From Antiquity until recently, philosophers and mathematicians have continually discussed the concept of angle and its relation to archimedean and non-archimedean theories of measurement. For the first time, this book traces the history of these discussions in Greek and Arabic, from Euclid to Kamāl al-Dīn al-Fārisī, after whom the discussion was not resumed until Newton and Euler. The volume presents first editions of over twenty texts, either in Arabic or Greek and translated into Arabic, of the greatest mathematicians and philosophers (...) of the time. The texts are here translated into French and supplemented with extensive commentary. The book begins with the definitions and propositions of Euclid on angles and measurement, followed by the Greek commentary tradition represented by Proclus and Simplicius (only extant in Arabic) and the writings of the Arabic mathematicians and philosophers from the 9th through 14th century, placing the fundamental contributions by Avicenna and Ibn al-Haytham into their historical context and showing how numerous successors produced new syntheses of their work. (shrink)

Introduces young readers to Ibn Sina, telling his story as he might tell it himself. It provides a fascinating glimpse into the life of this philosopher, scientist and physician who was one of the greatest thinkers of his time.

Code of conduct in society according to Islam.

In this work the Persian and English texts are edited and published together for the first time. This is Tusi’s major Ismaili work and the most important primary source on Ismaili doctrines during the Alamut period.

We argue that there is an incompatibility between the two basic principles of Molinism, i.e., God’s middle knowledge of counterfactuals of creaturely freedom, and divine immutability. To this end, firstly, we set out the difference between strong and weak immutability: according to the latter only God’s essential attributes remain unchanged, while the former affirms that God cannot change in any way. Our next step is to argue that Molinism ascribes strong immutability to God. However, according to Molinism, some counterfactuals of (...) freedom need to be actualized by divine will. We argue that this claim does entail a change in God because it attributes a knowledge to God that involves moving from possibility to actuality through divine will. Therefore, claiming God knows counterfactuals of freedom leads us to reject the strong sense of divine immutability. Further, we argue that assuming God’s knowledge encompasses counterfactuals of freedom cannot be consistent even with weak immutability because, according to Molinism, a change in God’s knowledge requires a change in His essence. We conclude that Molinism is incoherent. (shrink)

Quʹest-ce que lʹêre? Cette question passe pour fonder la philosophie. Encore faut-il s'entendre sur le sens du mot "être ". L'essence des choses détermine-t-elle leur existence? Devons-nous affirmer, au contraire, que l'existence conditionne l'intensité d'être qui qualifie une certaine réalité? Molla Sadr Shirazi, dans ce traité écrit en Iran au siècle de Descartes et de Leibniz, médite ces questions qui sont encore les nôtres. Mais les solutions qu'il propose s'évadent hors de nos perspectives, après avoir opéré une révolution décisive dans (...) la métaphysique des Orientaux. Penseur shi'ite en butte à la persécution, Molla Sadra est la plus haute figure de la philosophie iranienne islamique au temps splendide de la cour safavide d'Ispahan. Sa doctrine du primat de l'existence, que le présent ouvrage expose complètement, ouvre sur une interprétation spirituelle de la résurrection des corps. Cette traduction par Henry Corbin, qui fut aussi l'éditeur du texte original, a fait événement : par son ample introduction, il situe la question de l'être et déploie une explication comparée de ce que l'Occident grec puis médiéval en ont fait, avec la tradition shi'iite. -- Back cover. (shrink)

The central issue in this work is self-knowledge. The human soul is created in the Image of God with a purpose.

The appearance of nonlinear equations in science, engineering, economics, and medicine cannot be denied. Solving such equations requires numerical methods having higher-order convergence with cost-effectiveness, for the equations do not have exact solutions. In the pursuit of efficient numerical methods, an attempt is made to devise a modified strategy for approximating the solution of nonlinear models in either scalar or vector versions. Two numerical methods of second-and sixth-order convergence are carefully merged to obtain a hybrid multi-step numerical method with twelfth-order (...) convergence while using seven function evaluations per iteration, resulting in the efficiency index of about 1.4262. The convergence is also ascertained theoretically, and the asymptotic error constant is computed. Furthermore, various numerical methods of varying orders are used to compare the numerical results obtained with the proposed hybrid method in approximate solution, number of iterations, absolute error, absolute functional value, and the machine time measured in seconds. The obtained results outperformed the chosen methods when applied models arising from physical and natural fields were solved. Finally, to observe the convergence graphically, some complex polynomials are plotted as polynomiographs, wherein the rapid convergence of the proposed method is guaranteed. (shrink)

Semantic relationships have an active role in textual study, as they are an essential tool through which the text is constructed, this is done through the sequence of sentences of saying, and these relationships lead to the growth and continuation of the subject of the text, and then linking speech, which in turn achieves textual harmony. The aim of this study is to highlight the importance of these relationships and to elaborate on them, this research dealt with two additional linkage (...) relationships: (equivalent additional relationship), and (different additional relationship), with a breakdown of each of them, and then the inclusion of poetic applications from the texts of the poet Hazem Rushak Al-Tamimi, showing the extent of the harmony, plot and coherence of these texts. (shrink)

al-Tabarsī is one of the glossators in the Shī‘ah gloss tradition in the second middle period or first sagacity period. al-Tabarsī who had a wide knowledge in the various knowledge branches was mentioned as a glossator, narrator of Mohammad’s all sayings, deeds and approvals and scribe. One of compilations that al-Tabarsī wrote it in the field of gloss is Macmau-l-bayān fī tafsīri-l-Qur’ān. The glossator who widely included the recitations in this work used some evidence related to their averment while he (...) was reporting the recitations, and he made the recitations’ justification in the framework. The averment is a science which determines the correct recitations as distinguishing the correct one of recitation’s differences from the deficient one, and which founds an aspect of the correct category with all the other transferred and linguistic arguments of recitation in the predilection besides the imputation, the formal Qur’ān. Al-Tabarsī first mentioned the recitations under the subtitle of recitation related to the verses in each sura and then transferred the argument of recitations with the term of argument. So the glossator applied to give evidence on them with the linguistic and transferred arguments in each of the parts that the recitations were nearly mentioned. He mentioned the imputation, the Qur’ān lettering, verse, hadith, companion and natural people’s readings. He used Arabic poetry, Arabic idiom, dialect, grammar and syntax rules for the linguistic arguments. In this study, the evidences which were used in the recitations’ averment are reviewed in the sample of al-Tabarsī’s gloss in the name of Majmau-l-bayān. Summary: Full name of al-Tabarsī who was one of the leading scholar of Shī‘a is Fadl b. Hasan b Fadl al-Tabarsī. He was born in Thabaristan. According to some narration he was born in village named Tafrish which is between Kashan and Isfahan. He was called al-Tabarsī by reference to his hometown Thabaristan, according to another opinion he was called al-Tabarsī which comes from his birth place known as Tafrish located between Kashan and Isfahan. Tafrish was translated into Arabic as Tabars. Also, the commentator was known with nicknames such as Amīnü’l-islām, Amīnü’d-dīn and Umdatü’l-Mufassīrīn. He was called Sebzevarī due to the place where he died and named Maşhadī and Ṭūsī because of the place where he was buried. Although he is proficient in many fields, he has been described in the sources as commentator, muhaddīth and faqīh. Mufassīr has written many works in Islamic sciences. one of his works written in the field of commentary is Mujmau-l-bayān fī tafsīri-l-Qurʾān. Mufassīr stated that he wrote this commentary by taking advantage of Ṭūsī 's (d. 460/1067) al-Tibyān by saying “It is a guide from which I benefited from Tibiān light, and I write the subjects on the basis of his method”. The author started to write this work with the encouragement of some of his friends after he had aged quite a bit and his hair turned white. and he saw a gap in this area. He spent a lot of effort to fill that gap. This commentary, written during the first dirayet of the Shī‘a exegesis, is more moderate than the previous periods of Shī‘a commentators. The most basic indicator of this is the definitive rejection of the falsification of the Qurʾān in this period. The second important indicator is that insults and degrading expressions about the first three of the hulafā-i rashid and some of the companions are not accepted. The third important indicator is that most of the verses have been interpreted in a manner that corresponds to the views of the Ahl al-Sunnah school in linguistic analyses and proved by appealing to Arabic poems and sayings. al-Tabarsī mentioned recitation almost in all verses as a subtopic. He performed this in the surah by using subtopics. Then he has used “hujjatuhu” (its evidence) expression to narrate the evident of qirāʾāt. By doing so, commentator grounded qirāʾāts by using their evidences utilizing linguistic and narrative evidences in nearly every mentioned qirāʾāts. İhtijaj is a science that determines the authentic readings by distinguishing authentic readings from the weak ones, and that grounds the reading in the choice of an angle, which is mentioned in the authentic category, with isnād, Mushaf script and all other narrative and linguistic evidences. There are two types of ihtijaj which are ihtijaj bi-l-qirāʾāt ve ihtijaj li-l-qirāʾāt. İhtijaj li-l-qirāʾāt uses the linguistic evidences such as isnād, Mushaf line, Arabic language, consumables-nahiv pedestals, polish differences and the narrative evidences such as verses, hadith, qirāʾāt, Arabic words and poetry in determination and preference of a reading aspect. ihtijaj bi-l-qirāʾāt is the use of kıraa as evidence for any matter of science. al-Tabarsī has also mentioned detection proofs which reveal the authentic ways of qirāʾāt like isnād and rasm al-mushaf. Isnād is attribution to whom take the qirāʾāt from previous persons. This proportion reaches up to the Prophet. The persons in the chain of isnād constitute this chain. al-Tabarsī has given in preface the names of the recitors and narrators, which are famous in the cities, based on the fact that an authentic attribute is the basic element in the determination of the qirāʾāh. Thus he passed on the chains of isnād that reached up to the Prophet. Another thing that al-Tabarsī used in the determination proof of qirāʾāh is rasm al-mushaf. The commentator has used the spelling of al-mushaf scripture as evidence by saying “written in al-mushaf like this”. al-Tabarsī, also mentioned preferable evidences about ways of qirāʾā’s proof. Preferred proofs, are evidence to make choosing between qirāʾāh whose authenticity is defined by means of determination proofs. These evidences are divided into two parts which are determination proofs-based and special. Special evidence has not relation with the determination proofs. It contains evidence categories used to prefer one of the two authentic qirāʾāh as special. These categories are divided into four parts: linguistic, transplant, mental and private. al-Tabarsī has evidenced with verses of narrative proofs in the preferred evidence category. The commentator has mentioned about this method for qirāʾā evidence extensively. He has grounded qirāʾāh by using verses. al-Tabarsī also has evidenced these matters by using words of the Prophet from narrative proofs in the preferred evidence category. In this method commentator has evidenced from hadith after mentioning qirāʾāh ways. al-Tabarsī evidences from narrative proofs with qirāʾāh preferred evidence category. In this context, the commentator mentioned recitation of companion and followers by saying his qirāʾāh after reporting qirāʾāh. Moreover, the commentator has sometimes mentioned recitations which is related with reading seven of the recitation and reading ten of the recitation sciences qurra recitation and sometimes mentioned recitations which are known as shadhdh. Then, he has examined these recitations with the qirāʾāh of companions and followers. al-Tabarsī has benefited from narrative evidences, Arabic poetry and phrase in the preferred evidence category extensively. Another evidence used for examination of qirāʾāh is linguistic evidences. Qirāʾāh are related with Arabic language because it has connection with Qur’ānic wording which revelated in Arabic. al-Tabarsī has benefited from some things such as Arabic grammar rules and dialectic differences extensively. The commentator has benefited from Arabic grammar by emphasizing the meaning of the words with the literary features. He has explained grammar statement related with qirāʾāh aspects. He has also explained linguistic rules which are about aspects. (shrink)

When the teachers’ training practicum was paralyzed during the COVID-19 pandemic, preservice teachers in Malaysia were required to adapt to the online practicum. This qualitative case study was conducted with 20 preservice teachers to investigate their online teaching practicum experiences. The study drew on the Engagement Theory and Disaster Management Cycle framework to further suggest teaching approaches that might be effective during a tragic situation. Data were collected from interviews and video observations, and analyzed thematically. The findings contribute to the (...) understanding of how preservice teachers learn to modify their teaching practices during the challenging context. A number of themes related to positive experience were identified: higher confidence level, improved interaction, engagement in active learning, and adapting to online syllabus. On the other hand, the negative experience revolves around the problem with Internet connection. It is hoped that the findings of this study will encourage preservice teachers to consider hybrid approaches and online teaching in the future. (shrink)

Similar words and utterances in the Qurʾān are the subject of the technical term lafẓī mutashābih. The rephrasing of meanings (maʿnā) and use of different words (lafẓ) in the Qurʾān are dealt with under the rubric of the theme “Qurʾānic style.” The stylistic variations in the Qurʾān are expressed as takrār al-Qurʾān, tasrīf (Affix and Paraphrase), ʿudūl (inversion), and tafannun (stylistic variation). However, when compared with other terms of exegesis, “tafannun” remained in the background and its conceptualization was thwarted. This (...) could be attributed not only to other concepts brought to the fore but also to the fact that tafannun underwent semantic restriction and was confined to iftinān within the framework of badīʿ. This study aims to clarify the true meaning of tafannun which reflects stylistic variations in the Qurʾān and revealing the contribution of this term to the more appropriate interpretation of the Qurʾān, assessing its significance for the field of tafsīr. The first chapter of this study deals with the etymology of tafannun, its historical background and conceptualization as well as the relationship between iʿjāz (inimitability) and tafannun in the history of tafsīr, while the second one identifies and illustrates the kinds of tafannun to expound on the true nature of this concept.Summary: Similar words and utterances in the Qurʾān are the subject of the technical term lafẓī mutashābih. The change and variety of the rephrasing of meanings (maʿnā) and words (lafẓ) in the Qurʾān are dealt with under the rubric of the theme “Qurʾānic style.” The stylistic differences and variations in the Qurʾān are expressed in the literature with terms such as takrār al-Qurʾān, tasrīf (affix and paraphrase), ʿudūl (inversion), tafannun (stylistic variation). However, in the terminology of exegesis, the term “tafannun” remained in the background, and its conceptualization was thwarted. This could be attributed not only to other concepts brought to the fore but also to the fact that the word tafannun underwent semantic restriction and therefore was confined to iftinān within the framework of badīʿ. Yet in earlier times it was widely used in the exegesis literature as part of Arabic language to identify the stylistic variations in the Qurʾān. Starting with 8th century AH, there have been numerous references to the term tafannun. From 9th century AH to present, many Muslim exegetes, especially Ibn Āshūr (1879-1973) used tafannun as one of the fundamental concepts to understand and explain the proper meaning of the Qurʾān. This study aims to clarify the true meaning of tafannun which reflects stylistic variations in the Qurʾān and revealing the contribution of it to the proper interpretation of the Qurʾān, assessing its significance for tafsīr. The first chapter of this study deals with the etymology of tafannun, its historical background and conceptualization as well as the relationship between iʿjāz (inimitability) and tafannun in the history of tafsīr, while the second one identifies and illustrates the kinds of tafannun to expound on the true nature of this concept.According to the result of this research, iftinān means following various styles and genres (types), while tafannun denotes variations in styles and genres (types). In vernacular, these two terms are considered the same. The term iftinān was dealt with in some works under the subject of muhassināt al-maʿnaviyya within the framework of badīʿ. In the Arabic literature, when the definition of the term iftinān was given, the term tafannun was not defined under any section of any book or any other place in the rhetoric of science. Tafannun is used to express the way any action is carried out, as it is mentioned in the definition of iftinān.The word tafannun was used to demonstrate the expertise, depth and mastery of Islamic scholars in one or various fields of Islamic studies in the early works of Islamic literature. In later times, the term iftinān was used to show rhetorical and oracy skills of a person. Abū Hilāl al-ʿAskarī (d. 400/1009) define tafannun as “the variation in words while two paragraphs bear the same meaning.” His definition proved to be a turning point in the conceptualization process of the word tafannun. Al-Zamakhsharī (d. 538/1144) was the first Islamic scholar to refer to the word tafannun in the interpretation of the Qurʾān. He used the words iftinān and tafannun in the same sense in his works. He mostly regarded examples of iltifāt as iftinān. Abū Bakr al-Rāzī (d. 666/1268), establishing a connection between tafannun and repetition, stated that the term tafannun was used to avoid boredom of repetitive diction.Among other authors who used the term tafannun in their works, Bayḍāwī, (d. 685/1286), Nīsābūrī (d. 730/1329), Ibn Cemāʿa (d. 733/1333), Abū Ḥayyān (d. 745/1344), Samīn al-Ḥalabī (d. 756/1355), Zarkashī (d. 794/1392), Suyūṭī, (d. 911/1505), Ḥaṭīb al-Shirbīnī (d. 977/1570), Shihāb al-Dīn al-Khafājī (d. 1069/1659), Ālūsī, (d. 1270/1854), Muḥammad ʿAbduh (1849-1905)-Rashīd Riḍā (1865-1935) and Ibn Āshūr are the notable ones. Rather than merely defining the term tafannun, the majority of these commentators emphasized the function, benefit and aim of this word. Thanks to the use of this word by these commentators, a distinction was made between tafannun called iftinān as a literary device in the science of badīʿ and tafannun gaining a new meaning used to express stylistic variations. As a result, two words with the same dictionary definition were distinguished from each other during the conceptualization process. Among the authors using the word tafannun, Ibn Āshūr clearly defined the term and contributed significantly to its conceptualization. He defines the word tafannun as the uniqueness of the Qurʾān in employing stylistic variations by offering synonymous words in case of iʾtirāz (discursive), tanzīr, (resemblance), tazyīl (appendix) and takrār (repetition), creating the most comprehensive definition until that time.Tafannun is also defined as expression of the same meaning through re-signifying, stylistic variation in two verses, difference in the repetition of parables, variations in choice of diction and synonymous words, and avoidance of repetition. As a result of its definition, the word tafannun also denotes providing stylistic variations, using vivid language, avoiding prosaic diction, using denotative and connotative language, helping readers to grasp shades of meaning and read between the lines in the most clear and economic way.In the related literature, there are a lot of references to the word tafannun when demonstrating iʿjāz of the Qurʾān. When looked at the historical development of the relationship between iʿjāz and tafannun, it is observed that tafannun was accepted to be an element of iʿjāz. Defined as providing stylistic variation, tafannun is employed in various ways. The literary devices used to carry out tafannun are through ʿudūl, iltifāt, taqdīm and taʾhīr, change of utterances, use of synonymous words, objection, resemblance, and addition. In the proper interpretation of the Qurʾān, tafannun has a comprehensive usage, making many more academic studies a necessity with a view to making a significant contribution to a deeper and better grasp of words and shades of meanings employed in the Qurʾān. (shrink)

Applying the resolution–scale relativity principle to develop a mechanics of non-differentiable dynamical paths, we find that, in one dimension, stationary motion corresponds to an Itô process driven by the solutions of a Riccati equation. We verify that the corresponding Fokker–Planck equation is solved for a probability density corresponding to the squared modulus of the solution of the Schrödinger equation for the same problem. Inspired by the treatment of the one-dimensional case, we identify a generalization to time dependent problems in any (...) number of dimensions. The Itô process is then driven by a function which is identified as establishing the link between non-differentiable dynamics and standard quantum mechanics. This is the basis for the scale relativistic interpretation of standard quantum mechanics and, in the case of applications to chaotic systems, it leads us to identify quantum-like states as characterizing the entire system rather than the motion of its individual constituents. (shrink)

Awḥad al-Dīn Kirmānī and the Controversy of the Sufi Gaze By RidgeonLloyd, 289 pp. Price HB £105.00. EAN 978–1138057135.

Recently, in ‘An inquiry on Fakhr al-Dīn Rāzī’s authorship of Al-manṭiq al-kabι¯r (MS Aḥmad iii, no. 3401)’, we refuted the quite common view among historians of Arabic logic as to attribute Al-manṭiq al-kabι¯r (Major [book on] logic) to Fakhr al-dīn Rāzī; however, in that paper, we could not identify the real author of the book. In this paper, we try to show that Al-manṭiq al-kabι¯r was written by Burhān al-dīn Nasafī (1203–1288), who authored another book, Sharḥ Asās al-kiyāsa whose logical (...) part is very similar to Al-manṭiq al-kabι¯r in the following significant features: the titles of chapters and sections, the style of writing, some technical as well as some non-technical terms, many sentences word by word. None of these features we find in any other Arabic logical work. So, Al-manṭiq al-kabι¯r and Sharḥ Asās al-kiyāsa are so close to each other that we might most possibly identify the authors of the books as the same scholar, i.e. Burhān al-dīn Nasafī. Fortunately, this has been verified recently by two manuscripts of a medieval Arabic logical book. (shrink)

This paper is a technical study of the systematic observations and computations made by Muḥyī al-Dīn al-Maghribī (d. 1283) at the Maragha observatory (north-western Iran, c. 1259–1320) in order to newly determine the parameters of the Ptolemaic lunar model, as explained in his Talkhīṣ al-majisṭī, “Compendium of the Almagest.” He used three lunar eclipses on March 7, 1262, April 7, 1270, and January 24, 1274, in order to measure the lunar epicycle radius and mean motions; an observation on April 20, (...) 1264, to determine the lunar eccentricity; an observation on August 29, 1264, to test the model; and another on March 15, 1262, for measuring the lunar parallax. In the second period of activity at the Maragha observatory, Shams al-Dīn Muḥammad al-Wābkanawī (c. 1254–1320) adopted all of al-Maghribī’s parameter values in his Zīj, but decreased his value for the mean longitude of the moon at epoch by 0;13,11∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{\circ }$$\end{document}. By comparing the times of the new moons and lunar eclipses in the period of 1270–1320 as computed from the astronomical tables of the Maragha tradition with the true modern ones, it is argued that this correction was very probably the result of actual observations. (shrink)

The author gives a clear explanation of the philosophy of Sard al-Din Shirazi.