimedean-Apollonian mathematical 'School of Baghdad'. This
constellation of works illustrates the historical and
epistemological development of 'infinitesimal mathematics' as it
became clearly articulated in the oeuvre of Ibn al-Haytham.
Contributing to a more informed and balanced understanding of the
internal currents of the history of mathematics and the exact
sciences in Islam, and of its adaptive interpretation and
assimilation in the European context, this fundamental text will
appeal to historians of ideas, epistemologists and mathematicians
at the most advanced levels of research.
This volume provides a unique primary source on the history and
philosophy of mathematics and the exact sciences in the mediaeval
Arab world. The second of five comprehensive volumes, this book
offers a detailed exploration of Arabic mathematics in the eleventh
century as embodied in the legacy of the celebrated polymath
al-Hasan ibn al-Haytham.
Extensive analyses and annotations from the eminent scholar,
Roshdi Rashed, support a number of key Arabic texts from Ibn
al-Haytham s treatises in infinitesimal mathematics, translated
here into English for the first time. Rashed shows how Ibn
al-Haytham s works demonstrate a remarkable mathematical competence
in mathematical subjects like the quadrature of the circle and of
lunes, the calculation of the volumes of paraboloids, the problem
of isoperimetric plane figures and solid figures with equal surface
areas, along with the extraction of square and cubic roots.
The present text is complemented by the first volume of "A"
"History of Arabic Sciences and Mathematics," which focused on
founding figures and commentators in the ninth and tenth centuries
Archimedean-Apollonian mathematical School of Baghdad . This
constellation of works illustrates the historical and
epistemological development of infinitesimal mathematics as it
became clearly articulated in the oeuvre of Ibn al-Haytham.
Contributing to a more informed and balanced understanding of
the internal currents of the history of mathematics and the exact
sciences in Islam, and of its adaptive interpretation and
assimilation in the European context, this fundamental text will
appeal to historians of ideas, epistemologists and mathematicians
at the most advanced levels of research.
In this unique insight into the history and philosophy of
mathematics and science in the mediaeval Arab world, the eminent
scholar Roshdi Rashed illuminates the various historical, textual
and epistemic threads that underpinned the history of Arabic
mathematical and scientific knowledge up to the seventeenth
century. The first of five wide-ranging and comprehensive volumes,
this book provides a detailed exploration of Arabic mathematics and
sciences in the ninth and tenth centuries. Extensive and detailed
analyses and annotations support a number of key Arabic texts,
which are translated here into English for the first time. In this
volume Rashed focuses on the traditions of celebrated polymaths
from the ninth and tenth centuries 'School of Baghdad' - such as
the Banu Musa, Thabit ibn Qurra, Ibrahim ibn Sinan, Abu Jafar
al-Khazin, Abu Sahl Wayjan ibn Rustam al-Quhi - and
eleventh-century Andalusian mathematicians like Abu al-Qasim ibn
al-Samh, and al-Mu'taman ibn Hud. The Archimedean-Apollonian
traditions of these polymaths are thematically explored to
illustrate the historical and epistemological development of
'infinitesimal mathematics' as it became more clearly articulated
in the eleventh-century influential legacy of al-Hasan ibn
al-Haytham ('Alhazen'). Contributing to a more informed and
balanced understanding of the internal currents of the history of
mathematics and the exact sciences in Islam, and of its adaptive
interpretation and assimilation in the European context, this
fundamental text will appeal to historians of ideas,
epistemologists, mathematicians at the most advanced levels of
research.
This book discusses light-based science, emphasizing its pervasive
influence in science, technology, policy, and education. A wide
range of contributors offers a comprehensive study of the
tremendous, and indeed foundational, contributions of Ibn al
Haytham, a scholar from the medieval period. The analysis then
moves into the future development of light-based technology.
Written as a multi-disciplinary reference book by leading scholars
in the history of science and /or photonics, it covers Ibn al
Haytham's optics, LED lighting for sustainable development, global
and atomic-scale time with new light sources, advanced technology,
and vision science. Cutting-edge optical technologies and their
global impact is addressed in detail, and the later chapters also
explore challenges with renewable energy, the global impact of
photonics, and optical and photonic education technology. Practical
examples and illustrations are provided throughout the text.
Until recently, only six of thirteen books comprising Diophantus
Arithmetica were known to us. Four other books in an Arabic
translation have been discovered recently. We can now understand
the organization of this work and its long-lasting impact on
mathematics. The present book offers the first historical and
mathematical study of the work as it has survived in ten books."
This fifth volume of A History of Arabic Sciences and Mathematics
is complemented by four preceding volumes which focused on the main
chapters of classical mathematics: infinitesimal geometry, theory
of conics and its applications, spherical geometry, mathematical
astronomy, etc. This book includes seven main works of Ibn
al-Haytham (Alhazen) and of two of his predecessors, Thabit ibn
Qurra and al-Sijzi: The circle, its transformations and its
properties; Analysis and synthesis: the founding of analytical art;
A new mathematical discipline: the Knowns; The geometrisation of
place; Analysis and synthesis: examples of the geometry of
triangles; Axiomatic method and invention: Thabit ibn Qurra; The
idea of an Ars Inveniendi: al-Sijzi. Including extensive commentary
from one of the world's foremost authorities on the subject, this
fundamental text is essential reading for historians and
mathematicians at the most advanced levels of research.
This book follows the development of classical mathematics and the
relation between work done in the Arab and Islamic worlds and that
undertaken by the likes of Descartes and Fermat. 'Early modern,'
mathematics is a term widely used to refer to the mathematics which
developed in the West during the sixteenth and seventeenth century.
For many historians and philosophers this is the watershed which
marks a radical departure from 'classical mathematics,' to more
modern mathematics; heralding the arrival of algebra, geometrical
algebra, and the mathematics of the continuous. In this book,
Roshdi Rashed demonstrates that 'early modern,' mathematics is
actually far more composite than previously assumed, with each
branch having different traceable origins which span the
millennium. Going back to the beginning of these parts, the aim of
this book is to identify the concepts and practices of key figures
in their development, thereby presenting a fuller reality of these
mathematics. This book will be of interest to students and scholars
specialising in Islamic science and mathematics, as well as to
those with an interest in the more general history of science and
mathematics and the transmission of ideas and culture.
The treatise De Rationis Sectione by Apollonius of Perge, which
deals with a unique and difficult problem, is a remarkable, complex
example of the study of the necessary pre-conditions for the
existence of a solution. This volume presents the editio princeps
of the text, which has only survived in an Arabic version. It is
made accessible in the form of a French translation and a
commentary that reveals the mechanisms of Apolloniusa (TM)
difficult proof, and draws particular attention to its conceptual
innovations.
The mathematical works of Ab? K?mil (floruit circa 880) were
produced two generations after the works of Al-Khwarizm?, the
founder of algebra. They opened up fields of research that proved
fertile up until the seventeenth century, and were soon to become
both a reference and a model. Their influence was decisive on the
development of algebra in Arabic no less than in Latin and Hebrew.
There will be found in the present publication the first rigorously
critical edition of Ab? K?mil s works, as well as the first ever
translation into a modern language. Text and translation are
preceded by an exhaustive commentary, at once mathematical and
historical."
This fifth volume of A History of Arabic Sciences and Mathematics
is complemented by four preceding volumes which focused on the main
chapters of classical mathematics: infinitesimal geometry, theory
of conics and its applications, spherical geometry, mathematical
astronomy, etc. This book includes seven main works of Ibn
al-Haytham (Alhazen) and of two of his predecessors, Thabit ibn
Qurra and al-Sijzi: The circle, its transformations and its
properties; Analysis and synthesis: the founding of analytical art;
A new mathematical discipline: the Knowns; The geometrisation of
place; Analysis and synthesis: examples of the geometry of
triangles; Axiomatic method and invention: Thabit ibn Qurra; The
idea of an Ars Inveniendi: al-Sijzi. Including extensive commentary
from one of the world's foremost authorities on the subject, this
fundamental text is essential reading for historians and
mathematicians at the most advanced levels of research.
Book VI of the Konika is essentially devoted to the question of the
identity and similarity of two conic sections, or two parts of
conic sections. In Book VII Apollonius deals with the various
relationships between the lengths of diameters and conjugate
diameters. The results are applied to the exposition of a number of
problems, as well as to some problems which Apollonius indicates
will be demonstrated and solved in Book VIII, which was lost in
Antiquity. Books VI and VII have only survived in an Arabic
translation, and are presented here in a critical edition, together
with a faithful translation and a historical-mathematical
commentary.
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